A New Approach to Predict Microbial Community Assembly and Function Using a Stochastic, Genome-Enabled Modeling Framework

NASA Astrophysics Data System (ADS)

King, E.; Brodie, E.; Anantharaman, K.; Karaoz, U.; Bouskill, N.; Banfield, J. F.; Steefel, C. I.; Molins, S.

2016-12-01

Characterizing and predicting the microbial and chemical compositions of subsurface aquatic systems necessitates an understanding of the metabolism and physiology of organisms that are often uncultured or studied under conditions not relevant for one's environment of interest. Cultivation-independent approaches are therefore important and have greatly enhanced our ability to characterize functional microbial diversity. The capability to reconstruct genomes representing thousands of populations from microbial communities using metagenomic techniques provides a foundation for development of predictive models for community structure and function. Here, we discuss a genome-informed stochastic trait-based model incorporated into a reactive transport framework to represent the activities of coupled guilds of hypothetical microorganisms. Metabolic pathways for each microbe within a functional guild are parameterized from metagenomic data with a unique combination of traits governing organism fitness under dynamic environmental conditions. We simulate the thermodynamics of coupled electron donor and acceptor reactions to predict the energy available for cellular maintenance, respiration, biomass development, and enzyme production. While `omics analyses can now characterize the metabolic potential of microbial communities, it is functionally redundant as well as computationally prohibitive to explicitly include the thousands of recovered organisms into biogeochemical models. However, one can derive potential metabolic pathways from genomes along with trait-linkages to build probability distributions of traits. These distributions are used to assemble groups of microbes that couple one or more of these pathways. From the initial ensemble of microbes, only a subset will persist based on the interaction of their physiological and metabolic traits with environmental conditions, competing organisms, etc. Here, we analyze the predicted niches of these hypothetical microbes and assess the ability of a stochastically assembled community of organisms to predict subsurface biogeochemical dynamics.

Stochastic theory of photon flow in homogeneous and heterogeneous anisotropic biological and artificial material

NASA Astrophysics Data System (ADS)

Miller, Steven D.

1995-05-01

Standard Monte Carlo methods used in photon diffusion score absorbed photons or statistical weight deposited within voxels comprising a mesh. An alternative approach to a stochastic description is considered for rapid surface flux calculations and finite medias. Matrix elements are assigned to a spatial lattice whose function is to score vector intersections of scattered photons making transitions into either the forward or back solid angle half spaces. These complete matrix elements can be related to the directional fluxes within the lattice space. This model differentiates between ballistic, quasi-ballistic, and highly diffuse photon contributions, and effectively models the subsurface generation of a scattered light flux from a ballistic source. The connection between a path integral and diffusion is illustrated. Flux perturbations can be effectively illustrated for tissue-tumor-tissue and for 3 layer systems with strong absorption in one or more layers. For conditions where the diffusion theory has difficulties such as strong absorption, highly collimated sources, small finite volumes, and subsurface regions, the computation time of the algorithm is rapid with good accuracy and compliments other description of photon diffusion. The model has the potential to do computations relevant to photodynamic therapy (PDT) and analysis of laser beam interaction with tissues.

Influence of bedrock topography on the runoff generation under use of ERT data

NASA Astrophysics Data System (ADS)

Kiese, Nina; Loritz, Ralf; Allroggen, Niklas; Zehe, Erwin

2017-04-01

Subsurface topography has been identified to play a major role for the runoff generation in different hydrological landscapes. Sinks and ridges in the bedrock can control how water is stored and transported to the stream. Detecting the subsurface structure is difficult and laborious and frequently done by auger measurements. Recently, the geophysical imaging of the subsurface by Electrical Resistivity Tomography (ERT) gained much interest in the field of hydrology, as it is a non-invasive method to collect information on the subsurface characteristics and particularly bedrock topography. As it is impossible to characterize the subsurface of an entire hydrological landscape using ERT, it is of key interest to identify the bedrock characteristics which dominate runoff generation to adapt and optimize the sampling design to the question of interest. For this study, we used 2D ERT images and auger measurements, collected on different sites in the Attert basin in Luxembourg, to characterize bedrock topography using geostatistics and shed light on those aspects which dominate runoff generation. Based on ERT images, we generated stochastic bedrock topographies and implemented them in a physically-based 2D hillslope model. With this approach, we were able to test the influence of different subsurface structures on the runoff generation. Our results highlight that ERT images can be useful for hydrological modelling. Especially the connection from the hillslope to the stream could be identified as important feature in the subsurface for the runoff generation whereas the microtopography of the bedrock seemed to be less relevant.

Assessment of BTEX-induced health risk under multiple uncertainties at a petroleum-contaminated site: An integrated fuzzy stochastic approach

NASA Astrophysics Data System (ADS)

Zhang, Xiaodong; Huang, Guo H.

2011-12-01

Groundwater pollution has gathered more and more attention in the past decades. Conducting an assessment of groundwater contamination risk is desired to provide sound bases for supporting risk-based management decisions. Therefore, the objective of this study is to develop an integrated fuzzy stochastic approach to evaluate risks of BTEX-contaminated groundwater under multiple uncertainties. It consists of an integrated interval fuzzy subsurface modeling system (IIFMS) and an integrated fuzzy second-order stochastic risk assessment (IFSOSRA) model. The IIFMS is developed based on factorial design, interval analysis, and fuzzy sets approach to predict contaminant concentrations under hybrid uncertainties. Two input parameters (longitudinal dispersivity and porosity) are considered to be uncertain with known fuzzy membership functions, and intrinsic permeability is considered to be an interval number with unknown distribution information. A factorial design is conducted to evaluate interactive effects of the three uncertain factors on the modeling outputs through the developed IIFMS. The IFSOSRA model can systematically quantify variability and uncertainty, as well as their hybrids, presented as fuzzy, stochastic and second-order stochastic parameters in health risk assessment. The developed approach haw been applied to the management of a real-world petroleum-contaminated site within a western Canada context. The results indicate that multiple uncertainties, under a combination of information with various data-quality levels, can be effectively addressed to provide supports in identifying proper remedial efforts. A unique contribution of this research is the development of an integrated fuzzy stochastic approach for handling various forms of uncertainties associated with simulation and risk assessment efforts.

Sensitivity of transpiration to subsurface properties: Exploration with a 1-D model

DOE PAGES

Vrettas, Michail D.; Fung, Inez Y.

2017-05-04

The amount of moisture transpired by vegetation is critically tied to the moisture supply accessible to the root zone. In a Mediterranean climate, integrated evapotranspiration (ET) is typically greater in the dry summer when there is an uninterrupted period of high insolation. We present a 1-D model to explore the subsurface factors that may sustain ET through the dry season. The model includes a stochastic parameterization of hydraulic conductivity, root water uptake efficiency, and hydraulic redistribution by plant roots. Model experiments vary the precipitation, the magnitude and seasonality of ET demand, as well as rooting profiles and rooting depths ofmore » the vegetation. The results show that the amount of subsurface moisture remaining at the end of the wet winter is determined by the competition among abundant precipitation input, fast infiltration, and winter ET demand. The weathered bedrock retains math formula of the winter rain and provides a substantial moisture reservoir that may sustain ET of deep-rooted (>8 m) trees through the dry season. A small negative feedback exists in the root zone, where the depletion of moisture by ET decreases hydraulic conductivity and enhances the retention of moisture. Hence, hydraulic redistribution by plant roots is impactful in a dry season, or with a less conductive subsurface. Suggestions for implementing the model in the CESM are discussed.« less

Groundwater Model Validation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ahmed E. Hassan

2006-01-24

Models have an inherent uncertainty. The difficulty in fully characterizing the subsurface environment makes uncertainty an integral component of groundwater flow and transport models, which dictates the need for continuous monitoring and improvement. Building and sustaining confidence in closure decisions and monitoring networks based on models of subsurface conditions require developing confidence in the models through an iterative process. The definition of model validation is postulated as a confidence building and long-term iterative process (Hassan, 2004a). Model validation should be viewed as a process not an end result. Following Hassan (2004b), an approach is proposed for the validation process ofmore » stochastic groundwater models. The approach is briefly summarized herein and detailed analyses of acceptance criteria for stochastic realizations and of using validation data to reduce input parameter uncertainty are presented and applied to two case studies. During the validation process for stochastic models, a question arises as to the sufficiency of the number of acceptable model realizations (in terms of conformity with validation data). Using a hierarchical approach to make this determination is proposed. This approach is based on computing five measures or metrics and following a decision tree to determine if a sufficient number of realizations attain satisfactory scores regarding how they represent the field data used for calibration (old) and used for validation (new). The first two of these measures are applied to hypothetical scenarios using the first case study and assuming field data consistent with the model or significantly different from the model results. In both cases it is shown how the two measures would lead to the appropriate decision about the model performance. Standard statistical tests are used to evaluate these measures with the results indicating they are appropriate measures for evaluating model realizations. The use of validation data to constrain model input parameters is shown for the second case study using a Bayesian approach known as Markov Chain Monte Carlo. The approach shows a great potential to be helpful in the validation process and in incorporating prior knowledge with new field data to derive posterior distributions for both model input and output.« less

Differential subsidence and its effect on subsurface infrastructure: predicting probability of pipeline failure (STOOP project)

NASA Astrophysics Data System (ADS)

de Bruijn, Renée; Dabekaussen, Willem; Hijma, Marc; Wiersma, Ane; Abspoel-Bukman, Linda; Boeije, Remco; Courage, Wim; van der Geest, Johan; Hamburg, Marc; Harmsma, Edwin; Helmholt, Kristian; van den Heuvel, Frank; Kruse, Henk; Langius, Erik; Lazovik, Elena

2017-04-01

Due to heterogeneity of the subsurface in the delta environment of the Netherlands, differential subsidence over short distances results in tension and subsequent wear of subsurface infrastructure, such as water and gas pipelines. Due to uncertainties in the build-up of the subsurface, however, it is unknown where this problem is the most prominent. This is a problem for asset managers deciding when a pipeline needs replacement: damaged pipelines endanger security of supply and pose a significant threat to safety, yet premature replacement raises needless expenses. In both cases, costs - financial or other - are high. Therefore, an interdisciplinary research team of geotechnicians, geologists and Big Data engineers from research institutes TNO, Deltares and SkyGeo developed a stochastic model to predict differential subsidence and the probability of consequent pipeline failure on a (sub-)street level. In this project pipeline data from company databases is combined with a stochastic geological model and information on (historical) groundwater levels and overburden material. Probability of pipeline failure is modelled by a coupling with a subsidence model and two separate models on pipeline behaviour under stress, using a probabilistic approach. The total length of pipelines (approx. 200.000 km operational in the Netherlands) and the complexity of the model chain that is needed to calculate a chance of failure, results in large computational challenges, as it requires massive evaluation of possible scenarios to reach the required level of confidence. To cope with this, a scalable computational infrastructure has been developed, composing a model workflow in which components have a heterogeneous technological basis. Three pilot areas covering an urban, a rural and a mixed environment, characterised by different groundwater-management strategies and different overburden histories, are used to evaluate the differences in subsidence and uncertainties that come with different types of land use. Furthermore, the model provides results with a measure of reliability, and determines what is the limiting input factor causing most uncertainty. The model results can be validated and further improved using inSAR data for these pilot areas, by iteratively revising model parameters. The design of the model is such, that it can be applied to the whole of the Netherlands. By assessing differential subsidence and its effect on pipelines over time, the model helps to establish when and where maintenance is due, by indicating what areas are particularly vulnerable, thereby increasing safety and lowering maintenance costs.

The effect of soil heterogeneity on ATES performance

NASA Astrophysics Data System (ADS)

Sommer, W.; Rijnaarts, H.; Grotenhuis, T.; van Gaans, P.

2012-04-01

Due to an increasing demand for sustainable energy, application of Aquifer Thermal Energy Storage (ATES) is growing rapidly. Large-scale application of ATES is limited by the space that is available in the subsurface. Especially in urban areas, suboptimal performance is expected due to thermal interference between individual wells of a single system, or interference with other ATES systems or groundwater abstractions. To avoid thermal interference there are guidelines on well spacing. However, these guidelines, and also design calculations, are based on the assumption of a homogeneous subsurface, while studies report a standard deviation in logpermeability of 1 to 2 for unconsolidated aquifers (Gelhar, 1993). Such heterogeneity may create preferential pathways, reducing ATES performance due to increased advective heat loss or interference between ATES wells. The role of hydraulic heterogeneity of the subsurface related to ATES performance has received little attention in literature. Previous research shows that even small amounts of heterogeneity can result in considerable uncertainty in the distribution of thermal energy in the subsurface and an increased radius of influence (Ferguson, 2007). This is supported by subsurface temperature measurements around ATES wells, which suggest heterogeneity gives rise to preferential pathways and short-circuiting between ATES wells (Bridger and Allen, 2010). Using 3-dimensional stochastic heat transport modeling, we quantified the influence of heterogeneity on the performance of a doublet well energy storage system. The following key parameters are varied to study their influence on thermal recovery and thermal balance: 1) regional flow velocity, 2) distance between wells and 3) characteristics of the heterogeneity. Results show that heterogeneity at the scale of a doublet ATES system introduces an uncertainty up to 18% in expected thermal recovery. The uncertainty increases with decreasing distance between ATES wells. The uncertainty in the thermal balance ratio related to heterogeneity is limited (smaller than 3%). If thermal interference should be avoided, wells in heterogeneous aquifers should be placed further apart than in homogeneous aquifers, leading to larger volume claim in the subsurface. By relating the number of ATES systems in an area to their expected performance, these results can be used to optimize regional application of ATES. Bridger, D. W. and D. M. Allen (2010). "Heat transport simulations in a heterogeneous aquifer used for aquifer thermal energy storage (ATES)." Canadian Geotechnical Journal 47(1): 96-115. Ferguson, G. (2007). "Heterogeneity and thermal modeling of ground water." Ground Water 45(4): 485-490. Gelhar, L. W. (1993). Stochastic Subsurface Hydrology, Prentice Hall.

Bayesian Model Selection in Geophysics: The evidence

NASA Astrophysics Data System (ADS)

Vrugt, J. A.

2016-12-01

Bayesian inference has found widespread application and use in science and engineering to reconcile Earth system models with data, including prediction in space (interpolation), prediction in time (forecasting), assimilation of observations and deterministic/stochastic model output, and inference of the model parameters. Per Bayes theorem, the posterior probability, , P(H|D), of a hypothesis, H, given the data D, is equivalent to the product of its prior probability, P(H), and likelihood, L(H|D), divided by a normalization constant, P(D). In geophysics, the hypothesis, H, often constitutes a description (parameterization) of the subsurface for some entity of interest (e.g. porosity, moisture content). The normalization constant, P(D), is not required for inference of the subsurface structure, yet of great value for model selection. Unfortunately, it is not particularly easy to estimate P(D) in practice. Here, I will introduce the various building blocks of a general purpose method which provides robust and unbiased estimates of the evidence, P(D). This method uses multi-dimensional numerical integration of the posterior (parameter) distribution. I will then illustrate this new estimator by application to three competing subsurface models (hypothesis) using GPR travel time data from the South Oyster Bacterial Transport Site, in Virginia, USA. The three subsurface models differ in their treatment of the porosity distribution and use (a) horizontal layering with fixed layer thicknesses, (b) vertical layering with fixed layer thicknesses and (c) a multi-Gaussian field. The results of the new estimator are compared against the brute force Monte Carlo method, and the Laplace-Metropolis method.

An efficient Bayesian data-worth analysis using a multilevel Monte Carlo method

NASA Astrophysics Data System (ADS)

Lu, Dan; Ricciuto, Daniel; Evans, Katherine

2018-03-01

Improving the understanding of subsurface systems and thus reducing prediction uncertainty requires collection of data. As the collection of subsurface data is costly, it is important that the data collection scheme is cost-effective. Design of a cost-effective data collection scheme, i.e., data-worth analysis, requires quantifying model parameter, prediction, and both current and potential data uncertainties. Assessment of these uncertainties in large-scale stochastic subsurface hydrological model simulations using standard Monte Carlo (MC) sampling or surrogate modeling is extremely computationally intensive, sometimes even infeasible. In this work, we propose an efficient Bayesian data-worth analysis using a multilevel Monte Carlo (MLMC) method. Compared to the standard MC that requires a significantly large number of high-fidelity model executions to achieve a prescribed accuracy in estimating expectations, the MLMC can substantially reduce computational costs using multifidelity approximations. Since the Bayesian data-worth analysis involves a great deal of expectation estimation, the cost saving of the MLMC in the assessment can be outstanding. While the proposed MLMC-based data-worth analysis is broadly applicable, we use it for a highly heterogeneous two-phase subsurface flow simulation to select an optimal candidate data set that gives the largest uncertainty reduction in predicting mass flow rates at four production wells. The choices made by the MLMC estimation are validated by the actual measurements of the potential data, and consistent with the standard MC estimation. But compared to the standard MC, the MLMC greatly reduces the computational costs.

Quantifying and communicating the uncertainty of mineral resource evaluations

NASA Astrophysics Data System (ADS)

Mee, Katy; Marchant, Ben; Mankelow, Joseph; Deady, Eimear

2015-04-01

Three-dimensional subsurface models are increasingly being used to assess the value of sand and gravel mineral deposits. Planners might use this information to decide when deposits should be protected from new developments. The models are generally based on interpretations of relatively sparse boreholes and are therefore uncertain. This uncertainty propagates into the predictions of the value of the deposit and must be quantified and communicated to planners in a manner which permits informed decision-making. We discuss these issues in relation to a 60 km by 40 km study area in the south of England. We use the interpretations of 630 boreholes to build statistical models of the subsurface. Mineral deposit categories are defined in terms of the ratio of mineral depth to overburden depth and the proportion of fine particles within the mineral. We use a linear model of coregionalization to model the spatial distribution of these parameters. Furthermore, we use stochastic simulation methods to produce maps of the probability of each category of mineral deposit occurring at each location in the study area. These maps indicate where deposits of suitable sand and gravel might be expected to occur. However, they are only telling us the probability that if a borehole was to be drilled at a location that its contents would satisfy the criteria of each mineral category. Planners require information for areas much larger than a single borehole. Therefore, we demonstrate how the model can be up-scaled to a 1 km2 site. We again use a stochastic simulation method to produce box-whisker plots which illustrate the proportions of gravels, sands, fine sands and fine material that are predicted to occur in the region and the uncertainty associated with the predictions.

Detecting seasonal variations of soil parameters via field measurements and stochastic simulations in the hillslope

NASA Astrophysics Data System (ADS)

Noh, Seong Jin; An, Hyunuk; Kim, Sanghyun

2015-04-01

Soil moisture, a critical factor in hydrologic systems, plays a key role in synthesizing interactions among soil, climate, hydrological response, solute transport and ecosystem dynamics. The spatial and temporal distribution of soil moisture at a hillslope scale is essential for understanding hillslope runoff generation processes. In this study, we implement Monte Carlo simulations in the hillslope scale using a three-dimensional surface-subsurface integrated model (3D model). Numerical simulations are compared with multiple soil moistures which had been measured using TDR(Mini_TRASE) for 22 locations in 2 or 3 depths during a whole year at a hillslope (area: 2100 square meters) located in Bongsunsa Watershed, South Korea. In stochastic simulations via Monte Carlo, uncertainty of the soil parameters and input forcing are considered and model ensembles showing good performance are selected separately for several seasonal periods. The presentation will be focused on the characterization of seasonal variations of model parameters based on simulations with field measurements. In addition, structural limitations of the contemporary modeling method will be discussed.

From intuition to statistics in building subsurface structural models

USGS Publications Warehouse

Brandenburg, J.P.; Alpak, F.O.; Naruk, S.; Solum, J.

2011-01-01

Experts associated with the oil and gas exploration industry suggest that combining forward trishear models with stochastic global optimization algorithms allows a quantitative assessment of the uncertainty associated with a given structural model. The methodology is applied to incompletely imaged structures related to deepwater hydrocarbon reservoirs and results are compared to prior manual palinspastic restorations and borehole data. This methodology is also useful for extending structural interpretations into other areas of limited resolution, such as subsalt in addition to extrapolating existing data into seismic data gaps. This technique can be used for rapid reservoir appraisal and potentially have other applications for seismic processing, well planning, and borehole stability analysis.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gutierrez, Marte

Colorado School of Mines conducted research and training in the development and validation of an advanced CO{sub 2} GS (Geological Sequestration) probabilistic simulation and risk assessment model. CO{sub 2} GS simulation and risk assessment is used to develop advanced numerical simulation models of the subsurface to forecast CO2 behavior and transport; optimize site operational practices; ensure site safety; and refine site monitoring, verification, and accounting efforts. As simulation models are refined with new data, the uncertainty surrounding the identified risks decrease, thereby providing more accurate risk assessment. The models considered the full coupling of multiple physical processes (geomechanical and fluidmore » flow) and describe the effects of stochastic hydro-mechanical (H-M) parameters on the modeling of CO{sub 2} flow and transport in fractured porous rocks. Graduate students were involved in the development and validation of the model that can be used to predict the fate, movement, and storage of CO{sub 2} in subsurface formations, and to evaluate the risk of potential leakage to the atmosphere and underground aquifers. The main major contributions from the project include the development of: 1) an improved procedure to rigorously couple the simulations of hydro-thermomechanical (H-M) processes involved in CO{sub 2} GS; 2) models for the hydro-mechanical behavior of fractured porous rocks with random fracture patterns; and 3) probabilistic methods to account for the effects of stochastic fluid flow and geomechanical properties on flow, transport, storage and leakage associated with CO{sub 2} GS. The research project provided the means to educate and train graduate students in the science and technology of CO{sub 2} GS, with a focus on geologic storage. Specifically, the training included the investigation of an advanced CO{sub 2} GS simulation and risk assessment model that can be used to predict the fate, movement, and storage of CO{sub 2} in underground formations, and the evaluation of the risk of potential CO{sub 2} leakage to the atmosphere and underground aquifers.« less

An improved multilevel Monte Carlo method for estimating probability distribution functions in stochastic oil reservoir simulations

DOE PAGES

Lu, Dan; Zhang, Guannan; Webster, Clayton G.; ...

2016-12-30

In this paper, we develop an improved multilevel Monte Carlo (MLMC) method for estimating cumulative distribution functions (CDFs) of a quantity of interest, coming from numerical approximation of large-scale stochastic subsurface simulations. Compared with Monte Carlo (MC) methods, that require a significantly large number of high-fidelity model executions to achieve a prescribed accuracy when computing statistical expectations, MLMC methods were originally proposed to significantly reduce the computational cost with the use of multifidelity approximations. The improved performance of the MLMC methods depends strongly on the decay of the variance of the integrand as the level increases. However, the main challengemore » in estimating CDFs is that the integrand is a discontinuous indicator function whose variance decays slowly. To address this difficult task, we approximate the integrand using a smoothing function that accelerates the decay of the variance. In addition, we design a novel a posteriori optimization strategy to calibrate the smoothing function, so as to balance the computational gain and the approximation error. The combined proposed techniques are integrated into a very general and practical algorithm that can be applied to a wide range of subsurface problems for high-dimensional uncertainty quantification, such as a fine-grid oil reservoir model considered in this effort. The numerical results reveal that with the use of the calibrated smoothing function, the improved MLMC technique significantly reduces the computational complexity compared to the standard MC approach. Finally, we discuss several factors that affect the performance of the MLMC method and provide guidance for effective and efficient usage in practice.« less

Estimating and mapping ecological processes influencing microbial community assembly

PubMed Central

Stegen, James C.; Lin, Xueju; Fredrickson, Jim K.; Konopka, Allan E.

2015-01-01

Ecological community assembly is governed by a combination of (i) selection resulting from among-taxa differences in performance; (ii) dispersal resulting from organismal movement; and (iii) ecological drift resulting from stochastic changes in population sizes. The relative importance and nature of these processes can vary across environments. Selection can be homogeneous or variable, and while dispersal is a rate, we conceptualize extreme dispersal rates as two categories; dispersal limitation results from limited exchange of organisms among communities, and homogenizing dispersal results from high levels of organism exchange. To estimate the influence and spatial variation of each process we extend a recently developed statistical framework, use a simulation model to evaluate the accuracy of the extended framework, and use the framework to examine subsurface microbial communities over two geologic formations. For each subsurface community we estimate the degree to which it is influenced by homogeneous selection, variable selection, dispersal limitation, and homogenizing dispersal. Our analyses revealed that the relative influences of these ecological processes vary substantially across communities even within a geologic formation. We further identify environmental and spatial features associated with each ecological process, which allowed mapping of spatial variation in ecological-process-influences. The resulting maps provide a new lens through which ecological systems can be understood; in the subsurface system investigated here they revealed that the influence of variable selection was associated with the rate at which redox conditions change with subsurface depth. PMID:25983725

A FRACTAL-BASED STOCHASTIC INTERPOLATION SCHEME IN SUBSURFACE HYDROLOGY

EPA Science Inventory

The need for a realistic and rational method for interpolating sparse data sets is widespread. Real porosity and hydraulic conductivity data do not vary smoothly over space, so an interpolation scheme that preserves irregularity is desirable. Such a scheme based on the properties...

Assessing the value of different data sets and modeling schemes for flow and transport simulations

NASA Astrophysics Data System (ADS)

Hyndman, D. W.; Dogan, M.; Van Dam, R. L.; Meerschaert, M. M.; Butler, J. J., Jr.; Benson, D. A.

2014-12-01

Accurate modeling of contaminant transport has been hampered by an inability to characterize subsurface flow and transport properties at a sufficiently high resolution. However mathematical extrapolation combined with different measurement methods can provide realistic three-dimensional fields of highly heterogeneous hydraulic conductivity (K). This study demonstrates an approach to evaluate the time, cost, and efficiency of subsurface K characterization. We quantify the value of different data sets at the highly heterogeneous Macro Dispersion Experiment (MADE) Site in Mississippi, which is a flagship test site that has been used for several macro- and small-scale tracer tests that revealed non-Gaussian tracer behavior. Tracer data collected at the site are compared to models that are based on different types and resolution of geophysical and hydrologic data. We present a cost-benefit analysis of several techniques including: 1) flowmeter K data, 2) direct-push K data, 3) ground penetrating radar, and 4) two stochastic methods to generate K fields. This research provides an initial assessment of the level of data necessary to accurately simulate solute transport with the traditional advection dispersion equation; it also provides a basis to design lower cost and more efficient remediation schemes at highly heterogeneous sites.

Remote sensing science for the Nineties; Proceedings of IGARSS '90 - 10th Annual International Geoscience and Remote Sensing Symposium, University of Maryland, College Park, May 20-24, 1990. Vols. 1, 2, & 3

NASA Technical Reports Server (NTRS)

1990-01-01

Various papers on remote sensing (RS) for the nineties are presented. The general topics addressed include: subsurface methods, radar scattering, oceanography, microwave models, atmospheric correction, passive microwave systems, RS in tropical forests, moderate resolution land analysis, SAR geometry and SNR improvement, image analysis, inversion and signal processing for geoscience, surface scattering, rain measurements, sensor calibration, wind measurements, terrestrial ecology, agriculture, geometric registration, subsurface sediment geology, radar modulation mechanisms, radar ocean scattering, SAR calibration, airborne radar systems, water vapor retrieval, forest ecosystem dynamics, land analysis, multisensor data fusion. Also considered are: geologic RS, RS sensor optical measurements, RS of snow, temperature retrieval, vegetation structure, global change, artificial intelligence, SAR processing techniques, geologic RS field experiment, stochastic modeling, topography and Digital Elevation model, SAR ocean waves, spaceborne lidar and optical, sea ice field measurements, millimeter waves, advanced spectroscopy, spatial analysis and data compression, SAR polarimetry techniques. Also discussed are: plant canopy modeling, optical RS techniques, optical and IR oceanography, soil moisture, sea ice back scattering, lightning cloud measurements, spatial textural analysis, SAR systems and techniques, active microwave sensing, lidar and optical, radar scatterometry, RS of estuaries, vegetation modeling, RS systems, EOS/SAR Alaska, applications for developing countries, SAR speckle and texture.

Competing Uses of Underground Systems Related to Energy Supply: Applying Single- and Multiphase Simulations for Site Characterization and Risk-Analysis

NASA Astrophysics Data System (ADS)

Kissinger, A.; Walter, L.; Darcis, M.; Flemisch, B.; Class, H.

2012-04-01

Global climate change, shortage of resources and the resulting turn towards renewable sources of energy lead to a growing demand for the utilization of subsurface systems. Among these competing uses are Carbon Capture and Storage (CCS), geothermal energy, nuclear waste disposal, "renewable" methane or hydrogen storage as well as the ongoing production of fossil resources like oil, gas, and coal. Besides competing among themselves, these technologies may also create conflicts with essential public interests like water supply. For example, the injection of CO2 into the underground causes an increase in pressure reaching far beyond the actual radius of influence of the CO2 plume, potentially leading to large amounts of displaced salt water. Finding suitable sites is a demanding task for several reasons. Natural systems as opposed to technical systems are always characterized by heterogeneity. Therefore, parameter uncertainty impedes reliable predictions towards capacity and safety of a site. State of the art numerical simulations combined with stochastic approaches need to be used to obtain a more reliable assessment of the involved risks and the radii of influence of the different processes. These simulations may include the modeling of single- and multiphase non-isothermal flow, geo-chemical and geo-mechanical processes in order to describe all relevant physical processes adequately. Stochastic approaches have the aim to estimate a bandwidth of the key output parameters based on uncertain input parameters. Risks for these different underground uses can then be made comparable with each other. Along with the importance and the urgency of the competing processes this may lead to a more profound basis for a decision. Communicating risks to stake holders and a concerned public is crucial for the success of finding a suitable site for CCS (or other subsurface utilization). We present and discuss first steps towards an approach for addressing the issue of competitive utilization of the subsurface and the required process of communication between scientists, engineers, policy makers, and societies.

Effects of turbulent hyporheic mixing on reach-scale solute transport

NASA Astrophysics Data System (ADS)

Roche, K. R.; Li, A.; Packman, A. I.

2017-12-01

Turbulence rapidly mixes solutes and fine particles into coarse-grained streambeds. Both hyporheic exchange rates and spatial variability of hyporheic mixing are known to be controlled by turbulence, but it is unclear how turbulent mixing influences mass transport at the scale of stream reaches. We used a process-based particle-tracking model to simulate local- and reach-scale solute transport for a coarse-bed stream. Two vertical mixing profiles, one with a smooth transition from in-stream to hyporheic transport conditions and a second with enhanced turbulent transport at the sediment-water interface, were fit to steady-state subsurface concentration profiles observed in laboratory experiments. The mixing profile with enhanced interfacial transport better matched the observed concentration profiles and overall mass retention in the streambed. The best-fit mixing profiles were then used to simulate upscaled solute transport in a stream. Enhanced mixing coupled in-stream and hyporheic solute transport, causing solutes exchanged into the shallow subsurface to have travel times similar to the water column. This extended the exponential region of the in-stream solute breakthrough curve, and delayed the onset of the heavy power-law tailing induced by deeper and slower hyporheic porewater velocities. Slopes of observed power-law tails were greater than those predicted from stochastic transport theory, and also changed in time. In addition, rapid hyporheic transport velocities truncated the hyporheic residence time distribution by causing mass to exit the stream reach via subsurface advection, yielding strong exponential tempering in the in-stream breakthrough curves at the timescale of advective hyporheic transport through the reach. These results show that strong turbulent mixing across the sediment-water interface violates the conventional separation of surface and subsurface flows used in current models for solute transport in rivers. Instead, the full distribution of flow and mixing over the surface-subsurface continuum must be explicitly considered to properly interpret solute transport in coarse-bed streams.

Estimating and mapping ecological processes influencing microbial community assembly

DOE PAGES

Stegen, James C.; Lin, Xueju; Fredrickson, Jim K.; ...

2015-05-01

Ecological community assembly is governed by a combination of (i) selection resulting from among-taxa differences in performance; (ii) dispersal resulting from organismal movement; and (iii) ecological drift resulting from stochastic changes in population sizes. The relative importance and nature of these processes can vary across environments. Selection can be homogeneous or variable, and while dispersal is a rate, we conceptualize extreme dispersal rates as two categories; dispersal limitation results from limited exchange of organisms among communities, and homogenizing dispersal results from high levels of organism exchange. To estimate the influence and spatial variation of each process we extend a recentlymore » developed statistical framework, use a simulation model to evaluate the accuracy of the extended framework, and use the framework to examine subsurface microbial communities over two geologic formations. For each subsurface community we estimate the degree to which it is influenced by homogeneous selection, variable selection, dispersal limitation, and homogenizing dispersal. Our analyses revealed that the relative influences of these ecological processes vary substantially across communities even within a geologic formation. We further identify environmental and spatial features associated with each ecological process, which allowed mapping of spatial variation in ecological-process-influences. The resulting maps provide a new lens through which ecological systems can be understood; in the subsurface system investigated here they revealed that the influence of variable selection was associated with the rate at which redox conditions change with subsurface depth.« less

Efficient Data-Worth Analysis Using a Multilevel Monte Carlo Method Applied in Oil Reservoir Simulations

NASA Astrophysics Data System (ADS)

Lu, D.; Ricciuto, D. M.; Evans, K. J.

2017-12-01

Data-worth analysis plays an essential role in improving the understanding of the subsurface system, in developing and refining subsurface models, and in supporting rational water resources management. However, data-worth analysis is computationally expensive as it requires quantifying parameter uncertainty, prediction uncertainty, and both current and potential data uncertainties. Assessment of these uncertainties in large-scale stochastic subsurface simulations using standard Monte Carlo (MC) sampling or advanced surrogate modeling is extremely computationally intensive, sometimes even infeasible. In this work, we propose efficient Bayesian analysis of data-worth using a multilevel Monte Carlo (MLMC) method. Compared to the standard MC that requires a significantly large number of high-fidelity model executions to achieve a prescribed accuracy in estimating expectations, the MLMC can substantially reduce the computational cost with the use of multifidelity approximations. As the data-worth analysis involves a great deal of expectation estimations, the cost savings from MLMC in the assessment can be very outstanding. While the proposed MLMC-based data-worth analysis is broadly applicable, we use it to a highly heterogeneous oil reservoir simulation to select an optimal candidate data set that gives the largest uncertainty reduction in predicting mass flow rates at four production wells. The choices made by the MLMC estimation are validated by the actual measurements of the potential data, and consistent with the estimation obtained from the standard MC. But compared to the standard MC, the MLMC greatly reduces the computational costs in the uncertainty reduction estimation, with up to 600 days cost savings when one processor is used.

Bayesian inference of spectral induced polarization parameters for laboratory complex resistivity measurements of rocks and soils

NASA Astrophysics Data System (ADS)

Bérubé, Charles L.; Chouteau, Michel; Shamsipour, Pejman; Enkin, Randolph J.; Olivo, Gema R.

2017-08-01

Spectral induced polarization (SIP) measurements are now widely used to infer mineralogical or hydrogeological properties from the low-frequency electrical properties of the subsurface in both mineral exploration and environmental sciences. We present an open-source program that performs fast multi-model inversion of laboratory complex resistivity measurements using Markov-chain Monte Carlo simulation. Using this stochastic method, SIP parameters and their uncertainties may be obtained from the Cole-Cole and Dias models, or from the Debye and Warburg decomposition approaches. The program is tested on synthetic and laboratory data to show that the posterior distribution of a multiple Cole-Cole model is multimodal in particular cases. The Warburg and Debye decomposition approaches yield unique solutions in all cases. It is shown that an adaptive Metropolis algorithm performs faster and is less dependent on the initial parameter values than the Metropolis-Hastings step method when inverting SIP data through the decomposition schemes. There are no advantages in using an adaptive step method for well-defined Cole-Cole inversion. Finally, the influence of measurement noise on the recovered relaxation time distribution is explored. We provide the geophysics community with a open-source platform that can serve as a base for further developments in stochastic SIP data inversion and that may be used to perform parameter analysis with various SIP models.

dfnWorks: A discrete fracture network framework for modeling subsurface flow and transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hyman, Jeffrey D.; Karra, Satish; Makedonska, Nataliia

DFNWORKS is a parallelized computational suite to generate three-dimensional discrete fracture networks (DFN) and simulate flow and transport. Developed at Los Alamos National Laboratory over the past five years, it has been used to study flow and transport in fractured media at scales ranging from millimeters to kilometers. The networks are created and meshed using DFNGEN, which combines FRAM (the feature rejection algorithm for meshing) methodology to stochastically generate three-dimensional DFNs with the LaGriT meshing toolbox to create a high-quality computational mesh representation. The representation produces a conforming Delaunay triangulation suitable for high performance computing finite volume solvers in anmore » intrinsically parallel fashion. Flow through the network is simulated in dfnFlow, which utilizes the massively parallel subsurface flow and reactive transport finite volume code PFLOTRAN. A Lagrangian approach to simulating transport through the DFN is adopted within DFNTRANS to determine pathlines and solute transport through the DFN. Example applications of this suite in the areas of nuclear waste repository science, hydraulic fracturing and CO 2 sequestration are also included.« less

dfnWorks: A discrete fracture network framework for modeling subsurface flow and transport

DOE PAGES

Hyman, Jeffrey D.; Karra, Satish; Makedonska, Nataliia; ...

2015-11-01

DFNWORKS is a parallelized computational suite to generate three-dimensional discrete fracture networks (DFN) and simulate flow and transport. Developed at Los Alamos National Laboratory over the past five years, it has been used to study flow and transport in fractured media at scales ranging from millimeters to kilometers. The networks are created and meshed using DFNGEN, which combines FRAM (the feature rejection algorithm for meshing) methodology to stochastically generate three-dimensional DFNs with the LaGriT meshing toolbox to create a high-quality computational mesh representation. The representation produces a conforming Delaunay triangulation suitable for high performance computing finite volume solvers in anmore » intrinsically parallel fashion. Flow through the network is simulated in dfnFlow, which utilizes the massively parallel subsurface flow and reactive transport finite volume code PFLOTRAN. A Lagrangian approach to simulating transport through the DFN is adopted within DFNTRANS to determine pathlines and solute transport through the DFN. Example applications of this suite in the areas of nuclear waste repository science, hydraulic fracturing and CO 2 sequestration are also included.« less

A comparison of numerical solutions of partial differential equations with probabilistic and possibilistic parameters for the quantification of uncertainty in subsurface solute transport.

PubMed

Zhang, Kejiang; Achari, Gopal; Li, Hua

2009-11-03

Traditionally, uncertainty in parameters are represented as probabilistic distributions and incorporated into groundwater flow and contaminant transport models. With the advent of newer uncertainty theories, it is now understood that stochastic methods cannot properly represent non random uncertainties. In the groundwater flow and contaminant transport equations, uncertainty in some parameters may be random, whereas those of others may be non random. The objective of this paper is to develop a fuzzy-stochastic partial differential equation (FSPDE) model to simulate conditions where both random and non random uncertainties are involved in groundwater flow and solute transport. Three potential solution techniques namely, (a) transforming a probability distribution to a possibility distribution (Method I) then a FSPDE becomes a fuzzy partial differential equation (FPDE), (b) transforming a possibility distribution to a probability distribution (Method II) and then a FSPDE becomes a stochastic partial differential equation (SPDE), and (c) the combination of Monte Carlo methods and FPDE solution techniques (Method III) are proposed and compared. The effects of these three methods on the predictive results are investigated by using two case studies. The results show that the predictions obtained from Method II is a specific case of that got from Method I. When an exact probabilistic result is needed, Method II is suggested. As the loss or gain of information during a probability-possibility (or vice versa) transformation cannot be quantified, their influences on the predictive results is not known. Thus, Method III should probably be preferred for risk assessments.

3D voxel modelling of the marine subsurface: the Belgian Continental Shelf case

NASA Astrophysics Data System (ADS)

Hademenos, Vasileios; Kint, Lars; Missiaen, Tine; Stafleu, Jan; Van Lancker, Vera

2017-04-01

The need for marine space grows bigger by the year. Dredging, wind farms, aggregate extraction and many other activities take up more space than ever before. As a result, the need for an accurate model that describes the properties of the areas in use is a priority. To address this need a 3D voxel model of the subsurface of the Belgian part of the North Sea has been created in the scope of the Belgian Science Policy project TILES ('Transnational and Integrated Long-term Marine Exploitation Strategies'). Since borehole data in the marine environment are a costly endeavour and therefore relatively scarce, seismic data have been incorporated in order to improve the data coverage. Lithostratigraphic units have been defined and lithoclasses are attributed to the voxels using a stochastic interpolation. As a result each voxel contains a unique value of one of 7 lithological classes (spanning in grain size from clay to gravel) in association with the geological layer it belongs to. In addition other forms of interpolation like sequential indicator simulation have allowed us to calculate the probability occurrence of each lithoclass, thus providing additional info from which the uncertainty of the model can be derived. The resulting 3D voxel model gives a detailed image of the distribution of different sediment types and provides valuable insight on the different geological settings. The voxel model also allows to estimate resource volumes (e.g. the availability of particular sand classes), enabling a more targeted exploitation. The primary information of the model is related to geology, but the model can additionally host any type of information.

Modelling of spatial contaminant probabilities of occurrence of chlorinated hydrocarbons in an urban aquifer.

PubMed

Greis, Tillman; Helmholz, Kathrin; Schöniger, Hans Matthias; Haarstrick, Andreas

2012-06-01

In this study, a 3D urban groundwater model is presented which serves for calculation of multispecies contaminant transport in the subsurface on the regional scale. The total model consists of two submodels, the groundwater flow and reactive transport model, and is validated against field data. The model equations are solved applying finite element method. A sensitivity analysis is carried out to perform parameter identification of flow, transport and reaction processes. Coming from the latter, stochastic variation of flow, transport, and reaction input parameters and Monte Carlo simulation are used in calculating probabilities of pollutant occurrence in the domain. These probabilities could be part of determining future spots of contamination and their measure of damages. Application and validation is exemplarily shown for a contaminated site in Braunschweig (Germany), where a vast plume of chlorinated ethenes pollutes the groundwater. With respect to field application, the methods used for modelling reveal feasible and helpful tools to assess natural attenuation (MNA) and the risk that might be reduced by remediation actions.

Employing Eigenvalue Ratios to Generate Prior Fracture-like Features for Stochastic Hydrogeophysical Characterization of a Fractured Aquifer System

NASA Astrophysics Data System (ADS)

Brewster, J.; Oware, E. K.

2017-12-01

Groundwater hosted in fractured rocks constitutes almost 65% of the principal aquifers in the US. The exploitation and contaminant management of fractured aquifers require fracture flow and transport modeling, which in turn requires a detailed understanding of the structure of the aquifer. The widely used equivalent porous medium approach to modeling fractured aquifer systems is inadequate to accurately predict fracture transport processes due to the averaging of the sharp lithological contrast between the matrix and the fractures. The potential of geophysical imaging (GI) to estimate spatially continuous subsurface profiles in a minimally invasive fashion is well proven. Conventional deterministic GI strategies, however, produce geologically unrealistic, smoothed-out results due to commonly enforced smoothing constraints. Stochastic GI of fractured aquifers is becoming increasing appealing due to its ability to recover realistic fracture features while providing multiple likely realizations that enable uncertainty assessment. Generating prior spatial features consistent with the expected target structures is crucial in stochastic imaging. We propose to utilize eigenvalue ratios to resolve the elongated fracture features expected in a fractured aquifer system. Eigenvalues capture the major and minor directions of variability in a region, which can be employed to evaluate shape descriptors, such as eccentricity (elongation) and orientation of features in the region. Eccentricity ranges from zero to one, representing a circularly sharped to a line feature, respectively. Here, we apply eigenvalue ratios to define a joint objective parameter consisting of eccentricity (shape) and direction terms to guide the generation of prior fracture-like features in some predefined principal directions for stochastic GI. Preliminary unconditional, synthetic experiments reveal the potential of the algorithm to simulate prior fracture-like features. We illustrate the strategy with a 2D, cross-borehole electrical resistivity tomography (ERT) in a fractured aquifer at the UB Environmental Geophysics Imaging Site, with tomograms validated with gamma and caliper logs obtained from the two ERT wells.

The emergence of hydrogeophysics for improved understanding of subsurface processes over multiple scales

DOE PAGES

Binley, Andrew; Hubbard, Susan S.; Huisman, Johan A.; ...

2015-06-15

Geophysics provides a multidimensional suite of investigative methods that are transforming our ability to see into the very fabric of the subsurface environment, and monitor the dynamics of its fluids and the biogeochemical reactions that occur within it. Here we document how geophysical methods have emerged as valuable tools for investigating shallow subsurface processes over the past two decades and offer a vision for future developments relevant to hydrology and also ecosystem science. The field of “hydrogeophysics” arose in the late 1990s, prompted, in part, by the wealth of studies on stochastic subsurface hydrology that argued for better field-based investigativemore » techniques. These new hydrogeophysical approaches benefited from the emergence of practical and robust data inversion techniques, in many cases with a view to quantify shallow subsurface heterogeneity and the associated dynamics of subsurface fluids. Furthermore, the need for quantitative characterization stimulated a wealth of new investigations into petrophysical relationships that link hydrologically relevant properties to measurable geophysical parameters. Development of time-lapse approaches provided a new suite of tools for hydrological investigation, enhanced further with the realization that some geophysical properties may be sensitive to biogeochemical transformations in the subsurface environment, thus opening up the new field of “biogeophysics.” Early hydrogeophysical studies often concentrated on relatively small “plot-scale” experiments. More recently, however, the translation to larger-scale characterization has been the focus of a number of studies. In conclusion, geophysical technologies continue to develop, driven, in part, by the increasing need to understand and quantify key processes controlling sustainable water resources and ecosystem services.« less

The emergence of hydrogeophysics for improved understanding of subsurface processes over multiple scales

DOE Office of Scientific and Technical Information (OSTI.GOV)

Binley, Andrew; Hubbard, Susan S.; Huisman, Johan A.

Geophysics provides a multidimensional suite of investigative methods that are transforming our ability to see into the very fabric of the subsurface environment, and monitor the dynamics of its fluids and the biogeochemical reactions that occur within it. Here we document how geophysical methods have emerged as valuable tools for investigating shallow subsurface processes over the past two decades and offer a vision for future developments relevant to hydrology and also ecosystem science. The field of “hydrogeophysics” arose in the late 1990s, prompted, in part, by the wealth of studies on stochastic subsurface hydrology that argued for better field-based investigativemore » techniques. These new hydrogeophysical approaches benefited from the emergence of practical and robust data inversion techniques, in many cases with a view to quantify shallow subsurface heterogeneity and the associated dynamics of subsurface fluids. Furthermore, the need for quantitative characterization stimulated a wealth of new investigations into petrophysical relationships that link hydrologically relevant properties to measurable geophysical parameters. Development of time-lapse approaches provided a new suite of tools for hydrological investigation, enhanced further with the realization that some geophysical properties may be sensitive to biogeochemical transformations in the subsurface environment, thus opening up the new field of “biogeophysics.” Early hydrogeophysical studies often concentrated on relatively small “plot-scale” experiments. More recently, however, the translation to larger-scale characterization has been the focus of a number of studies. In conclusion, geophysical technologies continue to develop, driven, in part, by the increasing need to understand and quantify key processes controlling sustainable water resources and ecosystem services.« less

The emergence of hydrogeophysics for improved understanding of subsurface processes over multiple scales

PubMed Central

Hubbard, Susan S.; Huisman, Johan A.; Revil, André; Robinson, David A.; Singha, Kamini; Slater, Lee D.

2015-01-01

Abstract Geophysics provides a multidimensional suite of investigative methods that are transforming our ability to see into the very fabric of the subsurface environment, and monitor the dynamics of its fluids and the biogeochemical reactions that occur within it. Here we document how geophysical methods have emerged as valuable tools for investigating shallow subsurface processes over the past two decades and offer a vision for future developments relevant to hydrology and also ecosystem science. The field of “hydrogeophysics” arose in the late 1990s, prompted, in part, by the wealth of studies on stochastic subsurface hydrology that argued for better field‐based investigative techniques. These new hydrogeophysical approaches benefited from the emergence of practical and robust data inversion techniques, in many cases with a view to quantify shallow subsurface heterogeneity and the associated dynamics of subsurface fluids. Furthermore, the need for quantitative characterization stimulated a wealth of new investigations into petrophysical relationships that link hydrologically relevant properties to measurable geophysical parameters. Development of time‐lapse approaches provided a new suite of tools for hydrological investigation, enhanced further with the realization that some geophysical properties may be sensitive to biogeochemical transformations in the subsurface environment, thus opening up the new field of “biogeophysics.” Early hydrogeophysical studies often concentrated on relatively small “plot‐scale” experiments. More recently, however, the translation to larger‐scale characterization has been the focus of a number of studies. Geophysical technologies continue to develop, driven, in part, by the increasing need to understand and quantify key processes controlling sustainable water resources and ecosystem services. PMID:26900183

A Multilevel, Hierarchical Sampling Technique for Spatially Correlated Random Fields

DOE PAGES

Osborn, Sarah; Vassilevski, Panayot S.; Villa, Umberto

2017-10-26

In this paper, we propose an alternative method to generate samples of a spatially correlated random field with applications to large-scale problems for forward propagation of uncertainty. A classical approach for generating these samples is the Karhunen--Loève (KL) decomposition. However, the KL expansion requires solving a dense eigenvalue problem and is therefore computationally infeasible for large-scale problems. Sampling methods based on stochastic partial differential equations provide a highly scalable way to sample Gaussian fields, but the resulting parametrization is mesh dependent. We propose a multilevel decomposition of the stochastic field to allow for scalable, hierarchical sampling based on solving amore » mixed finite element formulation of a stochastic reaction-diffusion equation with a random, white noise source function. Lastly, numerical experiments are presented to demonstrate the scalability of the sampling method as well as numerical results of multilevel Monte Carlo simulations for a subsurface porous media flow application using the proposed sampling method.« less

A Multilevel, Hierarchical Sampling Technique for Spatially Correlated Random Fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Osborn, Sarah; Vassilevski, Panayot S.; Villa, Umberto

In this paper, we propose an alternative method to generate samples of a spatially correlated random field with applications to large-scale problems for forward propagation of uncertainty. A classical approach for generating these samples is the Karhunen--Loève (KL) decomposition. However, the KL expansion requires solving a dense eigenvalue problem and is therefore computationally infeasible for large-scale problems. Sampling methods based on stochastic partial differential equations provide a highly scalable way to sample Gaussian fields, but the resulting parametrization is mesh dependent. We propose a multilevel decomposition of the stochastic field to allow for scalable, hierarchical sampling based on solving amore » mixed finite element formulation of a stochastic reaction-diffusion equation with a random, white noise source function. Lastly, numerical experiments are presented to demonstrate the scalability of the sampling method as well as numerical results of multilevel Monte Carlo simulations for a subsurface porous media flow application using the proposed sampling method.« less

Scale-free distribution of Dead Sea sinkholes: Observations and modeling

NASA Astrophysics Data System (ADS)

Yizhaq, H.; Ish-Shalom, C.; Raz, E.; Ashkenazy, Y.

2017-05-01

There are currently more than 5500 sinkholes along the Dead Sea in Israel. These were formed due to the dissolution of subsurface salt layers as a result of the replacement of hypersaline groundwater by fresh brackish groundwater. This process has been associated with a sharp decline in the Dead Sea water level, currently more than 1 m/yr, resulting in a lower water table that has allowed the intrusion of fresher brackish water. We studied the distribution of the sinkhole sizes and found that it is scale free with a power law exponent close to 2. We constructed a stochastic cellular automata model to understand the observed scale-free behavior and the growth of the sinkhole area in time. The model consists of a lower salt layer and an upper soil layer in which cavities that develop in the lower layer lead to collapses in the upper layer. The model reproduces the observed power law distribution without involving the threshold behavior commonly associated with criticality.

Effect of spatial organisation behaviour on upscaling the overland flow formation in an arable land

NASA Astrophysics Data System (ADS)

Silasari, Rasmiaditya; Blöschl, Günter

2014-05-01

Overland flow during rainfall events on arable land is important to investigate as it affects the land erosion process and water quality in the river. The formation of overland flow may happen through different ways (i.e. Hortonian overland flow, saturation excess overland flow) which is influenced by the surface and subsurface soil characteristics (i.e. land cover, soil infiltration rate). As the soil characteristics vary throughout the entire catchment, it will form distinct spatial patterns with organised or random behaviour. During the upscaling of hydrological processes from plot to catchment scale, this behaviour will become substantial since organised patterns will result in higher spatial connectivity and thus higher conductivity. However, very few of the existing studies explicitly address this effect of spatial organisations of the patterns in upscaling the hydrological processes to the catchment scale. This study will assess the upscaling of overland flow formation with concerns of spatial organisation behaviour of the patterns by application of direct field observations under natural conditions using video camera and soil moisture sensors and investigation of the underlying processes using a physical-based hydrology model. The study area is a Hydrological Open Air Laboratory (HOAL) located at Petzenkirchen, Lower Austria. It is a 64 ha catchment with land use consisting of arable land (87%), forest (6%), pasture (5%) and paved surfaces (2%). A video camera is installed 7m above the ground on a weather station mast in the middle of the arable land to monitor the overland flow patterns during rainfall events in a 2m x 6m plot scale. Soil moisture sensors with continuous measurement at different depth (5, 10, 20 and 50cm) are installed at points where the field is monitored by the camera. The patterns of overland flow formation and subsurface flow state at the plot scale will be generated using a coupled surface-subsurface flow physical-based hydrology model. The observation data will be assimilated into the model to verify the corresponding processes between surface and subsurface flow during the rainfall events. The patterns of conductivity then will be analyzed at catchment scale using the spatial stochastic analysis based on the classification of soil characteristics of the entire catchment. These patterns of conductivity then will be applied in the model at catchment scale to see how the organisational behaviour can affect the spatial connectivity of the hydrological processes and the results of the catchment response. A detailed modelling of the underlying processes in the physical-based model will allow us to see the direct effect of the spatial connectivity to the occurring surface and subsurface flow. This will improve the analysis of the effect of spatial organisations of the patterns in upscaling the hydrological processes from plot to catchment scale.

Accounting for model error in Bayesian solutions to hydrogeophysical inverse problems using a local basis approach

NASA Astrophysics Data System (ADS)

Köpke, Corinna; Irving, James; Elsheikh, Ahmed H.

2018-06-01

Bayesian solutions to geophysical and hydrological inverse problems are dependent upon a forward model linking subsurface physical properties to measured data, which is typically assumed to be perfectly known in the inversion procedure. However, to make the stochastic solution of the inverse problem computationally tractable using methods such as Markov-chain-Monte-Carlo (MCMC), fast approximations of the forward model are commonly employed. This gives rise to model error, which has the potential to significantly bias posterior statistics if not properly accounted for. Here, we present a new methodology for dealing with the model error arising from the use of approximate forward solvers in Bayesian solutions to hydrogeophysical inverse problems. Our approach is geared towards the common case where this error cannot be (i) effectively characterized through some parametric statistical distribution; or (ii) estimated by interpolating between a small number of computed model-error realizations. To this end, we focus on identification and removal of the model-error component of the residual during MCMC using a projection-based approach, whereby the orthogonal basis employed for the projection is derived in each iteration from the K-nearest-neighboring entries in a model-error dictionary. The latter is constructed during the inversion and grows at a specified rate as the iterations proceed. We demonstrate the performance of our technique on the inversion of synthetic crosshole ground-penetrating radar travel-time data considering three different subsurface parameterizations of varying complexity. Synthetic data are generated using the eikonal equation, whereas a straight-ray forward model is assumed for their inversion. In each case, our developed approach enables us to remove posterior bias and obtain a more realistic characterization of uncertainty.

Nationwide lithological interpretation of cone penetration tests using neural networks

NASA Astrophysics Data System (ADS)

van Maanen, Peter-Paul; Schokker, Jeroen; Harting, Ronald; de Bruijn, Renée

2017-04-01

The Geological Survey of the Netherlands (GSN) systematically produces 3D stochastic geological models of the Dutch subsurface. These voxel models are regarded essential in answering subsurface-related questions on, for example, aggregate resource potential, groundwater flow, land subsidence hazard and the planning and realization of large-scale infrastructural works. GeoTOP is the most recent and detailed generation of 3D voxel models. This model describes 3D stratigraphical and lithological variability up to a depth of 50 m using voxels of 100 × 100 × 0.5 m. Currently, visually described borehole samples are the primary input of these large-scale 3D geological models, both when modeling architecture and composition. Although tens of thousands of cone penetration tests (CPTs) are performed each year, mainly in the reconnaissance phase of construction activities, these data are hardly used as geological model input. There are many reasons why it is of interest to utilize CPT data for geological and lithological modeling of the Dutch subsurface, such as: 1) CPTs are more abundant than borehole descriptions, 2) CPTs are cheaper and easier to gather, and 3) CPT data are more quantitative and uniform than visual sample descriptions. This study uses CPTs and the lithological descriptions of associated nearby undisturbed drilling cores collected by the GSN to establish a nationwide reference dataset for physical and chemical properties of the shallow subsurface. The 167 CPT-core pairs were collected at 160 locations situated in the North, West and South of the Netherlands. These locations were chosen to cover the full extent of geological units and lithological composition in the upper 30 to 40 m of the subsurface in these areas. The distance between the CPT location and associated borehole is small, varying between 0 and 30 m, with an average of 6 m. For each 2 cm CPT interval the data was automatically annotated with the lithoclass from the associated core using a lithological classification script that is also used in GeoTOP to classify the visual sample descriptions. Based on this data a three-layer feedforward neural network was trained containing 5 different inputs: cone resistance, friction ratio, coordinates x and y, and interval depth z. Previous training attempts showed an increased performance when using additional inputs such as pore water pressure, but since these variables are not measured in the majority of CPTs, these were left out in the training procedure. The Newton conjugate-gradient algorithm was applied to train the network. 20-Fold cross-validation yielded 20 different trained nets and independent performance outcomes. Significant performance increase was found as compared to performances of conventional lithological classification charts. A similar neural network was then applied to new CPT data from a pilot area in the city of Rotterdam. This area has a limited number of visual sample descriptions and therefore, additional lithological information of the subsurface is desirable. The results of an evaluation of the neural network's outcomes in this area by geological experts are positive, which paves the way for future nationwide application of this method.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Foxall, W; Cunningham, C; Mellors, R

Many clandestine development and production activities can be conducted underground to evade surveillance. The purpose of the study reported here was to develop a technique to detect underground facilities by broad-area search and then to characterize the facilities by inversion of the collected data. This would enable constraints to be placed on the types of activities that would be feasible at each underground site, providing a basis the design of targeted surveillance and analysis for more complete characterization. Excavation of underground cavities causes deformation in the host material and overburden that produces displacements at the ground surface. Such displacements aremore » often measurable by a variety of surveying or geodetic techniques. One measurement technique, Interferometric Synthetic Aperture Radar (InSAR), uses data from satellite-borne (or airborne) synthetic aperture radars (SARs) and so is ideal for detecting and measuring surface displacements in denied access regions. Depending on the radar frequency and the acquisition mode and the surface conditions, displacement maps derived from SAR interferograms can provide millimeter- to centimeter-level measurement accuracy on regional and local scales at spatial resolution of {approx}1-10 m. Relatively low-resolution ({approx}20 m, say) maps covering large regions can be used for broad-area detection, while finer resolutions ({approx}1 m) can be used to image details of displacement fields over targeted small areas. Surface displacements are generally expected to be largest during or a relatively short time after active excavation, but, depending on the material properties, measurable displacement may continue at a decreasing rate for a considerable time after completion. For a given excavated volume in a given geological setting, the amplitude of the surface displacements decreases as the depth of excavation increases, while the area of the discernable displacement pattern increases. Therefore, the ability to detect evidence for an underground facility using InSAR depends on the displacement sensitivity and spatial resolution of the interferogram, as well as on the size and depth of the facility and the time since its completion. The methodology development described in this report focuses on the exploitation of synthetic aperture radar data that are available commercially from a number of satellite missions. Development of the method involves three components: (1) Evaluation of the capability of InSAR to detect and characterize underground facilities ; (2) inversion of InSAR data to infer the location, depth, shape and volume of a subsurface facility; and (3) evaluation and selection of suitable geomechanical forward models to use in the inversion. We adapted LLNL's general-purpose Bayesian Markov Chain-Monte Carlo procedure, the 'Stochastic Engine' (SE), to carry out inversions to characterize subsurface void geometries. The SE performs forward simulations for a large number of trial source models to identify the set of models that are consistent with the observations and prior constraints. The inverse solution produced by this kind of stochastic method is a posterior probability density function (pdf) over alternative models, which forms an appropriate input to risk-based decision analyses to evaluate subsequent response strategies. One major advantage of a stochastic inversion approach is its ability to deal with complex, non-linear forward models employing empirical, analytical or numerical methods. However, while a geomechanical model must incorporate adequate physics to enable sufficiently accurate prediction of surface displacements, it must also be computationally fast enough to render the large number of forward realizations needed in stochastic inversion feasible. This latter requirement prompted us first to investigate computationally efficient empirical relations and closed-form analytical solutions. However, our evaluation revealed severe limitations in the ability of existing empirical and analytical forms to predict deformations from underground cavities with an accuracy consistent with the potential resolution and precision of InSAR data. We followed two approaches to overcoming these limitations. The first was to develop a new analytical solution for a 3D cavity excavated in an elastic half-space. The second was to adapt a fast parallelized finite element method to the SE and evaluate the feasibility of using in the stochastic inversion. To date we have demonstrated the ability of InSAR to detect underground facilities and measure the associated surface displacements by mapping surface deformations that track the excavation of the Los Angeles Metro system. The Stochastic Engine implementation has been completed and undergone functional testing.« less

Stochastic, goal-oriented rapid impact modeling of uncertainty and environmental impacts in poorly-sampled sites using ex-situ priors

NASA Astrophysics Data System (ADS)

Li, Xiaojun; Li, Yandong; Chang, Ching-Fu; Tan, Benjamin; Chen, Ziyang; Sege, Jon; Wang, Changhong; Rubin, Yoram

2018-01-01

Modeling of uncertainty associated with subsurface dynamics has long been a major research topic. Its significance is widely recognized for real-life applications. Despite the huge effort invested in the area, major obstacles still remain on the way from theory and applications. Particularly problematic here is the confusion between modeling uncertainty and modeling spatial variability, which translates into a (mis)conception, in fact an inconsistency, in that it suggests that modeling of uncertainty and modeling of spatial variability are equivalent, and as such, requiring a lot of data. This paper investigates this challenge against the backdrop of a 7 km, deep underground tunnel in China, where environmental impacts are of major concern. We approach the data challenge by pursuing a new concept for Rapid Impact Modeling (RIM), which bypasses altogether the need to estimate posterior distributions of model parameters, focusing instead on detailed stochastic modeling of impacts, conditional to all information available, including prior, ex-situ information and in-situ measurements as well. A foundational element of RIM is the construction of informative priors for target parameters using ex-situ data, relying on ensembles of well-documented sites, pre-screened for geological and hydrological similarity to the target site. The ensembles are built around two sets of similarity criteria: a physically-based set of criteria and an additional set covering epistemic criteria. In another variation to common Bayesian practice, we update the priors to obtain conditional distributions of the target (environmental impact) dependent variables and not the hydrological variables. This recognizes that goal-oriented site characterization is in many cases more useful in applications compared to parameter-oriented characterization.

Uncertainty Analysis of Runoff Simulations and Parameter Identifiability in the Community Land Model – Evidence from MOPEX Basins

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Maoyi; Hou, Zhangshuan; Leung, Lai-Yung R.

2013-12-01

With the emergence of earth system models as important tools for understanding and predicting climate change and implications to mitigation and adaptation, it has become increasingly important to assess the fidelity of the land component within earth system models to capture realistic hydrological processes and their response to the changing climate and quantify the associated uncertainties. This study investigates the sensitivity of runoff simulations to major hydrologic parameters in version 4 of the Community Land Model (CLM4) by integrating CLM4 with a stochastic exploratory sensitivity analysis framework at 20 selected watersheds from the Model Parameter Estimation Experiment (MOPEX) spanning amore » wide range of climate and site conditions. We found that for runoff simulations, the most significant parameters are those related to the subsurface runoff parameterizations. Soil texture related parameters and surface runoff parameters are of secondary significance. Moreover, climate and soil conditions play important roles in the parameter sensitivity. In general, site conditions within water-limited hydrologic regimes and with finer soil texture result in stronger sensitivity of output variables, such as runoff and its surface and subsurface components, to the input parameters in CLM4. This study demonstrated the feasibility of parameter inversion for CLM4 using streamflow observations to improve runoff simulations. By ranking the significance of the input parameters, we showed that the parameter set dimensionality could be reduced for CLM4 parameter calibration under different hydrologic and climatic regimes so that the inverse problem is less ill posed.« less

Sensitivities in a game theoretic approach to analyze allocation of water resources in the Nagobo basin, Ghana

NASA Astrophysics Data System (ADS)

Hossler, T. H. H. H.; Caers, J.; Lakshmi, V.; Harris, J. M.

2016-12-01

Changing weather patterns, such as shorter duration of rainfall have made water sourcesunreliable for local farmers in the Nagbo basin located in Northern Ghana. Farmers are thereforestarting to use groundwater as a secondary source (and sometimes primary source) of water fortheir needs. Groundwater will therefore be most likely subject to considerable stress in the nearfuture with longer dry spells and increasing water demand from users with different interests.Strategies must be adopted to optimally allocate water between the various stakeholders in anuncertain environment. Game Theory (GT) provides a framework for analyzing watermanagement in the Nagobo Basin. GT has recently gained attention in analyzing the impact androle of stakeholders in water resources management but the hydrological and hydrogeologicalmodels fail to account for the numerous data sources and leading uncertainties of thehydrogeological cycle. In this work, we describe by means of a synthetic model a situation in theNagobo basin with a 2-players game, considering both cooperation and non-cooperation. Ahydrological model of the basin is built using the different data available (surface and subsurface).We are interested in quantifying the impact of the uncertainty of the model parameters on thegame, affecting both player's strategies and the equilibrium. In particular, the stochastic nature insupply (recharge of the aquifer) and the uncertain nature of the subsurface (externalities) are areaof focus. A sensitivity analysis has been carried out and these results will be presented as well asthe outcome of the different games.

Stochastic analysis of multiphase flow in porous media: II. Numerical simulations

NASA Astrophysics Data System (ADS)

Abin, A.; Kalurachchi, J. J.; Kemblowski, M. W.; Chang, C.-M.

1996-08-01

The first paper (Chang et al., 1995b) of this two-part series described the stochastic analysis using spectral/perturbation approach to analyze steady state two-phase (water and oil) flow in a, liquid-unsaturated, three fluid-phase porous medium. In this paper, the results between the numerical simulations and closed-form expressions obtained using the perturbation approach are compared. We present the solution to the one-dimensional, steady-state oil and water flow equations. The stochastic input processes are the spatially correlated logk where k is the intrinsic permeability and the soil retention parameter, α. These solutions are subsequently used in the numerical simulations to estimate the statistical properties of the key output processes. The comparison between the results of the perturbation analysis and numerical simulations showed a good agreement between the two methods over a wide range of logk variability with three different combinations of input stochastic processes of logk and soil parameter α. The results clearly demonstrated the importance of considering the spatial variability of key subsurface properties under a variety of physical scenarios. The variability of both capillary pressure and saturation is affected by the type of input stochastic process used to represent the spatial variability. The results also demonstrated the applicability of perturbation theory in predicting the system variability and defining effective fluid properties through the ergodic assumption.

Modelisations et inversions tri-dimensionnelles en prospections gravimetrique et electrique

NASA Astrophysics Data System (ADS)

Boulanger, Olivier

The aim of this thesis is the application of gravity and resistivity methods for mining prospecting. The objectives of the present study are: (1) to build a fast gravity inversion method to interpret surface data; (2) to develop a tool for modelling the electrical potential acquired at surface and in boreholes when the resistivity distribution is heterogeneous; and (3) to define and implement a stochastic inversion scheme allowing the estimation of the subsurface resistivity from electrical data. The first technique concerns the elaboration of a three dimensional (3D) inversion program allowing the interpretation of gravity data using a selection of constraints such as the minimum distance, the flatness, the smoothness and the compactness. These constraints are integrated in a Lagrangian formulation. A multi-grid technique is also implemented to resolve separately large and short gravity wavelengths. The subsurface in the survey area is divided into juxtaposed rectangular prismatic blocks. The problem is solved by calculating the model parameters, i.e. the densities of each block. Weights are given to each block depending on depth, a priori information on density, and density range allowed for the region under investigation. The present code is tested on synthetic data. Advantages and behaviour of each method are compared in the 3D reconstruction. Recovery of geometry (depth, size) and density distribution of the original model is dependent on the set of constraints used. The best combination of constraints experimented for multiple bodies seems to be flatness and minimum volume for multiple bodies. The inversion method is tested on real gravity data. The second tool developed in this thesis is a three-dimensional electrical resistivity modelling code to interpret surface and subsurface data. Based on the integral equation, it calculates the charge density caused by conductivity gradients at each interface of the mesh allowing an exact estimation of the potential. Modelling generates a huge matrix made of Green's functions which is stored by using the method of pyramidal compression. The third method consists to interpret electrical potential measurements from a non-linear geostatistical approach including new constraints. This method estimates an analytical covariance model for the resistivity parameters from the potential data. (Abstract shortened by UMI.)

Inverse Modeling of Hydrologic Parameters Using Surface Flux and Runoff Observations in the Community Land Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sun, Yu; Hou, Zhangshuan; Huang, Maoyi

2013-12-10

This study demonstrates the possibility of inverting hydrologic parameters using surface flux and runoff observations in version 4 of the Community Land Model (CLM4). Previous studies showed that surface flux and runoff calculations are sensitive to major hydrologic parameters in CLM4 over different watersheds, and illustrated the necessity and possibility of parameter calibration. Two inversion strategies, the deterministic least-square fitting and stochastic Markov-Chain Monte-Carlo (MCMC) - Bayesian inversion approaches, are evaluated by applying them to CLM4 at selected sites. The unknowns to be estimated include surface and subsurface runoff generation parameters and vadose zone soil water parameters. We find thatmore » using model parameters calibrated by the least-square fitting provides little improvements in the model simulations but the sampling-based stochastic inversion approaches are consistent - as more information comes in, the predictive intervals of the calibrated parameters become narrower and the misfits between the calculated and observed responses decrease. In general, parameters that are identified to be significant through sensitivity analyses and statistical tests are better calibrated than those with weak or nonlinear impacts on flux or runoff observations. Temporal resolution of observations has larger impacts on the results of inverse modeling using heat flux data than runoff data. Soil and vegetation cover have important impacts on parameter sensitivities, leading to the different patterns of posterior distributions of parameters at different sites. Overall, the MCMC-Bayesian inversion approach effectively and reliably improves the simulation of CLM under different climates and environmental conditions. Bayesian model averaging of the posterior estimates with different reference acceptance probabilities can smooth the posterior distribution and provide more reliable parameter estimates, but at the expense of wider uncertainty bounds.« less

Quantifying geological uncertainty for flow and transport modeling in multi-modal heterogeneous formations

NASA Astrophysics Data System (ADS)

Feyen, Luc; Caers, Jef

2006-06-01

In this work, we address the problem of characterizing the heterogeneity and uncertainty of hydraulic properties for complex geological settings. Hereby, we distinguish between two scales of heterogeneity, namely the hydrofacies structure and the intrafacies variability of the hydraulic properties. We employ multiple-point geostatistics to characterize the hydrofacies architecture. The multiple-point statistics are borrowed from a training image that is designed to reflect the prior geological conceptualization. The intrafacies variability of the hydraulic properties is represented using conventional two-point correlation methods, more precisely, spatial covariance models under a multi-Gaussian spatial law. We address the different levels and sources of uncertainty in characterizing the subsurface heterogeneity, and explore their effect on groundwater flow and transport predictions. Typically, uncertainty is assessed by way of many images, termed realizations, of a fixed statistical model. However, in many cases, sampling from a fixed stochastic model does not adequately represent the space of uncertainty. It neglects the uncertainty related to the selection of the stochastic model and the estimation of its input parameters. We acknowledge the uncertainty inherent in the definition of the prior conceptual model of aquifer architecture and in the estimation of global statistics, anisotropy, and correlation scales. Spatial bootstrap is used to assess the uncertainty of the unknown statistical parameters. As an illustrative example, we employ a synthetic field that represents a fluvial setting consisting of an interconnected network of channel sands embedded within finer-grained floodplain material. For this highly non-stationary setting we quantify the groundwater flow and transport model prediction uncertainty for various levels of hydrogeological uncertainty. Results indicate the importance of accurately describing the facies geometry, especially for transport predictions.

Inverse modeling of hydrologic parameters using surface flux and runoff observations in the Community Land Model

NASA Astrophysics Data System (ADS)

Sun, Y.; Hou, Z.; Huang, M.; Tian, F.; Leung, L. Ruby

2013-12-01

This study demonstrates the possibility of inverting hydrologic parameters using surface flux and runoff observations in version 4 of the Community Land Model (CLM4). Previous studies showed that surface flux and runoff calculations are sensitive to major hydrologic parameters in CLM4 over different watersheds, and illustrated the necessity and possibility of parameter calibration. Both deterministic least-square fitting and stochastic Markov-chain Monte Carlo (MCMC)-Bayesian inversion approaches are evaluated by applying them to CLM4 at selected sites with different climate and soil conditions. The unknowns to be estimated include surface and subsurface runoff generation parameters and vadose zone soil water parameters. We find that using model parameters calibrated by the sampling-based stochastic inversion approaches provides significant improvements in the model simulations compared to using default CLM4 parameter values, and that as more information comes in, the predictive intervals (ranges of posterior distributions) of the calibrated parameters become narrower. In general, parameters that are identified to be significant through sensitivity analyses and statistical tests are better calibrated than those with weak or nonlinear impacts on flux or runoff observations. Temporal resolution of observations has larger impacts on the results of inverse modeling using heat flux data than runoff data. Soil and vegetation cover have important impacts on parameter sensitivities, leading to different patterns of posterior distributions of parameters at different sites. Overall, the MCMC-Bayesian inversion approach effectively and reliably improves the simulation of CLM under different climates and environmental conditions. Bayesian model averaging of the posterior estimates with different reference acceptance probabilities can smooth the posterior distribution and provide more reliable parameter estimates, but at the expense of wider uncertainty bounds.

Sensitivities of Near-field Tsunami Forecasts to Megathrust Deformation Predictions

NASA Astrophysics Data System (ADS)

Tung, S.; Masterlark, T.

2018-02-01

This study reveals how modeling configurations of forward and inverse analyses of coseismic deformation data influence the estimations of seismic and tsunami sources. We illuminate how the predictions of near-field tsunami change when (1) a heterogeneous (HET) distribution of crustal material is introduced to the elastic dislocation model, and (2) the near-trench rupture is either encouraged or suppressed to invert spontaneous coseismic displacements. Hypothetical scenarios of megathrust earthquakes are studied with synthetic Global Positioning System displacements in Cascadia. Finite-element models are designed to mimic the subsurface heterogeneity across the curved subduction margin. The HET lithospheric domain modifies the seafloor displacement field and alters tsunami predictions from those of a homogeneous (HOM) crust. Uncertainties persist as the inverse analyses of geodetic data produce nonrealistic slip artifacts over the HOM domain, which propagates into the prediction errors of subsequent tsunami arrival and amplitudes. A stochastic analysis further shows that the uncertainties of seismic tomography models do not degrade the solution accuracy of HET over HOM. Whether the source ruptures near the trench also controls the details of the seafloor disturbance. Deeper subsurface slips induce more seafloor uplift near the coast and cause an earlier arrival of tsunami waves than surface-slipping events. We suggest using the solutions of zero-updip-slip and zero-updip-slip-gradient rupture boundary conditions as end-members to constrain the tsunami behavior for forecasting purposes. The findings are important for the near-field tsunami warning that primarily relies on the near-real-time geodetic or seismic data for source calibration before megawaves hit the nearest shore upon tsunamigenic events.

Identification and Simulation of Subsurface Soil patterns using hidden Markov random fields and remote sensing and geophysical EMI data sets

NASA Astrophysics Data System (ADS)

Wang, Hui; Wellmann, Florian; Verweij, Elizabeth; von Hebel, Christian; van der Kruk, Jan

2017-04-01

Lateral and vertical spatial heterogeneity of subsurface properties such as soil texture and structure influences the available water and resource supply for crop growth. High-resolution mapping of subsurface structures using non-invasive geo-referenced geophysical measurements, like electromagnetic induction (EMI), enables a characterization of 3D soil structures, which have shown correlations to remote sensing information of the crop states. The benefit of EMI is that it can return 3D subsurface information, however the spatial dimensions are limited due to the labor intensive measurement procedure. Although active and passive sensors mounted on air- or space-borne platforms return 2D images, they have much larger spatial dimensions. Combining both approaches provides us with a potential pathway to extend the detailed 3D geophysical information to a larger area by using remote sensing information. In this study, we aim at extracting and providing insights into the spatial and statistical correlation of the geophysical and remote sensing observations of the soil/vegetation continuum system. To this end, two key points need to be addressed: 1) how to detect and recognize the geometric patterns (i.e., spatial heterogeneity) from multiple data sets, and 2) how to quantitatively describe the statistical correlation between remote sensing information and geophysical measurements. In the current study, the spatial domain is restricted to shallow depths up to 3 meters, and the geostatistical database contains normalized difference vegetation index (NDVI) derived from RapidEye satellite images and apparent electrical conductivities (ECa) measured from multi-receiver EMI sensors for nine depths of exploration ranging from 0-2.7 m. The integrated data sets are mapped into both the physical space (i.e. the spatial domain) and feature space (i.e. a two-dimensional space framed by the NDVI and the ECa data). Hidden Markov Random Fields (HMRF) are employed to model the underlying heterogeneities in spatial domain and finite Gaussian mixture models are adopted to quantitatively describe the statistical patterns in terms of center vectors and covariance matrices in feature space. A recently developed parallel stochastic clustering algorithm is adopted to implement the HMRF models and the Markov chain Monte Carlo based Bayesian inference. Certain spatial patterns such as buried paleo-river channels covered by shallow sediments are investigated as typical examples. The results indicate that the geometric patterns of the subsurface heterogeneity can be represented and quantitatively characterized by HMRF. Furthermore, the statistical patterns of the NDVI and the EMI data from the soil/vegetation-continuum system can be inferred and analyzed in a quantitative manner.

Bayesian assessment of the expected data impact on prediction confidence in optimal sampling design

NASA Astrophysics Data System (ADS)

Leube, P. C.; Geiges, A.; Nowak, W.

2012-02-01

Incorporating hydro(geo)logical data, such as head and tracer data, into stochastic models of (subsurface) flow and transport helps to reduce prediction uncertainty. Because of financial limitations for investigation campaigns, information needs toward modeling or prediction goals should be satisfied efficiently and rationally. Optimal design techniques find the best one among a set of investigation strategies. They optimize the expected impact of data on prediction confidence or related objectives prior to data collection. We introduce a new optimal design method, called PreDIA(gnosis) (Preposterior Data Impact Assessor). PreDIA derives the relevant probability distributions and measures of data utility within a fully Bayesian, generalized, flexible, and accurate framework. It extends the bootstrap filter (BF) and related frameworks to optimal design by marginalizing utility measures over the yet unknown data values. PreDIA is a strictly formal information-processing scheme free of linearizations. It works with arbitrary simulation tools, provides full flexibility concerning measurement types (linear, nonlinear, direct, indirect), allows for any desired task-driven formulations, and can account for various sources of uncertainty (e.g., heterogeneity, geostatistical assumptions, boundary conditions, measurement values, model structure uncertainty, a large class of model errors) via Bayesian geostatistics and model averaging. Existing methods fail to simultaneously provide these crucial advantages, which our method buys at relatively higher-computational costs. We demonstrate the applicability and advantages of PreDIA over conventional linearized methods in a synthetic example of subsurface transport. In the example, we show that informative data is often invisible for linearized methods that confuse zero correlation with statistical independence. Hence, PreDIA will often lead to substantially better sampling designs. Finally, we extend our example to specifically highlight the consideration of conceptual model uncertainty.

Modeling climate change impacts on groundwater resources using transient stochastic climatic scenarios

NASA Astrophysics Data System (ADS)

Goderniaux, Pascal; BrouyèRe, Serge; Blenkinsop, Stephen; Burton, Aidan; Fowler, Hayley J.; Orban, Philippe; Dassargues, Alain

2011-12-01

Several studies have highlighted the potential negative impact of climate change on groundwater reserves, but additional work is required to help water managers plan for future changes. In particular, existing studies provide projections for a stationary climate representative of the end of the century, although information is demanded for the near future. Such time-slice experiments fail to account for the transient nature of climatic changes over the century. Moreover, uncertainty linked to natural climate variability is not explicitly considered in previous studies. In this study we substantially improve upon the state-of-the-art by using a sophisticated transient weather generator in combination with an integrated surface-subsurface hydrological model (Geer basin, Belgium) developed with the finite element modeling software "HydroGeoSphere." This version of the weather generator enables the stochastic generation of large numbers of equiprobable climatic time series, representing transient climate change, and used to assess impacts in a probabilistic way. For the Geer basin, 30 equiprobable climate change scenarios from 2010 to 2085 have been generated for each of six different regional climate models (RCMs). Results show that although the 95% confidence intervals calculated around projected groundwater levels remain large, the climate change signal becomes stronger than that of natural climate variability by 2085. Additionally, the weather generator's ability to simulate transient climate change enabled the assessment of the likely time scale and associated uncertainty of a specific impact, providing managers with additional information when planning further investment. This methodology constitutes a real improvement in the field of groundwater projections under climate change conditions.

Coupled Land Surface-Subsurface Hydrogeophysical Inverse Modeling to Estimate Soil Organic Carbon Content in an Arctic Tundra

NASA Astrophysics Data System (ADS)

Tran, A. P.; Dafflon, B.; Hubbard, S.

2017-12-01

Soil organic carbon (SOC) is crucial for predicting carbon climate feedbacks in the vulnerable organic-rich Arctic region. However, it is challenging to achieve this property due to the general limitations of conventional core sampling and analysis methods. In this study, we develop an inversion scheme that uses single or multiple datasets, including soil liquid water content, temperature and ERT data, to estimate the vertical profile of SOC content. Our approach relies on the fact that SOC content strongly influences soil hydrological-thermal parameters, and therefore, indirectly controls the spatiotemporal dynamics of soil liquid water content, temperature and their correlated electrical resistivity. The scheme includes several advantages. First, this is the first time SOC content is estimated by using a coupled hydrogeophysical inversion. Second, by using the Community Land Model, we can account for the land surface dynamics (evapotranspiration, snow accumulation and melting) and ice/liquid phase transition. Third, we combine a deterministic and an adaptive Markov chain Monte Carlo optimization algorithm to better estimate the posterior distributions of desired model parameters. Finally, the simulated subsurface variables are explicitly linked to soil electrical resistivity via petrophysical and geophysical models. We validate the developed scheme using synthetic experiments. The results show that compared to inversion of single dataset, joint inversion of these datasets significantly reduces parameter uncertainty. The joint inversion approach is able to estimate SOC content within the shallow active layer with high reliability. Next, we apply the scheme to estimate OC content along an intensive ERT transect in Barrow, Alaska using multiple datasets acquired in the 2013-2015 period. The preliminary results show a good agreement between modeled and measured soil temperature, thaw layer thickness and electrical resistivity. The accuracy of estimated SOC content will be evaluated by comparison with measurements from soil samples along the transect. Our study presents a new surface-subsurface, deterministic-stochastic hydrogeophysical inversion approach, as well as the benefit of including multiple types of data to estimate SOC and associated hydrological-thermal dynamics.

Stochastic models for inferring genetic regulation from microarray gene expression data.

PubMed

Tian, Tianhai

2010-03-01

Microarray expression profiles are inherently noisy and many different sources of variation exist in microarray experiments. It is still a significant challenge to develop stochastic models to realize noise in microarray expression profiles, which has profound influence on the reverse engineering of genetic regulation. Using the target genes of the tumour suppressor gene p53 as the test problem, we developed stochastic differential equation models and established the relationship between the noise strength of stochastic models and parameters of an error model for describing the distribution of the microarray measurements. Numerical results indicate that the simulated variance from stochastic models with a stochastic degradation process can be represented by a monomial in terms of the hybridization intensity and the order of the monomial depends on the type of stochastic process. The developed stochastic models with multiple stochastic processes generated simulations whose variance is consistent with the prediction of the error model. This work also established a general method to develop stochastic models from experimental information. 2009 Elsevier Ireland Ltd. All rights reserved.

Coupled land surface-subsurface hydrogeophysical inverse modeling to estimate soil organic carbon content and explore associated hydrological and thermal dynamics in the Arctic tundra

NASA Astrophysics Data System (ADS)

Phuong Tran, Anh; Dafflon, Baptiste; Hubbard, Susan S.

2017-09-01

Quantitative characterization of soil organic carbon (OC) content is essential due to its significant impacts on surface-subsurface hydrological-thermal processes and microbial decomposition of OC, which both in turn are important for predicting carbon-climate feedbacks. While such quantification is particularly important in the vulnerable organic-rich Arctic region, it is challenging to achieve due to the general limitations of conventional core sampling and analysis methods, and to the extremely dynamic nature of hydrological-thermal processes associated with annual freeze-thaw events. In this study, we develop and test an inversion scheme that can flexibly use single or multiple datasets - including soil liquid water content, temperature and electrical resistivity tomography (ERT) data - to estimate the vertical distribution of OC content. Our approach relies on the fact that OC content strongly influences soil hydrological-thermal parameters and, therefore, indirectly controls the spatiotemporal dynamics of soil liquid water content, temperature and their correlated electrical resistivity. We employ the Community Land Model to simulate nonisothermal surface-subsurface hydrological dynamics from the bedrock to the top of canopy, with consideration of land surface processes (e.g., solar radiation balance, evapotranspiration, snow accumulation and melting) and ice-liquid water phase transitions. For inversion, we combine a deterministic and an adaptive Markov chain Monte Carlo (MCMC) optimization algorithm to estimate a posteriori distributions of desired model parameters. For hydrological-thermal-to-geophysical variable transformation, the simulated subsurface temperature, liquid water content and ice content are explicitly linked to soil electrical resistivity via petrophysical and geophysical models. We validate the developed scheme using different numerical experiments and evaluate the influence of measurement errors and benefit of joint inversion on the estimation of OC and other parameters. We also quantify the propagation of uncertainty from the estimated parameters to prediction of hydrological-thermal responses. We find that, compared to inversion of single dataset (temperature, liquid water content or apparent resistivity), joint inversion of these datasets significantly reduces parameter uncertainty. We find that the joint inversion approach is able to estimate OC and sand content within the shallow active layer (top 0.3 m of soil) with high reliability. Due to the small variations of temperature and moisture within the shallow permafrost (here at about 0.6 m depth), the approach is unable to estimate OC with confidence. However, if the soil porosity is functionally related to the OC and mineral content, which is often observed in organic-rich Arctic soil, the uncertainty of OC estimate at this depth remarkably decreases. Our study documents the value of the new surface-subsurface, deterministic-stochastic inversion approach, as well as the benefit of including multiple types of data to estimate OC and associated hydrological-thermal dynamics.

Accounting for model error in Bayesian solutions to hydrogeophysical inverse problems using a local basis approach

NASA Astrophysics Data System (ADS)

Irving, J.; Koepke, C.; Elsheikh, A. H.

2017-12-01

Bayesian solutions to geophysical and hydrological inverse problems are dependent upon a forward process model linking subsurface parameters to measured data, which is typically assumed to be known perfectly in the inversion procedure. However, in order to make the stochastic solution of the inverse problem computationally tractable using, for example, Markov-chain-Monte-Carlo (MCMC) methods, fast approximations of the forward model are commonly employed. This introduces model error into the problem, which has the potential to significantly bias posterior statistics and hamper data integration efforts if not properly accounted for. Here, we present a new methodology for addressing the issue of model error in Bayesian solutions to hydrogeophysical inverse problems that is geared towards the common case where these errors cannot be effectively characterized globally through some parametric statistical distribution or locally based on interpolation between a small number of computed realizations. Rather than focusing on the construction of a global or local error model, we instead work towards identification of the model-error component of the residual through a projection-based approach. In this regard, pairs of approximate and detailed model runs are stored in a dictionary that grows at a specified rate during the MCMC inversion procedure. At each iteration, a local model-error basis is constructed for the current test set of model parameters using the K-nearest neighbour entries in the dictionary, which is then used to separate the model error from the other error sources before computing the likelihood of the proposed set of model parameters. We demonstrate the performance of our technique on the inversion of synthetic crosshole ground-penetrating radar traveltime data for three different subsurface parameterizations of varying complexity. The synthetic data are generated using the eikonal equation, whereas a straight-ray forward model is assumed in the inversion procedure. In each case, the developed model-error approach enables to remove posterior bias and obtain a more realistic characterization of uncertainty.

Stochastic modeling of a lava-flow aquifer system

USGS Publications Warehouse

Cronkite-Ratcliff, Collin; Phelps, Geoffrey A.

2014-01-01

This report describes preliminary three-dimensional geostatistical modeling of a lava-flow aquifer system using a multiple-point geostatistical model. The purpose of this study is to provide a proof-of-concept for this modeling approach. An example of the method is demonstrated using a subset of borehole geologic data and aquifer test data from a portion of the Calico Hills Formation, a lava-flow aquifer system that partially underlies Pahute Mesa, Nevada. Groundwater movement in this aquifer system is assumed to be controlled by the spatial distribution of two geologic units—rhyolite lava flows and zeolitized tuffs. The configuration of subsurface lava flows and tuffs is largely unknown because of limited data. The spatial configuration of the lava flows and tuffs is modeled by using a multiple-point geostatistical simulation algorithm that generates a large number of alternative realizations, each honoring the available geologic data and drawn from a geologic conceptual model of the lava-flow aquifer system as represented by a training image. In order to demonstrate how results from the geostatistical model could be analyzed in terms of available hydrologic data, a numerical simulation of part of an aquifer test was applied to the realizations of the geostatistical model.

A Parallel Stochastic Framework for Reservoir Characterization and History Matching

DOE PAGES

Thomas, Sunil G.; Klie, Hector M.; Rodriguez, Adolfo A.; ...

2011-01-01

The spatial distribution of parameters that characterize the subsurface is never known to any reasonable level of accuracy required to solve the governing PDEs of multiphase flow or species transport through porous media. This paper presents a numerically cheap, yet efficient, accurate and parallel framework to estimate reservoir parameters, for example, medium permeability, using sensor information from measurements of the solution variables such as phase pressures, phase concentrations, fluxes, and seismic and well log data. Numerical results are presented to demonstrate the method.

A flexible Bayesian assessment for the expected impact of data on prediction confidence for optimal sampling designs

NASA Astrophysics Data System (ADS)

Leube, Philipp; Geiges, Andreas; Nowak, Wolfgang

2010-05-01

Incorporating hydrogeological data, such as head and tracer data, into stochastic models of subsurface flow and transport helps to reduce prediction uncertainty. Considering limited financial resources available for the data acquisition campaign, information needs towards the prediction goal should be satisfied in a efficient and task-specific manner. For finding the best one among a set of design candidates, an objective function is commonly evaluated, which measures the expected impact of data on prediction confidence, prior to their collection. An appropriate approach to this task should be stochastically rigorous, master non-linear dependencies between data, parameters and model predictions, and allow for a wide variety of different data types. Existing methods fail to fulfill all these requirements simultaneously. For this reason, we introduce a new method, denoted as CLUE (Cross-bred Likelihood Uncertainty Estimator), that derives the essential distributions and measures of data utility within a generalized, flexible and accurate framework. The method makes use of Bayesian GLUE (Generalized Likelihood Uncertainty Estimator) and extends it to an optimal design method by marginalizing over the yet unknown data values. Operating in a purely Bayesian Monte-Carlo framework, CLUE is a strictly formal information processing scheme free of linearizations. It provides full flexibility associated with the type of measurements (linear, non-linear, direct, indirect) and accounts for almost arbitrary sources of uncertainty (e.g. heterogeneity, geostatistical assumptions, boundary conditions, model concepts) via stochastic simulation and Bayesian model averaging. This helps to minimize the strength and impact of possible subjective prior assumptions, that would be hard to defend prior to data collection. Our study focuses on evaluating two different uncertainty measures: (i) expected conditional variance and (ii) expected relative entropy of a given prediction goal. The applicability and advantages are shown in a synthetic example. Therefor, we consider a contaminant source, posing a threat on a drinking water well in an aquifer. Furthermore, we assume uncertainty in geostatistical parameters, boundary conditions and hydraulic gradient. The two mentioned measures evaluate the sensitivity of (1) general prediction confidence and (2) exceedance probability of a legal regulatory threshold value on sampling locations.

Inference of multi-Gaussian property fields by probabilistic inversion of crosshole ground penetrating radar data using an improved dimensionality reduction

NASA Astrophysics Data System (ADS)

Hunziker, Jürg; Laloy, Eric; Linde, Niklas

2016-04-01

Deterministic inversion procedures can often explain field data, but they only deliver one final subsurface model that depends on the initial model and regularization constraints. This leads to poor insights about the uncertainties associated with the inferred model properties. In contrast, probabilistic inversions can provide an ensemble of model realizations that accurately span the range of possible models that honor the available calibration data and prior information allowing a quantitative description of model uncertainties. We reconsider the problem of inferring the dielectric permittivity (directly related to radar velocity) structure of the subsurface by inversion of first-arrival travel times from crosshole ground penetrating radar (GPR) measurements. We rely on the DREAM_(ZS) algorithm that is a state-of-the-art Markov chain Monte Carlo (MCMC) algorithm. Such algorithms need several orders of magnitude more forward simulations than deterministic algorithms and often become infeasible in high parameter dimensions. To enable high-resolution imaging with MCMC, we use a recently proposed dimensionality reduction approach that allows reproducing 2D multi-Gaussian fields with far fewer parameters than a classical grid discretization. We consider herein a dimensionality reduction from 5000 to 257 unknowns. The first 250 parameters correspond to a spectral representation of random and uncorrelated spatial fluctuations while the remaining seven geostatistical parameters are (1) the standard deviation of the data error, (2) the mean and (3) the variance of the relative electric permittivity, (4) the integral scale along the major axis of anisotropy, (5) the anisotropy angle, (6) the ratio of the integral scale along the minor axis of anisotropy to the integral scale along the major axis of anisotropy and (7) the shape parameter of the Matérn function. The latter essentially defines the type of covariance function (e.g., exponential, Whittle, Gaussian). We present an improved formulation of the dimensionality reduction, and numerically show how it reduces artifacts in the generated models and provides better posterior estimation of the subsurface geostatistical structure. We next show that the results of the method compare very favorably against previous deterministic and stochastic inversion results obtained at the South Oyster Bacterial Transport Site in Virginia, USA. The long-term goal of this work is to enable MCMC-based full waveform inversion of crosshole GPR data.

Multi-year predictability in a coupled general circulation model

NASA Astrophysics Data System (ADS)

Power, Scott; Colman, Rob

2006-02-01

Multi-year to decadal variability in a 100-year integration of a BMRC coupled atmosphere-ocean general circulation model (CGCM) is examined. The fractional contribution made by the decadal component generally increases with depth and latitude away from surface waters in the equatorial Indo-Pacific Ocean. The relative importance of decadal variability is enhanced in off-equatorial “ wings” in the subtropical eastern Pacific. The model and observations exhibit “ENSO-like” decadal patterns. Analytic results are derived, which show that the patterns can, in theory, occur in the absence of any predictability beyond ENSO time-scales. In practice, however, modification to this stochastic view is needed to account for robust differences between ENSO-like decadal patterns and their interannual counterparts. An analysis of variability in the CGCM, a wind-forced shallow water model, and a simple mixed layer model together with existing and new theoretical results are used to improve upon this stochastic paradigm and to provide a new theory for the origin of decadal ENSO-like patterns like the Interdecadal Pacific Oscillation and Pacific Decadal Oscillation. In this theory, ENSO-driven wind-stress variability forces internal equatorially-trapped Kelvin waves that propagate towards the eastern boundary. Kelvin waves can excite reflected internal westward propagating equatorially-trapped Rossby waves (RWs) and coastally-trapped waves (CTWs). CTWs have no impact on the off-equatorial sub-surface ocean outside the coastal wave guide, whereas the RWs do. If the frequency of the incident wave is too high, then only CTWs are excited. At lower frequencies, both CTWs and RWs can be excited. The lower the frequency, the greater the fraction of energy transmitted to RWs. This lowers the characteristic frequency (reddens the spectrum) of variability off the equator relative to its equatorial counterpart. At low frequencies, dissipation acts as an additional low pass filter that becomes more effective, as latitude increases. At the same time, ENSO-driven off-equatorial surface heating anomalies drive mixed layer temperature responses in both hemispheres. Both the eastern boundary interactions and the accumulation of surface heat fluxes by the surface mixed layer act to low pass filter the ENSO-forcing. The resulting off-equatorial variability is therefore more coherent with low pass filtered (decadal) ENSO indices [e.g. NINO3 sea-surface temperature (SST)] than with unfiltered ENSO indices. Consequently large correlations between variability and NINO3 extend further poleward on decadal time-scales than they do on interannual time-scales. This explains why decadal ENSO-like patterns have a broader meridional structure than their interannual counterparts. This difference in appearance can occur even if ENSO indices do not have any predictability beyond interannual time-scales. The wings around 15-20°S, and sub-surface variability at many other locations are predictable on interannual and multi-year time-scales. This includes westward propagating internal RWs within about 25° of the equator. The slowest of these take up to 4 years to reach the western boundary. This sub-surface predictability has significant oceanographic interest. However, it is linked to only low levels of SST variability. Consequently, extrapolation of delayed action oscillator theory to decadal time-scales might not be justified.

ENSO regimes and the late 1970's climate shift: The role of synoptic weather and South Pacific ocean spiciness

DOE Office of Scientific and Technical Information (OSTI.GOV)

O'Kane, Terence J.; Matear, Richard J.; Chamberlain, Matthew A.

South Pacific subtropical density compensated temperature and salinity (spiciness) anomalies are known to be associated with decadal equatorial variability, however, the mechanisms by which such disturbances are generated, advect and the degree to which they modulate the equatorial thermocline remains controversial. During the late 1970's a climate regime transition preceded a period of strong and sustained El Nino events. Using an ocean general circulation model forced by the constituent mechanical and thermodynamic components of the reanalysed atmosphere we show that the late 1970's transition coincided with the arrival of a large-scale, subsurface cold and fresh water anomaly in the centralmore » tropical Pacific. An ocean reanalysis for the period 1990–2007 that assimilates subsurface Argo, XBT and CTD data, reveals that disturbances occur due to the subduction of negative surface salinity anomalies from near 30° S, 100° W which are advected along the σ=25–26 kgm{sup −3} isopycnal surfaces. These anomalies take, on average, seven years to reach the central equatorial Pacific where they may substantially perturb the thermocline before the remnants ultimately ventilate in the region of the western Pacific warm pool. Positive (warm–salty) disturbances, known to occur due to late winter diapycnal mixing and isopycnal outcropping, arise due to both subduction of subtropical mode waters and subsurface injection. On reaching the equatorial band (10° S–0° S) these disturbances tend to deepen the thermocline reducing the model's ENSO. In contrast the emergence of negative (cold–fresh) disturbances at the equator are associated with a shoaling of the thermocline and El Nino events. Process studies are used to show that the generation and advection of anomalous density compensated thermocline disturbances critically depend on stochastic forcing of the intrinsic ocean by weather. We further show that in the absence of the inter-annual component of the atmosphere forcing Central Pacific El Nino events are manifest.« less

Multilevel Monte Carlo for two phase flow and Buckley–Leverett transport in random heterogeneous porous media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Müller, Florian, E-mail: florian.mueller@sam.math.ethz.ch; Jenny, Patrick, E-mail: jenny@ifd.mavt.ethz.ch; Meyer, Daniel W., E-mail: meyerda@ethz.ch

2013-10-01

Monte Carlo (MC) is a well known method for quantifying uncertainty arising for example in subsurface flow problems. Although robust and easy to implement, MC suffers from slow convergence. Extending MC by means of multigrid techniques yields the multilevel Monte Carlo (MLMC) method. MLMC has proven to greatly accelerate MC for several applications including stochastic ordinary differential equations in finance, elliptic stochastic partial differential equations and also hyperbolic problems. In this study, MLMC is combined with a streamline-based solver to assess uncertain two phase flow and Buckley–Leverett transport in random heterogeneous porous media. The performance of MLMC is compared tomore » MC for a two dimensional reservoir with a multi-point Gaussian logarithmic permeability field. The influence of the variance and the correlation length of the logarithmic permeability on the MLMC performance is studied.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Han, Yong; Lii-Rosales, A.; Zhou, Y.

Theory and stochastic lattice-gas modeling is developed for the formation of intercalated metal islands in the gallery between the top layer and the underlying layer at the surface of layered materials. Our model for this process involves deposition of atoms, some fraction of which then enter the gallery through well-separated pointlike defects in the top layer. Subsequently, these atoms diffuse within the subsurface gallery leading to nucleation and growth of intercalated islands nearby the defect point source. For the case of a single point defect, continuum diffusion equation analysis provides insight into the nucleation kinetics. However, complementary tailored lattice-gas modelingmore » produces a more comprehensive and quantitative characterization. We analyze the large spread in nucleation times and positions relative to the defect for the first nucleated island. We also consider the formation of subsequent islands and the evolution of island growth shapes. The shapes reflect in part our natural adoption of a hexagonal close-packed island structure. As a result, motivation and support for the model is provided by scanning tunneling microscopy observations of the formation of intercalated metal islands in highly-ordered pyrolytic graphite at higher temperatures.« less

Report on an Informal Survey of Groundwater Modeling Practitioners About How They Quantify Uncertainty: Which Tools They Use, Why, and Why Not.

NASA Astrophysics Data System (ADS)

Ginn, T. R.; Scheibe, T. D.

2006-12-01

Hydrogeology is among the most data-limited of the earth sciences, so that uncertainty arises in every aspect of subsurface flow and transport modeling, from conceptual model to spatial discretization to parameter values. Thus treatment of uncertainty is unavoidable, and the literature and conference proceedings are replete with approaches, templates, paradigms and such for doing so. However, such tools remain not well used, especially those of the stochastic analytic sort, leading recently to explicit inquiries about why this is the case, in response to which entire journal issues have been dedicated. In an effort to continue this discussion in a constructive way we report on an informal yet extensive survey of hydrogeology practitioners, as the "marketplace" for techniques to deal with uncertainty. We include scientists, engineers, regulators, and others in the survey, that reports on quantitative (or not) methods for uncertainty characterization and analysis, frequency and level of usage, and reasons behind the selection or avoidance of available methods. Results shed light on fruitful directions for future research in uncertainty quantification in hydrogeology.

Modelling rapid subsurface flow at the hillslope scale with explicit representation of preferential flow paths

NASA Astrophysics Data System (ADS)

Wienhöfer, J.; Zehe, E.

2012-04-01

Rapid lateral flow processes via preferential flow paths are widely accepted to play a key role for rainfall-runoff response in temperate humid headwater catchments. A quantitative description of these processes, however, is still a major challenge in hydrological research, not least because detailed information about the architecture of subsurface flow paths are often impossible to obtain at a natural site without disturbing the system. Our study combines physically based modelling and field observations with the objective to better understand how flow network configurations influence the hydrological response of hillslopes. The system under investigation is a forested hillslope with a small perennial spring at the study area Heumöser, a headwater catchment of the Dornbirnerach in Vorarlberg, Austria. In-situ points measurements of field-saturated hydraulic conductivity and dye staining experiments at the plot scale revealed that shrinkage cracks and biogenic macropores function as preferential flow paths in the fine-textured soils of the study area, and these preferential flow structures were active in fast subsurface transport of artificial tracers at the hillslope scale. For modelling of water and solute transport, we followed the approach of implementing preferential flow paths as spatially explicit structures of high hydraulic conductivity and low retention within the 2D process-based model CATFLOW. Many potential configurations of the flow path network were generated as realisations of a stochastic process informed by macropore characteristics derived from the plot scale observations. Together with different realisations of soil hydraulic parameters, this approach results in a Monte Carlo study. The model setups were used for short-term simulation of a sprinkling and tracer experiment, and the results were evaluated against measured discharges and tracer breakthrough curves. Although both criteria were taken for model evaluation, still several model setups produced acceptable matches to the observed behaviour. These setups were selected for long-term simulation, the results of which were compared against water level measurements at two piezometers along the hillslope and the integral discharge response of the spring to reject some non-behavioural model setups and further reduce equifinality. The results of this study indicate that process-based modelling can provide a means to distinguish preferential flow networks on the hillslope scale when complementary measurements to constrain the range of behavioural model setups are available. These models can further be employed as a virtual reality to investigate the characteristics of flow path architectures and explore effective parameterisations for larger scale applications.

Coupled land surface–subsurface hydrogeophysical inverse modeling to estimate soil organic carbon content and explore associated hydrological and thermal dynamics in the Arctic tundra

DOE PAGES

Tran, Anh Phuong; Dafflon, Baptiste; Hubbard, Susan S.

2017-09-06

Quantitative characterization of soil organic carbon (OC) content is essential due to its significant impacts on surface–subsurface hydrological–thermal processes and microbial decomposition of OC, which both in turn are important for predicting carbon–climate feedbacks. While such quantification is particularly important in the vulnerable organic-rich Arctic region, it is challenging to achieve due to the general limitations of conventional core sampling and analysis methods, and to the extremely dynamic nature of hydrological–thermal processes associated with annual freeze–thaw events. In this study, we develop and test an inversion scheme that can flexibly use single or multiple datasets – including soil liquid watermore » content, temperature and electrical resistivity tomography (ERT) data – to estimate the vertical distribution of OC content. Our approach relies on the fact that OC content strongly influences soil hydrological–thermal parameters and, therefore, indirectly controls the spatiotemporal dynamics of soil liquid water content, temperature and their correlated electrical resistivity. We employ the Community Land Model to simulate nonisothermal surface–subsurface hydrological dynamics from the bedrock to the top of canopy, with consideration of land surface processes (e.g., solar radiation balance, evapotranspiration, snow accumulation and melting) and ice–liquid water phase transitions. For inversion, we combine a deterministic and an adaptive Markov chain Monte Carlo (MCMC) optimization algorithm to estimate a posteriori distributions of desired model parameters. For hydrological–thermal-to-geophysical variable transformation, the simulated subsurface temperature, liquid water content and ice content are explicitly linked to soil electrical resistivity via petrophysical and geophysical models. We validate the developed scheme using different numerical experiments and evaluate the influence of measurement errors and benefit of joint inversion on the estimation of OC and other parameters. We also quantify the propagation of uncertainty from the estimated parameters to prediction of hydrological–thermal responses. We find that, compared to inversion of single dataset (temperature, liquid water content or apparent resistivity), joint inversion of these datasets significantly reduces parameter uncertainty. We find that the joint inversion approach is able to estimate OC and sand content within the shallow active layer (top 0.3 m of soil) with high reliability. Due to the small variations of temperature and moisture within the shallow permafrost (here at about 0.6 m depth), the approach is unable to estimate OC with confidence. However, if the soil porosity is functionally related to the OC and mineral content, which is often observed in organic-rich Arctic soil, the uncertainty of OC estimate at this depth remarkably decreases. Our study documents the value of the new surface–subsurface, deterministic–stochastic inversion approach, as well as the benefit of including multiple types of data to estimate OC and associated hydrological–thermal dynamics.« less

Coupled land surface–subsurface hydrogeophysical inverse modeling to estimate soil organic carbon content and explore associated hydrological and thermal dynamics in the Arctic tundra

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tran, Anh Phuong; Dafflon, Baptiste; Hubbard, Susan S.

Quantitative characterization of soil organic carbon (OC) content is essential due to its significant impacts on surface–subsurface hydrological–thermal processes and microbial decomposition of OC, which both in turn are important for predicting carbon–climate feedbacks. While such quantification is particularly important in the vulnerable organic-rich Arctic region, it is challenging to achieve due to the general limitations of conventional core sampling and analysis methods, and to the extremely dynamic nature of hydrological–thermal processes associated with annual freeze–thaw events. In this study, we develop and test an inversion scheme that can flexibly use single or multiple datasets – including soil liquid watermore » content, temperature and electrical resistivity tomography (ERT) data – to estimate the vertical distribution of OC content. Our approach relies on the fact that OC content strongly influences soil hydrological–thermal parameters and, therefore, indirectly controls the spatiotemporal dynamics of soil liquid water content, temperature and their correlated electrical resistivity. We employ the Community Land Model to simulate nonisothermal surface–subsurface hydrological dynamics from the bedrock to the top of canopy, with consideration of land surface processes (e.g., solar radiation balance, evapotranspiration, snow accumulation and melting) and ice–liquid water phase transitions. For inversion, we combine a deterministic and an adaptive Markov chain Monte Carlo (MCMC) optimization algorithm to estimate a posteriori distributions of desired model parameters. For hydrological–thermal-to-geophysical variable transformation, the simulated subsurface temperature, liquid water content and ice content are explicitly linked to soil electrical resistivity via petrophysical and geophysical models. We validate the developed scheme using different numerical experiments and evaluate the influence of measurement errors and benefit of joint inversion on the estimation of OC and other parameters. We also quantify the propagation of uncertainty from the estimated parameters to prediction of hydrological–thermal responses. We find that, compared to inversion of single dataset (temperature, liquid water content or apparent resistivity), joint inversion of these datasets significantly reduces parameter uncertainty. We find that the joint inversion approach is able to estimate OC and sand content within the shallow active layer (top 0.3 m of soil) with high reliability. Due to the small variations of temperature and moisture within the shallow permafrost (here at about 0.6 m depth), the approach is unable to estimate OC with confidence. However, if the soil porosity is functionally related to the OC and mineral content, which is often observed in organic-rich Arctic soil, the uncertainty of OC estimate at this depth remarkably decreases. Our study documents the value of the new surface–subsurface, deterministic–stochastic inversion approach, as well as the benefit of including multiple types of data to estimate OC and associated hydrological–thermal dynamics.« less

Stochastic model simulation using Kronecker product analysis and Zassenhaus formula approximation.

PubMed

Caglar, Mehmet Umut; Pal, Ranadip

2013-01-01

Probabilistic Models are regularly applied in Genetic Regulatory Network modeling to capture the stochastic behavior observed in the generation of biological entities such as mRNA or proteins. Several approaches including Stochastic Master Equations and Probabilistic Boolean Networks have been proposed to model the stochastic behavior in genetic regulatory networks. It is generally accepted that Stochastic Master Equation is a fundamental model that can describe the system being investigated in fine detail, but the application of this model is computationally enormously expensive. On the other hand, Probabilistic Boolean Network captures only the coarse-scale stochastic properties of the system without modeling the detailed interactions. We propose a new approximation of the stochastic master equation model that is able to capture the finer details of the modeled system including bistabilities and oscillatory behavior, and yet has a significantly lower computational complexity. In this new method, we represent the system using tensors and derive an identity to exploit the sparse connectivity of regulatory targets for complexity reduction. The algorithm involves an approximation based on Zassenhaus formula to represent the exponential of a sum of matrices as product of matrices. We derive upper bounds on the expected error of the proposed model distribution as compared to the stochastic master equation model distribution. Simulation results of the application of the model to four different biological benchmark systems illustrate performance comparable to detailed stochastic master equation models but with considerably lower computational complexity. The results also demonstrate the reduced complexity of the new approach as compared to commonly used Stochastic Simulation Algorithm for equivalent accuracy.

Stability analysis of multi-group deterministic and stochastic epidemic models with vaccination rate

NASA Astrophysics Data System (ADS)

Wang, Zhi-Gang; Gao, Rui-Mei; Fan, Xiao-Ming; Han, Qi-Xing

2014-09-01

We discuss in this paper a deterministic multi-group MSIR epidemic model with a vaccination rate, the basic reproduction number ℛ0, a key parameter in epidemiology, is a threshold which determines the persistence or extinction of the disease. By using Lyapunov function techniques, we show if ℛ0 is greater than 1 and the deterministic model obeys some conditions, then the disease will prevail, the infective persists and the endemic state is asymptotically stable in a feasible region. If ℛ0 is less than or equal to 1, then the infective disappear so the disease dies out. In addition, stochastic noises around the endemic equilibrium will be added to the deterministic MSIR model in order that the deterministic model is extended to a system of stochastic ordinary differential equations. In the stochastic version, we carry out a detailed analysis on the asymptotic behavior of the stochastic model. In addition, regarding the value of ℛ0, when the stochastic system obeys some conditions and ℛ0 is greater than 1, we deduce the stochastic system is stochastically asymptotically stable. Finally, the deterministic and stochastic model dynamics are illustrated through computer simulations.

STakeholder-Objective Risk Model (STORM): Determining the aggregated risk of multiple contaminant hazards in groundwater well catchments

NASA Astrophysics Data System (ADS)

Enzenhoefer, R.; Binning, P. J.; Nowak, W.

2015-09-01

Risk is often defined as the product of probability, vulnerability and value. Drinking water supply from groundwater abstraction is often at risk due to multiple hazardous land use activities in the well catchment. Each hazard might or might not introduce contaminants into the subsurface at any point in time, which then affects the pumped quality upon transport through the aquifer. In such situations, estimating the overall risk is not trivial, and three key questions emerge: (1) How to aggregate the impacts from different contaminants and spill locations to an overall, cumulative impact on the value at risk? (2) How to properly account for the stochastic nature of spill events when converting the aggregated impact to a risk estimate? (3) How will the overall risk and subsequent decision making depend on stakeholder objectives, where stakeholder objectives refer to the values at risk, risk attitudes and risk metrics that can vary between stakeholders. In this study, we provide a STakeholder-Objective Risk Model (STORM) for assessing the total aggregated risk. Or concept is a quantitative, probabilistic and modular framework for simulation-based risk estimation. It rests on the source-pathway-receptor concept, mass-discharge-based aggregation of stochastically occuring spill events, accounts for uncertainties in the involved flow and transport models through Monte Carlo simulation, and can address different stakeholder objectives. We illustrate the application of STORM in a numerical test case inspired by a German drinking water catchment. As one may expect, the results depend strongly on the chosen stakeholder objectives, but they are equally sensitive to different approaches for risk aggregation across different hazards, contaminant types, and over time.

Unification theory of optimal life histories and linear demographic models in internal stochasticity.

PubMed

Oizumi, Ryo

2014-01-01

Life history of organisms is exposed to uncertainty generated by internal and external stochasticities. Internal stochasticity is generated by the randomness in each individual life history, such as randomness in food intake, genetic character and size growth rate, whereas external stochasticity is due to the environment. For instance, it is known that the external stochasticity tends to affect population growth rate negatively. It has been shown in a recent theoretical study using path-integral formulation in structured linear demographic models that internal stochasticity can affect population growth rate positively or negatively. However, internal stochasticity has not been the main subject of researches. Taking account of effect of internal stochasticity on the population growth rate, the fittest organism has the optimal control of life history affected by the stochasticity in the habitat. The study of this control is known as the optimal life schedule problems. In order to analyze the optimal control under internal stochasticity, we need to make use of "Stochastic Control Theory" in the optimal life schedule problem. There is, however, no such kind of theory unifying optimal life history and internal stochasticity. This study focuses on an extension of optimal life schedule problems to unify control theory of internal stochasticity into linear demographic models. First, we show the relationship between the general age-states linear demographic models and the stochastic control theory via several mathematical formulations, such as path-integral, integral equation, and transition matrix. Secondly, we apply our theory to a two-resource utilization model for two different breeding systems: semelparity and iteroparity. Finally, we show that the diversity of resources is important for species in a case. Our study shows that this unification theory can address risk hedges of life history in general age-states linear demographic models.

Unification Theory of Optimal Life Histories and Linear Demographic Models in Internal Stochasticity

PubMed Central

Oizumi, Ryo

2014-01-01

Life history of organisms is exposed to uncertainty generated by internal and external stochasticities. Internal stochasticity is generated by the randomness in each individual life history, such as randomness in food intake, genetic character and size growth rate, whereas external stochasticity is due to the environment. For instance, it is known that the external stochasticity tends to affect population growth rate negatively. It has been shown in a recent theoretical study using path-integral formulation in structured linear demographic models that internal stochasticity can affect population growth rate positively or negatively. However, internal stochasticity has not been the main subject of researches. Taking account of effect of internal stochasticity on the population growth rate, the fittest organism has the optimal control of life history affected by the stochasticity in the habitat. The study of this control is known as the optimal life schedule problems. In order to analyze the optimal control under internal stochasticity, we need to make use of “Stochastic Control Theory” in the optimal life schedule problem. There is, however, no such kind of theory unifying optimal life history and internal stochasticity. This study focuses on an extension of optimal life schedule problems to unify control theory of internal stochasticity into linear demographic models. First, we show the relationship between the general age-states linear demographic models and the stochastic control theory via several mathematical formulations, such as path–integral, integral equation, and transition matrix. Secondly, we apply our theory to a two-resource utilization model for two different breeding systems: semelparity and iteroparity. Finally, we show that the diversity of resources is important for species in a case. Our study shows that this unification theory can address risk hedges of life history in general age-states linear demographic models. PMID:24945258

Can Geostatistical Models Represent Nature's Variability? An Analysis Using Flume Experiments

NASA Astrophysics Data System (ADS)

Scheidt, C.; Fernandes, A. M.; Paola, C.; Caers, J.

2015-12-01

The lack of understanding in the Earth's geological and physical processes governing sediment deposition render subsurface modeling subject to large uncertainty. Geostatistics is often used to model uncertainty because of its capability to stochastically generate spatially varying realizations of the subsurface. These methods can generate a range of realizations of a given pattern - but how representative are these of the full natural variability? And how can we identify the minimum set of images that represent this natural variability? Here we use this minimum set to define the geostatistical prior model: a set of training images that represent the range of patterns generated by autogenic variability in the sedimentary environment under study. The proper definition of the prior model is essential in capturing the variability of the depositional patterns. This work starts with a set of overhead images from an experimental basin that showed ongoing autogenic variability. We use the images to analyze the essential characteristics of this suite of patterns. In particular, our goal is to define a prior model (a minimal set of selected training images) such that geostatistical algorithms, when applied to this set, can reproduce the full measured variability. A necessary prerequisite is to define a measure of variability. In this study, we measure variability using a dissimilarity distance between the images. The distance indicates whether two snapshots contain similar depositional patterns. To reproduce the variability in the images, we apply an MPS algorithm to the set of selected snapshots of the sedimentary basin that serve as training images. The training images are chosen from among the initial set by using the distance measure to ensure that only dissimilar images are chosen. Preliminary investigations show that MPS can reproduce fairly accurately the natural variability of the experimental depositional system. Furthermore, the selected training images provide process information. They fall into three basic patterns: a channelized end member, a sheet flow end member, and one intermediate case. These represent the continuum between autogenic bypass or erosion, and net deposition.

Large-Scale CTRW Analysis of Push-Pull Tracer Tests and Other Transport in Heterogeneous Porous Media

NASA Astrophysics Data System (ADS)

Hansen, S. K.; Berkowitz, B.

2014-12-01

Recently, we developed an alternative CTRW formulation which uses a "latching" upscaling scheme to rigorously map continuous or fine-scale stochastic solute motion onto discrete transitions on an arbitrarily coarse lattice (with spacing potentially on the meter scale or more). This approach enables model simplification, among many other things. Under advection, for example, we see that many relevant anomalous transport problems may be mapped into 1D, with latching to a sequence of successive, uniformly spaced planes. On this formulation (which we term RP-CTRW), the spatial transition vector may generally be made deterministic, with CTRW waiting time distributions encapsulating all the stochastic behavior. We demonstrate the excellent performance of this technique alongside Pareto-distributed waiting times in explaining experiments across a variety of scales using only two degrees of freedom. An interesting new application of the RP-CTRW technique is the analysis of radial (push-pull) tracer tests. Given modern computational power, random walk simulations are a natural fit for the inverse problem of inferring subsurface parameters from push-pull test data, and we propose them as an alternative to the classical type curve approach. In particular, we explore the visibility of heterogeneity through non-Fickian behavior in push-pull tests, and illustrate the ability of a radial RP-CTRW technique to encapsulate this behavior using a sparse parameterization which has predictive value.

Inverse and forward modeling under uncertainty using MRE-based Bayesian approach

NASA Astrophysics Data System (ADS)

Hou, Z.; Rubin, Y.

2004-12-01

A stochastic inverse approach for subsurface characterization is proposed and applied to shallow vadose zone at a winery field site in north California and to a gas reservoir at the Ormen Lange field site in the North Sea. The approach is formulated in a Bayesian-stochastic framework, whereby the unknown parameters are identified in terms of their statistical moments or their probabilities. Instead of the traditional single-valued estimation /prediction provided by deterministic methods, the approach gives a probability distribution for an unknown parameter. This allows calculating the mean, the mode, and the confidence interval, which is useful for a rational treatment of uncertainty and its consequences. The approach also allows incorporating data of various types and different error levels, including measurements of state variables as well as information such as bounds on or statistical moments of the unknown parameters, which may represent prior information. To obtain minimally subjective prior probabilities required for the Bayesian approach, the principle of Minimum Relative Entropy (MRE) is employed. The approach is tested in field sites for flow parameters identification and soil moisture estimation in the vadose zone and for gas saturation estimation at great depth below the ocean floor. Results indicate the potential of coupling various types of field data within a MRE-based Bayesian formalism for improving the estimation of the parameters of interest.

Hydraulic tomography offers improved imaging of heterogeneity in fractured rocks.

PubMed

Illman, Walter A

2014-01-01

Fractured rocks have presented formidable challenges for accurately predicting groundwater flow and contaminant transport. This is mainly due to our difficulty in mapping the fracture-rock matrix system, their hydraulic properties and connectivity at resolutions that are meaningful for groundwater modeling. Over the last several decades, considerable effort has gone into creating maps of subsurface heterogeneity in hydraulic conductivity (K) and specific storage (Ss ) of fractured rocks. Developed methods include kriging, stochastic simulation, stochastic inverse modeling, and hydraulic tomography. In this article, I review the evolution of various heterogeneity mapping approaches and contend that hydraulic tomography, a recently developed aquifer characterization technique for unconsolidated deposits, is also a promising approach in yielding robust maps (or tomograms) of K and Ss heterogeneity for fractured rocks. While hydraulic tomography has recently been shown to be a robust technique, the resolution of the K and Ss tomograms mainly depends on the density of pumping and monitoring locations and the quality of data. The resolution will be improved through the development of new devices for higher density monitoring of pressure responses at discrete intervals in boreholes and potentially through the integration of other data from single-hole tests, borehole flowmeter profiling, and tracer tests. Other data from temperature and geophysical surveys as well as geological investigations may improve the accuracy of the maps, but more research is needed. Technological advances will undoubtedly lead to more accurate maps. However, more effort should go into evaluating these maps so that one can gain more confidence in their reliability. © 2013, National Ground Water Association.

Hydraulic tomography offers improved imaging of heterogeneity in fractured rocks

NASA Astrophysics Data System (ADS)

Illman, W. A.

2013-12-01

Fractured rocks have presented formidable challenges for accurately predicting groundwater flow and contaminant transport. This is mainly due to our difficulty in mapping the fracture-rock matrix system, their hydraulic properties and connectivity at resolutions that are meaningful for groundwater flow and especially transport modeling. Over the last several decades, considerable effort has gone into creating maps of subsurface heterogeneity in hydraulic conductivity (K) and specific storage (Ss) of fractured rocks. Developed methods include kriging, stochastic simulation, stochastic inverse modeling, and hydraulic tomography. In this presentation, I review the evolution of various heterogeneity mapping approaches and contend that hydraulic tomography, a recently developed aquifer characterization technique for unconsolidated deposits, is also a promising approach in yielding robust maps (or tomograms) of K and Ss heterogeneity for fractured rocks. While hydraulic tomography has recently been shown to be a robust technique, the resolution of the K and Ss tomograms mainly depends on the density of pumping and monitoring locations and the quality of data. The resolution will be improved through the development of new devices for higher density monitoring of pressure responses at discrete intervals in boreholes and potentially through the integration of other data from single-hole tests, borehole flowmeter profiling and tracer tests. Other data from temperature and geophysical surveys as well as geological investigations may improve the accuracy of the maps, but more research is needed. Technological advances will undoubtedly lead to more accurate maps. However, more effort should go into evaluating these maps so that one can gain more confidence in their reliability.

Stochastic Lanchester Air-to-Air Campaign Model: Model Description and Users Guides

DTIC Science & Technology

2009-01-01

STOCHASTIC LANCHESTER AIR-TO-AIR CAMPAIGN MODEL MODEL DESCRIPTION AND USERS GUIDES—2009 REPORT PA702T1 Rober t V. Hemm Jr. Dav id A . Lee...LMI © 2009. ALL RIGHTS RESERVED. Stochastic Lanchester Air-to-Air Campaign Model: Model Description and Users Guides—2009 PA702T1/JANUARY...2009 Executive Summary This report documents the latest version of the Stochastic Lanchester Air-to-Air Campaign Model (SLAACM), developed by LMI for

Stochastic Multi-Timescale Power System Operations With Variable Wind Generation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Hongyu; Krad, Ibrahim; Florita, Anthony

This paper describes a novel set of stochastic unit commitment and economic dispatch models that consider stochastic loads and variable generation at multiple operational timescales. The stochastic model includes four distinct stages: stochastic day-ahead security-constrained unit commitment (SCUC), stochastic real-time SCUC, stochastic real-time security-constrained economic dispatch (SCED), and deterministic automatic generation control (AGC). These sub-models are integrated together such that they are continually updated with decisions passed from one to another. The progressive hedging algorithm (PHA) is applied to solve the stochastic models to maintain the computational tractability of the proposed models. Comparative case studies with deterministic approaches are conductedmore » in low wind and high wind penetration scenarios to highlight the advantages of the proposed methodology, one with perfect forecasts and the other with current state-of-the-art but imperfect deterministic forecasts. The effectiveness of the proposed method is evaluated with sensitivity tests using both economic and reliability metrics to provide a broader view of its impact.« less

Mixed Effects Modeling Using Stochastic Differential Equations: Illustrated by Pharmacokinetic Data of Nicotinic Acid in Obese Zucker Rats.

PubMed

Leander, Jacob; Almquist, Joachim; Ahlström, Christine; Gabrielsson, Johan; Jirstrand, Mats

2015-05-01

Inclusion of stochastic differential equations in mixed effects models provides means to quantify and distinguish three sources of variability in data. In addition to the two commonly encountered sources, measurement error and interindividual variability, we also consider uncertainty in the dynamical model itself. To this end, we extend the ordinary differential equation setting used in nonlinear mixed effects models to include stochastic differential equations. The approximate population likelihood is derived using the first-order conditional estimation with interaction method and extended Kalman filtering. To illustrate the application of the stochastic differential mixed effects model, two pharmacokinetic models are considered. First, we use a stochastic one-compartmental model with first-order input and nonlinear elimination to generate synthetic data in a simulated study. We show that by using the proposed method, the three sources of variability can be successfully separated. If the stochastic part is neglected, the parameter estimates become biased, and the measurement error variance is significantly overestimated. Second, we consider an extension to a stochastic pharmacokinetic model in a preclinical study of nicotinic acid kinetics in obese Zucker rats. The parameter estimates are compared between a deterministic and a stochastic NiAc disposition model, respectively. Discrepancies between model predictions and observations, previously described as measurement noise only, are now separated into a comparatively lower level of measurement noise and a significant uncertainty in model dynamics. These examples demonstrate that stochastic differential mixed effects models are useful tools for identifying incomplete or inaccurate model dynamics and for reducing potential bias in parameter estimates due to such model deficiencies.

Stochastic modelling of microstructure formation in solidification processes

NASA Astrophysics Data System (ADS)

Nastac, Laurentiu; Stefanescu, Doru M.

1997-07-01

To relax many of the assumptions used in continuum approaches, a general stochastic model has been developed. The stochastic model can be used not only for an accurate description of the fraction of solid evolution, and therefore accurate cooling curves, but also for simulation of microstructure formation in castings. The advantage of using the stochastic approach is to give a time- and space-dependent description of solidification processes. Time- and space-dependent processes can also be described by partial differential equations. Unlike a differential formulation which, in most cases, has to be transformed into a difference equation and solved numerically, the stochastic approach is essentially a direct numerical algorithm. The stochastic model is comprehensive, since the competition between various phases is considered. Furthermore, grain impingement is directly included through the structure of the model. In the present research, all grain morphologies are simulated with this procedure. The relevance of the stochastic approach is that the simulated microstructures can be directly compared with microstructures obtained from experiments. The computer becomes a `dynamic metallographic microscope'. A comparison between deterministic and stochastic approaches has been performed. An important objective of this research was to answer the following general questions: (1) `Would fully deterministic approaches continue to be useful in solidification modelling?' and (2) `Would stochastic algorithms be capable of entirely replacing purely deterministic models?'

A Rigorous Temperature-Dependent Stochastic Modelling and Testing for MEMS-Based Inertial Sensor Errors.

PubMed

El-Diasty, Mohammed; Pagiatakis, Spiros

2009-01-01

In this paper, we examine the effect of changing the temperature points on MEMS-based inertial sensor random error. We collect static data under different temperature points using a MEMS-based inertial sensor mounted inside a thermal chamber. Rigorous stochastic models, namely Autoregressive-based Gauss-Markov (AR-based GM) models are developed to describe the random error behaviour. The proposed AR-based GM model is initially applied to short stationary inertial data to develop the stochastic model parameters (correlation times). It is shown that the stochastic model parameters of a MEMS-based inertial unit, namely the ADIS16364, are temperature dependent. In addition, field kinematic test data collected at about 17 °C are used to test the performance of the stochastic models at different temperature points in the filtering stage using Unscented Kalman Filter (UKF). It is shown that the stochastic model developed at 20 °C provides a more accurate inertial navigation solution than the ones obtained from the stochastic models developed at -40 °C, -20 °C, 0 °C, +40 °C, and +60 °C. The temperature dependence of the stochastic model is significant and should be considered at all times to obtain optimal navigation solution for MEMS-based INS/GPS integration.

Stochastic effects in a seasonally forced epidemic model

NASA Astrophysics Data System (ADS)

Rozhnova, G.; Nunes, A.

2010-10-01

The interplay of seasonality, the system’s nonlinearities and intrinsic stochasticity, is studied for a seasonally forced susceptible-exposed-infective-recovered stochastic model. The model is explored in the parameter region that corresponds to childhood infectious diseases such as measles. The power spectrum of the stochastic fluctuations around the attractors of the deterministic system that describes the model in the thermodynamic limit is computed analytically and validated by stochastic simulations for large system sizes. Size effects are studied through additional simulations. Other effects such as switching between coexisting attractors induced by stochasticity often mentioned in the literature as playing an important role in the dynamics of childhood infectious diseases are also investigated. The main conclusion is that stochastic amplification, rather than these effects, is the key ingredient to understand the observed incidence patterns.

Stochastic Modelling, Analysis, and Simulations of the Solar Cycle Dynamic Process

NASA Astrophysics Data System (ADS)

Turner, Douglas C.; Ladde, Gangaram S.

2018-03-01

Analytical solutions, discretization schemes and simulation results are presented for the time delay deterministic differential equation model of the solar dynamo presented by Wilmot-Smith et al. In addition, this model is extended under stochastic Gaussian white noise parametric fluctuations. The introduction of stochastic fluctuations incorporates variables affecting the dynamo process in the solar interior, estimation error of parameters, and uncertainty of the α-effect mechanism. Simulation results are presented and analyzed to exhibit the effects of stochastic parametric volatility-dependent perturbations. The results generalize and extend the work of Hazra et al. In fact, some of these results exhibit the oscillatory dynamic behavior generated by the stochastic parametric additative perturbations in the absence of time delay. In addition, the simulation results of the modified stochastic models influence the change in behavior of the very recently developed stochastic model of Hazra et al.

Agent based reasoning for the non-linear stochastic models of long-range memory

NASA Astrophysics Data System (ADS)

Kononovicius, A.; Gontis, V.

2012-02-01

We extend Kirman's model by introducing variable event time scale. The proposed flexible time scale is equivalent to the variable trading activity observed in financial markets. Stochastic version of the extended Kirman's agent based model is compared to the non-linear stochastic models of long-range memory in financial markets. The agent based model providing matching macroscopic description serves as a microscopic reasoning of the earlier proposed stochastic model exhibiting power law statistics.

Persistence and extinction of a stochastic single-species model under regime switching in a polluted environment II.

PubMed

Liu, Meng; Wang, Ke

2010-12-07

This is a continuation of our paper [Liu, M., Wang, K., 2010. Persistence and extinction of a stochastic single-species model under regime switching in a polluted environment, J. Theor. Biol. 264, 934-944]. Taking both white noise and colored noise into account, a stochastic single-species model under regime switching in a polluted environment is studied. Sufficient conditions for extinction, stochastic nonpersistence in the mean, stochastic weak persistence and stochastic permanence are established. The threshold between stochastic weak persistence and extinction is obtained. The results show that a different type of noise has a different effect on the survival results. Copyright © 2010 Elsevier Ltd. All rights reserved.

Hybrid approaches for multiple-species stochastic reaction–diffusion models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Spill, Fabian, E-mail: fspill@bu.edu; Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139; Guerrero, Pilar

2015-10-15

Reaction–diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and smallmore » in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction–diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model. - Highlights: • A novel hybrid stochastic/deterministic reaction–diffusion simulation method is given. • Can massively speed up stochastic simulations while preserving stochastic effects. • Can handle multiple reacting species. • Can handle moving boundaries.« less

Modelling the cancer growth process by Stochastic Differential Equations with the effect of Chondroitin Sulfate (CS) as anticancer therapeutics

NASA Astrophysics Data System (ADS)

Syahidatul Ayuni Mazlan, Mazma; Rosli, Norhayati; Jauhari Arief Ichwan, Solachuddin; Suhaity Azmi, Nina

2017-09-01

A stochastic model is introduced to describe the growth of cancer affected by anti-cancer therapeutics of Chondroitin Sulfate (CS). The parameters values of the stochastic model are estimated via maximum likelihood function. The numerical method of Euler-Maruyama will be employed to solve the model numerically. The efficiency of the stochastic model is measured by comparing the simulated result with the experimental data.

Internal fracture heterogeneity in discrete fracture network modelling: Effect of correlation length and textures with connected and disconnected permeability field

NASA Astrophysics Data System (ADS)

Frampton, A.; Hyman, J.; Zou, L.

2017-12-01

Analysing flow and transport in sparsely fractured media is important for understanding how crystalline bedrock environments function as barriers to transport of contaminants, with important applications towards subsurface repositories for storage of spent nuclear fuel. Crystalline bedrocks are particularly favourable due to their geological stability, low advective flow and strong hydrogeochemical retention properties, which can delay transport of radionuclides, allowing decay to limit release to the biosphere. There are however many challenges involved in quantifying and modelling subsurface flow and transport in fractured media, largely due to geological complexity and heterogeneity, where the interplay between advective and dispersive flow strongly impacts both inert and reactive transport. A key to modelling transport in a Lagrangian framework involves quantifying pathway travel times and the hydrodynamic control of retention, and both these quantities strongly depend on heterogeneity of the fracture network at different scales. In this contribution, we present recent analysis of flow and transport considering fracture networks with single-fracture heterogeneity described by different multivariate normal distributions. A coherent triad of fields with identical correlation length and variance are created but which greatly differ in structure, corresponding to textures with well-connected low, medium and high permeability structures. Through numerical modelling of multiple scales in a stochastic setting we quantify the relative impact of texture type and correlation length against network topological measures, and identify key thresholds for cases where flow dispersion is controlled by single-fracture heterogeneity versus network-scale heterogeneity. This is achieved by using a recently developed novel numerical discrete fracture network model. Furthermore, we highlight enhanced flow channelling for cases where correlation structure continues across intersections in a network, and discuss application to realistic fracture networks using field data of sparsely fractured crystalline rock from the Swedish candidate repository site for spent nuclear fuel.

Dynamics of a stochastic tuberculosis model with constant recruitment and varying total population size

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing; Shi, Ningzhong; Hayat, Tasawar; Alsaedi, Ahmed

2017-03-01

In this paper, we develop a mathematical model for a tuberculosis model with constant recruitment and varying total population size by incorporating stochastic perturbations. By constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of an ergodic stationary distribution as well as extinction of the disease to the stochastic system.

Individualism in plant populations: using stochastic differential equations to model individual neighbourhood-dependent plant growth.

PubMed

Lv, Qiming; Schneider, Manuel K; Pitchford, Jonathan W

2008-08-01

We study individual plant growth and size hierarchy formation in an experimental population of Arabidopsis thaliana, within an integrated analysis that explicitly accounts for size-dependent growth, size- and space-dependent competition, and environmental stochasticity. It is shown that a Gompertz-type stochastic differential equation (SDE) model, involving asymmetric competition kernels and a stochastic term which decreases with the logarithm of plant weight, efficiently describes individual plant growth, competition, and variability in the studied population. The model is evaluated within a Bayesian framework and compared to its deterministic counterpart, and to several simplified stochastic models, using distributional validation. We show that stochasticity is an important determinant of size hierarchy and that SDE models outperform the deterministic model if and only if structural components of competition (asymmetry; size- and space-dependence) are accounted for. Implications of these results are discussed in the context of plant ecology and in more general modelling situations.

Gompertzian stochastic model with delay effect to cervical cancer growth

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti; Bahar, Arifah

2015-02-03

In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.

Improved ensemble-mean forecasting of ENSO events by a zero-mean stochastic error model of an intermediate coupled model

NASA Astrophysics Data System (ADS)

Zheng, Fei; Zhu, Jiang

2017-04-01

How to design a reliable ensemble prediction strategy with considering the major uncertainties of a forecasting system is a crucial issue for performing an ensemble forecast. In this study, a new stochastic perturbation technique is developed to improve the prediction skills of El Niño-Southern Oscillation (ENSO) through using an intermediate coupled model. We first estimate and analyze the model uncertainties from the ensemble Kalman filter analysis results through assimilating the observed sea surface temperatures. Then, based on the pre-analyzed properties of model errors, we develop a zero-mean stochastic model-error model to characterize the model uncertainties mainly induced by the missed physical processes of the original model (e.g., stochastic atmospheric forcing, extra-tropical effects, Indian Ocean Dipole). Finally, we perturb each member of an ensemble forecast at each step by the developed stochastic model-error model during the 12-month forecasting process, and add the zero-mean perturbations into the physical fields to mimic the presence of missing processes and high-frequency stochastic noises. The impacts of stochastic model-error perturbations on ENSO deterministic predictions are examined by performing two sets of 21-yr hindcast experiments, which are initialized from the same initial conditions and differentiated by whether they consider the stochastic perturbations. The comparison results show that the stochastic perturbations have a significant effect on improving the ensemble-mean prediction skills during the entire 12-month forecasting process. This improvement occurs mainly because the nonlinear terms in the model can form a positive ensemble-mean from a series of zero-mean perturbations, which reduces the forecasting biases and then corrects the forecast through this nonlinear heating mechanism.

An efficient distribution method for nonlinear transport problems in stochastic porous media

NASA Astrophysics Data System (ADS)

Ibrahima, F.; Tchelepi, H.; Meyer, D. W.

2015-12-01

Because geophysical data are inexorably sparse and incomplete, stochastic treatments of simulated responses are convenient to explore possible scenarios and assess risks in subsurface problems. In particular, understanding how uncertainties propagate in porous media with nonlinear two-phase flow is essential, yet challenging, in reservoir simulation and hydrology. We give a computationally efficient and numerically accurate method to estimate the one-point probability density (PDF) and cumulative distribution functions (CDF) of the water saturation for the stochastic Buckley-Leverett problem when the probability distributions of the permeability and porosity fields are available. The method draws inspiration from the streamline approach and expresses the distributions of interest essentially in terms of an analytically derived mapping and the distribution of the time of flight. In a large class of applications the latter can be estimated at low computational costs (even via conventional Monte Carlo). Once the water saturation distribution is determined, any one-point statistics thereof can be obtained, especially its average and standard deviation. Moreover, rarely available in other approaches, yet crucial information such as the probability of rare events and saturation quantiles (e.g. P10, P50 and P90) can be derived from the method. We provide various examples and comparisons with Monte Carlo simulations to illustrate the performance of the method.

Effects of stochastic sodium channels on extracellular excitation of myelinated nerve fibers.

PubMed

Mino, Hiroyuki; Grill, Warren M

2002-06-01

The effects of the stochastic gating properties of sodium channels on the extracellular excitation properties of mammalian nerve fibers was determined by computer simulation. To reduce computation time, a hybrid multicompartment cable model including five central nodes of Ranvier containing stochastic sodium channels and 16 flanking nodes containing detenninistic membrane dynamics was developed. The excitation properties of the hybrid cable model were comparable with those of a full stochastic cable model including 21 nodes of Ranvier containing stochastic sodium channels, indicating the validity of the hybrid cable model. The hybrid cable model was used to investigate whether or not the excitation properties of extracellularly activated fibers were influenced by the stochastic gating of sodium channels, including spike latencies, strength-duration (SD), current-distance (IX), and recruitment properties. The stochastic properties of the sodium channels in the hybrid cable model had the greatest impact when considering the temporal dynamics of nerve fibers, i.e., a large variability in latencies, while they did not influence the SD, IX, or recruitment properties as compared with those of the conventional deterministic cable model. These findings suggest that inclusion of stochastic nodes is not important for model-based design of stimulus waveforms for activation of motor nerve fibers. However, in cases where temporal fine structure is important, for example in sensory neural prostheses in the auditory and visual systems, the stochastic properties of the sodium channels may play a key role in the design of stimulus waveforms.

Modeling stochasticity and robustness in gene regulatory networks.

PubMed

Garg, Abhishek; Mohanram, Kartik; Di Cara, Alessandro; De Micheli, Giovanni; Xenarios, Ioannis

2009-06-15

Understanding gene regulation in biological processes and modeling the robustness of underlying regulatory networks is an important problem that is currently being addressed by computational systems biologists. Lately, there has been a renewed interest in Boolean modeling techniques for gene regulatory networks (GRNs). However, due to their deterministic nature, it is often difficult to identify whether these modeling approaches are robust to the addition of stochastic noise that is widespread in gene regulatory processes. Stochasticity in Boolean models of GRNs has been addressed relatively sparingly in the past, mainly by flipping the expression of genes between different expression levels with a predefined probability. This stochasticity in nodes (SIN) model leads to over representation of noise in GRNs and hence non-correspondence with biological observations. In this article, we introduce the stochasticity in functions (SIF) model for simulating stochasticity in Boolean models of GRNs. By providing biological motivation behind the use of the SIF model and applying it to the T-helper and T-cell activation networks, we show that the SIF model provides more biologically robust results than the existing SIN model of stochasticity in GRNs. Algorithms are made available under our Boolean modeling toolbox, GenYsis. The software binaries can be downloaded from http://si2.epfl.ch/ approximately garg/genysis.html.

Analysis of a novel stochastic SIRS epidemic model with two different saturated incidence rates

NASA Astrophysics Data System (ADS)

Chang, Zhengbo; Meng, Xinzhu; Lu, Xiao

2017-04-01

This paper presents a stochastic SIRS epidemic model with two different nonlinear incidence rates and double epidemic asymmetrical hypothesis, and we devote to develop a mathematical method to obtain the threshold of the stochastic epidemic model. We firstly investigate the boundness and extinction of the stochastic system. Furthermore, we use Ito's formula, the comparison theorem and some new inequalities techniques of stochastic differential systems to discuss persistence in mean of two diseases on three cases. The results indicate that stochastic fluctuations can suppress the disease outbreak. Finally, numerical simulations about different noise disturbance coefficients are carried out to illustrate the obtained theoretical results.

Nucleation and growth kinetics for intercalated islands during deposition on layered materials with isolated pointlike surface defects

DOE PAGES

Han, Yong; Lii-Rosales, A.; Zhou, Y.; ...

2017-10-13

Theory and stochastic lattice-gas modeling is developed for the formation of intercalated metal islands in the gallery between the top layer and the underlying layer at the surface of layered materials. Our model for this process involves deposition of atoms, some fraction of which then enter the gallery through well-separated pointlike defects in the top layer. Subsequently, these atoms diffuse within the subsurface gallery leading to nucleation and growth of intercalated islands nearby the defect point source. For the case of a single point defect, continuum diffusion equation analysis provides insight into the nucleation kinetics. However, complementary tailored lattice-gas modelingmore » produces a more comprehensive and quantitative characterization. We analyze the large spread in nucleation times and positions relative to the defect for the first nucleated island. We also consider the formation of subsequent islands and the evolution of island growth shapes. The shapes reflect in part our natural adoption of a hexagonal close-packed island structure. As a result, motivation and support for the model is provided by scanning tunneling microscopy observations of the formation of intercalated metal islands in highly-ordered pyrolytic graphite at higher temperatures.« less

Stochastic Human Exposure and Dose Simulation Model for Pesticides

EPA Science Inventory

SHEDS-Pesticides (Stochastic Human Exposure and Dose Simulation Model for Pesticides) is a physically-based stochastic model developed to quantify exposure and dose of humans to multimedia, multipathway pollutants. Probabilistic inputs are combined in physical/mechanistic algorit...

Approximation of Quantum Stochastic Differential Equations for Input-Output Model Reduction

DTIC Science & Technology

2016-02-25

Approximation of Quantum Stochastic Differential Equations for Input-Output Model Reduction We have completed a short program of theoretical research...on dimensional reduction and approximation of models based on quantum stochastic differential equations. Our primary results lie in the area of...2211 quantum probability, quantum stochastic differential equations REPORT DOCUMENTATION PAGE 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 10. SPONSOR

Developing a trend prediction model of subsurface damage for fixed-abrasive grinding of optics by cup wheels.

PubMed

Dong, Zhichao; Cheng, Haobo

2016-11-10

Fixed-abrasive grinding by cup wheels plays an important role in the production of precision optics. During cup wheel grinding, we strive for a large removal rate while maintaining fine integrity on the surface and subsurface layers (academically recognized as surface roughness and subsurface damage, respectively). This study develops a theoretical model used to predict the trend of subsurface damage of optics (with respect to various grinding parameters) in fixed-abrasive grinding by cup wheels. It is derived from the maximum undeformed chip thickness model, and it successfully correlates the pivotal parameters of cup wheel grinding with the subsurface damage depth. The efficiency of this model is then demonstrated by a set of experiments performed on a cup wheel grinding machine. In these experiments, the characteristics of subsurface damage are inspected by a wedge-polishing plus microscopic inspection method, revealing that the subsurface damage induced in cup wheel grinding is composed of craterlike morphologies and slender cracks, with depth ranging from ∼6.2 to ∼13.2  μm under the specified grinding parameters. With the help of the proposed model, an optimized grinding strategy is suggested for realizing fine subsurface integrity as well as high removal rate, which can alleviate the workload of subsequent lapping and polishing.

Phenomenology of stochastic exponential growth

NASA Astrophysics Data System (ADS)

Pirjol, Dan; Jafarpour, Farshid; Iyer-Biswas, Srividya

2017-06-01

Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on modeling the phenomenology of these stochastic dynamics has predominantly focused on one model, geometric Brownian motion (GBM), which can be described as the solution of a Langevin equation with linear drift and linear multiplicative noise. Using recent experimental results on stochastic exponential growth of individual bacterial cell sizes, we motivate the need for a more general class of phenomenological models of stochastic exponential growth, which are consistent with the observation that the mean-rescaled distributions are approximately stationary at long times. We show that this behavior is not consistent with GBM, instead it is consistent with power-law multiplicative noise with positive fractional powers. Therefore, we consider this general class of phenomenological models for stochastic exponential growth, provide analytical solutions, and identify the important dimensionless combination of model parameters, which determines the shape of the mean-rescaled distribution. We also provide a prescription for robustly inferring model parameters from experimentally observed stochastic growth trajectories.

Dynamics of a stochastic multi-strain SIS epidemic model driven by Lévy noise

NASA Astrophysics Data System (ADS)

Chen, Can; Kang, Yanmei

2017-01-01

A stochastic multi-strain SIS epidemic model is formulated by introducing Lévy noise into the disease transmission rate of each strain. First, we prove that the stochastic model admits a unique global positive solution, and, by the comparison theorem, we show that the solution remains within a positively invariant set almost surely. Next we investigate stochastic stability of the disease-free equilibrium, including stability in probability and pth moment asymptotic stability. Then sufficient conditions for persistence in the mean of the disease are established. Finally, based on an Euler scheme for Lévy-driven stochastic differential equations, numerical simulations for a stochastic two-strain model are carried out to verify the theoretical results. Moreover, numerical comparison results of the stochastic two-strain model and the deterministic version are also given. Lévy noise can cause the two strains to become extinct almost surely, even though there is a dominant strain that persists in the deterministic model. It can be concluded that the introduction of Lévy noise reduces the disease extinction threshold, which indicates that Lévy noise may suppress the disease outbreak.

Stochastic dynamics of melt ponds and sea ice-albedo climate feedback

NASA Astrophysics Data System (ADS)

Sudakov, Ivan

Evolution of melt ponds on the Arctic sea surface is a complicated stochastic process. We suggest a low-order model with ice-albedo feedback which describes stochastic dynamics of melt ponds geometrical characteristics. The model is a stochastic dynamical system model of energy balance in the climate system. We describe the equilibria in this model. We conclude the transition in fractal dimension of melt ponds affects the shape of the sea ice albedo curve.

Effects of Stochastic Traffic Flow Model on Expected System Performance

DTIC Science & Technology

2012-12-01

NSWC-PCD has made considerable improvements to their pedestrian flow modeling . In addition to the linear paths, the 2011 version now includes...using stochastic paths. 2.2 Linear Paths vs. Stochastic Paths 2.2.1 Linear Paths and Direct Maximum Pd Calculation Modeling pedestrian traffic flow...as a stochastic process begins with the linear path model . Let the detec- tion area be R x C voxels. This creates C 2 total linear paths, path(Cs

Translucent Radiosity: Efficiently Combining Diffuse Inter-Reflection and Subsurface Scattering.

PubMed

Sheng, Yu; Shi, Yulong; Wang, Lili; Narasimhan, Srinivasa G

2014-07-01

It is hard to efficiently model the light transport in scenes with translucent objects for interactive applications. The inter-reflection between objects and their environments and the subsurface scattering through the materials intertwine to produce visual effects like color bleeding, light glows, and soft shading. Monte-Carlo based approaches have demonstrated impressive results but are computationally expensive, and faster approaches model either only inter-reflection or only subsurface scattering. In this paper, we present a simple analytic model that combines diffuse inter-reflection and isotropic subsurface scattering. Our approach extends the classical work in radiosity by including a subsurface scattering matrix that operates in conjunction with the traditional form factor matrix. This subsurface scattering matrix can be constructed using analytic, measurement-based or simulation-based models and can capture both homogeneous and heterogeneous translucencies. Using a fast iterative solution to radiosity, we demonstrate scene relighting and dynamically varying object translucencies at near interactive rates.

Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology.

PubMed

Schaff, James C; Gao, Fei; Li, Ye; Novak, Igor L; Slepchenko, Boris M

2016-12-01

Hybrid deterministic-stochastic methods provide an efficient alternative to a fully stochastic treatment of models which include components with disparate levels of stochasticity. However, general-purpose hybrid solvers for spatially resolved simulations of reaction-diffusion systems are not widely available. Here we describe fundamentals of a general-purpose spatial hybrid method. The method generates realizations of a spatially inhomogeneous hybrid system by appropriately integrating capabilities of a deterministic partial differential equation solver with a popular particle-based stochastic simulator, Smoldyn. Rigorous validation of the algorithm is detailed, using a simple model of calcium 'sparks' as a testbed. The solver is then applied to a deterministic-stochastic model of spontaneous emergence of cell polarity. The approach is general enough to be implemented within biologist-friendly software frameworks such as Virtual Cell.

Groundwater modelling in conceptual hydrological models - introducing space

NASA Astrophysics Data System (ADS)

Boje, Søren; Skaugen, Thomas; Møen, Knut; Myrabø, Steinar

2017-04-01

The tiny Sæternbekken Minifelt (Muren) catchment (7500 m2) in Bærumsmarka, Norway, was during the 1990s, densely instrumented with more than a 100 observation points for measuring groundwater levels. The aim was to investigate the link between shallow groundwater dynamics and runoff. The DDD (Distance Distribution Dynamics) model is a newly developed rainfall-runoff model used operationally by the Norwegian Flood-Forecasting service at NVE. The model estimates the capacity of the subsurface reservoir at different levels of saturation and predicts overland flow. The subsurface in the DDD model has a 2-D representation that calculates the saturated and unsaturated soil moisture along a hillslope representing the entire catchment in question. The groundwater observations from more than two decades ago are used to verify assumptions of the subsurface reservoir in the DDD model and to validate its spatial representation of the subsurface reservoir. The Muren catchment will, during 2017, be re-instrumented in order to continue the work to bridge the gap between conceptual hydrological models, with typically single value or 0-dimension representation of the subsurface, and models with more realistic 2- or 3-dimension representation of the subsurface.

The relationship between stochastic and deterministic quasi-steady state approximations.

PubMed

Kim, Jae Kyoung; Josić, Krešimir; Bennett, Matthew R

2015-11-23

The quasi steady-state approximation (QSSA) is frequently used to reduce deterministic models of biochemical networks. The resulting equations provide a simplified description of the network in terms of non-elementary reaction functions (e.g. Hill functions). Such deterministic reductions are frequently a basis for heuristic stochastic models in which non-elementary reaction functions are used to define reaction propensities. Despite their popularity, it remains unclear when such stochastic reductions are valid. It is frequently assumed that the stochastic reduction can be trusted whenever its deterministic counterpart is accurate. However, a number of recent examples show that this is not necessarily the case. Here we explain the origin of these discrepancies, and demonstrate a clear relationship between the accuracy of the deterministic and the stochastic QSSA for examples widely used in biological systems. With an analysis of a two-state promoter model, and numerical simulations for a variety of other models, we find that the stochastic QSSA is accurate whenever its deterministic counterpart provides an accurate approximation over a range of initial conditions which cover the likely fluctuations from the quasi steady-state (QSS). We conjecture that this relationship provides a simple and computationally inexpensive way to test the accuracy of reduced stochastic models using deterministic simulations. The stochastic QSSA is one of the most popular multi-scale stochastic simulation methods. While the use of QSSA, and the resulting non-elementary functions has been justified in the deterministic case, it is not clear when their stochastic counterparts are accurate. In this study, we show how the accuracy of the stochastic QSSA can be tested using their deterministic counterparts providing a concrete method to test when non-elementary rate functions can be used in stochastic simulations.

Stochastic Petri Net extension of a yeast cell cycle model.

PubMed

Mura, Ivan; Csikász-Nagy, Attila

2008-10-21

This paper presents the definition, solution and validation of a stochastic model of the budding yeast cell cycle, based on Stochastic Petri Nets (SPN). A specific family of SPNs is selected for building a stochastic version of a well-established deterministic model. We describe the procedure followed in defining the SPN model from the deterministic ODE model, a procedure that can be largely automated. The validation of the SPN model is conducted with respect to both the results provided by the deterministic one and the experimental results available from literature. The SPN model catches the behavior of the wild type budding yeast cells and a variety of mutants. We show that the stochastic model matches some characteristics of budding yeast cells that cannot be found with the deterministic model. The SPN model fine-tunes the simulation results, enriching the breadth and the quality of its outcome.

Stochasticity and determinism in models of hematopoiesis.

PubMed

Kimmel, Marek

2014-01-01

This chapter represents a novel view of modeling in hematopoiesis, synthesizing both deterministic and stochastic approaches. Whereas the stochastic models work in situations where chance dominates, for example when the number of cells is small, or under random mutations, the deterministic models are more important for large-scale, normal hematopoiesis. New types of models are on the horizon. These models attempt to account for distributed environments such as hematopoietic niches and their impact on dynamics. Mixed effects of such structures and chance events are largely unknown and constitute both a challenge and promise for modeling. Our discussion is presented under the separate headings of deterministic and stochastic modeling; however, the connections between both are frequently mentioned. Four case studies are included to elucidate important examples. We also include a primer of deterministic and stochastic dynamics for the reader's use.

Hybrid ODE/SSA methods and the cell cycle model

NASA Astrophysics Data System (ADS)

Wang, S.; Chen, M.; Cao, Y.

2017-07-01

Stochastic effect in cellular systems has been an important topic in systems biology. Stochastic modeling and simulation methods are important tools to study stochastic effect. Given the low efficiency of stochastic simulation algorithms, the hybrid method, which combines an ordinary differential equation (ODE) system with a stochastic chemically reacting system, shows its unique advantages in the modeling and simulation of biochemical systems. The efficiency of hybrid method is usually limited by reactions in the stochastic subsystem, which are modeled and simulated using Gillespie's framework and frequently interrupt the integration of the ODE subsystem. In this paper we develop an efficient implementation approach for the hybrid method coupled with traditional ODE solvers. We also compare the efficiency of hybrid methods with three widely used ODE solvers RADAU5, DASSL, and DLSODAR. Numerical experiments with three biochemical models are presented. A detailed discussion is presented for the performances of three ODE solvers.

p-adic stochastic hidden variable model

NASA Astrophysics Data System (ADS)

Khrennikov, Andrew

1998-03-01

We propose stochastic hidden variables model in which hidden variables have a p-adic probability distribution ρ(λ) and at the same time conditional probabilistic distributions P(U,λ), U=A,A',B,B', are ordinary probabilities defined on the basis of the Kolmogorov measure-theoretical axiomatics. A frequency definition of p-adic probability is quite similar to the ordinary frequency definition of probability. p-adic frequency probability is defined as the limit of relative frequencies νn but in the p-adic metric. We study a model with p-adic stochastics on the level of the hidden variables description. But, of course, responses of macroapparatuses have to be described by ordinary stochastics. Thus our model describes a mixture of p-adic stochastics of the microworld and ordinary stochastics of macroapparatuses. In this model probabilities for physical observables are the ordinary probabilities. At the same time Bell's inequality is violated.

Study on individual stochastic model of GNSS observations for precise kinematic applications

NASA Astrophysics Data System (ADS)

Próchniewicz, Dominik; Szpunar, Ryszard

2015-04-01

The proper definition of mathematical positioning model, which is defined by functional and stochastic models, is a prerequisite to obtain the optimal estimation of unknown parameters. Especially important in this definition is realistic modelling of stochastic properties of observations, which are more receiver-dependent and time-varying than deterministic relationships. This is particularly true with respect to precise kinematic applications which are characterized by weakening model strength. In this case, incorrect or simplified definition of stochastic model causes that the performance of ambiguity resolution and accuracy of position estimation can be limited. In this study we investigate the methods of describing the measurement noise of GNSS observations and its impact to derive precise kinematic positioning model. In particular stochastic modelling of individual components of the variance-covariance matrix of observation noise performed using observations from a very short baseline and laboratory GNSS signal generator, is analyzed. Experimental test results indicate that the utilizing the individual stochastic model of observations including elevation dependency and cross-correlation instead of assumption that raw measurements are independent with the same variance improves the performance of ambiguity resolution as well as rover positioning accuracy. This shows that the proposed stochastic assessment method could be a important part in complex calibration procedure of GNSS equipment.

Portfolio Optimization with Stochastic Dividends and Stochastic Volatility

ERIC Educational Resources Information Center

Varga, Katherine Yvonne

2015-01-01

We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…

Influence of Hydrological Perturbations and Riverbed Sediment Characteristics on Hyporheic Zone Respiration of CO2 and N2

NASA Astrophysics Data System (ADS)

Newcomer, Michelle E.; Hubbard, Susan S.; Fleckenstein, Jan H.; Maier, Ulrich; Schmidt, Christian; Thullner, Martin; Ulrich, Craig; Flipo, Nicolas; Rubin, Yoram

2018-03-01

Rivers in climatic zones characterized by dry and wet seasons often experience periodic transitions between losing and gaining conditions across the river-aquifer continuum. Infiltration shifts can stimulate hyporheic microbial biomass growth and cycling of riverine carbon and nitrogen leading to major exports of biogenic CO2 and N2 to rivers. In this study, we develop and test a numerical model that simulates biological-physical feedback in the hyporheic zone. We used the model to explore different initial conditions in terms of dissolved organic carbon availability, sediment characteristics, and stochastic variability in aerobic and anaerobic conditions from water table fluctuations. Our results show that while highly losing rivers have greater hyporheic CO2 and N2 production, gaining rivers allowed the greatest fraction of CO2 and N2 production to return to the river. Hyporheic aerobic respiration and denitrification contributed 0.1-2 g/m2/d of CO2 and 0.01-0.2 g/m2/d of N2; however, the suite of potential microbial behaviors varied greatly among sediment characteristics. We found that losing rivers that consistently lacked an exit pathway can store up to 100% of the entering C/N as subsurface biomass and dissolved gas. Our results demonstrate the importance of subsurface feedbacks whereby microbes and hydrology jointly control fate of C and N and are strongly linked to wet-season control of initial sediment conditions and hydrologic control of seepage direction. These results provide a new understanding of hydrobiological and sediment-based controls on hyporheic zone respiration, including a new explanation for the occurrence of anoxic microzones and large denitrification rates in gravelly riverbeds.

Clustering P-Wave Receiver Functions To Constrain Subsurface Seismic Structure

NASA Astrophysics Data System (ADS)

Chai, C.; Larmat, C. S.; Maceira, M.; Ammon, C. J.; He, R.; Zhang, H.

2017-12-01

The acquisition of high-quality data from permanent and temporary dense seismic networks provides the opportunity to apply statistical and machine learning techniques to a broad range of geophysical observations. Lekic and Romanowicz (2011) used clustering analysis on tomographic velocity models of the western United States to perform tectonic regionalization and the velocity-profile clusters agree well with known geomorphic provinces. A complementary and somewhat less restrictive approach is to apply cluster analysis directly to geophysical observations. In this presentation, we apply clustering analysis to teleseismic P-wave receiver functions (RFs) continuing efforts of Larmat et al. (2015) and Maceira et al. (2015). These earlier studies validated the approach with surface waves and stacked EARS RFs from the USArray stations. In this study, we experiment with both the K-means and hierarchical clustering algorithms. We also test different distance metrics defined in the vector space of RFs following Lekic and Romanowicz (2011). We cluster data from two distinct data sets. The first, corresponding to the western US, was by smoothing/interpolation of receiver-function wavefield (Chai et al. 2015). Spatial coherence and agreement with geologic region increase with this simpler, spatially smoothed set of observations. The second data set is composed of RFs for more than 800 stations of the China Digital Seismic Network (CSN). Preliminary results show a first order agreement between clusters and tectonic region and each region cluster includes a distinct Ps arrival, which probably reflects differences in crustal thickness. Regionalization remains an important step to characterize a model prior to application of full waveform and/or stochastic imaging techniques because of the computational expense of these types of studies. Machine learning techniques can provide valuable information that can be used to design and characterize formal geophysical inversion, providing information on spatial variability in the subsurface geology.

Some Stochastic-Duel Models of Combat.

DTIC Science & Technology

1983-03-01

AD-R127 879 SOME STOCHASTIC- DUEL MODELS OF CONBAT(U) NAVAL - / POSTGRADUATE SCHOOL MONTEREY CA J S CHOE MAR 83 UNCLASSiIED FC1/Ehhh1; F/ 12/ ,iE...SCHOOL Monterey, California DTIC ELECTE :MAY 10 1983 "T !H ES IS SOME STOCHASTIC- DUEL MODELS OF COMBAT by Jum Soo Choe March 1983 Thesis Advisor: J. G...TYPE OF RETORT a PERIOD COVIOCe Master’s Thesis Some Stochastic- Duel Models of Combat March 1983 S. PERFORINGi *no. 44POOi umet 7. AUTHORW.) a

The Use of a Geomorphometric Classification to Estimate Subsurface Heterogeneity in the Unconsolidated Sediments of Mountain Watersheds

NASA Astrophysics Data System (ADS)

Cairns, D.; Byrne, J. M.; Jiskoot, H.; McKenzie, J. M.; Johnson, D. L.

2013-12-01

Groundwater controls many aspects of water quantity and quality in mountain watersheds. Groundwater recharge and flow originating in mountain watersheds are often difficult to quantify due to challenges in the characterization of the local geology, as subsurface data are sparse and difficult to collect. Remote sensing data are more readily available and are beneficial for the characterization of watershed hydrodynamics. We present an automated geomorphometric model to identify the approximate spatial distribution of geomorphic features, and to segment each of these features based on relative hydrostratigraphic differences. A digital elevation model (DEM) dataset and predefined indices are used as inputs in a mountain watershed. The model uses periglacial, glacial, fluvial, slope evolution and lacustrine processes to identify regions that are subsequently delineated using morphometric principles. A 10 m cell size DEM from the headwaters of the St. Mary River watershed in Glacier National Park, Montana, was considered sufficient for this research. Morphometric parameters extracted from the DEM that were found to be useful for the calibration of the model were elevation, slope, flow direction, flow accumulation, and surface roughness. Algorithms were developed to utilize these parameters and delineate the distributions of bedrock outcrops, periglacial landscapes, alluvial channels, fans and outwash plains, glacial depositional features, talus slopes, and other mass wasted material. Theoretical differences in sedimentation and hydrofacies associated with each of the geomorphic features were used to segment the watershed into units reflecting similar hydrogeologic properties such as hydraulic conductivity and thickness. The results of the model were verified by comparing the distribution of geomorphic features with published geomorphic maps. Although agreement in semantics between datasets caused difficulties, a consensus yielded a comparison Dice Coefficient of 0.65. The results can be used to assist in groundwater model calibration, or to estimate spatial differences in near-surface groundwater behaviour. Verification of the geomorphometric model would be augmented by evaluating its success after use in the calibration of the groundwater simulation. These results may also be used directly in momentum-based equations to create a stochastic routing routine beneath the soil interface for a hydrometeorological model.

Stochastic Geometric Models with Non-stationary Spatial Correlations in Lagrangian Fluid Flows

NASA Astrophysics Data System (ADS)

Gay-Balmaz, François; Holm, Darryl D.

2018-01-01

Inspired by spatiotemporal observations from satellites of the trajectories of objects drifting near the surface of the ocean in the National Oceanic and Atmospheric Administration's "Global Drifter Program", this paper develops data-driven stochastic models of geophysical fluid dynamics (GFD) with non-stationary spatial correlations representing the dynamical behaviour of oceanic currents. Three models are considered. Model 1 from Holm (Proc R Soc A 471:20140963, 2015) is reviewed, in which the spatial correlations are time independent. Two new models, called Model 2 and Model 3, introduce two different symmetry breaking mechanisms by which the spatial correlations may be advected by the flow. These models are derived using reduction by symmetry of stochastic variational principles, leading to stochastic Hamiltonian systems, whose momentum maps, conservation laws and Lie-Poisson bracket structures are used in developing the new stochastic Hamiltonian models of GFD.

Stochastic Geometric Models with Non-stationary Spatial Correlations in Lagrangian Fluid Flows

NASA Astrophysics Data System (ADS)

Gay-Balmaz, François; Holm, Darryl D.

2018-06-01

Inspired by spatiotemporal observations from satellites of the trajectories of objects drifting near the surface of the ocean in the National Oceanic and Atmospheric Administration's "Global Drifter Program", this paper develops data-driven stochastic models of geophysical fluid dynamics (GFD) with non-stationary spatial correlations representing the dynamical behaviour of oceanic currents. Three models are considered. Model 1 from Holm (Proc R Soc A 471:20140963, 2015) is reviewed, in which the spatial correlations are time independent. Two new models, called Model 2 and Model 3, introduce two different symmetry breaking mechanisms by which the spatial correlations may be advected by the flow. These models are derived using reduction by symmetry of stochastic variational principles, leading to stochastic Hamiltonian systems, whose momentum maps, conservation laws and Lie-Poisson bracket structures are used in developing the new stochastic Hamiltonian models of GFD.

A spatial stochastic programming model for timber and core area management under risk of stand-replacing fire

Treesearch

Dung Tuan Nguyen

2012-01-01

Forest harvest scheduling has been modeled using deterministic and stochastic programming models. Past models seldom address explicit spatial forest management concerns under the influence of natural disturbances. In this research study, we employ multistage full recourse stochastic programming models to explore the challenges and advantages of building spatial...

A spatial stochastic programming model for timber and core area management under risk of fires

Treesearch

Yu Wei; Michael Bevers; Dung Nguyen; Erin Belval

2014-01-01

Previous stochastic models in harvest scheduling seldom address explicit spatial management concerns under the influence of natural disturbances. We employ multistage stochastic programming models to explore the challenges and advantages of building spatial optimization models that account for the influences of random stand-replacing fires. Our exploratory test models...

Peeking Beneath the Caldera: Communicating Subsurface Knowledge of Newberry Volcano

NASA Astrophysics Data System (ADS)

Mark-Moser, M.; Rose, K.; Schultz, J.; Cameron, E.

2016-12-01

"Imaging the Subsurface: Enhanced Geothermal Systems and Exploring Beneath Newberry Volcano" is an interactive website that presents a three-dimensional subsurface model of Newberry Volcano developed at National Energy Technology Laboratory (NETL). Created using the Story Maps application by ArcGIS Online, this format's dynamic capabilities provide the user the opportunity for multimedia engagement with the datasets and information used to build the subsurface model. This website allows for an interactive experience that the user dictates, including interactive maps, instructive videos and video capture of the subsurface model, and linked information throughout the text. This Story Map offers a general background on the technology of enhanced geothermal systems and the geologic and development history of Newberry Volcano before presenting NETL's modeling efforts that support the installation of enhanced geothermal systems. The model is driven by multiple geologic and geophysical datasets to compare and contrast results which allow for the targeting of potential EGS sites and the reduction of subsurface uncertainty. This Story Map aims to communicate to a broad audience, and provides a platform to effectively introduce the model to researchers and stakeholders.

Scalable hierarchical PDE sampler for generating spatially correlated random fields using nonmatching meshes: Scalable hierarchical PDE sampler using nonmatching meshes

DOE PAGES

Osborn, Sarah; Zulian, Patrick; Benson, Thomas; ...

2018-01-30

This work describes a domain embedding technique between two nonmatching meshes used for generating realizations of spatially correlated random fields with applications to large-scale sampling-based uncertainty quantification. The goal is to apply the multilevel Monte Carlo (MLMC) method for the quantification of output uncertainties of PDEs with random input coefficients on general and unstructured computational domains. We propose a highly scalable, hierarchical sampling method to generate realizations of a Gaussian random field on a given unstructured mesh by solving a reaction–diffusion PDE with a stochastic right-hand side. The stochastic PDE is discretized using the mixed finite element method on anmore » embedded domain with a structured mesh, and then, the solution is projected onto the unstructured mesh. This work describes implementation details on how to efficiently transfer data from the structured and unstructured meshes at coarse levels, assuming that this can be done efficiently on the finest level. We investigate the efficiency and parallel scalability of the technique for the scalable generation of Gaussian random fields in three dimensions. An application of the MLMC method is presented for quantifying uncertainties of subsurface flow problems. Here, we demonstrate the scalability of the sampling method with nonmatching mesh embedding, coupled with a parallel forward model problem solver, for large-scale 3D MLMC simulations with up to 1.9·109 unknowns.« less

Scalable hierarchical PDE sampler for generating spatially correlated random fields using nonmatching meshes: Scalable hierarchical PDE sampler using nonmatching meshes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Osborn, Sarah; Zulian, Patrick; Benson, Thomas

This work describes a domain embedding technique between two nonmatching meshes used for generating realizations of spatially correlated random fields with applications to large-scale sampling-based uncertainty quantification. The goal is to apply the multilevel Monte Carlo (MLMC) method for the quantification of output uncertainties of PDEs with random input coefficients on general and unstructured computational domains. We propose a highly scalable, hierarchical sampling method to generate realizations of a Gaussian random field on a given unstructured mesh by solving a reaction–diffusion PDE with a stochastic right-hand side. The stochastic PDE is discretized using the mixed finite element method on anmore » embedded domain with a structured mesh, and then, the solution is projected onto the unstructured mesh. This work describes implementation details on how to efficiently transfer data from the structured and unstructured meshes at coarse levels, assuming that this can be done efficiently on the finest level. We investigate the efficiency and parallel scalability of the technique for the scalable generation of Gaussian random fields in three dimensions. An application of the MLMC method is presented for quantifying uncertainties of subsurface flow problems. Here, we demonstrate the scalability of the sampling method with nonmatching mesh embedding, coupled with a parallel forward model problem solver, for large-scale 3D MLMC simulations with up to 1.9·109 unknowns.« less

Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology

PubMed Central

Gao, Fei; Li, Ye; Novak, Igor L.; Slepchenko, Boris M.

2016-01-01

Hybrid deterministic-stochastic methods provide an efficient alternative to a fully stochastic treatment of models which include components with disparate levels of stochasticity. However, general-purpose hybrid solvers for spatially resolved simulations of reaction-diffusion systems are not widely available. Here we describe fundamentals of a general-purpose spatial hybrid method. The method generates realizations of a spatially inhomogeneous hybrid system by appropriately integrating capabilities of a deterministic partial differential equation solver with a popular particle-based stochastic simulator, Smoldyn. Rigorous validation of the algorithm is detailed, using a simple model of calcium ‘sparks’ as a testbed. The solver is then applied to a deterministic-stochastic model of spontaneous emergence of cell polarity. The approach is general enough to be implemented within biologist-friendly software frameworks such as Virtual Cell. PMID:27959915

Relations between Vegetation and Geologic Framework in Barrier Island

NASA Astrophysics Data System (ADS)

Smart, N. H.; Ferguson, J. B.; Lehner, J. D.; Taylor, D.; Tuttle, L. F., II; Wernette, P. A.

2017-12-01

Barrier islands provide valuable ecosystems and protective services to coastal communities. The longevity of barrier islands is threatened by sea-level rise, human impacts, and extreme storms. The purpose of this research is to evaluate how vegetation dynamics interact with the subsurface and offshore framework geology to influence the beach and dune morphology. Beach and dune morphology can be viewed as free and/or forced behavior, where free systems are stochastic and the morphology is dependent on variations in the storm surge run-up, aeolian sediment supply and transport potential, and vegetation dynamics and persistence. Forced systems are those where patterns in the coastal morphology are determined by some other structural control, such as the underlying and offshore framework geology. Previous studies have documented the effects of geologic framework or vegetation dynamics on the beach and dunes, although none have examined possible control by vegetation dynamics in context of the geologic framework (i.e. combined free and forced behavior). Padre Island National Seashore (PAIS) was used to examine the interaction of free and forced morphology because the subsurface framework geology and surface beach and dune morphology are variable along the island. Vegetation dynamics were assessed by classifying geographically referenced historical aerial imagery into areas with vegetation and areas without vegetation, as well as LiDAR data to verify this imagery. The subsurface geologic structure was assessed using a combination of geophysical surveys (i.e. electromagnetic induction, ground-penetrating radar, and offshore seismic surveys). Comparison of the observed vegetation patterns and geologic framework leads to a series of questions surrounding how mechanistically these two drivers of coastal morphology are related. Upcoming coring and geophysical surveys will enable us to validate new and existing geophysical data. Results of this paper will help us better understand how barrier islands have responded to environmental change in the past should be integrated into current models of barrier island evolution in order to more accurately predict how the island will change over time in response to continued climatic variability.

Variational principles for stochastic fluid dynamics

PubMed Central

Holm, Darryl D.

2015-01-01

This paper derives stochastic partial differential equations (SPDEs) for fluid dynamics from a stochastic variational principle (SVP). The paper proceeds by taking variations in the SVP to derive stochastic Stratonovich fluid equations; writing their Itô representation; and then investigating the properties of these stochastic fluid models in comparison with each other, and with the corresponding deterministic fluid models. The circulation properties of the stochastic Stratonovich fluid equations are found to closely mimic those of the deterministic ideal fluid models. As with deterministic ideal flows, motion along the stochastic Stratonovich paths also preserves the helicity of the vortex field lines in incompressible stochastic flows. However, these Stratonovich properties are not apparent in the equivalent Itô representation, because they are disguised by the quadratic covariation drift term arising in the Stratonovich to Itô transformation. This term is a geometric generalization of the quadratic covariation drift term already found for scalar densities in Stratonovich's famous 1966 paper. The paper also derives motion equations for two examples of stochastic geophysical fluid dynamics; namely, the Euler–Boussinesq and quasi-geostropic approximations. PMID:27547083

Persistence and extinction of a stochastic single-specie model under regime switching in a polluted environment.

PubMed

Liu, Meng; Wang, Ke

2010-06-07

A new single-species model disturbed by both white noise and colored noise in a polluted environment is developed and analyzed. Sufficient criteria for extinction, stochastic nonpersistence in the mean, stochastic weak persistence in the mean, stochastic strong persistence in the mean and stochastic permanence of the species are established. The threshold between stochastic weak persistence in the mean and extinction is obtained. The results show that both white and colored environmental noises have sufficient effect to the survival results. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

Model selection for integrated pest management with stochasticity.

PubMed

Akman, Olcay; Comar, Timothy D; Hrozencik, Daniel

2018-04-07

In Song and Xiang (2006), an integrated pest management model with periodically varying climatic conditions was introduced. In order to address a wider range of environmental effects, the authors here have embarked upon a series of studies resulting in a more flexible modeling approach. In Akman et al. (2013), the impact of randomly changing environmental conditions is examined by incorporating stochasticity into the birth pulse of the prey species. In Akman et al. (2014), the authors introduce a class of models via a mixture of two birth-pulse terms and determined conditions for the global and local asymptotic stability of the pest eradication solution. With this work, the authors unify the stochastic and mixture model components to create further flexibility in modeling the impacts of random environmental changes on an integrated pest management system. In particular, we first determine the conditions under which solutions of our deterministic mixture model are permanent. We then analyze the stochastic model to find the optimal value of the mixing parameter that minimizes the variance in the efficacy of the pesticide. Additionally, we perform a sensitivity analysis to show that the corresponding pesticide efficacy determined by this optimization technique is indeed robust. Through numerical simulations we show that permanence can be preserved in our stochastic model. Our study of the stochastic version of the model indicates that our results on the deterministic model provide informative conclusions about the behavior of the stochastic model. Copyright © 2017 Elsevier Ltd. All rights reserved.

Analysis of novel stochastic switched SILI epidemic models with continuous and impulsive control

NASA Astrophysics Data System (ADS)

Gao, Shujing; Zhong, Deming; Zhang, Yan

2018-04-01

In this paper, we establish two new stochastic switched epidemic models with continuous and impulsive control. The stochastic perturbations are considered for the natural death rate in each equation of the models. Firstly, a stochastic switched SILI model with continuous control schemes is investigated. By using Lyapunov-Razumikhin method, the sufficient conditions for extinction in mean are established. Our result shows that the disease could be die out theoretically if threshold value R is less than one, regardless of whether the disease-free solutions of the corresponding subsystems are stable or unstable. Then, a stochastic switched SILI model with continuous control schemes and pulse vaccination is studied. The threshold value R is derived. The global attractivity of the model is also obtained. At last, numerical simulations are carried out to support our results.

Stochastic and deterministic models for agricultural production networks.

PubMed

Bai, P; Banks, H T; Dediu, S; Govan, A Y; Last, M; Lloyd, A L; Nguyen, H K; Olufsen, M S; Rempala, G; Slenning, B D

2007-07-01

An approach to modeling the impact of disturbances in an agricultural production network is presented. A stochastic model and its approximate deterministic model for averages over sample paths of the stochastic system are developed. Simulations, sensitivity and generalized sensitivity analyses are given. Finally, it is shown how diseases may be introduced into the network and corresponding simulations are discussed.

From Complex to Simple: Interdisciplinary Stochastic Models

ERIC Educational Resources Information Center

Mazilu, D. A.; Zamora, G.; Mazilu, I.

2012-01-01

We present two simple, one-dimensional, stochastic models that lead to a qualitative understanding of very complex systems from biology, nanoscience and social sciences. The first model explains the complicated dynamics of microtubules, stochastic cellular highways. Using the theory of random walks in one dimension, we find analytical expressions…

One-Week Module on Stochastic Groundwater Modeling

ERIC Educational Resources Information Center

Mays, David C.

2010-01-01

This article describes a one-week introduction to stochastic groundwater modeling, intended for the end of a first course on groundwater hydrology, or the beginning of a second course on stochastic hydrogeology or groundwater modeling. The motivation for this work is to strengthen groundwater education, which has been identified among the factors…

A Stochastic Tick-Borne Disease Model: Exploring the Probability of Pathogen Persistence.

PubMed

Maliyoni, Milliward; Chirove, Faraimunashe; Gaff, Holly D; Govinder, Keshlan S

2017-09-01

We formulate and analyse a stochastic epidemic model for the transmission dynamics of a tick-borne disease in a single population using a continuous-time Markov chain approach. The stochastic model is based on an existing deterministic metapopulation tick-borne disease model. We compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in tick-borne disease dynamics. The probability of disease extinction and that of a major outbreak are computed and approximated using the multitype Galton-Watson branching process and numerical simulations, respectively. Analytical and numerical results show some significant differences in model predictions between the stochastic and deterministic models. In particular, we find that a disease outbreak is more likely if the disease is introduced by infected deer as opposed to infected ticks. These insights demonstrate the importance of host movement in the expansion of tick-borne diseases into new geographic areas.

Stochastic Watershed Models for Risk Based Decision Making

NASA Astrophysics Data System (ADS)

Vogel, R. M.

2017-12-01

Over half a century ago, the Harvard Water Program introduced the field of operational or synthetic hydrology providing stochastic streamflow models (SSMs), which could generate ensembles of synthetic streamflow traces useful for hydrologic risk management. The application of SSMs, based on streamflow observations alone, revolutionized water resources planning activities, yet has fallen out of favor due, in part, to their inability to account for the now nearly ubiquitous anthropogenic influences on streamflow. This commentary advances the modern equivalent of SSMs, termed `stochastic watershed models' (SWMs) useful as input to nearly all modern risk based water resource decision making approaches. SWMs are deterministic watershed models implemented using stochastic meteorological series, model parameters and model errors, to generate ensembles of streamflow traces that represent the variability in possible future streamflows. SWMs combine deterministic watershed models, which are ideally suited to accounting for anthropogenic influences, with recent developments in uncertainty analysis and principles of stochastic simulation

On the efficacy of stochastic collocation, stochastic Galerkin, and stochastic reduced order models for solving stochastic problems

DOE PAGES

Richard V. Field, Jr.; Emery, John M.; Grigoriu, Mircea Dan

2015-05-19

The stochastic collocation (SC) and stochastic Galerkin (SG) methods are two well-established and successful approaches for solving general stochastic problems. A recently developed method based on stochastic reduced order models (SROMs) can also be used. Herein we provide a comparison of the three methods for some numerical examples; our evaluation only holds for the examples considered in the paper. The purpose of the comparisons is not to criticize the SC or SG methods, which have proven very useful for a broad range of applications, nor is it to provide overall ratings of these methods as compared to the SROM method.more » Furthermore, our objectives are to present the SROM method as an alternative approach to solving stochastic problems and provide information on the computational effort required by the implementation of each method, while simultaneously assessing their performance for a collection of specific problems.« less

Cox process representation and inference for stochastic reaction-diffusion processes

NASA Astrophysics Data System (ADS)

Schnoerr, David; Grima, Ramon; Sanguinetti, Guido

2016-05-01

Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to the social sciences, yet they are notoriously difficult to simulate and calibrate to observational data. Here we use ideas from statistical physics and machine learning to provide a solution to the inverse problem of learning a stochastic reaction-diffusion process from data. Our solution relies on a non-trivial connection between stochastic reaction-diffusion processes and spatio-temporal Cox processes, a well-studied class of models from computational statistics. This connection leads to an efficient and flexible algorithm for parameter inference and model selection. Our approach shows excellent accuracy on numeric and real data examples from systems biology and epidemiology. Our work provides both insights into spatio-temporal stochastic systems, and a practical solution to a long-standing problem in computational modelling.

Stochastic growth logistic model with aftereffect for batch fermentation process

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah

2014-06-19

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

Stochastic growth logistic model with aftereffect for batch fermentation process

NASA Astrophysics Data System (ADS)

Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah; Rahman, Haliza Abdul; Salleh, Madihah Md

2014-06-01

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

Distributed parallel computing in stochastic modeling of groundwater systems.

PubMed

Dong, Yanhui; Li, Guomin; Xu, Haizhen

2013-03-01

Stochastic modeling is a rapidly evolving, popular approach to the study of the uncertainty and heterogeneity of groundwater systems. However, the use of Monte Carlo-type simulations to solve practical groundwater problems often encounters computational bottlenecks that hinder the acquisition of meaningful results. To improve the computational efficiency, a system that combines stochastic model generation with MODFLOW-related programs and distributed parallel processing is investigated. The distributed computing framework, called the Java Parallel Processing Framework, is integrated into the system to allow the batch processing of stochastic models in distributed and parallel systems. As an example, the system is applied to the stochastic delineation of well capture zones in the Pinggu Basin in Beijing. Through the use of 50 processing threads on a cluster with 10 multicore nodes, the execution times of 500 realizations are reduced to 3% compared with those of a serial execution. Through this application, the system demonstrates its potential in solving difficult computational problems in practical stochastic modeling. © 2012, The Author(s). Groundwater © 2012, National Ground Water Association.

Modeling subsurface stormflow initiation in low-relief landscapes

NASA Astrophysics Data System (ADS)

Hopp, Luisa; Vaché, Kellie B.; Rhett Jackson, C.; McDonnell, Jeffrey J.

2015-04-01

Shallow lateral subsurface flow as a runoff generating mechanism at the hillslope scale has mostly been studied in steeper terrain with typical hillside angles of 10 - 45 degrees. These studies have shown that subsurface stormflow is often initiated at the interface between a permeable upper soil layer and a lower conductivity impeding layer, e.g. a B horizon or bedrock. Many studies have identified thresholds of event size and soil moisture states that need to be exceeded before subsurface stormflow is initiated. However, subsurface stormflow generation on low-relief hillslopes has been much less studied. Here we present a modeling study that investigates the initiation of subsurface stormflow on low-relief hillslopes in the Upper Coastal Plain of South Carolina, USA. Hillslopes in this region typically have slope angles of 2-5 degrees. Topsoils are sandy, underlain by a low-conductivity sandy clay loam Bt horizon. Subsurface stormflow has only been intercepted occasionally in a 120 m long trench, and often subsurface flow was not well correlated with stream signals, suggesting a disconnect between subsurface flow on the hillslopes and stream flow. We therefore used a hydrologic model to better understand which conditions promote the initiation of subsurface flow in this landscape, addressing following questions: Is there a threshold event size and soil moisture state for producing lateral subsurface flow? What role does the spatial pattern of depth to the impeding clay layer play for subsurface stormflow dynamics? We reproduced a section of a hillslope, for which high-resolution topographic data and depth to clay measurements were available, in the hydrologic model HYDRUS-3D. Soil hydraulic parameters were based on experimentally-derived data. The threshold analysis was first performed using hourly climate data records for 2009-2010 from the study site to drive the simulation. For this period also trench measurements of subsurface flow were available. In addition, we also ran a longer-term simulation, using daily climate data for a nine year period to include more variable climate conditions in the threshold analysis. The model captured the observed subsurface flow instances very well. The threshold analysis indicated that the occurrence of subsurface stormflow uncommon, with a large proportion of the water perching above the clay layer percolating vertically into the clay layer. Event sizes of approximately 70-80 mm were required for initiating subsurface stormflow. The hourly data from 2009-2010 was subsequently used to test if the actual spatial distribution of depth to clay is a major control for the occurrence and magnitude of lateral subsurface flow. Results suggest that in this low-relief landscape also a spatially uniform mean depth to clay reproduces well the hydrologic behavior.

Deterministic and stochastic CTMC models from Zika disease transmission

NASA Astrophysics Data System (ADS)

Zevika, Mona; Soewono, Edy

2018-03-01

Zika infection is one of the most important mosquito-borne diseases in the world. Zika virus (ZIKV) is transmitted by many Aedes-type mosquitoes including Aedes aegypti. Pregnant women with the Zika virus are at risk of having a fetus or infant with a congenital defect and suffering from microcephaly. Here, we formulate a Zika disease transmission model using two approaches, a deterministic model and a continuous-time Markov chain stochastic model. The basic reproduction ratio is constructed from a deterministic model. Meanwhile, the CTMC stochastic model yields an estimate of the probability of extinction and outbreaks of Zika disease. Dynamical simulations and analysis of the disease transmission are shown for the deterministic and stochastic models.

Hybrid approaches for multiple-species stochastic reaction-diffusion models

NASA Astrophysics Data System (ADS)

Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K.; Byrne, Helen

2015-10-01

Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.

Hybrid approaches for multiple-species stochastic reaction-diffusion models.

PubMed

Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K; Byrne, Helen

2015-10-15

Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.

Hybrid approaches for multiple-species stochastic reaction–diffusion models

PubMed Central

Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K.; Byrne, Helen

2015-01-01

Reaction–diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction–diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model. PMID:26478601

Constraining Stochastic Parametrisation Schemes Using High-Resolution Model Simulations

NASA Astrophysics Data System (ADS)

Christensen, H. M.; Dawson, A.; Palmer, T.

2017-12-01

Stochastic parametrisations are used in weather and climate models as a physically motivated way to represent model error due to unresolved processes. Designing new stochastic schemes has been the target of much innovative research over the last decade. While a focus has been on developing physically motivated approaches, many successful stochastic parametrisation schemes are very simple, such as the European Centre for Medium-Range Weather Forecasts (ECMWF) multiplicative scheme `Stochastically Perturbed Parametrisation Tendencies' (SPPT). The SPPT scheme improves the skill of probabilistic weather and seasonal forecasts, and so is widely used. However, little work has focused on assessing the physical basis of the SPPT scheme. We address this matter by using high-resolution model simulations to explicitly measure the `error' in the parametrised tendency that SPPT seeks to represent. The high resolution simulations are first coarse-grained to the desired forecast model resolution before they are used to produce initial conditions and forcing data needed to drive the ECMWF Single Column Model (SCM). By comparing SCM forecast tendencies with the evolution of the high resolution model, we can measure the `error' in the forecast tendencies. In this way, we provide justification for the multiplicative nature of SPPT, and for the temporal and spatial scales of the stochastic perturbations. However, we also identify issues with the SPPT scheme. It is therefore hoped these measurements will improve both holistic and process based approaches to stochastic parametrisation. Figure caption: Instantaneous snapshot of the optimal SPPT stochastic perturbation, derived by comparing high-resolution simulations with a low resolution forecast model.

Cell survival fraction estimation based on the probability densities of domain and cell nucleus specific energies using improved microdosimetric kinetic models.

PubMed

Sato, Tatsuhiko; Furusawa, Yoshiya

2012-10-01

Estimation of the survival fractions of cells irradiated with various particles over a wide linear energy transfer (LET) range is of great importance in the treatment planning of charged-particle therapy. Two computational models were developed for estimating survival fractions based on the concept of the microdosimetric kinetic model. They were designated as the double-stochastic microdosimetric kinetic and stochastic microdosimetric kinetic models. The former model takes into account the stochastic natures of both domain and cell nucleus specific energies, whereas the latter model represents the stochastic nature of domain specific energy by its approximated mean value and variance to reduce the computational time. The probability densities of the domain and cell nucleus specific energies are the fundamental quantities for expressing survival fractions in these models. These densities are calculated using the microdosimetric and LET-estimator functions implemented in the Particle and Heavy Ion Transport code System (PHITS) in combination with the convolution or database method. Both the double-stochastic microdosimetric kinetic and stochastic microdosimetric kinetic models can reproduce the measured survival fractions for high-LET and high-dose irradiations, whereas a previously proposed microdosimetric kinetic model predicts lower values for these fractions, mainly due to intrinsic ignorance of the stochastic nature of cell nucleus specific energies in the calculation. The models we developed should contribute to a better understanding of the mechanism of cell inactivation, as well as improve the accuracy of treatment planning of charged-particle therapy.

Bayesian parameter inference for stochastic biochemical network models using particle Markov chain Monte Carlo

PubMed Central

Golightly, Andrew; Wilkinson, Darren J.

2011-01-01

Computational systems biology is concerned with the development of detailed mechanistic models of biological processes. Such models are often stochastic and analytically intractable, containing uncertain parameters that must be estimated from time course data. In this article, we consider the task of inferring the parameters of a stochastic kinetic model defined as a Markov (jump) process. Inference for the parameters of complex nonlinear multivariate stochastic process models is a challenging problem, but we find here that algorithms based on particle Markov chain Monte Carlo turn out to be a very effective computationally intensive approach to the problem. Approximations to the inferential model based on stochastic differential equations (SDEs) are considered, as well as improvements to the inference scheme that exploit the SDE structure. We apply the methodology to a Lotka–Volterra system and a prokaryotic auto-regulatory network. PMID:23226583

An efficient distribution method for nonlinear transport problems in highly heterogeneous stochastic porous media

NASA Astrophysics Data System (ADS)

Ibrahima, Fayadhoi; Meyer, Daniel; Tchelepi, Hamdi

2016-04-01

Because geophysical data are inexorably sparse and incomplete, stochastic treatments of simulated responses are crucial to explore possible scenarios and assess risks in subsurface problems. In particular, nonlinear two-phase flows in porous media are essential, yet challenging, in reservoir simulation and hydrology. Adding highly heterogeneous and uncertain input, such as the permeability and porosity fields, transforms the estimation of the flow response into a tough stochastic problem for which computationally expensive Monte Carlo (MC) simulations remain the preferred option.We propose an alternative approach to evaluate the probability distribution of the (water) saturation for the stochastic Buckley-Leverett problem when the probability distributions of the permeability and porosity fields are available. We give a computationally efficient and numerically accurate method to estimate the one-point probability density (PDF) and cumulative distribution functions (CDF) of the (water) saturation. The distribution method draws inspiration from a Lagrangian approach of the stochastic transport problem and expresses the saturation PDF and CDF essentially in terms of a deterministic mapping and the distribution and statistics of scalar random fields. In a large class of applications these random fields can be estimated at low computational costs (few MC runs), thus making the distribution method attractive. Even though the method relies on a key assumption of fixed streamlines, we show that it performs well for high input variances, which is the case of interest. Once the saturation distribution is determined, any one-point statistics thereof can be obtained, especially the saturation average and standard deviation. Moreover, the probability of rare events and saturation quantiles (e.g. P10, P50 and P90) can be efficiently derived from the distribution method. These statistics can then be used for risk assessment, as well as data assimilation and uncertainty reduction in the prior knowledge of input distributions. We provide various examples and comparisons with MC simulations to illustrate the performance of the method.

Tests of oceanic stochastic parameterisation in a seasonal forecast system.

NASA Astrophysics Data System (ADS)

Cooper, Fenwick; Andrejczuk, Miroslaw; Juricke, Stephan; Zanna, Laure; Palmer, Tim

2015-04-01

Over seasonal time scales, our aim is to compare the relative impact of ocean initial condition and model uncertainty, upon the ocean forecast skill and reliability. Over seasonal timescales we compare four oceanic stochastic parameterisation schemes applied in a 1x1 degree ocean model (NEMO) with a fully coupled T159 atmosphere (ECMWF IFS). The relative impacts upon the ocean of the resulting eddy induced activity, wind forcing and typical initial condition perturbations are quantified. Following the historical success of stochastic parameterisation in the atmosphere, two of the parameterisations tested were multiplicitave in nature: A stochastic variation of the Gent-McWilliams scheme and a stochastic diffusion scheme. We also consider a surface flux parameterisation (similar to that introduced by Williams, 2012), and stochastic perturbation of the equation of state (similar to that introduced by Brankart, 2013). The amplitude of the stochastic term in the Williams (2012) scheme was set to the physically reasonable amplitude considered in that paper. The amplitude of the stochastic term in each of the other schemes was increased to the limits of model stability. As expected, variability was increased. Up to 1 month after initialisation, ensemble spread induced by stochastic parameterisation is greater than that induced by the atmosphere, whilst being smaller than the initial condition perturbations currently used at ECMWF. After 1 month, the wind forcing becomes the dominant source of model ocean variability, even at depth.

Validation of the Poisson Stochastic Radiative Transfer Model

NASA Technical Reports Server (NTRS)

Zhuravleva, Tatiana; Marshak, Alexander

2004-01-01

A new approach to validation of the Poisson stochastic radiative transfer method is proposed. In contrast to other validations of stochastic models, the main parameter of the Poisson model responsible for cloud geometrical structure - cloud aspect ratio - is determined entirely by matching measurements and calculations of the direct solar radiation. If the measurements of the direct solar radiation is unavailable, it was shown that there is a range of the aspect ratios that allows the stochastic model to accurately approximate the average measurements of surface downward and cloud top upward fluxes. Realizations of the fractionally integrated cascade model are taken as a prototype of real measurements.

Analytical pricing formulas for hybrid variance swaps with regime-switching

NASA Astrophysics Data System (ADS)

Roslan, Teh Raihana Nazirah; Cao, Jiling; Zhang, Wenjun

2017-11-01

The problem of pricing discretely-sampled variance swaps under stochastic volatility, stochastic interest rate and regime-switching is being considered in this paper. An extension of the Heston stochastic volatility model structure is done by adding the Cox-Ingersoll-Ross (CIR) stochastic interest rate model. In addition, the parameters of the model are permitted to have transitions following a Markov chain process which is continuous and discoverable. This hybrid model can be used to illustrate certain macroeconomic conditions, for example the changing phases of business stages. The outcome of our regime-switching hybrid model is presented in terms of analytical pricing formulas for variance swaps.

Stochasticity in staged models of epidemics: quantifying the dynamics of whooping cough

PubMed Central

Black, Andrew J.; McKane, Alan J.

2010-01-01

Although many stochastic models can accurately capture the qualitative epidemic patterns of many childhood diseases, there is still considerable discussion concerning the basic mechanisms generating these patterns; much of this stems from the use of deterministic models to try to understand stochastic simulations. We argue that a systematic method of analysing models of the spread of childhood diseases is required in order to consistently separate out the effects of demographic stochasticity, external forcing and modelling choices. Such a technique is provided by formulating the models as master equations and using the van Kampen system-size expansion to provide analytical expressions for quantities of interest. We apply this method to the susceptible–exposed–infected–recovered (SEIR) model with distributed exposed and infectious periods and calculate the form that stochastic oscillations take on in terms of the model parameters. With the use of a suitable approximation, we apply the formalism to analyse a model of whooping cough which includes seasonal forcing. This allows us to more accurately interpret the results of simulations and to make a more quantitative assessment of the predictions of the model. We show that the observed dynamics are a result of a macroscopic limit cycle induced by the external forcing and resonant stochastic oscillations about this cycle. PMID:20164086

Tensor methods for parameter estimation and bifurcation analysis of stochastic reaction networks

PubMed Central

Liao, Shuohao; Vejchodský, Tomáš; Erban, Radek

2015-01-01

Stochastic modelling of gene regulatory networks provides an indispensable tool for understanding how random events at the molecular level influence cellular functions. A common challenge of stochastic models is to calibrate a large number of model parameters against the experimental data. Another difficulty is to study how the behaviour of a stochastic model depends on its parameters, i.e. whether a change in model parameters can lead to a significant qualitative change in model behaviour (bifurcation). In this paper, tensor-structured parametric analysis (TPA) is developed to address these computational challenges. It is based on recently proposed low-parametric tensor-structured representations of classical matrices and vectors. This approach enables simultaneous computation of the model properties for all parameter values within a parameter space. The TPA is illustrated by studying the parameter estimation, robustness, sensitivity and bifurcation structure in stochastic models of biochemical networks. A Matlab implementation of the TPA is available at http://www.stobifan.org. PMID:26063822

Tensor methods for parameter estimation and bifurcation analysis of stochastic reaction networks.

PubMed

Liao, Shuohao; Vejchodský, Tomáš; Erban, Radek

2015-07-06

Stochastic modelling of gene regulatory networks provides an indispensable tool for understanding how random events at the molecular level influence cellular functions. A common challenge of stochastic models is to calibrate a large number of model parameters against the experimental data. Another difficulty is to study how the behaviour of a stochastic model depends on its parameters, i.e. whether a change in model parameters can lead to a significant qualitative change in model behaviour (bifurcation). In this paper, tensor-structured parametric analysis (TPA) is developed to address these computational challenges. It is based on recently proposed low-parametric tensor-structured representations of classical matrices and vectors. This approach enables simultaneous computation of the model properties for all parameter values within a parameter space. The TPA is illustrated by studying the parameter estimation, robustness, sensitivity and bifurcation structure in stochastic models of biochemical networks. A Matlab implementation of the TPA is available at http://www.stobifan.org.

A multistage stochastic programming model for a multi-period strategic expansion of biofuel supply chain under evolving uncertainties

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xie, Fei; Huang, Yongxi

Here, we develop a multistage, stochastic mixed-integer model to support biofuel supply chain expansion under evolving uncertainties. By utilizing the block-separable recourse property, we reformulate the multistage program in an equivalent two-stage program and solve it using an enhanced nested decomposition method with maximal non-dominated cuts. We conduct extensive numerical experiments and demonstrate the application of the model and algorithm in a case study based on the South Carolina settings. The value of multistage stochastic programming method is also explored by comparing the model solution with the counterparts of an expected value based deterministic model and a two-stage stochastic model.

A multistage stochastic programming model for a multi-period strategic expansion of biofuel supply chain under evolving uncertainties

DOE PAGES

Xie, Fei; Huang, Yongxi

2018-02-04

Here, we develop a multistage, stochastic mixed-integer model to support biofuel supply chain expansion under evolving uncertainties. By utilizing the block-separable recourse property, we reformulate the multistage program in an equivalent two-stage program and solve it using an enhanced nested decomposition method with maximal non-dominated cuts. We conduct extensive numerical experiments and demonstrate the application of the model and algorithm in a case study based on the South Carolina settings. The value of multistage stochastic programming method is also explored by comparing the model solution with the counterparts of an expected value based deterministic model and a two-stage stochastic model.

Spatially Distributed Characterization of Catchment Dynamics Using Travel-Time Distributions

NASA Astrophysics Data System (ADS)

Heße, F.; Zink, M.; Attinger, S.

2015-12-01

The description of storage and transport of both water and solved contaminants in catchments is very difficult due to the high heterogeneity of the subsurface properties that govern their fate. This heterogeneity, combined with a generally limited knowledge about the subsurface, results in high degrees of uncertainty. As a result, stochastic methods are increasingly applied, where the relevant processes are modeled as being random. Within these methods, quantities like the catchment travel or residence time of a water parcel are described using probability density functions (PDF). The derivation of these PDF's is typically done by using the water fluxes and states of the catchment. A successful application of such frameworks is therefore contingent on a good quantification of these fluxes and states across the different spatial scales. The objective of this study is to use travel times for the characterization of an ca. 1000 square kilometer, humid catchment in Central Germany. To determine the states and fluxes, we apply the mesoscale Hydrological Model mHM, a spatially distributed hydrological model to the catchment. Using detailed data of precipitation, land cover, morphology and soil type as inputs, mHM is able to determine fluxes like recharge and evapotranspiration and states like soil moisture as outputs. Using these data, we apply the above theoretical framework to our catchment. By virtue of the aforementioned properties of mHM, we are able to describe the storage and release of water with a high spatial resolution. This allows for a comprehensive description of the flow and transport dynamics taking place in the catchment. The spatial distribution of such dynamics is then compared with land cover and soil moisture maps as well as driving forces like precipitation and temperature to determine the most predictive factors. In addition, we investigate how non-local data like the age distribution of discharge flows are impacted by, and therefore allow to infer, local properties of the catchment.

Machine learning from computer simulations with applications in rail vehicle dynamics

NASA Astrophysics Data System (ADS)

Taheri, Mehdi; Ahmadian, Mehdi

2016-05-01

The application of stochastic modelling for learning the behaviour of a multibody dynamics (MBD) models is investigated. Post-processing data from a simulation run are used to train the stochastic model that estimates the relationship between model inputs (suspension relative displacement and velocity) and the output (sum of suspension forces). The stochastic model can be used to reduce the computational burden of the MBD model by replacing a computationally expensive subsystem in the model (suspension subsystem). With minor changes, the stochastic modelling technique is able to learn the behaviour of a physical system and integrate its behaviour within MBD models. The technique is highly advantageous for MBD models where real-time simulations are necessary, or with models that have a large number of repeated substructures, e.g. modelling a train with a large number of railcars. The fact that the training data are acquired prior to the development of the stochastic model discards the conventional sampling plan strategies like Latin Hypercube sampling plans where simulations are performed using the inputs dictated by the sampling plan. Since the sampling plan greatly influences the overall accuracy and efficiency of the stochastic predictions, a sampling plan suitable for the process is developed where the most space-filling subset of the acquired data with ? number of sample points that best describes the dynamic behaviour of the system under study is selected as the training data.

Stochastic von Bertalanffy models, with applications to fish recruitment.

PubMed

Lv, Qiming; Pitchford, Jonathan W

2007-02-21

We consider three individual-based models describing growth in stochastic environments. Stochastic differential equations (SDEs) with identical von Bertalanffy deterministic parts are formulated, with a stochastic term which decreases, remains constant, or increases with organism size, respectively. Probability density functions for hitting times are evaluated in the context of fish growth and mortality. Solving the hitting time problem analytically or numerically shows that stochasticity can have a large positive impact on fish recruitment probability. It is also demonstrated that the observed mean growth rate of surviving individuals always exceeds the mean population growth rate, which itself exceeds the growth rate of the equivalent deterministic model. The consequences of these results in more general biological situations are discussed.

A chance-constrained stochastic approach to intermodal container routing problems.

PubMed

Zhao, Yi; Liu, Ronghui; Zhang, Xi; Whiteing, Anthony

2018-01-01

We consider a container routing problem with stochastic time variables in a sea-rail intermodal transportation system. The problem is formulated as a binary integer chance-constrained programming model including stochastic travel times and stochastic transfer time, with the objective of minimising the expected total cost. Two chance constraints are proposed to ensure that the container service satisfies ship fulfilment and cargo on-time delivery with pre-specified probabilities. A hybrid heuristic algorithm is employed to solve the binary integer chance-constrained programming model. Two case studies are conducted to demonstrate the feasibility of the proposed model and to analyse the impact of stochastic variables and chance-constraints on the optimal solution and total cost.

A chance-constrained stochastic approach to intermodal container routing problems

PubMed Central

Zhao, Yi; Zhang, Xi; Whiteing, Anthony

2018-01-01

We consider a container routing problem with stochastic time variables in a sea-rail intermodal transportation system. The problem is formulated as a binary integer chance-constrained programming model including stochastic travel times and stochastic transfer time, with the objective of minimising the expected total cost. Two chance constraints are proposed to ensure that the container service satisfies ship fulfilment and cargo on-time delivery with pre-specified probabilities. A hybrid heuristic algorithm is employed to solve the binary integer chance-constrained programming model. Two case studies are conducted to demonstrate the feasibility of the proposed model and to analyse the impact of stochastic variables and chance-constraints on the optimal solution and total cost. PMID:29438389

A stochastic SIS epidemic model with vaccination

NASA Astrophysics Data System (ADS)

Cao, Boqiang; Shan, Meijing; Zhang, Qimin; Wang, Weiming

2017-11-01

In this paper, we investigate the basic features of an SIS type infectious disease model with varying population size and vaccinations in presence of environment noise. By applying the Markov semigroup theory, we propose a stochastic reproduction number R0s which can be seen as a threshold parameter to utilize in identifying the stochastic extinction and persistence: If R0s < 1, under some mild extra conditions, there exists a disease-free absorbing set for the stochastic epidemic model, which implies that disease dies out with probability one; while if R0s > 1, under some mild extra conditions, the SDE model has an endemic stationary distribution which results in the stochastic persistence of the infectious disease. The most interesting finding is that large environmental noise can suppress the outbreak of the disease.

Stochastic sensitivity analysis of the variability of dynamics and transition to chaos in the business cycles model

NASA Astrophysics Data System (ADS)

Bashkirtseva, Irina; Ryashko, Lev; Ryazanova, Tatyana

2018-01-01

A problem of mathematical modeling of complex stochastic processes in macroeconomics is discussed. For the description of dynamics of income and capital stock, the well-known Kaldor model of business cycles is used as a basic example. The aim of the paper is to give an overview of the variety of stochastic phenomena which occur in Kaldor model forced by additive and parametric random noise. We study a generation of small- and large-amplitude stochastic oscillations, and their mixed-mode intermittency. To analyze these phenomena, we suggest a constructive approach combining the study of the peculiarities of deterministic phase portrait, and stochastic sensitivity of attractors. We show how parametric noise can stabilize the unstable equilibrium and transform dynamics of Kaldor system from order to chaos.

Calibration of Complex Subsurface Reaction Models Using a Surrogate-Model Approach

EPA Science Inventory

Application of model assessment techniques to complex subsurface reaction models involves numerous difficulties, including non-trivial model selection, parameter non-uniqueness, and excessive computational burden. To overcome these difficulties, this study introduces SAMM (Simult...

Stochastic volatility of the futures prices of emission allowances: A Bayesian approach

NASA Astrophysics Data System (ADS)

Kim, Jungmu; Park, Yuen Jung; Ryu, Doojin

2017-01-01

Understanding the stochastic nature of the spot volatility of emission allowances is crucial for risk management in emissions markets. In this study, by adopting a stochastic volatility model with or without jumps to represent the dynamics of European Union Allowances (EUA) futures prices, we estimate the daily volatilities and model parameters by using the Markov Chain Monte Carlo method for stochastic volatility (SV), stochastic volatility with return jumps (SVJ) and stochastic volatility with correlated jumps (SVCJ) models. Our empirical results reveal three important features of emissions markets. First, the data presented herein suggest that EUA futures prices exhibit significant stochastic volatility. Second, the leverage effect is noticeable regardless of whether or not jumps are included. Third, the inclusion of jumps has a significant impact on the estimation of the volatility dynamics. Finally, the market becomes very volatile and large jumps occur at the beginning of a new phase. These findings are important for policy makers and regulators.

Optimal Control Inventory Stochastic With Production Deteriorating

NASA Astrophysics Data System (ADS)

Affandi, Pardi

2018-01-01

In this paper, we are using optimal control approach to determine the optimal rate in production. Most of the inventory production models deal with a single item. First build the mathematical models inventory stochastic, in this model we also assume that the items are in the same store. The mathematical model of the problem inventory can be deterministic and stochastic models. In this research will be discussed how to model the stochastic as well as how to solve the inventory model using optimal control techniques. The main tool in the study problems for the necessary optimality conditions in the form of the Pontryagin maximum principle involves the Hamilton function. So we can have the optimal production rate in a production inventory system where items are subject deterioration.

Stochastic Game Analysis and Latency Awareness for Self-Adaptation

DTIC Science & Technology

2014-01-01

this paper, we introduce a formal analysis technique based on model checking of stochastic multiplayer games (SMGs) that enables us to quantify the...Additional Key Words and Phrases: Proactive adaptation, Stochastic multiplayer games , Latency 1. INTRODUCTION When planning how to adapt, self-adaptive...contribution of this paper is twofold: (1) A novel analysis technique based on model checking of stochastic multiplayer games (SMGs) that enables us to

Subsurface conditions in hydrothermal vents inferred from diffuse flow composition, and models of reaction and transport

NASA Astrophysics Data System (ADS)

Larson, B. I.; Houghton, J. L.; Lowell, R. P.; Farough, A.; Meile, C. D.

2015-08-01

Chemical gradients in the subsurface of mid-ocean ridge hydrothermal systems create an environment where minerals precipitate and dissolve and where chemosynthetic organisms thrive. However, owing to the lack of easy access to the subsurface, robust knowledge of the nature and extent of chemical transformations remains elusive. Here, we combine measurements of vent fluid chemistry with geochemical and transport modeling to give new insights into the under-sampled subsurface. Temperature-composition relationships from a geochemical mixing model are superimposed on the subsurface temperature distribution determined using a heat flow model to estimate the spatial distribution of fluid composition. We then estimate the distribution of Gibb's free energies of reaction beneath mid oceanic ridges and by combining flow simulations with speciation calculations estimate anhydrite deposition rates. Applied to vent endmembers observed at the fast spreading ridge at the East Pacific Rise, our results suggest that sealing times due to anhydrite formation are longer than the typical time between tectonic and magmatic events. The chemical composition of the neighboring low temperature flow indicates relatively uniform energetically favorable conditions for commonly inferred microbial processes such as methanogenesis, sulfate reduction and numerous oxidation reactions, suggesting that factors other than energy availability may control subsurface microbial biomass distribution. Thus, these model simulations complement fluid-sample datasets from surface venting and help infer the chemical distribution and transformations in subsurface flow.

Stochastic analysis of a novel nonautonomous periodic SIRI epidemic system with random disturbances

NASA Astrophysics Data System (ADS)

Zhang, Weiwei; Meng, Xinzhu

2018-02-01

In this paper, a new stochastic nonautonomous SIRI epidemic model is formulated. Given that the incidence rates of diseases may change with the environment, we propose a novel type of transmission function. The main aim of this paper is to obtain the thresholds of the stochastic SIRI epidemic model. To this end, we investigate the dynamics of the stochastic system and establish the conditions for extinction and persistence in mean of the disease by constructing some suitable Lyapunov functions and using stochastic analysis technique. Furthermore, we show that the stochastic system has at least one nontrivial positive periodic solution. Finally, numerical simulations are introduced to illustrate our results.

Stochastic dynamic modeling of regular and slow earthquakes

NASA Astrophysics Data System (ADS)

Aso, N.; Ando, R.; Ide, S.

2017-12-01

Both regular and slow earthquakes are slip phenomena on plate boundaries and are simulated by a (quasi-)dynamic modeling [Liu and Rice, 2005]. In these numerical simulations, spatial heterogeneity is usually considered not only for explaining real physical properties but also for evaluating the stability of the calculations or the sensitivity of the results on the condition. However, even though we discretize the model space with small grids, heterogeneity at smaller scales than the grid size is not considered in the models with deterministic governing equations. To evaluate the effect of heterogeneity at the smaller scales we need to consider stochastic interactions between slip and stress in a dynamic modeling. Tidal stress is known to trigger or affect both regular and slow earthquakes [Yabe et al., 2015; Ide et al., 2016], and such an external force with fluctuation can also be considered as a stochastic external force. A healing process of faults may also be stochastic, so we introduce stochastic friction law. In the present study, we propose a stochastic dynamic model to explain both regular and slow earthquakes. We solve mode III problem, which corresponds to the rupture propagation along the strike direction. We use BIEM (boundary integral equation method) scheme to simulate slip evolution, but we add stochastic perturbations in the governing equations, which is usually written in a deterministic manner. As the simplest type of perturbations, we adopt Gaussian deviations in the formulation of the slip-stress kernel, external force, and friction. By increasing the amplitude of perturbations of the slip-stress kernel, we reproduce complicated rupture process of regular earthquakes including unilateral and bilateral ruptures. By perturbing external force, we reproduce slow rupture propagation at a scale of km/day. The slow propagation generated by a combination of fast interaction at S-wave velocity is analogous to the kinetic theory of gasses: thermal diffusion appears much slower than the particle velocity of each molecule. The concept of stochastic triggering originates in the Brownian walk model [Ide, 2008], and the present study introduces the stochastic dynamics into dynamic simulations. The stochastic dynamic model has the potential to explain both regular and slow earthquakes more realistically.

Reduced linear noise approximation for biochemical reaction networks with time-scale separation: The stochastic tQSSA+

NASA Astrophysics Data System (ADS)

Herath, Narmada; Del Vecchio, Domitilla

2018-03-01

Biochemical reaction networks often involve reactions that take place on different time scales, giving rise to "slow" and "fast" system variables. This property is widely used in the analysis of systems to obtain dynamical models with reduced dimensions. In this paper, we consider stochastic dynamics of biochemical reaction networks modeled using the Linear Noise Approximation (LNA). Under time-scale separation conditions, we obtain a reduced-order LNA that approximates both the slow and fast variables in the system. We mathematically prove that the first and second moments of this reduced-order model converge to those of the full system as the time-scale separation becomes large. These mathematical results, in particular, provide a rigorous justification to the accuracy of LNA models derived using the stochastic total quasi-steady state approximation (tQSSA). Since, in contrast to the stochastic tQSSA, our reduced-order model also provides approximations for the fast variable stochastic properties, we term our method the "stochastic tQSSA+". Finally, we demonstrate the application of our approach on two biochemical network motifs found in gene-regulatory and signal transduction networks.

Final Report, DOE Early Career Award: Predictive modeling of complex physical systems: new tools for statistical inference, uncertainty quantification, and experimental design

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marzouk, Youssef

Predictive simulation of complex physical systems increasingly rests on the interplay of experimental observations with computational models. Key inputs, parameters, or structural aspects of models may be incomplete or unknown, and must be developed from indirect and limited observations. At the same time, quantified uncertainties are needed to qualify computational predictions in the support of design and decision-making. In this context, Bayesian statistics provides a foundation for inference from noisy and limited data, but at prohibitive computional expense. This project intends to make rigorous predictive modeling *feasible* in complex physical systems, via accelerated and scalable tools for uncertainty quantification, Bayesianmore » inference, and experimental design. Specific objectives are as follows: 1. Develop adaptive posterior approximations and dimensionality reduction approaches for Bayesian inference in high-dimensional nonlinear systems. 2. Extend accelerated Bayesian methodologies to large-scale {\\em sequential} data assimilation, fully treating nonlinear models and non-Gaussian state and parameter distributions. 3. Devise efficient surrogate-based methods for Bayesian model selection and the learning of model structure. 4. Develop scalable simulation/optimization approaches to nonlinear Bayesian experimental design, for both parameter inference and model selection. 5. Demonstrate these inferential tools on chemical kinetic models in reacting flow, constructing and refining thermochemical and electrochemical models from limited data. Demonstrate Bayesian filtering on canonical stochastic PDEs and in the dynamic estimation of inhomogeneous subsurface properties and flow fields.« less

Modeling the lake eutrophication stochastic ecosystem and the research of its stability.

PubMed

Wang, Bo; Qi, Qianqian

2018-06-01

In the reality, the lake system will be disturbed by stochastic factors including the external and internal factors. By adding the additive noise and the multiplicative noise to the right-hand sides of the model equation, the additive stochastic model and the multiplicative stochastic model are established respectively in order to reduce model errors induced by the absence of some physical processes. For both the two kinds of stochastic ecosystems, the authors studied the bifurcation characteristics with the FPK equation and the Lyapunov exponent method based on the Stratonovich-Khasminiskii stochastic average principle. Results show that, for the additive stochastic model, when control parameter (i.e., nutrient loading rate) falls into the interval [0.388644, 0.66003825], there exists bistability for the ecosystem and the additive noise intensities cannot make the bifurcation point drift. In the region of the bistability, the external stochastic disturbance which is one of the main triggers causing the lake eutrophication, may make the ecosystem unstable and induce a transition. When control parameter (nutrient loading rate) falls into the interval (0,  0.388644) and (0.66003825,  1.0), there only exists a stable equilibrium state and the additive noise intensity could not change it. For the multiplicative stochastic model, there exists more complex bifurcation performance and the multiplicative ecosystem will be broken by the multiplicative noise. Also, the multiplicative noise could reduce the extent of the bistable region, ultimately, the bistable region vanishes for sufficiently large noise. What's more, both the nutrient loading rate and the multiplicative noise will make the ecosystem have a regime shift. On the other hand, for the two kinds of stochastic ecosystems, the authors also discussed the evolution of the ecological variable in detail by using the Four-stage Runge-Kutta method of strong order γ=1.5. The numerical method was found to be capable of effectively explaining the regime shift theory and agreed with the realistic analyze. These conclusions also confirms the two paths for the system to move from one stable state to another proposed by Beisner et al. [3], which may help understand the occurrence mechanism related to the lake eutrophication from the view point of the stochastic model and mathematical analysis. Copyright © 2018 Elsevier Inc. All rights reserved.

Importance of vesicle release stochasticity in neuro-spike communication.

PubMed

Ramezani, Hamideh; Akan, Ozgur B

2017-07-01

Aim of this paper is proposing a stochastic model for vesicle release process, a part of neuro-spike communication. Hence, we study biological events occurring in this process and use microphysiological simulations to observe functionality of these events. Since the most important source of variability in vesicle release probability is opening of voltage dependent calcium channels (VDCCs) followed by influx of calcium ions through these channels, we propose a stochastic model for this event, while using a deterministic model for other variability sources. To capture the stochasticity of calcium influx to pre-synaptic neuron in our model, we study its statistics and find that it can be modeled by a distribution defined based on Normal and Logistic distributions.

Simultaneous estimation of deterministic and fractal stochastic components in non-stationary time series

NASA Astrophysics Data System (ADS)

García, Constantino A.; Otero, Abraham; Félix, Paulo; Presedo, Jesús; Márquez, David G.

2018-07-01

In the past few decades, it has been recognized that 1 / f fluctuations are ubiquitous in nature. The most widely used mathematical models to capture the long-term memory properties of 1 / f fluctuations have been stochastic fractal models. However, physical systems do not usually consist of just stochastic fractal dynamics, but they often also show some degree of deterministic behavior. The present paper proposes a model based on fractal stochastic and deterministic components that can provide a valuable basis for the study of complex systems with long-term correlations. The fractal stochastic component is assumed to be a fractional Brownian motion process and the deterministic component is assumed to be a band-limited signal. We also provide a method that, under the assumptions of this model, is able to characterize the fractal stochastic component and to provide an estimate of the deterministic components present in a given time series. The method is based on a Bayesian wavelet shrinkage procedure that exploits the self-similar properties of the fractal processes in the wavelet domain. This method has been validated over simulated signals and over real signals with economical and biological origin. Real examples illustrate how our model may be useful for exploring the deterministic-stochastic duality of complex systems, and uncovering interesting patterns present in time series.

Stochastic Modeling of Laminar-Turbulent Transition

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Choudhari, Meelan

2002-01-01

Stochastic versions of stability equations are developed in order to develop integrated models of transition and turbulence and to understand the effects of uncertain initial conditions on disturbance growth. Stochastic forms of the resonant triad equations, a high Reynolds number asymptotic theory, and the parabolized stability equations are developed.

Stochastic modeling of consumer preferences for health care institutions.

PubMed

Malhotra, N K

1983-01-01

This paper proposes a stochastic procedure for modeling consumer preferences via LOGIT analysis. First, a simple, non-technical exposition of the use of a stochastic approach in health care marketing is presented. Second, a study illustrating the application of the LOGIT model in assessing consumer preferences for hospitals is given. The paper concludes with several implications of the proposed approach.

Fusion of Hard and Soft Information in Nonparametric Density Estimation

DTIC Science & Technology

2015-06-10

and stochastic optimization models, in analysis of simulation output, and when instantiating probability models. We adopt a constrained maximum...particular, density estimation is needed for generation of input densities to simulation and stochastic optimization models, in analysis of simulation output...an essential step in simulation analysis and stochastic optimization is the generation of probability densities for input random variables; see for

The threshold of a stochastic avian-human influenza epidemic model with psychological effect

NASA Astrophysics Data System (ADS)

Zhang, Fengrong; Zhang, Xinhong

2018-02-01

In this paper, a stochastic avian-human influenza epidemic model with psychological effect in human population and saturation effect within avian population is investigated. This model describes the transmission of avian influenza among avian population and human population in random environments. For stochastic avian-only system, persistence in the mean and extinction of the infected avian population are studied. For the avian-human influenza epidemic system, sufficient conditions for the existence of an ergodic stationary distribution are obtained. Furthermore, a threshold of this stochastic model which determines the outcome of the disease is obtained. Finally, numerical simulations are given to support the theoretical results.

Coevolution Maintains Diversity in the Stochastic "Kill the Winner" Model

NASA Astrophysics Data System (ADS)

Xue, Chi; Goldenfeld, Nigel

2017-12-01

The "kill the winner" hypothesis is an attempt to address the problem of diversity in biology. It argues that host-specific predators control the population of each prey, preventing a winner from emerging and thus maintaining the coexistence of all species in the system. We develop a stochastic model for the kill the winner paradigm and show that the stable coexistence state of the deterministic kill the winner model is destroyed by demographic stochasticity, through a cascade of extinction events. We formulate an individual-level stochastic model in which predator-prey coevolution promotes the high diversity of the ecosystem by generating a persistent population flux of species.

Stochastic mixed-mode oscillations in a three-species predator-prey model

NASA Astrophysics Data System (ADS)

Sadhu, Susmita; Kuehn, Christian

2018-03-01

The effect of demographic stochasticity, in the form of Gaussian white noise, in a predator-prey model with one fast and two slow variables is studied. We derive the stochastic differential equations (SDEs) from a discrete model. For suitable parameter values, the deterministic drift part of the model admits a folded node singularity and exhibits a singular Hopf bifurcation. We focus on the parameter regime near the Hopf bifurcation, where small amplitude oscillations exist as stable dynamics in the absence of noise. In this regime, the stochastic model admits noise-driven mixed-mode oscillations (MMOs), which capture the intermediate dynamics between two cycles of population outbreaks. We perform numerical simulations to calculate the distribution of the random number of small oscillations between successive spikes for varying noise intensities and distance to the Hopf bifurcation. We also study the effect of noise on a suitable Poincaré map. Finally, we prove that the stochastic model can be transformed into a normal form near the folded node, which can be linked to recent results on the interplay between deterministic and stochastic small amplitude oscillations. The normal form can also be used to study the parameter influence on the noise level near folded singularities.

Tsunamis: stochastic models of occurrence and generation mechanisms

USGS Publications Warehouse

Geist, Eric L.; Oglesby, David D.

2014-01-01

The devastating consequences of the 2004 Indian Ocean and 2011 Japan tsunamis have led to increased research into many different aspects of the tsunami phenomenon. In this entry, we review research related to the observed complexity and uncertainty associated with tsunami generation, propagation, and occurrence described and analyzed using a variety of stochastic methods. In each case, seismogenic tsunamis are primarily considered. Stochastic models are developed from the physical theories that govern tsunami evolution combined with empirical models fitted to seismic and tsunami observations, as well as tsunami catalogs. These stochastic methods are key to providing probabilistic forecasts and hazard assessments for tsunamis. The stochastic methods described here are similar to those described for earthquakes (Vere-Jones 2013) and volcanoes (Bebbington 2013) in this encyclopedia.

Hiereachical Bayesian Model for Combining Geochemical and Geophysical Data for Environmental Applications Software

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Jinsong

2013-05-01

Development of a hierarchical Bayesian model to estimate the spatiotemporal distribution of aqueous geochemical parameters associated with in-situ bioremediation using surface spectral induced polarization (SIP) data and borehole geochemical measurements collected during a bioremediation experiment at a uranium-contaminated site near Rifle, Colorado. The SIP data are first inverted for Cole-Cole parameters including chargeability, time constant, resistivity at the DC frequency and dependence factor, at each pixel of two-dimensional grids using a previously developed stochastic method. Correlations between the inverted Cole-Cole parameters and the wellbore-based groundwater chemistry measurements indicative of key metabolic processes within the aquifer (e.g. ferrous iron, sulfate, uranium)more » were established and used as a basis for petrophysical model development. The developed Bayesian model consists of three levels of statistical sub-models: 1) data model, providing links between geochemical and geophysical attributes, 2) process model, describing the spatial and temporal variability of geochemical properties in the subsurface system, and 3) parameter model, describing prior distributions of various parameters and initial conditions. The unknown parameters are estimated using Markov chain Monte Carlo methods. By combining the temporally distributed geochemical data with the spatially distributed geophysical data, we obtain the spatio-temporal distribution of ferrous iron, sulfate and sulfide, and their associated uncertainity information. The obtained results can be used to assess the efficacy of the bioremediation treatment over space and time and to constrain reactive transport models.« less

Post-injection Multiphase Flow Modeling and Risk Assessments for Subsurface CO2 Storage in Naturally Fractured Reservoirs

NASA Astrophysics Data System (ADS)

Jin, G.

2015-12-01

Subsurface storage of carbon dioxide in geological formations is widely regarded as a promising tool for reducing global atmospheric CO2 emissions. Successful geologic storage for sequestrated carbon dioxides must prove to be safe by means of risk assessments including post-injection analysis of injected CO2 plumes. Because fractured reservoirs exhibit a higher degree of heterogeneity, it is imperative to conduct such simulation studies in order to reliably predict the geometric evolution of plumes and risk assessment of post CO2injection. The research has addressed the pressure footprint of CO2 plumes through the development of new techniques which combine discrete fracture network and stochastic continuum modeling of multiphase flow in fractured geologic formations. A subsequent permeability tensor map in 3-D, derived from our preciously developed method, can accurately describe the heterogeneity of fracture reservoirs. A comprehensive workflow integrating the fracture permeability characterization and multiphase flow modeling has been developed to simulate the CO2plume migration and risk assessments. A simulated fractured reservoir model based on high-priority geological carbon sinks in central Alabama has been employed for preliminary study. Discrete fracture networks were generated with an NE-oriented regional fracture set and orthogonal NW-fractures. Fracture permeability characterization revealed high permeability heterogeneity with an order of magnitude of up to three. A multiphase flow model composed of supercritical CO2 and saline water was then applied to predict CO2 plume volume, geometry, pressure footprint, and containment during and post injection. Injection simulation reveals significant permeability anisotropy that favors development of northeast-elongate CO2 plumes, which are aligned with systematic fractures. The diffusive spreading front of the CO2 plume shows strong viscous fingering effects. Post-injection simulation indicates significant upward lateral spreading of CO2 resulting in accumulation of CO2 directly under the seal unit because of its buoyancy and strata-bound vertical fractures. Risk assessment shows that lateral movement of CO2 along interconnected fractures requires widespread seals with high integrity to confine the injected CO2.

Addressing model uncertainty through stochastic parameter perturbations within the High Resolution Rapid Refresh (HRRR) ensemble

NASA Astrophysics Data System (ADS)

Wolff, J.; Jankov, I.; Beck, J.; Carson, L.; Frimel, J.; Harrold, M.; Jiang, H.

2016-12-01

It is well known that global and regional numerical weather prediction ensemble systems are under-dispersive, producing unreliable and overconfident ensemble forecasts. Typical approaches to alleviate this problem include the use of multiple dynamic cores, multiple physics suite configurations, or a combination of the two. While these approaches may produce desirable results, they have practical and theoretical deficiencies and are more difficult and costly to maintain. An active area of research that promotes a more unified and sustainable system for addressing the deficiencies in ensemble modeling is the use of stochastic physics to represent model-related uncertainty. Stochastic approaches include Stochastic Parameter Perturbations (SPP), Stochastic Kinetic Energy Backscatter (SKEB), Stochastic Perturbation of Physics Tendencies (SPPT), or some combination of all three. The focus of this study is to assess the model performance within a convection-permitting ensemble at 3-km grid spacing across the Contiguous United States (CONUS) when using stochastic approaches. For this purpose, the test utilized a single physics suite configuration based on the operational High-Resolution Rapid Refresh (HRRR) model, with ensemble members produced by employing stochastic methods. Parameter perturbations were employed in the Rapid Update Cycle (RUC) land surface model and Mellor-Yamada-Nakanishi-Niino (MYNN) planetary boundary layer scheme. Results will be presented in terms of bias, error, spread, skill, accuracy, reliability, and sharpness using the Model Evaluation Tools (MET) verification package. Due to the high level of complexity of running a frequently updating (hourly), high spatial resolution (3 km), large domain (CONUS) ensemble system, extensive high performance computing (HPC) resources were needed to meet this objective. Supercomputing resources were provided through the National Center for Atmospheric Research (NCAR) Strategic Capability (NSC) project support, allowing for a more extensive set of tests over multiple seasons, consequently leading to more robust results. Through the use of these stochastic innovations and powerful supercomputing at NCAR, further insights and advancements in ensemble forecasting at convection-permitting scales will be possible.

Applying model abstraction techniques to optimize monitoring networks for detecting subsurface contaminant transport

USDA-ARS?s Scientific Manuscript database

Improving strategies for monitoring subsurface contaminant transport includes performance comparison of competing models, developed independently or obtained via model abstraction. Model comparison and parameter discrimination involve specific performance indicators selected to better understand s...

The ISI distribution of the stochastic Hodgkin-Huxley neuron.

PubMed

Rowat, Peter F; Greenwood, Priscilla E

2014-01-01

The simulation of ion-channel noise has an important role in computational neuroscience. In recent years several approximate methods of carrying out this simulation have been published, based on stochastic differential equations, and all giving slightly different results. The obvious, and essential, question is: which method is the most accurate and which is most computationally efficient? Here we make a contribution to the answer. We compare interspike interval histograms from simulated data using four different approximate stochastic differential equation (SDE) models of the stochastic Hodgkin-Huxley neuron, as well as the exact Markov chain model simulated by the Gillespie algorithm. One of the recent SDE models is the same as the Kurtz approximation first published in 1978. All the models considered give similar ISI histograms over a wide range of deterministic and stochastic input. Three features of these histograms are an initial peak, followed by one or more bumps, and then an exponential tail. We explore how these features depend on deterministic input and on level of channel noise, and explain the results using the stochastic dynamics of the model. We conclude with a rough ranking of the four SDE models with respect to the similarity of their ISI histograms to the histogram of the exact Markov chain model.

A stochastic visco-hyperelastic model of human placenta tissue for finite element crash simulations.

PubMed

Hu, Jingwen; Klinich, Kathleen D; Miller, Carl S; Rupp, Jonathan D; Nazmi, Giseli; Pearlman, Mark D; Schneider, Lawrence W

2011-03-01

Placental abruption is the most common cause of fetal deaths in motor-vehicle crashes, but studies on the mechanical properties of human placenta are rare. This study presents a new method of developing a stochastic visco-hyperelastic material model of human placenta tissue using a combination of uniaxial tensile testing, specimen-specific finite element (FE) modeling, and stochastic optimization techniques. In our previous study, uniaxial tensile tests of 21 placenta specimens have been performed using a strain rate of 12/s. In this study, additional uniaxial tensile tests were performed using strain rates of 1/s and 0.1/s on 25 placenta specimens. Response corridors for the three loading rates were developed based on the normalized data achieved by test reconstructions of each specimen using specimen-specific FE models. Material parameters of a visco-hyperelastic model and their associated standard deviations were tuned to match both the means and standard deviations of all three response corridors using a stochastic optimization method. The results show a very good agreement between the tested and simulated response corridors, indicating that stochastic analysis can improve estimation of variability in material model parameters. The proposed method can be applied to develop stochastic material models of other biological soft tissues.

Weak Galilean invariance as a selection principle for coarse-grained diffusive models.

PubMed

Cairoli, Andrea; Klages, Rainer; Baule, Adrian

2018-05-29

How does the mathematical description of a system change in different reference frames? Galilei first addressed this fundamental question by formulating the famous principle of Galilean invariance. It prescribes that the equations of motion of closed systems remain the same in different inertial frames related by Galilean transformations, thus imposing strong constraints on the dynamical rules. However, real world systems are often described by coarse-grained models integrating complex internal and external interactions indistinguishably as friction and stochastic forces. Since Galilean invariance is then violated, there is seemingly no alternative principle to assess a priori the physical consistency of a given stochastic model in different inertial frames. Here, starting from the Kac-Zwanzig Hamiltonian model generating Brownian motion, we show how Galilean invariance is broken during the coarse-graining procedure when deriving stochastic equations. Our analysis leads to a set of rules characterizing systems in different inertial frames that have to be satisfied by general stochastic models, which we call "weak Galilean invariance." Several well-known stochastic processes are invariant in these terms, except the continuous-time random walk for which we derive the correct invariant description. Our results are particularly relevant for the modeling of biological systems, as they provide a theoretical principle to select physically consistent stochastic models before a validation against experimental data.

Dynamics of a stochastic HIV-1 infection model with logistic growth

NASA Astrophysics Data System (ADS)

Jiang, Daqing; Liu, Qun; Shi, Ningzhong; Hayat, Tasawar; Alsaedi, Ahmed; Xia, Peiyan

2017-03-01

This paper is concerned with a stochastic HIV-1 infection model with logistic growth. Firstly, by constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution of the solution to the HIV-1 infection model. Then we obtain sufficient conditions for extinction of the infection. The stationary distribution shows that the infection can become persistent in vivo.

Stochastic Radiative Transfer Model for Contaminated Rough Surfaces: A Framework for Detection System Design

DTIC Science & Technology

2013-11-01

STOCHASTIC RADIATIVE TRANSFER MODEL FOR CONTAMINATED ROUGH SURFACES: A...of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid ...COVERED (From - To) Jan 2013 - Sep 2013 4. TITLE AND SUBTITLE Stochastic Radiative Transfer Model for Contaminated Rough Surfaces: A Framework for

Universal fuzzy integral sliding-mode controllers for stochastic nonlinear systems.

PubMed

Gao, Qing; Liu, Lu; Feng, Gang; Wang, Yong

2014-12-01

In this paper, the universal integral sliding-mode controller problem for the general stochastic nonlinear systems modeled by Itô type stochastic differential equations is investigated. One of the main contributions is that a novel dynamic integral sliding mode control (DISMC) scheme is developed for stochastic nonlinear systems based on their stochastic T-S fuzzy approximation models. The key advantage of the proposed DISMC scheme is that two very restrictive assumptions in most existing ISMC approaches to stochastic fuzzy systems have been removed. Based on the stochastic Lyapunov theory, it is shown that the closed-loop control system trajectories are kept on the integral sliding surface almost surely since the initial time, and moreover, the stochastic stability of the sliding motion can be guaranteed in terms of linear matrix inequalities. Another main contribution is that the results of universal fuzzy integral sliding-mode controllers for two classes of stochastic nonlinear systems, along with constructive procedures to obtain the universal fuzzy integral sliding-mode controllers, are provided, respectively. Simulation results from an inverted pendulum example are presented to illustrate the advantages and effectiveness of the proposed approaches.

Application of model abstraction techniques to simulate transport in soils

USDA-ARS?s Scientific Manuscript database

Successful understanding and modeling of contaminant transport in soils is the precondition of risk-informed predictions of the subsurface contaminant transport. Exceedingly complex models of subsurface contaminant transport are often inefficient. Model abstraction is the methodology for reducing th...

Evaluation of Stochastic Rainfall Models in Capturing Climate Variability for Future Drought and Flood Risk Assessment

NASA Astrophysics Data System (ADS)

Chowdhury, A. F. M. K.; Lockart, N.; Willgoose, G. R.; Kuczera, G. A.; Kiem, A.; Nadeeka, P. M.

2016-12-01

One of the key objectives of stochastic rainfall modelling is to capture the full variability of climate system for future drought and flood risk assessment. However, it is not clear how well these models can capture the future climate variability when they are calibrated to Global/Regional Climate Model data (GCM/RCM) as these datasets are usually available for very short future period/s (e.g. 20 years). This study has assessed the ability of two stochastic daily rainfall models to capture climate variability by calibrating them to a dynamically downscaled RCM dataset in an east Australian catchment for 1990-2010, 2020-2040, and 2060-2080 epochs. The two stochastic models are: (1) a hierarchical Markov Chain (MC) model, which we developed in a previous study and (2) a semi-parametric MC model developed by Mehrotra and Sharma (2007). Our hierarchical model uses stochastic parameters of MC and Gamma distribution, while the semi-parametric model uses a modified MC process with memory of past periods and kernel density estimation. This study has generated multiple realizations of rainfall series by using parameters of each model calibrated to the RCM dataset for each epoch. The generated rainfall series are used to generate synthetic streamflow by using a SimHyd hydrology model. Assessing the synthetic rainfall and streamflow series, this study has found that both stochastic models can incorporate a range of variability in rainfall as well as streamflow generation for both current and future periods. However, the hierarchical model tends to overestimate the multiyear variability of wet spell lengths (therefore, is less likely to simulate long periods of drought and flood), while the semi-parametric model tends to overestimate the mean annual rainfall depths and streamflow volumes (hence, simulated droughts are likely to be less severe). Sensitivity of these limitations of both stochastic models in terms of future drought and flood risk assessment will be discussed.

Stochastic Approaches Within a High Resolution Rapid Refresh Ensemble

NASA Astrophysics Data System (ADS)

Jankov, I.

2017-12-01

It is well known that global and regional numerical weather prediction (NWP) ensemble systems are under-dispersive, producing unreliable and overconfident ensemble forecasts. Typical approaches to alleviate this problem include the use of multiple dynamic cores, multiple physics suite configurations, or a combination of the two. While these approaches may produce desirable results, they have practical and theoretical deficiencies and are more difficult and costly to maintain. An active area of research that promotes a more unified and sustainable system is the use of stochastic physics. Stochastic approaches include Stochastic Parameter Perturbations (SPP), Stochastic Kinetic Energy Backscatter (SKEB), and Stochastic Perturbation of Physics Tendencies (SPPT). The focus of this study is to assess model performance within a convection-permitting ensemble at 3-km grid spacing across the Contiguous United States (CONUS) using a variety of stochastic approaches. A single physics suite configuration based on the operational High-Resolution Rapid Refresh (HRRR) model was utilized and ensemble members produced by employing stochastic methods. Parameter perturbations (using SPP) for select fields were employed in the Rapid Update Cycle (RUC) land surface model (LSM) and Mellor-Yamada-Nakanishi-Niino (MYNN) Planetary Boundary Layer (PBL) schemes. Within MYNN, SPP was applied to sub-grid cloud fraction, mixing length, roughness length, mass fluxes and Prandtl number. In the RUC LSM, SPP was applied to hydraulic conductivity and tested perturbing soil moisture at initial time. First iterative testing was conducted to assess the initial performance of several configuration settings (e.g. variety of spatial and temporal de-correlation lengths). Upon selection of the most promising candidate configurations using SPP, a 10-day time period was run and more robust statistics were gathered. SKEB and SPPT were included in additional retrospective tests to assess the impact of using all three stochastic approaches to address model uncertainty. Results from the stochastic perturbation testing were compared to a baseline multi-physics control ensemble. For probabilistic forecast performance the Model Evaluation Tools (MET) verification package was used.

Partial ASL extensions for stochastic programming.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gay, David

2010-03-31

partially completed extensions for stochastic programming to the AMPL/solver interface library (ASL).modeling and experimenting with stochastic recourse problems. This software is not primarily for military applications

Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes.

PubMed

Pendar, Hodjat; Platini, Thierry; Kulkarni, Rahul V

2013-04-01

Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations; hence, there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expression. The mapping leads to exact protein distributions using results for mRNA distributions in models with promoter-based regulation. Using this approach, we derive exact analytical results for steady-state and time-dependent distributions for the basic two-stage model of gene expression. Furthermore, we show how the mapping leads to exact protein distributions for extensions of the basic model that include the effects of posttranscriptional and posttranslational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.

Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes

NASA Astrophysics Data System (ADS)

Pendar, Hodjat; Platini, Thierry; Kulkarni, Rahul V.

2013-04-01

Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations; hence, there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expression. The mapping leads to exact protein distributions using results for mRNA distributions in models with promoter-based regulation. Using this approach, we derive exact analytical results for steady-state and time-dependent distributions for the basic two-stage model of gene expression. Furthermore, we show how the mapping leads to exact protein distributions for extensions of the basic model that include the effects of posttranscriptional and posttranslational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.

Information-theoretic model selection for optimal prediction of stochastic dynamical systems from data

NASA Astrophysics Data System (ADS)

Darmon, David

2018-03-01

In the absence of mechanistic or phenomenological models of real-world systems, data-driven models become necessary. The discovery of various embedding theorems in the 1980s and 1990s motivated a powerful set of tools for analyzing deterministic dynamical systems via delay-coordinate embeddings of observations of their component states. However, in many branches of science, the condition of operational determinism is not satisfied, and stochastic models must be brought to bear. For such stochastic models, the tool set developed for delay-coordinate embedding is no longer appropriate, and a new toolkit must be developed. We present an information-theoretic criterion, the negative log-predictive likelihood, for selecting the embedding dimension for a predictively optimal data-driven model of a stochastic dynamical system. We develop a nonparametric estimator for the negative log-predictive likelihood and compare its performance to a recently proposed criterion based on active information storage. Finally, we show how the output of the model selection procedure can be used to compare candidate predictors for a stochastic system to an information-theoretic lower bound.

Stochastic foundations of undulatory transport phenomena: generalized Poisson-Kac processes—part III extensions and applications to kinetic theory and transport

NASA Astrophysics Data System (ADS)

Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro

2017-08-01

This third part extends the theory of Generalized Poisson-Kac (GPK) processes to nonlinear stochastic models and to a continuum of states. Nonlinearity is treated in two ways: (i) as a dependence of the parameters (intensity of the stochastic velocity, transition rates) of the stochastic perturbation on the state variable, similarly to the case of nonlinear Langevin equations, and (ii) as the dependence of the stochastic microdynamic equations of motion on the statistical description of the process itself (nonlinear Fokker-Planck-Kac models). Several numerical and physical examples illustrate the theory. Gathering nonlinearity and a continuum of states, GPK theory provides a stochastic derivation of the nonlinear Boltzmann equation, furnishing a positive answer to the Kac’s program in kinetic theory. The transition from stochastic microdynamics to transport theory within the framework of the GPK paradigm is also addressed.

Interpretation of Ground Temperature Anomalies in Hydrothermal Discharge Areas

NASA Astrophysics Data System (ADS)

Price, A. N.; Lindsey, C.; Fairley, J. P., Jr.

2017-12-01

Researchers have long noted the potential for shallow hydrothermal fluids to perturb near-surface temperatures. Several investigators have made qualitative or semi-quantitative use of elevated surface temperatures; for example, in snowfall calorimetry, or for tracing subsurface flow paths. However, little effort has been expended to develop a quantitative framework connecting surface temperature observations with conditions in the subsurface. Here, we examine an area of shallow subsurface flow at Burgdorf Hot Springs, in the Payette National Forest, north of McCall, Idaho USA. We present a simple analytical model that uses easily-measured surface data to infer the temperatures of laterally-migrating shallow hydrothermal fluids. The model is calibrated using shallow ground temperature measurements and overburden thickness estimates from seismic refraction studies. The model predicts conditions in the shallow subsurface, and suggests that the Biot number may place a more important control on the expression of near-surface thermal perturbations than previously thought. In addition, our model may have application in inferring difficult-to-measure parameters, such as shallow subsurface discharge from hydrothermal springs.

Variational formulation for Black-Scholes equations in stochastic volatility models

NASA Astrophysics Data System (ADS)

Gyulov, Tihomir B.; Valkov, Radoslav L.

2012-11-01

In this note we prove existence and uniqueness of weak solutions to a boundary value problem arising from stochastic volatility models in financial mathematics. Our settings are variational in weighted Sobolev spaces. Nevertheless, as it will become apparent our variational formulation agrees well with the stochastic part of the problem.

Temperature variation effects on stochastic characteristics for low-cost MEMS-based inertial sensor error

NASA Astrophysics Data System (ADS)

El-Diasty, M.; El-Rabbany, A.; Pagiatakis, S.

2007-11-01

We examine the effect of varying the temperature points on MEMS inertial sensors' noise models using Allan variance and least-squares spectral analysis (LSSA). Allan variance is a method of representing root-mean-square random drift error as a function of averaging times. LSSA is an alternative to the classical Fourier methods and has been applied successfully by a number of researchers in the study of the noise characteristics of experimental series. Static data sets are collected at different temperature points using two MEMS-based IMUs, namely MotionPakII and Crossbow AHRS300CC. The performance of the two MEMS inertial sensors is predicted from the Allan variance estimation results at different temperature points and the LSSA is used to study the noise characteristics and define the sensors' stochastic model parameters. It is shown that the stochastic characteristics of MEMS-based inertial sensors can be identified using Allan variance estimation and LSSA and the sensors' stochastic model parameters are temperature dependent. Also, the Kaiser window FIR low-pass filter is used to investigate the effect of de-noising stage on the stochastic model. It is shown that the stochastic model is also dependent on the chosen cut-off frequency.

A developmental basis for stochasticity in floral organ numbers

PubMed Central

Kitazawa, Miho S.; Fujimoto, Koichi

2014-01-01

Stochasticity ubiquitously inevitably appears at all levels from molecular traits to multicellular, morphological traits. Intrinsic stochasticity in biochemical reactions underlies the typical intercellular distributions of chemical concentrations, e.g., morphogen gradients, which can give rise to stochastic morphogenesis. While the universal statistics and mechanisms underlying the stochasticity at the biochemical level have been widely analyzed, those at the morphological level have not. Such morphological stochasticity is found in foral organ numbers. Although the floral organ number is a hallmark of floral species, it can distribute stochastically even within an individual plant. The probability distribution of the floral organ number within a population is usually asymmetric, i.e., it is more likely to increase rather than decrease from the modal value, or vice versa. We combined field observations, statistical analysis, and mathematical modeling to study the developmental basis of the variation in floral organ numbers among 50 species mainly from Ranunculaceae and several other families from core eudicots. We compared six hypothetical mechanisms and found that a modified error function reproduced much of the asymmetric variation found in eudicot floral organ numbers. The error function is derived from mathematical modeling of floral organ positioning, and its parameters represent measurable distances in the floral bud morphologies. The model predicts two developmental sources of the organ-number distributions: stochastic shifts in the expression boundaries of homeotic genes and a semi-concentric (whorled-type) organ arrangement. Other models species- or organ-specifically reproduced different types of distributions that reflect different developmental processes. The organ-number variation could be an indicator of stochasticity in organ fate determination and organ positioning. PMID:25404932

A Stochastic-Variational Model for Soft Mumford-Shah Segmentation

PubMed Central

2006-01-01

In contemporary image and vision analysis, stochastic approaches demonstrate great flexibility in representing and modeling complex phenomena, while variational-PDE methods gain enormous computational advantages over Monte Carlo or other stochastic algorithms. In combination, the two can lead to much more powerful novel models and efficient algorithms. In the current work, we propose a stochastic-variational model for soft (or fuzzy) Mumford-Shah segmentation of mixture image patterns. Unlike the classical hard Mumford-Shah segmentation, the new model allows each pixel to belong to each image pattern with some probability. Soft segmentation could lead to hard segmentation, and hence is more general. The modeling procedure, mathematical analysis on the existence of optimal solutions, and computational implementation of the new model are explored in detail, and numerical examples of both synthetic and natural images are presented. PMID:23165059

Studying Resist Stochastics with the Multivariate Poisson Propagation Model

DOE PAGES

Naulleau, Patrick; Anderson, Christopher; Chao, Weilun; ...

2014-01-01

Progress in the ultimate performance of extreme ultraviolet resist has arguably decelerated in recent years suggesting an approach to stochastic limits both in photon counts and material parameters. Here we report on the performance of a variety of leading extreme ultraviolet resist both with and without chemical amplification. The measured performance is compared to stochastic modeling results using the Multivariate Poisson Propagation Model. The results show that the best materials are indeed nearing modeled performance limits.

A non-stochastic iterative computational method to model light propagation in turbid media

NASA Astrophysics Data System (ADS)

McIntyre, Thomas J.; Zemp, Roger J.

2015-03-01

Monte Carlo models are widely used to model light transport in turbid media, however their results implicitly contain stochastic variations. These fluctuations are not ideal, especially for inverse problems where Jacobian matrix errors can lead to large uncertainties upon matrix inversion. Yet Monte Carlo approaches are more computationally favorable than solving the full Radiative Transport Equation. Here, a non-stochastic computational method of estimating fluence distributions in turbid media is proposed, which is called the Non-Stochastic Propagation by Iterative Radiance Evaluation method (NSPIRE). Rather than using stochastic means to determine a random walk for each photon packet, the propagation of light from any element to all other elements in a grid is modelled simultaneously. For locally homogeneous anisotropic turbid media, the matrices used to represent scattering and projection are shown to be block Toeplitz, which leads to computational simplifications via convolution operators. To evaluate the accuracy of the algorithm, 2D simulations were done and compared against Monte Carlo models for the cases of an isotropic point source and a pencil beam incident on a semi-infinite turbid medium. The model was shown to have a mean percent error less than 2%. The algorithm represents a new paradigm in radiative transport modelling and may offer a non-stochastic alternative to modeling light transport in anisotropic scattering media for applications where the diffusion approximation is insufficient.

Stochastic Ocean Eddy Perturbations in a Coupled General Circulation Model.

NASA Astrophysics Data System (ADS)

Howe, N.; Williams, P. D.; Gregory, J. M.; Smith, R. S.

2014-12-01

High-resolution ocean models, which are eddy permitting and resolving, require large computing resources to produce centuries worth of data. Also, some previous studies have suggested that increasing resolution does not necessarily solve the problem of unresolved scales, because it simply introduces a new set of unresolved scales. Applying stochastic parameterisations to ocean models is one solution that is expected to improve the representation of small-scale (eddy) effects without increasing run-time. Stochastic parameterisation has been shown to have an impact in atmosphere-only models and idealised ocean models, but has not previously been studied in ocean general circulation models. Here we apply simple stochastic perturbations to the ocean temperature and salinity tendencies in the low-resolution coupled climate model, FAMOUS. The stochastic perturbations are implemented according to T(t) = T(t-1) + (ΔT(t) + ξ(t)), where T is temperature or salinity, ΔT is the corresponding deterministic increment in one time step, and ξ(t) is Gaussian noise. We use high-resolution HiGEM data coarse-grained to the FAMOUS grid to provide information about the magnitude and spatio-temporal correlation structure of the noise to be added to the lower resolution model. Here we present results of adding white and red noise, showing the impacts of an additive stochastic perturbation on mean climate state and variability in an AOGCM.

Structural adjustment for accurate conditioning in large-scale subsurface systems

NASA Astrophysics Data System (ADS)

Tahmasebi, Pejman

2017-03-01

Most of the current subsurface simulation approaches consider a priority list for honoring the well and any other auxiliary data, and eventually adopt a middle ground between the quality of the model and conditioning it to hard data. However, as the number of datasets increases, such methods often produce undesirable features in the subsurface model. Due to their high flexibility, subsurface modeling based on training images (TIs) is becoming popular. Providing comprehensive TIs remains, however, an outstanding problem. In addition, identifying a pattern similar to those in the TI that honors the well and other conditioning data is often difficult. Moreover, the current subsurface modeling approaches do not account for small perturbations that may occur in a subsurface system. Such perturbations are active in most of the depositional systems. In this paper, a new methodology is presented that is based on an irregular gridding scheme that accounts for incomplete TIs and minor offsets. Use of the methodology enables one to use a small or incomplete TI and adaptively change the patterns in the simulation grid in order to simultaneously honor the well data and take into account the effect of the local offsets. Furthermore, the proposed method was used on various complex process-based models and their structures are deformed for matching with the conditioning point data. The accuracy and robustness of the proposed algorithm are successfully demonstrated by applying it to models of several complex examples.

Phase-Space Transport of Stochastic Chaos in Population Dynamics of Virus Spread

NASA Astrophysics Data System (ADS)

Billings, Lora; Bollt, Erik M.; Schwartz, Ira B.

2002-06-01

A general way to classify stochastic chaos is presented and applied to population dynamics models. A stochastic dynamical theory is used to develop an algorithmic tool to measure the transport across basin boundaries and predict the most probable regions of transport created by noise. The results of this tool are illustrated on a model of virus spread in a large population, where transport regions reveal how noise completes the necessary manifold intersections for the creation of emerging stochastic chaos.

Three-Dimensional Subsurface Flow, Fate and Transport of Microbes and Chemicals (3DFATMIC) Model

EPA Pesticide Factsheets

This model simulates subsurface flow, fate and transport of contaminants that are undergoing chemical or biological transformations. The model is applicable to transient conditions in both saturated and unsaturated zones.

Two-Dimensional Subsurface Flow, Fate and Transport of Microbes and Chemicals (2DFATMIC) Model

EPA Pesticide Factsheets

This model simulates subsurface flow, fate, and transport of contaminants that are undergoing chemical or biological transformations. This model is applicable to transient conditions in both saturated and unsaturated zones.

Control of Networked Traffic Flow Distribution - A Stochastic Distribution System Perspective

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Hong; Aziz, H M Abdul; Young, Stan

Networked traffic flow is a common scenario for urban transportation, where the distribution of vehicle queues either at controlled intersections or highway segments reflect the smoothness of the traffic flow in the network. At signalized intersections, the traffic queues are controlled by traffic signal control settings and effective traffic lights control would realize both smooth traffic flow and minimize fuel consumption. Funded by the Energy Efficient Mobility Systems (EEMS) program of the Vehicle Technologies Office of the US Department of Energy, we performed a preliminary investigation on the modelling and control framework in context of urban network of signalized intersections.more » In specific, we developed a recursive input-output traffic queueing models. The queue formation can be modeled as a stochastic process where the number of vehicles entering each intersection is a random number. Further, we proposed a preliminary B-Spline stochastic model for a one-way single-lane corridor traffic system based on theory of stochastic distribution control.. It has been shown that the developed stochastic model would provide the optimal probability density function (PDF) of the traffic queueing length as a dynamic function of the traffic signal setting parameters. Based upon such a stochastic distribution model, we have proposed a preliminary closed loop framework on stochastic distribution control for the traffic queueing system to make the traffic queueing length PDF follow a target PDF that potentially realizes the smooth traffic flow distribution in a concerned corridor.« less

Improved Climate Simulations through a Stochastic Parameterization of Ocean Eddies

NASA Astrophysics Data System (ADS)

Williams, Paul; Howe, Nicola; Gregory, Jonathan; Smith, Robin; Joshi, Manoj

2016-04-01

In climate simulations, the impacts of the sub-grid scales on the resolved scales are conventionally represented using deterministic closure schemes, which assume that the impacts are uniquely determined by the resolved scales. Stochastic parameterization relaxes this assumption, by sampling the sub-grid variability in a computationally inexpensive manner. This presentation shows that the simulated climatological state of the ocean is improved in many respects by implementing a simple stochastic parameterization of ocean eddies into a coupled atmosphere-ocean general circulation model. Simulations from a high-resolution, eddy-permitting ocean model are used to calculate the eddy statistics needed to inject realistic stochastic noise into a low-resolution, non-eddy-permitting version of the same model. A suite of four stochastic experiments is then run to test the sensitivity of the simulated climate to the noise definition, by varying the noise amplitude and decorrelation time within reasonable limits. The addition of zero-mean noise to the ocean temperature tendency is found to have a non-zero effect on the mean climate. Specifically, in terms of the ocean temperature and salinity fields both at the surface and at depth, the noise reduces many of the biases in the low-resolution model and causes it to more closely resemble the high-resolution model. The variability of the strength of the global ocean thermohaline circulation is also improved. It is concluded that stochastic ocean perturbations can yield reductions in climate model error that are comparable to those obtained by refining the resolution, but without the increased computational cost. Therefore, stochastic parameterizations of ocean eddies have the potential to significantly improve climate simulations. Reference PD Williams, NJ Howe, JM Gregory, RS Smith, and MM Joshi (2016) Improved Climate Simulations through a Stochastic Parameterization of Ocean Eddies. Journal of Climate, under revision.

Disentangling Mechanisms That Mediate the Balance Between Stochastic and Deterministic Processes in Microbial Succession

DOE PAGES

Dini-Andreote, Francisco; Stegen, James C.; van Elsas, Jan D.; ...

2015-03-17

Despite growing recognition that deterministic and stochastic factors simultaneously influence bacterial communities, little is known about mechanisms shifting their relative importance. To better understand underlying mechanisms, we developed a conceptual model linking ecosystem development during primary succession to shifts in the stochastic/deterministic balance. To evaluate the conceptual model we coupled spatiotemporal data on soil bacterial communities with environmental conditions spanning 105 years of salt marsh development. At the local scale there was a progression from stochasticity to determinism due to Na accumulation with increasing ecosystem age, supporting a main element of the conceptual model. At the regional-scale, soil organic mattermore » (SOM) governed the relative influence of stochasticity and the type of deterministic ecological selection, suggesting scale-dependency in how deterministic ecological selection is imposed. Analysis of a new ecological simulation model supported these conceptual inferences. Looking forward, we propose an extended conceptual model that integrates primary and secondary succession in microbial systems.« less

Stochastic-field cavitation model

NASA Astrophysics Data System (ADS)

Dumond, J.; Magagnato, F.; Class, A.

2013-07-01

Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.

A cavitation model based on Eulerian stochastic fields

NASA Astrophysics Data System (ADS)

Magagnato, F.; Dumond, J.

2013-12-01

Non-linear phenomena can often be described using probability density functions (pdf) and pdf transport models. Traditionally the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and in particular to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. Firstly, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.

Stochastic-field cavitation model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dumond, J., E-mail: julien.dumond@areva.com; AREVA GmbH, Erlangen, Paul-Gossen-Strasse 100, D-91052 Erlangen; Magagnato, F.

2013-07-15

Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian “particles” or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-fieldmore » cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.« less

Modeling of stochastic motion of bacteria propelled spherical microbeads

NASA Astrophysics Data System (ADS)

Arabagi, Veaceslav; Behkam, Bahareh; Cheung, Eugene; Sitti, Metin

2011-06-01

This work proposes a stochastic dynamic model of bacteria propelled spherical microbeads as potential swimming microrobotic bodies. Small numbers of S. marcescens bacteria are attached with their bodies to surfaces of spherical microbeads. Average-behavior stochastic models that are normally adopted when studying such biological systems are generally not effective for cases in which a small number of agents are interacting in a complex manner, hence a stochastic model is proposed to simulate the behavior of 8-41 bacteria assembled on a curved surface. Flexibility of the flagellar hook is studied via comparing simulated and experimental results for scenarios of increasing bead size and the number of attached bacteria on a bead. Although requiring more experimental data to yield an exact, certain flagellar hook stiffness value, the examined results favor a stiffer flagella. The stochastic model is intended to be used as a design and simulation tool for future potential targeted drug delivery and disease diagnosis applications of bacteria propelled microrobots.

Ground motion simulation for the 23 August 2011, Mineral, Virginia earthquake using physics-based and stochastic broadband methods

USGS Publications Warehouse

Sun, Xiaodan; Hartzell, Stephen; Rezaeian, Sanaz

2015-01-01

Three broadband simulation methods are used to generate synthetic ground motions for the 2011 Mineral, Virginia, earthquake and compare with observed motions. The methods include a physics‐based model by Hartzell et al. (1999, 2005), a stochastic source‐based model by Boore (2009), and a stochastic site‐based model by Rezaeian and Der Kiureghian (2010, 2012). The ground‐motion dataset consists of 40 stations within 600 km of the epicenter. Several metrics are used to validate the simulations: (1) overall bias of response spectra and Fourier spectra (from 0.1 to 10 Hz); (2) spatial distribution of residuals for GMRotI50 peak ground acceleration (PGA), peak ground velocity, and pseudospectral acceleration (PSA) at various periods; (3) comparison with ground‐motion prediction equations (GMPEs) for the eastern United States. Our results show that (1) the physics‐based model provides satisfactory overall bias from 0.1 to 10 Hz and produces more realistic synthetic waveforms; (2) the stochastic site‐based model also yields more realistic synthetic waveforms and performs superiorly for frequencies greater than about 1 Hz; (3) the stochastic source‐based model has larger bias at lower frequencies (<0.5  Hz) and cannot reproduce the varying frequency content in the time domain. The spatial distribution of GMRotI50 residuals shows that there is no obvious pattern with distance in the simulation bias, but there is some azimuthal variability. The comparison between synthetics and GMPEs shows similar fall‐off with distance for all three models, comparable PGA and PSA amplitudes for the physics‐based and stochastic site‐based models, and systematic lower amplitudes for the stochastic source‐based model at lower frequencies (<0.5  Hz).

Population stochastic modelling (PSM)--an R package for mixed-effects models based on stochastic differential equations.

PubMed

Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode; Overgaard, Rune Viig; Madsen, Henrik

2009-06-01

The extension from ordinary to stochastic differential equations (SDEs) in pharmacokinetic and pharmacodynamic (PK/PD) modelling is an emerging field and has been motivated in a number of articles [N.R. Kristensen, H. Madsen, S.H. Ingwersen, Using stochastic differential equations for PK/PD model development, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 109-141; C.W. Tornøe, R.V. Overgaard, H. Agersø, H.A. Nielsen, H. Madsen, E.N. Jonsson, Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations, Pharm. Res. 22 (August(8)) (2005) 1247-1258; R.V. Overgaard, N. Jonsson, C.W. Tornøe, H. Madsen, Non-linear mixed-effects models with stochastic differential equations: implementation of an estimation algorithm, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 85-107; U. Picchini, S. Ditlevsen, A. De Gaetano, Maximum likelihood estimation of a time-inhomogeneous stochastic differential model of glucose dynamics, Math. Med. Biol. 25 (June(2)) (2008) 141-155]. PK/PD models are traditionally based ordinary differential equations (ODEs) with an observation link that incorporates noise. This state-space formulation only allows for observation noise and not for system noise. Extending to SDEs allows for a Wiener noise component in the system equations. This additional noise component enables handling of autocorrelated residuals originating from natural variation or systematic model error. Autocorrelated residuals are often partly ignored in PK/PD modelling although violating the hypothesis for many standard statistical tests. This article presents a package for the statistical program R that is able to handle SDEs in a mixed-effects setting. The estimation method implemented is the FOCE(1) approximation to the population likelihood which is generated from the individual likelihoods that are approximated using the Extended Kalman Filter's one-step predictions.

Stochastic Geomorphology: A Framework for Creating General Principles on Erosion and Sedimentation in River Basins (Invited)

NASA Astrophysics Data System (ADS)

Benda, L. E.

2009-12-01

Stochastic geomorphology refers to the interaction of the stochastic field of sediment supply with hierarchically branching river networks where erosion, sediment flux and sediment storage are described by their probability densities. There are a number of general principles (hypotheses) that stem from this conceptual and numerical framework that may inform the science of erosion and sedimentation in river basins. Rainstorms and other perturbations, characterized by probability distributions of event frequency and magnitude, stochastically drive sediment influx to channel networks. The frequency-magnitude distribution of sediment supply that is typically skewed reflects strong interactions among climate, topography, vegetation, and geotechnical controls that vary between regions; the distribution varies systematically with basin area and the spatial pattern of erosion sources. Probability densities of sediment flux and storage evolve from more to less skewed forms downstream in river networks due to the convolution of the population of sediment sources in a watershed that should vary with climate, network patterns, topography, spatial scale, and degree of erosion asynchrony. The sediment flux and storage distributions are also transformed downstream due to diffusion, storage, interference, and attrition. In stochastic systems, the characteristically pulsed sediment supply and transport can create translational or stationary-diffusive valley and channel depositional landforms, the geometries of which are governed by sediment flux-network interactions. Episodic releases of sediment to the network can also drive a system memory reflected in a Hurst Effect in sediment yields and thus in sedimentological records. Similarly, discreet events of punctuated erosion on hillslopes can lead to altered surface and subsurface properties of a population of erosion source areas that can echo through time and affect subsequent erosion and sediment flux rates. Spatial patterns of probability densities have implications for the frequency and magnitude of sediment transport and storage and thus for the formation of alluvial and colluvial landforms throughout watersheds. For instance, the combination and interference of probability densities of sediment flux at confluences creates patterns of riverine heterogeneity, including standing waves of sediment with associated age distributions of deposits that can vary from younger to older depending on network geometry and position. Although the watershed world of probability densities is rarified and typically confined to research endeavors, it has real world implications for the day-to-day work on hillslopes and in fluvial systems, including measuring erosion, sediment transport, mapping channel morphology and aquatic habitats, interpreting deposit stratigraphy, conducting channel restoration, and applying environmental regulations. A question for the geomorphology community is whether the stochastic framework is useful for advancing our understanding of erosion and sedimentation and whether it should stimulate research to further develop, refine and test these and other principles. For example, a changing climate should lead to shifts in probability densities of erosion, sediment flux, storage, and associated habitats and thus provide a useful index of climate change in earth science forecast models.

An accurate nonlinear stochastic model for MEMS-based inertial sensor error with wavelet networks

NASA Astrophysics Data System (ADS)

El-Diasty, Mohammed; El-Rabbany, Ahmed; Pagiatakis, Spiros

2007-12-01

The integration of Global Positioning System (GPS) with Inertial Navigation System (INS) has been widely used in many applications for positioning and orientation purposes. Traditionally, random walk (RW), Gauss-Markov (GM), and autoregressive (AR) processes have been used to develop the stochastic model in classical Kalman filters. The main disadvantage of classical Kalman filter is the potentially unstable linearization of the nonlinear dynamic system. Consequently, a nonlinear stochastic model is not optimal in derivative-based filters due to the expected linearization error. With a derivativeless-based filter such as the unscented Kalman filter or the divided difference filter, the filtering process of a complicated highly nonlinear dynamic system is possible without linearization error. This paper develops a novel nonlinear stochastic model for inertial sensor error using a wavelet network (WN). A wavelet network is a highly nonlinear model, which has recently been introduced as a powerful tool for modelling and prediction. Static and kinematic data sets are collected using a MEMS-based IMU (DQI-100) to develop the stochastic model in the static mode and then implement it in the kinematic mode. The derivativeless-based filtering method using GM, AR, and the proposed WN-based processes are used to validate the new model. It is shown that the first-order WN-based nonlinear stochastic model gives superior positioning results to the first-order GM and AR models with an overall improvement of 30% when 30 and 60 seconds GPS outages are introduced.

Toward Development of a Stochastic Wake Model: Validation Using LES and Turbine Loads

DOE PAGES

Moon, Jae; Manuel, Lance; Churchfield, Matthew; ...

2017-12-28

Wind turbines within an array do not experience free-stream undisturbed flow fields. Rather, the flow fields on internal turbines are influenced by wakes generated by upwind unit and exhibit different dynamic characteristics relative to the free stream. The International Electrotechnical Commission (IEC) standard 61400-1 for the design of wind turbines only considers a deterministic wake model for the design of a wind plant. This study is focused on the development of a stochastic model for waked wind fields. First, high-fidelity physics-based waked wind velocity fields are generated using Large-Eddy Simulation (LES). Stochastic characteristics of these LES waked wind velocity field,more » including mean and turbulence components, are analyzed. Wake-related mean and turbulence field-related parameters are then estimated for use with a stochastic model, using Multivariate Multiple Linear Regression (MMLR) with the LES data. To validate the simulated wind fields based on the stochastic model, wind turbine tower and blade loads are generated using aeroelastic simulation for utility-scale wind turbine models and compared with those based directly on the LES inflow. The study's overall objective is to offer efficient and validated stochastic approaches that are computationally tractable for assessing the performance and loads of turbines operating in wakes.« less

Toward Development of a Stochastic Wake Model: Validation Using LES and Turbine Loads

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moon, Jae; Manuel, Lance; Churchfield, Matthew

Wind turbines within an array do not experience free-stream undisturbed flow fields. Rather, the flow fields on internal turbines are influenced by wakes generated by upwind unit and exhibit different dynamic characteristics relative to the free stream. The International Electrotechnical Commission (IEC) standard 61400-1 for the design of wind turbines only considers a deterministic wake model for the design of a wind plant. This study is focused on the development of a stochastic model for waked wind fields. First, high-fidelity physics-based waked wind velocity fields are generated using Large-Eddy Simulation (LES). Stochastic characteristics of these LES waked wind velocity field,more » including mean and turbulence components, are analyzed. Wake-related mean and turbulence field-related parameters are then estimated for use with a stochastic model, using Multivariate Multiple Linear Regression (MMLR) with the LES data. To validate the simulated wind fields based on the stochastic model, wind turbine tower and blade loads are generated using aeroelastic simulation for utility-scale wind turbine models and compared with those based directly on the LES inflow. The study's overall objective is to offer efficient and validated stochastic approaches that are computationally tractable for assessing the performance and loads of turbines operating in wakes.« less

Stochastic 3D modeling of Ostwald ripening at ultra-high volume fractions of the coarsening phase

NASA Astrophysics Data System (ADS)

Spettl, A.; Wimmer, R.; Werz, T.; Heinze, M.; Odenbach, S.; Krill, C. E., III; Schmidt, V.

2015-09-01

We present a (dynamic) stochastic simulation model for 3D grain morphologies undergoing a grain coarsening phenomenon known as Ostwald ripening. For low volume fractions of the coarsening phase, the classical LSW theory predicts a power-law evolution of the mean particle size and convergence toward self-similarity of the particle size distribution; experiments suggest that this behavior holds also for high volume fractions. In the present work, we have analyzed 3D images that were recorded in situ over time in semisolid Al-Cu alloys manifesting ultra-high volume fractions of the coarsening (solid) phase. Using this information we developed a stochastic simulation model for the 3D morphology of the coarsening grains at arbitrary time steps. Our stochastic model is based on random Laguerre tessellations and is by definition self-similar—i.e. it depends only on the mean particle diameter, which in turn can be estimated at each point in time. For a given mean diameter, the stochastic model requires only three additional scalar parameters, which influence the distribution of particle sizes and their shapes. An evaluation shows that even with this minimal information the stochastic model yields an excellent representation of the statistical properties of the experimental data.

Inflow forecasting model construction with stochastic time series for coordinated dam operation

NASA Astrophysics Data System (ADS)

Kim, T.; Jung, Y.; Kim, H.; Heo, J. H.

2014-12-01

Dam inflow forecasting is one of the most important tasks in dam operation for an effective water resources management and control. In general, dam inflow forecasting with stochastic time series model is possible to apply when the data is stationary because most of stochastic process based on stationarity. However, recent hydrological data cannot be satisfied the stationarity anymore because of climate change. Therefore a stochastic time series model, which can consider seasonality and trend in the data series, named SARIMAX(Seasonal Autoregressive Integrated Average with eXternal variable) model were constructed in this study. This SARIMAX model could increase the performance of stochastic time series model by considering the nonstationarity components and external variable such as precipitation. For application, the models were constructed for four coordinated dams on Han river in South Korea with monthly time series data. As a result, the models of each dam have similar performance and it would be possible to use the model for coordinated dam operation.Acknowledgement This research was supported by a grant 'Establishing Active Disaster Management System of Flood Control Structures by using 3D BIM Technique' [NEMA-NH-12-57] from the Natural Hazard Mitigation Research Group, National Emergency Management Agency of Korea.

Influence of stochastic sea ice parametrization on climate and the role of atmosphere–sea ice–ocean interaction

PubMed Central

Juricke, Stephan; Jung, Thomas

2014-01-01

The influence of a stochastic sea ice strength parametrization on the mean climate is investigated in a coupled atmosphere–sea ice–ocean model. The results are compared with an uncoupled simulation with a prescribed atmosphere. It is found that the stochastic sea ice parametrization causes an effective weakening of the sea ice. In the uncoupled model this leads to an Arctic sea ice volume increase of about 10–20% after an accumulation period of approximately 20–30 years. In the coupled model, no such increase is found. Rather, the stochastic perturbations lead to a spatial redistribution of the Arctic sea ice thickness field. A mechanism involving a slightly negative atmospheric feedback is proposed that can explain the different responses in the coupled and uncoupled system. Changes in integrated Antarctic sea ice quantities caused by the stochastic parametrization are generally small, as memory is lost during the melting season because of an almost complete loss of sea ice. However, stochastic sea ice perturbations affect regional sea ice characteristics in the Southern Hemisphere, both in the uncoupled and coupled model. Remote impacts of the stochastic sea ice parametrization on the mean climate of non-polar regions were found to be small. PMID:24842027

Association between mean and interannual equatorial Indian Ocean subsurface temperature bias in a coupled model

NASA Astrophysics Data System (ADS)

Srinivas, G.; Chowdary, Jasti S.; Gnanaseelan, C.; Prasad, K. V. S. R.; Karmakar, Ananya; Parekh, Anant

2018-03-01

In the present study the association between mean and interannual subsurface temperature bias over the equatorial Indian Ocean (EIO) is investigated during boreal summer (June through September; JJAS) in the National Centers for Environmental Prediction (NCEP) Climate Forecast System (CFSv2) hindcast. Anomalously high subsurface warm bias (greater than 3 °C) over the eastern EIO (EEIO) region is noted in CFSv2 during summer, which is higher compared to other parts of the tropical Indian Ocean. Prominent eastward current bias in the upper 100 m over the EIO region induced by anomalous westerly winds is primarily responsible for subsurface temperature bias. The eastward currents transport warm water to the EEIO and is pushed down to subsurface due to downwelling. Thus biases in both horizontal and vertical currents over the EIO region support subsurface warm bias. The evolution of systematic subsurface warm bias in the model shows strong interannual variability. These maximum subsurface warming episodes over the EEIO are mainly associated with La Niña like forcing. Strong convergence of low level winds over the EEIO and Maritime continent enhanced the westerly wind bias over the EIO during maximum warming years. This low level convergence of wind is induced by the bias in the gradient in the mean sea level pressure with positive bias over western EIO and negative bias over EEIO and parts of western Pacific. Consequently, changes in the atmospheric circulation associated with La Niña like conditions affected the ocean dynamics by modulating the current bias thereby enhancing the subsurface warm bias over the EEIO. It is identified that EEIO subsurface warming is stronger when La Niña co-occurred with negative Indian Ocean Dipole events as compared to La Niña only years in the model. Ocean general circulation model (OGCM) experiments forced with CFSv2 winds clearly support our hypothesis that ocean dynamics influenced by westerly winds bias is primarily responsible for the strong subsurface warm bias over the EEIO. This study advocates the importance of understanding the ability of the models in representing the large scale air-sea interactions over the tropics and their impact on ocean biases for better monsoon forecast.

Improved management of winter operations to limit subsurface contamination with degradable deicing chemicals in cold regions.

PubMed

French, Helen K; van der Zee, Sjoerd E A T M

2014-01-01

This paper gives an overview of management considerations required for better control of deicing chemicals in the unsaturated zone at sites with winter maintenance operations in cold regions. Degradable organic deicing chemicals are the main focus. The importance of the heterogeneity of both the infiltration process, due to frozen ground and snow melt including the contact between the melting snow cover and the soil, and unsaturated flow is emphasised. In this paper, the applicability of geophysical methods for characterising soil heterogeneity is considered, aimed at modelling and monitoring changes in contamination. To deal with heterogeneity, a stochastic modelling framework may be appropriate, emphasizing the more robust spatial and temporal moments. Examples of a combination of different field techniques for measuring subsoil properties and monitoring contaminants and integration through transport modelling are provided by the SoilCAM project and previous work. Commonly, the results of flow and contaminant fate modelling are quite detailed and complex and require post-processing before communication and advising stakeholders. The managers' perspectives with respect to monitoring strategies and challenges still unresolved have been analysed with basis in experience with research collaboration with one of the case study sites, Oslo airport, Gardermoen, Norway. Both scientific challenges of monitoring subsoil contaminants in cold regions and the effective interaction between investigators and management are illustrated.

Small County: Development of a Virtual Environment for Instruction in Geological Characterization of Petroleum Reservoirs

NASA Astrophysics Data System (ADS)

Banz, B.; Bohling, G.; Doveton, J.

2008-12-01

Traditional programs of geological education continue to be focused primarily on the evaluation of surface or near-surface geology accessed at outcrops and shallow boreholes. However, most students who graduate to careers in geology work almost entirely on subsurface problems, interpreting drilling records and petrophysical logs from exploration and production wells. Thus, college graduates commonly find themselves ill-prepared when they enter the petroleum industry and require specialized training in drilling and petrophysical log interpretation. To aid in this training process, we are developing an environment for interactive instruction in the geological aspects of petroleum reservoir characterization employing a virtual subsurface closely reflecting the geology of the US mid-continent, in the fictional setting of Small County, Kansas. Stochastic simulation techniques are used to generate the subsurface characteristics, including the overall geological structure, distributions of facies, porosity, and fluid saturations, and petrophysical logs. The student then explores this subsurface by siting exploratory wells and examining drilling and petrophysical log records obtained from those wells. We are developing the application using the Eclipse Rich Client Platform, which allows for the rapid development of a platform-agnostic application while providing an immersive graphical interface. The application provides an array of views to enable relevant data display and student interaction. One such view is an interactive map of the county allowing the student to view the locations of existing well bores and select pertinent data overlays such as a contour map of the elevation of an interesting interval. Additionally, from this view a student may choose the site of a new well. Another view emulates a drilling log, complete with drilling rate plot and iconic representation of examined drill cuttings. From here, students are directed to stipulate subsurface lithology and interval tops as they progress through the drilling operation. Once the interpretation process is complete, the student is guided through an exercise emulating a drill stem test and then is prompted to decide on perforation intervals. The application provides a graphical framework by which the student is guided through well site selection, drilling data interpretation, and well completion or dry-hole abandonment, creating a tight feedback loop by which the student gains an over-arching view of drilling logistics and the subsurface data evaluation process.

Chemical event chain model of coupled genetic oscillators.

PubMed

Jörg, David J; Morelli, Luis G; Jülicher, Frank

2018-03-01

We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events involved in gene regulation and expression are represented as sequences of Poisson processes. We characterize steady states by their frequency, their quality factor, and their synchrony by the oscillator cross correlation. The steady state is determined by coupling and exhibits stochastic transitions between different modes. The interplay of stochasticity and nonlinearity leads to isolated regions in parameter space in which the coupled system works best as a biological pacemaker. Key features of the stochastic oscillations can be captured by an effective model for phase oscillators that are coupled by signals with distributed delays.

Chemical event chain model of coupled genetic oscillators

NASA Astrophysics Data System (ADS)

Jörg, David J.; Morelli, Luis G.; Jülicher, Frank

2018-03-01

We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events involved in gene regulation and expression are represented as sequences of Poisson processes. We characterize steady states by their frequency, their quality factor, and their synchrony by the oscillator cross correlation. The steady state is determined by coupling and exhibits stochastic transitions between different modes. The interplay of stochasticity and nonlinearity leads to isolated regions in parameter space in which the coupled system works best as a biological pacemaker. Key features of the stochastic oscillations can be captured by an effective model for phase oscillators that are coupled by signals with distributed delays.

Doubly stochastic Poisson process models for precipitation at fine time-scales

NASA Astrophysics Data System (ADS)

Ramesh, Nadarajah I.; Onof, Christian; Xie, Dichao

2012-09-01

This paper considers a class of stochastic point process models, based on doubly stochastic Poisson processes, in the modelling of rainfall. We examine the application of this class of models, a neglected alternative to the widely-known Poisson cluster models, in the analysis of fine time-scale rainfall intensity. These models are mainly used to analyse tipping-bucket raingauge data from a single site but an extension to multiple sites is illustrated which reveals the potential of this class of models to study the temporal and spatial variability of precipitation at fine time-scales.

Stochastic modelling of intermittency.

PubMed

Stemler, Thomas; Werner, Johannes P; Benner, Hartmut; Just, Wolfram

2010-01-13

Recently, methods have been developed to model low-dimensional chaotic systems in terms of stochastic differential equations. We tested such methods in an electronic circuit experiment. We aimed to obtain reliable drift and diffusion coefficients even without a pronounced time-scale separation of the chaotic dynamics. By comparing the analytical solutions of the corresponding Fokker-Planck equation with experimental data, we show here that crisis-induced intermittency can be described in terms of a stochastic model which is dominated by state-space-dependent diffusion. Further on, we demonstrate and discuss some limits of these modelling approaches using numerical simulations. This enables us to state a criterion that can be used to decide whether a stochastic model will capture the essential features of a given time series. This journal is © 2010 The Royal Society

Low Frequency Predictive Skill Despite Structural Instability and Model Error

DTIC Science & Technology

2014-09-30

Majda, based on earlier theoretical work. 1. Dynamic Stochastic Superresolution of sparseley observed turbulent systems M. Branicki (Post doc...of numerical models. Here, we introduce and study a suite of general Dynamic Stochastic Superresolution (DSS) algorithms and show that, by...resolving subgridscale turbulence through Dynamic Stochastic Superresolution utilizing aliased grids is a potential breakthrough for practical online

Nontrivial periodic solution of a stochastic non-autonomous SISV epidemic model

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing; Shi, Ningzhong; Hayat, Tasawar; Alsaedi, Ahmed

2016-11-01

In this paper, we consider a stochastic non-autonomous SISV epidemic model. For the non-autonomous periodic system, firstly, we get the threshold of the system which determines whether the epidemic occurs or not. Then in the case of persistence, we show that there exists at least one nontrivial positive periodic solution of the stochastic system.

Appropriate Domain Size for Groundwater Flow Modeling with a Discrete Fracture Network Model.

PubMed

Ji, Sung-Hoon; Koh, Yong-Kwon

2017-01-01

When a discrete fracture network (DFN) is constructed from statistical conceptualization, uncertainty in simulating the hydraulic characteristics of a fracture network can arise due to the domain size. In this study, the appropriate domain size, where less significant uncertainty in the stochastic DFN model is expected, was suggested for the Korea Atomic Energy Research Institute Underground Research Tunnel (KURT) site. The stochastic DFN model for the site was established, and the appropriate domain size was determined with the density of the percolating cluster and the percolation probability using the stochastically generated DFNs for various domain sizes. The applicability of the appropriate domain size to our study site was evaluated by comparing the statistical properties of stochastically generated fractures of varying domain sizes and estimating the uncertainty in the equivalent permeability of the generated DFNs. Our results show that the uncertainty of the stochastic DFN model is acceptable when the modeling domain is larger than the determined appropriate domain size, and the appropriate domain size concept is applicable to our study site. © 2016, National Ground Water Association.

A coupled stochastic rainfall-evapotranspiration model for hydrological impact analysis

NASA Astrophysics Data System (ADS)

Pham, Minh Tu; Vernieuwe, Hilde; De Baets, Bernard; Verhoest, Niko E. C.

2018-02-01

A hydrological impact analysis concerns the study of the consequences of certain scenarios on one or more variables or fluxes in the hydrological cycle. In such an exercise, discharge is often considered, as floods originating from extremely high discharges often cause damage. Investigating the impact of extreme discharges generally requires long time series of precipitation and evapotranspiration to be used to force a rainfall-runoff model. However, such kinds of data may not be available and one should resort to stochastically generated time series, even though the impact of using such data on the overall discharge, and especially on the extreme discharge events, is not well studied. In this paper, stochastically generated rainfall and corresponding evapotranspiration time series, generated by means of vine copulas, are used to force a simple conceptual hydrological model. The results obtained are comparable to the modelled discharge using observed forcing data. Yet, uncertainties in the modelled discharge increase with an increasing number of stochastically generated time series used. Notwithstanding this finding, it can be concluded that using a coupled stochastic rainfall-evapotranspiration model has great potential for hydrological impact analysis.

Modeling Phosphorus Losses through Surface Runoff and Subsurface Drainage Using ICECREAM.

PubMed

Qi, Hongkai; Qi, Zhiming; Zhang, T Q; Tan, C S; Sadhukhan, Debasis

2018-03-01

Modeling soil phosphorus (P) losses by surface and subsurface flow pathways is essential in developing successful strategies for P pollution control. We used the ICECREAM model to simultaneously simulate P losses in surface and subsurface flow, as well as to assess effectiveness of field practices in reducing P losses. Monitoring data from a mineral-P-fertilized clay loam field in southwestern Ontario, Canada, were used for calibration and validation. After careful adjustment of model parameters, ICECREAM was shown to satisfactorily simulate all major processes of surface and subsurface P losses. When the calibrated model was used to assess tillage and fertilizer management scenarios, results point to a 10% reduction in total P losses by shifting autumn tillage to spring, and a 25.4% reduction in total P losses by injecting fertilizer rather than broadcasting. Although the ICECREAM model was effective in simulating surface and subsurface P losses when thoroughly calibrated, further testing is needed to confirm these results with manure P application. As illustrated here, successful use of simulation models requires careful verification of model routines and comprehensive calibration to ensure that site-specific processes are accurately represented. Copyright © by the American Society of Agronomy, Crop Science Society of America, and Soil Science Society of America, Inc.

Stochastic simulations on a model of circadian rhythm generation.

PubMed

Miura, Shigehiro; Shimokawa, Tetsuya; Nomura, Taishin

2008-01-01

Biological phenomena are often modeled by differential equations, where states of a model system are described by continuous real values. When we consider concentrations of molecules as dynamical variables for a set of biochemical reactions, we implicitly assume that numbers of the molecules are large enough so that their changes can be regarded as continuous and they are described deterministically. However, for a system with small numbers of molecules, changes in their numbers are apparently discrete and molecular noises become significant. In such cases, models with deterministic differential equations may be inappropriate, and the reactions must be described by stochastic equations. In this study, we focus a clock gene expression for a circadian rhythm generation, which is known as a system involving small numbers of molecules. Thus it is appropriate for the system to be modeled by stochastic equations and analyzed by methodologies of stochastic simulations. The interlocked feedback model proposed by Ueda et al. as a set of deterministic ordinary differential equations provides a basis of our analyses. We apply two stochastic simulation methods, namely Gillespie's direct method and the stochastic differential equation method also by Gillespie, to the interlocked feedback model. To this end, we first reformulated the original differential equations back to elementary chemical reactions. With those reactions, we simulate and analyze the dynamics of the model using two methods in order to compare them with the dynamics obtained from the original deterministic model and to characterize dynamics how they depend on the simulation methodologies.

A comparison between modeled and measured permafrost temperatures at Ritigraben borehole, Switzerland

NASA Astrophysics Data System (ADS)

Mitterer-Hoinkes, Susanna; Lehning, Michael; Phillips, Marcia; Sailer, Rudolf

2013-04-01

The area-wide distribution of permafrost is sparsely known in mountainous terrain (e.g. Alps). Permafrost monitoring can only be based on point or small scale measurements such as boreholes, active rock glaciers, BTS measurements or geophysical measurements. To get a better understanding of permafrost distribution, it is necessary to focus on modeling permafrost temperatures and permafrost distribution patterns. A lot of effort on these topics has been already expended using different kinds of models. In this study, the evolution of subsurface temperatures over successive years has been modeled at the location Ritigraben borehole (Mattertal, Switzerland) by using the one-dimensional snow cover model SNOWPACK. The model needs meteorological input and in our case information on subsurface properties. We used meteorological input variables of the automatic weather station Ritigraben (2630 m) in combination with the automatic weather station Saas Seetal (2480 m). Meteorological data between 2006 and 2011 on an hourly basis were used to drive the model. As former studies showed, the snow amount and the snow cover duration have a great influence on the thermal regime. Low snow heights allow for deeper penetration of low winter temperatures into the ground, strong winters with a high amount of snow attenuate this effect. In addition, variations in subsurface conditions highly influence the temperature regime. Therefore, we conducted sensitivity runs by defining a series of different subsurface properties. The modeled subsurface temperature profiles of Ritigraben were then compared to the measured temperatures in the Ritigraben borehole. This allows a validation of the influence of subsurface properties on the temperature regime. As expected, the influence of the snow cover is stronger than the influence of sub-surface material properties, which are significant, however. The validation presented here serves to prepare a larger spatial simulation with the complex hydro-meteorological 3-dimensional model Alpine 3D, which is based on a distributed application of SNOWPACK.

Stochastic Model of Fracture Frequency Heterogeneity in a Welded Tuff EGS reservoir, Snake River Plain, Idaho, USA

NASA Astrophysics Data System (ADS)

Moody, A.; Fairley, J. P., Jr.

2014-12-01

In light of recent advancements in reservoir enhancement and injection tests at active geothermal fields, there is interest in investigating the geothermal potential of widespread subsurface welded tuffs related to caldera collapse on the Snake River Plain (SRP). Before considering stimulation strategies, simulating heat extraction from the reservoir under in-situ fracture geometries will give a first-order estimation of extractable heat. With only limited deep boreholes drilled on the SRP, few analyses of the bulk hydrologic properties of the tuffs exist. Acknowledging the importance of the spatial heterogeneity of fractures to the permeability and injectivity of reservoirs hosted in impermeable volcanic units, we present fracture distributions from ICDP hole 5036-2A drilled as a part of Project HOTSPOT. The core documents more than 1200 m of largely homogeneous densely welded tuff hosting an isothermal warm-water reservoir at ~60˚ C. Multiple realizations of a hypothetical reservoir are created using sequential indicator algorithms that honor the observed vertical fracture frequency statistics. Results help form criteria for producing geothermal energy from the SRP.

Helioseismic Holography of Simulated Sunspots: dependence of the travel time on magnetic field strength and Wilson depression

PubMed Central

Felipe, T.; Braun, D. C.; Birch, A. C.

2018-01-01

Improving methods for determining the subsurface structure of sunspots from their seismic signature requires a better understanding of the interaction of waves with magnetic field concentrations. We aim to quantify the impact of changes in the internal structure of sunspots on local helioseismic signals. We have numerically simulated the propagation of a stochastic wave field through sunspot models with different properties, accounting for changes in the Wilson depression between 250 and 550 km and in the photospheric umbral magnetic field between 1500 and 3500 G. The results show that travel-time shifts at frequencies above approximately 3.50 mHz (depending on the phase-speed filter) are insensitive to the magnetic field strength. The travel time of these waves is determined exclusively by the Wilson depression and sound-speed perturbation. The travel time of waves with lower frequencies is affected by the direct effect of the magnetic field, although photospheric field strengths below 1500 G do not leave a significant trace on the travel-time measurements. These results could potentially be used to develop simplified travel-time inversion methods. PMID:29670298

Helioseismic Holography of Simulated Sunspots: dependence of the travel time on magnetic field strength and Wilson depression.

PubMed

Felipe, T; Braun, D C; Birch, A C

2017-01-01

Improving methods for determining the subsurface structure of sunspots from their seismic signature requires a better understanding of the interaction of waves with magnetic field concentrations. We aim to quantify the impact of changes in the internal structure of sunspots on local helioseismic signals. We have numerically simulated the propagation of a stochastic wave field through sunspot models with different properties, accounting for changes in the Wilson depression between 250 and 550 km and in the photospheric umbral magnetic field between 1500 and 3500 G. The results show that travel-time shifts at frequencies above approximately 3.50 mHz (depending on the phase-speed filter) are insensitive to the magnetic field strength. The travel time of these waves is determined exclusively by the Wilson depression and sound-speed perturbation. The travel time of waves with lower frequencies is affected by the direct effect of the magnetic field, although photospheric field strengths below 1500 G do not leave a significant trace on the travel-time measurements. These results could potentially be used to develop simplified travel-time inversion methods.

Deterministic and stochastic models for middle east respiratory syndrome (MERS)

NASA Astrophysics Data System (ADS)

Suryani, Dessy Rizki; Zevika, Mona; Nuraini, Nuning

2018-03-01

World Health Organization (WHO) data stated that since September 2012, there were 1,733 cases of Middle East Respiratory Syndrome (MERS) with 628 death cases that occurred in 27 countries. MERS was first identified in Saudi Arabia in 2012 and the largest cases of MERS outside Saudi Arabia occurred in South Korea in 2015. MERS is a disease that attacks the respiratory system caused by infection of MERS-CoV. MERS-CoV transmission occurs directly through direct contact between infected individual with non-infected individual or indirectly through contaminated object by the free virus. Suspected, MERS can spread quickly because of the free virus in environment. Mathematical modeling is used to illustrate the transmission of MERS disease using deterministic model and stochastic model. Deterministic model is used to investigate the temporal dynamic from the system to analyze the steady state condition. Stochastic model approach using Continuous Time Markov Chain (CTMC) is used to predict the future states by using random variables. From the models that were built, the threshold value for deterministic models and stochastic models obtained in the same form and the probability of disease extinction can be computed by stochastic model. Simulations for both models using several of different parameters are shown, and the probability of disease extinction will be compared with several initial conditions.

Stochastic modeling of experimental chaotic time series.

PubMed

Stemler, Thomas; Werner, Johannes P; Benner, Hartmut; Just, Wolfram

2007-01-26

Methods developed recently to obtain stochastic models of low-dimensional chaotic systems are tested in electronic circuit experiments. We demonstrate that reliable drift and diffusion coefficients can be obtained even when no excessive time scale separation occurs. Crisis induced intermittent motion can be described in terms of a stochastic model showing tunneling which is dominated by state space dependent diffusion. Analytical solutions of the corresponding Fokker-Planck equation are in excellent agreement with experimental data.

PREDICTING SUBSURFACE CONTAMINANT TRANSPORT AND TRANSFORMATION: CONSIDERATIONS FOR MODEL SELECTION AND FIELD VALIDATION

EPA Science Inventory

Predicting subsurface contaminant transport and transformation requires mathematical models based on a variety of physical, chemical, and biological processes. The mathematical model is an attempt to quantitatively describe observed processes in order to permit systematic forecas...

Integrated surface/subsurface permafrost thermal hydrology: Model formulation and proof-of-concept simulations

DOE PAGES

Painter, Scott L.; Coon, Ethan T.; Atchley, Adam L.; ...

2016-08-11

The need to understand potential climate impacts and feedbacks in Arctic regions has prompted recent interest in modeling of permafrost dynamics in a warming climate. A new fine-scale integrated surface/subsurface thermal hydrology modeling capability is described and demonstrated in proof-of-concept simulations. The new modeling capability combines a surface energy balance model with recently developed three-dimensional subsurface thermal hydrology models and new models for nonisothermal surface water flows and snow distribution in the microtopography. Surface water flows are modeled using the diffusion wave equation extended to include energy transport and phase change of ponded water. Variation of snow depth in themore » microtopography, physically the result of wind scour, is also modeled heuristically with a diffusion wave equation. The multiple surface and subsurface processes are implemented by leveraging highly parallel community software. Fully integrated thermal hydrology simulations on the tilted open book catchment, an important test case for integrated surface/subsurface flow modeling, are presented. Fine-scale 100-year projections of the integrated permafrost thermal hydrological system on an ice wedge polygon at Barrow Alaska in a warming climate are also presented. Finally, these simulations demonstrate the feasibility of microtopography-resolving, process-rich simulations as a tool to help understand possible future evolution of the carbon-rich Arctic tundra in a warming climate.« less

Doubly stochastic Poisson processes in artificial neural learning.

PubMed

Card, H C

1998-01-01

This paper investigates neuron activation statistics in artificial neural networks employing stochastic arithmetic. It is shown that a doubly stochastic Poisson process is an appropriate model for the signals in these circuits.

Stochastic receding horizon control: application to an octopedal robot

NASA Astrophysics Data System (ADS)

Shah, Shridhar K.; Tanner, Herbert G.

2013-06-01

Miniature autonomous systems are being developed under ARL's Micro Autonomous Systems and Technology (MAST). These systems can only be fitted with a small-size processor, and their motion behavior is inherently uncertain due to manufacturing and platform-ground interactions. One way to capture this uncertainty is through a stochastic model. This paper deals with stochastic motion control design and implementation for MAST- specific eight-legged miniature crawling robots, which have been kinematically modeled as systems exhibiting the behavior of a Dubin's car with stochastic noise. The control design takes the form of stochastic receding horizon control, and is implemented on a Gumstix Overo Fire COM with 720 MHz processor and 512 MB RAM, weighing 5.5 g. The experimental results show the effectiveness of this control law for miniature autonomous systems perturbed by stochastic noise.

Expansion or extinction: deterministic and stochastic two-patch models with Allee effects.

PubMed

Kang, Yun; Lanchier, Nicolas

2011-06-01

We investigate the impact of Allee effect and dispersal on the long-term evolution of a population in a patchy environment. Our main focus is on whether a population already established in one patch either successfully invades an adjacent empty patch or undergoes a global extinction. Our study is based on the combination of analytical and numerical results for both a deterministic two-patch model and a stochastic counterpart. The deterministic model has either two, three or four attractors. The existence of a regime with exactly three attractors only appears when patches have distinct Allee thresholds. In the presence of weak dispersal, the analysis of the deterministic model shows that a high-density and a low-density populations can coexist at equilibrium in nearby patches, whereas the analysis of the stochastic model indicates that this equilibrium is metastable, thus leading after a large random time to either a global expansion or a global extinction. Up to some critical dispersal, increasing the intensity of the interactions leads to an increase of both the basin of attraction of the global extinction and the basin of attraction of the global expansion. Above this threshold, for both the deterministic and the stochastic models, the patches tend to synchronize as the intensity of the dispersal increases. This results in either a global expansion or a global extinction. For the deterministic model, there are only two attractors, while the stochastic model no longer exhibits a metastable behavior. In the presence of strong dispersal, the limiting behavior is entirely determined by the value of the Allee thresholds as the global population size in the deterministic and the stochastic models evolves as dictated by their single-patch counterparts. For all values of the dispersal parameter, Allee effects promote global extinction in terms of an expansion of the basin of attraction of the extinction equilibrium for the deterministic model and an increase of the probability of extinction for the stochastic model.

Multi-element least square HDMR methods and their applications for stochastic multiscale model reduction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiang, Lijian, E-mail: ljjiang@hnu.edu.cn; Li, Xinping, E-mail: exping@126.com

Stochastic multiscale modeling has become a necessary approach to quantify uncertainty and characterize multiscale phenomena for many practical problems such as flows in stochastic porous media. The numerical treatment of the stochastic multiscale models can be very challengeable as the existence of complex uncertainty and multiple physical scales in the models. To efficiently take care of the difficulty, we construct a computational reduced model. To this end, we propose a multi-element least square high-dimensional model representation (HDMR) method, through which the random domain is adaptively decomposed into a few subdomains, and a local least square HDMR is constructed in eachmore » subdomain. These local HDMRs are represented by a finite number of orthogonal basis functions defined in low-dimensional random spaces. The coefficients in the local HDMRs are determined using least square methods. We paste all the local HDMR approximations together to form a global HDMR approximation. To further reduce computational cost, we present a multi-element reduced least-square HDMR, which improves both efficiency and approximation accuracy in certain conditions. To effectively treat heterogeneity properties and multiscale features in the models, we integrate multiscale finite element methods with multi-element least-square HDMR for stochastic multiscale model reduction. This approach significantly reduces the original model's complexity in both the resolution of the physical space and the high-dimensional stochastic space. We analyze the proposed approach, and provide a set of numerical experiments to demonstrate the performance of the presented model reduction techniques. - Highlights: • Multi-element least square HDMR is proposed to treat stochastic models. • Random domain is adaptively decomposed into some subdomains to obtain adaptive multi-element HDMR. • Least-square reduced HDMR is proposed to enhance computation efficiency and approximation accuracy in certain conditions. • Integrating MsFEM and multi-element least square HDMR can significantly reduce computation complexity.« less

Dependence of Perpendicular Viscosity on Magnetic Fluctuations in a Stochastic Topology

NASA Astrophysics Data System (ADS)

Fridström, R.; Chapman, B. E.; Almagri, A. F.; Frassinetti, L.; Brunsell, P. R.; Nishizawa, T.; Sarff, J. S.

2018-06-01

In a magnetically confined plasma with a stochastic magnetic field, the dependence of the perpendicular viscosity on the magnetic fluctuation amplitude is measured for the first time. With a controlled, ˜ tenfold variation in the fluctuation amplitude, the viscosity increases ˜100 -fold, exhibiting the same fluctuation-amplitude-squared dependence as the predicted rate of stochastic field line diffusion. The absolute value of the viscosity is well predicted by a model based on momentum transport in a stochastic field, the first in-depth test of this model.

Simulating biological processes: stochastic physics from whole cells to colonies.

PubMed

Earnest, Tyler M; Cole, John A; Luthey-Schulten, Zaida

2018-05-01

The last few decades have revealed the living cell to be a crowded spatially heterogeneous space teeming with biomolecules whose concentrations and activities are governed by intrinsically random forces. It is from this randomness, however, that a vast array of precisely timed and intricately coordinated biological functions emerge that give rise to the complex forms and behaviors we see in the biosphere around us. This seemingly paradoxical nature of life has drawn the interest of an increasing number of physicists, and recent years have seen stochastic modeling grow into a major subdiscipline within biological physics. Here we review some of the major advances that have shaped our understanding of stochasticity in biology. We begin with some historical context, outlining a string of important experimental results that motivated the development of stochastic modeling. We then embark upon a fairly rigorous treatment of the simulation methods that are currently available for the treatment of stochastic biological models, with an eye toward comparing and contrasting their realms of applicability, and the care that must be taken when parameterizing them. Following that, we describe how stochasticity impacts several key biological functions, including transcription, translation, ribosome biogenesis, chromosome replication, and metabolism, before considering how the functions may be coupled into a comprehensive model of a 'minimal cell'. Finally, we close with our expectation for the future of the field, focusing on how mesoscopic stochastic methods may be augmented with atomic-scale molecular modeling approaches in order to understand life across a range of length and time scales.

Simulating biological processes: stochastic physics from whole cells to colonies

NASA Astrophysics Data System (ADS)

Earnest, Tyler M.; Cole, John A.; Luthey-Schulten, Zaida

2018-05-01

The last few decades have revealed the living cell to be a crowded spatially heterogeneous space teeming with biomolecules whose concentrations and activities are governed by intrinsically random forces. It is from this randomness, however, that a vast array of precisely timed and intricately coordinated biological functions emerge that give rise to the complex forms and behaviors we see in the biosphere around us. This seemingly paradoxical nature of life has drawn the interest of an increasing number of physicists, and recent years have seen stochastic modeling grow into a major subdiscipline within biological physics. Here we review some of the major advances that have shaped our understanding of stochasticity in biology. We begin with some historical context, outlining a string of important experimental results that motivated the development of stochastic modeling. We then embark upon a fairly rigorous treatment of the simulation methods that are currently available for the treatment of stochastic biological models, with an eye toward comparing and contrasting their realms of applicability, and the care that must be taken when parameterizing them. Following that, we describe how stochasticity impacts several key biological functions, including transcription, translation, ribosome biogenesis, chromosome replication, and metabolism, before considering how the functions may be coupled into a comprehensive model of a ‘minimal cell’. Finally, we close with our expectation for the future of the field, focusing on how mesoscopic stochastic methods may be augmented with atomic-scale molecular modeling approaches in order to understand life across a range of length and time scales.

Model-assisted probability of detection of flaws in aluminum blocks using polynomial chaos expansions

NASA Astrophysics Data System (ADS)

Du, Xiaosong; Leifsson, Leifur; Grandin, Robert; Meeker, William; Roberts, Ronald; Song, Jiming

2018-04-01

Probability of detection (POD) is widely used for measuring reliability of nondestructive testing (NDT) systems. Typically, POD is determined experimentally, while it can be enhanced by utilizing physics-based computational models in combination with model-assisted POD (MAPOD) methods. With the development of advanced physics-based methods, such as ultrasonic NDT testing, the empirical information, needed for POD methods, can be reduced. However, performing accurate numerical simulations can be prohibitively time-consuming, especially as part of stochastic analysis. In this work, stochastic surrogate models for computational physics-based measurement simulations are developed for cost savings of MAPOD methods while simultaneously ensuring sufficient accuracy. The stochastic surrogate is used to propagate the random input variables through the physics-based simulation model to obtain the joint probability distribution of the output. The POD curves are then generated based on those results. Here, the stochastic surrogates are constructed using non-intrusive polynomial chaos (NIPC) expansions. In particular, the NIPC methods used are the quadrature, ordinary least-squares (OLS), and least-angle regression sparse (LARS) techniques. The proposed approach is demonstrated on the ultrasonic testing simulation of a flat bottom hole flaw in an aluminum block. The results show that the stochastic surrogates have at least two orders of magnitude faster convergence on the statistics than direct Monte Carlo sampling (MCS). Moreover, the evaluation of the stochastic surrogate models is over three orders of magnitude faster than the underlying simulation model for this case, which is the UTSim2 model.

Modeling a SI epidemic with stochastic transmission: hyperbolic incidence rate.

PubMed

Christen, Alejandra; Maulén-Yañez, M Angélica; González-Olivares, Eduardo; Curé, Michel

2018-03-01

In this paper a stochastic susceptible-infectious (SI) epidemic model is analysed, which is based on the model proposed by Roberts and Saha (Appl Math Lett 12: 37-41, 1999), considering a hyperbolic type nonlinear incidence rate. Assuming the proportion of infected population varies with time, our new model is described by an ordinary differential equation, which is analogous to the equation that describes the double Allee effect. The limit of the solution of this equation (deterministic model) is found when time tends to infinity. Then, the asymptotic behaviour of a stochastic fluctuation due to the environmental variation in the coefficient of disease transmission is studied. Thus a stochastic differential equation (SDE) is obtained and the existence of a unique solution is proved. Moreover, the SDE is analysed through the associated Fokker-Planck equation to obtain the invariant measure when the proportion of the infected population reaches steady state. An explicit expression for invariant measure is found and we study some of its properties. The long time behaviour of deterministic and stochastic models are compared by simulations. According to our knowledge this incidence rate has not been previously used for this type of epidemic models.

Experimental Design for Stochastic Models of Nonlinear Signaling Pathways Using an Interval-Wise Linear Noise Approximation and State Estimation.

PubMed

Zimmer, Christoph

2016-01-01

Computational modeling is a key technique for analyzing models in systems biology. There are well established methods for the estimation of the kinetic parameters in models of ordinary differential equations (ODE). Experimental design techniques aim at devising experiments that maximize the information encoded in the data. For ODE models there are well established approaches for experimental design and even software tools. However, data from single cell experiments on signaling pathways in systems biology often shows intrinsic stochastic effects prompting the development of specialized methods. While simulation methods have been developed for decades and parameter estimation has been targeted for the last years, only very few articles focus on experimental design for stochastic models. The Fisher information matrix is the central measure for experimental design as it evaluates the information an experiment provides for parameter estimation. This article suggest an approach to calculate a Fisher information matrix for models containing intrinsic stochasticity and high nonlinearity. The approach makes use of a recently suggested multiple shooting for stochastic systems (MSS) objective function. The Fisher information matrix is calculated by evaluating pseudo data with the MSS technique. The performance of the approach is evaluated with simulation studies on an Immigration-Death, a Lotka-Volterra, and a Calcium oscillation model. The Calcium oscillation model is a particularly appropriate case study as it contains the challenges inherent to signaling pathways: high nonlinearity, intrinsic stochasticity, a qualitatively different behavior from an ODE solution, and partial observability. The computational speed of the MSS approach for the Fisher information matrix allows for an application in realistic size models.

Stochastic Parameterization: Toward a New View of Weather and Climate Models

DOE PAGES

Berner, Judith; Achatz, Ulrich; Batté, Lauriane; ...

2017-03-31

The last decade has seen the success of stochastic parameterizations in short-term, medium-range, and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to represent model inadequacy better and to improve the quantification of forecast uncertainty. Developed initially for numerical weather prediction, the inclusion of stochastic parameterizations not only provides better estimates of uncertainty, but it is also extremely promising for reducing long-standing climate biases and is relevant for determining the climate response to external forcing. This article highlights recent developments from different research groups that show that the stochastic representation of unresolved processes in the atmosphere, oceans,more » land surface, and cryosphere of comprehensive weather and climate models 1) gives rise to more reliable probabilistic forecasts of weather and climate and 2) reduces systematic model bias. We make a case that the use of mathematically stringent methods for the derivation of stochastic dynamic equations will lead to substantial improvements in our ability to accurately simulate weather and climate at all scales. Recent work in mathematics, statistical mechanics, and turbulence is reviewed; its relevance for the climate problem is demonstrated; and future research directions are outlined« less

Stochastic Parameterization: Toward a New View of Weather and Climate Models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berner, Judith; Achatz, Ulrich; Batté, Lauriane

The last decade has seen the success of stochastic parameterizations in short-term, medium-range, and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to represent model inadequacy better and to improve the quantification of forecast uncertainty. Developed initially for numerical weather prediction, the inclusion of stochastic parameterizations not only provides better estimates of uncertainty, but it is also extremely promising for reducing long-standing climate biases and is relevant for determining the climate response to external forcing. This article highlights recent developments from different research groups that show that the stochastic representation of unresolved processes in the atmosphere, oceans,more » land surface, and cryosphere of comprehensive weather and climate models 1) gives rise to more reliable probabilistic forecasts of weather and climate and 2) reduces systematic model bias. We make a case that the use of mathematically stringent methods for the derivation of stochastic dynamic equations will lead to substantial improvements in our ability to accurately simulate weather and climate at all scales. Recent work in mathematics, statistical mechanics, and turbulence is reviewed; its relevance for the climate problem is demonstrated; and future research directions are outlined« less

A stochastic hybrid systems based framework for modeling dependent failure processes

PubMed Central

Fan, Mengfei; Zeng, Zhiguo; Zio, Enrico; Kang, Rui; Chen, Ying

2017-01-01

In this paper, we develop a framework to model and analyze systems that are subject to dependent, competing degradation processes and random shocks. The degradation processes are described by stochastic differential equations, whereas transitions between the system discrete states are triggered by random shocks. The modeling is, then, based on Stochastic Hybrid Systems (SHS), whose state space is comprised of a continuous state determined by stochastic differential equations and a discrete state driven by stochastic transitions and reset maps. A set of differential equations are derived to characterize the conditional moments of the state variables. System reliability and its lower bounds are estimated from these conditional moments, using the First Order Second Moment (FOSM) method and Markov inequality, respectively. The developed framework is applied to model three dependent failure processes from literature and a comparison is made to Monte Carlo simulations. The results demonstrate that the developed framework is able to yield an accurate estimation of reliability with less computational costs compared to traditional Monte Carlo-based methods. PMID:28231313

A stochastic hybrid systems based framework for modeling dependent failure processes.

PubMed

Fan, Mengfei; Zeng, Zhiguo; Zio, Enrico; Kang, Rui; Chen, Ying

2017-01-01

In this paper, we develop a framework to model and analyze systems that are subject to dependent, competing degradation processes and random shocks. The degradation processes are described by stochastic differential equations, whereas transitions between the system discrete states are triggered by random shocks. The modeling is, then, based on Stochastic Hybrid Systems (SHS), whose state space is comprised of a continuous state determined by stochastic differential equations and a discrete state driven by stochastic transitions and reset maps. A set of differential equations are derived to characterize the conditional moments of the state variables. System reliability and its lower bounds are estimated from these conditional moments, using the First Order Second Moment (FOSM) method and Markov inequality, respectively. The developed framework is applied to model three dependent failure processes from literature and a comparison is made to Monte Carlo simulations. The results demonstrate that the developed framework is able to yield an accurate estimation of reliability with less computational costs compared to traditional Monte Carlo-based methods.

Stochastic simulation of human pulmonary blood flow and transit time frequency distribution based on anatomic and elasticity data.

PubMed

Huang, Wei; Shi, Jun; Yen, R T

2012-12-01

The objective of our study was to develop a computing program for computing the transit time frequency distributions of red blood cell in human pulmonary circulation, based on our anatomic and elasticity data of blood vessels in human lung. A stochastic simulation model was introduced to simulate blood flow in human pulmonary circulation. In the stochastic simulation model, the connectivity data of pulmonary blood vessels in human lung was converted into a probability matrix. Based on this model, the transit time of red blood cell in human pulmonary circulation and the output blood pressure were studied. Additionally, the stochastic simulation model can be used to predict the changes of blood flow in human pulmonary circulation with the advantage of the lower computing cost and the higher flexibility. In conclusion, a stochastic simulation approach was introduced to simulate the blood flow in the hierarchical structure of a pulmonary circulation system, and to calculate the transit time distributions and the blood pressure outputs.

Stochastic and Perturbed Parameter Representations of Model Uncertainty in Convection Parameterization

NASA Astrophysics Data System (ADS)

Christensen, H. M.; Moroz, I.; Palmer, T.

2015-12-01

It is now acknowledged that representing model uncertainty in atmospheric simulators is essential for the production of reliable probabilistic ensemble forecasts, and a number of different techniques have been proposed for this purpose. Stochastic convection parameterization schemes use random numbers to represent the difference between a deterministic parameterization scheme and the true atmosphere, accounting for the unresolved sub grid-scale variability associated with convective clouds. An alternative approach varies the values of poorly constrained physical parameters in the model to represent the uncertainty in these parameters. This study presents new perturbed parameter schemes for use in the European Centre for Medium Range Weather Forecasts (ECMWF) convection scheme. Two types of scheme are developed and implemented. Both schemes represent the joint uncertainty in four of the parameters in the convection parametrisation scheme, which was estimated using the Ensemble Prediction and Parameter Estimation System (EPPES). The first scheme developed is a fixed perturbed parameter scheme, where the values of uncertain parameters are changed between ensemble members, but held constant over the duration of the forecast. The second is a stochastically varying perturbed parameter scheme. The performance of these schemes was compared to the ECMWF operational stochastic scheme, Stochastically Perturbed Parametrisation Tendencies (SPPT), and to a model which does not represent uncertainty in convection. The skill of probabilistic forecasts made using the different models was evaluated. While the perturbed parameter schemes improve on the stochastic parametrisation in some regards, the SPPT scheme outperforms the perturbed parameter approaches when considering forecast variables that are particularly sensitive to convection. Overall, SPPT schemes are the most skilful representations of model uncertainty due to convection parametrisation. Reference: H. M. Christensen, I. M. Moroz, and T. N. Palmer, 2015: Stochastic and Perturbed Parameter Representations of Model Uncertainty in Convection Parameterization. J. Atmos. Sci., 72, 2525-2544.

Problems of Mathematical Finance by Stochastic Control Methods

NASA Astrophysics Data System (ADS)

Stettner, Łukasz

The purpose of this paper is to present main ideas of mathematics of finance using the stochastic control methods. There is an interplay between stochastic control and mathematics of finance. On the one hand stochastic control is a powerful tool to study financial problems. On the other hand financial applications have stimulated development in several research subareas of stochastic control in the last two decades. We start with pricing of financial derivatives and modeling of asset prices, studying the conditions for the absence of arbitrage. Then we consider pricing of defaultable contingent claims. Investments in bonds lead us to the term structure modeling problems. Special attention is devoted to historical static portfolio analysis called Markowitz theory. We also briefly sketch dynamic portfolio problems using viscosity solutions to Hamilton-Jacobi-Bellman equation, martingale-convex analysis method or stochastic maximum principle together with backward stochastic differential equation. Finally, long time portfolio analysis for both risk neutral and risk sensitive functionals is introduced.

Approach for computing 1D fracture density: application to fracture corridor characterization

NASA Astrophysics Data System (ADS)

Viseur, Sophie; Chatelée, Sebastien; Akriche, Clement; Lamarche, Juliette

2016-04-01

Fracture density is an important parameter for characterizing fractured reservoirs. Many stochastic simulation algorithms that generate fracture networks indeed rely on the determination of a fracture density on volumes (P30) to populate the reservoir zones with individual fracture surfaces. However, only 1D fracture density (P10) are available from subsurface data and it is then important to be able to accurately estimate this entity. In this paper, a novel approach is proposed to estimate fracture density from scan-line or well data. This method relies on regression, hypothesis testing and clustering techniques. The objective of the proposed approach is to highlight zones where fracture density are statistically very different or similar. This technique has been applied on both synthetic and real case studies. These studies concern fracture corridors, which are particular tectonic features that are generally difficult to characterize from subsurface data. These tectonic features are still not well known and studies must be conducted to better understand their internal spatial organization and variability. The presented synthetic cases aim at showing the ability of the approach to extract known features. The real case study illustrates how this approach allows the internal spatial organization of fracture corridors to be characterized.

Stochastic models of the Social Security trust funds.

PubMed

Burdick, Clark; Manchester, Joyce

Each year in March, the Board of Trustees of the Social Security trust funds reports on the current and projected financial condition of the Social Security programs. Those programs, which pay monthly benefits to retired workers and their families, to the survivors of deceased workers, and to disabled workers and their families, are financed through the Old-Age, Survivors, and Disability Insurance (OASDI) Trust Funds. In their 2003 report, the Trustees present, for the first time, results from a stochastic model of the combined OASDI trust funds. Stochastic modeling is an important new tool for Social Security policy analysis and offers the promise of valuable new insights into the financial status of the OASDI trust funds and the effects of policy changes. The results presented in this article demonstrate that several stochastic models deliver broadly consistent results even though they use very different approaches and assumptions. However, they also show that the variation in trust fund outcomes differs as the approach and assumptions are varied. Which approach and assumptions are best suited for Social Security policy analysis remains an open question. Further research is needed before the promise of stochastic modeling is fully realized. For example, neither parameter uncertainty nor variability in ultimate assumption values is recognized explicitly in the analyses. Despite this caveat, stochastic modeling results are already shedding new light on the range and distribution of trust fund outcomes that might occur in the future.

Quality control of 3D Geological Models using an Attention Model based on Gaze

NASA Astrophysics Data System (ADS)

Busschers, Freek S.; van Maanen, Peter-Paul; Brouwer, Anne-Marie

2014-05-01

The Geological Survey of the Netherlands (GSN) produces 3D stochastic geological models of the upper 50 meters of the Dutch subsurface. The voxel models are regarded essential in answering subsurface questions on, for example, aggregate resources, groundwater flow, land subsidence studies and the planning of large-scale infrastructural works such as tunnels. GeoTOP is the most recent and detailed generation of 3D voxel models. This model describes 3D lithological variability up to a depth of 50 m using voxels of 100*100*0.5m. Due to the expected increase in data-flow, model output and user demands, the development of (semi-)automated quality control systems is getting more important in the near future. Besides numerical control systems, capturing model errors as seen from the expert geologist viewpoint is of increasing interest. We envision the use of eye gaze to support and speed up detection of errors in the geological voxel models. As a first step in this direction we explore gaze behavior of 12 geological experts from the GSN during quality control of part of the GeoTOP 3D geological model using an eye-tracker. Gaze is used as input of an attention model that results in 'attended areas' for each individual examined image of the GeoTOP model and each individual expert. We compared these attended areas to errors as marked by the experts using a mouse. Results show that: 1) attended areas as determined from experts' gaze data largely match with GeoTOP errors as indicated by the experts using a mouse, and 2) a substantial part of the match can be reached using only gaze data from the first few seconds of the time geologists spend to search for errors. These results open up the possibility of faster GeoTOP model control using gaze if geologists accept a small decrease of error detection accuracy. Attention data may also be used to make independent comparisons between different geologists varying in focus and expertise. This would facilitate a more effective use of experts in specific different projects or areas. Part of such a procedure could be to confront geological experts with their own results, allowing possible training steps in order to improve their geological expertise and eventually improve the GeoTop model. Besides the directions as indicated above, future research should focus on concrete implementation of facilitating and optimizing error detection in present and future 3D voxel models that are commonly characterized by very large amounts of data.

Amerciamysis bahia Stochastic Matrix Population Model for Laboratory Populations

EPA Science Inventory

The population model described here is a stochastic, density-independent matrix model for integrating the effects of toxicants on survival and reproduction of the marine invertebrate, Americamysis bahia. The model was constructed using Microsoft® Excel 2003. The focus of the mode...

Mapping of the stochastic Lotka-Volterra model to models of population genetics and game theory

NASA Astrophysics Data System (ADS)

Constable, George W. A.; McKane, Alan J.

2017-08-01

The relationship between the M -species stochastic Lotka-Volterra competition (SLVC) model and the M -allele Moran model of population genetics is explored via timescale separation arguments. When selection for species is weak and the population size is large but finite, precise conditions are determined for the stochastic dynamics of the SLVC model to be mappable to the neutral Moran model, the Moran model with frequency-independent selection, and the Moran model with frequency-dependent selection (equivalently a game-theoretic formulation of the Moran model). We demonstrate how these mappings can be used to calculate extinction probabilities and the times until a species' extinction in the SLVC model.

Integrated surface-subsurface model to investigate the role of groundwater in headwater catchment runoff generation: A minimalist approach to parameterisation

NASA Astrophysics Data System (ADS)

Ala-aho, Pertti; Soulsby, Chris; Wang, Hailong; Tetzlaff, Doerthe

2017-04-01

Understanding the role of groundwater for runoff generation in headwater catchments is a challenge in hydrology, particularly so in data-scarce areas. Fully-integrated surface-subsurface modelling has shown potential in increasing process understanding for runoff generation, but high data requirements and difficulties in model calibration are typically assumed to preclude their use in catchment-scale studies. We used a fully integrated surface-subsurface hydrological simulator to enhance groundwater-related process understanding in a headwater catchment with a rich background in empirical data. To set up the model we used minimal data that could be reasonably expected to exist for any experimental catchment. A novel aspect of our approach was in using simplified model parameterisation and including parameters from all model domains (surface, subsurface, evapotranspiration) in automated model calibration. Calibration aimed not only to improve model fit, but also to test the information content of the observations (streamflow, remotely sensed evapotranspiration, median groundwater level) used in calibration objective functions. We identified sensitive parameters in all model domains (subsurface, surface, evapotranspiration), demonstrating that model calibration should be inclusive of parameters from these different model domains. Incorporating groundwater data in calibration objectives improved the model fit for groundwater levels, but simulations did not reproduce well the remotely sensed evapotranspiration time series even after calibration. Spatially explicit model output improved our understanding of how groundwater functions in maintaining streamflow generation primarily via saturation excess overland flow. Steady groundwater inputs created saturated conditions in the valley bottom riparian peatlands, leading to overland flow even during dry periods. Groundwater on the hillslopes was more dynamic in its response to rainfall, acting to expand the saturated area extent and thereby promoting saturation excess overland flow during rainstorms. Our work shows the potential of using integrated surface-subsurface modelling alongside with rigorous model calibration to better understand and visualise the role of groundwater in runoff generation even with limited datasets.

Maximum principle for a stochastic delayed system involving terminal state constraints.

PubMed

Wen, Jiaqiang; Shi, Yufeng

2017-01-01

We investigate a stochastic optimal control problem where the controlled system is depicted as a stochastic differential delayed equation; however, at the terminal time, the state is constrained in a convex set. We firstly introduce an equivalent backward delayed system depicted as a time-delayed backward stochastic differential equation. Then a stochastic maximum principle is obtained by virtue of Ekeland's variational principle. Finally, applications to a state constrained stochastic delayed linear-quadratic control model and a production-consumption choice problem are studied to illustrate the main obtained result.

Threshold for extinction and survival in stochastic tumor immune system

NASA Astrophysics Data System (ADS)

Li, Dongxi; Cheng, Fangjuan

2017-10-01

This paper mainly investigates the stochastic character of tumor growth and extinction in the presence of immune response of a host organism. Firstly, the mathematical model describing the interaction and competition between the tumor cells and immune system is established based on the Michaelis-Menten enzyme kinetics. Then, the threshold conditions for extinction, weak persistence and stochastic persistence of tumor cells are derived by the rigorous theoretical proofs. Finally, stochastic simulation are taken to substantiate and illustrate the conclusion we have derived. The modeling results will be beneficial to understand to concept of immunoediting, and develop the cancer immunotherapy. Besides, our simple theoretical model can help to obtain new insight into the complexity of tumor growth.

Digital hardware implementation of a stochastic two-dimensional neuron model.

PubMed

Grassia, F; Kohno, T; Levi, T

2016-11-01

This study explores the feasibility of stochastic neuron simulation in digital systems (FPGA), which realizes an implementation of a two-dimensional neuron model. The stochasticity is added by a source of current noise in the silicon neuron using an Ornstein-Uhlenbeck process. This approach uses digital computation to emulate individual neuron behavior using fixed point arithmetic operation. The neuron model's computations are performed in arithmetic pipelines. It was designed in VHDL language and simulated prior to mapping in the FPGA. The experimental results confirmed the validity of the developed stochastic FPGA implementation, which makes the implementation of the silicon neuron more biologically plausible for future hybrid experiments. Copyright © 2017 Elsevier Ltd. All rights reserved.

A New Methodology for Open Pit Slope Design in Karst-Prone Ground Conditions Based on Integrated Stochastic-Limit Equilibrium Analysis

NASA Astrophysics Data System (ADS)

Zhang, Ke; Cao, Ping; Ma, Guowei; Fan, Wenchen; Meng, Jingjing; Li, Kaihui

2016-07-01

Using the Chengmenshan Copper Mine as a case study, a new methodology for open pit slope design in karst-prone ground conditions is presented based on integrated stochastic-limit equilibrium analysis. The numerical modeling and optimization design procedure contain a collection of drill core data, karst cave stochastic model generation, SLIDE simulation and bisection method optimization. Borehole investigations are performed, and the statistical result shows that the length of the karst cave fits a negative exponential distribution model, but the length of carbonatite does not exactly follow any standard distribution. The inverse transform method and acceptance-rejection method are used to reproduce the length of the karst cave and carbonatite, respectively. A code for karst cave stochastic model generation, named KCSMG, is developed. The stability of the rock slope with the karst cave stochastic model is analyzed by combining the KCSMG code and the SLIDE program. This approach is then applied to study the effect of the karst cave on the stability of the open pit slope, and a procedure to optimize the open pit slope angle is presented.

Allocating risk capital for a brownfields redevelopment project under hydrogeological and financial uncertainty.

PubMed

Yu, Soonyoung; Unger, Andre J A; Parker, Beth; Kim, Taehee

2012-06-15

In this study, we defined risk capital as the contingency fee or insurance premium that a brownfields redeveloper needs to set aside from the sale of each house in case they need to repurchase it at a later date because the indoor air has been detrimentally affected by subsurface contamination. The likelihood that indoor air concentrations will exceed a regulatory level subject to subsurface heterogeneity and source zone location uncertainty is simulated by a physics-based hydrogeological model using Monte Carlo realizations, yielding the probability of failure. The cost of failure is the future value of the house indexed to the stochastic US National Housing index. The risk capital is essentially the probability of failure times the cost of failure with a surcharge to compensate the developer against hydrogeological and financial uncertainty, with the surcharge acting as safety loading reflecting the developers' level of risk aversion. We review five methodologies taken from the actuarial and financial literature to price the risk capital for a highly stylized brownfield redevelopment project, with each method specifically adapted to accommodate our notion of the probability of failure. The objective of this paper is to develop an actuarially consistent approach for combining the hydrogeological and financial uncertainty into a contingency fee that the brownfields developer should reserve (i.e. the risk capital) in order to hedge their risk exposure during the project. Results indicate that the price of the risk capital is much more sensitive to hydrogeological rather than financial uncertainty. We use the Capital Asset Pricing Model to estimate the risk-adjusted discount rate to depreciate all costs to present value for the brownfield redevelopment project. A key outcome of this work is that the presentation of our risk capital valuation methodology is sufficiently generalized for application to a wide variety of engineering projects. Copyright © 2012 Elsevier Ltd. All rights reserved.

Identification and stochastic control of helicopter dynamic modes

NASA Technical Reports Server (NTRS)

Molusis, J. A.; Bar-Shalom, Y.

1983-01-01

A general treatment of parameter identification and stochastic control for use on helicopter dynamic systems is presented. Rotor dynamic models, including specific applications to rotor blade flapping and the helicopter ground resonance problem are emphasized. Dynamic systems which are governed by periodic coefficients as well as constant coefficient models are addressed. The dynamic systems are modeled by linear state variable equations which are used in the identification and stochastic control formulation. The pure identification problem as well as the stochastic control problem which includes combined identification and control for dynamic systems is addressed. The stochastic control problem includes the effect of parameter uncertainty on the solution and the concept of learning and how this is affected by the control's duel effect. The identification formulation requires algorithms suitable for on line use and thus recursive identification algorithms are considered. The applications presented use the recursive extended kalman filter for parameter identification which has excellent convergence for systems without process noise.

Effect of sample volume on metastable zone width and induction time

NASA Astrophysics Data System (ADS)

Kubota, Noriaki

2012-04-01

The metastable zone width (MSZW) and the induction time, measured for a large sample (say>0.1 L) are reproducible and deterministic, while, for a small sample (say<1 mL), these values are irreproducible and stochastic. Such behaviors of MSZW and induction time were theoretically discussed both with stochastic and deterministic models. Equations for the distribution of stochastic MSZW and induction time were derived. The average values of stochastic MSZW and induction time both decreased with an increase in sample volume, while, the deterministic MSZW and induction time remained unchanged. Such different behaviors with variation in sample volume were explained in terms of detection sensitivity of crystallization events. The average values of MSZW and induction time in the stochastic model were compared with the deterministic MSZW and induction time, respectively. Literature data reported for paracetamol aqueous solution were explained theoretically with the presented models.

GillesPy: A Python Package for Stochastic Model Building and Simulation.

PubMed

Abel, John H; Drawert, Brian; Hellander, Andreas; Petzold, Linda R

2016-09-01

GillesPy is an open-source Python package for model construction and simulation of stochastic biochemical systems. GillesPy consists of a Python framework for model building and an interface to the StochKit2 suite of efficient simulation algorithms based on the Gillespie stochastic simulation algorithms (SSA). To enable intuitive model construction and seamless integration into the scientific Python stack, we present an easy to understand, action-oriented programming interface. Here, we describe the components of this package and provide a detailed example relevant to the computational biology community.

GillesPy: A Python Package for Stochastic Model Building and Simulation

PubMed Central

Abel, John H.; Drawert, Brian; Hellander, Andreas; Petzold, Linda R.

2017-01-01

GillesPy is an open-source Python package for model construction and simulation of stochastic biochemical systems. GillesPy consists of a Python framework for model building and an interface to the StochKit2 suite of efficient simulation algorithms based on the Gillespie stochastic simulation algorithms (SSA). To enable intuitive model construction and seamless integration into the scientific Python stack, we present an easy to understand, action-oriented programming interface. Here, we describe the components of this package and provide a detailed example relevant to the computational biology community. PMID:28630888

Dynamics of a stochastic cell-to-cell HIV-1 model with distributed delay

NASA Astrophysics Data System (ADS)

Ji, Chunyan; Liu, Qun; Jiang, Daqing

2018-02-01

In this paper, we consider a stochastic cell-to-cell HIV-1 model with distributed delay. Firstly, we show that there is a global positive solution of this model before exploring its long-time behavior. Then sufficient conditions for extinction of the disease are established. Moreover, we obtain sufficient conditions for the existence of an ergodic stationary distribution of the model by constructing a suitable stochastic Lyapunov function. The stationary distribution implies that the disease is persistent in the mean. Finally, we provide some numerical examples to illustrate theoretical results.

Let's Go Off the Grid: Subsurface Flow Modeling With Analytic Elements

NASA Astrophysics Data System (ADS)

Bakker, M.

2017-12-01

Subsurface flow modeling with analytic elements has the major advantage that no grid or time stepping are needed. Analytic element formulations exist for steady state and transient flow in layered aquifers and unsaturated flow in the vadose zone. Analytic element models are vector-based and consist of points, lines and curves that represent specific features in the subsurface. Recent advances allow for the simulation of partially penetrating wells and multi-aquifer wells, including skin effect and wellbore storage, horizontal wells of poly-line shape including skin effect, sharp changes in subsurface properties, and surface water features with leaky beds. Input files for analytic element models are simple, short and readable, and can easily be generated from, for example, GIS databases. Future plans include the incorporation of analytic element in parts of grid-based models where additional detail is needed. This presentation will give an overview of advanced flow features that can be modeled, many of which are implemented in free and open-source software.

A stochastic chemostat model with an inhibitor and noise independent of population sizes

NASA Astrophysics Data System (ADS)

Sun, Shulin; Zhang, Xiaolu

2018-02-01

In this paper, a stochastic chemostat model with an inhibitor is considered, here the inhibitor is input from an external source and two organisms in chemostat compete for a nutrient. Firstly, we show that the system has a unique global positive solution. Secondly, by constructing some suitable Lyapunov functions, we investigate that the average in time of the second moment of the solutions of the stochastic model is bounded for a relatively small noise. That is, the asymptotic behaviors of the stochastic system around the equilibrium points of the deterministic system are studied. However, the sufficient large noise can make the microorganisms become extinct with probability one, although the solutions to the original deterministic model may be persistent. Finally, the obtained analytical results are illustrated by computer simulations.

Dynamics of stochastic SEIS epidemic model with varying population size

NASA Astrophysics Data System (ADS)

Liu, Jiamin; Wei, Fengying

2016-12-01

We introduce the stochasticity into a deterministic model which has state variables susceptible-exposed-infected with varying population size in this paper. The infected individuals could return into susceptible compartment after recovering. We show that the stochastic model possesses a unique global solution under building up a suitable Lyapunov function and using generalized Itô's formula. The densities of the exposed and infected tend to extinction when some conditions are being valid. Moreover, the conditions of persistence to a global solution are derived when the parameters are subject to some simple criteria. The stochastic model admits a stationary distribution around the endemic equilibrium, which means that the disease will prevail. To check the validity of the main results, numerical simulations are demonstrated as end of this contribution.

Study on the threshold of a stochastic SIR epidemic model and its extensions

NASA Astrophysics Data System (ADS)

Zhao, Dianli

2016-09-01

This paper provides a simple but effective method for estimating the threshold of a class of the stochastic epidemic models by use of the nonnegative semimartingale convergence theorem. Firstly, the threshold R0SIR is obtained for the stochastic SIR model with a saturated incidence rate, whose value is below 1 or above 1 will completely determine the disease to go extinct or prevail for any size of the white noise. Besides, when R0SIR > 1 , the system is proved to be convergent in time mean. Then, the threshold of the stochastic SIVS models with or without saturated incidence rate are also established by the same method. Comparing with the previously-known literatures, the related results are improved, and the method is simpler than before.

Impacts of microtopographic snow-redistribution and lateral subsurface processeson hydrologic and thermal states in an Arctic polygonal ground ecosystem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bisht, Gautam; Riley, William J.; Wainwright, Haruko M.

Microtopographic features, such as polygonal ground, are characteristic sources of landscape heterogeneity in the Alaskan Arctic coastal plain. We analyze the effects of snow redistribution (SR) and lateral subsurface processes on hydrologic and thermal states at a polygonal tundra site near Barrow, Alaska. We extended the land model integrated in the ACME Earth System Model (ESM) to redistribute incoming snow by accounting for microtopography and incorporated subsurface lateral transport of water and energy (ALMv0-3D). Three 10-years long simulations were performed for a transect across polygonal tundra landscape at the Barrow Environmental Observatory in Alaska to isolate the impact of SRmore » and subsurface process representation. When SR was included, model results show a better agreement (higher R 2 with lower bias and RMSE) for the observed differences in snow depth between polygonal rims and centers. The model was also able to accurately reproduce observed soil temperature vertical profiles in the polygon rims and centers (overall bias, RMSE, and R 2 of 0.59°C, 1.82°C, and 0.99, respectively). The spatial heterogeneity of snow depth during the winter due to SR generated surface soil temperature heterogeneity that propagated in depth and time and led to ~10 cm shallower and ~5 cm deeper maximum annual thaw depths under the polygon rims and centers, respectively. Additionally, SR led to spatial heterogeneity in surface energy fluxes and soil moisture during the summer. Excluding lateral subsurface hydrologic and thermal processes led to small effects on mean states but an overestimation of spatial variability in soil moisture and soil temperature as subsurface liquid pressure and thermal gradients were artificially prevented from spatially dissipating over time. The effect of lateral subsurface processes on active layer depths was modest with mean absolute difference of ~3 cm. Finally, our integration of three-dimensional subsurface hydrologic and thermal subsurface dynamics in the ACME land model will facilitate a wide range of analyses heretofore impossible in an ESM context.« less

Impacts of microtopographic snow-redistribution and lateral subsurface processeson hydrologic and thermal states in an Arctic polygonal ground ecosystem

DOE PAGES

Bisht, Gautam; Riley, William J.; Wainwright, Haruko M.; ...

2018-01-08

Microtopographic features, such as polygonal ground, are characteristic sources of landscape heterogeneity in the Alaskan Arctic coastal plain. We analyze the effects of snow redistribution (SR) and lateral subsurface processes on hydrologic and thermal states at a polygonal tundra site near Barrow, Alaska. We extended the land model integrated in the ACME Earth System Model (ESM) to redistribute incoming snow by accounting for microtopography and incorporated subsurface lateral transport of water and energy (ALMv0-3D). Three 10-years long simulations were performed for a transect across polygonal tundra landscape at the Barrow Environmental Observatory in Alaska to isolate the impact of SRmore » and subsurface process representation. When SR was included, model results show a better agreement (higher R 2 with lower bias and RMSE) for the observed differences in snow depth between polygonal rims and centers. The model was also able to accurately reproduce observed soil temperature vertical profiles in the polygon rims and centers (overall bias, RMSE, and R 2 of 0.59°C, 1.82°C, and 0.99, respectively). The spatial heterogeneity of snow depth during the winter due to SR generated surface soil temperature heterogeneity that propagated in depth and time and led to ~10 cm shallower and ~5 cm deeper maximum annual thaw depths under the polygon rims and centers, respectively. Additionally, SR led to spatial heterogeneity in surface energy fluxes and soil moisture during the summer. Excluding lateral subsurface hydrologic and thermal processes led to small effects on mean states but an overestimation of spatial variability in soil moisture and soil temperature as subsurface liquid pressure and thermal gradients were artificially prevented from spatially dissipating over time. The effect of lateral subsurface processes on active layer depths was modest with mean absolute difference of ~3 cm. Finally, our integration of three-dimensional subsurface hydrologic and thermal subsurface dynamics in the ACME land model will facilitate a wide range of analyses heretofore impossible in an ESM context.« less

Role of demographic stochasticity in a speciation model with sexual reproduction

NASA Astrophysics Data System (ADS)

Lafuerza, Luis F.; McKane, Alan J.

2016-03-01

Recent theoretical studies have shown that demographic stochasticity can greatly increase the tendency of asexually reproducing phenotypically diverse organisms to spontaneously evolve into localized clusters, suggesting a simple mechanism for sympatric speciation. Here we study the role of demographic stochasticity in a model of competing organisms subject to assortative mating. We find that in models with sexual reproduction, noise can also lead to the formation of phenotypic clusters in parameter ranges where deterministic models would lead to a homogeneous distribution. In some cases, noise can have a sizable effect, rendering the deterministic modeling insufficient to understand the phenotypic distribution.

Stochastic Ordering Using the Latent Trait and the Sum Score in Polytomous IRT Models.

ERIC Educational Resources Information Center

Hemker, Bas T.; Sijtsma, Klaas; Molenaar, Ivo W.; Junker, Brian W.

1997-01-01

Stochastic ordering properties are investigated for a broad class of item response theory (IRT) models for which the monotone likelihood ratio does not hold. A taxonomy is given for nonparametric and parametric models for polytomous models based on the hierarchical relationship between the models. (SLD)

Stochastic analysis of future vehicle populations

DOT National Transportation Integrated Search

1979-05-01

The purpose of this study was to build a stochastic model of future vehicle populations. Such a model can be used to investigate the uncertainties inherent in Future Vehicle Populations. The model, which is called the Future Automobile Population Sto...

Evidence-based Controls for Epidemics Using Spatio-temporal Stochastic Model as a Bayesian Framwork

USDA-ARS?s Scientific Manuscript database

The control of highly infectious diseases of agricultural and plantation crops and livestock represents a key challenge in epidemiological and ecological modelling, with implemented control strategies often being controversial. Mathematical models, including the spatio-temporal stochastic models con...

On the impact of a refined stochastic model for airborne LiDAR measurements

NASA Astrophysics Data System (ADS)

Bolkas, Dimitrios; Fotopoulos, Georgia; Glennie, Craig

2016-09-01

Accurate topographic information is critical for a number of applications in science and engineering. In recent years, airborne light detection and ranging (LiDAR) has become a standard tool for acquiring high quality topographic information. The assessment of airborne LiDAR derived DEMs is typically based on (i) independent ground control points and (ii) forward error propagation utilizing the LiDAR geo-referencing equation. The latter approach is dependent on the stochastic model information of the LiDAR observation components. In this paper, the well-known statistical tool of variance component estimation (VCE) is implemented for a dataset in Houston, Texas, in order to refine the initial stochastic information. Simulations demonstrate the impact of stochastic-model refinement for two practical applications, namely coastal inundation mapping and surface displacement estimation. Results highlight scenarios where erroneous stochastic information is detrimental. Furthermore, the refined stochastic information provides insights on the effect of each LiDAR measurement in the airborne LiDAR error budget. The latter is important for targeting future advancements in order to improve point cloud accuracy.

A kinetic theory for age-structured stochastic birth-death processes

NASA Astrophysics Data System (ADS)

Chou, Tom; Greenman, Chris

Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but they are structurally unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Conversely, current theories that include size-dependent population dynamics (e.g., carrying capacity) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a BBGKY-like hierarchy. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution. NSF.

Stochastic IMT (Insulator-Metal-Transition) Neurons: An Interplay of Thermal and Threshold Noise at Bifurcation

PubMed Central

Parihar, Abhinav; Jerry, Matthew; Datta, Suman; Raychowdhury, Arijit

2018-01-01

Artificial neural networks can harness stochasticity in multiple ways to enable a vast class of computationally powerful models. Boltzmann machines and other stochastic neural networks have been shown to outperform their deterministic counterparts by allowing dynamical systems to escape local energy minima. Electronic implementation of such stochastic networks is currently limited to addition of algorithmic noise to digital machines which is inherently inefficient; albeit recent efforts to harness physical noise in devices for stochasticity have shown promise. To succeed in fabricating electronic neuromorphic networks we need experimental evidence of devices with measurable and controllable stochasticity which is complemented with the development of reliable statistical models of such observed stochasticity. Current research literature has sparse evidence of the former and a complete lack of the latter. This motivates the current article where we demonstrate a stochastic neuron using an insulator-metal-transition (IMT) device, based on electrically induced phase-transition, in series with a tunable resistance. We show that an IMT neuron has dynamics similar to a piecewise linear FitzHugh-Nagumo (FHN) neuron and incorporates all characteristics of a spiking neuron in the device phenomena. We experimentally demonstrate spontaneous stochastic spiking along with electrically controllable firing probabilities using Vanadium Dioxide (VO2) based IMT neurons which show a sigmoid-like transfer function. The stochastic spiking is explained by two noise sources - thermal noise and threshold fluctuations, which act as precursors of bifurcation. As such, the IMT neuron is modeled as an Ornstein-Uhlenbeck (OU) process with a fluctuating boundary resulting in transfer curves that closely match experiments. The moments of interspike intervals are calculated analytically by extending the first-passage-time (FPT) models for Ornstein-Uhlenbeck (OU) process to include a fluctuating boundary. We find that the coefficient of variation of interspike intervals depend on the relative proportion of thermal and threshold noise, where threshold noise is the dominant source in the current experimental demonstrations. As one of the first comprehensive studies of a stochastic neuron hardware and its statistical properties, this article would enable efficient implementation of a large class of neuro-mimetic networks and algorithms. PMID:29670508

Stochastic IMT (Insulator-Metal-Transition) Neurons: An Interplay of Thermal and Threshold Noise at Bifurcation.

PubMed

Parihar, Abhinav; Jerry, Matthew; Datta, Suman; Raychowdhury, Arijit

2018-01-01

Artificial neural networks can harness stochasticity in multiple ways to enable a vast class of computationally powerful models. Boltzmann machines and other stochastic neural networks have been shown to outperform their deterministic counterparts by allowing dynamical systems to escape local energy minima. Electronic implementation of such stochastic networks is currently limited to addition of algorithmic noise to digital machines which is inherently inefficient; albeit recent efforts to harness physical noise in devices for stochasticity have shown promise. To succeed in fabricating electronic neuromorphic networks we need experimental evidence of devices with measurable and controllable stochasticity which is complemented with the development of reliable statistical models of such observed stochasticity. Current research literature has sparse evidence of the former and a complete lack of the latter. This motivates the current article where we demonstrate a stochastic neuron using an insulator-metal-transition (IMT) device, based on electrically induced phase-transition, in series with a tunable resistance. We show that an IMT neuron has dynamics similar to a piecewise linear FitzHugh-Nagumo (FHN) neuron and incorporates all characteristics of a spiking neuron in the device phenomena. We experimentally demonstrate spontaneous stochastic spiking along with electrically controllable firing probabilities using Vanadium Dioxide (VO 2 ) based IMT neurons which show a sigmoid-like transfer function. The stochastic spiking is explained by two noise sources - thermal noise and threshold fluctuations, which act as precursors of bifurcation. As such, the IMT neuron is modeled as an Ornstein-Uhlenbeck (OU) process with a fluctuating boundary resulting in transfer curves that closely match experiments. The moments of interspike intervals are calculated analytically by extending the first-passage-time (FPT) models for Ornstein-Uhlenbeck (OU) process to include a fluctuating boundary. We find that the coefficient of variation of interspike intervals depend on the relative proportion of thermal and threshold noise, where threshold noise is the dominant source in the current experimental demonstrations. As one of the first comprehensive studies of a stochastic neuron hardware and its statistical properties, this article would enable efficient implementation of a large class of neuro-mimetic networks and algorithms.

Fast stochastic algorithm for simulating evolutionary population dynamics

NASA Astrophysics Data System (ADS)

Tsimring, Lev; Hasty, Jeff; Mather, William

2012-02-01

Evolution and co-evolution of ecological communities are stochastic processes often characterized by vastly different rates of reproduction and mutation and a coexistence of very large and very small sub-populations of co-evolving species. This creates serious difficulties for accurate statistical modeling of evolutionary dynamics. In this talk, we introduce a new exact algorithm for fast fully stochastic simulations of birth/death/mutation processes. It produces a significant speedup compared to the direct stochastic simulation algorithm in a typical case when the total population size is large and the mutation rates are much smaller than birth/death rates. We illustrate the performance of the algorithm on several representative examples: evolution on a smooth fitness landscape, NK model, and stochastic predator-prey system.

Nonholonomic relativistic diffusion and exact solutions for stochastic Einstein spaces

NASA Astrophysics Data System (ADS)

Vacaru, S. I.

2012-03-01

We develop an approach to the theory of nonholonomic relativistic stochastic processes in curved spaces. The Itô and Stratonovich calculus are formulated for spaces with conventional horizontal (holonomic) and vertical (nonholonomic) splitting defined by nonlinear connection structures. Geometric models of the relativistic diffusion theory are elaborated for nonholonomic (pseudo) Riemannian manifolds and phase velocity spaces. Applying the anholonomic deformation method, the field equations in Einstein's gravity and various modifications are formally integrated in general forms, with generic off-diagonal metrics depending on some classes of generating and integration functions. Choosing random generating functions we can construct various classes of stochastic Einstein manifolds. We show how stochastic gravitational interactions with mixed holonomic/nonholonomic and random variables can be modelled in explicit form and study their main geometric and stochastic properties. Finally, the conditions when non-random classical gravitational processes transform into stochastic ones and inversely are analyzed.

Effects of stochastic interest rates in decision making under risk: A Markov decision process model for forest management

Treesearch

Mo Zhou; Joseph Buongiorno

2011-01-01

Most economic studies of forest decision making under risk assume a fixed interest rate. This paper investigated some implications of this stochastic nature of interest rates. Markov decision process (MDP) models, used previously to integrate stochastic stand growth and prices, can be extended to include variable interest rates as well. This method was applied to...

Agent-based model of angiogenesis simulates capillary sprout initiation in multicellular networks

PubMed Central

Walpole, J.; Chappell, J.C.; Cluceru, J.G.; Mac Gabhann, F.; Bautch, V.L.; Peirce, S. M.

2015-01-01

Many biological processes are controlled by both deterministic and stochastic influences. However, efforts to model these systems often rely on either purely stochastic or purely rule-based methods. To better understand the balance between stochasticity and determinism in biological processes a computational approach that incorporates both influences may afford additional insight into underlying biological mechanisms that give rise to emergent system properties. We apply a combined approach to the simulation and study of angiogenesis, the growth of new blood vessels from existing networks. This complex multicellular process begins with selection of an initiating endothelial cell, or tip cell, which sprouts from the parent vessels in response to stimulation by exogenous cues. We have constructed an agent-based model of sprouting angiogenesis to evaluate endothelial cell sprout initiation frequency and location, and we have experimentally validated it using high-resolution time-lapse confocal microscopy. ABM simulations were then compared to a Monte Carlo model, revealing that purely stochastic simulations could not generate sprout locations as accurately as the rule-informed agent-based model. These findings support the use of rule-based approaches for modeling the complex mechanisms underlying sprouting angiogenesis over purely stochastic methods. PMID:26158406

Agent-based model of angiogenesis simulates capillary sprout initiation in multicellular networks.

PubMed

Walpole, J; Chappell, J C; Cluceru, J G; Mac Gabhann, F; Bautch, V L; Peirce, S M

2015-09-01

Many biological processes are controlled by both deterministic and stochastic influences. However, efforts to model these systems often rely on either purely stochastic or purely rule-based methods. To better understand the balance between stochasticity and determinism in biological processes a computational approach that incorporates both influences may afford additional insight into underlying biological mechanisms that give rise to emergent system properties. We apply a combined approach to the simulation and study of angiogenesis, the growth of new blood vessels from existing networks. This complex multicellular process begins with selection of an initiating endothelial cell, or tip cell, which sprouts from the parent vessels in response to stimulation by exogenous cues. We have constructed an agent-based model of sprouting angiogenesis to evaluate endothelial cell sprout initiation frequency and location, and we have experimentally validated it using high-resolution time-lapse confocal microscopy. ABM simulations were then compared to a Monte Carlo model, revealing that purely stochastic simulations could not generate sprout locations as accurately as the rule-informed agent-based model. These findings support the use of rule-based approaches for modeling the complex mechanisms underlying sprouting angiogenesis over purely stochastic methods.

Need to improve SWMM's subsurface flow routing algorithm for green infrastructure modeling

EPA Science Inventory

SWMM can simulate various subsurface flows, including groundwater (GW) release from a subcatchment to a node, percolation out of storage units and low impact development (LID) controls, and rainfall derived inflow and infiltration (RDII) at a node. Originally, the subsurface flow...

Shallow subsurface storm flow in a forested headwater catchment: Observations and modeling using a modified TOPMODEL

USGS Publications Warehouse

Scanlon, Todd M.; Raffensperger, Jeff P.; Hornberger, George M.; Clapp, Roger B.

2000-01-01

Transient, perched water tables in the shallow subsurface are observed at the South Fork Brokenback Run catchment in Shenandoah National Park, Virginia. Crest piezometers installed along a hillslope transect show that the development of saturated conditions in the upper 1.5 m of the subsurface is controlled by total precipitation and antecedent conditions, not precipitation intensity, although soil heterogeneities strongly influence local response. The macroporous subsurface storm flow zone provides a hydrological pathway for rapid runoff generation apart from the underlying groundwater zone, a conceptualization supported by the two‐storage system exhibited by hydrograph recession analysis. A modified version of TOPMODEL is used to simulate the observed catchment dynamics. In this model, generalized topographic index theory is applied to the subsurface storm flow zone to account for logarithmic storm flow recessions, indicative of linearly decreasing transmissivity with depth. Vertical drainage to the groundwater zone is required, and both subsurface reservoirs are considered to contribute to surface saturation.

Improved Climate Simulations through a Stochastic Parameterization of Ocean Eddies

NASA Astrophysics Data System (ADS)

Williams, Paul; Howe, Nicola; Gregory, Jonathan; Smith, Robin; Joshi, Manoj

2017-04-01

In climate simulations, the impacts of the subgrid scales on the resolved scales are conventionally represented using deterministic closure schemes, which assume that the impacts are uniquely determined by the resolved scales. Stochastic parameterization relaxes this assumption, by sampling the subgrid variability in a computationally inexpensive manner. This study shows that the simulated climatological state of the ocean is improved in many respects by implementing a simple stochastic parameterization of ocean eddies into a coupled atmosphere-ocean general circulation model. Simulations from a high-resolution, eddy-permitting ocean model are used to calculate the eddy statistics needed to inject realistic stochastic noise into a low-resolution, non-eddy-permitting version of the same model. A suite of four stochastic experiments is then run to test the sensitivity of the simulated climate to the noise definition by varying the noise amplitude and decorrelation time within reasonable limits. The addition of zero-mean noise to the ocean temperature tendency is found to have a nonzero effect on the mean climate. Specifically, in terms of the ocean temperature and salinity fields both at the surface and at depth, the noise reduces many of the biases in the low-resolution model and causes it to more closely resemble the high-resolution model. The variability of the strength of the global ocean thermohaline circulation is also improved. It is concluded that stochastic ocean perturbations can yield reductions in climate model error that are comparable to those obtained by refining the resolution, but without the increased computational cost. Therefore, stochastic parameterizations of ocean eddies have the potential to significantly improve climate simulations. Reference Williams PD, Howe NJ, Gregory JM, Smith RS, and Joshi MM (2016) Improved Climate Simulations through a Stochastic Parameterization of Ocean Eddies. Journal of Climate, 29, 8763-8781. http://dx.doi.org/10.1175/JCLI-D-15-0746.1

A non-linear dimension reduction methodology for generating data-driven stochastic input models

NASA Astrophysics Data System (ADS)

Ganapathysubramanian, Baskar; Zabaras, Nicholas

2008-06-01

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem of manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space Rn. An isometric mapping F from M to a low-dimensional, compact, connected set A⊂Rd(d≪n) is constructed. Given only a finite set of samples of the data, the methodology uses arguments from graph theory and differential geometry to construct the isometric transformation F:M→A. Asymptotic convergence of the representation of M by A is shown. This mapping F serves as an accurate, low-dimensional, data-driven representation of the property variations. The reduced-order model of the material topology and thermal diffusivity variations is subsequently used as an input in the solution of stochastic partial differential equations that describe the evolution of dependant variables. A sparse grid collocation strategy (Smolyak algorithm) is utilized to solve these stochastic equations efficiently. We showcase the methodology by constructing low-dimensional input stochastic models to represent thermal diffusivity in two-phase microstructures. This model is used in analyzing the effect of topological variations of two-phase microstructures on the evolution of temperature in heat conduction processes.

Improving the long-lead predictability of El Niño using a novel forecasting scheme based on a dynamic components model

NASA Astrophysics Data System (ADS)

Petrova, Desislava; Koopman, Siem Jan; Ballester, Joan; Rodó, Xavier

2017-02-01

El Niño (EN) is a dominant feature of climate variability on inter-annual time scales driving changes in the climate throughout the globe, and having wide-spread natural and socio-economic consequences. In this sense, its forecast is an important task, and predictions are issued on a regular basis by a wide array of prediction schemes and climate centres around the world. This study explores a novel method for EN forecasting. In the state-of-the-art the advantageous statistical technique of unobserved components time series modeling, also known as structural time series modeling, has not been applied. Therefore, we have developed such a model where the statistical analysis, including parameter estimation and forecasting, is based on state space methods, and includes the celebrated Kalman filter. The distinguishing feature of this dynamic model is the decomposition of a time series into a range of stochastically time-varying components such as level (or trend), seasonal, cycles of different frequencies, irregular, and regression effects incorporated as explanatory covariates. These components are modeled separately and ultimately combined in a single forecasting scheme. Customary statistical models for EN prediction essentially use SST and wind stress in the equatorial Pacific. In addition to these, we introduce a new domain of regression variables accounting for the state of the subsurface ocean temperature in the western and central equatorial Pacific, motivated by our analysis, as well as by recent and classical research, showing that subsurface processes and heat accumulation there are fundamental for the genesis of EN. An important feature of the scheme is that different regression predictors are used at different lead months, thus capturing the dynamical evolution of the system and rendering more efficient forecasts. The new model has been tested with the prediction of all warm events that occurred in the period 1996-2015. Retrospective forecasts of these events were made for long lead times of at least two and a half years. Hence, the present study demonstrates that the theoretical limit of ENSO prediction should be sought much longer than the commonly accepted "Spring Barrier". The high correspondence between the forecasts and observations indicates that the proposed model outperforms all current operational statistical models, and behaves comparably to the best dynamical models used for EN prediction. Thus, the novel way in which the modeling scheme has been structured could also be used for improving other statistical and dynamical modeling systems.

MODELING THREE-DIMENSIONAL SUBSURFACE FLOW, FATE AND TRANSPORT OF MICROBES AND CHEMICALS (3DFATMIC)

EPA Science Inventory

A three-dimensional model simulating the subsurface flow, microbial growth and degradation, microbial-chemical reaction, and transport of microbes and chemicals has been developed. he model is designed to solve the coupled flow and transport equations. asically, the saturated-uns...

Surface and subsurface geologic risk factors to ground water affecting brownfield redevelopment potential.

PubMed

Kaufman, Martin M; Murray, Kent S; Rogers, Daniel T

2003-01-01

A model is created for assessing the redevelopment potential of brownfields. The model is derived from a space and time conceptual framework that identifies and measures the surface and subsurface risk factors present at brownfield sites. The model then combines these factors with a contamination extent multiplier at each site to create an index of redevelopment potential. Results from the application of the model within an urbanized watershed demonstrate clear differences between the redevelopment potential present within five different near-surface geologic units, with those units containing clay being less vulnerable to subsurface contamination. With and without the extent multiplier, the total risk present at the brownfield sites within all the geologic units is also strongly correlated to the actual costs of remediation. Thus, computing the total surface and subsurface risk within a watershed can help guide the remediation efforts at broad geographic scales, and prioritize the locations for redevelopment.

Two-dimensional resistivity investigation of the North Cavalcade Street site, Houston, Texas, August 2003

USGS Publications Warehouse

Kress, Wade H.; Teeple, Andrew

2005-01-01

Forward modeling was used as an interpretative tool to relate the subsurface distribution of resistivity from four DC resistivity lines to known, assumed, and hypothetical information on subsurface lithologies. The final forward models were used as an estimate of the true resistivity structure for the field data. The forward models and the inversion results of the forward models show the depth, thickness, and extent of strata as well as the resistive anomalies occurring along the four lines and the displacement of strata resulting from the Pecore Fault along two of the four DC resistivity lines. Ten additional DC resistivity lines show similarly distributed shallow subsurface lithologies of silty sand and clay strata. Eight priority areas of resistive anomalies were identified for evaluation in future studies. The interpreted DC resistivity data allowed subsurface stratigraphy to be extrapolated between existing boreholes resulting in an improved understanding of lithologies that can influence contaminant migration.

Three-dimensional modelling and geothermal process simulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burns, K.L.

1990-01-01

The subsurface geological model or 3-D GIS is constructed from three kinds of objects, which are a lithotope (in boundary representation), a number of fault systems, and volumetric textures (vector fields). The chief task of the model is to yield an estimate of the conductance tensors (fluid permeability and thermal conductivity) throughout an array of voxels. This is input as material properties to a FEHM numerical physical process model. The main task of the FEHM process model is to distinguish regions of convective from regions of conductive heat flow, and to estimate the fluid phase, pressure and flow paths. Themore » temperature, geochemical, and seismic data provide the physical constraints on the process. The conductance tensors in the Franciscan Complex are to be derived by the addition of two components. The isotropic component is a stochastic spatial variable due to disruption of lithologies in melange. The deviatoric component is deterministic, due to smoothness and continuity in the textural vector fields. This decomposition probably also applies to the engineering hydrogeological properties of shallow terrestrial fluvial systems. However there are differences in quantity. The isotropic component is much more variable in the Franciscan, to the point where volumetric averages are misleading, and it may be necessary to select that component from several, discrete possible states. The deviatoric component is interpolated using a textural vector field. The Franciscan field is much more complicated, and contains internal singularities. 27 refs., 10 figs.« less

Three-dimensional hydrogeologic framework model of the Rio Grande transboundary region of New Mexico and Texas, USA, and northern Chihuahua, Mexico

USGS Publications Warehouse

Sweetkind, Donald S.

2017-09-08

As part of a U.S. Geological Survey study in cooperation with the Bureau of Reclamation, a digital three-dimensional hydrogeologic framework model was constructed for the Rio Grande transboundary region of New Mexico and Texas, USA, and northern Chihuahua, Mexico. This model was constructed to define the aquifer system geometry and subsurface lithologic characteristics and distribution for use in a regional numerical hydrologic model. The model includes five hydrostratigraphic units: river channel alluvium, three informal subdivisions of Santa Fe Group basin fill, and an undivided pre-Santa Fe Group bedrock unit. Model input data were compiled from published cross sections, well data, structure contour maps, selected geophysical data, and contiguous compilations of surficial geology and structural features in the study area. These data were used to construct faulted surfaces that represent the upper and lower subsurface hydrostratigraphic unit boundaries. The digital three-dimensional hydrogeologic framework model is constructed through combining faults, the elevation of the tops of each hydrostratigraphic unit, and boundary lines depicting the subsurface extent of each hydrostratigraphic unit. The framework also compiles a digital representation of the distribution of sedimentary facies within each hydrostratigraphic unit. The digital three-dimensional hydrogeologic model reproduces with reasonable accuracy the previously published subsurface hydrogeologic conceptualization of the aquifer system and represents the large-scale geometry of the subsurface aquifers. The model is at a scale and resolution appropriate for use as the foundation for a numerical hydrologic model of the study area.

Price sensitive demand with random sales price - a newsboy problem

NASA Astrophysics Data System (ADS)

Sankar Sana, Shib

2012-03-01

Up to now, many newsboy problems have been considered in the stochastic inventory literature. Some assume that stochastic demand is independent of selling price (p) and others consider the demand as a function of stochastic shock factor and deterministic sales price. This article introduces a price-dependent demand with stochastic selling price into the classical Newsboy problem. The proposed model analyses the expected average profit for a general distribution function of p and obtains an optimal order size. Finally, the model is discussed for various appropriate distribution functions of p and illustrated with numerical examples.

Biochemical Network Stochastic Simulator (BioNetS): software for stochastic modeling of biochemical networks.

PubMed

Adalsteinsson, David; McMillen, David; Elston, Timothy C

2004-03-08

Intrinsic fluctuations due to the stochastic nature of biochemical reactions can have large effects on the response of biochemical networks. This is particularly true for pathways that involve transcriptional regulation, where generally there are two copies of each gene and the number of messenger RNA (mRNA) molecules can be small. Therefore, there is a need for computational tools for developing and investigating stochastic models of biochemical networks. We have developed the software package Biochemical Network Stochastic Simulator (BioNetS) for efficiently and accurately simulating stochastic models of biochemical networks. BioNetS has a graphical user interface that allows models to be entered in a straightforward manner, and allows the user to specify the type of random variable (discrete or continuous) for each chemical species in the network. The discrete variables are simulated using an efficient implementation of the Gillespie algorithm. For the continuous random variables, BioNetS constructs and numerically solves the appropriate chemical Langevin equations. The software package has been developed to scale efficiently with network size, thereby allowing large systems to be studied. BioNetS runs as a BioSpice agent and can be downloaded from http://www.biospice.org. BioNetS also can be run as a stand alone package. All the required files are accessible from http://x.amath.unc.edu/BioNetS. We have developed BioNetS to be a reliable tool for studying the stochastic dynamics of large biochemical networks. Important features of BioNetS are its ability to handle hybrid models that consist of both continuous and discrete random variables and its ability to model cell growth and division. We have verified the accuracy and efficiency of the numerical methods by considering several test systems.

The Role of Subsurface Properties on Transport of Water and Trace Gases: 1D Simulations at Selected Mars Landing Sites.

NASA Astrophysics Data System (ADS)

Karatekin, O.; Gloesener, E.; Dehant, V. M. A.

2017-12-01

In this work, water ice stability and water vapour transport through porous martian subsurface are studied using a 1D diffusive model. The role of adsorption on water transfer in martian conditions is investigated as well as the range of parameters that have the largest effect on gas transport. In addition, adsorption kinetics is considered to examine its influence on the water vapor exchange between the subsurface and the atmosphere. As methane has been detected in the martian atmosphere, the subsurface model is then used to study methane diffusion in the CH4/CO2/H2O system from variable depths under the surface. The results of subsurface gas transport at selected locations/landing sites are shown and implications for present/future observations are discussed.

Simple and Hierarchical Models for Stochastic Test Misgrading.

ERIC Educational Resources Information Center

Wang, Jianjun

1993-01-01

Test misgrading is treated as a stochastic process. The expected number of misgradings, inter-occurrence time of misgradings, and waiting time for the "n"th misgrading are discussed based on a simple Poisson model and a hierarchical Beta-Poisson model. Examples of model construction are given. (SLD)

AUTOMATIC CALIBRATION OF A STOCHASTIC-LAGRANGIAN TRANSPORT MODEL (SLAM)

EPA Science Inventory

Numerical models are a useful tool in evaluating and designing NAPL remediation systems. Traditional constitutive finite difference and finite element models are complex and expensive to apply. For this reason, this paper presents the application of a simplified stochastic-Lagran...

Stochastic lattice model of synaptic membrane protein domains.

PubMed

Li, Yiwei; Kahraman, Osman; Haselwandter, Christoph A

2017-05-01

Neurotransmitter receptor molecules, concentrated in synaptic membrane domains along with scaffolds and other kinds of proteins, are crucial for signal transmission across chemical synapses. In common with other membrane protein domains, synaptic domains are characterized by low protein copy numbers and protein crowding, with rapid stochastic turnover of individual molecules. We study here in detail a stochastic lattice model of the receptor-scaffold reaction-diffusion dynamics at synaptic domains that was found previously to capture, at the mean-field level, the self-assembly, stability, and characteristic size of synaptic domains observed in experiments. We show that our stochastic lattice model yields quantitative agreement with mean-field models of nonlinear diffusion in crowded membranes. Through a combination of analytic and numerical solutions of the master equation governing the reaction dynamics at synaptic domains, together with kinetic Monte Carlo simulations, we find substantial discrepancies between mean-field and stochastic models for the reaction dynamics at synaptic domains. Based on the reaction and diffusion properties of synaptic receptors and scaffolds suggested by previous experiments and mean-field calculations, we show that the stochastic reaction-diffusion dynamics of synaptic receptors and scaffolds provide a simple physical mechanism for collective fluctuations in synaptic domains, the molecular turnover observed at synaptic domains, key features of the observed single-molecule trajectories, and spatial heterogeneity in the effective rates at which receptors and scaffolds are recycled at the cell membrane. Our work sheds light on the physical mechanisms and principles linking the collective properties of membrane protein domains to the stochastic dynamics that rule their molecular components.

Integrated Coupling of Surface and Subsurface Flow with HYDRUS-2D

NASA Astrophysics Data System (ADS)

Hartmann, Anne; Šimůnek, Jirka; Wöhling, Thomas; Schütze, Niels

2016-04-01

Describing interactions between surface and subsurface flow processes is important to adequately define water flow in natural systems. Since overland flow generation is highly influenced by rainfall and infiltration, both highly spatially heterogeneous processes, overland flow is unsteady and varies spatially. The prediction of overland flow needs to include an appropriate description of the interactions between the surface and subsurface flow. Coupling surface and subsurface water flow is a challenging task. Different approaches have been developed during the last few years, each having its own advantages and disadvantages. A new approach by Weill et al. (2009) to couple overland flow and subsurface flow based on a generalized Richards equation was implemented into the well-known subsurface flow model HYDRUS-2D (Šimůnek et al., 2011). This approach utilizes the one-dimensional diffusion wave equation to model overland flow. The diffusion wave model is integrated in HYDRUS-2D by replacing the terms of the Richards equation in a pre-defined runoff layer by terms defining the diffusion wave equation. Using this approach, pressure and flux continuity along the interface between both flow domains is provided. This direct coupling approach provides a strong coupling of both systems based on the definition of a single global system matrix to numerically solve the coupled flow problem. The advantage of the direct coupling approach, compared to the loosely coupled approach, is supposed to be a higher robustness, when many convergence problems can be avoided (Takizawa et al., 2014). The HYDRUS-2D implementation was verified using a) different test cases, including a direct comparison with the results of Weill et al. (2009), b) an analytical solution of the kinematic wave equation, and c) the results of a benchmark test of Maxwell et al. (2014), that included several known coupled surface subsurface flow models. Additionally, a sensitivity analysis evaluating the effects of various model parameters on simulated overland flow (while considering or neglecting the effects of subsurface flow) was carried out to verify the applicability of the model to different problems. The model produced reasonable results in describing the diffusion wave approximation and its interactions with subsurface flow processes. The model could handle coupled surface-subsurface processes for conditions involving runoff generated by infiltration excess, saturation excess, or run-on, as well as a combination of these runoff generating processes. Several standard features of the HYDRUS 2D model, such as root water uptake and evaporation from the soil surface, as well as evaporation from runoff layer, can still be considered by the new model. The code required relatively small time steps when overland flow was active, resulting in long simulation times, and sometimes produced poor mass balance. The model nevertheless showed potential to be a useful tool for addressing various issues related to irrigation research and to natural generation of overland flow at the hillslope scale. Maxwell, R., Putti, M., Meyerhoff, S., Delf, J., Ferguson, I., Ivanov, V., Kim, J., Kolditz, O., Kollet, S., Kumar, M., Lopez, S., Niu, J., Paniconi, C., Park, Y.-J., Phanikumar, M., Shen, C., Sudicky, E., and Sulis, M. (2014). Surface-subsurface model intercomparison: A first set of benchmark results to diagnose integrated hydrology and feedbacks. Water Resourc. Res., 50:1531-1549. Šimůnek, J., van Genuchten, M. T., and Šejna, M. (2011). The HYDRUS Software Package for Simulating Two- and Three-Dimensional Movement of Water, Heat, and Multiple Solutes in Variably-Saturated Media. Technical Manual, Version 2.0, PC Progress, Prague, Czech Republic. Takizawa, K., Bazilevs Y., Tezduyar, T. E., Long, C.C., Marsden, A. L. and Schjodt.K., Patient-Specific Cardiovascular Fluid Mechanics Analysis with the ST and ALE-VMS Method in Idelsohn, S. R. (2014). Numerical Simulations of Coupled Problems in Engineering. Springer. Weill, S., Mouche, E., and Patin, J. (2009). A generalized Richards equation for surface/subsurface flow modelling. Journal of Hydrology, 366:9-20.

Coarse-graining and hybrid methods for efficient simulation of stochastic multi-scale models of tumour growth.

PubMed

de la Cruz, Roberto; Guerrero, Pilar; Calvo, Juan; Alarcón, Tomás

2017-12-01

The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction-diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction-diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge of front, which cannot be accounted for by the coarse-grained model. Such fluctuations have non-trivial effects on the wave velocity. Beyond the development of a new hybrid method, we thus conclude that birth-rate fluctuations are central to a quantitatively accurate description of invasive phenomena such as tumour growth.

Coarse-graining and hybrid methods for efficient simulation of stochastic multi-scale models of tumour growth

NASA Astrophysics Data System (ADS)

de la Cruz, Roberto; Guerrero, Pilar; Calvo, Juan; Alarcón, Tomás

2017-12-01

The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction-diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction-diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge of front, which cannot be accounted for by the coarse-grained model. Such fluctuations have non-trivial effects on the wave velocity. Beyond the development of a new hybrid method, we thus conclude that birth-rate fluctuations are central to a quantitatively accurate description of invasive phenomena such as tumour growth.

Application of an NLME-Stochastic Deconvolution Approach to Level A IVIVC Modeling.

PubMed

Kakhi, Maziar; Suarez-Sharp, Sandra; Shepard, Terry; Chittenden, Jason

2017-07-01

Stochastic deconvolution is a parameter estimation method that calculates drug absorption using a nonlinear mixed-effects model in which the random effects associated with absorption represent a Wiener process. The present work compares (1) stochastic deconvolution and (2) numerical deconvolution, using clinical pharmacokinetic (PK) data generated for an in vitro-in vivo correlation (IVIVC) study of extended release (ER) formulations of a Biopharmaceutics Classification System class III drug substance. The preliminary analysis found that numerical and stochastic deconvolution yielded superimposable fraction absorbed (F abs ) versus time profiles when supplied with exactly the same externally determined unit impulse response parameters. In a separate analysis, a full population-PK/stochastic deconvolution was applied to the clinical PK data. Scenarios were considered in which immediate release (IR) data were either retained or excluded to inform parameter estimation. The resulting F abs profiles were then used to model level A IVIVCs. All the considered stochastic deconvolution scenarios, and numerical deconvolution, yielded on average similar results with respect to the IVIVC validation. These results could be achieved with stochastic deconvolution without recourse to IR data. Unlike numerical deconvolution, this also implies that in crossover studies where certain individuals do not receive an IR treatment, their ER data alone can still be included as part of the IVIVC analysis. Published by Elsevier Inc.

Stochastic noncooperative and cooperative evolutionary game strategies of a population of biological networks under natural selection.

PubMed

Chen, Bor-Sen; Yeh, Chin-Hsun

2017-12-01

We review current static and dynamic evolutionary game strategies of biological networks and discuss the lack of random genetic variations and stochastic environmental disturbances in these models. To include these factors, a population of evolving biological networks is modeled as a nonlinear stochastic biological system with Poisson-driven genetic variations and random environmental fluctuations (stimuli). To gain insight into the evolutionary game theory of stochastic biological networks under natural selection, the phenotypic robustness and network evolvability of noncooperative and cooperative evolutionary game strategies are discussed from a stochastic Nash game perspective. The noncooperative strategy can be transformed into an equivalent multi-objective optimization problem and is shown to display significantly improved network robustness to tolerate genetic variations and buffer environmental disturbances, maintaining phenotypic traits for longer than the cooperative strategy. However, the noncooperative case requires greater effort and more compromises between partly conflicting players. Global linearization is used to simplify the problem of solving nonlinear stochastic evolutionary games. Finally, a simple stochastic evolutionary model of a metabolic pathway is simulated to illustrate the procedure of solving for two evolutionary game strategies and to confirm and compare their respective characteristics in the evolutionary process. Copyright © 2017 Elsevier B.V. All rights reserved.

Persistence and ergodicity of a stochastic single species model with Allee effect under regime switching

NASA Astrophysics Data System (ADS)

Yu, Xingwang; Yuan, Sanling; Zhang, Tonghua

2018-06-01

Allee effect can interact with environment stochasticity and is active when population numbers are small. Our goal of this paper is to investigate such effect on population dynamics. More precisely, we develop and investigate a stochastic single species model with Allee effect under regime switching. We first prove the existence of global positive solution of the model. Then, we perform the survival analysis to seek sufficient conditions for the extinction, non-persistence in mean, persistence in mean and stochastic permanence. By constructing a suitable Lyapunov function, we show that the model is positive recurrent and ergodic. Our results indicate that the regime switching can suppress the extinction of the species. Finally, numerical simulations are carried out to illustrate the obtained theoretical results, where a real-life example is also discussed showing the inclusion of Allee effect in the model provides a better match to the data.

A stochastic spatiotemporal model of a response-regulator network in the Caulobacter crescentus cell cycle

NASA Astrophysics Data System (ADS)

Li, Fei; Subramanian, Kartik; Chen, Minghan; Tyson, John J.; Cao, Yang

2016-06-01

The asymmetric cell division cycle in Caulobacter crescentus is controlled by an elaborate molecular mechanism governing the production, activation and spatial localization of a host of interacting proteins. In previous work, we proposed a deterministic mathematical model for the spatiotemporal dynamics of six major regulatory proteins. In this paper, we study a stochastic version of the model, which takes into account molecular fluctuations of these regulatory proteins in space and time during early stages of the cell cycle of wild-type Caulobacter cells. We test the stochastic model with regard to experimental observations of increased variability of cycle time in cells depleted of the divJ gene product. The deterministic model predicts that overexpression of the divK gene blocks cell cycle progression in the stalked stage; however, stochastic simulations suggest that a small fraction of the mutants cells do complete the cell cycle normally.

Experimental Design for Stochastic Models of Nonlinear Signaling Pathways Using an Interval-Wise Linear Noise Approximation and State Estimation

PubMed Central

Zimmer, Christoph

2016-01-01

Background Computational modeling is a key technique for analyzing models in systems biology. There are well established methods for the estimation of the kinetic parameters in models of ordinary differential equations (ODE). Experimental design techniques aim at devising experiments that maximize the information encoded in the data. For ODE models there are well established approaches for experimental design and even software tools. However, data from single cell experiments on signaling pathways in systems biology often shows intrinsic stochastic effects prompting the development of specialized methods. While simulation methods have been developed for decades and parameter estimation has been targeted for the last years, only very few articles focus on experimental design for stochastic models. Methods The Fisher information matrix is the central measure for experimental design as it evaluates the information an experiment provides for parameter estimation. This article suggest an approach to calculate a Fisher information matrix for models containing intrinsic stochasticity and high nonlinearity. The approach makes use of a recently suggested multiple shooting for stochastic systems (MSS) objective function. The Fisher information matrix is calculated by evaluating pseudo data with the MSS technique. Results The performance of the approach is evaluated with simulation studies on an Immigration-Death, a Lotka-Volterra, and a Calcium oscillation model. The Calcium oscillation model is a particularly appropriate case study as it contains the challenges inherent to signaling pathways: high nonlinearity, intrinsic stochasticity, a qualitatively different behavior from an ODE solution, and partial observability. The computational speed of the MSS approach for the Fisher information matrix allows for an application in realistic size models. PMID:27583802

Enceladus Plume Structure and Time Variability: Comparison of Cassini Observations

PubMed Central

Perry, Mark E.; Hansen, Candice J.; Waite, J. Hunter; Porco, Carolyn C.; Spencer, John R.; Howett, Carly J. A.

2017-01-01

Abstract During three low-altitude (99, 66, 66 km) flybys through the Enceladus plume in 2010 and 2011, Cassini's ion neutral mass spectrometer (INMS) made its first high spatial resolution measurements of the plume's gas density and distribution, detecting in situ the individual gas jets within the broad plume. Since those flybys, more detailed Imaging Science Subsystem (ISS) imaging observations of the plume's icy component have been reported, which constrain the locations and orientations of the numerous gas/grain jets. In the present study, we used these ISS imaging results, together with ultraviolet imaging spectrograph stellar and solar occultation measurements and modeling of the three-dimensional structure of the vapor cloud, to constrain the magnitudes, velocities, and time variability of the plume gas sources from the INMS data. Our results confirm a mixture of both low and high Mach gas emission from Enceladus' surface tiger stripes, with gas accelerated as fast as Mach 10 before escaping the surface. The vapor source fluxes and jet intensities/densities vary dramatically and stochastically, up to a factor 10, both spatially along the tiger stripes and over time between flyby observations. This complex spatial variability and dynamics may result from time-variable tidal stress fields interacting with subsurface fissure geometry and tortuosity beyond detectability, including changing gas pathways to the surface, and fluid flow and boiling in response evolving lithostatic stress conditions. The total plume gas source has 30% uncertainty depending on the contributions assumed for adiabatic and nonadiabatic gas expansion/acceleration to the high Mach emission. The overall vapor plume source rate exhibits stochastic time variability up to a factor ∼5 between observations, reflecting that found in the individual gas sources/jets. Key Words: Cassini at Saturn—Geysers—Enceladus—Gas dynamics—Icy satellites. Astrobiology 17, 926–940. PMID:28872900

Particle Simulations on Plasma and Dust Environment near Lunar Vertical Holes

NASA Astrophysics Data System (ADS)

Miyake, Y.; Funaki, Y.; Nishino, M. N.

2016-12-01

The Japanese lunar orbiter KAGUYA has revealed the existence of vertical holes on the Moon, which have spatial scales of tens of meters and are possible lava tube skylights. The hole structure has recently received particular attention, because the structure is regarded as evidence for past existence of underground lava flows. Furthermore, the holes have high potential as locations for constructing future lunar bases, because of fewer extra-lunar rays/particles and micrometeorites reaching the hole bottoms. In this sense, these holes are not only of significance in selenology, but are also interesting from the viewpoint of plasma environments. The dayside electrostatic environment near the lunar surface is governed by interactions among the solar wind plasma, photoelectrons, and the charged lunar surface, providing topologically complex boundaries to the plasma. Thus we applied three-dimensional, massively-parallelized, particle-in-cell simulations to the near-hole environment on the Moon. This year we have introduced a horizontal cavern opened at the vertical wall of the hole, assuming the presence of a subsurface lave tube. We will show some preliminary results on the surface potential and its nearly plasma environments. We also started to study the dynamics of submicron-sized charged dust grains around the distinctive landscape. We particularly focus on an effect of a stochastic charging process of such small dust grains. Because of their small surface areas, the dusts will get/lose one elementary charge infrequently, and thus charge amount owned by each dust should be a stochastic variable unlike a widely-known spacecraft charging process. We develop a numerical model of such a charging process, which will be embedded into the test particle analysis of the dust dynamics. We report some results from our simulations on the dust charging process and dynamics around the lunar hole.

A deterministic and stochastic model for the system dynamics of tumor-immune responses to chemotherapy

NASA Astrophysics Data System (ADS)

Liu, Xiangdong; Li, Qingze; Pan, Jianxin

2018-06-01

Modern medical studies show that chemotherapy can help most cancer patients, especially for those diagnosed early, to stabilize their disease conditions from months to years, which means the population of tumor cells remained nearly unchanged in quite a long time after fighting against immune system and drugs. In order to better understand the dynamics of tumor-immune responses under chemotherapy, deterministic and stochastic differential equation models are constructed to characterize the dynamical change of tumor cells and immune cells in this paper. The basic dynamical properties, such as boundedness, existence and stability of equilibrium points, are investigated in the deterministic model. Extended stochastic models include stochastic differential equations (SDEs) model and continuous-time Markov chain (CTMC) model, which accounts for the variability in cellular reproduction, growth and death, interspecific competitions, and immune response to chemotherapy. The CTMC model is harnessed to estimate the extinction probability of tumor cells. Numerical simulations are performed, which confirms the obtained theoretical results.

Fluvial reservoir characterization using topological descriptors based on spectral analysis of graphs

NASA Astrophysics Data System (ADS)

Viseur, Sophie; Chiaberge, Christophe; Rhomer, Jérémy; Audigane, Pascal

2015-04-01

Fluvial systems generate highly heterogeneous reservoir. These heterogeneities have major impact on fluid flow behaviors. However, the modelling of such reservoirs is mainly performed in under-constrained contexts as they include complex features, though only sparse and indirect data are available. Stochastic modeling is the common strategy to solve such problems. Multiple 3D models are generated from the available subsurface dataset. The generated models represent a sampling of plausible subsurface structure representations. From this model sampling, statistical analysis on targeted parameters (e.g.: reserve estimations, flow behaviors, etc.) and a posteriori uncertainties are performed to assess risks. However, on one hand, uncertainties may be huge, which requires many models to be generated for scanning the space of possibilities. On the other hand, some computations performed on the generated models are time consuming and cannot, in practice, be applied on all of them. This issue is particularly critical in: 1) geological modeling from outcrop data only, as these data types are generally sparse and mainly distributed in 2D at large scale but they may locally include high-resolution descriptions (e.g.: facies, strata local variability, etc.); 2) CO2 storage studies as many scales of investigations are required, from meter to regional ones, to estimate storage capacities and associated risks. Recent approaches propose to define distances between models to allow sophisticated multivariate statistics to be applied on the space of uncertainties so that only sub-samples, representative of initial set, are investigated for dynamic time-consuming studies. This work focuses on defining distances between models that characterize the topology of the reservoir rock network, i.e. its compactness or connectivity degree. The proposed strategy relies on the study of the reservoir rock skeleton. The skeleton of an object corresponds to its median feature. A skeleton is computed for each reservoir rock geobody and studied through a graph spectral analysis. To achieve this, the skeleton is converted into a graph structure. The spectral analysis applied on this graph structure allows a distance to be defined between pairs of graphs. Therefore, this distance is used as support for clustering analysis to gather models that share the same reservoir rock topology. To show the ability of the defined distances to discriminate different types of reservoir connectivity, a synthetic data set of fluvial models with different geological settings was generated and studied using the proposed approach. The results of the clustering analysis are shown and discussed.

Lifetime prediction for the subsurface crack propagation using three-dimensional dynamic FEA model

NASA Astrophysics Data System (ADS)

Yin, Yuan; Chen, Yun-Xia; Liu, Le

2017-03-01

The subsurface crack propagation is one of the major interests for gear system research. The subsurface crack propagation lifetime is the number of cycles remaining for a spall to appear, which can be obtained through either stress intensity factor or accumulated plastic strain analysis. In this paper, the heavy loads are applied to the gear system. When choosing stress intensity factor, the high compressive stress suppresses Mode I stress intensities and severely reduces Mode II stress intensities in the heavily loaded lubricated contacts. Such that, the accumulated plastic strain is selected to calculate the subsurface crack propagation lifetime from the three-dimensional FEA model through ANSYS Workbench transient analysis. The three-dimensional gear FEA dynamic model with the subsurface crack is built through dividing the gears into several small elements. The calculation of the total cycles of the elements is proposed based on the time-varying accumulated plastic strain, which then will be used to calculate the subsurface crack propagation lifetime. During this process, the demonstration from a subsurface crack to a spall can be uncovered. In addition, different sizes of the elements around the subsurface crack are compared in this paper. The influences of the frictional coefficient and external torque on the crack propagation lifetime are also discussed. The results show that the lifetime of crack propagation decreases significantly when the external load T increasing from 100 N m to 150 N m. Given from the distributions of the accumulated plastic strain, the lifetime shares no significant difference when the frictional coefficient f ranging in 0.04-0.06.

Parameter discovery in stochastic biological models using simulated annealing and statistical model checking.

PubMed

Hussain, Faraz; Jha, Sumit K; Jha, Susmit; Langmead, Christopher J

2014-01-01

Stochastic models are increasingly used to study the behaviour of biochemical systems. While the structure of such models is often readily available from first principles, unknown quantitative features of the model are incorporated into the model as parameters. Algorithmic discovery of parameter values from experimentally observed facts remains a challenge for the computational systems biology community. We present a new parameter discovery algorithm that uses simulated annealing, sequential hypothesis testing, and statistical model checking to learn the parameters in a stochastic model. We apply our technique to a model of glucose and insulin metabolism used for in-silico validation of artificial pancreata and demonstrate its effectiveness by developing parallel CUDA-based implementation for parameter synthesis in this model.

Stochastic volatility models and Kelvin waves

NASA Astrophysics Data System (ADS)

Lipton, Alex; Sepp, Artur

2008-08-01

We use stochastic volatility models to describe the evolution of an asset price, its instantaneous volatility and its realized volatility. In particular, we concentrate on the Stein and Stein model (SSM) (1991) for the stochastic asset volatility and the Heston model (HM) (1993) for the stochastic asset variance. By construction, the volatility is not sign definite in SSM and is non-negative in HM. It is well known that both models produce closed-form expressions for the prices of vanilla option via the Lewis-Lipton formula. However, the numerical pricing of exotic options by means of the finite difference and Monte Carlo methods is much more complex for HM than for SSM. Until now, this complexity was considered to be an acceptable price to pay for ensuring that the asset volatility is non-negative. We argue that having negative stochastic volatility is a psychological rather than financial or mathematical problem, and advocate using SSM rather than HM in most applications. We extend SSM by adding volatility jumps and obtain a closed-form expression for the density of the asset price and its realized volatility. We also show that the current method of choice for solving pricing problems with stochastic volatility (via the affine ansatz for the Fourier-transformed density function) can be traced back to the Kelvin method designed in the 19th century for studying wave motion problems arising in fluid dynamics.

Dynamics of a Stochastic Predator-Prey Model with Stage Structure for Predator and Holling Type II Functional Response

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing; Hayat, Tasawar; Alsaedi, Ahmed

2018-01-01

In this paper, we develop and study a stochastic predator-prey model with stage structure for predator and Holling type II functional response. First of all, by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then, we obtain sufficient conditions for extinction of the predator populations in two cases, that is, the first case is that the prey population survival and the predator populations extinction; the second case is that all the prey and predator populations extinction. The existence of a stationary distribution implies stochastic weak stability. Numerical simulations are carried out to demonstrate the analytical results.

Dynamics of a Stochastic Predator-Prey Model with Stage Structure for Predator and Holling Type II Functional Response

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing; Hayat, Tasawar; Alsaedi, Ahmed

2018-06-01

In this paper, we develop and study a stochastic predator-prey model with stage structure for predator and Holling type II functional response. First of all, by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then, we obtain sufficient conditions for extinction of the predator populations in two cases, that is, the first case is that the prey population survival and the predator populations extinction; the second case is that all the prey and predator populations extinction. The existence of a stationary distribution implies stochastic weak stability. Numerical simulations are carried out to demonstrate the analytical results.

Didactic discussion of stochastic resonance effects and weak signals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adair, R.K.

1996-12-01

A simple, paradigmatic, model is used to illustrate some general properties of effects subsumed under the label stochastic resonance. In particular, analyses of the transparent model show that (1) a small amount of noise added to a much larger signal can greatly increase the response to the signal, but (2) a weak signal added to much larger noise will not generate a substantial added response. The conclusions drawn from the model illustrate the general result that stochastic resonance effects do not provide an avenue for signals that are much smaller than noise to affect biology. A further analysis demonstrates themore » effects of small signals in the shifting of biologically important chemical equilibria under conditions where stochastic resonance effects are significant.« less

3DHYDROGEOCHEM: A 3-DIMENSIONAL MODEL OF DENSITY-DEPENDENT SUBSURFACE FLOW AND THERMAL MULTISPECIES-MULTICOMPONENT HYDROGEOCHEMICAL TRANSPORT

EPA Science Inventory

This report presents a three-dimensional finite-element numerical model designed to simulate chemical transport in subsurface systems with temperature effect taken into account. The three-dimensional model is developed to provide (1) a tool of application, with which one is able...

Multiple well-shutdown tests and site-scale flow simulation in fractured rocks

USGS Publications Warehouse

Tiedeman, Claire; Lacombe, Pierre J.; Goode, Daniel J.

2010-01-01

A new method was developed for conducting aquifer tests in fractured-rock flow systems that have a pump-and-treat (P&T) operation for containing and removing groundwater contaminants. The method involves temporary shutdown of individual pumps in wells of the P&T system. Conducting aquifer tests in this manner has several advantages, including (1) no additional contaminated water is withdrawn, and (2) hydraulic containment of contaminants remains largely intact because pumping continues at most wells. The well-shutdown test method was applied at the former Naval Air Warfare Center (NAWC), West Trenton, New Jersey, where a P&T operation is designed to contain and remove trichloroethene and its daughter products in the dipping fractured sedimentary rocks underlying the site. The detailed site-scale subsurface geologic stratigraphy, a three-dimensional MODFLOW model, and inverse methods in UCODE_2005 were used to analyze the shutdown tests. In the model, a deterministic method was used for representing the highly heterogeneous hydraulic conductivity distribution and simulations were conducted using an equivalent porous media method. This approach was very successful for simulating the shutdown tests, contrary to a common perception that flow in fractured rocks must be simulated using a stochastic or discrete fracture representation of heterogeneity. Use of inverse methods to simultaneously calibrate the model to the multiple shutdown tests was integral to the effectiveness of the approach.

Stochastic Gabor reflectivity and acoustic impedance inversion

NASA Astrophysics Data System (ADS)

Hariri Naghadeh, Diako; Morley, Christopher Keith; Ferguson, Angus John

2018-02-01

To delineate subsurface lithology to estimate petrophysical properties of a reservoir, it is possible to use acoustic impedance (AI) which is the result of seismic inversion. To change amplitude to AI, removal of wavelet effects from the seismic signal in order to get a reflection series, and subsequently transforming those reflections to AI, is vital. To carry out seismic inversion correctly it is important to not assume that the seismic signal is stationary. However, all stationary deconvolution methods are designed following that assumption. To increase temporal resolution and interpretation ability, amplitude compensation and phase correction are inevitable. Those are pitfalls of stationary reflectivity inversion. Although stationary reflectivity inversion methods are trying to estimate reflectivity series, because of incorrect assumptions their estimations will not be correct, but may be useful. Trying to convert those reflection series to AI, also merging with the low frequency initial model, can help us. The aim of this study was to apply non-stationary deconvolution to eliminate time variant wavelet effects from the signal and to convert the estimated reflection series to the absolute AI by getting bias from well logs. To carry out this aim, stochastic Gabor inversion in the time domain was used. The Gabor transform derived the signal’s time-frequency analysis and estimated wavelet properties from different windows. Dealing with different time windows gave an ability to create a time-variant kernel matrix, which was used to remove matrix effects from seismic data. The result was a reflection series that does not follow the stationary assumption. The subsequent step was to convert those reflections to AI using well information. Synthetic and real data sets were used to show the ability of the introduced method. The results highlight that the time cost to get seismic inversion is negligible related to general Gabor inversion in the frequency domain. Also, obtaining bias could help the method to estimate reliable AI. To justify the effect of random noise on deterministic and stochastic inversion results, a stationary noisy trace with signal-to-noise ratio equal to 2 was used. The results highlight the inability of deterministic inversion in dealing with a noisy data set even using a high number of regularization parameters. Also, despite the low level of signal, stochastic Gabor inversion not only can estimate correctly the wavelet’s properties but also, because of bias from well logs, the inversion result is very close to the real AI. Comparing deterministic and introduced inversion results on a real data set shows that low resolution results, especially in the deeper parts of seismic sections using deterministic inversion, creates significant reliability problems for seismic prospects, but this pitfall is solved completely using stochastic Gabor inversion. The estimated AI using Gabor inversion in the time domain is much better and faster than general Gabor inversion in the frequency domain. This is due to the extra number of windows required to analyze the time-frequency information and also the amount of temporal increment between windows. In contrast, stochastic Gabor inversion can estimate trustable physical properties close to the real characteristics. Applying to a real data set could give an ability to detect the direction of volcanic intrusion and the ability of lithology distribution delineation along the fan. Comparing the inversion results highlights the efficiency of stochastic Gabor inversion to delineate lateral lithology changes because of the improved frequency content and zero phasing of the final inversion volume.

EXPOSURE ASSESSMENT MODELING FOR HYDROCARBON SPILLS INTO THE SUBSURFACE

EPA Science Inventory

Hydrocarbons which enter the subsurface through spills or leaks may create serious, long-lived ground-water contamination problems. onventional finite difference and finite element models of multiphase, multicomponent flow often have extreme requirements for both computer time an...

CALIBRATION OF SUBSURFACE BATCH AND REACTIVE-TRANSPORT MODELS INVOLVING COMPLEX BIOGEOCHEMICAL PROCESSES

EPA Science Inventory

In this study, the calibration of subsurface batch and reactive-transport models involving complex biogeochemical processes was systematically evaluated. Two hypothetical nitrate biodegradation scenarios were developed and simulated in numerical experiments to evaluate the perfor...

3D subsurface geological modeling using GIS, remote sensing, and boreholes data

NASA Astrophysics Data System (ADS)

Kavoura, Katerina; Konstantopoulou, Maria; Kyriou, Aggeliki; Nikolakopoulos, Konstantinos G.; Sabatakakis, Nikolaos; Depountis, Nikolaos

2016-08-01

The current paper presents the combined use of geological-geotechnical insitu data, remote sensing data and GIS techniques for the evaluation of a subsurface geological model. High accuracy Digital Surface Model (DSM), airphotos mosaic and satellite data, with a spatial resolution of 0.5m were used for an othophoto base map compilation of the study area. Geological - geotechnical data obtained from exploratory boreholes and the 1:5000 engineering geological maps were digitized and implemented in a GIS platform for a three - dimensional subsurface model evaluation. The study is located at the North part of Peloponnese along the new national road.

On Local Homogeneity and Stochastically Ordered Mixed Rasch Models

ERIC Educational Resources Information Center

Kreiner, Svend; Hansen, Mogens; Hansen, Carsten Rosenberg

2006-01-01

Mixed Rasch models add latent classes to conventional Rasch models, assuming that the Rasch model applies within each class and that relative difficulties of items are different in two or more latent classes. This article considers a family of stochastically ordered mixed Rasch models, with ordinal latent classes characterized by increasing total…

Kinetic theory of age-structured stochastic birth-death processes

NASA Astrophysics Data System (ADS)

Greenman, Chris D.; Chou, Tom

2016-01-01

Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov--Born--Green--Kirkwood--Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution.

The critical domain size of stochastic population models.

PubMed

Reimer, Jody R; Bonsall, Michael B; Maini, Philip K

2017-02-01

Identifying the critical domain size necessary for a population to persist is an important question in ecology. Both demographic and environmental stochasticity impact a population's ability to persist. Here we explore ways of including this variability. We study populations with distinct dispersal and sedentary stages, which have traditionally been modelled using a deterministic integrodifference equation (IDE) framework. Individual-based models (IBMs) are the most intuitive stochastic analogues to IDEs but yield few analytic insights. We explore two alternate approaches; one is a scaling up to the population level using the Central Limit Theorem, and the other a variation on both Galton-Watson branching processes and branching processes in random environments. These branching process models closely approximate the IBM and yield insight into the factors determining the critical domain size for a given population subject to stochasticity.

Stochastic Approximation Methods for Latent Regression Item Response Models

ERIC Educational Resources Information Center

von Davier, Matthias; Sinharay, Sandip

2010-01-01

This article presents an application of a stochastic approximation expectation maximization (EM) algorithm using a Metropolis-Hastings (MH) sampler to estimate the parameters of an item response latent regression model. Latent regression item response models are extensions of item response theory (IRT) to a latent variable model with covariates…

Stochastic models for regulatory networks of the genetic toggle switch.

PubMed

Tian, Tianhai; Burrage, Kevin

2006-05-30

Bistability arises within a wide range of biological systems from the lambda phage switch in bacteria to cellular signal transduction pathways in mammalian cells. Changes in regulatory mechanisms may result in genetic switching in a bistable system. Recently, more and more experimental evidence in the form of bimodal population distributions indicates that noise plays a very important role in the switching of bistable systems. Although deterministic models have been used for studying the existence of bistability properties under various system conditions, these models cannot realize cell-to-cell fluctuations in genetic switching. However, there is a lag in the development of stochastic models for studying the impact of noise in bistable systems because of the lack of detailed knowledge of biochemical reactions, kinetic rates, and molecular numbers. In this work, we develop a previously undescribed general technique for developing quantitative stochastic models for large-scale genetic regulatory networks by introducing Poisson random variables into deterministic models described by ordinary differential equations. Two stochastic models have been proposed for the genetic toggle switch interfaced with either the SOS signaling pathway or a quorum-sensing signaling pathway, and we have successfully realized experimental results showing bimodal population distributions. Because the introduced stochastic models are based on widely used ordinary differential equation models, the success of this work suggests that this approach is a very promising one for studying noise in large-scale genetic regulatory networks.

Stochastic models for regulatory networks of the genetic toggle switch

PubMed Central

Tian, Tianhai; Burrage, Kevin

2006-01-01

Bistability arises within a wide range of biological systems from the λ phage switch in bacteria to cellular signal transduction pathways in mammalian cells. Changes in regulatory mechanisms may result in genetic switching in a bistable system. Recently, more and more experimental evidence in the form of bimodal population distributions indicates that noise plays a very important role in the switching of bistable systems. Although deterministic models have been used for studying the existence of bistability properties under various system conditions, these models cannot realize cell-to-cell fluctuations in genetic switching. However, there is a lag in the development of stochastic models for studying the impact of noise in bistable systems because of the lack of detailed knowledge of biochemical reactions, kinetic rates, and molecular numbers. In this work, we develop a previously undescribed general technique for developing quantitative stochastic models for large-scale genetic regulatory networks by introducing Poisson random variables into deterministic models described by ordinary differential equations. Two stochastic models have been proposed for the genetic toggle switch interfaced with either the SOS signaling pathway or a quorum-sensing signaling pathway, and we have successfully realized experimental results showing bimodal population distributions. Because the introduced stochastic models are based on widely used ordinary differential equation models, the success of this work suggests that this approach is a very promising one for studying noise in large-scale genetic regulatory networks. PMID:16714385

Stochastic cellular automata model of cell migration, proliferation and differentiation: validation with in vitro cultures of muscle satellite cells.

PubMed

Garijo, N; Manzano, R; Osta, R; Perez, M A

2012-12-07

Cell migration and proliferation has been modelled in the literature as a process similar to diffusion. However, using diffusion models to simulate the proliferation and migration of cells tends to create a homogeneous distribution in the cell density that does not correlate to empirical observations. In fact, the mechanism of cell dispersal is not diffusion. Cells disperse by crawling or proliferation, or are transported in a moving fluid. The use of cellular automata, particle models or cell-based models can overcome this limitation. This paper presents a stochastic cellular automata model to simulate the proliferation, migration and differentiation of cells. These processes are considered as completely stochastic as well as discrete. The model developed was applied to predict the behaviour of in vitro cell cultures performed with adult muscle satellite cells. Moreover, non homogeneous distribution of cells has been observed inside the culture well and, using the above mentioned stochastic cellular automata model, we have been able to predict this heterogeneous cell distribution and compute accurate quantitative results. Differentiation was also incorporated into the computational simulation. The results predicted the myotube formation that typically occurs with adult muscle satellite cells. In conclusion, we have shown how a stochastic cellular automata model can be implemented and is capable of reproducing the in vitro behaviour of adult muscle satellite cells. Copyright © 2012 Elsevier Ltd. All rights reserved.

Change in ocean subsurface environment to suppress tropical cyclone intensification under global warming.

PubMed

Huang, Ping; Lin, I-I; Chou, Chia; Huang, Rong-Hui

2015-05-18

Tropical cyclones (TCs) are hazardous natural disasters. Because TC intensification is significantly controlled by atmosphere and ocean environments, changes in these environments may cause changes in TC intensity. Changes in surface and subsurface ocean conditions can both influence a TC's intensification. Regarding global warming, minimal exploration of the subsurface ocean has been undertaken. Here we investigate future subsurface ocean environment changes projected by 22 state-of-the-art climate models and suggest a suppressive effect of subsurface oceans on the intensification of future TCs. Under global warming, the subsurface vertical temperature profile can be sharpened in important TC regions, which may contribute to a stronger ocean coupling (cooling) effect during the intensification of future TCs. Regarding a TC, future subsurface ocean environments may be more suppressive than the existing subsurface ocean environments. This suppressive effect is not spatially uniform and may be weak in certain local areas.

Change in ocean subsurface environment to suppress tropical cyclone intensification under global warming

PubMed Central

Huang, Ping; Lin, I. -I; Chou, Chia; Huang, Rong-Hui

2015-01-01

Tropical cyclones (TCs) are hazardous natural disasters. Because TC intensification is significantly controlled by atmosphere and ocean environments, changes in these environments may cause changes in TC intensity. Changes in surface and subsurface ocean conditions can both influence a TC's intensification. Regarding global warming, minimal exploration of the subsurface ocean has been undertaken. Here we investigate future subsurface ocean environment changes projected by 22 state-of-the-art climate models and suggest a suppressive effect of subsurface oceans on the intensification of future TCs. Under global warming, the subsurface vertical temperature profile can be sharpened in important TC regions, which may contribute to a stronger ocean coupling (cooling) effect during the intensification of future TCs. Regarding a TC, future subsurface ocean environments may be more suppressive than the existing subsurface ocean environments. This suppressive effect is not spatially uniform and may be weak in certain local areas. PMID:25982028

Stochastic Stability of Sampled Data Systems with a Jump Linear Controller

NASA Technical Reports Server (NTRS)

Gonzalez, Oscar R.; Herencia-Zapana, Heber; Gray, W. Steven

2004-01-01

In this paper an equivalence between the stochastic stability of a sampled-data system and its associated discrete-time representation is established. The sampled-data system consists of a deterministic, linear, time-invariant, continuous-time plant and a stochastic, linear, time-invariant, discrete-time, jump linear controller. The jump linear controller models computer systems and communication networks that are subject to stochastic upsets or disruptions. This sampled-data model has been used in the analysis and design of fault-tolerant systems and computer-control systems with random communication delays without taking into account the inter-sample response. This paper shows that the known equivalence between the stability of a deterministic sampled-data system and the associated discrete-time representation holds even in a stochastic framework.

Effects of stochastic time-delayed feedback on a dynamical system modeling a chemical oscillator.

PubMed

González Ochoa, Héctor O; Perales, Gualberto Solís; Epstein, Irving R; Femat, Ricardo

2018-05-01

We examine how stochastic time-delayed negative feedback affects the dynamical behavior of a model oscillatory reaction. We apply constant and stochastic time-delayed negative feedbacks to a point Field-Körös-Noyes photosensitive oscillator and compare their effects. Negative feedback is applied in the form of simulated inhibitory electromagnetic radiation with an intensity proportional to the concentration of oxidized light-sensitive catalyst in the oscillator. We first characterize the system under nondelayed inhibitory feedback; then we explore and compare the effects of constant (deterministic) versus stochastic time-delayed feedback. We find that the oscillatory amplitude, frequency, and waveform are essentially preserved when low-dispersion stochastic delayed feedback is used, whereas small but measurable changes appear when a large dispersion is applied.

Effects of stochastic time-delayed feedback on a dynamical system modeling a chemical oscillator

NASA Astrophysics Data System (ADS)

González Ochoa, Héctor O.; Perales, Gualberto Solís; Epstein, Irving R.; Femat, Ricardo

2018-05-01

We examine how stochastic time-delayed negative feedback affects the dynamical behavior of a model oscillatory reaction. We apply constant and stochastic time-delayed negative feedbacks to a point Field-Körös-Noyes photosensitive oscillator and compare their effects. Negative feedback is applied in the form of simulated inhibitory electromagnetic radiation with an intensity proportional to the concentration of oxidized light-sensitive catalyst in the oscillator. We first characterize the system under nondelayed inhibitory feedback; then we explore and compare the effects of constant (deterministic) versus stochastic time-delayed feedback. We find that the oscillatory amplitude, frequency, and waveform are essentially preserved when low-dispersion stochastic delayed feedback is used, whereas small but measurable changes appear when a large dispersion is applied.

A one-dimensional model of subsurface hillslope flow

Treesearch

Jason C. Fisher

1997-01-01

Abstract - A one-dimensional, finite difference model of saturated subsurface flow within a hillslope was developed. The model uses rainfall, elevation data, a hydraulic conductivity, and a storage coefficient to predict the saturated thickness in time and space. The model was tested against piezometric data collected in a swale located in the headwaters of the North...

Stochastic modeling of Lagrangian accelerations

NASA Astrophysics Data System (ADS)

Reynolds, Andy

2002-11-01

It is shown how Sawford's second-order Lagrangian stochastic model (Phys. Fluids A 3, 1577-1586, 1991) for fluid-particle accelerations can be combined with a model for the evolution of the dissipation rate (Pope and Chen, Phys. Fluids A 2, 1437-1449, 1990) to produce a Lagrangian stochastic model that is consistent with both the measured distribution of Lagrangian accelerations (La Porta et al., Nature 409, 1017-1019, 2001) and Kolmogorov's similarity theory. The later condition is found not to be satisfied when a constant dissipation rate is employed and consistency with prescribed acceleration statistics is enforced through fulfilment of a well-mixed condition.

Dynamical behavior of a stochastic SVIR epidemic model with vaccination

NASA Astrophysics Data System (ADS)

Zhang, Xinhong; Jiang, Daqing; Hayat, Tasawar; Ahmad, Bashir

2017-10-01

In this paper, we investigate the dynamical behavior of SVIR models in random environments. Firstly, we show that if R0s < 1, the disease of stochastic autonomous SVIR model will die out exponentially; if R˜0s > 1, the disease will be prevail. Moreover, this system admits a unique stationary distribution and it is ergodic when R˜0s > 1. Results show that environmental white noise is helpful for disease control. Secondly, we give sufficient conditions for the existence of nontrivial periodic solutions to stochastic SVIR model with periodic parameters. Finally, numerical simulations validate the analytical results.

Universality in stochastic exponential growth.

PubMed

Iyer-Biswas, Srividya; Crooks, Gavin E; Scherer, Norbert F; Dinner, Aaron R

2014-07-11

Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.

An inexact mixed risk-aversion two-stage stochastic programming model for water resources management under uncertainty.

PubMed

Li, W; Wang, B; Xie, Y L; Huang, G H; Liu, L

2015-02-01

Uncertainties exist in the water resources system, while traditional two-stage stochastic programming is risk-neutral and compares the random variables (e.g., total benefit) to identify the best decisions. To deal with the risk issues, a risk-aversion inexact two-stage stochastic programming model is developed for water resources management under uncertainty. The model was a hybrid methodology of interval-parameter programming, conditional value-at-risk measure, and a general two-stage stochastic programming framework. The method extends on the traditional two-stage stochastic programming method by enabling uncertainties presented as probability density functions and discrete intervals to be effectively incorporated within the optimization framework. It could not only provide information on the benefits of the allocation plan to the decision makers but also measure the extreme expected loss on the second-stage penalty cost. The developed model was applied to a hypothetical case of water resources management. Results showed that that could help managers generate feasible and balanced risk-aversion allocation plans, and analyze the trade-offs between system stability and economy.

Universality in Stochastic Exponential Growth

NASA Astrophysics Data System (ADS)

Iyer-Biswas, Srividya; Crooks, Gavin E.; Scherer, Norbert F.; Dinner, Aaron R.

2014-07-01

Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hammond, Glenn Edward; Bao, J; Huang, M

Hyporheic exchange is a critical mechanism shaping hydrological and biogeochemical processes along a river corridor. Recent studies on quantifying the hyporheic exchange were mostly limited to local scales due to field inaccessibility, computational demand, and complexity of geomorphology and subsurface geology. Surface flow conditions and subsurface physical properties are well known factors on modulating the hyporheic exchange, but quantitative understanding of their impacts on the strength and direction of hyporheic exchanges at reach scales is absent. In this study, a high resolution computational fluid dynamics (CFD) model that couples surface and subsurface flow and transport is employed to simulate hyporheicmore » exchanges in a 7-km long reach along the main-stem of the Columbia River. Assuming that the hyporheic exchange does not affect surface water flow conditions due to its negligible magnitude compared to the volume and velocity of river water, we developed a one-way coupled surface and subsurface water flow model using the commercial CFD software STAR-CCM+. The model integrates the Reynolds-averaged Navier-Stokes (RANS) equation solver with a realizable κ-ε two-layer turbulence model, a two-layer all y + wall treatment, and the volume of fluid (VOF) method, and is used to simulate hyporheic exchanges by tracking the free water-air interface as well as flow in the river and the subsurface porous media. The model is validated against measurements from acoustic Doppler current profiler (ADCP) in the stream water and hyporheic fluxes derived from a set of temperature profilers installed across the riverbed. The validated model is then employed to systematically investigate how hyporheic exchanges are influenced by surface water fluid dynamics strongly regulated by upstream dam operations, as well as subsurface structures (e.g. thickness of riverbed and subsurface formation layers) and hydrogeological properties (e.g. permeability). The results suggest that the thickness of riverbed alluvium layer is the dominant factor for reach-scale hyporheic exchanges, followed by the alluvium permeability, the depth of the underlying impermeable layer, and the assumption of hydrostatic pressure.« less

A multi-scale experimental and simulation approach for fractured subsurface systems

NASA Astrophysics Data System (ADS)

Viswanathan, H. S.; Carey, J. W.; Frash, L.; Karra, S.; Hyman, J.; Kang, Q.; Rougier, E.; Srinivasan, G.

2017-12-01

Fractured systems play an important role in numerous subsurface applications including hydraulic fracturing, carbon sequestration, geothermal energy and underground nuclear test detection. Fractures that range in scale from microns to meters and their structure control the behavior of these systems which provide over 85% of our energy and 50% of US drinking water. Determining the key mechanisms in subsurface fractured systems has been impeded due to the lack of sophisticated experimental methods to measure fracture aperture and connectivity, multiphase permeability, and chemical exchange capacities at the high temperature, pressure, and stresses present in the subsurface. In this study, we developed and use microfluidic and triaxial core flood experiments required to reveal the fundamental dynamics of fracture-fluid interactions. In addition we have developed high fidelity fracture propagation and discrete fracture network flow models to simulate these fractured systems. We also have developed reduced order models of these fracture simulators in order to conduct uncertainty quantification for these systems. We demonstrate an integrated experimental/modeling approach that allows for a comprehensive characterization of fractured systems and develop models that can be used to optimize the reservoir operating conditions over a range of subsurface conditions.

MONALISA for stochastic simulations of Petri net models of biochemical systems.

PubMed

Balazki, Pavel; Lindauer, Klaus; Einloft, Jens; Ackermann, Jörg; Koch, Ina

2015-07-10

The concept of Petri nets (PN) is widely used in systems biology and allows modeling of complex biochemical systems like metabolic systems, signal transduction pathways, and gene expression networks. In particular, PN allows the topological analysis based on structural properties, which is important and useful when quantitative (kinetic) data are incomplete or unknown. Knowing the kinetic parameters, the simulation of time evolution of such models can help to study the dynamic behavior of the underlying system. If the number of involved entities (molecules) is low, a stochastic simulation should be preferred against the classical deterministic approach of solving ordinary differential equations. The Stochastic Simulation Algorithm (SSA) is a common method for such simulations. The combination of the qualitative and semi-quantitative PN modeling and stochastic analysis techniques provides a valuable approach in the field of systems biology. Here, we describe the implementation of stochastic analysis in a PN environment. We extended MONALISA - an open-source software for creation, visualization and analysis of PN - by several stochastic simulation methods. The simulation module offers four simulation modes, among them the stochastic mode with constant firing rates and Gillespie's algorithm as exact and approximate versions. The simulator is operated by a user-friendly graphical interface and accepts input data such as concentrations and reaction rate constants that are common parameters in the biological context. The key features of the simulation module are visualization of simulation, interactive plotting, export of results into a text file, mathematical expressions for describing simulation parameters, and up to 500 parallel simulations of the same parameter sets. To illustrate the method we discuss a model for insulin receptor recycling as case study. We present a software that combines the modeling power of Petri nets with stochastic simulation of dynamic processes in a user-friendly environment supported by an intuitive graphical interface. The program offers a valuable alternative to modeling, using ordinary differential equations, especially when simulating single-cell experiments with low molecule counts. The ability to use mathematical expressions provides an additional flexibility in describing the simulation parameters. The open-source distribution allows further extensions by third-party developers. The software is cross-platform and is licensed under the Artistic License 2.0.

A Stochastic Differential Equation Model for the Spread of HIV amongst People Who Inject Drugs.

PubMed

Liang, Yanfeng; Greenhalgh, David; Mao, Xuerong

2016-01-01

We introduce stochasticity into the deterministic differential equation model for the spread of HIV amongst people who inject drugs (PWIDs) studied by Greenhalgh and Hay (1997). This was based on the original model constructed by Kaplan (1989) which analyses the behaviour of HIV/AIDS amongst a population of PWIDs. We derive a stochastic differential equation (SDE) for the fraction of PWIDs who are infected with HIV at time. The stochasticity is introduced using the well-known standard technique of parameter perturbation. We first prove that the resulting SDE for the fraction of infected PWIDs has a unique solution in (0, 1) provided that some infected PWIDs are initially present and next construct the conditions required for extinction and persistence. Furthermore, we show that there exists a stationary distribution for the persistence case. Simulations using realistic parameter values are then constructed to illustrate and support our theoretical results. Our results provide new insight into the spread of HIV amongst PWIDs. The results show that the introduction of stochastic noise into a model for the spread of HIV amongst PWIDs can cause the disease to die out in scenarios where deterministic models predict disease persistence.

A study about the existence of the leverage effect in stochastic volatility models

NASA Astrophysics Data System (ADS)

Florescu, Ionuţ; Pãsãricã, Cristian Gabriel

2009-02-01

The empirical relationship between the return of an asset and the volatility of the asset has been well documented in the financial literature. Named the leverage effect or sometimes risk-premium effect, it is observed in real data that, when the return of the asset decreases, the volatility increases and vice versa. Consequently, it is important to demonstrate that any formulated model for the asset price is capable of generating this effect observed in practice. Furthermore, we need to understand the conditions on the parameters present in the model that guarantee the apparition of the leverage effect. In this paper we analyze two general specifications of stochastic volatility models and their capability of generating the perceived leverage effect. We derive conditions for the apparition of leverage effect in both of these stochastic volatility models. We exemplify using stochastic volatility models used in practice and we explicitly state the conditions for the existence of the leverage effect in these examples.

Modelling and simulating decision processes of linked lives: An approach based on concurrent processes and stochastic race.

PubMed

Warnke, Tom; Reinhardt, Oliver; Klabunde, Anna; Willekens, Frans; Uhrmacher, Adelinde M

2017-10-01

Individuals' decision processes play a central role in understanding modern migration phenomena and other demographic processes. Their integration into agent-based computational demography depends largely on suitable support by a modelling language. We are developing the Modelling Language for Linked Lives (ML3) to describe the diverse decision processes of linked lives succinctly in continuous time. The context of individuals is modelled by networks the individual is part of, such as family ties and other social networks. Central concepts, such as behaviour conditional on agent attributes, age-dependent behaviour, and stochastic waiting times, are tightly integrated in the language. Thereby, alternative decisions are modelled by concurrent processes that compete by stochastic race. Using a migration model, we demonstrate how this allows for compact description of complex decisions, here based on the Theory of Planned Behaviour. We describe the challenges for the simulation algorithm posed by stochastic race between multiple concurrent complex decisions.

Stochastic Spectral Descent for Discrete Graphical Models

DOE PAGES

Carlson, David; Hsieh, Ya-Ping; Collins, Edo; ...

2015-12-14

Interest in deep probabilistic graphical models has in-creased in recent years, due to their state-of-the-art performance on many machine learning applications. Such models are typically trained with the stochastic gradient method, which can take a significant number of iterations to converge. Since the computational cost of gradient estimation is prohibitive even for modestly sized models, training becomes slow and practically usable models are kept small. In this paper we propose a new, largely tuning-free algorithm to address this problem. Our approach derives novel majorization bounds based on the Schatten- norm. Intriguingly, the minimizers of these bounds can be interpreted asmore » gradient methods in a non-Euclidean space. We thus propose using a stochastic gradient method in non-Euclidean space. We both provide simple conditions under which our algorithm is guaranteed to converge, and demonstrate empirically that our algorithm leads to dramatically faster training and improved predictive ability compared to stochastic gradient descent for both directed and undirected graphical models.« less

Performance of stochastic approaches for forecasting river water quality.

PubMed

Ahmad, S; Khan, I H; Parida, B P

2001-12-01

This study analysed water quality data collected from the river Ganges in India from 1981 to 1990 for forecasting using stochastic models. Initially the box and whisker plots and Kendall's tau test were used to identify the trends during the study period. For detecting the possible intervention in the data the time series plots and cusum charts were used. The three approaches of stochastic modelling which account for the effect of seasonality in different ways. i.e. multiplicative autoregressive integrated moving average (ARIMA) model. deseasonalised model and Thomas-Fiering model were used to model the observed pattern in water quality. The multiplicative ARIMA model having both nonseasonal and seasonal components were, in general, identified as appropriate models. In the deseasonalised modelling approach, the lower order ARIMA models were found appropriate for the stochastic component. The set of Thomas-Fiering models were formed for each month for all water quality parameters. These models were then used to forecast the future values. The error estimates of forecasts from the three approaches were compared to identify the most suitable approach for the reliable forecast. The deseasonalised modelling approach was recommended for forecasting of water quality parameters of a river.

Stochastic bifurcation in a model of love with colored noise

NASA Astrophysics Data System (ADS)

Yue, Xiaokui; Dai, Honghua; Yuan, Jianping

2015-07-01

In this paper, we wish to examine the stochastic bifurcation induced by multiplicative Gaussian colored noise in a dynamical model of love where the random factor is used to describe the complexity and unpredictability of psychological systems. First, the dynamics in deterministic love-triangle model are considered briefly including equilibrium points and their stability, chaotic behaviors and chaotic attractors. Then, the influences of Gaussian colored noise with different parameters are explored such as the phase plots, top Lyapunov exponents, stationary probability density function (PDF) and stochastic bifurcation. The stochastic P-bifurcation through a qualitative change of the stationary PDF will be observed and bifurcation diagram on parameter plane of correlation time and noise intensity is presented to find the bifurcation behaviors in detail. Finally, the top Lyapunov exponent is computed to determine the D-bifurcation when the noise intensity achieves to a critical value. By comparison, we find there is no connection between two kinds of stochastic bifurcation.

Understanding the Impacts of Climate Change and Land Use Dynamics Using a Fully Coupled Hydrologic Feedback Model between Surface and Subsurface Systems

NASA Astrophysics Data System (ADS)

Park, C.; Lee, J.; Koo, M.

2011-12-01

Climate is the most critical driving force of the hydrologic system of the Earth. Since the industrial revolution, the impacts of anthropogenic activities to the Earth environment have been expanded and accelerated. Especially, the global emission of carbon dioxide into the atmosphere is known to have significantly increased temperature and affected the hydrologic system. Many hydrologists have contributed to the studies regarding the climate change on the hydrologic system since the Intergovernmental Panel on Climate Change (IPCC) was created in 1988. Among many components in the hydrologic system groundwater and its response to the climate change and anthropogenic activities are not fully understood due to the complexity of subsurface conditions between the surface and the groundwater table. A new spatio-temporal hydrologic model has been developed to estimate the impacts of climate change and land use dynamics on the groundwater. The model consists of two sub-models: a surface model and a subsurface model. The surface model involves three surface processes: interception, runoff, and evapotranspiration, and the subsurface model does also three subsurface processes: soil moisture balance, recharge, and groundwater flow. The surface model requires various input data including land use, soil types, vegetation types, topographical elevations, and meteorological data. The surface model simulates daily hydrological processes for rainfall interception, surface runoff varied by land use change and crop growth, and evapotranspiration controlled by soil moisture balance. The daily soil moisture balance is a key element to link two sub-models as it calculates infiltration and groundwater recharge by considering a time delay routing through a vadose zone down to the groundwater table. MODFLOW is adopted to simulate groundwater flow and interaction with surface water components as well. The model is technically flexible to add new model or modify existing model as it is developed with an object-oriented language - Python. The model also can easily be localized by simple modification of soil and crop properties. The actual application of the model after calibration was successful and results showed reliable water balance and interaction between the surface and subsurface hydrologic systems.

The threshold of a stochastic delayed SIR epidemic model with vaccination

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing

2016-11-01

In this paper, we study the threshold dynamics of a stochastic delayed SIR epidemic model with vaccination. We obtain sufficient conditions for extinction and persistence in the mean of the epidemic. The threshold between persistence in the mean and extinction of the stochastic system is also obtained. Compared with the corresponding deterministic model, the threshold affected by the white noise is smaller than the basic reproduction number Rbar0 of the deterministic system. Results show that time delay has important effects on the persistence and extinction of the epidemic.

Reflected stochastic differential equation models for constrained animal movement

USGS Publications Warehouse

Hanks, Ephraim M.; Johnson, Devin S.; Hooten, Mevin B.

2017-01-01

Movement for many animal species is constrained in space by barriers such as rivers, shorelines, or impassable cliffs. We develop an approach for modeling animal movement constrained in space by considering a class of constrained stochastic processes, reflected stochastic differential equations. Our approach generalizes existing methods for modeling unconstrained animal movement. We present methods for simulation and inference based on augmenting the constrained movement path with a latent unconstrained path and illustrate this augmentation with a simulation example and an analysis of telemetry data from a Steller sea lion (Eumatopias jubatus) in southeast Alaska.

Development and validation of a stochastic model for potential growth of Listeria monocytogenes in naturally contaminated lightly preserved seafood.

PubMed

Mejlholm, Ole; Bøknæs, Niels; Dalgaard, Paw

2015-02-01

A new stochastic model for the simultaneous growth of Listeria monocytogenes and lactic acid bacteria (LAB) was developed and validated on data from naturally contaminated samples of cold-smoked Greenland halibut (CSGH) and cold-smoked salmon (CSS). During industrial processing these samples were added acetic and/or lactic acids. The stochastic model was developed from an existing deterministic model including the effect of 12 environmental parameters and microbial interaction (O. Mejlholm and P. Dalgaard, Food Microbiology, submitted for publication). Observed maximum population density (MPD) values of L. monocytogenes in naturally contaminated samples of CSGH and CSS were accurately predicted by the stochastic model based on measured variability in product characteristics and storage conditions. Results comparable to those from the stochastic model were obtained, when product characteristics of the least and most preserved sample of CSGH and CSS were used as input for the existing deterministic model. For both modelling approaches, it was shown that lag time and the effect of microbial interaction needs to be included to accurately predict MPD values of L. monocytogenes. Addition of organic acids to CSGH and CSS was confirmed as a suitable mitigation strategy against the risk of growth by L. monocytogenes as both types of products were in compliance with the EU regulation on ready-to-eat foods. Copyright © 2014 Elsevier Ltd. All rights reserved.

A Hybrid Stochastic-Neuro-Fuzzy Model-Based System for In-Flight Gas Turbine Engine Diagnostics

DTIC Science & Technology

2001-04-05

Margin (ADM) and (ii) Fault Detection Margin (FDM). Key Words: ANFIS, Engine Health Monitoring , Gas Path Analysis, and Stochastic Analysis Adaptive Network...The paper illustrates the application of a hybrid Stochastic- Fuzzy -Inference Model-Based System (StoFIS) to fault diagnostics and prognostics for both...operational history monitored on-line by the engine health management (EHM) system. To capture the complex functional relationships between different

Estimation of stochastic volatility by using Ornstein-Uhlenbeck type models

NASA Astrophysics Data System (ADS)

Mariani, Maria C.; Bhuiyan, Md Al Masum; Tweneboah, Osei K.

2018-02-01

In this study, we develop a technique for estimating the stochastic volatility (SV) of a financial time series by using Ornstein-Uhlenbeck type models. Using the daily closing prices from developed and emergent stock markets, we conclude that the incorporation of stochastic volatility into the time varying parameter estimation significantly improves the forecasting performance via Maximum Likelihood Estimation. Furthermore, our estimation algorithm is feasible with large data sets and have good convergence properties.

Stochastic differential equation model for linear growth birth and death processes with immigration and emigration

DOE Office of Scientific and Technical Information (OSTI.GOV)

Granita, E-mail: granitafc@gmail.com; Bahar, A.

This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found.

Stochastic Investigation of Natural Frequency for Functionally Graded Plates

NASA Astrophysics Data System (ADS)

Karsh, P. K.; Mukhopadhyay, T.; Dey, S.

2018-03-01

This paper presents the stochastic natural frequency analysis of functionally graded plates by applying artificial neural network (ANN) approach. Latin hypercube sampling is utilised to train the ANN model. The proposed algorithm for stochastic natural frequency analysis of FGM plates is validated and verified with original finite element method and Monte Carlo simulation (MCS). The combined stochastic variation of input parameters such as, elastic modulus, shear modulus, Poisson ratio, and mass density are considered. Power law is applied to distribute the material properties across the thickness. The present ANN model reduces the sample size and computationally found efficient as compared to conventional Monte Carlo simulation.

Scalable domain decomposition solvers for stochastic PDEs in high performance computing

DOE PAGES

Desai, Ajit; Khalil, Mohammad; Pettit, Chris; ...

2017-09-21

Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolutionmore » in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.« less

Scalable domain decomposition solvers for stochastic PDEs in high performance computing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Desai, Ajit; Khalil, Mohammad; Pettit, Chris

Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolutionmore » in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.« less

A 3D object-based model to simulate highly-heterogeneous, coarse, braided river deposits

NASA Astrophysics Data System (ADS)

Huber, E.; Huggenberger, P.; Caers, J.

2016-12-01

There is a critical need in hydrogeological modeling for geologically more realistic representation of the subsurface. Indeed, widely-used representations of the subsurface heterogeneity based on smooth basis functions such as cokriging or the pilot-point approach fail at reproducing the connectivity of high permeable geological structures that control subsurface solute transport. To realistically model the connectivity of high permeable structures of coarse, braided river deposits, multiple-point statistics and object-based models are promising alternatives. We therefore propose a new object-based model that, according to a sedimentological model, mimics the dominant processes of floodplain dynamics. Contrarily to existing models, this object-based model possesses the following properties: (1) it is consistent with field observations (outcrops, ground-penetrating radar data, etc.), (2) it allows different sedimentological dynamics to be modeled that result in different subsurface heterogeneity patterns, (3) it is light in memory and computationally fast, and (4) it can be conditioned to geophysical data. In this model, the main sedimentological elements (scour fills with open-framework-bimodal gravel cross-beds, gravel sheet deposits, open-framework and sand lenses) and their internal structures are described by geometrical objects. Several spatial distributions are proposed that allow to simulate the horizontal position of the objects on the floodplain as well as the net rate of sediment deposition. The model is grid-independent and any vertical section can be computed algebraically. Furthermore, model realizations can serve as training images for multiple-point statistics. The significance of this model is shown by its impact on the subsurface flow distribution that strongly depends on the sedimentological dynamics modeled. The code will be provided as a free and open-source R-package.

Inducing Tropical Cyclones to Undergo Brownian Motion

NASA Astrophysics Data System (ADS)

Hodyss, D.; McLay, J.; Moskaitis, J.; Serra, E.

2014-12-01

Stochastic parameterization has become commonplace in numerical weather prediction (NWP) models used for probabilistic prediction. Here, a specific stochastic parameterization will be related to the theory of stochastic differential equations and shown to be affected strongly by the choice of stochastic calculus. From an NWP perspective our focus will be on ameliorating a common trait of the ensemble distributions of tropical cyclone (TC) tracks (or position), namely that they generally contain a bias and an underestimate of the variance. With this trait in mind we present a stochastic track variance inflation parameterization. This parameterization makes use of a properly constructed stochastic advection term that follows a TC and induces its position to undergo Brownian motion. A central characteristic of Brownian motion is that its variance increases with time, which allows for an effective inflation of an ensemble's TC track variance. Using this stochastic parameterization we present a comparison of the behavior of TCs from the perspective of the stochastic calculi of Itô and Stratonovich within an operational NWP model. The central difference between these two perspectives as pertains to TCs is shown to be properly predicted by the stochastic calculus and the Itô correction. In the cases presented here these differences will manifest as overly intense TCs, which, depending on the strength of the forcing, could lead to problems with numerical stability and physical realism.

Stochastic spectral projection of electrochemical thermal model for lithium-ion cell state estimation

NASA Astrophysics Data System (ADS)

Tagade, Piyush; Hariharan, Krishnan S.; Kolake, Subramanya Mayya; Song, Taewon; Oh, Dukjin

2017-03-01

A novel approach for integrating a pseudo-two dimensional electrochemical thermal (P2D-ECT) model and data assimilation algorithm is presented for lithium-ion cell state estimation. This approach refrains from making any simplifications in the P2D-ECT model while making it amenable for online state estimation. Though deterministic, uncertainty in the initial states induces stochasticity in the P2D-ECT model. This stochasticity is resolved by spectrally projecting the stochastic P2D-ECT model on a set of orthogonal multivariate Hermite polynomials. Volume averaging in the stochastic dimensions is proposed for efficient numerical solution of the resultant model. A state estimation framework is developed using a transformation of the orthogonal basis to assimilate the measurables with this system of equations. Effectiveness of the proposed method is first demonstrated by assimilating the cell voltage and temperature data generated using a synthetic test bed. This validated method is used with the experimentally observed cell voltage and temperature data for state estimation at different operating conditions and drive cycle protocols. The results show increased prediction accuracy when the data is assimilated every 30s. High accuracy of the estimated states is exploited to infer temperature dependent behavior of the lithium-ion cell.

Stochastic simulation of the spray formation assisted by a high pressure

NASA Astrophysics Data System (ADS)

Gorokhovski, M.; Chtab-Desportes, A.; Voloshina, I.; Askarova, A.

2010-03-01

The stochastic model of spray formation in the vicinity of the injector and in the far-field has been described and assessed by comparison with measurements in Diesel-like conditions. In the proposed mesh-free approach, the 3D configuration of continuous liquid core is simulated stochastically by ensemble of spatial trajectories of the specifically introduced stochastic particles. The parameters of the stochastic process are presumed from the physics of primary atomization. The spray formation model consists in computation of spatial distribution of the probability of finding the non-fragmented liquid jet in the near-to-injector region. This model is combined with KIVA II computation of atomizing Diesel spray in two-ways. First, simultaneously with the gas phase RANS computation, the ensemble of stochastic particles is tracking and the probability field of their positions is calculated, which is used for sampling of initial locations of primary blobs. Second, the velocity increment of the gas due to the liquid injection is computed from the mean volume fraction of the simulated liquid core. Two novelties are proposed in the secondary atomization modeling. The first one is due to unsteadiness of the injection velocity. When the injection velocity increment in time is decreasing, the supplementary breakup may be induced. Therefore the critical Weber number is based on such increment. Second, a new stochastic model of the secondary atomization is proposed, in which the intermittent turbulent stretching is taken into account as the main mechanism. The measurements reported by Arcoumanis et al. (time-history of the mean axial centre-line velocity of droplet, and of the centre-line Sauter Mean Diameter), are compared with computations.

Option pricing, stochastic volatility, singular dynamics and constrained path integrals

NASA Astrophysics Data System (ADS)

Contreras, Mauricio; Hojman, Sergio A.

2014-01-01

Stochastic volatility models have been widely studied and used in the financial world. The Heston model (Heston, 1993) [7] is one of the best known models to deal with this issue. These stochastic volatility models are characterized by the fact that they explicitly depend on a correlation parameter ρ which relates the two Brownian motions that drive the stochastic dynamics associated to the volatility and the underlying asset. Solutions to the Heston model in the context of option pricing, using a path integral approach, are found in Lemmens et al. (2008) [21] while in Baaquie (2007,1997) [12,13] propagators for different stochastic volatility models are constructed. In all previous cases, the propagator is not defined for extreme cases ρ=±1. It is therefore necessary to obtain a solution for these extreme cases and also to understand the origin of the divergence of the propagator. In this paper we study in detail a general class of stochastic volatility models for extreme values ρ=±1 and show that in these two cases, the associated classical dynamics corresponds to a system with second class constraints, which must be dealt with using Dirac’s method for constrained systems (Dirac, 1958,1967) [22,23] in order to properly obtain the propagator in the form of a Euclidean Hamiltonian path integral (Henneaux and Teitelboim, 1992) [25]. After integrating over momenta, one gets an Euclidean Lagrangian path integral without constraints, which in the case of the Heston model corresponds to a path integral of a repulsive radial harmonic oscillator. In all the cases studied, the price of the underlying asset is completely determined by one of the second class constraints in terms of volatility and plays no active role in the path integral.

Generalised filtering and stochastic DCM for fMRI.

PubMed

Li, Baojuan; Daunizeau, Jean; Stephan, Klaas E; Penny, Will; Hu, Dewen; Friston, Karl

2011-09-15

This paper is about the fitting or inversion of dynamic causal models (DCMs) of fMRI time series. It tries to establish the validity of stochastic DCMs that accommodate random fluctuations in hidden neuronal and physiological states. We compare and contrast deterministic and stochastic DCMs, which do and do not ignore random fluctuations or noise on hidden states. We then compare stochastic DCMs, which do and do not ignore conditional dependence between hidden states and model parameters (generalised filtering and dynamic expectation maximisation, respectively). We first characterise state-noise by comparing the log evidence of models with different a priori assumptions about its amplitude, form and smoothness. Face validity of the inversion scheme is then established using data simulated with and without state-noise to ensure that DCM can identify the parameters and model that generated the data. Finally, we address construct validity using real data from an fMRI study of internet addiction. Our analyses suggest the following. (i) The inversion of stochastic causal models is feasible, given typical fMRI data. (ii) State-noise has nontrivial amplitude and smoothness. (iii) Stochastic DCM has face validity, in the sense that Bayesian model comparison can distinguish between data that have been generated with high and low levels of physiological noise and model inversion provides veridical estimates of effective connectivity. (iv) Relaxing conditional independence assumptions can have greater construct validity, in terms of revealing group differences not disclosed by variational schemes. Finally, we note that the ability to model endogenous or random fluctuations on hidden neuronal (and physiological) states provides a new and possibly more plausible perspective on how regionally specific signals in fMRI are generated. Copyright © 2011. Published by Elsevier Inc.

Stochastic Models of Quality Control on Test Misgrading.

ERIC Educational Resources Information Center

Wang, Jianjun

Stochastic models are developed in this article to examine the rate of test misgrading in educational and psychological measurement. The estimation of inadvertent grading errors can serve as a basis for quality control in measurement. Limitations of traditional Poisson models have been reviewed to highlight the need to introduce new models using…

The phenotypic equilibrium of cancer cells: From average-level stability to path-wise convergence.

PubMed

Niu, Yuanling; Wang, Yue; Zhou, Da

2015-12-07

The phenotypic equilibrium, i.e. heterogeneous population of cancer cells tending to a fixed equilibrium of phenotypic proportions, has received much attention in cancer biology very recently. In the previous literature, some theoretical models were used to predict the experimental phenomena of the phenotypic equilibrium, which were often explained by different concepts of stabilities of the models. Here we present a stochastic multi-phenotype branching model by integrating conventional cellular hierarchy with phenotypic plasticity mechanisms of cancer cells. Based on our model, it is shown that: (i) our model can serve as a framework to unify the previous models for the phenotypic equilibrium, and then harmonizes the different kinds of average-level stabilities proposed in these models; and (ii) path-wise convergence of our model provides a deeper understanding to the phenotypic equilibrium from stochastic point of view. That is, the emergence of the phenotypic equilibrium is rooted in the stochastic nature of (almost) every sample path, the average-level stability just follows from it by averaging stochastic samples. Copyright © 2015 Elsevier Ltd. All rights reserved.

Approaches for modeling within subject variability in pharmacometric count data analysis: dynamic inter-occasion variability and stochastic differential equations.

PubMed

Deng, Chenhui; Plan, Elodie L; Karlsson, Mats O

2016-06-01

Parameter variation in pharmacometric analysis studies can be characterized as within subject parameter variability (WSV) in pharmacometric models. WSV has previously been successfully modeled using inter-occasion variability (IOV), but also stochastic differential equations (SDEs). In this study, two approaches, dynamic inter-occasion variability (dIOV) and adapted stochastic differential equations, were proposed to investigate WSV in pharmacometric count data analysis. These approaches were applied to published count models for seizure counts and Likert pain scores. Both approaches improved the model fits significantly. In addition, stochastic simulation and estimation were used to explore further the capability of the two approaches to diagnose and improve models where existing WSV is not recognized. The results of simulations confirmed the gain in introducing WSV as dIOV and SDEs when parameters vary randomly over time. Further, the approaches were also informative as diagnostics of model misspecification, when parameters changed systematically over time but this was not recognized in the structural model. The proposed approaches in this study offer strategies to characterize WSV and are not restricted to count data.

Models Show Subsurface Cracking May Complicate Groundwater Cleanup at Hazardous Waste Sites

EPA Science Inventory

Chlorinated solvents like trichloroethylene contaminate groundwater at numerous sites nationwide. This modeling study, conducted at the Air Force Institute of Technology, shows that subsurface cracks, either natural or due to the presence of the contaminant itself, may result in...

VIRUS TRANSPORT IN PHYSICALLY AND GEOCHEMICALLY HETEROGENEOUS SUBSURFACE POROUS MEDIA. (R826179)

EPA Science Inventory

A two-dimensional model for virus transport in physically and geochemically heterogeneous subsurface porous media is presented. The model involves solution of the advection–dispersion equation, which additionally considers virus inactivation in the solution, as well as ...

Stochastic Galerkin methods for the steady-state Navier–Stokes equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sousedík, Bedřich, E-mail: sousedik@umbc.edu; Elman, Howard C., E-mail: elman@cs.umd.edu

2016-07-01

We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmarkmore » problems.« less

Stochastic Galerkin methods for the steady-state Navier–Stokes equations

DOE PAGES

Sousedík, Bedřich; Elman, Howard C.

2016-04-12

We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmarkmore » problems.« less

Time-ordered product expansions for computational stochastic system biology.

PubMed

Mjolsness, Eric

2013-06-01

The time-ordered product framework of quantum field theory can also be used to understand salient phenomena in stochastic biochemical networks. It is used here to derive Gillespie's stochastic simulation algorithm (SSA) for chemical reaction networks; consequently, the SSA can be interpreted in terms of Feynman diagrams. It is also used here to derive other, more general simulation and parameter-learning algorithms including simulation algorithms for networks of stochastic reaction-like processes operating on parameterized objects, and also hybrid stochastic reaction/differential equation models in which systems of ordinary differential equations evolve the parameters of objects that can also undergo stochastic reactions. Thus, the time-ordered product expansion can be used systematically to derive simulation and parameter-fitting algorithms for stochastic systems.

Stochastic hybrid systems for studying biochemical processes.

PubMed

Singh, Abhyudai; Hespanha, João P

2010-11-13

Many protein and mRNA species occur at low molecular counts within cells, and hence are subject to large stochastic fluctuations in copy numbers over time. Development of computationally tractable frameworks for modelling stochastic fluctuations in population counts is essential to understand how noise at the cellular level affects biological function and phenotype. We show that stochastic hybrid systems (SHSs) provide a convenient framework for modelling the time evolution of population counts of different chemical species involved in a set of biochemical reactions. We illustrate recently developed techniques that allow fast computations of the statistical moments of the population count, without having to run computationally expensive Monte Carlo simulations of the biochemical reactions. Finally, we review different examples from the literature that illustrate the benefits of using SHSs for modelling biochemical processes.

Impacts of microtopographic snow redistribution and lateral subsurface processes on hydrologic and thermal states in an Arctic polygonal ground ecosystem: a case study using ELM-3D v1.0

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bisht, Gautam; Riley, William J.; Wainwright, Haruko M.

Microtopographic features, such as polygonal ground, are characteristic sources of landscape heterogeneity in the Alaskan Arctic coastal plain. In this study, we analyze the effects of snow redistribution (SR) and lateral subsurface processes on hydrologic and thermal states at a polygonal tundra site near Barrow, Alaska. We extended the land model integrated in the E3SM to redistribute incoming snow by accounting for microtopography and incorporated subsurface lateral transport of water and energy (ELM-3D v1.0). Multiple 10-year-long simulations were performed for a transect across a polygonal tundra landscape at the Barrow Environmental Observatory in Alaska to isolate the impact of SRmore » and subsurface process representation. When SR was included, model predictions better agreed (higher R 2, lower bias and RMSE) with observed differences in snow depth between polygonal rims and centers. The model was also able to accurately reproduce observed soil temperature vertical profiles in the polygon rims and centers (overall bias, RMSE, and R 2 of 0.59°C, 1.82°C, and 0.99, respectively). The spatial heterogeneity of snow depth during the winter due to SR generated surface soil temperature heterogeneity that propagated in depth and time and led to ~ 10 cm shallower and ~ 5 cm deeper maximum annual thaw depths under the polygon rims and centers, respectively. Additionally, SR led to spatial heterogeneity in surface energy fluxes and soil moisture during the summer. Excluding lateral subsurface hydrologic and thermal processes led to small effects on mean states but an overestimation of spatial variability in soil moisture and soil temperature as subsurface liquid pressure and thermal gradients were artificially prevented from spatially dissipating over time. The effect of lateral subsurface processes on maximum thaw depths was modest, with mean absolute differences of ~ 3 cm. Our integration of three-dimensional subsurface hydrologic and thermal subsurface dynamics in the E3SM land model will facilitate a wide range of analyses heretofore impossible in an ESM context.« less

Impacts of microtopographic snow redistribution and lateral subsurface processes on hydrologic and thermal states in an Arctic polygonal ground ecosystem: a case study using ELM-3D v1.0

DOE PAGES

Bisht, Gautam; Riley, William J.; Wainwright, Haruko M.; ...

2018-01-08

Microtopographic features, such as polygonal ground, are characteristic sources of landscape heterogeneity in the Alaskan Arctic coastal plain. In this study, we analyze the effects of snow redistribution (SR) and lateral subsurface processes on hydrologic and thermal states at a polygonal tundra site near Barrow, Alaska. We extended the land model integrated in the E3SM to redistribute incoming snow by accounting for microtopography and incorporated subsurface lateral transport of water and energy (ELM-3D v1.0). Multiple 10-year-long simulations were performed for a transect across a polygonal tundra landscape at the Barrow Environmental Observatory in Alaska to isolate the impact of SRmore » and subsurface process representation. When SR was included, model predictions better agreed (higher R 2, lower bias and RMSE) with observed differences in snow depth between polygonal rims and centers. The model was also able to accurately reproduce observed soil temperature vertical profiles in the polygon rims and centers (overall bias, RMSE, and R 2 of 0.59°C, 1.82°C, and 0.99, respectively). The spatial heterogeneity of snow depth during the winter due to SR generated surface soil temperature heterogeneity that propagated in depth and time and led to ~ 10 cm shallower and ~ 5 cm deeper maximum annual thaw depths under the polygon rims and centers, respectively. Additionally, SR led to spatial heterogeneity in surface energy fluxes and soil moisture during the summer. Excluding lateral subsurface hydrologic and thermal processes led to small effects on mean states but an overestimation of spatial variability in soil moisture and soil temperature as subsurface liquid pressure and thermal gradients were artificially prevented from spatially dissipating over time. The effect of lateral subsurface processes on maximum thaw depths was modest, with mean absolute differences of ~ 3 cm. Our integration of three-dimensional subsurface hydrologic and thermal subsurface dynamics in the E3SM land model will facilitate a wide range of analyses heretofore impossible in an ESM context.« less

Impacts of microtopographic snow redistribution and lateral subsurface processes on hydrologic and thermal states in an Arctic polygonal ground ecosystem: a case study using ELM-3D v1.0

NASA Astrophysics Data System (ADS)

Bisht, Gautam; Riley, William J.; Wainwright, Haruko M.; Dafflon, Baptiste; Yuan, Fengming; Romanovsky, Vladimir E.

2018-01-01

Microtopographic features, such as polygonal ground, are characteristic sources of landscape heterogeneity in the Alaskan Arctic coastal plain. Here, we analyze the effects of snow redistribution (SR) and lateral subsurface processes on hydrologic and thermal states at a polygonal tundra site near Barrow, Alaska. We extended the land model integrated in the E3SM to redistribute incoming snow by accounting for microtopography and incorporated subsurface lateral transport of water and energy (ELM-3D v1.0). Multiple 10-year-long simulations were performed for a transect across a polygonal tundra landscape at the Barrow Environmental Observatory in Alaska to isolate the impact of SR and subsurface process representation. When SR was included, model predictions better agreed (higher R2, lower bias and RMSE) with observed differences in snow depth between polygonal rims and centers. The model was also able to accurately reproduce observed soil temperature vertical profiles in the polygon rims and centers (overall bias, RMSE, and R2 of 0.59 °C, 1.82 °C, and 0.99, respectively). The spatial heterogeneity of snow depth during the winter due to SR generated surface soil temperature heterogeneity that propagated in depth and time and led to ˜ 10 cm shallower and ˜ 5 cm deeper maximum annual thaw depths under the polygon rims and centers, respectively. Additionally, SR led to spatial heterogeneity in surface energy fluxes and soil moisture during the summer. Excluding lateral subsurface hydrologic and thermal processes led to small effects on mean states but an overestimation of spatial variability in soil moisture and soil temperature as subsurface liquid pressure and thermal gradients were artificially prevented from spatially dissipating over time. The effect of lateral subsurface processes on maximum thaw depths was modest, with mean absolute differences of ˜ 3 cm. Our integration of three-dimensional subsurface hydrologic and thermal subsurface dynamics in the E3SM land model will facilitate a wide range of analyses heretofore impossible in an ESM context.

Stochastic Robust Mathematical Programming Model for Power System Optimization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Cong; Changhyeok, Lee; Haoyong, Chen

2016-01-01

This paper presents a stochastic robust framework for two-stage power system optimization problems with uncertainty. The model optimizes the probabilistic expectation of different worst-case scenarios with ifferent uncertainty sets. A case study of unit commitment shows the effectiveness of the proposed model and algorithms.

Statement Verification: A Stochastic Model of Judgment and Response.

ERIC Educational Resources Information Center

Wallsten, Thomas S.; Gonzalez-Vallejo, Claudia

1994-01-01

A stochastic judgment model (SJM) is presented as a framework for addressing issues in statement verification and probability judgment. Results of 5 experiments with 264 undergraduates support the validity of the model and provide new information that is interpreted in terms of the SJM. (SLD)

A stochastic method for stand-alone photovoltaic system sizing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cabral, Claudia Valeria Tavora; Filho, Delly Oliveira; Martins, Jose Helvecio

Photovoltaic systems utilize solar energy to generate electrical energy to meet load demands. Optimal sizing of these systems includes the characterization of solar radiation. Solar radiation at the Earth's surface has random characteristics and has been the focus of various academic studies. The objective of this study was to stochastically analyze parameters involved in the sizing of photovoltaic generators and develop a methodology for sizing of stand-alone photovoltaic systems. Energy storage for isolated systems and solar radiation were analyzed stochastically due to their random behavior. For the development of the methodology proposed stochastic analysis were studied including the Markov chainmore » and beta probability density function. The obtained results were compared with those for sizing of stand-alone using from the Sandia method (deterministic), in which the stochastic model presented more reliable values. Both models present advantages and disadvantages; however, the stochastic one is more complex and provides more reliable and realistic results. (author)« less

Deterministic and stochastic bifurcations in the Hindmarsh-Rose neuronal model

NASA Astrophysics Data System (ADS)

Dtchetgnia Djeundam, S. R.; Yamapi, R.; Kofane, T. C.; Aziz-Alaoui, M. A.

2013-09-01

We analyze the bifurcations occurring in the 3D Hindmarsh-Rose neuronal model with and without random signal. When under a sufficient stimulus, the neuron activity takes place; we observe various types of bifurcations that lead to chaotic transitions. Beside the equilibrium solutions and their stability, we also investigate the deterministic bifurcation. It appears that the neuronal activity consists of chaotic transitions between two periodic phases called bursting and spiking solutions. The stochastic bifurcation, defined as a sudden change in character of a stochastic attractor when the bifurcation parameter of the system passes through a critical value, or under certain condition as the collision of a stochastic attractor with a stochastic saddle, occurs when a random Gaussian signal is added. Our study reveals two kinds of stochastic bifurcation: the phenomenological bifurcation (P-bifurcations) and the dynamical bifurcation (D-bifurcations). The asymptotical method is used to analyze phenomenological bifurcation. We find that the neuronal activity of spiking and bursting chaos remains for finite values of the noise intensity.

A DG approach to the numerical solution of the Stein-Stein stochastic volatility option pricing model

NASA Astrophysics Data System (ADS)

Hozman, J.; Tichý, T.

2017-12-01

Stochastic volatility models enable to capture the real world features of the options better than the classical Black-Scholes treatment. Here we focus on pricing of European-style options under the Stein-Stein stochastic volatility model when the option value depends on the time, on the price of the underlying asset and on the volatility as a function of a mean reverting Orstein-Uhlenbeck process. A standard mathematical approach to this model leads to the non-stationary second-order degenerate partial differential equation of two spatial variables completed by the system of boundary and terminal conditions. In order to improve the numerical valuation process for a such pricing equation, we propose a numerical technique based on the discontinuous Galerkin method and the Crank-Nicolson scheme. Finally, reference numerical experiments on real market data illustrate comprehensive empirical findings on options with stochastic volatility.

MOLNs: A CLOUD PLATFORM FOR INTERACTIVE, REPRODUCIBLE, AND SCALABLE SPATIAL STOCHASTIC COMPUTATIONAL EXPERIMENTS IN SYSTEMS BIOLOGY USING PyURDME.

PubMed

Drawert, Brian; Trogdon, Michael; Toor, Salman; Petzold, Linda; Hellander, Andreas

2016-01-01

Computational experiments using spatial stochastic simulations have led to important new biological insights, but they require specialized tools and a complex software stack, as well as large and scalable compute and data analysis resources due to the large computational cost associated with Monte Carlo computational workflows. The complexity of setting up and managing a large-scale distributed computation environment to support productive and reproducible modeling can be prohibitive for practitioners in systems biology. This results in a barrier to the adoption of spatial stochastic simulation tools, effectively limiting the type of biological questions addressed by quantitative modeling. In this paper, we present PyURDME, a new, user-friendly spatial modeling and simulation package, and MOLNs, a cloud computing appliance for distributed simulation of stochastic reaction-diffusion models. MOLNs is based on IPython and provides an interactive programming platform for development of sharable and reproducible distributed parallel computational experiments.

A stochastic thermostat algorithm for coarse-grained thermomechanical modeling of large-scale soft matters: Theory and application to microfilaments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Tong; Gu, YuanTong, E-mail: yuantong.gu@qut.edu.au

As all-atom molecular dynamics method is limited by its enormous computational cost, various coarse-grained strategies have been developed to extend the length scale of soft matters in the modeling of mechanical behaviors. However, the classical thermostat algorithm in highly coarse-grained molecular dynamics method would underestimate the thermodynamic behaviors of soft matters (e.g. microfilaments in cells), which can weaken the ability of materials to overcome local energy traps in granular modeling. Based on all-atom molecular dynamics modeling of microfilament fragments (G-actin clusters), a new stochastic thermostat algorithm is developed to retain the representation of thermodynamic properties of microfilaments at extra coarse-grainedmore » level. The accuracy of this stochastic thermostat algorithm is validated by all-atom MD simulation. This new stochastic thermostat algorithm provides an efficient way to investigate the thermomechanical properties of large-scale soft matters.« less

Forecasting financial asset processes: stochastic dynamics via learning neural networks.

PubMed

Giebel, S; Rainer, M

2010-01-01

Models for financial asset dynamics usually take into account their inherent unpredictable nature by including a suitable stochastic component into their process. Unknown (forward) values of financial assets (at a given time in the future) are usually estimated as expectations of the stochastic asset under a suitable risk-neutral measure. This estimation requires the stochastic model to be calibrated to some history of sufficient length in the past. Apart from inherent limitations, due to the stochastic nature of the process, the predictive power is also limited by the simplifying assumptions of the common calibration methods, such as maximum likelihood estimation and regression methods, performed often without weights on the historic time series, or with static weights only. Here we propose a novel method of "intelligent" calibration, using learning neural networks in order to dynamically adapt the parameters of the stochastic model. Hence we have a stochastic process with time dependent parameters, the dynamics of the parameters being themselves learned continuously by a neural network. The back propagation in training the previous weights is limited to a certain memory length (in the examples we consider 10 previous business days), which is similar to the maximal time lag of autoregressive processes. We demonstrate the learning efficiency of the new algorithm by tracking the next-day forecasts for the EURTRY and EUR-HUF exchange rates each.

Investigation of lunar maria structure from cross-analysis of GRAIL gravity and Kaguya radar data

NASA Astrophysics Data System (ADS)

Zuber, M. T.; Ermakov, A.; Smith, D. E.; Mastroguiseppe, M.; Raguso, M.

2016-12-01

The Lunar Radar Sounder (LRS) on JAXA's Kaguya spacecraft investigated the subsurface structure of the Moon to a depth of a few km. GRAIL gravity models are potentially sensitive to subsurface structure at such depths. GRAIL gravity and LRS radar data are complementary since both are sensitive to density/compositional heterogeneities. Cross-correlation of GRAIL and LRS data has the potential to produce new constraints on the structure and evolution of the lunar maria. Originally, subsurface reflections within the lunar maria were detected with Lunar Sounder Experiment aboard Apollo 17. Subsurface layering was attributed to multiple episodes of volcanism. Later, Kaguya's LRS produced similar measurements but with global-scale coverage. Laboratory measurements show that density variations among mare basalts can be up to 200 kg m-3 or 7%. The LRS measurements have detected subsurface reflection in the upper 1 km of the crust. Combining these two estimates and using the Bouguer slab approximation, we estimate that anomalies of order 1-10 mGal are expected due to potentially varying density of surface and/or subsurface horizons. This accuracy is achievable with the latest GRAIL gravity models. The LRS surface backscattering power is indicative of surface and near sub-surface dielectric properties, which are sensitive to target density and roughness. We investigate the northwestern part of the Procellarum basin because it is the region with the strongest signal-to-noise ratios in gravity models within maria. To examine shallow subsurface structure, we map the surface received power by tracking the first return of radar echoes and compare it with gravity gradients, which are particularly sensitive to small-scale structures.

Approximation methods of European option pricing in multiscale stochastic volatility model

NASA Astrophysics Data System (ADS)

Ni, Ying; Canhanga, Betuel; Malyarenko, Anatoliy; Silvestrov, Sergei

2017-01-01

In the classical Black-Scholes model for financial option pricing, the asset price follows a geometric Brownian motion with constant volatility. Empirical findings such as volatility smile/skew, fat-tailed asset return distributions have suggested that the constant volatility assumption might not be realistic. A general stochastic volatility model, e.g. Heston model, GARCH model and SABR volatility model, in which the variance/volatility itself follows typically a mean-reverting stochastic process, has shown to be superior in terms of capturing the empirical facts. However in order to capture more features of the volatility smile a two-factor, of double Heston type, stochastic volatility model is more useful as shown in Christoffersen, Heston and Jacobs [12]. We consider one modified form of such two-factor volatility models in which the volatility has multiscale mean-reversion rates. Our model contains two mean-reverting volatility processes with a fast and a slow reverting rate respectively. We consider the European option pricing problem under one type of the multiscale stochastic volatility model where the two volatility processes act as independent factors in the asset price process. The novelty in this paper is an approximating analytical solution using asymptotic expansion method which extends the authors earlier research in Canhanga et al. [5, 6]. In addition we propose a numerical approximating solution using Monte-Carlo simulation. For completeness and for comparison we also implement the semi-analytical solution by Chiarella and Ziveyi [11] using method of characteristics, Fourier and bivariate Laplace transforms.

Optimal Stochastic Modeling and Control of Flexible Structures

DTIC Science & Technology

1988-09-01

1.37] and McLane [1.18] considered multivariable systems and derived their optimal control characteristics. Kleinman, Gorman and Zaborsky considered...Leondes [1.72,1.73] studied various aspects of multivariable linear stochastic, discrete-time systems that are partly deterministic, and partly stochastic...June 1966. 1.8. A.V. Balaknishnan, Applied Functional Analaysis , 2nd ed., New York, N.Y.: Springer-Verlag, 1981 1.9. Peter S. Maybeck, Stochastic

Multivariate moment closure techniques for stochastic kinetic models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lakatos, Eszter, E-mail: e.lakatos13@imperial.ac.uk; Ale, Angelique; Kirk, Paul D. W.

2015-09-07

Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporallymore » evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.« less

Organic and Inorganic Carbon in the Rio Tinto (Spain) Deep Subsurface System: a Possible Model for Subsurface Carbon and Lithoautotrophs on Mars.

NASA Astrophysics Data System (ADS)

Bonaccorsi, R.; Stoker, C. R.; MARTE Science Team

2007-12-01

The subsurface is the key environment for searching for life on planets lacking surface life. Subsurface ecosystems are of great relevance to astrobiology including the search for past/present life on Mars. Conditions on the Martian surface do not support biological activity but the subsurface might preserve organics and host subsurface life [1]. A key requirement for the analysis of subsurface samples on Mars is the ability to characterize organic vs. inorganic carbon pools. This information is needed to determine if the sample contains organic material of biological origin and/ or to establish if pools of inorganic carbon can support subsurface biospheres. The Mars Analog Rio Tinto Experiment (MARTE) performed deep drilling of cores i.e., down to 165-m depth, in a volcanically-hosted-massive-sulfide deposit at Rio Tinto, Spain, which is considered an important analog of the Sinus Meridiani site on Mars. Results from MARTE suggest the existence of a relatively complex subsurface life including aerobic and anaerobic chemoautotrophs, and strict anaerobic methanogens sustained by Fe and S minerals in anoxic conditions, which is an ideal model analog for a deep subsurface Martian environment. We report here on the distribution of organic (C-org: 0.01-0.3Wt% and inorganic carbon (IC = 0.01-7.0 Wt%) in a subsurface rock system including weathered/oxidized i.e., gossan, and unaltered pyrite stockwork. Cores were analyzed from 3 boreholes (BH-4, BH-7, and BH-8) that penetrated down to a depth of ~165 m into massive sulfide. Nearsurface phyllosilicate rich-pockets contain the highest amounts of organics (0.3Wt%) [2], while the deeper rocks contain the highest amount of carbonates. Assessing the amount of C pools available throughout the RT subsurface brings key insight on the type of trophic system sustaining its microbial ecosystem (i.e., heterotrophs vs. autotrophs) and the biogeochemical relationships that characterize a new type of subsurface biosphere at RT. This potentially novel biosphere on Earth could be used as a model to test for extant and extinct life on Mars. Furthermore, having found carbonates in an hyperacidic system (pH ~2.3) brings new insights on the possible occurrence of deep carbonates deposits under low-pH condition on Mars. [1] Boston, P.J., et al., 1992. Icarus 95,300-308; Bonaccorsi, Stoker and Sutter, 2007 Accepted with review in Astrobiology.

A Bayesian estimation of a stochastic predator-prey model of economic fluctuations

NASA Astrophysics Data System (ADS)

Dibeh, Ghassan; Luchinsky, Dmitry G.; Luchinskaya, Daria D.; Smelyanskiy, Vadim N.

2007-06-01

In this paper, we develop a Bayesian framework for the empirical estimation of the parameters of one of the best known nonlinear models of the business cycle: The Marx-inspired model of a growth cycle introduced by R. M. Goodwin. The model predicts a series of closed cycles representing the dynamics of labor's share and the employment rate in the capitalist economy. The Bayesian framework is used to empirically estimate a modified Goodwin model. The original model is extended in two ways. First, we allow for exogenous periodic variations of the otherwise steady growth rates of the labor force and productivity per worker. Second, we allow for stochastic variations of those parameters. The resultant modified Goodwin model is a stochastic predator-prey model with periodic forcing. The model is then estimated using a newly developed Bayesian estimation method on data sets representing growth cycles in France and Italy during the years 1960-2005. Results show that inference of the parameters of the stochastic Goodwin model can be achieved. The comparison of the dynamics of the Goodwin model with the inferred values of parameters demonstrates quantitative agreement with the growth cycle empirical data.

The Impact of STTP on the GEFS Forecast of Week-2 and Beyond in the Presence of Stochastic Physics

NASA Astrophysics Data System (ADS)

Hou, D.

2015-12-01

The Stochastic Total Tendency Perturbation (STTP) scheme was designed to represent the model related uncertainties not considered in the numerical model itself and the physics based stochastic schemes. It has been applied in NCEP's Global Ensemble Forecast System (GEFS) since 2010, showing significant positive impacts on the forecast with improved spread-error ratio and probabilistic forecast skills. The scheme is robust and it went well with the resolution increases and model improvements in 2012 and 2015 with minimum changes. Recently, a set of stochastic physics schemes are coded in the Global Forecast System model and tested in the GEFS package. With these schemes turned on and STTP off, the forecast performance is comparable or even superior to the operational GEFS, in which STTP is the only contributor to the model related uncertainties. This is true especially in week one. However, over the second week and beyond, both the experimental and the operational GEFS has insufficient spread, especially over the warmer seasons. This is a major challenge when the GEFS is extended to sub-seasonal (week 4-6) time scales. The impact of STTP on the GEFS forecast in the presence of stochastic physics is investigated by turning both the stochastic physics schemes and STTP on and carefully tuning their amplitudes. Analysis will be focused on the forecast of extended range, especially week 2. Its impacts on week 3-4 will also be addressed.

Robust Representation of Integrated Surface-subsurface Hydrology at Watershed Scales

NASA Astrophysics Data System (ADS)

Painter, S. L.; Tang, G.; Collier, N.; Jan, A.; Karra, S.

2015-12-01

A representation of integrated surface-subsurface hydrology is the central component to process-rich watershed models that are emerging as alternatives to traditional reduced complexity models. These physically based systems are important for assessing potential impacts of climate change and human activities on groundwater-dependent ecosystems and water supply and quality. Integrated surface-subsurface models typically couple three-dimensional solutions for variably saturated flow in the subsurface with the kinematic- or diffusion-wave equation for surface flows. The computational scheme for coupling the surface and subsurface systems is key to the robustness, computational performance, and ease-of-implementation of the integrated system. A new, robust approach for coupling the subsurface and surface systems is developed from the assumption that the vertical gradient in head is negligible at the surface. This tight-coupling assumption allows the surface flow system to be incorporated directly into the subsurface system; effects of surface flow and surface water accumulation are represented as modifications to the subsurface flow and accumulation terms but are not triggered until the subsurface pressure reaches a threshold value corresponding to the appearance of water on the surface. The new approach has been implemented in the highly parallel PFLOTRAN (www.pflotran.org) code. Several synthetic examples and three-dimensional examples from the Walker Branch Watershed in Oak Ridge TN demonstrate the utility and robustness of the new approach using unstructured computational meshes. Representation of solute transport in the new approach is also discussed. Notice: This manuscript has been authored by UT-Battelle, LLC, under Contract No. DE-AC0500OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for the United States Government purposes.

MODELING MULTIPHASE ORGANIC CHEMICAL TRANSPORT IN SOILS AND GROUND WATER

EPA Science Inventory

Subsurface contamination due to immiscible organic liquids is a widespread problem which poses a serious threat to ground-water resources. n order to understand the movement of such materials in the subsurface, a mathematical model was developed for multiphase flow and multicompo...

3DFATMIC: THREE DIMENSIONAL SUBSURFACE FLOW, FATE AND TRANSPORT OF MICROBES AND CHEMICALS MODEL - USER'S MANUAL VERSION 1.0

EPA Science Inventory

This document is the user's manual of 3DFATMIC, a 3-Dimensional Subsurface Flow, Fate and Transport of Microbes and Chemicals Model using a Lagrangian-Eulerian adapted zooming and peak capturing (LEZOOMPC) algorithm.

RESEARCH ACTIVITIES AT U.S. GOVERNMENT AGENCIES IN SUBSURFACE REACTIVE TRANSPORT MODELING

EPA Science Inventory

The fate of contaminants in the environment is controlled by both chemical reactions and transport phenomena in the subsurface. Our ability to understand the significance of these processes over time requires an accurate conceptual model that incorporates the various mechanisms ...

Parameterization of norfolk sandy loam properties for stochastic modeling of light in-wheel motor UGV

USDA-ARS?s Scientific Manuscript database

To accurately develop a mathematical model for an In-Wheel Motor Unmanned Ground Vehicle (IWM UGV) on soft terrain, parameterization of terrain properties is essential to stochastically model tire-terrain interaction for each wheel independently. Operating in off-road conditions requires paying clos...

Simulating pathways of subsurface oil in the Faroe-Shetland Channel using an ocean general circulation model.

PubMed

Main, C E; Yool, A; Holliday, N P; Popova, E E; Jones, D O B; Ruhl, H A

2017-01-15

Little is known about the fate of subsurface hydrocarbon plumes from deep-sea oil well blowouts and their effects on processes and communities. As deepwater drilling expands in the Faroe-Shetland Channel (FSC), oil well blowouts are a possibility, and the unusual ocean circulation of this region presents challenges to understanding possible subsurface oil pathways in the event of a spill. Here, an ocean general circulation model was used with a particle tracking algorithm to assess temporal variability of the oil-plume distribution from a deep-sea oil well blowout in the FSC. The drift of particles was first tracked for one year following release. Then, ambient model temperatures were used to simulate temperature-mediated biodegradation, truncating the trajectories of particles accordingly. Release depth of the modeled subsurface plumes affected both their direction of transport and distance travelled from their release location, and there was considerable interannual variability in transport. Copyright © 2016 The Authors. Published by Elsevier Ltd.. All rights reserved.

Developing a stochastic conflict resolution model for urban runoff quality management: Application of info-gap and bargaining theories

NASA Astrophysics Data System (ADS)

Ghodsi, Seyed Hamed; Kerachian, Reza; Estalaki, Siamak Malakpour; Nikoo, Mohammad Reza; Zahmatkesh, Zahra

2016-02-01

In this paper, two deterministic and stochastic multilateral, multi-issue, non-cooperative bargaining methodologies are proposed for urban runoff quality management. In the proposed methodologies, a calibrated Storm Water Management Model (SWMM) is used to simulate stormwater runoff quantity and quality for different urban stormwater runoff management scenarios, which have been defined considering several Low Impact Development (LID) techniques. In the deterministic methodology, the best management scenario, representing location and area of LID controls, is identified using the bargaining model. In the stochastic methodology, uncertainties of some key parameters of SWMM are analyzed using the info-gap theory. For each water quality management scenario, robustness and opportuneness criteria are determined based on utility functions of different stakeholders. Then, to find the best solution, the bargaining model is performed considering a combination of robustness and opportuneness criteria for each scenario based on utility function of each stakeholder. The results of applying the proposed methodology in the Velenjak urban watershed located in the northeastern part of Tehran, the capital city of Iran, illustrate its practical utility for conflict resolution in urban water quantity and quality management. It is shown that the solution obtained using the deterministic model cannot outperform the result of the stochastic model considering the robustness and opportuneness criteria. Therefore, it can be concluded that the stochastic model, which incorporates the main uncertainties, could provide more reliable results.

A Markov Chain Monte Carlo Inversion Approach For Inverting InSAR Data With Application To Subsurface CO2 Injection

NASA Astrophysics Data System (ADS)

Ramirez, A. L.; Foxall, W.

2011-12-01

Surface displacements caused by reservoir pressure perturbations resulting from CO2 injection can often be measured by geodetic methods such as InSAR, tilt and GPS. We have developed a Markov Chain Monte Carlo (MCMC) approach to invert surface displacements measured by InSAR to map the pressure distribution associated with CO2 injection at the In Salah Krechba field, Algeria. The MCMC inversion entails sampling the solution space by proposing a series of trial 3D pressure-plume models. In the case of In Salah, the range of allowable models is constrained by prior information provided by well and geophysical data for the reservoir and possible fluid pathways in the overburden, and injection pressures and volumes. Each trial pressure distribution source is run through a (mathematical) forward model to calculate a set of synthetic surface deformation data. The likelihood that a particular proposal represents the true source is determined from the fit of the calculated data to the InSAR measurements, and those having higher likelihoods are passed to the posterior distribution. This procedure is repeated over typically ~104 - 105 trials until the posterior distribution converges to a stable solution. The solution to each stochastic inversion is in the form of Bayesian posterior probability density function (pdf) over the range of the alternative models that are consistent with the measured data and prior information. Therefore, the solution provides not only the highest likelihood model but also a realistic estimate of the solution uncertainty. Our InSalah work considered three flow model alternatives: 1) The first model assumed that the CO2 saturation and fluid pressure changes were confined to the reservoir; 2) the second model allowed the perturbations to occur also in a damage zone inferred in the lower caprock from 3D seismic surveys; and 3) the third model allowed fluid pressure changes anywhere within the reservoir and overburden. Alternative (2) yielded optimal fits to the data in inversions of InSAR data collected in 2007. The results indicate that pressure changes developed near the injection well and then penetrated into the lower caprock along the postulated damage zone. As in many geophysical inverse problems, inversion of surface displacement data for subsurface sources of deformation is inherently uncertain and non-unique. We will also discuss the approach used to characterize solution uncertainty. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Stochastic model for fatigue crack size and cost effective design decisions. [for aerospace structures

NASA Technical Reports Server (NTRS)

Hanagud, S.; Uppaluri, B.

1975-01-01

This paper describes a methodology for making cost effective fatigue design decisions. The methodology is based on a probabilistic model for the stochastic process of fatigue crack growth with time. The development of a particular model for the stochastic process is also discussed in the paper. The model is based on the assumption of continuous time and discrete space of crack lengths. Statistical decision theory and the developed probabilistic model are used to develop the procedure for making fatigue design decisions on the basis of minimum expected cost or risk function and reliability bounds. Selections of initial flaw size distribution, NDT, repair threshold crack lengths, and inspection intervals are discussed.

Oscillatory regulation of Hes1: Discrete stochastic delay modelling and simulation.

PubMed

Barrio, Manuel; Burrage, Kevin; Leier, André; Tian, Tianhai

2006-09-08

Discrete stochastic simulations are a powerful tool for understanding the dynamics of chemical kinetics when there are small-to-moderate numbers of certain molecular species. In this paper we introduce delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation. We then show that this process may well explain more faithfully than continuous deterministic models the observed sustained oscillations in expression levels of hes1 mRNA and Hes1 protein.

Binomial tau-leap spatial stochastic simulation algorithm for applications in chemical kinetics.

PubMed

Marquez-Lago, Tatiana T; Burrage, Kevin

2007-09-14

In cell biology, cell signaling pathway problems are often tackled with deterministic temporal models, well mixed stochastic simulators, and/or hybrid methods. But, in fact, three dimensional stochastic spatial modeling of reactions happening inside the cell is needed in order to fully understand these cell signaling pathways. This is because noise effects, low molecular concentrations, and spatial heterogeneity can all affect the cellular dynamics. However, there are ways in which important effects can be accounted without going to the extent of using highly resolved spatial simulators (such as single-particle software), hence reducing the overall computation time significantly. We present a new coarse grained modified version of the next subvolume method that allows the user to consider both diffusion and reaction events in relatively long simulation time spans as compared with the original method and other commonly used fully stochastic computational methods. Benchmarking of the simulation algorithm was performed through comparison with the next subvolume method and well mixed models (MATLAB), as well as stochastic particle reaction and transport simulations (CHEMCELL, Sandia National Laboratories). Additionally, we construct a model based on a set of chemical reactions in the epidermal growth factor receptor pathway. For this particular application and a bistable chemical system example, we analyze and outline the advantages of our presented binomial tau-leap spatial stochastic simulation algorithm, in terms of efficiency and accuracy, in scenarios of both molecular homogeneity and heterogeneity.

Stochastic Synapses Enable Efficient Brain-Inspired Learning Machines.

PubMed

Neftci, Emre O; Pedroni, Bruno U; Joshi, Siddharth; Al-Shedivat, Maruan; Cauwenberghs, Gert

2016-01-01

Recent studies have shown that synaptic unreliability is a robust and sufficient mechanism for inducing the stochasticity observed in cortex. Here, we introduce Synaptic Sampling Machines (S2Ms), a class of neural network models that uses synaptic stochasticity as a means to Monte Carlo sampling and unsupervised learning. Similar to the original formulation of Boltzmann machines, these models can be viewed as a stochastic counterpart of Hopfield networks, but where stochasticity is induced by a random mask over the connections. Synaptic stochasticity plays the dual role of an efficient mechanism for sampling, and a regularizer during learning akin to DropConnect. A local synaptic plasticity rule implementing an event-driven form of contrastive divergence enables the learning of generative models in an on-line fashion. S2Ms perform equally well using discrete-timed artificial units (as in Hopfield networks) or continuous-timed leaky integrate and fire neurons. The learned representations are remarkably sparse and robust to reductions in bit precision and synapse pruning: removal of more than 75% of the weakest connections followed by cursory re-learning causes a negligible performance loss on benchmark classification tasks. The spiking neuron-based S2Ms outperform existing spike-based unsupervised learners, while potentially offering substantial advantages in terms of power and complexity, and are thus promising models for on-line learning in brain-inspired hardware.

Stochastic Synapses Enable Efficient Brain-Inspired Learning Machines

PubMed Central

Neftci, Emre O.; Pedroni, Bruno U.; Joshi, Siddharth; Al-Shedivat, Maruan; Cauwenberghs, Gert

2016-01-01

Recent studies have shown that synaptic unreliability is a robust and sufficient mechanism for inducing the stochasticity observed in cortex. Here, we introduce Synaptic Sampling Machines (S2Ms), a class of neural network models that uses synaptic stochasticity as a means to Monte Carlo sampling and unsupervised learning. Similar to the original formulation of Boltzmann machines, these models can be viewed as a stochastic counterpart of Hopfield networks, but where stochasticity is induced by a random mask over the connections. Synaptic stochasticity plays the dual role of an efficient mechanism for sampling, and a regularizer during learning akin to DropConnect. A local synaptic plasticity rule implementing an event-driven form of contrastive divergence enables the learning of generative models in an on-line fashion. S2Ms perform equally well using discrete-timed artificial units (as in Hopfield networks) or continuous-timed leaky integrate and fire neurons. The learned representations are remarkably sparse and robust to reductions in bit precision and synapse pruning: removal of more than 75% of the weakest connections followed by cursory re-learning causes a negligible performance loss on benchmark classification tasks. The spiking neuron-based S2Ms outperform existing spike-based unsupervised learners, while potentially offering substantial advantages in terms of power and complexity, and are thus promising models for on-line learning in brain-inspired hardware. PMID:27445650

Stochastic reduced order models for inverse problems under uncertainty

PubMed Central

Warner, James E.; Aquino, Wilkins; Grigoriu, Mircea D.

2014-01-01

This work presents a novel methodology for solving inverse problems under uncertainty using stochastic reduced order models (SROMs). Given statistical information about an observed state variable in a system, unknown parameters are estimated probabilistically through the solution of a model-constrained, stochastic optimization problem. The point of departure and crux of the proposed framework is the representation of a random quantity using a SROM - a low dimensional, discrete approximation to a continuous random element that permits e cient and non-intrusive stochastic computations. Characterizing the uncertainties with SROMs transforms the stochastic optimization problem into a deterministic one. The non-intrusive nature of SROMs facilitates e cient gradient computations for random vector unknowns and relies entirely on calls to existing deterministic solvers. Furthermore, the method is naturally extended to handle multiple sources of uncertainty in cases where state variable data, system parameters, and boundary conditions are all considered random. The new and widely-applicable SROM framework is formulated for a general stochastic optimization problem in terms of an abstract objective function and constraining model. For demonstration purposes, however, we study its performance in the specific case of inverse identification of random material parameters in elastodynamics. We demonstrate the ability to efficiently recover random shear moduli given material displacement statistics as input data. We also show that the approach remains effective for the case where the loading in the problem is random as well. PMID:25558115

A non-linear dimension reduction methodology for generating data-driven stochastic input models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ganapathysubramanian, Baskar; Zabaras, Nicholas

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem ofmore » manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space R{sup n}. An isometric mapping F from M to a low-dimensional, compact, connected set A is contained in R{sup d}(d<

Definition and solution of a stochastic inverse problem for the Manning's n parameter field in hydrodynamic models.

PubMed

Butler, T; Graham, L; Estep, D; Dawson, C; Westerink, J J

2015-04-01

The uncertainty in spatially heterogeneous Manning's n fields is quantified using a novel formulation and numerical solution of stochastic inverse problems for physics-based models. The uncertainty is quantified in terms of a probability measure and the physics-based model considered here is the state-of-the-art ADCIRC model although the presented methodology applies to other hydrodynamic models. An accessible overview of the formulation and solution of the stochastic inverse problem in a mathematically rigorous framework based on measure theory is presented. Technical details that arise in practice by applying the framework to determine the Manning's n parameter field in a shallow water equation model used for coastal hydrodynamics are presented and an efficient computational algorithm and open source software package are developed. A new notion of "condition" for the stochastic inverse problem is defined and analyzed as it relates to the computation of probabilities. This notion of condition is investigated to determine effective output quantities of interest of maximum water elevations to use for the inverse problem for the Manning's n parameter and the effect on model predictions is analyzed.

Definition and solution of a stochastic inverse problem for the Manning's n parameter field in hydrodynamic models

NASA Astrophysics Data System (ADS)

Butler, T.; Graham, L.; Estep, D.; Dawson, C.; Westerink, J. J.

2015-04-01

The uncertainty in spatially heterogeneous Manning's n fields is quantified using a novel formulation and numerical solution of stochastic inverse problems for physics-based models. The uncertainty is quantified in terms of a probability measure and the physics-based model considered here is the state-of-the-art ADCIRC model although the presented methodology applies to other hydrodynamic models. An accessible overview of the formulation and solution of the stochastic inverse problem in a mathematically rigorous framework based on measure theory is presented. Technical details that arise in practice by applying the framework to determine the Manning's n parameter field in a shallow water equation model used for coastal hydrodynamics are presented and an efficient computational algorithm and open source software package are developed. A new notion of "condition" for the stochastic inverse problem is defined and analyzed as it relates to the computation of probabilities. This notion of condition is investigated to determine effective output quantities of interest of maximum water elevations to use for the inverse problem for the Manning's n parameter and the effect on model predictions is analyzed.

Stochastic optimization for modeling physiological time series: application to the heart rate response to exercise

NASA Astrophysics Data System (ADS)

Zakynthinaki, M. S.; Stirling, J. R.

2007-01-01

Stochastic optimization is applied to the problem of optimizing the fit of a model to the time series of raw physiological (heart rate) data. The physiological response to exercise has been recently modeled as a dynamical system. Fitting the model to a set of raw physiological time series data is, however, not a trivial task. For this reason and in order to calculate the optimal values of the parameters of the model, the present study implements the powerful stochastic optimization method ALOPEX IV, an algorithm that has been proven to be fast, effective and easy to implement. The optimal parameters of the model, calculated by the optimization method for the particular athlete, are very important as they characterize the athlete's current condition. The present study applies the ALOPEX IV stochastic optimization to the modeling of a set of heart rate time series data corresponding to different exercises of constant intensity. An analysis of the optimization algorithm, together with an analytic proof of its convergence (in the absence of noise), is also presented.

Uncertainty Aware Structural Topology Optimization Via a Stochastic Reduced Order Model Approach

NASA Technical Reports Server (NTRS)

Aguilo, Miguel A.; Warner, James E.

2017-01-01

This work presents a stochastic reduced order modeling strategy for the quantification and propagation of uncertainties in topology optimization. Uncertainty aware optimization problems can be computationally complex due to the substantial number of model evaluations that are necessary to accurately quantify and propagate uncertainties. This computational complexity is greatly magnified if a high-fidelity, physics-based numerical model is used for the topology optimization calculations. Stochastic reduced order model (SROM) methods are applied here to effectively 1) alleviate the prohibitive computational cost associated with an uncertainty aware topology optimization problem; and 2) quantify and propagate the inherent uncertainties due to design imperfections. A generic SROM framework that transforms the uncertainty aware, stochastic topology optimization problem into a deterministic optimization problem that relies only on independent calls to a deterministic numerical model is presented. This approach facilitates the use of existing optimization and modeling tools to accurately solve the uncertainty aware topology optimization problems in a fraction of the computational demand required by Monte Carlo methods. Finally, an example in structural topology optimization is presented to demonstrate the effectiveness of the proposed uncertainty aware structural topology optimization approach.

A nonlinear dynamic age-structured model of e-commerce in spain: Stability analysis of the equilibrium by delay and stochastic perturbations

NASA Astrophysics Data System (ADS)

Burgos, C.; Cortés, J.-C.; Shaikhet, L.; Villanueva, R.-J.

2018-11-01

First, we propose a deterministic age-structured epidemiological model to study the diffusion of e-commerce in Spain. Afterwards, we determine the parameters (death, birth and growth rates) of the underlying demographic model as well as the parameters (transmission of the use of e-commerce rates) of the proposed epidemiological model that best fit real data retrieved from the Spanish National Statistical Institute. Motivated by the two following facts: first the dynamics of acquiring the use of a new technology as e-commerce is mainly driven by the feedback after interacting with our peers (family, friends, mates, mass media, etc.), hence having a certain delay, and second the inherent uncertainty of sampled real data and the social complexity of the phenomena under analysis, we introduce aftereffect and stochastic perturbations in the initial deterministic model. This leads to a delayed stochastic model for e-commerce. We then investigate sufficient conditions in order to guarantee the stability in probability of the equilibrium point of the dynamic e-commerce delayed stochastic model. Our theoretical findings are numerically illustrated using real data.

Development of a Stochastically-driven, Forward Predictive Performance Model for PEMFCs

NASA Astrophysics Data System (ADS)

Harvey, David Benjamin Paul

A one-dimensional multi-scale coupled, transient, and mechanistic performance model for a PEMFC membrane electrode assembly has been developed. The model explicitly includes each of the 5 layers within a membrane electrode assembly and solves for the transport of charge, heat, mass, species, dissolved water, and liquid water. Key features of the model include the use of a multi-step implementation of the HOR reaction on the anode, agglomerate catalyst sub-models for both the anode and cathode catalyst layers, a unique approach that links the composition of the catalyst layer to key properties within the agglomerate model and the implementation of a stochastic input-based approach for component material properties. The model employs a new methodology for validation using statistically varying input parameters and statistically-based experimental performance data; this model represents the first stochastic input driven unit cell performance model. The stochastic input driven performance model was used to identify optimal ionomer content within the cathode catalyst layer, demonstrate the role of material variation in potential low performing MEA materials, provide explanation for the performance of low-Pt loaded MEAs, and investigate the validity of transient-sweep experimental diagnostic methods.

Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models.

PubMed

Daunizeau, J; Friston, K J; Kiebel, S J

2009-11-01

In this paper, we describe a general variational Bayesian approach for approximate inference on nonlinear stochastic dynamic models. This scheme extends established approximate inference on hidden-states to cover: (i) nonlinear evolution and observation functions, (ii) unknown parameters and (precision) hyperparameters and (iii) model comparison and prediction under uncertainty. Model identification or inversion entails the estimation of the marginal likelihood or evidence of a model. This difficult integration problem can be finessed by optimising a free-energy bound on the evidence using results from variational calculus. This yields a deterministic update scheme that optimises an approximation to the posterior density on the unknown model variables. We derive such a variational Bayesian scheme in the context of nonlinear stochastic dynamic hierarchical models, for both model identification and time-series prediction. The computational complexity of the scheme is comparable to that of an extended Kalman filter, which is critical when inverting high dimensional models or long time-series. Using Monte-Carlo simulations, we assess the estimation efficiency of this variational Bayesian approach using three stochastic variants of chaotic dynamic systems. We also demonstrate the model comparison capabilities of the method, its self-consistency and its predictive power.

3DHYDROGEOCHEM: A 3-DIMENSIONAL MODEL OF DENSITY-DEPENDENT SUBSURFACE FLOW AND THERMAL MULTISPECIES-MULTICOMPONENT HYDROGEOCHEMICAL TRANSPORT (EPA/600/SR-98/159)

EPA Science Inventory

This report presents a three-dimensional finite-element numerical model designed to simulate chemical transport in subsurface systems with temperature effect taken into account. The three-dimensional model is developed to provide (1) a tool of application, with which one is able ...

Neutron density profile in the lunar subsurface produced by galactic cosmic rays

NASA Astrophysics Data System (ADS)

Ota, Shuya; Sihver, Lembit; Kobayashi, Shingo; Hasebe, Nobuyuki

Neutron production by galactic cosmic rays (GCR) in the lunar subsurface is very important when performing lunar and planetary nuclear spectroscopy and space dosimetry. Further im-provements to estimate the production with increased accuracy is therefore required. GCR, which is a main contributor to the neutron production in the lunar subsurface, consists of not only protons but also of heavy components such as He, C, N, O, and Fe. Because of that, it is important to precisely estimate the neutron production from such components for the lunar spectroscopy and space dosimetry. Therefore, the neutron production from GCR particles in-cluding heavy components in the lunar subsurface was simulated with the Particle and Heavy ion Transport code System (PHITS), using several heavy ion interaction models. This work presents PHITS simulations of the neutron density as a function of depth (neutron density profile) in the lunar subsurface and the results are compared with experimental data obtained by Apollo 17 Lunar Neutron Probe Experiment (LNPE). From our previous study, it has been found that the accuracy of the proton-induced neutron production models is the most influen-tial factor when performing precise calculations of neutron production in the lunar subsurface. Therefore, a benchmarking of proton-induced neutron production models against experimental data was performed to estimate and improve the precision of the calculations. It was found that the calculated neutron production using the best model of Cugnon Old (E < 3 GeV) and JAM (E > 3 GeV) gave up to 30% higher values than experimental results. Therefore, a high energy nuclear data file (JENDL-HE) was used instead of the Cugnon Old model at the energies below 3 GeV. Then, the calculated neutron density profile successfully reproduced the experimental data from LNPE within experimental errors of 15% (measurement) + 30% (systematic). In this presentation, we summarize and discuss our calculated results of neutron production in the lunar subsurface.

Implications of random variation in the Stand Prognosis Model

Treesearch

David A. Hamilton

1991-01-01

Although the Stand Prognosis Model has several stochastic components, features have been included in the model in an attempt to minimize run-to-run variation attributable to these stochastic components. This has led many users to assume that comparisons of management alternatives could be made based on a single run of the model for each alternative. Recent analyses...

Using stochastic models to incorporate spatial and temporal variability [Exercise 14

Treesearch

Carolyn Hull Sieg; Rudy M. King; Fred Van Dyke

2003-01-01

To this point, our analysis of population processes and viability in the western prairie fringed orchid has used only deterministic models. In this exercise, we conduct a similar analysis, using a stochastic model instead. This distinction is of great importance to population biology in general and to conservation biology in particular. In deterministic models,...

Stochastic Approximation Methods for Latent Regression Item Response Models. Research Report. ETS RR-09-09

ERIC Educational Resources Information Center

von Davier, Matthias; Sinharay, Sandip

2009-01-01

This paper presents an application of a stochastic approximation EM-algorithm using a Metropolis-Hastings sampler to estimate the parameters of an item response latent regression model. Latent regression models are extensions of item response theory (IRT) to a 2-level latent variable model in which covariates serve as predictors of the…

Model for the prediction of subsurface strata movement due to underground mining

NASA Astrophysics Data System (ADS)

Cheng, Jianwei; Liu, Fangyuan; Li, Siyuan

2017-12-01

The problem of ground control stability due to large underground mining operations is often associated with large movements and deformations of strata. It is a complicated problem, and can induce severe safety or environmental hazards either at the surface or in strata. Hence, knowing the subsurface strata movement characteristics, and making any subsidence predictions in advance, are desirable for mining engineers to estimate any damage likely to affect the ground surface or subsurface strata. Based on previous research findings, this paper broadly applies a surface subsidence prediction model based on the influence function method to subsurface strata, in order to predict subsurface stratum movement. A step-wise prediction model is proposed, to investigate the movement of underground strata. The model involves a dynamic iteration calculation process to derive the movements and deformations for each stratum layer; modifications to the influence method function are also made for more precise calculations. The critical subsidence parameters, incorporating stratum mechanical properties and the spatial relationship of interest at the mining level, are thoroughly considered, with the purpose of improving the reliability of input parameters. Such research efforts can be very helpful to mining engineers’ understanding of the moving behavior of all strata over underground excavations, and assist in making any damage mitigation plan. In order to check the reliability of the model, two methods are carried out and cross-validation applied. One is to use a borehole TV monitor recording to identify the progress of subsurface stratum bedding and caving in a coal mine, the other is to conduct physical modelling of the subsidence in underground strata. The results of these two methods are used to compare with theoretical results calculated by the proposed mathematical model. The testing results agree well with each other, and the acceptable accuracy and reliability of the proposed prediction model are thus validated.

Automated Flight Routing Using Stochastic Dynamic Programming

NASA Technical Reports Server (NTRS)

Ng, Hok K.; Morando, Alex; Grabbe, Shon

2010-01-01

Airspace capacity reduction due to convective weather impedes air traffic flows and causes traffic congestion. This study presents an algorithm that reroutes flights in the presence of winds, enroute convective weather, and congested airspace based on stochastic dynamic programming. A stochastic disturbance model incorporates into the reroute design process the capacity uncertainty. A trajectory-based airspace demand model is employed for calculating current and future airspace demand. The optimal routes minimize the total expected traveling time, weather incursion, and induced congestion costs. They are compared to weather-avoidance routes calculated using deterministic dynamic programming. The stochastic reroutes have smaller deviation probability than the deterministic counterpart when both reroutes have similar total flight distance. The stochastic rerouting algorithm takes into account all convective weather fields with all severity levels while the deterministic algorithm only accounts for convective weather systems exceeding a specified level of severity. When the stochastic reroutes are compared to the actual flight routes, they have similar total flight time, and both have about 1% of travel time crossing congested enroute sectors on average. The actual flight routes induce slightly less traffic congestion than the stochastic reroutes but intercept more severe convective weather.

Bond-based linear indices of the non-stochastic and stochastic edge-adjacency matrix. 1. Theory and modeling of ChemPhys properties of organic molecules.

PubMed

Marrero-Ponce, Yovani; Martínez-Albelo, Eugenio R; Casañola-Martín, Gerardo M; Castillo-Garit, Juan A; Echevería-Díaz, Yunaimy; Zaldivar, Vicente Romero; Tygat, Jan; Borges, José E Rodriguez; García-Domenech, Ramón; Torrens, Francisco; Pérez-Giménez, Facundo

2010-11-01

Novel bond-level molecular descriptors are proposed, based on linear maps similar to the ones defined in algebra theory. The kth edge-adjacency matrix (E(k)) denotes the matrix of bond linear indices (non-stochastic) with regard to canonical basis set. The kth stochastic edge-adjacency matrix, ES(k), is here proposed as a new molecular representation easily calculated from E(k). Then, the kth stochastic bond linear indices are calculated using ES(k) as operators of linear transformations. In both cases, the bond-type formalism is developed. The kth non-stochastic and stochastic total linear indices are calculated by adding the kth non-stochastic and stochastic bond linear indices, respectively, of all bonds in molecule. First, the new bond-based molecular descriptors (MDs) are tested for suitability, for the QSPRs, by analyzing regressions of novel indices for selected physicochemical properties of octane isomers (first round). General performance of the new descriptors in this QSPR studies is evaluated with regard to the well-known sets of 2D/3D MDs. From the analysis, we can conclude that the non-stochastic and stochastic bond-based linear indices have an overall good modeling capability proving their usefulness in QSPR studies. Later, the novel bond-level MDs are also used for the description and prediction of the boiling point of 28 alkyl-alcohols (second round), and to the modeling of the specific rate constant (log k), partition coefficient (log P), as well as the antibacterial activity of 34 derivatives of 2-furylethylenes (third round). The comparison with other approaches (edge- and vertices-based connectivity indices, total and local spectral moments, and quantum chemical descriptors as well as E-state/biomolecular encounter parameters) exposes a good behavior of our method in this QSPR studies. Finally, the approach described in this study appears to be a very promising structural invariant, useful not only for QSPR studies but also for similarity/diversity analysis and drug discovery protocols.

Stochastic Processes in Physics: Deterministic Origins and Control

NASA Astrophysics Data System (ADS)

Demers, Jeffery

Stochastic processes are ubiquitous in the physical sciences and engineering. While often used to model imperfections and experimental uncertainties in the macroscopic world, stochastic processes can attain deeper physical significance when used to model the seemingly random and chaotic nature of the underlying microscopic world. Nowhere more prevalent is this notion than in the field of stochastic thermodynamics - a modern systematic framework used describe mesoscale systems in strongly fluctuating thermal environments which has revolutionized our understanding of, for example, molecular motors, DNA replication, far-from equilibrium systems, and the laws of macroscopic thermodynamics as they apply to the mesoscopic world. With progress, however, come further challenges and deeper questions, most notably in the thermodynamics of information processing and feedback control. Here it is becoming increasingly apparent that, due to divergences and subtleties of interpretation, the deterministic foundations of the stochastic processes themselves must be explored and understood. This thesis presents a survey of stochastic processes in physical systems, the deterministic origins of their emergence, and the subtleties associated with controlling them. First, we study time-dependent billiards in the quivering limit - a limit where a billiard system is indistinguishable from a stochastic system, and where the simplified stochastic system allows us to view issues associated with deterministic time-dependent billiards in a new light and address some long-standing problems. Then, we embark on an exploration of the deterministic microscopic Hamiltonian foundations of non-equilibrium thermodynamics, and we find that important results from mesoscopic stochastic thermodynamics have simple microscopic origins which would not be apparent without the benefit of both the micro and meso perspectives. Finally, we study the problem of stabilizing a stochastic Brownian particle with feedback control, and we find that in order to avoid paradoxes involving the first law of thermodynamics, we need a model for the fine details of the thermal driving noise. The underlying theme of this thesis is the argument that the deterministic microscopic perspective and stochastic mesoscopic perspective are both important and useful, and when used together, we can more deeply and satisfyingly understand the physics occurring over either scale.

Conceptual Model Evaluation using Advanced Parameter Estimation Techniques with Heat as a Tracer

NASA Astrophysics Data System (ADS)

Naranjo, R. C.; Morway, E. D.; Healy, R. W.

2016-12-01

Temperature measurements made at multiple depths beneath the sediment-water interface has proven useful for estimating seepage rates from surface-water channels and corresponding subsurface flow direction. Commonly, parsimonious zonal representations of the subsurface structure are defined a priori by interpretation of temperature envelopes, slug tests or analysis of soil cores. However, combining multiple observations into a single zone may limit the inverse model solution and does not take full advantage of the information content within the measured data. Further, simulating the correct thermal gradient, flow paths, and transient behavior of solutes may be biased by inadequacies in the spatial description of subsurface hydraulic properties. The use of pilot points in PEST offers a more sophisticated approach to estimate the structure of subsurface heterogeneity. This presentation evaluates seepage estimation in a cross-sectional model of a trapezoidal canal with intermittent flow representing four typical sedimentary environments. The recent improvements in heat as a tracer measurement techniques (i.e. multi-depth temperature probe) along with use of modern calibration techniques (i.e., pilot points) provides opportunities for improved calibration of flow models, and, subsequently, improved model predictions.

A consistent framework to predict mass fluxes and depletion times for DNAPL contaminations in heterogeneous aquifers under uncertainty

NASA Astrophysics Data System (ADS)

Koch, Jonas; Nowak, Wolfgang

2013-04-01

At many hazardous waste sites and accidental spills, dense non-aqueous phase liquids (DNAPLs) such as TCE, PCE, or TCA have been released into the subsurface. Once a DNAPL is released into the subsurface, it serves as persistent source of dissolved-phase contamination. In chronological order, the DNAPL migrates through the porous medium and penetrates the aquifer, it forms a complex pattern of immobile DNAPL saturation, it dissolves into the groundwater and forms a contaminant plume, and it slowly depletes and bio-degrades in the long-term. In industrial countries the number of such contaminated sites is tremendously high to the point that a ranking from most risky to least risky is advisable. Such a ranking helps to decide whether a site needs to be remediated or may be left to natural attenuation. Both the ranking and the designing of proper remediation or monitoring strategies require a good understanding of the relevant physical processes and their inherent uncertainty. To this end, we conceptualize a probabilistic simulation framework that estimates probability density functions of mass discharge, source depletion time, and critical concentration values at crucial target locations. Furthermore, it supports the inference of contaminant source architectures from arbitrary site data. As an essential novelty, the mutual dependencies of the key parameters and interacting physical processes are taken into account throughout the whole simulation. In an uncertain and heterogeneous subsurface setting, we identify three key parameter fields: the local velocities, the hydraulic permeabilities and the DNAPL phase saturations. Obviously, these parameters depend on each other during DNAPL infiltration, dissolution and depletion. In order to highlight the importance of these mutual dependencies and interactions, we present results of several model set ups where we vary the physical and stochastic dependencies of the input parameters and simulated processes. Under these changes, the probability density functions demonstrate strong statistical shifts in their expected values and in their uncertainty. Considering the uncertainties of all key parameters but neglecting their interactions overestimates the output uncertainty. However, consistently using all available physical knowledge when assigning input parameters and simulating all relevant interactions of the involved processes reduces the output uncertainty significantly back down to useful and plausible ranges. When using our framework in an inverse setting, omitting a parameter dependency within a crucial physical process would lead to physical meaningless identified parameters. Thus, we conclude that the additional complexity we propose is both necessary and adequate. Overall, our framework provides a tool for reliable and plausible prediction, risk assessment, and model based decision support for DNAPL contaminated sites.

Dynamics of non-holonomic systems with stochastic transport

NASA Astrophysics Data System (ADS)

Holm, D. D.; Putkaradze, V.

2018-01-01

This paper formulates a variational approach for treating observational uncertainty and/or computational model errors as stochastic transport in dynamical systems governed by action principles under non-holonomic constraints. For this purpose, we derive, analyse and numerically study the example of an unbalanced spherical ball rolling under gravity along a stochastic path. Our approach uses the Hamilton-Pontryagin variational principle, constrained by a stochastic rolling condition, which we show is equivalent to the corresponding stochastic Lagrange-d'Alembert principle. In the example of the rolling ball, the stochasticity represents uncertainty in the observation and/or error in the computational simulation of the angular velocity of rolling. The influence of the stochasticity on the deterministically conserved quantities is investigated both analytically and numerically. Our approach applies to a wide variety of stochastic, non-holonomically constrained systems, because it preserves the mathematical properties inherited from the variational principle.

A Two-Step Method to Select Major Surge-Producing Extratropical Cyclones from a 10,000-Year Stochastic Catalog

NASA Astrophysics Data System (ADS)

Keshtpoor, M.; Carnacina, I.; Yablonsky, R. M.

2016-12-01

Extratropical cyclones (ETCs) are the primary driver of storm surge events along the UK and northwest mainland Europe coastlines. In an effort to evaluate the storm surge risk in coastal communities in this region, a stochastic catalog is developed by perturbing the historical storm seeds of European ETCs to account for 10,000 years of possible ETCs. Numerical simulation of the storm surge generated by the full 10,000-year stochastic catalog, however, is computationally expensive and may take several months to complete with available computational resources. A new statistical regression model is developed to select the major surge-generating events from the stochastic ETC catalog. This regression model is based on the maximum storm surge, obtained via numerical simulations using a calibrated version of the Delft3D-FM hydrodynamic model with a relatively coarse mesh, of 1750 historical ETC events that occurred over the past 38 years in Europe. These numerically-simulated surge values were regressed to the local sea level pressure and the U and V components of the wind field at the location of 196 tide gauge stations near the UK and northwest mainland Europe coastal areas. The regression model suggests that storm surge values in the area of interest are highly correlated to the U- and V-component of wind speed, as well as the sea level pressure. Based on these correlations, the regression model was then used to select surge-generating storms from the 10,000-year stochastic catalog. Results suggest that roughly 105,000 events out of 480,000 stochastic storms are surge-generating events and need to be considered for numerical simulation using a hydrodynamic model. The selected stochastic storms were then simulated in Delft3D-FM, and the final refinement of the storm population was performed based on return period analysis of the 1750 historical event simulations at each of the 196 tide gauges in preparation for Delft3D-FM fine mesh simulations.

Asymptotic behavior of a stochastic delayed HIV-1 infection model with nonlinear incidence

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing; Hayat, Tasawar; Ahmad, Bashir

2017-11-01

In this paper, a stochastic delayed HIV-1 infection model with nonlinear incidence is proposed and investigated. First of all, we prove that there is a unique global positive solution as desired in any population dynamics. Then by constructing some suitable Lyapunov functions, we show that if the basic reproduction number R0 ≤ 1, then the solution of the stochastic system oscillates around the infection-free equilibrium E0, while if R0 > 1, then the solution of the stochastic system fluctuates around the infective equilibrium E∗. Sufficient conditions of these results are established. Finally, we give some examples and a series of numerical simulations to illustrate the analytical results.

A stochastic multi-agent optimization model for energy infrastructure planning under uncertainty and competition.

DOT National Transportation Integrated Search

2017-07-04

This paper presents a stochastic multi-agent optimization model that supports energy infrastruc- : ture planning under uncertainty. The interdependence between dierent decision entities in the : system is captured in an energy supply chain network, w...

Large Deviations for Stochastic Models of Two-Dimensional Second Grade Fluids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhai, Jianliang, E-mail: zhaijl@ustc.edu.cn; Zhang, Tusheng, E-mail: Tusheng.Zhang@manchester.ac.uk

2017-06-15

In this paper, we establish a large deviation principle for stochastic models of incompressible second grade fluids. The weak convergence method introduced by Budhiraja and Dupuis (Probab Math Statist 20:39–61, 2000) plays an important role.

Cash transportation vehicle routing and scheduling under stochastic travel times

NASA Astrophysics Data System (ADS)

Yan, Shangyao; Wang, Sin-Siang; Chang, Yu-Hsuan

2014-03-01

Stochastic disturbances occurring in real-world operations could have a significant influence on the planned routing and scheduling results of cash transportation vehicles. In this study, a time-space network flow technique is utilized to construct a cash transportation vehicle routing and scheduling model incorporating stochastic travel times. In addition, to help security carriers to formulate more flexible routes and schedules, a concept of the similarity of time and space for vehicle routing and scheduling is incorporated into the model. The test results show that the model could be useful for security carriers in actual practice.

Gryphon: A Hybrid Agent-Based Modeling and Simulation Platform for Infectious Diseases

NASA Astrophysics Data System (ADS)

Yu, Bin; Wang, Jijun; McGowan, Michael; Vaidyanathan, Ganesh; Younger, Kristofer

In this paper we present Gryphon, a hybrid agent-based stochastic modeling and simulation platform developed for characterizing the geographic spread of infectious diseases and the effects of interventions. We study both local and non-local transmission dynamics of stochastic simulations based on the published parameters and data for SARS. The results suggest that the expected numbers of infections and the timeline of control strategies predicted by our stochastic model are in reasonably good agreement with previous studies. These preliminary results indicate that Gryphon is able to characterize other future infectious diseases and identify endangered regions in advance.

On some stochastic formulations and related statistical moments of pharmacokinetic models.

PubMed

Matis, J H; Wehrly, T E; Metzler, C M

1983-02-01

This paper presents the deterministic and stochastic model for a linear compartment system with constant coefficients, and it develops expressions for the mean residence times (MRT) and the variances of the residence times (VRT) for the stochastic model. The expressions are relatively simple computationally, involving primarily matrix inversion, and they are elegant mathematically, in avoiding eigenvalue analysis and the complex domain. The MRT and VRT provide a set of new meaningful response measures for pharmacokinetic analysis and they give added insight into the system kinetics. The new analysis is illustrated with an example involving the cholesterol turnover in rats.

Subcritical Hopf Bifurcation and Stochastic Resonance of Electrical Activities in Neuron under Electromagnetic Induction

PubMed Central

Fu, Yu-Xuan; Kang, Yan-Mei; Xie, Yong

2018-01-01

The FitzHugh–Nagumo model is improved to consider the effect of the electromagnetic induction on single neuron. On the basis of investigating the Hopf bifurcation behavior of the improved model, stochastic resonance in the stochastic version is captured near the bifurcation point. It is revealed that a weak harmonic oscillation in the electromagnetic disturbance can be amplified through stochastic resonance, and it is the cooperative effect of random transition between the resting state and the large amplitude oscillating state that results in the resonant phenomenon. Using the noise dependence of the mean of interburst intervals, we essentially suggest a biologically feasible clue for detecting weak signal by means of neuron model with subcritical Hopf bifurcation. These observations should be helpful in understanding the influence of the magnetic field to neural electrical activity. PMID:29467642

Subcritical Hopf Bifurcation and Stochastic Resonance of Electrical Activities in Neuron under Electromagnetic Induction.

PubMed

Fu, Yu-Xuan; Kang, Yan-Mei; Xie, Yong

2018-01-01

The FitzHugh-Nagumo model is improved to consider the effect of the electromagnetic induction on single neuron. On the basis of investigating the Hopf bifurcation behavior of the improved model, stochastic resonance in the stochastic version is captured near the bifurcation point. It is revealed that a weak harmonic oscillation in the electromagnetic disturbance can be amplified through stochastic resonance, and it is the cooperative effect of random transition between the resting state and the large amplitude oscillating state that results in the resonant phenomenon. Using the noise dependence of the mean of interburst intervals, we essentially suggest a biologically feasible clue for detecting weak signal by means of neuron model with subcritical Hopf bifurcation. These observations should be helpful in understanding the influence of the magnetic field to neural electrical activity.

The distribution of lingering subsurface oil from the Exxon Valdez oil spill

USGS Publications Warehouse

Michel, Jacqueline; Nixon, Zachary; Hayes, Miles O.; Irvine, Gail V.; Short, Jeffrey W.

2011-01-01

This study used field data and a suite of geospatial models to identify areas where subsurface oil is likely to still be present on the shorelines of Prince William Sound (PWS) and the Gulf of Alaska (GOA) affected by the Exxon Valdez oil spill, as well as the factors related to continued presence of such oil. The goal was to identify factors and accompanying models that could serve as screening tools to prioritize shorelines for different remediation methods. The models were based on data collected at 314 shoreline segments surveyed between 2001 and 2007. These field data allowed us to identify a number of geomorphologic and hydrologic factors that have contributed to the persistence of subsurface oil within PWS and GOA two decades after the spill. Because synoptic data layers for describing each of these factors at all locations were not available, the models developed used existing data sets as surrogates to represent these factors, such as distance to a stream mouth or shoreline convexity. While the linkages between the data used and the physical phenomena that drive persistence are not clearly understood in all cases, the performance of these models was remarkably good. The models simultaneously evaluate all identified variables to predict the presence of different types of subsurface oiling in a rigorous, unbiased manner. The refined model results suggest there are a limited but significant number of as-yet unsurveyed locations in the study area that are likely to contain subsurface oil. Furthermore, the model results may be used to quantitatively prioritize shoreline for investigation with known uncertainty.

Stochastic and deterministic multiscale models for systems biology: an auxin-transport case study.

PubMed

Twycross, Jamie; Band, Leah R; Bennett, Malcolm J; King, John R; Krasnogor, Natalio

2010-03-26

Stochastic and asymptotic methods are powerful tools in developing multiscale systems biology models; however, little has been done in this context to compare the efficacy of these methods. The majority of current systems biology modelling research, including that of auxin transport, uses numerical simulations to study the behaviour of large systems of deterministic ordinary differential equations, with little consideration of alternative modelling frameworks. In this case study, we solve an auxin-transport model using analytical methods, deterministic numerical simulations and stochastic numerical simulations. Although the three approaches in general predict the same behaviour, the approaches provide different information that we use to gain distinct insights into the modelled biological system. We show in particular that the analytical approach readily provides straightforward mathematical expressions for the concentrations and transport speeds, while the stochastic simulations naturally provide information on the variability of the system. Our study provides a constructive comparison which highlights the advantages and disadvantages of each of the considered modelling approaches. This will prove helpful to researchers when weighing up which modelling approach to select. In addition, the paper goes some way to bridging the gap between these approaches, which in the future we hope will lead to integrative hybrid models.

Working Smarter Not Harder - Developing a Virtual Subsurface Data Framework for U.S. Energy R&D

NASA Astrophysics Data System (ADS)

Rose, K.; Baker, D.; Bauer, J.; Dehlin, M.; Jones, T. J.; Rowan, C.

2017-12-01

The data revolution has resulted in a proliferation of resources that span beyond commercial and social networking domains. Research, scientific, and engineering data resources, including subsurface characterization, modeling, and analytical datasets, are increasingly available through online portals, warehouses, and systems. Data for subsurface systems is still challenging to access, discontinuous, and varies in resolution. However, with the proliferation of online data there are significant opportunities to advance access and knowledge of subsurface systems. The Energy Data eXchange (EDX) is an online platform designed to address research data needs by improving access to energy R&D products through advanced search capabilities. In addition, EDX hosts private, virtualized computational workspaces in support of multi-organizational R&D. These collaborative workspaces allow teams to share working data resources and connect to a growing number of analytical tools to support research efforts. One recent application, a team digital data notebook tool, called DataBook, was introduced within EDX workspaces to allow teams to capture contextual and structured data resources. Starting with DOE's subsurface R&D community, the EDX team has been developing DataBook to support scientists and engineers working on subsurface energy research, allowing them to contribute and curate both structured and unstructured data and knowledge about subsurface systems. These resources span petrophysical, geologic, engineering, geophysical, interpretations, models, and analyses associated with carbon storage, water, oil, gas, geothermal, induced seismicity and other subsurface systems to support the development of a virtual subsurface data framework. The integration of EDX and DataBook allows for these systems to leverage each other's best features, such as the ability to interact with other systems (Earthcube, OpenEI.net, NGDS, etc.) and leverage custom machine learning algorithms and capabilities to enhance user experience, make access and connection to relevant subsurface data resources more efficient for research teams to use, analyze and draw insights. Ultimately, the public and private resources in EDX seek to make subsurface energy research more efficient, reduce redundancy, and drive innovation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pavlou, A. T.; Betzler, B. R.; Burke, T. P.

Uncertainties in the composition and fabrication of fuel compacts for the Fort St. Vrain (FSV) high temperature gas reactor have been studied by performing eigenvalue sensitivity studies that represent the key uncertainties for the FSV neutronic analysis. The uncertainties for the TRISO fuel kernels were addressed by developing a suite of models for an 'average' FSV fuel compact that models the fuel as (1) a mixture of two different TRISO fuel particles representing fissile and fertile kernels, (2) a mixture of four different TRISO fuel particles representing small and large fissile kernels and small and large fertile kernels and (3)more » a stochastic mixture of the four types of fuel particles where every kernel has its diameter sampled from a continuous probability density function. All of the discrete diameter and continuous diameter fuel models were constrained to have the same fuel loadings and packing fractions. For the non-stochastic discrete diameter cases, the MCNP compact model arranged the TRISO fuel particles on a hexagonal honeycomb lattice. This lattice-based fuel compact was compared to a stochastic compact where the locations (and kernel diameters for the continuous diameter cases) of the fuel particles were randomly sampled. Partial core configurations were modeled by stacking compacts into fuel columns containing graphite. The differences in eigenvalues between the lattice-based and stochastic models were small but the runtime of the lattice-based fuel model was roughly 20 times shorter than with the stochastic-based fuel model. (authors)« less

Analysis of the stochastic excitability in the flow chemical reactor

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bashkirtseva, Irina

2015-11-30

A dynamic model of the thermochemical process in the flow reactor is considered. We study an influence of the random disturbances on the stationary regime of this model. A phenomenon of noise-induced excitability is demonstrated. For the analysis of this phenomenon, a constructive technique based on the stochastic sensitivity functions and confidence domains is applied. It is shown how elaborated technique can be used for the probabilistic analysis of the generation of mixed-mode stochastic oscillations in the flow chemical reactor.

Oscillatory Regulation of Hes1: Discrete Stochastic Delay Modelling and Simulation

PubMed Central

Barrio, Manuel; Burrage, Kevin; Leier, André; Tian, Tianhai

2006-01-01

Discrete stochastic simulations are a powerful tool for understanding the dynamics of chemical kinetics when there are small-to-moderate numbers of certain molecular species. In this paper we introduce delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation. We then show that this process may well explain more faithfully than continuous deterministic models the observed sustained oscillations in expression levels of hes1 mRNA and Hes1 protein. PMID:16965175

Analysis of the stochastic excitability in the flow chemical reactor

NASA Astrophysics Data System (ADS)

Bashkirtseva, Irina

2015-11-01

A dynamic model of the thermochemical process in the flow reactor is considered. We study an influence of the random disturbances on the stationary regime of this model. A phenomenon of noise-induced excitability is demonstrated. For the analysis of this phenomenon, a constructive technique based on the stochastic sensitivity functions and confidence domains is applied. It is shown how elaborated technique can be used for the probabilistic analysis of the generation of mixed-mode stochastic oscillations in the flow chemical reactor.

A damage analysis for brittle materials using stochastic micro-structural information

NASA Astrophysics Data System (ADS)

Lin, Shih-Po; Chen, Jiun-Shyan; Liang, Shixue

2016-03-01

In this work, a micro-crack informed stochastic damage analysis is performed to consider the failures of material with stochastic microstructure. The derivation of the damage evolution law is based on the Helmholtz free energy equivalence between cracked microstructure and homogenized continuum. The damage model is constructed under the stochastic representative volume element (SRVE) framework. The characteristics of SRVE used in the construction of the stochastic damage model have been investigated based on the principle of the minimum potential energy. The mesh dependency issue has been addressed by introducing a scaling law into the damage evolution equation. The proposed methods are then validated through the comparison between numerical simulations and experimental observations of a high strength concrete. It is observed that the standard deviation of porosity in the microstructures has stronger effect on the damage states and the peak stresses than its effect on the Young's and shear moduli in the macro-scale responses.

Evolutionary stability concepts in a stochastic environment

NASA Astrophysics Data System (ADS)

Zheng, Xiu-Deng; Li, Cong; Lessard, Sabin; Tao, Yi

2017-09-01

Over the past 30 years, evolutionary game theory and the concept of an evolutionarily stable strategy have been not only extensively developed and successfully applied to explain the evolution of animal behaviors, but also widely used in economics and social sciences. Nonetheless, the stochastic dynamical properties of evolutionary games in randomly fluctuating environments are still unclear. In this study, we investigate conditions for stochastic local stability of fixation states and constant interior equilibria in a two-phenotype model with random payoffs following pairwise interactions. Based on this model, we develop the concepts of stochastic evolutionary stability (SES) and stochastic convergence stability (SCS). We show that the condition for a pure strategy to be SES and SCS is more stringent than in a constant environment, while the condition for a constant mixed strategy to be SES is less stringent than the condition to be SCS, which is less stringent than the condition in a constant environment.

Investigation for improving Global Positioning System (GPS) orbits using a discrete sequential estimator and stochastic models of selected physical processes

NASA Technical Reports Server (NTRS)

Goad, Clyde C.; Chadwell, C. David

1993-01-01

GEODYNII is a conventional batch least-squares differential corrector computer program with deterministic models of the physical environment. Conventional algorithms were used to process differenced phase and pseudorange data to determine eight-day Global Positioning system (GPS) orbits with several meter accuracy. However, random physical processes drive the errors whose magnitudes prevent improving the GPS orbit accuracy. To improve the orbit accuracy, these random processes should be modeled stochastically. The conventional batch least-squares algorithm cannot accommodate stochastic models, only a stochastic estimation algorithm is suitable, such as a sequential filter/smoother. Also, GEODYNII cannot currently model the correlation among data values. Differenced pseudorange, and especially differenced phase, are precise data types that can be used to improve the GPS orbit precision. To overcome these limitations and improve the accuracy of GPS orbits computed using GEODYNII, we proposed to develop a sequential stochastic filter/smoother processor by using GEODYNII as a type of trajectory preprocessor. Our proposed processor is now completed. It contains a correlated double difference range processing capability, first order Gauss Markov models for the solar radiation pressure scale coefficient and y-bias acceleration, and a random walk model for the tropospheric refraction correction. The development approach was to interface the standard GEODYNII output files (measurement partials and variationals) with software modules containing the stochastic estimator, the stochastic models, and a double differenced phase range processing routine. Thus, no modifications to the original GEODYNII software were required. A schematic of the development is shown. The observational data are edited in the preprocessor and the data are passed to GEODYNII as one of its standard data types. A reference orbit is determined using GEODYNII as a batch least-squares processor and the GEODYNII measurement partial (FTN90) and variational (FTN80, V-matrix) files are generated. These two files along with a control statement file and a satellite identification and mass file are passed to the filter/smoother to estimate time-varying parameter states at each epoch, improved satellite initial elements, and improved estimates of constant parameters.

Parameter estimation uncertainty: Comparing apples and apples?

NASA Astrophysics Data System (ADS)

Hart, D.; Yoon, H.; McKenna, S. A.

2012-12-01

Given a highly parameterized ground water model in which the conceptual model of the heterogeneity is stochastic, an ensemble of inverse calibrations from multiple starting points (MSP) provides an ensemble of calibrated parameters and follow-on transport predictions. However, the multiple calibrations are computationally expensive. Parameter estimation uncertainty can also be modeled by decomposing the parameterization into a solution space and a null space. From a single calibration (single starting point) a single set of parameters defining the solution space can be extracted. The solution space is held constant while Monte Carlo sampling of the parameter set covering the null space creates an ensemble of the null space parameter set. A recently developed null-space Monte Carlo (NSMC) method combines the calibration solution space parameters with the ensemble of null space parameters, creating sets of calibration-constrained parameters for input to the follow-on transport predictions. Here, we examine the consistency between probabilistic ensembles of parameter estimates and predictions using the MSP calibration and the NSMC approaches. A highly parameterized model of the Culebra dolomite previously developed for the WIPP project in New Mexico is used as the test case. A total of 100 estimated fields are retained from the MSP approach and the ensemble of results defining the model fit to the data, the reproduction of the variogram model and prediction of an advective travel time are compared to the same results obtained using NSMC. We demonstrate that the NSMC fields based on a single calibration model can be significantly constrained by the calibrated solution space and the resulting distribution of advective travel times is biased toward the travel time from the single calibrated field. To overcome this, newly proposed strategies to employ a multiple calibration-constrained NSMC approach (M-NSMC) are evaluated. Comparison of the M-NSMC and MSP methods suggests that M-NSMC can provide a computationally efficient and practical solution for predictive uncertainty analysis in highly nonlinear and complex subsurface flow and transport models. This material is based upon work supported as part of the Center for Frontiers of Subsurface Energy Security, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0001114. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Discharge-nitrate data clustering for characterizing surface-subsurface flow interaction and calibration of a hydrologic model

NASA Astrophysics Data System (ADS)

Shrestha, R. R.; Rode, M.

2008-12-01

Concentration of reactive chemicals has different chemical signatures in baseflow and surface runoff. Previous studies on nitrate export from a catchment indicate that the transport processes are driven by subsurface flow. Therefore nitrate signature can be used for understanding the event and pre-event contributions to streamflow and surface-subsurface flow interactions. The study uses flow and nitrate concentration time series data for understanding the relationship between these two variables. Unsupervised artificial neural network based learning method called self organizing map is used for the identification of clusters in the datasets. Based on the cluster results, five different pattern in the datasets are identified which correspond to (i) baseflow, (ii) subsurface flow increase, (iii) surface runoff increase, (iv) surface runoff recession, and (v) subsurface flow decrease regions. The cluster results in combination with a hydrologic model are used for discharge separation. For this purpose, a multi-objective optimization tool NSGA-II is used, where violation of cluster results is used as one of the objective functions. The results show that the use of cluster results as supplementary information for the calibration of a hydrologic model gives a plausible simulation of subsurface flow as well total runoff at the catchment outlet. The study is undertaken using data from the Weida catchment in the North-Eastern Germany, which is a sub-catchment of the Weisse Elster river in the Elbe river basin.

Modeling of Near-Surface Leakage and Seepage of CO2 for Risk Characterization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oldenburg, Curtis M.; Unger, Andre A.J.

2004-02-18

The injection of carbon dioxide (CO2) into deep geologic carbon sequestration sites entails risk that CO2 will leak away from the primary storage formation and migrate upwards to the unsaturated zone from which it can seep out of the ground. We have developed a coupled modeling framework called T2CA for simulating CO2 leakage and seepage in the subsurface and in the atmospheric surface layer. The results of model simulations can be used to calculate the two key health, safety, and environmental (HSE) risk drivers, namely CO2 seepage flux and nearsurface CO2 concentrations. Sensitivity studies for a subsurface system with amore » thick unsaturated zone show limited leakage attenuation resulting in correspondingly large CO2 concentrations in the shallow subsurface. Large CO2 concentrations in the shallow subsurface present a risk to plant and tree roots, and to humans and other animals in subsurface structures such as basements or utility vaults. Whereas CO2 concentrations in the subsurface can be high, surfacelayer winds reduce CO2 concentrations to low levels for the fluxes investigated. We recommend more verification and case studies be carried out with T2CA, along with the development of extensions to handle additional scenarios such as calm conditions, topographic effects, and catastrophic surface-layer discharge events.« less

An Anatomically Constrained, Stochastic Model of Eye Movement Control in Reading

ERIC Educational Resources Information Center

McDonald, Scott A.; Carpenter, R. H. S.; Shillcock, Richard C.

2005-01-01

This article presents SERIF, a new model of eye movement control in reading that integrates an established stochastic model of saccade latencies (LATER; R. H. S. Carpenter, 1981) with a fundamental anatomical constraint on reading: the vertically split fovea and the initial projection of information in either visual field to the contralateral…

Comparison of holstein and jersey milk production with a new stochastic animal reproduction model

USDA-ARS?s Scientific Manuscript database

Holsteins and Jerseys are the most popular breeds in the US dairy industry. We built a stochastic, Monte Carlo life events simulation model in Python to test if Jersey cattle’s higher conception rate offsets their lower milk production. The model simulates individual cows and their life events such ...

Development and Evaluation of a New Air Exchange Rate Algorithm for the Stochastic Human Exposure and Dose Simulation Model

EPA Science Inventory

between-home and between-city variability in residential pollutant infiltration. This is likely a result of differences in home ventilation, or air exchange rates (AER). The Stochastic Human Exposure and Dose Simulation (SHEDS) model is a population exposure model that uses a pro...

Ocean (de)oxygenation from the Last Glacial Maximum to the twenty-first century: insights from Earth System models.

PubMed

Bopp, L; Resplandy, L; Untersee, A; Le Mezo, P; Kageyama, M

2017-09-13

All Earth System models project a consistent decrease in the oxygen content of oceans for the coming decades because of ocean warming, reduced ventilation and increased stratification. But large uncertainties for these future projections of ocean deoxygenation remain for the subsurface tropical oceans where the major oxygen minimum zones are located. Here, we combine global warming projections, model-based estimates of natural short-term variability, as well as data and model estimates of the Last Glacial Maximum (LGM) ocean oxygenation to gain some insights into the major mechanisms of oxygenation changes across these different time scales. We show that the primary uncertainty on future ocean deoxygenation in the subsurface tropical oceans is in fact controlled by a robust compensation between decreasing oxygen saturation (O 2sat ) due to warming and decreasing apparent oxygen utilization (AOU) due to increased ventilation of the corresponding water masses. Modelled short-term natural variability in subsurface oxygen levels also reveals a compensation between O 2sat and AOU, controlled by the latter. Finally, using a model simulation of the LGM, reproducing data-based reconstructions of past ocean (de)oxygenation, we show that the deoxygenation trend of the subsurface ocean during deglaciation was controlled by a combination of warming-induced decreasing O 2sat and increasing AOU driven by a reduced ventilation of tropical subsurface waters.This article is part of the themed issue 'Ocean ventilation and deoxygenation in a warming world'. © 2017 The Author(s).

Ocean (de)oxygenation from the Last Glacial Maximum to the twenty-first century: insights from Earth System models

NASA Astrophysics Data System (ADS)

Bopp, L.; Resplandy, L.; Untersee, A.; Le Mezo, P.; Kageyama, M.

2017-08-01

All Earth System models project a consistent decrease in the oxygen content of oceans for the coming decades because of ocean warming, reduced ventilation and increased stratification. But large uncertainties for these future projections of ocean deoxygenation remain for the subsurface tropical oceans where the major oxygen minimum zones are located. Here, we combine global warming projections, model-based estimates of natural short-term variability, as well as data and model estimates of the Last Glacial Maximum (LGM) ocean oxygenation to gain some insights into the major mechanisms of oxygenation changes across these different time scales. We show that the primary uncertainty on future ocean deoxygenation in the subsurface tropical oceans is in fact controlled by a robust compensation between decreasing oxygen saturation (O2sat) due to warming and decreasing apparent oxygen utilization (AOU) due to increased ventilation of the corresponding water masses. Modelled short-term natural variability in subsurface oxygen levels also reveals a compensation between O2sat and AOU, controlled by the latter. Finally, using a model simulation of the LGM, reproducing data-based reconstructions of past ocean (de)oxygenation, we show that the deoxygenation trend of the subsurface ocean during deglaciation was controlled by a combination of warming-induced decreasing O2sat and increasing AOU driven by a reduced ventilation of tropical subsurface waters. This article is part of the themed issue 'Ocean ventilation and deoxygenation in a warming world'.

GPU-powered Shotgun Stochastic Search for Dirichlet process mixtures of Gaussian Graphical Models

PubMed Central

Mukherjee, Chiranjit; Rodriguez, Abel

2016-01-01

Gaussian graphical models are popular for modeling high-dimensional multivariate data with sparse conditional dependencies. A mixture of Gaussian graphical models extends this model to the more realistic scenario where observations come from a heterogenous population composed of a small number of homogeneous sub-groups. In this paper we present a novel stochastic search algorithm for finding the posterior mode of high-dimensional Dirichlet process mixtures of decomposable Gaussian graphical models. Further, we investigate how to harness the massive thread-parallelization capabilities of graphical processing units to accelerate computation. The computational advantages of our algorithms are demonstrated with various simulated data examples in which we compare our stochastic search with a Markov chain Monte Carlo algorithm in moderate dimensional data examples. These experiments show that our stochastic search largely outperforms the Markov chain Monte Carlo algorithm in terms of computing-times and in terms of the quality of the posterior mode discovered. Finally, we analyze a gene expression dataset in which Markov chain Monte Carlo algorithms are too slow to be practically useful. PMID:28626348

GPU-powered Shotgun Stochastic Search for Dirichlet process mixtures of Gaussian Graphical Models.

PubMed

Mukherjee, Chiranjit; Rodriguez, Abel

2016-01-01

Gaussian graphical models are popular for modeling high-dimensional multivariate data with sparse conditional dependencies. A mixture of Gaussian graphical models extends this model to the more realistic scenario where observations come from a heterogenous population composed of a small number of homogeneous sub-groups. In this paper we present a novel stochastic search algorithm for finding the posterior mode of high-dimensional Dirichlet process mixtures of decomposable Gaussian graphical models. Further, we investigate how to harness the massive thread-parallelization capabilities of graphical processing units to accelerate computation. The computational advantages of our algorithms are demonstrated with various simulated data examples in which we compare our stochastic search with a Markov chain Monte Carlo algorithm in moderate dimensional data examples. These experiments show that our stochastic search largely outperforms the Markov chain Monte Carlo algorithm in terms of computing-times and in terms of the quality of the posterior mode discovered. Finally, we analyze a gene expression dataset in which Markov chain Monte Carlo algorithms are too slow to be practically useful.

Health safety nets can break cycles of poverty and disease: a stochastic ecological model.

PubMed

Plucinski, Mateusz M; Ngonghala, Calistus N; Bonds, Matthew H

2011-12-07

The persistence of extreme poverty is increasingly attributed to dynamic interactions between biophysical processes and economics, though there remains a dearth of integrated theoretical frameworks that can inform policy. Here, we present a stochastic model of disease-driven poverty traps. Whereas deterministic models can result in poverty traps that can only be broken by substantial external changes to the initial conditions, in the stochastic model there is always some probability that a population will leave or enter a poverty trap. We show that a 'safety net', defined as an externally enforced minimum level of health or economic conditions, can guarantee ultimate escape from a poverty trap, even if the safety net is set within the basin of attraction of the poverty trap, and even if the safety net is only in the form of a public health measure. Whereas the deterministic model implies that small improvements in initial conditions near the poverty-trap equilibrium are futile, the stochastic model suggests that the impact of changes in the location of the safety net on the rate of development may be strongest near the poverty-trap equilibrium.

Stochastic evolutionary voluntary public goods game with punishment in a Quasi-birth-and-death process.

PubMed

Quan, Ji; Liu, Wei; Chu, Yuqing; Wang, Xianjia

2017-11-23

Traditional replication dynamic model and the corresponding concept of evolutionary stable strategy (ESS) only takes into account whether the system can return to the equilibrium after being subjected to a small disturbance. In the real world, due to continuous noise, the ESS of the system may not be stochastically stable. In this paper, a model of voluntary public goods game with punishment is studied in a stochastic situation. Unlike the existing model, we describe the evolutionary process of strategies in the population as a generalized quasi-birth-and-death process. And we investigate the stochastic stable equilibrium (SSE) instead. By numerical experiments, we get all possible SSEs of the system for any combination of parameters, and investigate the influence of parameters on the probabilities of the system to select different equilibriums. It is found that in the stochastic situation, the introduction of the punishment and non-participation strategies can change the evolutionary dynamics of the system and equilibrium of the game. There is a large range of parameters that the system selects the cooperative states as its SSE with a high probability. This result provides us an insight and control method for the evolution of cooperation in the public goods game in stochastic situations.