Formal language theory: refining the Chomsky hierarchy.

PubMed

Jäger, Gerhard; Rogers, James

2012-07-19

The first part of this article gives a brief overview of the four levels of the Chomsky hierarchy, with a special emphasis on context-free and regular languages. It then recapitulates the arguments why neither regular nor context-free grammar is sufficiently expressive to capture all phenomena in the natural language syntax. In the second part, two refinements of the Chomsky hierarchy are reviewed, which are both relevant to the extant research in cognitive science: the mildly context-sensitive languages (which are located between context-free and context-sensitive languages), and the sub-regular hierarchy (which distinguishes several levels of complexity within the class of regular languages).

Hydration thermodynamics of the SWy-1 montmorillonite saturated with alkali and alkaline-earth cations: A predictive model

NASA Astrophysics Data System (ADS)

Vieillard, Philippe; Blanc, Philippe; Fialips, Claire I.; Gailhanou, Hélène; Gaboreau, Stéphane

2011-10-01

The aim of the present work was to study the thermodynamic equilibria between water and a homo-ionic montmorillonite SWy-1 saturated by different cations. The choice of this smectite is justified by the large set of experimental data available from the literature for eight different interlayer cations: Na +, K +, Rb +, Cs +, Mg 2+, Ca 2+, Sr 2+, and Ba 2+. In particular, studies by Cases et al. (1992, 1997) and Bérend et al. (1995) are providing heat of adsorption data, pairs of desorption-adsorption isotherms, and information about the partition of adsorption-desorption water molecules between external surfaces and internal spaces. By calculating the effective amount of hydration water as the difference between the so-called gravimetric water and the surface covering water, a thermodynamic model was then developed, based on the concept of Ransom and Helgeson (1994) considering an asymmetric subregular binary solid solution between a fully hydrated and a anhydrous smectite. A set of six thermodynamic parameters ( ΔH∘hyd,S∘hyd and four Margules parameters) was extracted by a least square method from measurements of enthalpies of adsorption and paired adsorption-desorption isotherms for each interlayer cation. These six initial parameters were then used to determine a complete set of standard thermodynamic hydration parameters ( ΔH∘hyd,ΔG∘hyd,ΔS∘hyd, heat capacity, molar volume, and number of interlayer H 2O) and quantify, for each cation, the number of moles of hydration water molecules as a function of relative humidity and temperature. The validation of the standard state thermodynamic properties of hydration for each end member was carried out using three approaches: (1) a comparison with experimental isotherms obtained on hetero-ionic and homo-ionic SWy-1 smectite at different temperatures; (2) a comparison with the experimental integral enthalpy and entropy of hydration of the SWy-1 smectite; and (3) a comparison with experimental isotherms acquired on various smectites (Upton, MX80, Arizona) with different layer charges. Eventually, the present work demonstrates that, from a limited number of measurements, it is possible to provide the hydration thermodynamic parameters for hydrated smectites with different compositions and under different conditions of temperature and relative humidity, using the newly developed predictive model.

The behaviour of platelets in natural diamonds and the development of a new mantle thermometer

NASA Astrophysics Data System (ADS)

Speich, L.; Kohn, S. C.; Bulanova, G. P.; Smith, C. B.

2018-05-01

Platelets are one of the most common defects occurring in natural diamonds but their behaviour has not previously been well understood. Recent technical advances, and a much improved understanding of the correct interpretation of the main infrared (IR) feature associated with platelets (Speich et al. 2017), facilitated a systematic study of platelets in 40 natural diamonds. Three different types of platelet behaviour were identified here. Regular diamonds show linear correlations between both B-centre concentrations and platelet density and also between platelet size and platelet density. Irregular diamonds display reduced platelet density due to platelet breakdown, anomalously large or small platelets and a larger platelet size distribution. These features are indicative of high mantle storage temperatures. Finally, a previously unreported category of subregular diamonds is defined. These diamonds experienced low mantle residence temperatures and show smaller than expected platelets. Combining the systematic variation in platelet density with temperatures of mantle storage, determined by nitrogen aggregation, we can demonstrate that platelet degradation proceeds at a predictable rate. Thus, in platelet-bearing diamonds where N aggregation is complete, an estimate of annealing temperature can now be made for the first time.

Termochemical Models For Slags and Silicate Melts, Review and Perspectives

NASA Astrophysics Data System (ADS)

Ottonello, G.

Thermochemical models devoted to the comprehension of reactive and mixing properties of silicate melts and slags may be roughly grouped into four main classes: 1) fictive chemical; 2) quasi chemical; 3) fictive structural; 4) polymeric. In the first class we may group the fictive regular mixture approach of Ghiorso and Carmichael [1,2]and its extensions [3-5]and the subregular model of Berman and Brown [6]. To the second class belong the modified quasi chemical approach of Pelton and coworkers [7,8] , and the Kapoor - Froberg cellular model and its extensions [9-11]. The third class has much to share with the second one (and indeed the cellular model could be ascribed to this class as well). To this class belong the "central surround model" of Sastri and Lahiri [12] , the associated solution models of Bjorkman [13], Hastie and coworkers [14]and Goel and coworkers [15], the two sublattice model of Hillert and coworkers [16]and the polynomial expansions of Hoch and Arpshofen [17] . The fourth class encompasses the models of Masson[18-20] , Toop-Samis [21,22]and its extensions [23-25] . The phylosophy beyond each one of the four classes is basically different. Benefits and drawbacks are present in any of them, and applications are often limited to simple systems (or to sufficiently complex systems, in the case of arbitrary deconvolutions of type 1) and to limited P-T ranges. The crucial aspects of the various models will be outlined to some extent. It will be shown that, often, model conflictuality is only appartent and that, in some cases, model failure is unperceived by acritical utilizers. New perspectives in the future research devoted to the comprehension of melt reactivity in compositionally complex systems, with special enphasis on the solubility of gaseous components and unmixing, will be finally discussed. References: [1] Ghiorso M.S. and Carmichael I.S.E. (1980) Contrib. Mineral. Petrol., 71, 323-342. [2] Ghiorso M.S., Carmichael I.S.E., Rivers M.L. and Sack R.O. (1983) Contrib. Mineral. Petrol., 84, 107-145. [3] Papale P. (1997) Contrib. Mineral. Petrol., 126, 237-251. [4] Papale P. (1999) Amer. Mineral., 84, 477-492. [5] Nuccio P.M. and Paonita A. (2999) Earth Planet. Sci. Letters., 183, 499-512. [6] Berman R.G. and Brown T.H. (1984) Geochim. Cosmochim. Acta, 48, 661-678. [7] Lin P.L. and Pelton A.D. (1979) Metall. Trans. B., 10B, 667-675. [8] Pelton A.D. and Blander M. (1986) Metall. Trans. B., 17B, 805-15. [9] Kapoor M.L., Mehrotre G.M. and Frohberg M.G. (1975) Proc. Aust. Inst. Mining Metall., 254, 11. [10] Kapoor M.L., Frohberg G.M. (1971) Proc. Symp. "Chemical Metallurgy of Iron and Steel" Sheffield. [11] Taylor J.R. and Dinsdale A.T. (1990] CALPHAD, 14, 71-88. [12] Sastri P. and Lahiri A.K. (1986) Metall. Trans. B., 17B, 105-110. [13] Bjorkman B. (1985) CALPHAD, 9, 271-282. [14] Hastie J.W., Horton W.S., Plante E.R. and Bonnell D.W. (1982) High Temp. High Press., 14, 669-679. [15] Goel R.P., Kellogg H.H. and Larrain J.M. (1980) Metall. Trans. B., 11B, 107-117. [16] Hillert M., Sundman B. and Wang X. (1990) Metall. Trans. B., 21B, 303-12. [17] Hoch M. and Arpshofen I. (1984) Zeits. fur Metallkde., 75, 23-29. [18] Masson C.R. (1965) Proc. Roy. Soc. London, A287, 201-221. [19] Masson C.R. (1968) J. Amer. Ceram. Soc., 51, 134-143. [20] Masson C.R. (1972) Jour. Iron Steel Inst., 210, 89-96. [21] Toop G.W. and Samis C.S. (1962) Can. Met. Quart., 1, 129-52. [22] Toop G.W. and Samis C.S. (1962) Trans. AIME, 224, 878-87. [23] Ottonello G., Moretti R., Marini L. and Vetuschi Zuccolini M. (2000) Chem. Geol., 174, 157-179. [24] Ottonello G. (2001) J. Non-Cryst. Solids, 282, 72-85. [25] Moretti R. and Ottonello G. (2002) , Metall. Trans. (submitted).

A modified dynamical model of drying process of polymer blend solution coated on a flat substrate

NASA Astrophysics Data System (ADS)

Kagami, Hiroyuki

2008-05-01

We have proposed and modified a model of drying process of polymer solution coated on a flat substrate for flat polymer film fabrication. And for example numerical simulation of the model reproduces a typical thickness profile of the polymer film formed after drying. Then we have clarified dependence of distribution of polymer molecules on a flat substrate on a various parameters based on analysis of numerical simulations. Then we drove nonlinear equations of drying process from the dynamical model and the fruits were reported. The subject of above studies was limited to solution having one kind of solute though the model could essentially deal with solution having some kinds of solutes. But nowadays discussion of drying process of a solution having some kinds of solutes is needed because drying process of solution having some kinds of solutes appears in many industrial scenes. Polymer blend solution is one instance. And typical resist consists of a few kinds of polymers. Then we introduced a dynamical model of drying process of polymer blend solution coated on a flat substrate and results of numerical simulations of the dynamical model. But above model was the simplest one. In this study, we modify above dynamical model of drying process of polymer blend solution adding effects that some parameters change with time as functions of some variables to it. Then we consider essence of drying process of polymer blend solution through comparison between results of numerical simulations of the modified model and those of the former model.

SU-F-R-10: Selecting the Optimal Solution for Multi-Objective Radiomics Model

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

Zhou, Z; Folkert, M; Wang, J

2016-06-15

Purpose: To develop an evidential reasoning approach for selecting the optimal solution from a Pareto solution set obtained by a multi-objective radiomics model for predicting distant failure in lung SBRT. Methods: In the multi-objective radiomics model, both sensitivity and specificity are considered as the objective functions simultaneously. A Pareto solution set with many feasible solutions will be resulted from the multi-objective optimization. In this work, an optimal solution Selection methodology for Multi-Objective radiomics Learning model using the Evidential Reasoning approach (SMOLER) was proposed to select the optimal solution from the Pareto solution set. The proposed SMOLER method used the evidentialmore » reasoning approach to calculate the utility of each solution based on pre-set optimal solution selection rules. The solution with the highest utility was chosen as the optimal solution. In SMOLER, an optimal learning model coupled with clonal selection algorithm was used to optimize model parameters. In this study, PET, CT image features and clinical parameters were utilized for predicting distant failure in lung SBRT. Results: Total 126 solution sets were generated by adjusting predictive model parameters. Each Pareto set contains 100 feasible solutions. The solution selected by SMOLER within each Pareto set was compared to the manually selected optimal solution. Five-cross-validation was used to evaluate the optimal solution selection accuracy of SMOLER. The selection accuracies for five folds were 80.00%, 69.23%, 84.00%, 84.00%, 80.00%, respectively. Conclusion: An optimal solution selection methodology for multi-objective radiomics learning model using the evidential reasoning approach (SMOLER) was proposed. Experimental results show that the optimal solution can be found in approximately 80% cases.« less

Comparison of non-ideal solution theories for multi-solute solutions in cryobiology and tabulation of required coefficients.

PubMed

Zielinski, Michal W; McGann, Locksley E; Nychka, John A; Elliott, Janet A W

2014-10-01

Thermodynamic solution theories allow the prediction of chemical potentials in solutions of known composition. In cryobiology, such models are a critical component of many mathematical models that are used to simulate the biophysical processes occurring in cells and tissues during cryopreservation. A number of solution theories, both thermodynamically ideal and non-ideal, have been proposed for use with cryobiological solutions. In this work, we have evaluated two non-ideal solution theories for predicting water chemical potential (i.e. osmolality) in multi-solute solutions relevant to cryobiology: the Elliott et al. form of the multi-solute osmotic virial equation, and the Kleinhans and Mazur freezing point summation model. These two solution theories require fitting to only single-solute data, although they can make predictions in multi-solute solutions. The predictions of these non-ideal solution theories were compared to predictions made using ideal dilute assumptions and to available literature multi-solute experimental osmometric data. A single, consistent set of literature single-solute solution data was used to fit for the required solute-specific coefficients for each of the non-ideal models. Our results indicate that the two non-ideal solution theories have similar overall performance, and both give more accurate predictions than ideal models. These results can be used to select between the non-ideal models for a specific multi-solute solution, and the updated coefficients provided in this work can be used to make the desired predictions. Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.

Nonideal Solute Chemical Potential Equation and the Validity of the Grouped Solute Approach for Intracellular Solution Thermodynamics.

PubMed

Zielinski, Michal W; McGann, Locksley E; Nychka, John A; Elliott, Janet A W

2017-11-22

The prediction of nonideal chemical potentials in aqueous solutions is important in fields such as cryobiology, where models of water and solute transport-that is, osmotic transport-are used to help develop cryopreservation protocols and where solutions contain many varied solutes and are generally highly concentrated and thus thermodynamically nonideal. In this work, we further the development of a nonideal multisolute solution theory that has found application across a broad range of aqueous systems. This theory is based on the osmotic virial equation and does not depend on multisolute data. Specifically, we derive herein a novel solute chemical potential equation that is thermodynamically consistent with the existing model, and we establish the validity of a grouped solute model for the intracellular space. With this updated solution theory, it is now possible to model cellular osmotic behavior in nonideal solutions containing multiple permeating solutes, such as those commonly encountered by cells during cryopreservation. In addition, because we show here that for the osmotic virial equation the grouped solute approach is mathematically equivalent to treating each solute separately, multisolute solutions in other applications with fixed solute mass ratios can now be treated rigorously with such a model, even when all of the solutes cannot be enumerated.

Isotherm-Based Thermodynamic Model for Solute Activities of Asymmetric Electrolyte Aqueous Solutions.

PubMed

Nandy, Lucy; Dutcher, Cari S

2017-09-21

Adsorption isotherm-based statistical thermodynamic models can be used to determine solute concentration and solute and solvent activities in aqueous solutions. Recently, the number of adjustable parameters in the isotherm model of Dutcher et al. J. Phys. Chem. A/C 2011, 2012, 2013 were reduced for neutral solutes as well as symmetric 1:1 electrolytes by using a Coulombic model to describe the solute-solvent energy interactions (Ohm et al. J. Phys. Chem. A 2015, Nandy et al. J. Phys. Chem. A 2016). Here, the Coulombic treatment for symmetric electrolytes is extended to establish improved isotherm model equations for asymmetric 1-2 and 1-3 electrolyte systems. The Coulombic model developed here results in prediction of activities and other thermodynamic properties in multicomponent systems containing ions of arbitrary charge. The model is found to accurately calculate the osmotic coefficient over the entire solute concentration range with two model parameters, related to intermolecular solute-solute and solute-solvent spacing. The inorganic salts and acids treated here are generally considered to be fully dissociated. However, there are certain weak acids that do not dissociate completely, such as the bisulfate ion. In this work, partial dissociation of the bisulfate ion from sulfuric acid is treated as a mixture, with an additional model parameter that accounts for the dissociation ratio of the dissociated ions to nondissociated ions.

Modeling flow and solute transport in irrigation furrows

USDA-ARS?s Scientific Manuscript database

This paper presents an internally coupled flow and solute transport model for free-draining irrigation furrows. Furrow hydraulics is simulated with a numerical zero-inertia model and solute transport is computed with a model based on a numerical solution of the cross-section averaged advection-dispe...

Background-Error Correlation Model Based on the Implicit Solution of a Diffusion Equation

DTIC Science & Technology

2010-01-01

1 Background- Error Correlation Model Based on the Implicit Solution of a Diffusion Equation Matthew J. Carrier* and Hans Ngodock...4. TITLE AND SUBTITLE Background- Error Correlation Model Based on the Implicit Solution of a Diffusion Equation 5a. CONTRACT NUMBER 5b. GRANT...2001), which sought to model error correlations based on the explicit solution of a generalized diffusion equation. The implicit solution is

A two steps solution approach to solving large nonlinear models: application to a problem of conjunctive use.

PubMed

Vieira, J; Cunha, M C

2011-01-01

This article describes a solution method of solving large nonlinear problems in two steps. The two steps solution approach takes advantage of handling smaller and simpler models and having better starting points to improve solution efficiency. The set of nonlinear constraints (named as complicating constraints) which makes the solution of the model rather complex and time consuming is eliminated from step one. The complicating constraints are added only in the second step so that a solution of the complete model is then found. The solution method is applied to a large-scale problem of conjunctive use of surface water and groundwater resources. The results obtained are compared with solutions determined with the direct solve of the complete model in one single step. In all examples the two steps solution approach allowed a significant reduction of the computation time. This potential gain of efficiency of the two steps solution approach can be extremely important for work in progress and it can be particularly useful for cases where the computation time would be a critical factor for having an optimized solution in due time.

A biomechanical triphasic approach to the transport of nondilute solutions in articular cartilage.

PubMed

Abazari, Alireza; Elliott, Janet A W; Law, Garson K; McGann, Locksley E; Jomha, Nadr M

2009-12-16

Biomechanical models for biological tissues such as articular cartilage generally contain an ideal, dilute solution assumption. In this article, a biomechanical triphasic model of cartilage is described that includes nondilute treatment of concentrated solutions such as those applied in vitrification of biological tissues. The chemical potential equations of the triphasic model are modified and the transport equations are adjusted for the volume fraction and frictional coefficients of the solutes that are not negligible in such solutions. Four transport parameters, i.e., water permeability, solute permeability, diffusion coefficient of solute in solvent within the cartilage, and the cartilage stiffness modulus, are defined as four degrees of freedom for the model. Water and solute transport in cartilage were simulated using the model and predictions of average concentration increase and cartilage weight were fit to experimental data to obtain the values of the four transport parameters. As far as we know, this is the first study to formulate the solvent and solute transport equations of nondilute solutions in the cartilage matrix. It is shown that the values obtained for the transport parameters are within the ranges reported in the available literature, which confirms the proposed model approach.

A Biomechanical Triphasic Approach to the Transport of Nondilute Solutions in Articular Cartilage

PubMed Central

Abazari, Alireza; Elliott, Janet A.W.; Law, Garson K.; McGann, Locksley E.; Jomha, Nadr M.

2009-01-01

Abstract Biomechanical models for biological tissues such as articular cartilage generally contain an ideal, dilute solution assumption. In this article, a biomechanical triphasic model of cartilage is described that includes nondilute treatment of concentrated solutions such as those applied in vitrification of biological tissues. The chemical potential equations of the triphasic model are modified and the transport equations are adjusted for the volume fraction and frictional coefficients of the solutes that are not negligible in such solutions. Four transport parameters, i.e., water permeability, solute permeability, diffusion coefficient of solute in solvent within the cartilage, and the cartilage stiffness modulus, are defined as four degrees of freedom for the model. Water and solute transport in cartilage were simulated using the model and predictions of average concentration increase and cartilage weight were fit to experimental data to obtain the values of the four transport parameters. As far as we know, this is the first study to formulate the solvent and solute transport equations of nondilute solutions in the cartilage matrix. It is shown that the values obtained for the transport parameters are within the ranges reported in the available literature, which confirms the proposed model approach. PMID:20006942

Does a peer model's task proficiency influence children's solution choice and innovation?

PubMed

Wood, Lara A; Kendal, Rachel L; Flynn, Emma G

2015-11-01

The current study investigated whether 4- to 6-year-old children's task solution choice was influenced by the past proficiency of familiar peer models and the children's personal prior task experience. Peer past proficiency was established through behavioral assessments of interactions with novel tasks alongside peer and teacher predictions of each child's proficiency. Based on these assessments, one peer model with high past proficiency and one age-, sex-, dominance-, and popularity-matched peer model with lower past proficiency were trained to remove a capsule using alternative solutions from a three-solution artificial fruit task. Video demonstrations of the models were shown to children after they had either a personal successful interaction or no interaction with the task. In general, there was not a strong bias toward the high past-proficiency model, perhaps due to a motivation to acquire multiple methods and the salience of other transmission biases. However, there was some evidence of a model-based past-proficiency bias; when the high past-proficiency peer matched the participants' original solution, there was increased use of that solution, whereas if the high past-proficiency peer demonstrated an alternative solution, there was increased use of the alternative social solution and novel solutions. Thus, model proficiency influenced innovation. Copyright © 2015 Elsevier Inc. All rights reserved.

Analytically-derived sensitivities in one-dimensional models of solute transport in porous media

USGS Publications Warehouse

Knopman, D.S.

1987-01-01

Analytically-derived sensitivities are presented for parameters in one-dimensional models of solute transport in porous media. Sensitivities were derived by direct differentiation of closed form solutions for each of the odel, and by a time integral method for two of the models. Models are based on the advection-dispersion equation and include adsorption and first-order chemical decay. Boundary conditions considered are: a constant step input of solute, constant flux input of solute, and exponentially decaying input of solute at the upstream boundary. A zero flux is assumed at the downstream boundary. Initial conditions include a constant and spatially varying distribution of solute. One model simulates the mixing of solute in an observation well from individual layers in a multilayer aquifer system. Computer programs produce output files compatible with graphics software in which sensitivities are plotted as a function of either time or space. (USGS)

Analytical solutions for benchmarking cold regions subsurface water flow and energy transport models: one-dimensional soil thaw with conduction and advection

USGS Publications Warehouse

Kurylyk, Barret L.; McKenzie, Jeffrey M; MacQuarrie, Kerry T. B.; Voss, Clifford I.

2014-01-01

Numerous cold regions water flow and energy transport models have emerged in recent years. Dissimilarities often exist in their mathematical formulations and/or numerical solution techniques, but few analytical solutions exist for benchmarking flow and energy transport models that include pore water phase change. This paper presents a detailed derivation of the Lunardini solution, an approximate analytical solution for predicting soil thawing subject to conduction, advection, and phase change. Fifteen thawing scenarios are examined by considering differences in porosity, surface temperature, Darcy velocity, and initial temperature. The accuracy of the Lunardini solution is shown to be proportional to the Stefan number. The analytical solution results obtained for soil thawing scenarios with water flow and advection are compared to those obtained from the finite element model SUTRA. Three problems, two involving the Lunardini solution and one involving the classic Neumann solution, are recommended as standard benchmarks for future model development and testing.

Closed-form solutions of performability. [modeling of a degradable buffer/multiprocessor system

NASA Technical Reports Server (NTRS)

Meyer, J. F.

1981-01-01

Methods which yield closed form performability solutions for continuous valued variables are developed. The models are similar to those employed in performance modeling (i.e., Markovian queueing models) but are extended so as to account for variations in structure due to faults. In particular, the modeling of a degradable buffer/multiprocessor system is considered whose performance Y is the (normalized) average throughput rate realized during a bounded interval of time. To avoid known difficulties associated with exact transient solutions, an approximate decomposition of the model is employed permitting certain submodels to be solved in equilibrium. These solutions are then incorporated in a model with fewer transient states and by solving the latter, a closed form solution of the system's performability is obtained. In conclusion, some applications of this solution are discussed and illustrated, including an example of design optimization.

Sedimentary Geothermal Feasibility Study: October 2016

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

Augustine, Chad; Zerpa, Luis

The objective of this project is to analyze the feasibility of commercial geothermal projects using numerical reservoir simulation, considering a sedimentary reservoir with low permeability that requires productivity enhancement. A commercial thermal reservoir simulator (STARS, from Computer Modeling Group, CMG) is used in this work for numerical modeling. In the first stage of this project (FY14), a hypothetical numerical reservoir model was developed, and validated against an analytical solution. The following model parameters were considered to obtain an acceptable match between the numerical and analytical solutions: grid block size, time step and reservoir areal dimensions; the latter related to boundarymore » effects on the numerical solution. Systematic model runs showed that insufficient grid sizing generates numerical dispersion that causes the numerical model to underestimate the thermal breakthrough time compared to the analytic model. As grid sizing is decreased, the model results converge on a solution. Likewise, insufficient reservoir model area introduces boundary effects in the numerical solution that cause the model results to differ from the analytical solution.« less

Multi-cut solutions in Chern-Simons matrix models

NASA Astrophysics Data System (ADS)

Morita, Takeshi; Sugiyama, Kento

2018-04-01

We elaborate the Chern-Simons (CS) matrix models at large N. The saddle point equations of these matrix models have a curious structure which cannot be seen in the ordinary one matrix models. Thanks to this structure, an infinite number of multi-cut solutions exist in the CS matrix models. Particularly we exactly derive the two-cut solutions at finite 't Hooft coupling in the pure CS matrix model. In the ABJM matrix model, we argue that some of multi-cut solutions might be interpreted as a condensation of the D2-brane instantons.

Single-solute and bisolute sorption of phenol and trichloroethylene from aqueous solution onto modified montmorillonite and application of sorption models.

PubMed

Wu, C D; Wang, L; Hu, C X; He, M H

2013-01-01

The single-solute and bisolute sorption behaviour of phenol and trichloroethylene, two organic compounds with different structures, onto cetyltrimethylammonium bromide (CTAB)-montmorillonite was studied. The monolayer Langmuir model (MLM) and empirical Freundlich model (EFM) were applied to the single-solute sorption of phenol or trichloroethylene from water onto monolayer or multilayer CTAB-montmorillonite. The parameters contained in the MLM and EFM were determined for each solute by fitting to the single-solute isotherm data, and subsequently utilized in binary sorption. The extended Langmuir model (ELM) coupled with the single-solute MLM and the ideal adsorbed solution theory (IAST) coupled with the single-solute EFM were used to predict the binary sorption of phenol and trichloroethylene onto CTAB-montmorillonite. It was found that the EFM was better than the MLM at describing single-solute sorption from water onto CTAB-montmorillonite, and the IAST was better than the ELM at describing the binary sorption from water onto CTAB-montmorillonite.

Development of solute transport models in YMPYRÄ framework to simulate solute migration in military shooting and training areas

NASA Astrophysics Data System (ADS)

Warsta, L.; Karvonen, T.

2017-12-01

There are currently 25 shooting and training areas in Finland managed by The Finnish Defence Forces (FDF), where military activities can cause contamination of open waters and groundwater reservoirs. In the YMPYRÄ project, a computer software framework is being developed that combines existing open environmental data and proprietary information collected by FDF with computational models to investigate current and prevent future environmental problems. A data centric philosophy is followed in the development of the system, i.e. the models are updated and extended to handle available data from different areas. The results generated by the models are summarized as easily understandable flow and risk maps that can be opened in GIS programs and used in environmental assessments by experts. Substances investigated with the system include explosives and metals such as lead, and both surface and groundwater dominated areas can be simulated. The YMPYRÄ framework is composed of a three dimensional soil and groundwater flow model, several solute transport models and an uncertainty assessment system. Solute transport models in the framework include particle based, stream tube and finite volume based approaches. The models can be used to simulate solute dissolution from source area, transport in the unsaturated layers to groundwater and finally migration in groundwater to water extraction wells and springs. The models can be used to simulate advection, dispersion, equilibrium adsorption on soil particles, solubility and dissolution from solute phase and dendritic solute decay chains. Correct numerical solutions were confirmed by comparing results to analytical 1D and 2D solutions and by comparing the numerical solutions to each other. The particle based and stream tube type solute transport models were useful as they could complement the traditional finite volume based approach which in certain circumstances produced numerical dispersion due to piecewise solution of the governing equations in computational grids and included computationally intensive and in some cases unstable iterative solutions. The YMPYRÄ framework is being developed by WaterHope, Gain Oy, and SITO Oy consulting companies and funded by FDF.

Dynamics from a mathematical model of a two-state gas laser

NASA Astrophysics Data System (ADS)

Kleanthous, Antigoni; Hua, Tianshu; Manai, Alexandre; Yawar, Kamran; Van Gorder, Robert A.

2018-05-01

Motivated by recent work in the area, we consider the behavior of solutions to a nonlinear PDE model of a two-state gas laser. We first review the derivation of the two-state gas laser model, before deriving a non-dimensional model given in terms of coupled nonlinear partial differential equations. We then classify the steady states of this system, in order to determine the possible long-time asymptotic solutions to this model, as well as corresponding stability results, showing that the only uniform steady state (the zero motion state) is unstable, while a linear profile in space is stable. We then provide numerical simulations for the full unsteady model. We show for a wide variety of initial conditions that the solutions tend toward the stable linear steady state profiles. We also consider traveling wave solutions, and determine the unique wave speed (in terms of the other model parameters) which allows wave-like solutions to exist. Despite some similarities between the model and the inviscid Burger's equation, the solutions we obtain are much more regular than the solutions to the inviscid Burger's equation, with no evidence of shock formation or loss of regularity.

Lattice model for water-solute mixtures.

PubMed

Furlan, A P; Almarza, N G; Barbosa, M C

2016-10-14

A lattice model for the study of mixtures of associating liquids is proposed. Solvent and solute are modeled by adapting the associating lattice gas (ALG) model. The nature of interaction of solute/solvent is controlled by tuning the energy interactions between the patches of ALG model. We have studied three set of parameters, resulting in, hydrophilic, inert, and hydrophobic interactions. Extensive Monte Carlo simulations were carried out, and the behavior of pure components and the excess properties of the mixtures have been studied. The pure components, water (solvent) and solute, have quite similar phase diagrams, presenting gas, low density liquid, and high density liquid phases. In the case of solute, the regions of coexistence are substantially reduced when compared with both the water and the standard ALG models. A numerical procedure has been developed in order to attain series of results at constant pressure from simulations of the lattice gas model in the grand canonical ensemble. The excess properties of the mixtures, volume and enthalpy as the function of the solute fraction, have been studied for different interaction parameters of the model. Our model is able to reproduce qualitatively well the excess volume and enthalpy for different aqueous solutions. For the hydrophilic case, we show that the model is able to reproduce the excess volume and enthalpy of mixtures of small alcohols and amines. The inert case reproduces the behavior of large alcohols such as propanol, butanol, and pentanol. For the last case (hydrophobic), the excess properties reproduce the behavior of ionic liquids in aqueous solution.

Inattentive Drivers: Making the Solution Method the Model

ERIC Educational Resources Information Center

McCartney, Mark

2003-01-01

A simple car following model based on the solution of coupled ordinary differential equations is considered. The model is solved using Euler's method and this method of solution is itself interpreted as a mathematical model for car following. Examples of possible classroom use are given. (Contains 6 figures.)

Cancer treatment model with the Caputo-Fabrizio fractional derivative

NASA Astrophysics Data System (ADS)

Ali Dokuyucu, Mustafa; Celik, Ercan; Bulut, Hasan; Mehmet Baskonus, Haci

2018-03-01

In this article, a model for cancer treatment is examined. The model is integrated into the Caputo-Fabrizio fractional derivative first, to examine the existence of the solution. Then, the uniqueness of the solution is investigated and we identified under which conditions the model provides a unique solution.

A Framework to Implement IoT Network Performance Modelling Techniques for Network Solution Selection †

PubMed Central

Delaney, Declan T.; O’Hare, Gregory M. P.

2016-01-01

No single network solution for Internet of Things (IoT) networks can provide the required level of Quality of Service (QoS) for all applications in all environments. This leads to an increasing number of solutions created to fit particular scenarios. Given the increasing number and complexity of solutions available, it becomes difficult for an application developer to choose the solution which is best suited for an application. This article introduces a framework which autonomously chooses the best solution for the application given the current deployed environment. The framework utilises a performance model to predict the expected performance of a particular solution in a given environment. The framework can then choose an apt solution for the application from a set of available solutions. This article presents the framework with a set of models built using data collected from simulation. The modelling technique can determine with up to 85% accuracy the solution which performs the best for a particular performance metric given a set of solutions. The article highlights the fractured and disjointed practice currently in place for examining and comparing communication solutions and aims to open a discussion on harmonising testing procedures so that different solutions can be directly compared and offers a framework to achieve this within IoT networks. PMID:27916929

A Framework to Implement IoT Network Performance Modelling Techniques for Network Solution Selection.

PubMed

Delaney, Declan T; O'Hare, Gregory M P

2016-12-01

No single network solution for Internet of Things (IoT) networks can provide the required level of Quality of Service (QoS) for all applications in all environments. This leads to an increasing number of solutions created to fit particular scenarios. Given the increasing number and complexity of solutions available, it becomes difficult for an application developer to choose the solution which is best suited for an application. This article introduces a framework which autonomously chooses the best solution for the application given the current deployed environment. The framework utilises a performance model to predict the expected performance of a particular solution in a given environment. The framework can then choose an apt solution for the application from a set of available solutions. This article presents the framework with a set of models built using data collected from simulation. The modelling technique can determine with up to 85% accuracy the solution which performs the best for a particular performance metric given a set of solutions. The article highlights the fractured and disjointed practice currently in place for examining and comparing communication solutions and aims to open a discussion on harmonising testing procedures so that different solutions can be directly compared and offers a framework to achieve this within IoT networks.

Variational Implicit Solvation with Solute Molecular Mechanics: From Diffuse-Interface to Sharp-Interface Models.

PubMed

Li, Bo; Zhao, Yanxiang

2013-01-01

Central in a variational implicit-solvent description of biomolecular solvation is an effective free-energy functional of the solute atomic positions and the solute-solvent interface (i.e., the dielectric boundary). The free-energy functional couples together the solute molecular mechanical interaction energy, the solute-solvent interfacial energy, the solute-solvent van der Waals interaction energy, and the electrostatic energy. In recent years, the sharp-interface version of the variational implicit-solvent model has been developed and used for numerical computations of molecular solvation. In this work, we propose a diffuse-interface version of the variational implicit-solvent model with solute molecular mechanics. We also analyze both the sharp-interface and diffuse-interface models. We prove the existence of free-energy minimizers and obtain their bounds. We also prove the convergence of the diffuse-interface model to the sharp-interface model in the sense of Γ-convergence. We further discuss properties of sharp-interface free-energy minimizers, the boundary conditions and the coupling of the Poisson-Boltzmann equation in the diffuse-interface model, and the convergence of forces from diffuse-interface to sharp-interface descriptions. Our analysis relies on the previous works on the problem of minimizing surface areas and on our observations on the coupling between solute molecular mechanical interactions with the continuum solvent. Our studies justify rigorously the self consistency of the proposed diffuse-interface variational models of implicit solvation.

Hydration and conformational equilibria of simple hydrophobic and amphiphilic solutes.

PubMed Central

Ashbaugh, H S; Kaler, E W; Paulaitis, M E

1998-01-01

We consider whether the continuum model of hydration optimized to reproduce vacuum-to-water transfer free energies simultaneously describes the hydration free energy contributions to conformational equilibria of the same solutes in water. To this end, transfer and conformational free energies of idealized hydrophobic and amphiphilic solutes in water are calculated from explicit water simulations and compared to continuum model predictions. As benchmark hydrophobic solutes, we examine the hydration of linear alkanes from methane through hexane. Amphiphilic solutes were created by adding a charge of +/-1e to a terminal methyl group of butane. We find that phenomenological continuum parameters fit to transfer free energies are significantly different from those fit to conformational free energies of our model solutes. This difference is attributed to continuum model parameters that depend on solute conformation in water, and leads to effective values for the free energy/surface area coefficient and Born radii that best describe conformational equilibrium. In light of these results, we believe that continuum models of hydration optimized to fit transfer free energies do not accurately capture the balance between hydrophobic and electrostatic contributions that determines the solute conformational state in aqueous solution. PMID:9675177

A dual-porosity model for simulating solute transport in oil shale

USGS Publications Warehouse

Glover, K.C.

1987-01-01

A model is described for simulating three-dimensional groundwater flow and solute transport in oil shale and associated geohydrologic units. The model treats oil shale as a dual-porosity medium by simulating flow and transport within fractures using the finite-element method. Diffusion of solute between fractures and the essentially static water of the shale matrix is simulated by including an analytical solution that acts as a source-sink term to the differential equation of solute transport. While knowledge of fracture orientation and spacing is needed to effectively use the model, it is not necessary to map the locations of individual fractures. The computer program listed in the report incorporates many of the features of previous dual-porosity models while retaining a practical approach to solving field problems. As a result the theory of solute transport is not extended in any appreciable way. The emphasis is on bringing together various aspects of solute transport theory in a manner that is particularly suited to the unusual groundwater flow and solute transport characteristics of oil shale systems. (Author 's abstract)

Self-consistent large- N analytical solutions of inhomogeneous condensates in quantum ℂP N - 1 model

NASA Astrophysics Data System (ADS)

Nitta, Muneto; Yoshii, Ryosuke

2017-12-01

We give, for the first time, self-consistent large- N analytical solutions of inhomogeneous condensates in the quantum ℂP N - 1 model in the large- N limit. We find a map from a set of gap equations of the ℂP N - 1 model to those of the Gross-Neveu (GN) model (or the gap equation and the Bogoliubov-de Gennes equation), which enables us to find the self-consistent solutions. We find that the Higgs field of the ℂP N - 1 model is given as a zero mode of solutions of the GN model, and consequently only topologically non-trivial solutions of the GN model yield nontrivial solutions of the ℂP N - 1 model. A stable single soliton is constructed from an anti-kink of the GN model and has a broken (Higgs) phase inside its core, in which ℂP N - 1 modes are localized, with a symmetric (confining) phase outside. We further find a stable periodic soliton lattice constructed from a real kink crystal in the GN model, while the Ablowitz-Kaup-Newell-Segur hierarchy yields multiple solitons at arbitrary separations.

Solution of the classical Yang-Baxter equation with an exotic symmetry, and integrability of a multi-species boson tunnelling model

NASA Astrophysics Data System (ADS)

Links, Jon

2017-03-01

Solutions of the classical Yang-Baxter equation provide a systematic method to construct integrable quantum systems in an algebraic manner. A Lie algebra can be associated with any solution of the classical Yang-Baxter equation, from which commuting transfer matrices may be constructed. This procedure is reviewed, specifically for solutions without skew-symmetry. A particular solution with an exotic symmetry is identified, which is not obtained as a limiting expansion of the usual Yang-Baxter equation. This solution facilitates the construction of commuting transfer matrices which will be used to establish the integrability of a multi-species boson tunnelling model. The model generalises the well-known two-site Bose-Hubbard model, to which it reduces in the one-species limit. Due to the lack of an apparent reference state, application of the algebraic Bethe Ansatz to solve the model is prohibitive. Instead, the Bethe Ansatz solution is obtained by the use of operator identities and tensor product decompositions.

Solute diffusion in liquid metals

NASA Technical Reports Server (NTRS)

Bhat, B. N.

1973-01-01

A gas model of diffusion in liquid metals is presented. In this model, ions of liquid metals are assumed to behave like the molecules in a dense gas. Diffusion coefficient of solute is discussed with reference to its mass, ionic size, and pair potential. The model is applied to the case of solute diffusion in liquid silver. An attempt was made to predict diffusion coefficients of solutes with reasonable accuracy.

Quantum corrections to quasi-periodic solution of Sine-Gordon model and periodic solution of phi4 model

NASA Astrophysics Data System (ADS)

Kwiatkowski, G.; Leble, S.

2014-03-01

Analytical form of quantum corrections to quasi-periodic solution of Sine-Gordon model and periodic solution of phi4 model is obtained through zeta function regularisation with account of all rest variables of a d-dimensional theory. Qualitative dependence of quantum corrections on parameters of the classical systems is also evaluated for a much broader class of potentials u(x) = b2f(bx) + C with b and C as arbitrary real constants.

A nonequilibrium model for reactive contaminant transport through fractured porous media: Model development and semianalytical solution

NASA Astrophysics Data System (ADS)

Joshi, Nitin; Ojha, C. S. P.; Sharma, P. K.

2012-10-01

In this study a conceptual model that accounts for the effects of nonequilibrium contaminant transport in a fractured porous media is developed. Present model accounts for both physical and sorption nonequilibrium. Analytical solution was developed using the Laplace transform technique, which was then numerically inverted to obtain solute concentration in the fracture matrix system. The semianalytical solution developed here can incorporate both semi-infinite and finite fracture matrix extent. In addition, the model can account for flexible boundary conditions and nonzero initial condition in the fracture matrix system. The present semianalytical solution was validated against the existing analytical solutions for the fracture matrix system. In order to differentiate between various sorption/transport mechanism different cases of sorption and mass transfer were analyzed by comparing the breakthrough curves and temporal moments. It was found that significant differences in the signature of sorption and mass transfer exists. Applicability of the developed model was evaluated by simulating the published experimental data of Calcium and Strontium transport in a single fracture. The present model simulated the experimental data reasonably well in comparison to the model based on equilibrium sorption assumption in fracture matrix system, and multi rate mass transfer model.

ELASTIC NET FOR COX'S PROPORTIONAL HAZARDS MODEL WITH A SOLUTION PATH ALGORITHM.

PubMed

Wu, Yichao

2012-01-01

For least squares regression, Efron et al. (2004) proposed an efficient solution path algorithm, the least angle regression (LAR). They showed that a slight modification of the LAR leads to the whole LASSO solution path. Both the LAR and LASSO solution paths are piecewise linear. Recently Wu (2011) extended the LAR to generalized linear models and the quasi-likelihood method. In this work we extend the LAR further to handle Cox's proportional hazards model. The goal is to develop a solution path algorithm for the elastic net penalty (Zou and Hastie (2005)) in Cox's proportional hazards model. This goal is achieved in two steps. First we extend the LAR to optimizing the log partial likelihood plus a fixed small ridge term. Then we define a path modification, which leads to the solution path of the elastic net regularized log partial likelihood. Our solution path is exact and piecewise determined by ordinary differential equation systems.

Survey of three-dimensional numerical estuarine models

USGS Publications Warehouse

Cheng, Ralph T.; Smith, Peter E.

1989-01-01

This paper surveys the existing 3-D estuarine hydrodynamic and solute transport models by a review of the commonly used assumptions and approximations, and by an examination of the methods of solution. The model formulations, methods of solution, and known applications are surveyed and summarized in tables. In conclusion, the authors present their modeling philosophy and suggest future research needs.

Collaborative Research: Robust Climate Projections and Stochastic Stability of Dynamical Systems

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

Ilya Zaliapin

This project focused on conceptual exploration of El Nino/Southern Oscillation (ENSO) variability and sensitivity using a Delay Differential Equation developed in the project. We have (i) established the existence and continuous dependence of solutions of the model (ii) explored multiple models solutions, and the distribution of solutions extrema, and (iii) established and explored the phase locking phenomenon and the existence of multiple solutions for the same values of model parameters. In addition, we have applied to our model the concept of pullback attractor, which greatly facilitated predictive understanding of the nonlinear model's behavior.

Redox condition in molten salts and solute behavior: A first-principles molecular dynamics study

NASA Astrophysics Data System (ADS)

Nam, Hyo On; Morgan, Dane

2015-10-01

Molten salts technology is of significant interest for nuclear, solar, and other energy systems. In this work, first-principles molecular dynamics (FPMD) was used to model the solute behavior in eutectic LiCl-KCl and FLiBe (Li2BeF4) melts at 773 K and 973 K, respectively. The thermo-kinetic properties for solute systems such as the redox potential, solute diffusion coefficients and structural information surrounding the solute were predicted from FPMD modeling and the calculated properties are generally in agreement with the experiments. In particular, we formulate an approach to model redox energetics vs. chlorine (or fluorine) potential from first-principles approaches. This study develops approaches for, and demonstrates the capabilities of, FPMD to model solute properties in molten salts.

Modeling mass transfer and reaction of dilute solutes in a ternary phase system by the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Fu, Yu-Hang; Bai, Lin; Luo, Kai-Hong; Jin, Yong; Cheng, Yi

2017-04-01

In this work, we propose a general approach for modeling mass transfer and reaction of dilute solute(s) in incompressible three-phase flows by introducing a collision operator in lattice Boltzmann (LB) method. An LB equation was used to simulate the solute dynamics among three different fluids, in which the newly expanded collision operator was used to depict the interface behavior of dilute solute(s). The multiscale analysis showed that the presented model can recover the macroscopic transport equations derived from the Maxwell-Stefan equation for dilute solutes in three-phase systems. Compared with the analytical equation of state of solute and dynamic behavior, these results are proven to constitute a generalized framework to simulate solute distributions in three-phase flows, including compound soluble in one phase, compound adsorbed on single-interface, compound in two phases, and solute soluble in three phases. Moreover, numerical simulations of benchmark cases, such as phase decomposition, multilayered planar interfaces, and liquid lens, were performed to test the stability and efficiency of the model. Finally, the multiphase mass transfer and reaction in Janus droplet transport in a straight microchannel were well reproduced.

Osmosis and thermodynamics explained by solute blocking.

PubMed

Nelson, Peter Hugo

2017-01-01

A solute-blocking model is presented that provides a kinetic explanation of osmosis and ideal solution thermodynamics. It validates a diffusive model of osmosis that is distinct from the traditional convective flow model of osmosis. Osmotic equilibrium occurs when the fraction of water molecules in solution matches the fraction of pure water molecules that have enough energy to overcome the pressure difference. Solute-blocking also provides a kinetic explanation for why Raoult's law and the other colligative properties depend on the mole fraction (but not the size) of the solute particles, resulting in a novel kinetic explanation for the entropy of mixing and chemical potential of ideal solutions. Some of its novel predictions have been confirmed; others can be tested experimentally or by simulation.

Osmosis and thermodynamics explained by solute blocking

PubMed Central

Nelson, Peter Hugo

2016-01-01

A solute-blocking model is presented that provides a kinetic explanation of osmosis and ideal solution thermodynamics. It validates a diffusive model of osmosis that is distinct from the traditional convective flow model of osmosis. Osmotic equilibrium occurs when the fraction of water molecules in solution matches the fraction of pure water molecules that have enough energy to overcome the pressure difference. Solute-blocking also provides a kinetic explanation for why Raoult’s law and the other colligative properties depend on the mole fraction (but not the size) of the solute particles, resulting in a novel kinetic explanation for the entropy of mixing and chemical potential of ideal solutions. Some of its novel predictions have been confirmed, others can be tested experimentally or by simulation. PMID:27225298

Introductory lecture: interpreting and predicting Hofmeister salt ion and solute effects on biopolymer and model processes using the solute partitioning model.

PubMed

Record, M Thomas; Guinn, Emily; Pegram, Laurel; Capp, Michael

2013-01-01

Understanding how Hofmeister salt ions and other solutes interact with proteins, nucleic acids, other biopolymers and water and thereby affect protein and nucleic acid processes as well as model processes (e.g. solubility of model compounds) in aqueous solution is a longstanding goal of biophysical research. Empirical Hofmeister salt and solute "m-values" (derivatives of the observed standard free energy change for a model or biopolymer process with respect to solute or salt concentration m3) are equal to differences in chemical potential derivatives: m-value = delta(dmu2/dm3) = delta mu23, which quantify the preferential interactions of the solute or salt with the surface of the biopolymer or model system (component 2) exposed or buried in the process. Using the solute partitioning model (SPM), we dissect mu23 values for interactions of a solute or Hofmeister salt with a set of model compounds displaying the key functional groups of biopolymers to obtain interaction potentials (called alpha-values) that quantify the interaction of the solute or salt per unit area of each functional group or type of surface. Interpreted using the SPM, these alpha-values provide quantitative information about both the hydration of functional groups and the competitive interaction of water and the solute or salt with functional groups. The analysis corroborates and quantifies previous proposals that the Hofmeister anion and cation series for biopolymer processes are determined by ion-specific, mostly unfavorable interactions with hydrocarbon surfaces; the balance between these unfavorable nonpolar interactions and often-favorable interactions of ions with polar functional groups determine the series null points. The placement of urea and glycine betaine (GB) at opposite ends of the corresponding series of nonelectrolytes results from the favorable interactions of urea, and unfavorable interactions of GB, with many (but not all) biopolymer functional groups. Interaction potentials and local-bulk partition coefficients quantifying the distribution of solutes (e.g. urea, glycine betaine) and Hofmeister salt ions in the vicinity of each functional group make good chemical sense when interpreted in terms of competitive noncovalent interactions. These interaction potentials allow solute and Hofmeister (noncoulombic) salt effects on protein and nucleic acid processes to be interpreted or predicted, and allow the use of solutes and salts as probes of

Modification of ginseng flavors by bitter compounds found in chocolate and coffee.

PubMed

Sook Chung, Hee; Lee, Soo-Yeun

2012-06-01

Ginseng is not widely accepted by U.S. consumers due to its unfamiliar flavors, despite its numerous health benefits. Previous studies have suggested that the bitter compounds in chocolate and coffee may mask the off-flavors of ginseng. The objectives of this study were to: (1) profile sensory characteristics of ginseng extract solution, caffeine solution, cyclo (L-Pro-L-Val) solution, theobromine solution, and 2 model solutions simulating chocolate bitterness; and (2) determine the changes in the sensory characteristics of ginseng extract solution by the addition of the bitter compounds found in chocolate and coffee. Thirteen solutions were prepared in concentrations similar to the levels of the bitter compounds found in coffee and chocolate products. Twelve panelists participated in a descriptive analysis panel which included time-intensity ratings. Ginseng extract was characterized as sweeter, starchier, and more green tea than the other sample solutions. Those characteristics of ginseng extract were effectively modified by the addition of caffeine, cyclo (L-Pro-L-Val), and 2 model solutions. A model solution simulating dark chocolate bitterness was the least influenced in intensities of bitterness by the addition of ginseng extract. Results from time-intensity ratings show that the addition of ginseng extract increased duration time in certain bitterness of the 2 model solutions. Bitter compounds found in dark chocolate could be proposed to effectively mask the unique flavors of ginseng. Future studies blending aroma compounds of chocolate and coffee into such model solutions may be conducted to investigate the influence on the perception of the unique flavors through the congruent flavors. © 2012 Institute of Food Technologists®

Demonstrations in Solute Transport Using Dyes: Part II. Modeling.

ERIC Educational Resources Information Center

Butters, Greg; Bandaranayake, Wije

1993-01-01

A solution of the convection-dispersion equation is used to describe the solute breakthrough curves generated in the demonstrations in the companion paper. Estimation of the best fit model parameters (solute velocity, dispersion, and retardation) is illustrated using the method of moments for an example data set. (Author/MDH)

A Feminist Critique of Solution-Focused Therapy.

ERIC Educational Resources Information Center

Dermer, Shannon B.; Hemesath, Crystal Wilhite; Russell, Candyce S.

1998-01-01

Applying the feminist critique to solution-focused therapy highlights the strengths and weaknesses of this model from a feminist perspective. Although solution-focused therapy and feminist approaches share an emphasis on competence and strengths, solution-focused theory tends to overlook gender and power differences. In general, the model falls…

A mixture theory model of fluid and solute transport in the microvasculature of normal and malignant tissues. I. Theory.

PubMed

Schuff, M M; Gore, J P; Nauman, E A

2013-05-01

In order to better understand the mechanisms governing transport of drugs, nanoparticle-based treatments, and therapeutic biomolecules, and the role of the various physiological parameters, a number of mathematical models have previously been proposed. The limitations of the existing transport models indicate the need for a comprehensive model that includes transport in the vessel lumen, the vessel wall, and the interstitial space and considers the effects of the solute concentration on fluid flow. In this study, a general model to describe the transient distribution of fluid and multiple solutes at the microvascular level was developed using mixture theory. The model captures the experimentally observed dependence of the hydraulic permeability coefficient of the capillary wall on the concentration of solutes present in the capillary wall and the surrounding tissue. Additionally, the model demonstrates that transport phenomena across the capillary wall and in the interstitium are related to the solute concentration as well as the hydrostatic pressure. The model is used in a companion paper to examine fluid and solute transport for the simplified case of an axisymmetric geometry with no solid deformation or interconversion of mass.

MODELING SMALL-SCALE SPILLS OF AQUEOUS SOLUTIONS IN THE INDOOR ENVIRONMENT

EPA Science Inventory

A mass transfer model is proposed to estimate the rates of chemical emissions from aqueous solutions spilled on hard surfaces inside buildings. The model is presented in two forms: a set of four ordinary differential equations and a simplified exact solution. The latter can be ...

Mathematical Analysis of the Solidification Behavior of Plain Steel Based on Solute- and Heat-Transfer Equations in the Liquid-Solid Zone

NASA Astrophysics Data System (ADS)

Fujimura, Toshio; Takeshita, Kunimasa; Suzuki, Ryosuke O.

2018-04-01

An analytical approximate solution to non-linear solute- and heat-transfer equations in the unsteady-state mushy zone of Fe-C plain steel has been obtained, assuming a linear relationship between the solid fraction and the temperature of the mushy zone. The heat transfer equations for both the solid and liquid zone along with the boundary conditions have been linked with the equations to solve the whole equations. The model predictions ( e.g., the solidification constants and the effective partition ratio) agree with the generally accepted values and with a separately performed numerical analysis. The solidus temperature predicted by the model is in the intermediate range of the reported formulas. The model and Neuman's solution are consistent in the low carbon range. A conventional numerical heat analysis ( i.e., an equivalent specific heat method using the solidus temperature predicted by the model) is consistent with the model predictions for Fe-C plain steels. The model presented herein simplifies the computations to solve the solute- and heat-transfer simultaneous equations while searching for a solidus temperature as a part of the solution. Thus, this model can reduce the complexity of analyses considering the heat- and solute-transfer phenomena in the mushy zone.

A closed-form solution for steady-state coupled phloem/xylem flow using the Lambert-W function.

PubMed

Hall, A J; Minchin, P E H

2013-12-01

A closed-form solution for steady-state coupled phloem/xylem flow is presented. This incorporates the basic Münch flow model of phloem transport, the cohesion model of xylem flow, and local variation in the xylem water potential and lateral water flow along the transport pathway. Use of the Lambert-W function allows this solution to be obtained under much more general and realistic conditions than has previously been possible. Variation in phloem resistance (i.e. viscosity) with solute concentration, and deviations from the Van't Hoff expression for osmotic potential are included. It is shown that the model predictions match those of the equilibrium solution of a numerical time-dependent model based upon the same mechanistic assumptions. The effect of xylem flow upon phloem flow can readily be calculated, which has not been possible in any previous analytical model. It is also shown how this new analytical solution can handle multiple sources and sinks within a complex architecture, and can describe competition between sinks. The model provides new insights into Münch flow by explicitly including interactions with xylem flow and water potential in the closed-form solution, and is expected to be useful as a component part of larger numerical models of entire plants. © 2013 John Wiley & Sons Ltd.

Stationary Solutions of A One-dimensional Thermodynamic Radiative Sea Ice Model

NASA Astrophysics Data System (ADS)

Taylor, P. D.; Feltham, D. L.

A one-dimensional thermodynamic model of sea ice is coupled to a two-stream radi- ation model and the stationary (time-independent) solutions analysed. The stationary model represents the state of the sea ice subjected to persistent or slowly varying forc- ing. Two physically realisable stationary solutions (real and positive ice thickness) occur for a large range of positive oceanic heat flux ( 20,Wm-2). The two station- ary solutions are due to the two-stream radiation model, which allows radiation to be reflected at the ice-ocean interface. Thick ice ( 1,m) only absorbs radiation near its surface, whereas thin ice ( 0.1,m) absorbs radiation across its entire depth. The two stationary solutions are caused by these two different radiative regimes. The results of this analysis have relevance to the interpretation and implementation of thermody- namic models of sea ice and the interpretation of thickness data.

Analytical and Numerical solutions of a nonlinear alcoholism model via variable-order fractional differential equations

NASA Astrophysics Data System (ADS)

Gómez-Aguilar, J. F.

2018-03-01

In this paper, we analyze an alcoholism model which involves the impact of Twitter via Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives with constant- and variable-order. Two fractional mathematical models are considered, with and without delay. Special solutions using an iterative scheme via Laplace and Sumudu transform were obtained. We studied the uniqueness and existence of the solutions employing the fixed point postulate. The generalized model with variable-order was solved numerically via the Adams method and the Adams-Bashforth-Moulton scheme. Stability and convergence of the numerical solutions were presented in details. Numerical examples of the approximate solutions are provided to show that the numerical methods are computationally efficient. Therefore, by including both the fractional derivatives and finite time delays in the alcoholism model studied, we believe that we have established a more complete and more realistic indicator of alcoholism model and affect the spread of the drinking.

On integrability of the Yang-Baxter {sigma}-model

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

Klimcik, Ctirad

2009-04-15

We prove that the recently introduced Yang-Baxter {sigma}-model can be considered as an integrable deformation of the principal chiral model. We find also an explicit one-to-one map transforming every solution of the principal chiral model into a solution of the deformed model. With the help of this map, the standard procedure of the dressing of the principal chiral solutions can be directly transferred into the deformed Yang-Baxter context.

The effect of solution nonideality on modeling transmembrane water transport and diffusion-limited intracellular ice formation during cryopreservation

NASA Astrophysics Data System (ADS)

Zhao, Gang; Takamatsu, Hiroshi; He, Xiaoming

2014-04-01

A new model was developed to predict transmembrane water transport and diffusion-limited ice formation in cells during freezing without the ideal-solution assumption that has been used in previous models. The model was applied to predict cell dehydration and intracellular ice formation (IIF) during cryopreservation of mouse oocytes and bovine carotid artery endothelial cells in aqueous sodium chloride (NaCl) solution with glycerol as the cryoprotectant or cryoprotective agent. A comparison of the predictions between the present model and the previously reported models indicated that the ideal-solution assumption results in under-prediction of the amount of intracellular ice at slow cooling rates (<50 K/min). In addition, the lower critical cooling rates for IIF that is lethal to cells predicted by the present model were much lower than those estimated with the ideal-solution assumption. This study represents the first investigation on how accounting for solution nonideality in modeling water transport across the cell membrane could affect the prediction of diffusion-limited ice formation in biological cells during freezing. Future studies are warranted to look at other assumptions alongside nonideality to further develop the model as a useful tool for optimizing the protocol of cell cryopreservation for practical applications.

The effect of solution nonideality on modeling transmembrane water transport and diffusion-limited intracellular ice formation during cryopreservation.

PubMed

Zhao, Gang; Takamatsu, Hiroshi; He, Xiaoming

2014-04-14

A new model was developed to predict transmembrane water transport and diffusion-limited ice formation in cells during freezing without the ideal-solution assumption that has been used in previous models. The model was applied to predict cell dehydration and intracellular ice formation (IIF) during cryopreservation of mouse oocytes and bovine carotid artery endothelial cells in aqueous sodium chloride (NaCl) solution with glycerol as the cryoprotectant or cryoprotective agent. A comparison of the predictions between the present model and the previously reported models indicated that the ideal-solution assumption results in under-prediction of the amount of intracellular ice at slow cooling rates (<50 K/min). In addition, the lower critical cooling rates for IIF that is lethal to cells predicted by the present model were much lower than those estimated with the ideal-solution assumption. This study represents the first investigation on how accounting for solution nonideality in modeling water transport across the cell membrane could affect the prediction of diffusion-limited ice formation in biological cells during freezing. Future studies are warranted to look at other assumptions alongside nonideality to further develop the model as a useful tool for optimizing the protocol of cell cryopreservation for practical applications.

Predicting adsorptive removal of chlorophenol from aqueous solution using artificial intelligence based modeling approaches.

PubMed

Singh, Kunwar P; Gupta, Shikha; Ojha, Priyanka; Rai, Premanjali

2013-04-01

The research aims to develop artificial intelligence (AI)-based model to predict the adsorptive removal of 2-chlorophenol (CP) in aqueous solution by coconut shell carbon (CSC) using four operational variables (pH of solution, adsorbate concentration, temperature, and contact time), and to investigate their effects on the adsorption process. Accordingly, based on a factorial design, 640 batch experiments were conducted. Nonlinearities in experimental data were checked using Brock-Dechert-Scheimkman (BDS) statistics. Five nonlinear models were constructed to predict the adsorptive removal of CP in aqueous solution by CSC using four variables as input. Performances of the constructed models were evaluated and compared using statistical criteria. BDS statistics revealed strong nonlinearity in experimental data. Performance of all the models constructed here was satisfactory. Radial basis function network (RBFN) and multilayer perceptron network (MLPN) models performed better than generalized regression neural network, support vector machines, and gene expression programming models. Sensitivity analysis revealed that the contact time had highest effect on adsorption followed by the solution pH, temperature, and CP concentration. The study concluded that all the models constructed here were capable of capturing the nonlinearity in data. A better generalization and predictive performance of RBFN and MLPN models suggested that these can be used to predict the adsorption of CP in aqueous solution using CSC.

Constant curvature surfaces of the supersymmetric ℂP{sup N−1} sigma model

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

Delisle, L., E-mail: delisle@dms.umontreal.ca; Hussin, V., E-mail: hussin@dms.umontreal.ca; Centre de Recherches Mathématiques, Université de Montréal, C.P. 6128, Succ. Centre-ville, Montréal, Québec H3C 3J7

2015-02-15

Constant curvature surfaces are constructed from the finite action solutions of the supersymmetric ℂP{sup N−1} sigma model. It is shown that there is a unique holomorphic solution which leads to constant curvature surfaces: the generalized Veronese curve. We give a general criterion to construct non-holomorphic solutions of the model. We extend our analysis to general supersymmetric Grassmannian models.

Symmetry breaking in (gravitating) scalar field models describing interacting boson stars and Q-balls

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

Brihaye, Yves; Caebergs, Thierry; Hartmann, Betti

2009-09-15

We investigate the properties of interacting Q-balls and boson stars that sit on top of each other in great detail. The model that describes these solutions is essentially a (gravitating) two-scalar field model where both scalar fields are complex. We construct interacting Q-balls or boson stars with arbitrarily small charges but finite mass. We observe that in the interacting case--where the interaction can be either due to the potential or due to gravity--two types of solutions exist for equal frequencies: one for which the two-scalar fields are equal, but also one for which the two-scalar fields differ. This constitutes amore » symmetry breaking in the model. While for Q-balls asymmetric solutions have always corresponding symmetric solutions and are thus likely unstable to decay to symmetric solutions with lower energy, there exists a parameter regime for interacting boson stars, where only asymmetric solutions exist. We present the domain of existence for two interacting nonrotating solutions as well as for solutions describing the interaction between rotating and nonrotating Q-balls and boson stars, respectively.« less

General solutions of the supersymmetric ℂP{sup 2} sigma model and its generalisation to ℂP{sup N−1}

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

Delisle, L., E-mail: laurent.delisle@imj-prg.fr; Hussin, V., E-mail: hussin@dms.umontreal.ca; Centre de Recherches Mathématiques, Université de Montréal, C.P. 6128, Succ. Centre-ville, Montréal, Québec H3C 3J7

A new approach for the construction of finite action solutions of the supersymmetric ℂP{sup N−1} sigma model is presented. We show that this approach produces more non-holomorphic solutions than those obtained in previous approaches. We study the ℂP{sup 2} model in detail and present its solutions in an explicit form. We also show how to generalise this construction to N > 3.

Geometric model of pseudo-distance measurement in satellite location systems

NASA Astrophysics Data System (ADS)

Panchuk, K. L.; Lyashkov, A. A.; Lyubchinov, E. V.

2018-04-01

The existing mathematical model of pseudo-distance measurement in satellite location systems does not provide a precise solution of the problem, but rather an approximate one. The existence of such inaccuracy, as well as bias in measurement of distance from satellite to receiver, results in inaccuracy level of several meters. Thereupon, relevance of refinement of the current mathematical model becomes obvious. The solution of the system of quadratic equations used in the current mathematical model is based on linearization. The objective of the paper is refinement of current mathematical model and derivation of analytical solution of the system of equations on its basis. In order to attain the objective, geometric analysis is performed; geometric interpretation of the equations is given. As a result, an equivalent system of equations, which allows analytical solution, is derived. An example of analytical solution implementation is presented. Application of analytical solution algorithm to the problem of pseudo-distance measurement in satellite location systems allows to improve the accuracy such measurements.

ELASTIC NET FOR COX’S PROPORTIONAL HAZARDS MODEL WITH A SOLUTION PATH ALGORITHM

PubMed Central

Wu, Yichao

2012-01-01

For least squares regression, Efron et al. (2004) proposed an efficient solution path algorithm, the least angle regression (LAR). They showed that a slight modification of the LAR leads to the whole LASSO solution path. Both the LAR and LASSO solution paths are piecewise linear. Recently Wu (2011) extended the LAR to generalized linear models and the quasi-likelihood method. In this work we extend the LAR further to handle Cox’s proportional hazards model. The goal is to develop a solution path algorithm for the elastic net penalty (Zou and Hastie (2005)) in Cox’s proportional hazards model. This goal is achieved in two steps. First we extend the LAR to optimizing the log partial likelihood plus a fixed small ridge term. Then we define a path modification, which leads to the solution path of the elastic net regularized log partial likelihood. Our solution path is exact and piecewise determined by ordinary differential equation systems. PMID:23226932

Note on the coupled oscillator model solutions in crystalline optical activity

NASA Astrophysics Data System (ADS)

Vyšín, I.; Ríha, J.; Svácková, K.

2006-06-01

Many methods have been used in the crystalline optical activity solution, among them the traditional method of coupled oscillators. The two coupled oscillator model was first solved by Chandrasekhar, and the most general dispersion relations for the crystalline optical activity can be obtained from its next extensions. However, the Chandrasekhar solution method seems to be based on a mistake in the computations. For this reason, the solution of a more complicated model of coupled oscillators which better corresponds to the structure of real crystals using the Condon relations is presented. This solution leads to the conclusion that, although it is possible to object to the Chandrasekhar solution method, the form of his final dispersion relations is correct. On the other hand, the dispersion relations following from the solution of more complicated coupled oscillator models are more convenient for the interpretation of the crystalline optical activity experimental data, which is demonstrated in examples of crystals of tellurium and benzil.

Simulating contaminant attenuation, double-porosity exchange, and water age in aquifers using MOC3D

USGS Publications Warehouse

Goode, Daniel J.

1999-01-01

MOC3D is a general-purpose computer model developed by the U.S. Geological Survey (USGS) for simulation of three-dimensional solute transport in ground water (Konikow and others, 1996). The model is an update to the widely used USGS two-dimensional solute-transport model (MOC) and is implemented as an optional “package” for the ground-water flow model MODFLOW (Harbaugh and McDonald, 1996). Directly coupling the time-tested MOC transport algorithms with the widely used MODFLOW program makes MOC3D a powerful tool for simulation of solute transport in ground water in many hydrogeologic settings. The model simulates transport processes that include:Advection - Transport of dissolved solutes at the same rate as the average ground-water flow velocity.Diffusion - Spreading of solute from areas of high concentration to areas of low concentration, caused by “random” molecular motionDispersion - Diffusion-like spreading of solute that is caused primarily by spatial variability in aquifer properties, which results in spatial variability in transport velocity.Retardation - Reduction in the apparent solute velocity, compared to the ground-water velocity, caused by linear equilibrium sorption on aquifer materials.Decay - Disappearance of solute caused by reactions such as radioactive decay or biodegradation that are proportional to concentration.Growth - Creation (or disappearance) of solute mass caused by reactions that proceed independent of the solute concentration, such as some cases of biodegradationDouble-porosity exchange - rate-limited exchange of solute mass between mobile and immobile zones; for example, between fractures and the rock matrix.

Skyrmions, Skyrme stars and black holes with Skyrme hair in five spacetime dimension

NASA Astrophysics Data System (ADS)

Brihaye, Yves; Herdeiro, Carlos; Radu, Eugen; Tchrakian, D. H.

2017-11-01

We consider a class of generalizations of the Skyrme model to five spacetime dimensions ( d = 5), which is defined in terms of an O(5) sigma model. A special ansatz for the Skyrme field allows angular momentum to be present and equations of motion with a radial dependence only. Using it, we obtain: 1) everywhere regular solutions describing localised energy lumps ( Skyrmions); 2) Self-gravitating, asymptotically flat, everywhere non-singular solitonic solutions ( Skyrme stars), upon minimally coupling the model to Einstein's gravity; 3) both static and spinning black holes with Skyrme hair, the latter with rotation in two orthogonal planes, with both angular momenta of equal magnitude. In the absence of gravity we present an analytic solution that satisfies a BPS-type bound and explore numerically some of the non-BPS solutions. In the presence of gravity, we contrast the solutions to this model with solutions to a complex scalar field model, namely boson stars and black holes with synchronised hair. Remarkably, even though the two models present key differences, and in particular the Skyrme model allows static hairy black holes, when introducing rotation, the synchronisation condition becomes mandatory, providing further evidence for its generality in obtaining rotating hairy black holes.

Approximate analytic solutions to 3D unconfined groundwater flow within regional 2D models

NASA Astrophysics Data System (ADS)

Luther, K.; Haitjema, H. M.

2000-04-01

We present methods for finding approximate analytic solutions to three-dimensional (3D) unconfined steady state groundwater flow near partially penetrating and horizontal wells, and for combining those solutions with regional two-dimensional (2D) models. The 3D solutions use distributed singularities (analytic elements) to enforce boundary conditions on the phreatic surface and seepage faces at vertical wells, and to maintain fixed-head boundary conditions, obtained from the 2D model, at the perimeter of the 3D model. The approximate 3D solutions are analytic (continuous and differentiable) everywhere, including on the phreatic surface itself. While continuity of flow is satisfied exactly in the infinite 3D flow domain, water balance errors can occur across the phreatic surface.

Diffusion of Small Solute Particles in Viscous Liquids: Cage Diffusion, a Result of Decoupling of Solute-Solvent Dynamics, Leads to Amplification of Solute Diffusion.

PubMed

Acharya, Sayantan; Nandi, Manoj K; Mandal, Arkajit; Sarkar, Sucharita; Bhattacharyya, Sarika Maitra

2015-08-27

We study the diffusion of small solute particles through solvent by keeping the solute-solvent interaction repulsive and varying the solvent properties. The study involves computer simulations, development of a new model to describe diffusion of small solutes in a solvent, and also mode coupling theory (MCT) calculations. In a viscous solvent, a small solute diffuses via coupling to the solvent hydrodynamic modes and also through the transient cages formed by the solvent. The model developed can estimate the independent contributions from these two different channels of diffusion. Although the solute diffusion in all the systems shows an amplification, the degree of it increases with solvent viscosity. The model correctly predicts that when the solvent viscosity is high, the solute primarily diffuses by exploiting the solvent cages. In such a scenario the MCT diffusion performed for a static solvent provides a correct estimation of the cage diffusion.

Nonlocal Poisson-Fermi model for ionic solvent.

PubMed

Xie, Dexuan; Liu, Jinn-Liang; Eisenberg, Bob

2016-07-01

We propose a nonlocal Poisson-Fermi model for ionic solvent that includes ion size effects and polarization correlations among water molecules in the calculation of electrostatic potential. It includes the previous Poisson-Fermi models as special cases, and its solution is the convolution of a solution of the corresponding nonlocal Poisson dielectric model with a Yukawa-like kernel function. The Fermi distribution is shown to be a set of optimal ionic concentration functions in the sense of minimizing an electrostatic potential free energy. Numerical results are reported to show the difference between a Poisson-Fermi solution and a corresponding Poisson solution.

Supermodeling With A Global Atmospheric Model

NASA Astrophysics Data System (ADS)

Wiegerinck, Wim; Burgers, Willem; Selten, Frank

2013-04-01

In weather and climate prediction studies it often turns out to be the case that the multi-model ensemble mean prediction has the best prediction skill scores. One possible explanation is that the major part of the model error is random and is averaged out in the ensemble mean. In the standard multi-model ensemble approach, the models are integrated in time independently and the predicted states are combined a posteriori. Recently an alternative ensemble prediction approach has been proposed in which the models exchange information during the simulation and synchronize on a common solution that is closer to the truth than any of the individual model solutions in the standard multi-model ensemble approach or a weighted average of these. This approach is called the super modeling approach (SUMO). The potential of the SUMO approach has been demonstrated in the context of simple, low-order, chaotic dynamical systems. The information exchange takes the form of linear nudging terms in the dynamical equations that nudge the solution of each model to the solution of all other models in the ensemble. With a suitable choice of the connection strengths the models synchronize on a common solution that is indeed closer to the true system than any of the individual model solutions without nudging. This approach is called connected SUMO. An alternative approach is to integrate a weighted averaged model, weighted SUMO. At each time step all models in the ensemble calculate the tendency, these tendencies are weighted averaged and the state is integrated one time step into the future with this weighted averaged tendency. It was shown that in case the connected SUMO synchronizes perfectly, the connected SUMO follows the weighted averaged trajectory and both approaches yield the same solution. In this study we pioneer both approaches in the context of a global, quasi-geostrophic, three-level atmosphere model that is capable of simulating quite realistically the extra-tropical circulation in the Northern Hemisphere winter.

A multi-scale Lattice Boltzmann model for simulating solute transport in 3D X-ray micro-tomography images of aggregated porous materials

NASA Astrophysics Data System (ADS)

Zhang, Xiaoxian; Crawford, John W.; Flavel, Richard J.; Young, Iain M.

2016-10-01

The Lattice Boltzmann (LB) model and X-ray computed tomography (CT) have been increasingly used in combination over the past decade to simulate water flow and chemical transport at pore scale in porous materials. Because of its limitation in resolution and the hierarchical structure of most natural soils, the X-ray CT tomography can only identify pores that are greater than its resolution and treats other pores as solid. As a result, the so-called solid phase in X-ray images may in reality be a grey phase, containing substantial connected pores capable of conducing fluids and solute. Although modified LB models have been developed to simulate fluid flow in such media, models for solute transport are relatively limited. In this paper, we propose a LB model for simulating solute transport in binary soil images containing permeable solid phase. The model is based on the single-relaxation time approach and uses a modified partial bounce-back method to describe the resistance caused by the permeable solid phase to chemical transport. We derive the relationship between the diffusion coefficient and the parameter introduced in the partial bounce-back method, and test the model against analytical solution for movement of a pulse of tracer. We also validate it against classical finite volume method for solute diffusion in a simple 2D image, and then apply the model to a soil image acquired using X-ray tomography at resolution of 30 μm in attempts to analyse how the ability of the solid phase to diffuse solute at micron-scale affects the behaviour of the solute at macro-scale after a volumetric average. Based on the simulated results, we discuss briefly the danger in interpreting experimental results using the continuum model without fully understanding the pore-scale processes, as well as the potential of using pore-scale modelling and tomography to help improve the continuum models.

High-resolution CSR GRACE RL05 mascons

NASA Astrophysics Data System (ADS)

Save, Himanshu; Bettadpur, Srinivas; Tapley, Byron D.

2016-10-01

The determination of the gravity model for the Gravity Recovery and Climate Experiment (GRACE) is susceptible to modeling errors, measurement noise, and observability issues. The ill-posed GRACE estimation problem causes the unconstrained GRACE RL05 solutions to have north-south stripes. We discuss the development of global equal area mascon solutions to improve the GRACE gravity information for the study of Earth surface processes. These regularized mascon solutions are developed with a 1° resolution using Tikhonov regularization in a geodesic grid domain. These solutions are derived from GRACE information only, and no external model or data is used to inform the constraints. The regularization matrix is time variable and will not bias or attenuate future regional signals to some past statistics from GRACE or other models. The resulting Center for Space Research (CSR) mascon solutions have no stripe errors and capture all the signals observed by GRACE within the measurement noise level. The solutions are not tailored for specific applications and are global in nature. This study discusses the solution approach and compares the resulting solutions with postprocessed results from the RL05 spherical harmonic solutions and other global mascon solutions for studies of Arctic ice sheet processes, ocean bottom pressure variation, and land surface total water storage change. This suite of comparisons leads to the conclusion that the mascon solutions presented here are an enhanced representation of the RL05 GRACE solutions and provide accurate surface-based gridded information that can be used without further processing.

Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models

NASA Astrophysics Data System (ADS)

Ahmed, E.; El-Sayed, A. M. A.; El-Saka, H. A. A.

2007-01-01

In this paper we are concerned with the fractional-order predator-prey model and the fractional-order rabies model. Existence and uniqueness of solutions are proved. The stability of equilibrium points are studied. Numerical solutions of these models are given. An example is given where the equilibrium point is a centre for the integer order system but locally asymptotically stable for its fractional-order counterpart.

The Solution Construction of Heterotic Super-Liouville Model

NASA Astrophysics Data System (ADS)

Yang, Zhan-Ying; Zhen, Yi

2001-12-01

We investigate the heterotic super-Liouville model on the base of the basic Lie super-algebra Osp(1|2).Using the super extension of Leznov-Saveliev analysis and Drinfeld-Sokolov linear system, we construct the explicit solution of the heterotic super-Liouville system in component form. We also show that the solutions are local and periodic by calculating the exchange relation of the solution. Finally starting from the action of heterotic super-Liouville model, we obtain the conserved current and conserved charge which possessed the BRST properties.

Application of Harmony Search algorithm to the solution of groundwater management models

NASA Astrophysics Data System (ADS)

Tamer Ayvaz, M.

2009-06-01

This study proposes a groundwater resources management model in which the solution is performed through a combined simulation-optimization model. A modular three-dimensional finite difference groundwater flow model, MODFLOW is used as the simulation model. This model is then combined with a Harmony Search (HS) optimization algorithm which is based on the musical process of searching for a perfect state of harmony. The performance of the proposed HS based management model is tested on three separate groundwater management problems: (i) maximization of total pumping from an aquifer (steady-state); (ii) minimization of the total pumping cost to satisfy the given demand (steady-state); and (iii) minimization of the pumping cost to satisfy the given demand for multiple management periods (transient). The sensitivity of HS algorithm is evaluated by performing a sensitivity analysis which aims to determine the impact of related solution parameters on convergence behavior. The results show that HS yields nearly same or better solutions than the previous solution methods and may be used to solve management problems in groundwater modeling.

A Generalized Deduction of the Ideal-Solution Model

ERIC Educational Resources Information Center

Leo, Teresa J.; Perez-del-Notario, Pedro; Raso, Miguel A.

2006-01-01

A new general procedure for deriving the Gibbs energy of mixing is developed through general thermodynamic considerations, and the ideal-solution model is obtained as a special particular case of the general one. The deduction of the Gibbs energy of mixing for the ideal-solution model is a rational one and viewed suitable for advanced students who…

Exact static solutions for discrete phi4 models free of the Peierls-Nabarro barrier: discretized first-integral approach.

PubMed

Dmitriev, S V; Kevrekidis, P G; Yoshikawa, N; Frantzeskakis, D J

2006-10-01

We propose a generalization of the discrete Klein-Gordon models free of the Peierls-Nabarro barrier derived in Spreight [Nonlinearity 12, 1373 (1999)] and Barashenkov [Phys. Rev. E 72, 035602(R) (2005)], such that they support not only kinks but a one-parameter set of exact static solutions. These solutions can be obtained iteratively from a two-point nonlinear map whose role is played by the discretized first integral of the static Klein-Gordon field, as suggested by Dmitriev [J. Phys. A 38, 7617 (2005)]. We then discuss some discrete phi4 models free of the Peierls-Nabarro barrier and identify for them the full space of available static solutions, including those derived recently by Cooper [Phys. Rev. E 72, 036605 (2005)] but not limited to them. These findings are also relevant to standing wave solutions of discrete nonlinear Schrödinger models. We also study stability of the obtained solutions. As an interesting aside, we derive the list of solutions to the continuum phi4 equation that fill the entire two-dimensional space of parameters obtained as the continuum limit of the corresponding space of the discrete models.

Using a hybrid model to predict solute transfer from initially saturated soil into surface runoff with controlled drainage water.

PubMed

Tong, Juxiu; Hu, Bill X; Yang, Jinzhong; Zhu, Yan

2016-06-01

The mixing layer theory is not suitable for predicting solute transfer from initially saturated soil to surface runoff water under controlled drainage conditions. By coupling the mixing layer theory model with the numerical model Hydrus-1D, a hybrid solute transfer model has been proposed to predict soil solute transfer from an initially saturated soil into surface water, under controlled drainage water conditions. The model can also consider the increasing ponding water conditions on soil surface before surface runoff. The data of solute concentration in surface runoff and drainage water from a sand experiment is used as the reference experiment. The parameters for the water flow and solute transfer model and mixing layer depth under controlled drainage water condition are identified. Based on these identified parameters, the model is applied to another initially saturated sand experiment with constant and time-increasing mixing layer depth after surface runoff, under the controlled drainage water condition with lower drainage height at the bottom. The simulation results agree well with the observed data. Study results suggest that the hybrid model can accurately simulate the solute transfer from initially saturated soil into surface runoff under controlled drainage water condition. And it has been found that the prediction with increasing mixing layer depth is better than that with the constant one in the experiment with lower drainage condition. Since lower drainage condition and deeper ponded water depth result in later runoff start time, more solute sources in the mixing layer are needed for the surface water, and larger change rate results in the increasing mixing layer depth.

Exact solutions for network rewiring models

NASA Astrophysics Data System (ADS)

Evans, T. S.

2007-03-01

Evolving networks with a constant number of edges may be modelled using a rewiring process. These models are used to describe many real-world processes including the evolution of cultural artifacts such as family names, the evolution of gene variations, and the popularity of strategies in simple econophysics models such as the minority game. The model is closely related to Urn models used for glasses, quantum gravity and wealth distributions. The full mean field equation for the degree distribution is found and its exact solution and generating solution are given.

Fingerprinting breakthrough curves in soils

NASA Astrophysics Data System (ADS)

Koestel, J. K.

2017-12-01

Conservative solute transport through soil is predominantly modeled using a few standard solute transport models like the convection dispersion equation or the mobile-immobile model. The adequacy of these models is seldom investigated in detail as it would require knowledge on the 3-D spatio-temporal evolution of the solute plume that is normally not available. Instead, shape-measures of breakthrough curves (BTCs) such as the apparent dispersivity and the relative 5%-arrival time may be used to fingerprint breakthrough curves as well as forward solutions of solute transport models. In this fashion the similarity of features from measured and modeled BTC data becomes quantifiable. In this study I am presenting a new set of shape-measures that characterize the log-log tailings of BTC. I am using the new shape measures alongside with more established ones to map the features of BTCs obtained forward models of the convective dispersive equation, log-normal and Gamma transfer functions, the mobile-immobile model and the continuous time random walk model with respect to their input parameters. In a second step, I am comparing corresponding shape-measures for 206 measured BTCs extracted from peer-reviewed literature. Preliminary results show that power-law tailings are very common in BTCs from soil samples and that BTC features that are exclusive to a mobile-immobile type solute transport process are very rarely found.

Hierarchic models for laminated plates. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Actis, Ricardo Luis

1991-01-01

Structural plates and shells are three-dimensional bodies, one dimension of which happens to be much smaller than the other two. Thus, the quality of a plate or shell model must be judged on the basis of how well its exact solution approximates the corresponding three-dimensional problem. Of course, the exact solution depends not only on the choice of the model but also on the topology, material properties, loading and constraints. The desired degree of approximation depends on the analyst's goals in performing the analysis. For these reasons models have to be chosen adaptively. Hierarchic sequences of models make adaptive selection of the model which is best suited for the purposes of a particular analysis possible. The principles governing the formulation of hierarchic models for laminated plates are presented. The essential features of the hierarchic models described models are: (1) the exact solutions corresponding to the hierarchic sequence of models converge to the exact solution of the corresponding problem of elasticity for a fixed laminate thickness; and (2) the exact solution of each model converges to the same limit as the exact solution of the corresponding problem of elasticity with respect to the laminate thickness approaching zero. The formulation is based on one parameter (beta) which characterizes the hierarchic sequence of models, and a set of constants whose influence was assessed by a numerical sensitivity study. The recommended selection of these constants results in the number of fields increasing by three for each increment in the power of beta. Numerical examples analyzed with the proposed sequence of models are included and good correlation with the reference solutions was found. Results were obtained for laminated strips (plates in cylindrical bending) and for square and rectangular plates with uniform loading and with homogeneous boundary conditions. Cross-ply and angle-ply laminates were evaluated and the results compared with those of MSC/PROBE. Hierarchic models make the computation of any engineering data possible to an arbitrary level of precision within the framework of the theory of elasticity.

Elastic-Plastic J-Integral Solutions or Surface Cracks in Tension Using an Interpolation Methodology. Appendix C -- Finite Element Models Solution Database File, Appendix D -- Benchmark Finite Element Models Solution Database File

NASA Technical Reports Server (NTRS)

Allen, Phillip A.; Wells, Douglas N.

2013-01-01

No closed form solutions exist for the elastic-plastic J-integral for surface cracks due to the nonlinear, three-dimensional nature of the problem. Traditionally, each surface crack must be analyzed with a unique and time-consuming nonlinear finite element analysis. To overcome this shortcoming, the authors have developed and analyzed an array of 600 3D nonlinear finite element models for surface cracks in flat plates under tension loading. The solution space covers a wide range of crack shapes and depths (shape: 0.2 less than or equal to a/c less than or equal to 1, depth: 0.2 less than or equal to a/B less than or equal to 0.8) and material flow properties (elastic modulus-to-yield ratio: 100 less than or equal to E/ys less than or equal to 1,000, and hardening: 3 less than or equal to n less than or equal to 20). The authors have developed a methodology for interpolating between the goemetric and material property variables that allows the user to reliably evaluate the full elastic-plastic J-integral and force versus crack mouth opening displacement solution; thus, a solution can be obtained very rapidly by users without elastic-plastic fracture mechanics modeling experience. Complete solutions for the 600 models and 25 additional benchmark models are provided in tabular format.

Reliable and efficient solution of genome-scale models of Metabolism and macromolecular Expression

DOE PAGES

Ma, Ding; Yang, Laurence; Fleming, Ronan M. T.; ...

2017-01-18

Currently, Constraint-Based Reconstruction and Analysis (COBRA) is the only methodology that permits integrated modeling of Metabolism and macromolecular Expression (ME) at genome-scale. Linear optimization computes steady-state flux solutions to ME models, but flux values are spread over many orders of magnitude. Data values also have greatly varying magnitudes. Furthermore, standard double-precision solvers may return inaccurate solutions or report that no solution exists. Exact simplex solvers based on rational arithmetic require a near-optimal warm start to be practical on large problems (current ME models have 70,000 constraints and variables and will grow larger). We also developed a quadrupleprecision version of ourmore » linear and nonlinear optimizer MINOS, and a solution procedure (DQQ) involving Double and Quad MINOS that achieves reliability and efficiency for ME models and other challenging problems tested here. DQQ will enable extensive use of large linear and nonlinear models in systems biology and other applications involving multiscale data.« less

Reactive solute transport in streams: 1. Development of an equilibrium- based model

USGS Publications Warehouse

Runkel, Robert L.; Bencala, Kenneth E.; Broshears, Robert E.; Chapra, Steven C.

1996-01-01

An equilibrium-based solute transport model is developed for the simulation of trace metal fate and transport in streams. The model is formed by coupling a solute transport model with a chemical equilibrium submodel based on MINTEQ. The solute transport model considers the physical processes of advection, dispersion, lateral inflow, and transient storage, while the equilibrium submodel considers the speciation and complexation of aqueous species, precipitation/dissolution and sorption. Within the model, reactions in the water column may result in the formation of solid phases (precipitates and sorbed species) that are subject to downstream transport and settling processes. Solid phases on the streambed may also interact with the water column through dissolution and sorption/desorption reactions. Consideration of both mobile (water-borne) and immobile (streambed) solid phases requires a unique set of governing differential equations and solution techniques that are developed herein. The partial differential equations describing physical transport and the algebraic equations describing chemical equilibria are coupled using the sequential iteration approach.

Reliable and efficient solution of genome-scale models of Metabolism and macromolecular Expression

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

Ma, Ding; Yang, Laurence; Fleming, Ronan M. T.

Currently, Constraint-Based Reconstruction and Analysis (COBRA) is the only methodology that permits integrated modeling of Metabolism and macromolecular Expression (ME) at genome-scale. Linear optimization computes steady-state flux solutions to ME models, but flux values are spread over many orders of magnitude. Data values also have greatly varying magnitudes. Furthermore, standard double-precision solvers may return inaccurate solutions or report that no solution exists. Exact simplex solvers based on rational arithmetic require a near-optimal warm start to be practical on large problems (current ME models have 70,000 constraints and variables and will grow larger). We also developed a quadrupleprecision version of ourmore » linear and nonlinear optimizer MINOS, and a solution procedure (DQQ) involving Double and Quad MINOS that achieves reliability and efficiency for ME models and other challenging problems tested here. DQQ will enable extensive use of large linear and nonlinear models in systems biology and other applications involving multiscale data.« less

Indirect estimation of the Convective Lognormal Transfer function model parameters for describing solute transport in unsaturated and undisturbed soil.

PubMed

Mohammadi, Mohammad Hossein; Vanclooster, Marnik

2012-05-01

Solute transport in partially saturated soils is largely affected by fluid velocity distribution and pore size distribution within the solute transport domain. Hence, it is possible to describe the solute transport process in terms of the pore size distribution of the soil, and indirectly in terms of the soil hydraulic properties. In this paper, we present a conceptual approach that allows predicting the parameters of the Convective Lognormal Transfer model from knowledge of soil moisture and the Soil Moisture Characteristic (SMC), parameterized by means of the closed-form model of Kosugi (1996). It is assumed that in partially saturated conditions, the air filled pore volume act as an inert solid phase, allowing the use of the Arya et al. (1999) pragmatic approach to estimate solute travel time statistics from the saturation degree and SMC parameters. The approach is evaluated using a set of partially saturated transport experiments as presented by Mohammadi and Vanclooster (2011). Experimental results showed that the mean solute travel time, μ(t), increases proportionally with the depth (travel distance) and decreases with flow rate. The variance of solute travel time σ²(t) first decreases with flow rate up to 0.4-0.6 Ks and subsequently increases. For all tested BTCs predicted solute transport with μ(t) estimated from the conceptual model performed much better as compared to predictions with μ(t) and σ²(t) estimated from calibration of solute transport at shallow soil depths. The use of μ(t) estimated from the conceptual model therefore increases the robustness of the CLT model in predicting solute transport in heterogeneous soils at larger depths. In view of the fact that reasonable indirect estimates of the SMC can be made from basic soil properties using pedotransfer functions, the presented approach may be useful for predicting solute transport at field or watershed scales. Copyright © 2012 Elsevier B.V. All rights reserved.

Indirect estimation of the Convective Lognormal Transfer function model parameters for describing solute transport in unsaturated and undisturbed soil

NASA Astrophysics Data System (ADS)

Mohammadi, Mohammad Hossein; Vanclooster, Marnik

2012-05-01

Solute transport in partially saturated soils is largely affected by fluid velocity distribution and pore size distribution within the solute transport domain. Hence, it is possible to describe the solute transport process in terms of the pore size distribution of the soil, and indirectly in terms of the soil hydraulic properties. In this paper, we present a conceptual approach that allows predicting the parameters of the Convective Lognormal Transfer model from knowledge of soil moisture and the Soil Moisture Characteristic (SMC), parameterized by means of the closed-form model of Kosugi (1996). It is assumed that in partially saturated conditions, the air filled pore volume act as an inert solid phase, allowing the use of the Arya et al. (1999) pragmatic approach to estimate solute travel time statistics from the saturation degree and SMC parameters. The approach is evaluated using a set of partially saturated transport experiments as presented by Mohammadi and Vanclooster (2011). Experimental results showed that the mean solute travel time, μt, increases proportionally with the depth (travel distance) and decreases with flow rate. The variance of solute travel time σ2t first decreases with flow rate up to 0.4-0.6 Ks and subsequently increases. For all tested BTCs predicted solute transport with μt estimated from the conceptual model performed much better as compared to predictions with μt and σ2t estimated from calibration of solute transport at shallow soil depths. The use of μt estimated from the conceptual model therefore increases the robustness of the CLT model in predicting solute transport in heterogeneous soils at larger depths. In view of the fact that reasonable indirect estimates of the SMC can be made from basic soil properties using pedotransfer functions, the presented approach may be useful for predicting solute transport at field or watershed scales.

A new class of relativistic stellar models

NASA Astrophysics Data System (ADS)

Haggag, Salah

1995-03-01

Einstein field equations for a static and spherically symmetric perfect fluid are considered. A formulation given by Patino and Rago is used to obtain a class of nine solutions, two of them are Tolman solutions I, IV and the remaining seven are new. The solutions are the correct ones corresponding to expressions derived by Patino and Rago which have been shown by Knutsen to be incorrect. Similar to Tolan solution IV each of the new solutions satisfies energy conditions inside a sphere in some range of two independent parameters. Besides, each solution could be matched to the exterior Schwarzschild solution at a boundary where the pressure vanishes and thus the solutions constitute a class of new physically reasonable stellar models.

Effect of sodium metabisulfite on hydrogen peroxide production in light-exposed pediatric parenteral amino acid solutions.

PubMed

Brawley, V; Bhatia, J; Karp, W B

1998-06-15

The effect of sodium metabisulfite (MBS) on hydrogen peroxide (HP) production in model and commercial amino acid solutions exposed to phototherapy light was studied. Model and commercial pediatric amino acid solutions were prepared such that the amino acid concentration was 1%. MBS concentration, riboflavin concentration, and duration of exposure to phototherapy light were varied to determine the effect on HP production. Control solutions were kept in the dark. HP production was assayed in the model amino acid solutions by using potassium iodide in the presence of ammonium molybdate. In all experiments, HP production was measured at 360 nm in the presence and absence of catalase. In light-exposed solutions, HP production increased linearly for several hours and reached a plateau by eight hours. A mean maximum of 940 microM was produced (data pooled for all solutions). No detectable HP was generated in the solutions kept in the dark. After two hours of light exposure, it was necessary to add at least 10 times more MBS than is typically found in commercial total parenteral nutrient solutions to scavenge all the HP produced. An average of up to 940 microM of HP was produced in model and commercial pediatric parenteral 1% amino acid solutions in the presence of phototherapy light and clinically relevant concentrations of riboflavin and MBS. Light exposure decreased the antioxidant effect of MBS.

Sensitivity analysis of conservative and reactive stream transient storage models applied to field data from multiple-reach experiments

USGS Publications Warehouse

Gooseff, M.N.; Bencala, K.E.; Scott, D.T.; Runkel, R.L.; McKnight, Diane M.

2005-01-01

The transient storage model (TSM) has been widely used in studies of stream solute transport and fate, with an increasing emphasis on reactive solute transport. In this study we perform sensitivity analyses of a conservative TSM and two different reactive solute transport models (RSTM), one that includes first-order decay in the stream and the storage zone, and a second that considers sorption of a reactive solute on streambed sediments. Two previously analyzed data sets are examined with a focus on the reliability of these RSTMs in characterizing stream and storage zone solute reactions. Sensitivities of simulations to parameters within and among reaches, parameter coefficients of variation, and correlation coefficients are computed and analyzed. Our results indicate that (1) simulated values have the greatest sensitivity to parameters within the same reach, (2) simulated values are also sensitive to parameters in reaches immediately upstream and downstream (inter-reach sensitivity), (3) simulated values have decreasing sensitivity to parameters in reaches farther downstream, and (4) in-stream reactive solute data provide adequate data to resolve effective storage zone reaction parameters, given the model formulations. Simulations of reactive solutes are shown to be equally sensitive to transport parameters and effective reaction parameters of the model, evidence of the control of physical transport on reactive solute dynamics. Similar to conservative transport analysis, reactive solute simulations appear to be most sensitive to data collected during the rising and falling limb of the concentration breakthrough curve. ?? 2005 Elsevier Ltd. All rights reserved.

Existence of periodic solutions in a model of respiratory syncytial virus RSV

NASA Astrophysics Data System (ADS)

Arenas, Abraham J.; González, Gilberto; Jódar, Lucas

2008-08-01

In this paper we study the existence of a positive periodic solutions for nested models of respiratory syncytial virus RSV, by using a continuation theorem based on coincidence degree theory. Conditions for the existence of periodic solutions in the model are given. Numerical simulations related to the transmission of respiratory syncytial virus in Madrid and Rio Janeiro are included.

Stability analysis and wave dynamics of an extended hybrid traffic flow model

NASA Astrophysics Data System (ADS)

Wang, Yu-Qing; Zhou, Chao-Fan; Li, Wei-Kang; Yan, Bo-Wen; Jia, Bin; Wang, Ji-Xin

2018-02-01

The stability analysis and wave dynamic properties of an extended hybrid traffic flow model, WZY model, are intensively studied in this paper. The linear stable condition obtained by the linear stability analysis is presented. Besides, by means of analyzing Korteweg-de Vries equation, we present soliton waves in the metastable region. Moreover, the multiscale perturbation technique is applied to derive the traveling wave solution of the model. Furthermore, by means of performing Darboux transformation, the first-order and second-order doubly-periodic solutions and rational solutions are presented. It can be found that analytical solutions match well with numerical simulations.

Modeling the Transport Phenomena in the Solution Precursor Plasma Spraying

NASA Astrophysics Data System (ADS)

Shan, Yanguang

2008-10-01

Solution precursor plasma spraying has been used to produce finely structured ceramic coatings with nano- and sub-micrometric features. This process involves the injection of a solution spray of ceramic salts into a DC plasma jet under atmospheric condition. During the process, the solvent vaporizes as the droplet travel downstream. Solid particles are finally formed due to the precipitation of the solute, and the particle are heated up and accelerated to the substrate to generate the coating. This work describes a 3D model to simulate the transport phenomena and the trajectory and heating of the solution spray in the process. The jet-spray two-way interactions are considered. A simplified model is employed to simulate the evolution process and the formation of the solid particle from the solution droplet in the plasma jet. O'Rourke's droplet collision model is used to take into account of the influence of droplet collision. The influence of droplet breakup is also considered by implementing TAB droplet breakup models into the plasma jet model. The temperature and velocity fields of the jet are obtained and validated. The particle size, velocity, temperature and position distribution on the substrate are predicted.

Energetics of slope flows: linear and weakly nonlinear solutions of the extended Prandtl model

NASA Astrophysics Data System (ADS)

Güttler, Ivan; Marinović, Ivana; Večenaj, Željko; Grisogono, Branko

2016-07-01

The Prandtl model succinctly combines the 1D stationary boundary-layer dynamics and thermodynamics of simple anabatic and katabatic flows over uniformly inclined surfaces. It assumes a balance between the along-the-slope buoyancy component and adiabatic warming/cooling, and the turbulent mixing of momentum and heat. In this study, energetics of the Prandtl model is addressed in terms of the total energy (TE) concept. Furthermore, since the authors recently developed a weakly nonlinear version of the Prandtl model, the TE approach is also exercised on this extended model version, which includes an additional nonlinear term in the thermodynamic equation. Hence, interplay among diffusion, dissipation and temperature-wind interaction of the mean slope flow is further explored. The TE of the nonlinear Prandtl model is assessed in an ensemble of solutions where the Prandtl number, the slope angle and the nonlinearity parameter are perturbed. It is shown that nonlinear effects have the lowest impact on variability in the ensemble of solutions of the weakly nonlinear Prandtl model when compared to the other two governing parameters. The general behavior of the nonlinear solution is similar to the linear solution, except that the maximum of the along-the-slope wind speed in the nonlinear solution reduces for larger slopes. Also, the dominance of PE near the sloped surface, and the elevated maximum of KE in the linear and nonlinear energetics of the extended Prandtl model are found in the PASTEX-94 measurements. The corresponding level where KE>PE most likely marks the bottom of the sublayer subject to shear-driven instabilities. Finally, possible limitations of the weakly nonlinear solutions of the extended Prandtl model are raised. In linear solutions, the local storage of TE term is zero, reflecting the stationarity of solutions by definition. However, in nonlinear solutions, the diffusion, dissipation and interaction terms (where the height of the maximum interaction is proportional to the height of the low-level jet by the factor ≈4/9) do not balance and the local storage of TE attains non-zero values. In order to examine the issue of non-stationarity, the inclusion of velocity-pressure covariance in the momentum equation is suggested for future development of the extended Prandtl model.

A new solution method for wheel/rail rolling contact.

PubMed

Yang, Jian; Song, Hua; Fu, Lihua; Wang, Meng; Li, Wei

2016-01-01

To solve the problem of wheel/rail rolling contact of nonlinear steady-state curving, a three-dimensional transient finite element (FE) model is developed by the explicit software ANSYS/LS-DYNA. To improve the solving speed and efficiency, an explicit-explicit order solution method is put forward based on analysis of the features of implicit and explicit algorithm. The solution method was first applied to calculate the pre-loading of wheel/rail rolling contact with explicit algorithm, and then the results became the initial conditions in solving the dynamic process of wheel/rail rolling contact with explicit algorithm as well. Simultaneously, the common implicit-explicit order solution method is used to solve the FE model. Results show that the explicit-explicit order solution method has faster operation speed and higher efficiency than the implicit-explicit order solution method while the solution accuracy is almost the same. Hence, the explicit-explicit order solution method is more suitable for the wheel/rail rolling contact model with large scale and high nonlinearity.

Solute transport along preferential flow paths in unsaturated fractures

USGS Publications Warehouse

Su, Grace W.; Geller, Jil T.; Pruess, Karsten; Hunt, James R.

2001-01-01

Laboratory experiments were conducted to study solute transport along preferential flow paths in unsaturated, inclined fractures. Qualitative aspects of solute transport were identified in a miscible dye tracer experiment conducted in a transparent replica of a natural granite fracture. Additional experiments were conducted to measure the breakthrough curves of a conservative tracer introduced into an established preferential flow path in two different fracture replicas and a rock‐replica combination. The influence of gravity was investigated by varying fracture inclination. The relationship between the travel times of the solute and the relative influence of gravity was substantially affected by two modes of intermittent flow that occurred: the snapping rivulet and the pulsating blob modes. The measured travel times of the solute were evaluated with three transfer function models: the axial dispersion, the reactors‐in‐series, and the lognormal models. The three models described the solute travel times nearly equally well. A mechanistic model was also formulated to describe transport when the pulsating blob mode occurred which assumed blobs of water containing solute mixed with residual pools of water along the flow path.

Modeling Three-Dimensional Flow in Confined Aquifers by Superposition of Both Two- and Three-Dimensional Analytic Functions

NASA Astrophysics Data System (ADS)

Haitjema, Henk M.

1985-10-01

A technique is presented to incorporate three-dimensional flow in a Dupuit-Forchheimer model. The method is based on superposition of approximate analytic solutions to both two- and three-dimensional flow features in a confined aquifer of infinite extent. Three-dimensional solutions are used in the domain of interest, while farfield conditions are represented by two-dimensional solutions. Approximate three- dimensional solutions have been derived for a partially penetrating well and a shallow creek. Each of these solutions satisfies the condition that no flow occurs across the confining layers of the aquifer. Because of this condition, the flow at some distance of a three-dimensional feature becomes nearly horizontal. Consequently, remotely from a three-dimensional feature, its three-dimensional solution is replaced by a corresponding two-dimensional one. The latter solution is trivial as compared to its three-dimensional counterpart, and its use greatly enhances the computational efficiency of the model. As an example, the flow is modeled between a partially penetrating well and a shallow creek that occur in a regional aquifer system.

Grid-Independent Large-Eddy Simulation in Turbulent Channel Flow using Three-Dimensional Explicit Filtering

NASA Technical Reports Server (NTRS)

Gullbrand, Jessica

2003-01-01

In this paper, turbulence-closure models are evaluated using the 'true' LES approach in turbulent channel flow. The study is an extension of the work presented by Gullbrand (2001), where fourth-order commutative filter functions are applied in three dimensions in a fourth-order finite-difference code. The true LES solution is the grid-independent solution to the filtered governing equations. The solution is obtained by keeping the filter width constant while the computational grid is refined. As the grid is refined, the solution converges towards the true LES solution. The true LES solution will depend on the filter width used, but will be independent of the grid resolution. In traditional LES, because the filter is implicit and directly connected to the grid spacing, the solution converges towards a direct numerical simulation (DNS) as the grid is refined, and not towards the solution of the filtered Navier-Stokes equations. The effect of turbulence-closure models is therefore difficult to determine in traditional LES because, as the grid is refined, more turbulence length scales are resolved and less influence from the models is expected. In contrast, in the true LES formulation, the explicit filter eliminates all scales that are smaller than the filter cutoff, regardless of the grid resolution. This ensures that the resolved length-scales do not vary as the grid resolution is changed. In true LES, the cell size must be smaller than or equal to the cutoff length scale of the filter function. The turbulence-closure models investigated are the dynamic Smagorinsky model (DSM), the dynamic mixed model (DMM), and the dynamic reconstruction model (DRM). These turbulence models were previously studied using two-dimensional explicit filtering in turbulent channel flow by Gullbrand & Chow (2002). The DSM by Germano et al. (1991) is used as the USFS model in all the simulations. This enables evaluation of different reconstruction models for the RSFS stresses. The DMM consists of the scale-similarity model (SSM) by Bardina et al. (1983), which is an RSFS model, in linear combination with the DSM. In the DRM, the RSFS stresses are modeled by using an estimate of the unfiltered velocity in the unclosed term, while the USFS stresses are modeled by the DSM. The DSM and the DMM are two commonly used turbulence-closure models, while the DRM is a more recent model.

Evaluation and modeling of autonomous attitude thrust control for the Geostation Operational Environmental Satellite (GOES)-8 orbit determination

NASA Technical Reports Server (NTRS)

Forcey, W.; Minnie, C. R.; Defazio, R. L.

1995-01-01

The Geostationary Operational Environmental Satellite (GOES)-8 experienced a series of orbital perturbations from autonomous attitude control thrusting before perigee raising maneuvers. These perturbations influenced differential correction orbital state solutions determined by the Goddard Space Flight Center (GSFC) Goddard Trajectory Determination System (GTDS). The maneuvers induced significant variations in the converged state vector for solutions using increasingly longer tracking data spans. These solutions were used for planning perigee maneuvers as well as initial estimates for orbit solutions used to evaluate the effectiveness of the perigee raising maneuvers. This paper discusses models for the incorporation of attitude thrust effects into the orbit determination process. Results from definitive attitude solutions are modeled as impulsive thrusts in orbit determination solutions created for GOES-8 mission support. Due to the attitude orientation of GOES-8, analysis results are presented that attempt to absorb the effects of attitude thrusting by including a solution for the coefficient of reflectivity, C(R). Models to represent the attitude maneuvers are tested against orbit determination solutions generated during real-time support of the GOES-8 mission. The modeling techniques discussed in this investigation offer benefits to the remaining missions in the GOES NEXT series. Similar missions with large autonomous attitude control thrusting, such as the Solar and Heliospheric Observatory (SOHO) spacecraft and the INTELSAT series, may also benefit from these results.

Closed-form solution of the Ogden-Hill's compressible hyperelastic model for ramp loading

NASA Astrophysics Data System (ADS)

Berezvai, Szabolcs; Kossa, Attila

2017-05-01

This article deals with the visco-hyperelastic modelling approach for compressible polymer foam materials. Polymer foams can exhibit large elastic strains and displacements in case of volumetric compression. In addition, they often show significant rate-dependent properties. This material behaviour can be accurately modelled using the visco-hyperelastic approach, in which the large strain viscoelastic description is combined with the rate-independent hyperelastic material model. In case of polymer foams, the most widely used compressible hyperelastic material model, the so-called Ogden-Hill's model, was applied, which is implemented in the commercial finite element (FE) software Abaqus. The visco-hyperelastic model is defined in hereditary integral form, therefore, obtaining a closed-form solution for the stress is not a trivial task. However, the parameter-fitting procedure could be much faster and accurate if closed-form solution exists. In this contribution, exact stress solutions are derived in case of uniaxial, biaxial and volumetric compression loading cases using ramp-loading history. The analytical stress solutions are compared with the stress results in Abaqus using FE analysis. In order to highlight the benefits of the analytical closed-form solution during the parameter-fitting process experimental work has been carried out on a particular open-cell memory foam material. The results of the material identification process shows significant accuracy improvement in the fitting procedure by applying the derived analytical solutions compared to the so-called separated approach applied in the engineering practice.

Noncommutative wormhole solutions in F(T, T𝒢) gravity

NASA Astrophysics Data System (ADS)

Sharif, M.; Nazir, Kanwal

2017-04-01

This paper is devoted to the study of static spherically symmetric wormhole solutions along with noncommutative geometry in the background of F(T, T𝒢) gravity. We assume a nonzero redshift function as well as two well-known models of this gravity and discuss the behavior of null/weak energy conditions graphically. We conclude that there does not exist any physically acceptable wormhole solution for the first model, but there is a chance to develop physically acceptable wormhole solution in a particular region for the second model.

Flow and Heat Transfer Analysis of an Eyring-Powell Fluid in a Pipe

NASA Astrophysics Data System (ADS)

Ali, N.; Nazeer, F.; Nazeer, Mubbashar

2018-02-01

The steady non-isothermal flow of an Eyring-Powell fluid in a pipe is investigated using both perturbation and numerical methods. The results are presented for two viscosity models, namely the Reynolds model and the Vogel model. The shooting method is employed to compute the numerical solution. Criteria for validity of perturbation solution are developed. When these criteria are met, it is shown that the perturbation solution is in good agreement with the numerical solution. The influence of various emerging parameters on the velocity and temperature field is also shown.

Solute transport along a single fracture in a porous rock: a simple analytical solution and its extension for modeling velocity dispersion

NASA Astrophysics Data System (ADS)

Liu, Longcheng; Neretnieks, Ivars; Shahkarami, Pirouz; Meng, Shuo; Moreno, Luis

2018-02-01

A simple and robust solution is developed for the problem of solute transport along a single fracture in a porous rock. The solution is referred to as the solution to the single-flow-path model and takes the form of a convolution of two functions. The first function is the probability density function of residence-time distribution of a conservative solute in the fracture-only system as if the rock matrix is impermeable. The second function is the response of the fracture-matrix system to the input source when Fickian-type dispersion is completely neglected; thus, the effects of Fickian-type dispersion and matrix diffusion have been decoupled. It is also found that the solution can be understood in a way in line with the concept of velocity dispersion in fractured rocks. The solution is therefore extended into more general cases to also account for velocity variation between the channels. This leads to a development of the multi-channel model followed by detailed statistical descriptions of channel properties and sensitivity analysis of the model upon changes in the model key parameters. The simulation results obtained by the multi-channel model in this study fairly well agree with what is often observed in field experiments—i.e. the unchanged Peclet number with distance, which cannot be predicted by the classical advection-dispersion equation. In light of the findings from the aforementioned analysis, it is suggested that forced-gradient experiments can result in considerably different estimates of dispersivity compared to what can be found in natural-gradient systems for typical channel widths.

Aggregation work at polydisperse micellization: ideal solution and "dressed micelle" models comparing to molecular dynamics simulations.

PubMed

Burov, S V; Shchekin, A K

2010-12-28

General thermodynamic relations for the work of polydisperse micelle formation in the model of ideal solution of molecular aggregates in nonionic surfactant solution and the model of "dressed micelles" in ionic solution have been considered. In particular, the dependence of the aggregation work on the total concentration of nonionic surfactant has been analyzed. The analogous dependence for the work of formation of ionic aggregates has been examined with regard to existence of two variables of a state of an ionic aggregate, the aggregation numbers of surface active ions and counterions. To verify the thermodynamic models, the molecular dynamics simulations of micellization in nonionic and ionic surfactant solutions at two total surfactant concentrations have been performed. It was shown that for nonionic surfactants, even at relatively high total surfactant concentrations, the shape and behavior of the work of polydisperse micelle formation found within the model of the ideal solution at different total surfactant concentrations agrees fairly well with the numerical experiment. For ionic surfactant solutions, the numerical results indicate a strong screening of ionic aggregates by the bound counterions. This fact as well as independence of the coefficient in the law of mass action for ionic aggregates on total surfactant concentration and predictable behavior of the "waterfall" lines of surfaces of the aggregation work upholds the model of "dressed" ionic aggregates.

The construction of a two-dimensional reproducing kernel function and its application in a biomedical model.

PubMed

Guo, Qi; Shen, Shu-Ting

2016-04-29

There are two major classes of cardiac tissue models: the ionic model and the FitzHugh-Nagumo model. During computer simulation, each model entails solving a system of complex ordinary differential equations and a partial differential equation with non-flux boundary conditions. The reproducing kernel method possesses significant applications in solving partial differential equations. The derivative of the reproducing kernel function is a wavelet function, which has local properties and sensitivities to singularity. Therefore, study on the application of reproducing kernel would be advantageous. Applying new mathematical theory to the numerical solution of the ventricular muscle model so as to improve its precision in comparison with other methods at present. A two-dimensional reproducing kernel function inspace is constructed and applied in computing the solution of two-dimensional cardiac tissue model by means of the difference method through time and the reproducing kernel method through space. Compared with other methods, this method holds several advantages such as high accuracy in computing solutions, insensitivity to different time steps and a slow propagation speed of error. It is suitable for disorderly scattered node systems without meshing, and can arbitrarily change the location and density of the solution on different time layers. The reproducing kernel method has higher solution accuracy and stability in the solutions of the two-dimensional cardiac tissue model.

Soliton and periodic solutions for time-dependent coefficient non-linear equation

NASA Astrophysics Data System (ADS)

Guner, Ozkan

2016-01-01

In this article, we establish exact solutions for the generalized (3+1)-dimensional variable coefficient Kadomtsev-Petviashvili (GVCKP) equation. Using solitary wave ansatz in terms of ? functions and the modified sine-cosine method, we find exact analytical bright soliton solutions and exact periodic solutions for the considered model. The physical parameters in the soliton solutions are obtained as function of the dependent model coefficients. The effectiveness and reliability of the method are shown by its application to the GVCKP equation.

Primordial cosmology in mimetic born-infeld gravity

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

Bouhmadi-Lopez, Mariam; Chen, Che -Yu; Chen, Pisin

Here, the Eddington-inspired-Born-Infeld (EiBI) model is reformulated within the mimetic approach. In the presence of a mimetic field, the model contains non-trivial vacuum solutions which could be free of spacetime singularity because of the Born-Infeld nature of the theory. We study a realistic primordial vacuum universe and prove the existence of regular solutions, such as primordial inflationary solutions of de Sitter type or bouncing solutions. Besides, the linear instabilities present in the EiBI model are found to be avoidable for some interesting bouncing solutions in which the physical metric as well as the auxiliary metric are regular at the backgroundmore » level.« less

Primordial cosmology in mimetic born-infeld gravity

DOE PAGES

Bouhmadi-Lopez, Mariam; Chen, Che -Yu; Chen, Pisin

2017-11-29

Here, the Eddington-inspired-Born-Infeld (EiBI) model is reformulated within the mimetic approach. In the presence of a mimetic field, the model contains non-trivial vacuum solutions which could be free of spacetime singularity because of the Born-Infeld nature of the theory. We study a realistic primordial vacuum universe and prove the existence of regular solutions, such as primordial inflationary solutions of de Sitter type or bouncing solutions. Besides, the linear instabilities present in the EiBI model are found to be avoidable for some interesting bouncing solutions in which the physical metric as well as the auxiliary metric are regular at the backgroundmore » level.« less

High Fidelity Modeling of Field-Reversed Configuration (FRC) Thrusters (Briefing Charts)

DTIC Science & Technology

2017-05-24

Converged Math → Irrelevant Solutions? Validation: Fluids Example Stoke’s Flow MARTIN, SOUSA, TRAN (AFRL/RQRS) DISTRIBUTION A - APPROVED FOR PUBLIC RELEASE...Convergence Tests Converged Math → Irrelevant Solutions? Must be Aware of Valid Assumption Regions Validation: Fluids Example Stoke’s Flow Potential...AND VALIDATION Verification: Asymptotic Models → Analytical Solutions Yields Exact Convergence Tests Converged Math → Irrelevant Solutions? Must be

Plasticity solutions for soil behaviour around contracting cavities and tunnels

NASA Astrophysics Data System (ADS)

Yu, H. S.; Rowe, R. K.

1999-10-01

The action of tunnel excavation reduces the in-situ stresses along the excavated circumference and can therefore be simulated by unloading of cavities from the in-situ stress state. Increasing evidence suggests that soil behavior in the plane perpendicular to the tunnel axis can be modelled reasonably by a contracting cylindrical cavity, while movements ahead of an advancing tunnel heading can be better predicted by spherical cavity contraction theory. In the past, solutions for unloading of cavities from in-situ stresses in cohesive-frictional soils have mainly concentrated on the small strain, cylindrical cavity model. Large strain spherical cavity contraction solutions with a non-associated Mohr-Coulomb model do not seem to be widely available for tunnel applications. Also, cavity unloading solutions in undrained clays have been developed only in terms of total stresses with a linear elastic-perfectly plastic soil model. The total stress analyses do not account for the effects of strain hardening/softening, variable soil stiffness, and soil stress history (OCR). The effect of these simplifying assumptions on the predicted soil behavior around tunnels is not known.In this paper, analytical and semi-analytical solutions are presented for unloading of both cylindrical and spherical cavities from in-situ state of stresses under both drained and undrained conditions. The non-associated Mohr-Coulomb model and various critical state theories are used respectively to describe the drained and undrained stress-strain behaviors of the soils. The analytical solutions presented in this paper are developed in terms of large strain formulations. These solutions can be used to serve two main purposes: (1) to provide models for predicting soil behavior around tunnels; (2) to provide valuable benchmark solutions for verifying various numerical methods involving both Mohr-Coulomb and critical state plasticity models.

Can we model solute transfer in heterogeneous soils with MIM model?

NASA Astrophysics Data System (ADS)

Ben Slimene, Erij; Lassabatere, Laurent; Winiarski, Thierry; Gourdon, Remy

2017-04-01

The fate of pollutants in the vadose zone must be understood, in particular, underneath infiltration basins for an optimum management of these plants. Stormwaters carry pollutants (heavy metals, organics, emerging pollutant like nanoparticles, etc.) and thus constitute a risk for groundwater and soil quality. Most infiltration basins are settled over highly permeable soils that exhibit a strong lithological heterogeneity. The impact of such lithological heterogeneity on flow and solute transfer has already been questioned. Previous studies have already proved that lithological heterogeneity was prone to the establishment of preferential flows. In more details, the concomitance of several materials with contrasting hydraulic properties induces funneled flow at the interfaces between less permeable and more permeable lithofacies. Solutes are then carried by water fluxes quickly along preferential flow pathways and have restricted access to zones far from these pathways. It can clearly be imagined that such pattern could be modeled by a MIM model postulating water fraction into two fractions, one mobile and the other immobile, with solute transport by convection and dispersion in mobile water fraction and solute diffusion at the interface between mobile and immobile water fractions. The application of MIM approach to the case of solute transport in strongly heterogeneous soils may be quite advantageous: simplification of the problem, fewer parameters, ease of modeling, numerical computation, gain in computation time, etc. However, such consistency has never been investigated in details. In this paper, we focus on the possibility to model solute transport in a strongly heterogeneous deposit using MIM model. The deposit has been the subject of intensive campaigns of characterization of its lithology and the hydraulic and hydrodispersive properties of its lithofacies. Numerical computations were performed for a section of deposit 13.5 m wide and 2.5 m deep. Numerical results clearly showed the establishment of preferential flows with funneling mostly under unsaturated conditions. Solute elution at 2.5 m depth was characterized and discussed as a function of solute reactivity. Solutes breakthrough curves show clear evidence of MIM like pattern. In this paper, we clearly demonstrate that MIM model accurately reproduces solute elution at 2.5m depths but also at different depths. MIM approach accuracy is ensured provided that related parameters are optimized as a function of depth, hydric and hydraulic conditions and the contrast in hydraulic parameters of the lithofacies that constitute the deposit.

Stability of the Einstein static universe in open cosmological models

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

Canonico, Rosangela; Parisi, Luca; INFN, Sezione di Napoli, GC di Salerno, Via Ponte Don Melillo, I-84081 Baronissi

2010-09-15

The stability properties of the Einstein static solution of general relativity are altered when corrective terms arising from modification of the underlying gravitational theory appear in the cosmological equations. In this paper the existence and stability of static solutions are considered in the framework of two recently proposed quantum gravity models. The previously known analysis of the Einstein static solutions in the semiclassical regime of loop quantum cosmology with modifications to the gravitational sector is extended to open cosmological models where a static neutrally stable solution is found. A similar analysis is also performed in the framework of Horava-Lifshitz gravitymore » under detailed balance and projectability conditions. In the case of open cosmological models the two solutions found can be either unstable or neutrally stable according to the admitted values of the parameters.« less

Stability of the lepton bag model based on the Kerr–Newman solution

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

Burinskii, A., E-mail: bur@ibrae.ac.ru

2015-11-15

We show that the lepton bag model considered in our previous paper [10], generating the external gravitational and electromagnetic fields of the Kerr–Newman (KN) solution, is supersymmetric and represents a BPS-saturated soliton interpolating between the internal vacuum state and the external KN solution. We obtain Bogomolnyi equations for this phase transition and show that the Bogomolnyi bound determines all important features of this bag model, including its stable shape. In particular, for the stationary KN solution, the BPS bound provides stability of the ellipsoidal form of the bag and the formation of the ring–string structure at its border, while formore » the periodic electromagnetic excitations of the KN solution, the BPS bound controls the deformation of the surface of the bag, reproducing the known flexibility of bag models.« less

On the Possibilities of Predicting Geomagnetic Secular Variation with Geodynamo Modeling

NASA Technical Reports Server (NTRS)

Kuang, Wei-Jia; Tangborn, Andrew; Sabaka, Terrance

2004-01-01

We use our MoSST core dynamics model and geomagnetic field at the core-mantle boundary (CMB) continued downward from surface observations to investigate possibilities of geomagnetic data assimilation, so that model results and current geomagnetic observations can be used to predict geomagnetic secular variation in future. As the first attempt, we apply data insertion technique to examine evolution of the model solution that is modified by geomagnetic input. Our study demonstrate that, with a single data insertion, large-scale poloidal magnetic field obtained from subsequent numerical simulation evolves similarly to the observed geomagnetic variation, regardless of the initial choice of the model solution (so long it is a well developed numerical solution). The model solution diverges on the time scales on the order of 60 years, similar to the time scales of the torsional oscillations in the Earth's core. Our numerical test shows that geomagnetic data assimilation is promising with our MoSST model.

Unsteady free convection flow of viscous fluids with analytical results by employing time-fractional Caputo-Fabrizio derivative (without singular kernel)

NASA Astrophysics Data System (ADS)

Ali Shah, Nehad; Mahsud, Yasir; Ali Zafar, Azhar

2017-10-01

This article introduces a theoretical study for unsteady free convection flow of an incompressible viscous fluid. The fluid flows near an isothermal vertical plate. The plate has a translational motion with time-dependent velocity. The equations governing the fluid flow are expressed in fractional differential equations by using a newly defined time-fractional Caputo-Fabrizio derivative without singular kernel. Explicit solutions for velocity, temperature and solute concentration are obtained by applying the Laplace transform technique. As the fractional parameter approaches to one, solutions for the ordinary fluid model are extracted from the general solutions of the fractional model. The results showed that, for the fractional model, the obtained solutions for velocity, temperature and concentration exhibit stationary jumps discontinuity across the plane at t=0 , while the solutions are continuous functions in the case of the ordinary model. Finally, numerical results for flow features at small-time are illustrated through graphs for various pertinent parameters.

Co-existence and switching between fast and Ω-slow wind solutions in rapidly rotating massive stars

NASA Astrophysics Data System (ADS)

Araya, I.; Curé, M.; ud-Doula, A.; Santillán, A.; Cidale, L.

2018-06-01

Most radiation-driven winds of massive stars can be modelled with m-CAK theory, resulting in the so-called fast solution. However, the most rapidly rotating stars among them, especially when the rotational speed is higher than {˜ } 75 per cent of the critical rotational speed, can adopt a different solution, the so-called Ω-slow solution, characterized by a dense and slow wind. Here, we study the transition region of the solutions where the fast solution changes to the Ω-slow solution. Using both time-steady and time-dependent numerical codes, we study this transition region for various equatorial models of B-type stars. In all cases, in a certain range of rotational speeds we find a region where the fast and the Ω-slow solution can co-exist. We find that the type of solution obtained in this co-existence region depends stongly on the initial conditions of our models. We also test the stability of the solutions within the co-existence region by performing base-density perturbations in the wind. We find that under certain conditions, the fast solution can switch to the Ω-slow solution, or vice versa. Such solution-switching may be a possible contributor of material injected into the circumstellar environment of Be stars, without requiring rotational speeds near critical values.

Application of an interactive water simulation model in urban water management: a case study in Amsterdam.

PubMed

Leskens, J G; Brugnach, M; Hoekstra, A Y

2014-01-01

Water simulation models are available to support decision-makers in urban water management. To use current water simulation models, special expertise is required. Therefore, model information is prepared prior to work sessions, in which decision-makers weigh different solutions. However, this model information quickly becomes outdated when new suggestions for solutions arise and are therefore limited in use. We suggest that new model techniques, i.e. fast and flexible computation algorithms and realistic visualizations, allow this problem to be solved by using simulation models during work sessions. A new Interactive Water Simulation Model was applied for two case study areas in Amsterdam and was used in two workshops. In these workshops, the Interactive Water Simulation Model was positively received. It included non-specialist participants in the process of suggesting and selecting possible solutions and made them part of the accompanying discussions and negotiations. It also provided the opportunity to evaluate and enhance possible solutions more often within the time horizon of a decision-making process. Several preconditions proved to be important for successfully applying the Interactive Water Simulation Model, such as the willingness of the stakeholders to participate and the preparation of different general main solutions that can be used for further iterations during a work session.

Novel features of the nonlinear model arising in nano-ionic currents throughout microtubules

NASA Astrophysics Data System (ADS)

Celik, E.; Bulut, H.; Baskonus, H. M.

2018-05-01

In this manuscript, the modified exp (- Ω (ξ )) -expansion function method is implemented to find the new solutions to the nonlinear differential equation being the transmission line model. We obtain some new solutions to this model such as complex, exponential, trigonometric and hyperbolic functions. We plot the two- and three-dimensional surfaces of each solutions obtained in this manuscript.

Collaborative modelling: the future of computational neuroscience?

PubMed

Davison, Andrew P

2012-01-01

Given the complexity of biological neural circuits and of their component cells and synapses, building and simulating robust, well-validated, detailed models increasingly surpasses the resources of an individual researcher or small research group. In this article, I will briefly review possible solutions to this problem, argue for open, collaborative modelling as the optimal solution for advancing neuroscience knowledge, and identify potential bottlenecks and possible solutions.

Reflection matrices with U q [osp(2) (2|2m)] symmetry

NASA Astrophysics Data System (ADS)

Vieira, R. S.; Lima-Santos, A.

2017-09-01

We propose a classification of the reflection K-matrices (solutions of the boundary Yang-Baxter equation) for the Uq[osp(2)(2\\vert 2m)]=Uq[C(2)(m+1)] vertex-model. We found four families of solutions, namely, the complete solutions, in which no elements of the reflection K-matrix is null, the block-diagonal solutions, the X-shape solutions and the diagonal solutions. We highlight that these diagonal K-matrices also hold for the Uq[osp(2)(2n+2\\vert 2m)]=Uq[D(2)(n+1, m)] vertex-model.

Asymptotic traveling wave solution for a credit rating migration problem

NASA Astrophysics Data System (ADS)

Liang, Jin; Wu, Yuan; Hu, Bei

2016-07-01

In this paper, an asymptotic traveling wave solution of a free boundary model for pricing a corporate bond with credit rating migration risk is studied. This is the first study to associate the asymptotic traveling wave solution to the credit rating migration problem. The pricing problem with credit rating migration risk is modeled by a free boundary problem. The existence, uniqueness and regularity of the solution are obtained. Under some condition, we proved that the solution of our credit rating problem is convergent to a traveling wave solution, which has an explicit form. Furthermore, numerical examples are presented.

A new frequency domain analytical solution of a cascade of diffusive channels for flood routing

NASA Astrophysics Data System (ADS)

Cimorelli, Luigi; Cozzolino, Luca; Della Morte, Renata; Pianese, Domenico; Singh, Vijay P.

2015-04-01

Simplified flood propagation models are often employed in practical applications for hydraulic and hydrologic analyses. In this paper, we present a new numerical method for the solution of the Linear Parabolic Approximation (LPA) of the De Saint Venant equations (DSVEs), accounting for the space variation of model parameters and the imposition of appropriate downstream boundary conditions. The new model is based on the analytical solution of a cascade of linear diffusive channels in the Laplace Transform domain. The time domain solutions are obtained using a Fourier series approximation of the Laplace Inversion formula. The new Inverse Laplace Transform Diffusive Flood Routing model (ILTDFR) can be used as a building block for the construction of real-time flood forecasting models or in optimization models, because it is unconditionally stable and allows fast and fairly precise computation.

Further comments on sensitivities, parameter estimation, and sampling design in one-dimensional analysis of solute transport in porous media

USGS Publications Warehouse

Knopman, Debra S.; Voss, Clifford I.

1988-01-01

Sensitivities of solute concentration to parameters associated with first-order chemical decay, boundary conditions, initial conditions, and multilayer transport are examined in one-dimensional analytical models of transient solute transport in porous media. A sensitivity is a change in solute concentration resulting from a change in a model parameter. Sensitivity analysis is important because minimum information required in regression on chemical data for the estimation of model parameters by regression is expressed in terms of sensitivities. Nonlinear regression models of solute transport were tested on sets of noiseless observations from known models that exceeded the minimum sensitivity information requirements. Results demonstrate that the regression models consistently converged to the correct parameters when the initial sets of parameter values substantially deviated from the correct parameters. On the basis of the sensitivity analysis, several statements may be made about design of sampling for parameter estimation for the models examined: (1) estimation of parameters associated with solute transport in the individual layers of a multilayer system is possible even when solute concentrations in the individual layers are mixed in an observation well; (2) when estimating parameters in a decaying upstream boundary condition, observations are best made late in the passage of the front near a time chosen by adding the inverse of an hypothesized value of the source decay parameter to the estimated mean travel time at a given downstream location; (3) estimation of a first-order chemical decay parameter requires observations to be made late in the passage of the front, preferably near a location corresponding to a travel time of √2 times the half-life of the solute; and (4) estimation of a parameter relating to spatial variability in an initial condition requires observations to be made early in time relative to passage of the solute front.

Preliminary numerical analysis of improved gas chromatograph model

NASA Technical Reports Server (NTRS)

Woodrow, P. T.

1973-01-01

A mathematical model for the gas chromatograph was developed which incorporates the heretofore neglected transport mechanisms of intraparticle diffusion and rates of adsorption. Because a closed-form analytical solution to the model does not appear realizable, techniques for the numerical solution of the model equations are being investigated. Criteria were developed for using a finite terminal boundary condition in place of an infinite boundary condition used in analytical solution techniques. The class of weighted residual methods known as orthogonal collocation is presently being investigated and appears promising.

Modeling Hofmeister Effects

PubMed Central

Hribar-Lee, Barbara; Vlachy, Vojko; Dill, Ken A.

2009-01-01

A two dimensional model of water, so-called Mercedes-Benz model, was used to study effects of the size of hydrophobic solute on the insertion thermodynamics in electrolyte solutions. The model was examined by the constant pressure Monte Carlo computer simulation. The results were compared with the experimental data for noble gasses and methane in water and electrolyte solution. The influence of different ions at infinite dilution on the free energy of transfer was explored. Qualitative agreement with the experimental results was obtained. The mechanism of Hofmeister effects was proposed. PMID:20161468

Modeling Hofmeister Effects.

PubMed

Hribar-Lee, Barbara; Vlachy, Vojko; Dill, Ken A

2009-03-11

A two dimensional model of water, so-called Mercedes-Benz model, was used to study effects of the size of hydrophobic solute on the insertion thermodynamics in electrolyte solutions. The model was examined by the constant pressure Monte Carlo computer simulation. The results were compared with the experimental data for noble gasses and methane in water and electrolyte solution. The influence of different ions at infinite dilution on the free energy of transfer was explored. Qualitative agreement with the experimental results was obtained. The mechanism of Hofmeister effects was proposed.

Analysis of models for two solution crystal growth problems

NASA Technical Reports Server (NTRS)

Fehribach, Joseph D.; Rosenberger, Franz

1989-01-01

Two diffusive solution crystal growth models are considered which are characterized by two phases separated by an interface, a lack of convective mixing in either phase, and the presence of diffusion components differing widely in diffusivity. The first model describes precipitant-driven solution crystal growth and the second model describes a hanging drop evaporation problem. It is shown that for certain proteins sharp concentration gradients may develop in the drop during evaporation, while under the same conditions the concentrations of other proteins remain uniform.

Exact closed-form solutions of a fully nonlinear asymptotic two-fluid model

NASA Astrophysics Data System (ADS)

Cheviakov, Alexei F.

2018-05-01

A fully nonlinear model of Choi and Camassa (1999) describing one-dimensional incompressible dynamics of two non-mixing fluids in a horizontal channel, under a shallow water approximation, is considered. An equivalence transformation is presented, leading to a special dimensionless form of the system, involving a single dimensionless constant physical parameter, as opposed to five parameters present in the original model. A first-order dimensionless ordinary differential equation describing traveling wave solutions is analyzed. Several multi-parameter families of physically meaningful exact closed-form solutions of the two-fluid model are derived, corresponding to periodic, solitary, and kink-type bidirectional traveling waves; specific examples are given, and properties of the exact solutions are analyzed.

A potential model for sodium chloride solutions based on the TIP4P/2005 water model

NASA Astrophysics Data System (ADS)

Benavides, A. L.; Portillo, M. A.; Chamorro, V. C.; Espinosa, J. R.; Abascal, J. L. F.; Vega, C.

2017-09-01

Despite considerable efforts over more than two decades, our knowledge of the interactions in electrolyte solutions is not yet satisfactory. Not even one of the most simple and important aqueous solutions, NaCl(aq), escapes this assertion. A requisite for the development of a force field for any water solution is the availability of a good model for water. Despite the fact that TIP4P/2005 seems to fulfill the requirement, little work has been devoted to build a force field based on TIP4P/2005. In this work, we try to fill this gap for NaCl(aq). After unsuccessful attempts to produce accurate predictions for a wide range of properties using unity ionic charges, we decided to follow recent suggestions indicating that the charges should be scaled in the ionic solution. In this way, we have been able to develop a satisfactory non-polarizable force field for NaCl(aq). We evaluate a number of thermodynamic properties of the solution (equation of state, maximum in density, enthalpies of solution, activity coefficients, radial distribution functions, solubility, surface tension, diffusion coefficients, and viscosity). Overall the results for the solution are very good. An important achievement of our model is that it also accounts for the dynamical properties of the solution, a test for which the force fields so far proposed failed. The same is true for the solubility and for the maximum in density where the model describes the experimental results almost quantitatively. The price to pay is that the model is not so good at describing NaCl in the solid phase, although the results for several properties (density and melting temperature) are still acceptable. We conclude that the scaling of the charges improves the overall description of NaCl aqueous solutions when the polarization is not included.

Analytical solutions of the planar cyclic voltammetry process for two soluble species with equal diffusivities and fast electron transfer using the method of eigenfunction expansions

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

Samin, Adib; Lahti, Erik; Zhang, Jinsuo, E-mail: zhang.3558@osu.edu

Cyclic voltammetry is a powerful tool that is used for characterizing electrochemical processes. Models of cyclic voltammetry take into account the mass transport of species and the kinetics at the electrode surface. Analytical solutions of these models are not well-known due to the complexity of the boundary conditions. In this study we present closed form analytical solutions of the planar voltammetry model for two soluble species with fast electron transfer and equal diffusivities using the eigenfunction expansion method. Our solution methodology does not incorporate Laplace transforms and yields good agreement with the numerical solution. This solution method can be extendedmore » to cases that are more general and may be useful for benchmarking purposes.« less

Improved biochemical preservation of lung slices during cold storage.

PubMed

Bull, D A; Connors, R C; Reid, B B; Albanil, A; Stringham, J C; Karwande, S V

2000-05-15

Development of lung preservation solutions typically requires whole-organ models which are animal and labor intensive. These models rely on physiologic rather than biochemical endpoints, making accurate comparison of the relative efficacy of individual solution components difficult. We hypothesized that lung slices could be used to assess preservation of biochemical function during cold storage. Whole rat lungs were precision cut into slices with a thickness of 500 microm and preserved at 4 degrees C in the following solutions: University of Wisconsin (UW), Euro-Collins (EC), low-potassium-dextran (LPD), Kyoto (K), normal saline (NS), or a novel lung preservation solution (NPS) developed using this model. Lung biochemical function was assessed by ATP content (etamol ATP/mg wet wt) and capacity for protein synthesis (cpm/mg protein) immediately following slicing (0 h) and at 6, 12, 18, and 24 h of cold storage. Six slices were assayed at each time point for each solution. The data were analyzed using analysis of variance and are presented as means +/- SD. ATP content was significantly higher in the lung slices stored in NPS compared with all other solutions at each time point (P < 0.0001). Protein synthesis was significantly higher in the lung slices stored in NPS compared with all other solutions at 6, 12, and 18 h of preservation (P < 0.05). This lung slice model allows the rapid and efficient screening of lung preservation solutions and their components using quantifiable biochemical endpoints. Using this model, we have developed a novel solution that improves the biochemical preservation of lung slices during cold storage. Copyright 2000 Academic Press.

Mass transfer kinetics during osmotic dehydration of pomegranate arils.

PubMed

Mundada, Manoj; Hathan, Bahadur Singh; Maske, Swati

2011-01-01

The mass transfer kinetics during osmotic dehydration of pomegranate arils in osmotic solution of sucrose was studied to increase palatability and shelf life of arils. The freezing of the whole pomegranate at -18 °C was carried out prior to osmotic dehydration to increase the permeability of the outer cellular layer of the arils. The osmotic solution concentrations used were 40, 50, 60°Bx, osmotic solution temperatures were 35, 45, 55 °C. The fruit to solution ratio was kept 1:4 (w/w) during all the experiments and the process duration varied from 0 to 240 min. Azuara model and Peleg model were the best fitted as compared to other models for water loss and solute gain of pomegranate arils, respectively. Generalized Exponential Model had an excellent fit for water loss ratio and solute gain ratio of pomegranate arils. Effective moisture diffusivity of water as well as solute was estimated using the analytical solution of Fick's law of diffusion. For above conditions of osmotic dehydration, average effective diffusivity of water loss and solute gain varied from 2.718 × 10(-10) to 5.124 × 10(-10) m(2)/s and 1.471 × 10(-10) to 5.147 × 10(-10) m(2)/s, respectively. The final product was successfully utilized in some nutritional formulations such as ice cream and bakery products.

An isotherm-based thermodynamic model of multicomponent aqueous solutions, applicable over the entire concentration range.

PubMed

Dutcher, Cari S; Ge, Xinlei; Wexler, Anthony S; Clegg, Simon L

2013-04-18

In previous studies (Dutcher et al. J. Phys. Chem. C 2011, 115, 16474-16487; 2012, 116, 1850-1864), we derived equations for the Gibbs energy, solvent and solute activities, and solute concentrations in multicomponent liquid mixtures, based upon expressions for adsorption isotherms that include arbitrary numbers of hydration layers on each solute. In this work, the long-range electrostatic interactions that dominate in dilute solutions are added to the Gibbs energy expression, thus extending the range of concentrations for which the model can be used from pure liquid solute(s) to infinite dilution in the solvent, water. An equation for the conversion of the reference state for solute activity coefficients to infinite dilution in water has been derived. A number of simplifications are identified, notably the equivalence of the sorption site parameters r and the stoichiometric coefficients of the solutes, resulting in a reduction in the number of model parameters. Solute concentrations in mixtures conform to a modified Zdanovskii-Stokes-Robinson mixing rule, and solute activity coefficients to a modified McKay-Perring relation, when the effects of the long-range (Debye-Hückel) term in the equations are taken into account. Practical applications of the equations to osmotic and activity coefficients of pure aqueous electrolyte solutions and mixtures show both satisfactory accuracy from low to high concentrations, together with a thermodynamically reasonable extrapolation (beyond the range of measurements) to extreme concentration and to the pure liquid solute(s).

STABILITY OF A CYLINDRICAL SOLUTE-SOLVENT INTERFACE: EFFECT OF GEOMETRY, ELECTROSTATICS, AND HYDRODYNAMICS.

PubMed

Li, B O; Sun, Hui; Zhou, Shenggao

The solute-solvent interface that separates biological molecules from their surrounding aqueous solvent characterizes the conformation and dynamics of such molecules. In this work, we construct a solvent fluid dielectric boundary model for the solvation of charged molecules and apply it to study the stability of a model cylindrical solute-solvent interface. The motion of the solute-solvent interface is defined to be the same as that of solvent fluid at the interface. The solvent fluid is assumed to be incompressible and is described by the Stokes equation. The solute is modeled simply by the ideal-gas law. All the viscous force, hydrostatic pressure, solute-solvent van der Waals interaction, surface tension, and electrostatic force are balanced at the solute-solvent interface. We model the electrostatics by Poisson's equation in which the solute-solvent interface is treated as a dielectric boundary that separates the low-dielectric solute from the high-dielectric solvent. For a cylindrical geometry, we find multiple cylindrically shaped equilibrium interfaces that describe polymodal (e.g., dry and wet) states of hydration of an underlying molecular system. These steady-state solutions exhibit bifurcation behavior with respect to the charge density. For their linearized systems, we use the projection method to solve the fluid equation and find the dispersion relation. Our asymptotic analysis shows that, for large wavenumbers, the decay rate is proportional to wavenumber with the proportionality half of the ratio of surface tension to solvent viscosity, indicating that the solvent viscosity does affect the stability of a solute-solvent interface. Consequences of our analysis in the context of biomolecular interactions are discussed.

Robustness of the non-Markovian Alzheimer walk under stochastic perturbation

NASA Astrophysics Data System (ADS)

Cressoni, J. C.; da Silva, L. R.; Viswanathan, G. M.; da Silva, M. A. A.

2012-12-01

The elephant walk model originally proposed by Schütz and Trimper to investigate non-Markovian processes led to the investigation of a series of other random-walk models. Of these, the best known is the Alzheimer walk model, because it was the first model shown to have amnestically induced persistence —i.e. superdiffusion caused by loss of memory. Here we study the robustness of the Alzheimer walk by adding a memoryless stochastic perturbation. Surprisingly, the solution of the perturbed model can be formally reduced to the solutions of the unperturbed model. Specifically, we give an exact solution of the perturbed model by finding a surjective mapping to the unperturbed model.

Multimodal solutions for large scale evacuations.

DOT National Transportation Integrated Search

2009-12-30

In this research, a multimodal transportation model was developed attending the needs of emergency situations, : and the solutions provided by the model could be used to moderate congestion during such events. : The model incorporated features such a...

Deep Learning Fluid Mechanics

NASA Astrophysics Data System (ADS)

Barati Farimani, Amir; Gomes, Joseph; Pande, Vijay

2017-11-01

We have developed a new data-driven model paradigm for the rapid inference and solution of the constitutive equations of fluid mechanic by deep learning models. Using generative adversarial networks (GAN), we train models for the direct generation of solutions to steady state heat conduction and incompressible fluid flow without knowledge of the underlying governing equations. Rather than using artificial neural networks to approximate the solution of the constitutive equations, GANs can directly generate the solutions to these equations conditional upon an arbitrary set of boundary conditions. Both models predict temperature, velocity and pressure fields with great test accuracy (>99.5%). The application of our framework for inferring and generating the solutions of partial differential equations can be applied to any physical phenomena and can be used to learn directly from experiments where the underlying physical model is complex or unknown. We also have shown that our framework can be used to couple multiple physics simultaneously, making it amenable to tackle multi-physics problems.

Mathematical Model Formulation And Validation Of Water And Solute Transport In Whole Hamster Pancreatic Islets

PubMed Central

Benson, Charles T.; Critser, John K.

2014-01-01

Optimization of cryopreservation protocols for cells and tissues requires accurate models of heat and mass transport. Model selection often depends on the configuration of the tissue. Here, a mathematical and conceptual model of water and solute transport for whole hamster pancreatic islets has been developed and experimentally validated incorporating fundamental biophysical data from previous studies on individual hamster islet cells while retaining whole-islet structural information. It describes coupled transport of water and solutes through the islet by three methods: intracellularly, intercellularly, and in combination. In particular we use domain decomposition techniques to couple a transmembrane flux model with an interstitial mass transfer model. The only significant undetermined variable is the cellular surface area which is in contact with the intercellularly transported solutes, Ais. The model was validated and Ais determined using a 3 × 3 factorial experimental design blocked for experimental day. Whole islet physical experiments were compared with model predictions at three temperatures, three perfusing solutions, and three islet size groups. A mean of 4.4 islets were compared at each of the 27 experimental conditions and found to correlate with a coefficient of determination of 0.87 ± 0.06 (mean ± S.D.). Only the treatment variable of perfusing solution was found to be significant (p < 0.05). We have devised a model that retains much of the intrinsic geometric configuration of the system, and thus fewer laboratory experiments are needed to determine model parameters and thus to develop new optimized cryopreservation protocols. Additionally, extensions to ovarian follicles and other concentric tissue structures may be made. PMID:24950195

Applications of Analytical Self-Similar Solutions of Reynolds-Averaged Models for Instability-Induced Turbulent Mixing

NASA Astrophysics Data System (ADS)

Hartland, Tucker; Schilling, Oleg

2017-11-01

Analytical self-similar solutions to several families of single- and two-scale, eddy viscosity and Reynolds stress turbulence models are presented for Rayleigh-Taylor, Richtmyer-Meshkov, and Kelvin-Helmholtz instability-induced turbulent mixing. The use of algebraic relationships between model coefficients and physical observables (e.g., experimental growth rates) following from the self-similar solutions to calibrate a member of a given family of turbulence models is shown. It is demonstrated numerically that the algebraic relations accurately predict the value and variation of physical outputs of a Reynolds-averaged simulation in flow regimes that are consistent with the simplifying assumptions used to derive the solutions. The use of experimental and numerical simulation data on Reynolds stress anisotropy ratios to calibrate a Reynolds stress model is briefly illustrated. The implications of the analytical solutions for future Reynolds-averaged modeling of hydrodynamic instability-induced mixing are briefly discussed. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Faraday Discussion 160 Introductory Lecture: Interpreting and Predicting Hofmeister Salt Ion and Solute Effects on Biopolymer and Model Processes Using the Solute Partitioning Model

PubMed Central

Record, M. Thomas; Guinn, Emily; Pegram, Laurel; Capp, Michael

2013-01-01

Understanding how Hofmeister salt ions and other solutes interact with proteins, nucleic acids, other biopolymers and water and thereby affect protein and nucleic acid processes as well as model processes (e.g solubility of model compounds) in aqueous solution is a longstanding goal of biophysical research. Empirical Hofmeister salt and solute “m-values” (derivatives of the observed standard free energy change for a model or biopolymer process with respect to solute or salt concentration m3) are equal to differences in chemical potential derivatives: m-value = Δ(dμ2/dm3) = Δμ23 which quantify the preferential interactions of the solute or salt with the surface of the biopolymer or model system (component 2) exposed or buried in the process. Using the SPM, we dissect μ23 values for interactions of a solute or Hofmeister salt with a set of model compounds displaying the key functional groups of biopolymers to obtain interaction potentials (called α-values) that quantify the interaction of the solute or salt per unit area of each functional group or type of surface. Interpreted using the SPM, these α-values provide quantitative information about both the hydration of functional groups and the competitive interaction of water and the solute or salt with functional groups. The analysis corroborates and quantifies previous proposals that the Hofmeister anion and cation series for biopolymer processes are determined by ion-specific, mostly unfavorable interactions with hydrocarbon surfaces; the balance between these unfavorable nonpolar interactions and often-favorable interactions of ions with polar functional groups determine the series null points. The placement of urea and glycine betaine (GB) at opposite ends of the corresponding series of nonelectrolytes results from the favorable interactions of urea, and unfavorable interactions of GB, with many (but not all) biopolymer functional groups. Interaction potentials and local-bulk partition coefficients quantifying the distribution of solutes (e.g. urea, glycine betaine) and Hofmeister salt ions in the vicinity of each functional group make good chemical sense when interpreted in terms of competitive noncovalent interactions. These interaction potentials allow solute and Hofmeister (noncoulombic) salt effects on protein and nucleic acid processes to be interpreted or predicted, and allow the use of solutes and salts as probes of interface formation and large-scale conformational changes in the steps of a biopolymer mechanism. PMID:23795491

A perturbation analysis of a mechanical model for stable spatial patterning in embryology

NASA Astrophysics Data System (ADS)

Bentil, D. E.; Murray, J. D.

1992-12-01

We investigate a mechanical cell-traction mechanism that generates stationary spatial patterns. A linear analysis highlights the model's potential for these heterogeneous solutions. We use multiple-scale perturbation techniques to study the evolution of these solutions and compare our solutions with numerical simulations of the model system. We discuss some potential biological applications among which are the formation of ridge patterns, dermatoglyphs, and wound healing.

An analytical model for flow induced by a constant-head pumping in a leaky unconfined aquifer system with considering unsaturated flow

NASA Astrophysics Data System (ADS)

Lin, Ye-Chen; Li, Ming-Hsu; Yeh, Hund-Der

2017-09-01

A new mathematical model is developed to describe the flow in response to a constant-head pumping (or constant-head test, CHT) in a leaky unconfined aquifer system of infinite lateral extent with considering unsaturated flow. The model consists of an unsaturated zone on the top, an unconfined aquifer in the middle, and a second aquifer (aquitard) at the bottom. The unsaturated flow is described by Richard's equation, and the flows in unconfined aquifer and second layer are governed by the groundwater flow equation. The well partially penetrates the unconfined aquifer with a constant head in the well due to CHT. The governing equations of the model are linearized by the perturbation method and Gardner's exponential model is adopted to describe the soil retention curves. The solution of the model for drawdown distribution is obtained by applying the methods of Laplace transform and Weber transform. Then the solution for the wellbore flowrate is derived from the drawdown solution with Darcy's law. The issue of the equivalence of normalized drawdown predicted by the present solution for constant-head pumping and Tartakovsky and Neuman's (2007) solution for constant-rate pumping is discussed. On the basis of the wellbore flowrate solution, the results of the sensitivity analysis indicate that the wellbore flowrate is very sensitive to the changes in the radial hydraulic conductivity and the thickness of the saturated zone. Moreover, the results predicted from the present wellbore flowrate solution indicate that this new solution can reduce to Chang's et al. (2010a) solution for homogenous aquifers when the dimensionless unsaturated exponent approaches 100. The unsaturated zone can be considered as infinite extent in the vertical direction if the thickness ratio of the unsaturated zone to the unconfined aquifer is equal to or greater than one. As for the leakage effect, it can be ignored when the vertical hydraulic conductivity ratio (i.e., the vertical hydraulic conductivity of the lower layer over that of the unconfined aquifer) is smaller than 0.1. The present solution is compared with the numerical solution from FEMWATER for validation and the results indicate good match between these two solutions. Finally, the present solution is applied to a set of field drawdown data obtained from a CHT for the estimation of hydrogeologic parameters.

Partition of nonionic organic compounds in aquatic systems

USGS Publications Warehouse

Smith, James A.; Witkowski, Patrick J.; Chiou, Cary T.

1988-01-01

In aqueous systems, the distribution of many nonionic organic solutes in soil-sediment, aquatic organisms, and dissolved organic matter can be explained in terms of a partition model. The nonionic organic solute is distributed between water and different organic phases that behave as bulk solvents. Factors such as polarity, composition, and molecular size of the solute and organic phase determine the relative importance of partition to the environmental distribution of the solute. This chapter reviews these factors in the context of a partition model and also examines several environmental applications of the partition model for surface- and ground-water systems.

Documentation and verification of VST2D; a model for simulating transient, Variably Saturated, coupled water-heat-solute Transport in heterogeneous, anisotropic 2-Dimensional, ground-water systems with variable fluid density

USGS Publications Warehouse

Friedel, Michael J.

2001-01-01

This report describes a model for simulating transient, Variably Saturated, coupled water-heatsolute Transport in heterogeneous, anisotropic, 2-Dimensional, ground-water systems with variable fluid density (VST2D). VST2D was developed to help understand the effects of natural and anthropogenic factors on quantity and quality of variably saturated ground-water systems. The model solves simultaneously for one or more dependent variables (pressure, temperature, and concentration) at nodes in a horizontal or vertical mesh using a quasi-linearized general minimum residual method. This approach enhances computational speed beyond the speed of a sequential approach. Heterogeneous and anisotropic conditions are implemented locally using individual element property descriptions. This implementation allows local principal directions to differ among elements and from the global solution domain coordinates. Boundary conditions can include time-varying pressure head (or moisture content), heat, and/or concentration; fluxes distributed along domain boundaries and/or at internal node points; and/or convective moisture, heat, and solute fluxes along the domain boundaries; and/or unit hydraulic gradient along domain boundaries. Other model features include temperature and concentration dependent density (liquid and vapor) and viscosity, sorption and/or decay of a solute, and capability to determine moisture content beyond residual to zero. These features are described in the documentation together with development of the governing equations, application of the finite-element formulation (using the Galerkin approach), solution procedure, mass and energy balance considerations, input requirements, and output options. The VST2D model was verified, and results included solutions for problems of water transport under isohaline and isothermal conditions, heat transport under isobaric and isohaline conditions, solute transport under isobaric and isothermal conditions, and coupled water-heat-solute transport. The first three problems considered in model verification were compared to either analytical or numerical solutions, whereas the coupled problem was compared to measured laboratory results for which no known analytic solutions or numerical models are available. The test results indicate the model is accurate and applicable for a wide range of conditions, including when water (liquid and vapor), heat (sensible and latent), and solute are coupled in ground-water systems. The cumulative residual errors for the coupled problem tested was less than 10-8 cubic centimeter per cubic centimeter, 10-5 moles per kilogram, and 102 calories per cubic meter for liquid water content, solute concentration and heat content, respectively. This model should be useful to hydrologists, engineers, and researchers interested in studying coupled processes associated with variably saturated transport in ground-water systems.

COUPLING OF CORONAL AND HELIOSPHERIC MAGNETOHYDRODYNAMIC MODELS: SOLUTION COMPARISONS AND VERIFICATION

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

Merkin, V. G.; Lionello, R.; Linker, J.

2016-11-01

Two well-established magnetohydrodynamic (MHD) codes are coupled to model the solar corona and the inner heliosphere. The corona is simulated using the MHD algorithm outside a sphere (MAS) model. The Lyon–Fedder–Mobarry (LFM) model is used in the heliosphere. The interface between the models is placed in a spherical shell above the critical point and allows both models to work in either a rotating or an inertial frame. Numerical tests are presented examining the coupled model solutions from 20 to 50 solar radii. The heliospheric simulations are run with both LFM and the MAS extension into the heliosphere, and use themore » same polytropic coronal MAS solutions as the inner boundary condition. The coronal simulations are performed for idealized magnetic configurations, with an out-of-equilibrium flux rope inserted into an axisymmetric background, with and without including the solar rotation. The temporal evolution at the inner boundary of the LFM and MAS solutions is shown to be nearly identical, as are the steady-state background solutions, prior to the insertion of the flux rope. However, after the coronal mass ejection has propagated through the significant portion of the simulation domain, the heliospheric solutions diverge. Additional simulations with different resolution are then performed and show that the MAS heliospheric solutions approach those of LFM when run with progressively higher resolution. Following these detailed tests, a more realistic simulation driven by the thermodynamic coronal MAS is presented, which includes solar rotation and an azimuthally asymmetric background and extends to the Earth’s orbit.« less

Intercomparison of 3D pore-scale flow and solute transport simulation methods

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

Yang, Xiaofan; Mehmani, Yashar; Perkins, William A.

2016-09-01

Multiple numerical approaches have been developed to simulate porous media fluid flow and solute transport at the pore scale. These include methods that 1) explicitly model the three-dimensional geometry of pore spaces and 2) those that conceptualize the pore space as a topologically consistent set of stylized pore bodies and pore throats. In previous work we validated a model of class 1, based on direct numerical simulation using computational fluid dynamics (CFD) codes, against magnetic resonance velocimetry (MRV) measurements of pore-scale velocities. Here we expand that validation to include additional models of class 1 based on the immersed-boundary method (IMB),more » lattice Boltzmann method (LBM), smoothed particle hydrodynamics (SPH), as well as a model of class 2 (a pore-network model or PNM). The PNM approach used in the current study was recently improved and demonstrated to accurately simulate solute transport in a two-dimensional experiment. While the PNM approach is computationally much less demanding than direct numerical simulation methods, the effect of conceptualizing complex three-dimensional pore geometries on solute transport in the manner of PNMs has not been fully determined. We apply all four approaches (CFD, LBM, SPH and PNM) to simulate pore-scale velocity distributions and nonreactive solute transport, and intercompare the model results with previously reported experimental observations. Experimental observations are limited to measured pore-scale velocities, so solute transport comparisons are made only among the various models. Comparisons are drawn both in terms of macroscopic variables (e.g., permeability, solute breakthrough curves) and microscopic variables (e.g., local velocities and concentrations).« less

An Investigation of Two Finite Element Modeling Solutions for Biomechanical Simulation Using a Case Study of a Mandibular Bone.

PubMed

Liu, Yun-Feng; Fan, Ying-Ying; Dong, Hui-Yue; Zhang, Jian-Xing

2017-12-01

The method used in biomechanical modeling for finite element method (FEM) analysis needs to deliver accurate results. There are currently two solutions used in FEM modeling for biomedical model of human bone from computerized tomography (CT) images: one is based on a triangular mesh and the other is based on the parametric surface model and is more popular in practice. The outline and modeling procedures for the two solutions are compared and analyzed. Using a mandibular bone as an example, several key modeling steps are then discussed in detail, and the FEM calculation was conducted. Numerical calculation results based on the models derived from the two methods, including stress, strain, and displacement, are compared and evaluated in relation to accuracy and validity. Moreover, a comprehensive comparison of the two solutions is listed. The parametric surface based method is more helpful when using powerful design tools in computer-aided design (CAD) software, but the triangular mesh based method is more robust and efficient.

The screening Horndeski cosmologies

NASA Astrophysics Data System (ADS)

Starobinsky, Alexei A.; Sushkov, Sergey V.; Volkov, Mikhail S.

2016-06-01

We present a systematic analysis of homogeneous and isotropic cosmologies in a particular Horndeski model with Galileon shift symmetry, containing also a Λ-term and a matter. The model, sometimes called Fab Five, admits a rich spectrum of solutions. Some of them describe the standard late time cosmological dynamic dominated by the Λ-term and matter, while at the early times the universe expands with a constant Hubble rate determined by the value of the scalar kinetic coupling. For other solutions the Λ-term and matter are screened at all times but there are nevertheless the early and late accelerating phases. The model also admits bounces, as well as peculiar solutions describing ``the emergence of time''. Most of these solutions contain ghosts in the scalar and tensor sectors. However, a careful analysis reveals three different branches of ghost-free solutions, all showing a late time acceleration phase. We analyse the dynamical stability of these solutions and find that all of them are stable in the future, since all their perturbations stay bounded at late times. However, they all turn out to be unstable in the past, as their perturbations grow violently when one approaches the initial spacetime singularity. We therefore conclude that the model has no viable solutions describing the whole of the cosmological history, although it may describe the current acceleration phase. We also check that the flat space solution is ghost-free in the model, but it may acquire ghost in more general versions of the Horndeski theory.

Analytical steady-state solutions for water-limited cropping systems using saline irrigation water

NASA Astrophysics Data System (ADS)

Skaggs, T. H.; Anderson, R. G.; Corwin, D. L.; Suarez, D. L.

2014-12-01

Due to the diminishing availability of good quality water for irrigation, it is increasingly important that irrigation and salinity management tools be able to target submaximal crop yields and support the use of marginal quality waters. In this work, we present a steady-state irrigated systems modeling framework that accounts for reduced plant water uptake due to root zone salinity. Two explicit, closed-form analytical solutions for the root zone solute concentration profile are obtained, corresponding to two alternative functional forms of the uptake reduction function. The solutions express a general relationship between irrigation water salinity, irrigation rate, crop salt tolerance, crop transpiration, and (using standard approximations) crop yield. Example applications are illustrated, including the calculation of irrigation requirements for obtaining targeted submaximal yields, and the generation of crop-water production functions for varying irrigation waters, irrigation rates, and crops. Model predictions are shown to be mostly consistent with existing models and available experimental data. Yet the new solutions possess advantages over available alternatives, including: (i) the solutions were derived from a complete physical-mathematical description of the system, rather than based on an ad hoc formulation; (ii) the analytical solutions are explicit and can be evaluated without iterative techniques; (iii) the solutions permit consideration of two common functional forms of salinity induced reductions in crop water uptake, rather than being tied to one particular representation; and (iv) the utilized modeling framework is compatible with leading transient-state numerical models.

Three-dimensional eddy current solution of a polyphase machine test model (abstract)

NASA Astrophysics Data System (ADS)

Pahner, Uwe; Belmans, Ronnie; Ostovic, Vlado

1994-05-01

This abstract describes a three-dimensional (3D) finite element solution of a test model that has been reported in the literature. The model is a basis for calculating the current redistribution effects in the end windings of turbogenerators. The aim of the study is to see whether the analytical results of the test model can be found using a general purpose finite element package, thus indicating that the finite element model is accurate enough to treat real end winding problems. The real end winding problems cannot be solved analytically, as the geometry is far too complicated. The model consists of a polyphase coil set, containing 44 individual coils. This set generates a two pole mmf distribution on a cylindrical surface. The rotating field causes eddy currents to flow in the inner massive and conducting rotor. In the analytical solution a perfect sinusoidal mmf distribution is put forward. The finite element model contains 85824 tetrahedra and 16451 nodes. A complex single scalar potential representation is used in the nonconducting parts. The computation time required was 3 h and 42 min. The flux plots show that the field distribution is acceptable. Furthermore, the induced currents are calculated and compared with the values found from the analytical solution. The distribution of the eddy currents is very close to the distribution of the analytical solution. The most important results are the losses, both local and global. The value of the overall losses is less than 2% away from those of the analytical solution. Also the local distribution of the losses is at any given point less than 7% away from the analytical solution. The deviations of the results are acceptable and are partially due to the fact that the sinusoidal mmf distribution was not modeled perfectly in the finite element method.

Random-Walk Model of Diffusion in Three Dimensions in Brain Extracellular Space: Comparison with Microfiberoptic Photobleaching Measurements

PubMed Central

Jin, Songwan; Zador, Zsolt; Verkman, A. S.

2008-01-01

Diffusion through the extracellular space (ECS) in brain is important in drug delivery, intercellular communication, and extracellular ionic buffering. The ECS comprises ∼20% of brain parenchymal volume and contains cell-cell gaps ∼50 nm. We developed a random-walk model to simulate macromolecule diffusion in brain ECS in three dimensions using realistic ECS dimensions. Model inputs included ECS volume fraction (α), cell size, cell-cell gap geometry, intercellular lake (expanded regions of brain ECS) dimensions, and molecular size of the diffusing solute. Model output was relative solute diffusion in water versus brain ECS (Do/D). Experimental Do/D for comparison with model predictions was measured using a microfiberoptic fluorescence photobleaching method involving stereotaxic insertion of a micron-size optical fiber into mouse brain. Do/D for the small solute calcein in different regions of brain was in the range 3.0–4.1, and increased with brain cell swelling after water intoxication. Do/D also increased with increasing size of the diffusing solute, particularly in deep brain nuclei. Simulations of measured Do/D using realistic α, cell size and cell-cell gap required the presence of intercellular lakes at multicell contact points, and the contact length of cell-cell gaps to be least 50-fold smaller than cell size. The model accurately predicted Do/D for different solute sizes. Also, the modeling showed unanticipated effects on Do/D of changing ECS and cell dimensions that implicated solute trapping by lakes. Our model establishes the geometric constraints to account quantitatively for the relatively modest slowing of solute and macromolecule diffusion in brain ECS. PMID:18469079

Random-walk model of diffusion in three dimensions in brain extracellular space: comparison with microfiberoptic photobleaching measurements.

PubMed

Jin, Songwan; Zador, Zsolt; Verkman, A S

2008-08-01

Diffusion through the extracellular space (ECS) in brain is important in drug delivery, intercellular communication, and extracellular ionic buffering. The ECS comprises approximately 20% of brain parenchymal volume and contains cell-cell gaps approximately 50 nm. We developed a random-walk model to simulate macromolecule diffusion in brain ECS in three dimensions using realistic ECS dimensions. Model inputs included ECS volume fraction (alpha), cell size, cell-cell gap geometry, intercellular lake (expanded regions of brain ECS) dimensions, and molecular size of the diffusing solute. Model output was relative solute diffusion in water versus brain ECS (D(o)/D). Experimental D(o)/D for comparison with model predictions was measured using a microfiberoptic fluorescence photobleaching method involving stereotaxic insertion of a micron-size optical fiber into mouse brain. D(o)/D for the small solute calcein in different regions of brain was in the range 3.0-4.1, and increased with brain cell swelling after water intoxication. D(o)/D also increased with increasing size of the diffusing solute, particularly in deep brain nuclei. Simulations of measured D(o)/D using realistic alpha, cell size and cell-cell gap required the presence of intercellular lakes at multicell contact points, and the contact length of cell-cell gaps to be least 50-fold smaller than cell size. The model accurately predicted D(o)/D for different solute sizes. Also, the modeling showed unanticipated effects on D(o)/D of changing ECS and cell dimensions that implicated solute trapping by lakes. Our model establishes the geometric constraints to account quantitatively for the relatively modest slowing of solute and macromolecule diffusion in brain ECS.

Numerical techniques for the solution of the compressible Navier-Stokes equations and implementation of turbulence models. [separated turbulent boundary layer flow problems

NASA Technical Reports Server (NTRS)

Baldwin, B. S.; Maccormack, R. W.; Deiwert, G. S.

1975-01-01

The time-splitting explicit numerical method of MacCormack is applied to separated turbulent boundary layer flow problems. Modifications of this basic method are developed to counter difficulties associated with complicated geometry and severe numerical resolution requirements of turbulence model equations. The accuracy of solutions is investigated by comparison with exact solutions for several simple cases. Procedures are developed for modifying the basic method to improve the accuracy. Numerical solutions of high-Reynolds-number separated flows over an airfoil and shock-separated flows over a flat plate are obtained. A simple mixing length model of turbulence is used for the transonic flow past an airfoil. A nonorthogonal mesh of arbitrary configuration facilitates the description of the flow field. For the simpler geometry associated with the flat plate, a rectangular mesh is used, and solutions are obtained based on a two-equation differential model of turbulence.

Observed changes in the Earth's dynamic oblateness from GRACE data and geophysical models.

PubMed

Sun, Y; Ditmar, P; Riva, R

A new methodology is proposed to estimate changes in the Earth's dynamic oblateness ([Formula: see text] or equivalently, [Formula: see text]) on a monthly basis. The algorithm uses monthly Gravity Recovery and Climate Experiment (GRACE) gravity solutions, an ocean bottom pressure model and a glacial isostatic adjustment (GIA) model. The resulting time series agree remarkably well with a solution based on satellite laser ranging (SLR) data. Seasonal variations of the obtained time series show little sensitivity to the choice of GRACE solutions. Reducing signal leakage in coastal areas when dealing with GRACE data and accounting for self-attraction and loading effects when dealing with water redistribution in the ocean is crucial in achieving close agreement with the SLR-based solution in terms of de-trended solutions. The obtained trend estimates, on the other hand, may be less accurate due to their dependence on the GIA models, which still carry large uncertainties.

The Effect of Nondeterministic Parameters on Shock-Associated Noise Prediction Modeling

NASA Technical Reports Server (NTRS)

Dahl, Milo D.; Khavaran, Abbas

2010-01-01

Engineering applications for aircraft noise prediction contain models for physical phenomenon that enable solutions to be computed quickly. These models contain parameters that have an uncertainty not accounted for in the solution. To include uncertainty in the solution, nondeterministic computational methods are applied. Using prediction models for supersonic jet broadband shock-associated noise, fixed model parameters are replaced by probability distributions to illustrate one of these methods. The results show the impact of using nondeterministic parameters both on estimating the model output uncertainty and on the model spectral level prediction. In addition, a global sensitivity analysis is used to determine the influence of the model parameters on the output, and to identify the parameters with the least influence on model output.

Performance of the SMD and SM8 models for predicting solvation free energy of neutral solutes in methanol, dimethyl sulfoxide and acetonitrile.

PubMed

Zanith, Caroline C; Pliego, Josefredo R

2015-03-01

The continuum solvation models SMD and SM8 were developed using 2,346 solvation free energy values for 318 neutral molecules in 91 solvents as reference. However, no solvation data of neutral solutes in methanol was used in the parametrization, while only few solvation free energy values of solutes in dimethyl sulfoxide and acetonitrile were used. In this report, we have tested the performance of the models for these important solvents. Taking data from literature, we have generated solvation free energy, enthalpy and entropy values for 37 solutes in methanol, 21 solutes in dimethyl sulfoxide and 19 solutes in acetonitrile. Both SMD and SM8 models have presented a good performance in methanol and acetonitrile, with mean unsigned error equal or less than 0.66 and 0.55 kcal mol(-1) in methanol and acetonitrile, respectively. However, the correlation is worse in dimethyl sulfoxide, where the SMD and SM8 methods present mean unsigned error of 1.02 and 0.95 kcal mol(-1), respectively. Our results point out the SMx family of models need be improved for dimethyl sulfoxide solvent.

Performance of the SMD and SM8 models for predicting solvation free energy of neutral solutes in methanol, dimethyl sulfoxide and acetonitrile

NASA Astrophysics Data System (ADS)

Zanith, Caroline C.; Pliego, Josefredo R.

2015-03-01

The continuum solvation models SMD and SM8 were developed using 2,346 solvation free energy values for 318 neutral molecules in 91 solvents as reference. However, no solvation data of neutral solutes in methanol was used in the parametrization, while only few solvation free energy values of solutes in dimethyl sulfoxide and acetonitrile were used. In this report, we have tested the performance of the models for these important solvents. Taking data from literature, we have generated solvation free energy, enthalpy and entropy values for 37 solutes in methanol, 21 solutes in dimethyl sulfoxide and 19 solutes in acetonitrile. Both SMD and SM8 models have presented a good performance in methanol and acetonitrile, with mean unsigned error equal or less than 0.66 and 0.55 kcal mol-1 in methanol and acetonitrile, respectively. However, the correlation is worse in dimethyl sulfoxide, where the SMD and SM8 methods present mean unsigned error of 1.02 and 0.95 kcal mol-1, respectively. Our results point out the SMx family of models need be improved for dimethyl sulfoxide solvent.

Diffuse sorption modeling.

PubMed

Pivovarov, Sergey

2009-04-01

This work presents a simple solution for the diffuse double layer model, applicable to calculation of surface speciation as well as to simulation of ionic adsorption within the diffuse layer of solution in arbitrary salt media. Based on Poisson-Boltzmann equation, the Gaines-Thomas selectivity coefficient for uni-bivalent exchange on clay, K(GT)(Me(2+)/M(+))=(Q(Me)(0.5)/Q(M)){M(+)}/{Me(2+)}(0.5), (Q is the equivalent fraction of cation in the exchange capacity, and {M(+)} and {Me(2+)} are the ionic activities in solution) may be calculated as [surface charge, mueq/m(2)]/0.61. The obtained solution of the Poisson-Boltzmann equation was applied to calculation of ionic exchange on clays and to simulation of the surface charge of ferrihydrite in 0.01-6 M NaCl solutions. In addition, a new model of acid-base properties was developed. This model is based on assumption that the net proton charge is not located on the mathematical surface plane but diffusely distributed within the subsurface layer of the lattice. It is shown that the obtained solution of the Poisson-Boltzmann equation makes such calculations possible, and that this approach is more efficient than the original diffuse double layer model.

Model of transient drug diffusion across cornea.

PubMed

Zhang, Wensheng; Prausnitz, Mark R; Edwards, Aurélie

2004-09-30

A mathematical model of solute transient diffusion across the cornea to the anterior chamber of the eye was developed for topical drug delivery. Solute bioavailability was predicted given solute molecular radius and octanol-to-water distribution coefficient (Phi), ocular membrane ultrastructural parameters, tear fluid hydrodynamics, as well as solute distribution volume (Vd) and clearance rate (Cla) in the anterior chamber. The results suggest that drug bioavailability is primarily determined by solute lipophilicity. In human eyes, bioavailability is predicted to range between 1% and 5% for lipophilic molecules (Phi>1), and to be less than 0.5% for hydrophilic molecules (Phi<0.01). The simulations indicate that the distribution coefficient that maximizes bioavailability is on the order of 10. It was also found that the maximum solute concentration in the anterior chamber (Cmax) and the time needed to reach Cmax significantly depend on Phi, Vd, and Cla. Consistent with experimental findings, model predictions suggest that drug bioavailability can be increased by lowering the conjunctival-to-corneal permeability ratio and reducing precorneal solute drainage. Because of its mechanistic basis, this model will be useful to predict drug transport kinetics and bioavailability for new compounds and in diseased eyes.

Generalization of the binary structural phase field crystal model

NASA Astrophysics Data System (ADS)

Smith, Nathan; Provatas, Nikolas

2017-10-01

Two improvements to the binary structural phase field crystal (XPFC) theory are presented. The first is an improvement to the phenomenology for modelling density-density correlation functions and the second extends the free energy of the mixing term in the binary XPFC model beyond ideal mixing to a regular solution model. These improvements are applied to study kinetics of precipitation from solution. We observe a two-step nucleation pathway similar to recent experimental work [N. D. Loh, S. Sen, M. Bosman, S. F. Tan, J. Zhong, C. A. Nijhuis, P. Král, P. Matsudaira, and U. Mirsaidov, Nat. Chem. 9, 77 (2017), 10.1038/nchem.2618; A. F. Wallace, L. O. Hedges, A. Fernandez-Martinez, P. Raiteri, J. D. Gale, G. A. Waychunas, S. Whitelam, J. F. Banfield, and J. J. De Yoreo, Science 341, 885 (2013), 10.1126/science.1230915] in which the liquid solution first decomposes into solute-poor and solute-rich regions, followed by precipitate nucleation of the solute-rich regions. Additionally, we find a phenomenon not previously described in the literature in which the growth of precipitates is accelerated in the presence of uncrystallized solute-rich liquid regions.

Model-assisted template extraction SRAF application to contact holes patterns in high-end flash memory device fabrication

NASA Astrophysics Data System (ADS)

Seoud, Ahmed; Kim, Juhwan; Ma, Yuansheng; Jayaram, Srividya; Hong, Le; Chae, Gyu-Yeol; Lee, Jeong-Woo; Park, Dae-Jin; Yune, Hyoung-Soon; Oh, Se-Young; Park, Chan-Ha

2018-03-01

Sub-resolution assist feature (SRAF) insertion techniques have been effectively used for a long time now to increase process latitude in the lithography patterning process. Rule-based SRAF and model-based SRAF are complementary solutions, and each has its own benefits, depending on the objectives of applications and the criticality of the impact on manufacturing yield, efficiency, and productivity. Rule-based SRAF provides superior geometric output consistency and faster runtime performance, but the associated recipe development time can be of concern. Model-based SRAF provides better coverage for more complicated pattern structures in terms of shapes and sizes, with considerably less time required for recipe development, although consistency and performance may be impacted. In this paper, we introduce a new model-assisted template extraction (MATE) SRAF solution, which employs decision tree learning in a model-based solution to provide the benefits of both rule-based and model-based SRAF insertion approaches. The MATE solution is designed to automate the creation of rules/templates for SRAF insertion, and is based on the SRAF placement predicted by model-based solutions. The MATE SRAF recipe provides optimum lithographic quality in relation to various manufacturing aspects in a very short time, compared to traditional methods of rule optimization. Experiments were done using memory device pattern layouts to compare the MATE solution to existing model-based SRAF and pixelated SRAF approaches, based on lithographic process window quality, runtime performance, and geometric output consistency.

Multimodal Solutions for Large Scale Evacuation

DOT National Transportation Integrated Search

2009-12-30

In this research, a multimodal transportation model was developed attending the needs of emergency situations, and the solutions provided by the model could be used to moderate congestion during such events. The model incorporated features such as la...

[The Influence of Different Ionic Concentration in Cell Physiological Solution on Temperature Measurement by Near Infrared].

PubMed

Zheng, Yu; Chen, Xiong; Zhou, Mei; Wang, Meng-jun; Wang, Jin-hai; Li, Gang; Cui, Jun

2015-10-01

It is important to real-timely monitor and control the temperature of cell physiological solution in patch clamp experiments, which can eliminate the uncertainty due to temperature and improve the measurement accuracy. This paper studies the influence of different ions at different concentrations in the physiological solution on precision of a temperature model by using near infrared spectroscopy and chemometrics method. Firstly, we prepared twelve sample solutions respectively with the solutes of CaCl2, KCl and NaCl at four kinds of concentrations, and collected the spectra of different solutions at the setting temperature range 20-40 degrees C, the range of the spectra is 9 615-5 714 cm(-1). Then we divided the spectra of each solution at different temperatures into two parts (a training set and a prediction set) by three methods. Interval partial least squares method was used to select an effective wavelength range and develop calibration models between the spectra in the selected range and temperature velues. The experimental results show that RMSEP of CaCl2 solution with 0.25 g x mL(-1) is maximum, the result of the three tests are 0.386 3, 0.303 7 and 0.337 2 degrees C, RMSEP of NaCl with 0.005 g x mL(-1) solution is minimum, the result of the three tests are 0.220 8, 0.155 3 and 0.145 2 degrees C. The experimental results indicate that Ca2+ has the greatest influence on the accuracy of the temperature model of the cell physiological solution, then K+, and Na+ has the least influence. And with the ionic concentration increasing, the model accuracy decreases. Therefore; when we build the temperature model of cell physiological solution, it is necessary to change the proportion of the three kinds of main ions in cell physiological solution reasonably in order to correct the effects of different ionic concentrations in physiological solution and improve the accuracy of temperature measurements by near infrared spectroscopy.

Effect of Gravity Level on the Particle Shape and Size During Zeolite Crystal Growth

NASA Technical Reports Server (NTRS)

Song, Hong-Wei; Ilebusi, Olusegun J.; Sacco, Albert, Jr.

2003-01-01

A microscopic diffusion model is developed to represent solute transport in the boundary layer of a growing zeolite crystal. This model is used to describe the effect of gravity on particle shape and solute distribution. Particle dynamics and crystal growth kinetics serve as the boundary conditions of flow and convection-diffusion equations. A statistical rate theory is used to obtain the rate of solute transport across the growing interface, which is expressed in terms of concentration and velocity of solute species. Microgravity can significantly decrease the solute velocity across the growing interface compared to its earth-based counterpart. The extent of this reduction highly depends on solute diffusion constant in solution. Under gravity, the flow towards the crystal enhances solute transport rate across the growing interface while the flow away from crystals reduces this rate, suggesting a non-uniform growth rate and thus an elliptic final shape. However, microgravity can significantly reduce the influence of flow and obtain a final product with perfect spherical shape. The model predictions compare favorably with the data of space experiment of zeolites grown in space.

A model for the solution structure of the rod arrestin tetramer.

PubMed

Hanson, Susan M; Dawson, Eric S; Francis, Derek J; Van Eps, Ned; Klug, Candice S; Hubbell, Wayne L; Meiler, Jens; Gurevich, Vsevolod V

2008-06-01

Visual rod arrestin has the ability to self-associate at physiological concentrations. We previously demonstrated that only monomeric arrestin can bind the receptor and that the arrestin tetramer in solution differs from that in the crystal. We employed the Rosetta docking software to generate molecular models of the physiologically relevant solution tetramer based on the monomeric arrestin crystal structure. The resulting models were filtered using the Rosetta energy function, experimental intersubunit distances measured with DEER spectroscopy, and intersubunit contact sites identified by mutagenesis and site-directed spin labeling. This resulted in a unique model for subsequent evaluation. The validity of the model is strongly supported by model-directed crosslinking and targeted mutagenesis that yields arrestin variants deficient in self-association. The structure of the solution tetramer explains its inability to bind rhodopsin and paves the way for experimental studies of the physiological role of rod arrestin self-association.

3D Modeling of Transport Phenomena and the Injection of the Solution Droplets in the Solution Precursor Plasma Spraying

NASA Astrophysics Data System (ADS)

Shan, Yanguang; Coyle, Thomas W.; Mostaghimi, Javad

2007-12-01

Solution precursor plasma spraying has been used to produce finely structured ceramic coatings with nano- and sub-micrometric features. This process involves the injection of a solution spray of ceramic salts into a DC plasma jet under atmospheric condition. During the process, the solvent vaporizes as the droplet travel downstream. Solid particles are finally formed due to the precipitation of the solute, and the particle are heated up and accelerated to the substrate to generate the coating. This article describes a 3D model to simulate the transport phenomena and the trajectory and heating of the solution spray in the process. The jet-spray two-way interactions are considered. A simplified model is employed to simulate the evolution process and the formation of the solid particle from the solution droplet in the plasma jet. The temperature and velocity fields of the jet are obtained and validated. The particle size, velocity, temperature, and position distribution on the substrate are predicted.

Evaluation of strategies for nature-based solutions to drought: a decision support model at the national scale

NASA Astrophysics Data System (ADS)

Simpson, Mike; Ives, Matthew; Hall, Jim

2016-04-01

There is an increasing body of evidence in support of the use of nature based solutions as a strategy to mitigate drought. Restored or constructed wetlands, grasslands and in some cases forests have been used with success in numerous case studies. Such solutions remain underused in the UK, where they are not considered as part of long-term plans for supply by water companies. An important step is the translation of knowledge on the benefits of nature based solutions at the upland/catchment scale into a model of the impact of these solutions on national water resource planning in terms of financial costs, carbon benefits and robustness to drought. Our project, 'A National Scale Model of Green Infrastructure for Water Resources', addresses this issue through development of a model that can show the costs and benefits associated with a broad roll-out of nature based solutions for water supply. We have developed generalised models of both the hydrological effects of various classes and implementations of nature-based approaches and their economic impacts in terms of construction costs, running costs, time to maturity, land use and carbon benefits. Our next step will be to compare this work with our recent evaluation of conventional water infrastructure, allowing a case to be made in financial terms and in terms of security of water supply. By demonstrating the benefits of nature based solutions under multiple possible climate and population scenarios we aim to demonstrate the potential value of using nature based solutions as a component of future long-term water resource plans. Strategies for decision making regarding the selection of nature based and conventional approaches, developed through discussion with government and industry, will be applied to the final model. Our focus is on keeping our work relevant to the requirements of decision-makers involved in conventional water planning. We propose to present the outcomes of our model for the evaluation of nature-based solutions at catchment scale and ongoing results of our national-scale model.

Dependability and performability analysis

NASA Technical Reports Server (NTRS)

Trivedi, Kishor S.; Ciardo, Gianfranco; Malhotra, Manish; Sahner, Robin A.

1993-01-01

Several practical issues regarding specifications and solution of dependability and performability models are discussed. Model types with and without rewards are compared. Continuous-time Markov chains (CTMC's) are compared with (continuous-time) Markov reward models (MRM's) and generalized stochastic Petri nets (GSPN's) are compared with stochastic reward nets (SRN's). It is shown that reward-based models could lead to more concise model specifications and solution of a variety of new measures. With respect to the solution of dependability and performability models, three practical issues were identified: largeness, stiffness, and non-exponentiality, and a variety of approaches are discussed to deal with them, including some of the latest research efforts.

How accurate is automated gap filling of metabolic models?

PubMed

Karp, Peter D; Weaver, Daniel; Latendresse, Mario

2018-06-19

Reaction gap filling is a computational technique for proposing the addition of reactions to genome-scale metabolic models to permit those models to run correctly. Gap filling completes what are otherwise incomplete models that lack fully connected metabolic networks. The models are incomplete because they are derived from annotated genomes in which not all enzymes have been identified. Here we compare the results of applying an automated likelihood-based gap filler within the Pathway Tools software with the results of manually gap filling the same metabolic model. Both gap-filling exercises were applied to the same genome-derived qualitative metabolic reconstruction for Bifidobacterium longum subsp. longum JCM 1217, and to the same modeling conditions - anaerobic growth under four nutrients producing 53 biomass metabolites. The solution computed by the gap-filling program GenDev contained 12 reactions, but closer examination showed that solution was not minimal; two of the twelve reactions can be removed to yield a set of ten reactions that enable model growth. The manually curated solution contained 13 reactions, eight of which were shared with the 12-reaction computed solution. Thus, GenDev achieved recall of 61.5% and precision of 66.6%. These results suggest that although computational gap fillers are populating metabolic models with significant numbers of correct reactions, automatically gap-filled metabolic models also contain significant numbers of incorrect reactions. Our conclusion is that manual curation of gap-filler results is needed to obtain high-accuracy models. Many of the differences between the manual and automatic solutions resulted from using expert biological knowledge to direct the choice of reactions within the curated solution, such as reactions specific to the anaerobic lifestyle of B. longum.

The thermal stability of the nanograin structure in a weak solute segregation system.

PubMed

Tang, Fawei; Song, Xiaoyan; Wang, Haibin; Liu, Xuemei; Nie, Zuoren

2017-02-08

A hybrid model that combines first principles calculations and thermodynamic evaluation was developed to describe the thermal stability of a nanocrystalline solid solution with weak segregation. The dependence of the solute segregation behavior on the electronic structure, solute concentration, grain size and temperature was demonstrated, using the nanocrystalline Cu-Zn system as an example. The modeling results show that the segregation energy changes with the solute concentration in a form of nonmonotonic function. The change in the total Gibbs free energy indicates that at a constant solute concentration and a given temperature, a nanocrystalline structure can remain stable when the initial grain size is controlled in a critical range. In experiments, dense nanocrystalline Cu-Zn alloy bulk was prepared, and a series of annealing experiments were performed to examine the thermal stability of the nanograins. The experimental measurements confirmed the model predictions that with a certain solute concentration, a state of steady nanograin growth can be achieved at high temperatures when the initial grain size is controlled in a critical range. The present work proposes that in weak solute segregation systems, the nanograin structure can be kept thermally stable by adjusting the solute concentration and initial grain size.

A theoretical study of radar return and radiometric emission from the sea

NASA Technical Reports Server (NTRS)

Peake, W. H.

1972-01-01

The applicability of the various electromagnetic models of scattering from the ocean are reviewed. These models include the small perturbation method, the geometric optics solution, the composite model, and the exact integral equation solution. The restrictions on the electromagnetic models are discussed.

Eikonal solutions to optical model coupled-channel equations

NASA Technical Reports Server (NTRS)

Cucinotta, Francis A.; Khandelwal, Govind S.; Maung, Khin M.; Townsend, Lawrence W.; Wilson, John W.

1988-01-01

Methods of solution are presented for the Eikonal form of the nucleus-nucleus coupled-channel scattering amplitudes. Analytic solutions are obtained for the second-order optical potential for elastic scattering. A numerical comparison is made between the first and second order optical model solutions for elastic and inelastic scattering of H-1 and He-4 on C-12. The effects of bound-state excitations on total and reaction cross sections are also estimated.

Relativistic Modelling of Stable Anisotropic Super-Dense Star

NASA Astrophysics Data System (ADS)

Maurya, S. K.; Gupta, Y. K.; Jasim, M. K.

2015-08-01

In the present article we have obtained new set of exact solutions of Einstein field equations for anisotropic fluid spheres by using the Herrera et al. [1] algorithm. The anisotropic fluid solutions so obtained join continuously to the Schwarzschild exterior solution across the pressure-free boundary. It is observed that most of the new anisotropic solutions are well-behaved and are used to construct the super-dense star models such as neutron stars and pulsars.

The prediction of the flash point for binary aqueous-organic solutions.

PubMed

Liaw, Horng-Jang; Chiu, Yi-Yu

2003-07-18

A mathematical model, which may be used for predicting the flash point of aqueous-organic solutions, has been proposed and subsequently verified by experimentally-derived data. The results reveal that this model is able to precisely predict the flash point over the entire composition range of binary aqueous-organic solutions by way of utilizing the flash point data pertaining to the flammable component. The derivative of flash point with respect to composition (solution composition effect upon flash point) can be applied to process safety design/operation in order to identify as to whether the dilution of a flammable liquid solution with water is effective in reducing the fire and explosion hazard of the solution at a specified composition. Such a derivative equation was thus derived based upon the flash point prediction model referred to above and then verified by the application of experimentally-derived data.

Semianalytical Solution for the Deformation of an Elastic Layer under an Axisymmetrically Distributed Power-Form Load: Application to Fluid-Jet-Induced Indentation of Biological Soft Tissues.

PubMed

Lu, Minhua; Huang, Shuai; Yang, Xianglong; Yang, Lei; Mao, Rui

2017-01-01

Fluid-jet-based indentation is used as a noncontact excitation technique by systems measuring the mechanical properties of soft tissues. However, the application of these devices has been hindered by the lack of theoretical solutions. This study developed a mathematical model for testing the indentation induced by a fluid jet and determined a semianalytical solution. The soft tissue was modeled as an elastic layer bonded to a rigid base. The pressure of the fluid jet impinging on the soft tissue was assumed to have a power-form function. The semianalytical solution was verified in detail using finite-element modeling, with excellent agreement being achieved. The effects of several parameters on the solution behaviors are reported, and a method for applying the solution to determine the mechanical properties of soft tissues is suggested.

The steady state solutions of radiatively driven stellar winds for a non-Sobolev, pure absorption model

NASA Technical Reports Server (NTRS)

Poe, C. H.; Owocki, S. P.; Castor, J. I.

1990-01-01

The steady state solution topology for absorption line-driven flows is investigated for the condition that the Sobolev approximation is not used to compute the line force. The solution topology near the sonic point is of the nodal type with two positive slope solutions. The shallower of these slopes applies to reasonable lower boundary conditions and realistic ion thermal speed v(th) and to the Sobolev limit of zero of the usual Castor, Abbott, and Klein model. At finite v(th), this solution consists of a family of very similar solutions converging on the sonic point. It is concluded that a non-Sobolev, absorption line-driven flow with a realistic values of v(th) has no uniquely defined steady state. To the extent that a pure absorption model of the outflow of stellar winds is applicable, radiatively driven winds should be intrinsically variable.

Kinetic modeling of electro-Fenton reaction in aqueous solution.

PubMed

Liu, H; Li, X Z; Leng, Y J; Wang, C

2007-03-01

To well describe the electro-Fenton (E-Fenton) reaction in aqueous solution, a new kinetic model was established according to the generally accepted mechanism of E-Fenton reaction. The model has special consideration on the rates of hydrogen peroxide (H(2)O(2)) generation and consumption in the reaction solution. The model also embraces three key operating factors affecting the organic degradation in the E-Fenton reaction, including current density, dissolved oxygen concentration and initial ferrous ion concentration. This analytical model was then validated by the experiments of phenol degradation in aqueous solution. The experiments demonstrated that the H(2)O(2) gradually built up with time and eventually approached its maximum value in the reaction solution. The experiments also showed that phenol was degraded at a slow rate at the early stage of the reaction, a faster rate during the middle stage, and a slow rate again at the final stage. It was confirmed in all experiments that the curves of phenol degradation (concentration vs. time) appeared to be an inverted "S" shape. The experimental data were fitted using both the normal first-order model and our new model, respectively. The goodness of fittings demonstrated that the new model could better fit the experimental data than the first-order model appreciably, which indicates that this analytical model can better describe the kinetics of the E-Fenton reaction mathematically and also chemically.

Experimental validation of the influence of white matter anisotropy on the intracranial EEG forward solution.

PubMed

Bangera, Nitin B; Schomer, Donald L; Dehghani, Nima; Ulbert, Istvan; Cash, Sydney; Papavasiliou, Steve; Eisenberg, Solomon R; Dale, Anders M; Halgren, Eric

2010-12-01

Forward solutions with different levels of complexity are employed for localization of current generators, which are responsible for the electric and magnetic fields measured from the human brain. The influence of brain anisotropy on the forward solution is poorly understood. The goal of this study is to validate an anisotropic model for the intracranial electric forward solution by comparing with the directly measured 'gold standard'. Dipolar sources are created at known locations in the brain and intracranial electroencephalogram (EEG) is recorded simultaneously. Isotropic models with increasing level of complexity are generated along with anisotropic models based on Diffusion tensor imaging (DTI). A Finite Element Method based forward solution is calculated and validated using the measured data. Major findings are (1) An anisotropic model with a linear scaling between the eigenvalues of the electrical conductivity tensor and water self-diffusion tensor in brain tissue is validated. The greatest improvement was obtained when the stimulation site is close to a region of high anisotropy. The model with a global anisotropic ratio of 10:1 between the eigenvalues (parallel: tangential to the fiber direction) has the worst performance of all the anisotropic models. (2) Inclusion of cerebrospinal fluid as well as brain anisotropy in the forward model is necessary for an accurate description of the electric field inside the skull. The results indicate that an anisotropic model based on the DTI can be constructed non-invasively and shows an improved performance when compared to the isotropic models for the calculation of the intracranial EEG forward solution.

Salting-out effect in aqueous NaCl solutions: trends with size and polarity of solute molecules.

PubMed

Endo, Satoshi; Pfennigsdorff, Andrea; Goss, Kai-Uwe

2012-02-07

Salting-out in aqueous NaCl solutions is relevant for the environmental behavior of organic contaminants. In this study, Setschenow (or salting-out) coefficients (K(s) [M(-1)]) for 43 diverse neutral compounds in NaCl solutions were measured using a shared headspace passive dosing method and a negligible depletion solid phase microextraction technique. The results were used to calibrate and evaluate estimation models for K(s). The molar volume of the solute correlated only moderately with K(s) (R(2) = 0.49, SD = 0.052). The polyparameter linear free energy relationship (pp-LFER) model that uses five compound descriptors resulted in a more accurate fit to our data (R(2) = 0.83, SD = 0.031). The pp-LFER analysis revealed that Na(+) and Cl(-) in aqueous solutions increase the cavity formation energy cost and the polar interaction energies toward neutral organic solutes. Accordingly, the salting-out effect increases with the size and decreases with the polarity of the solute molecule. COSMO-RS, a quantum mechanics-based fully predictive model, generally overpredicted the experimental K(s), but the predicted values were moderately correlated with the experimental values (R(2) = 0.66, SD = 0.042). Literature data (n = 93) were predicted by the calibrated pp-LFER and COSMO-RS models with root mean squared errors of 0.047 and 0.050, respectively. This study offers prediction models to estimate K(s), allowing implementation of the salting-out effect in contaminant fate models, linkage of various partition coefficients (such as air-water, sediment-water, and extraction phase-water partition coefficients) measured for fresh water and seawater, and estimation of enhancement of extraction efficiency in analytical procedures.

Nonstatic radiating spheres in general relativity

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

Krori, K.D.; Borgohain, P.; Sarma, R.

1985-02-15

The method of Herrera, Jimenez, and Ruggeri of obtaining nonstatic solutions of Einstein's field equations to study the evolution of stellar bodies is applied to obtain two models of nonstatic radiating spheres from two well-known static solutions of field equations, viz., Tolman's solutions IV and V. Whereas Tolman's type-IV model is found to be contracting for the period under investigation, Tolman's type-V model shows a bounce after attaining a minimum radius.

Applications of Black Scholes Complexity Concepts to Combat Modelling

DTIC Science & Technology

2009-03-01

Lauren, G C McIntosh, N D Perry and J Moffat, Chaos 17, 2007. 4 Lanchester Models of Warfare Volumes 1 and 2, J G Taylor, Operations Research Society...transformation matrix A Lanchester Equation solution parameter bi Dependent model variables b(x,t) Variable variance rate B Lanchester Equation solution...distribution. The similarity between this equation and the Lanchester Equations (equation 1) is clear. This suggests an obvious solution to the question of

Cosmological reconstruction and stability in F(T,TG) gravity

NASA Astrophysics Data System (ADS)

Sharif, M.; Nazir, Kanwal

This study investigates the reconstruction scheme and stability of some well-known cosmological models in F(T,TG) gravity, where T and TG represent the torsion scalar and Gauss-Bonnet invariant torsion term, respectively. For this purpose, we consider isotropic homogeneous universe model and develop the corresponding field equations. It is found that we can reproduce cosmological evolution for power-law, de Sitter solutions, phantom/nonphantom era and Λ cold dark matter by applying reconstruction scheme in this gravity. Finally, we discuss stability of the reconstructed power-law and de Sitter solutions as well as two well-known F(T,TG) models. It is concluded that all these models provide stable solutions for suitable choices of the constants except power-law solutions.

Stochastic modeling of the migration of Cs-137 in the soil considering a power law tailing in space

NASA Astrophysics Data System (ADS)

Oka, Hiroki; Hatano, Yuko

2016-04-01

We develop a theoretical model to reproduce the measured data of Cs-137 in the soil due to the Fukushima Daiichi NPP accident. In our past study, we derived the analytic solution under the generalized Robin boundary condition (Oka-Yamamoto solution). This is a generalization of the He-Walling solution (1996). We compared our solution with the Fukushima soil data of for 3 years after the accident and found that the concentration of Cs-137 has a discrepancy from our solution, specifically in a deep part because the depth profiles have a power law tailing. Therefore, we improved our model in the following aspect. When Cs particle (or Cs solution) migrate in the soil, the diffusion coefficient should be the results of many processes in the soil. These processes include the effect of various materials which constitute the soil (clay, litter, sand), or the variations of pore size in the soil. Hence we regard the diffusion coefficient as the stochastic variable, we derive the model. Specifically, we consider the solution of ADE to be the conditional probability C(x,t|D) in terms of the diffusion coefficient D and calculate C(x,t)=∫_(0~∞) C(x,t|D)*f(D)*dD, where f(D) is the probability density function of D. This model has a power law tailing in space like the space-fractional ADE.

Combined structures-controls optimization of lattice trusses

NASA Technical Reports Server (NTRS)

Balakrishnan, A. V.

1991-01-01

The role that distributed parameter model can play in CSI is demonstrated, in particular in combined structures controls optimization problems of importance in preliminary design. Closed form solutions can be obtained for performance criteria such as rms attitude error, making possible analytical solutions of the optimization problem. This is in contrast to the need for numerical computer solution involving the inversion of large matrices in traditional finite element model (FEM) use. Another advantage of the analytic solution is that it can provide much needed insight into phenomena that can otherwise be obscured or difficult to discern from numerical computer results. As a compromise in level of complexity between a toy lab model and a real space structure, the lattice truss used in the EPS (Earth Pointing Satellite) was chosen. The optimization problem chosen is a generic one: of minimizing the structure mass subject to a specified stability margin and to a specified upper bond on the rms attitude error, using a co-located controller and sensors. Standard FEM treating each bar as a truss element is used, while the continuum model is anisotropic Timoshenko beam model. Performance criteria are derived for each model, except that for the distributed parameter model, explicit closed form solutions was obtained. Numerical results obtained by the two model show complete agreement.

Modeling solute clustering in the diffusion layer around a growing crystal.

PubMed

Shiau, Lie-Ding; Lu, Yung-Fang

2009-03-07

The mechanism of crystal growth from solution is often thought to consist of a mass transfer diffusion step followed by a surface reaction step. Solute molecules might form clusters in the diffusion step before incorporating into the crystal lattice. A model is proposed in this work to simulate the evolution of the cluster size distribution due to the simultaneous aggregation and breakage of solute molecules in the diffusion layer around a growing crystal in the stirred solution. The crystallization of KAl(SO(4))(2)12H(2)O from aqueous solution is studied to illustrate the effect of supersaturation and diffusion layer thickness on the number-average degree of clustering and the size distribution of solute clusters in the diffusion layer.

Temperature and solute-transport simulation in streamflow using a Lagrangian reference frame

USGS Publications Warehouse

Jobson, Harvey E.

1980-01-01

A computer program for simulating one-dimensional, unsteady temperature and solute transport in a river has been developed and documented for general use. The solution approach to the convective-diffusion equation uses a moving reference frame (Lagrangian) which greatly simplifies the mathematics of the solution procedure and dramatically reduces errors caused by numerical dispersion. The model documentation is presented as a series of four programs of increasing complexity. The conservative transport model can be used to route a single conservative substance. The simplified temperature model is used to predict water temperature in rivers when only temperature and windspeed data are available. The complete temperature model is highly accurate but requires rather complete meteorological data. Finally, the 10-parameter model can be used to route as many as 10 interacting constituents through a river reach. (USGS)

Time-reversibility and particle sedimentation

NASA Technical Reports Server (NTRS)

Golubitsky, Martin; Krupa, Martin; Lim, Chjan

1991-01-01

This paper studies an ODE model, called the Stokeslet model, and describes sedimentation of small clusters of particles in a highly viscous fluid. This model has a trivial solution in which the n particles arrange themselves at the vertices of a regular n-sided polygon. When n = 3, Hocking and Caflisch et al. (1988) proved the existence of periodic motion (in the frame moving with the center of gravity in the cluster) in which the particles form an isosceles triangle. Here, the study of periodic and quasi-periodic solutions of the Stokeslet model is continued, with emphasis on the spatial and time-reversal symmetry of the model. For three particles, the existence of a second family of periodic solutions and a family of quasi-periodic solutions is proved. It is also indicated how the methods generalize to the case of n particles.

Spikes and matter inhomogeneities in massless scalar field models

NASA Astrophysics Data System (ADS)

Coley, A. A.; Lim, W. C.

2016-01-01

We shall discuss the general relativistic generation of spikes in a massless scalar field or stiff perfect fluid model. We first investigate orthogonally transitive (OT) G 2 stiff fluid spike models both heuristically and numerically, and give a new exact OT G 2 stiff fluid spike solution. We then present a new two-parameter family of non-OT G 2 stiff fluid spike solutions, obtained by the generalization of non-OT G 2 vacuum spike solutions to the stiff fluid case by applying Geroch's transformation on a Jacobs seed. The dynamics of these new stiff fluid spike solutions is qualitatively different from that of the vacuum spike solutions in that the matter (stiff fluid) feels the spike directly and the stiff fluid spike solution can end up with a permanent spike. We then derive the evolution equations of non-OT G 2 stiff fluid models, including a second perfect fluid, in full generality, and briefly discuss some of their qualitative properties and their potential numerical analysis. Finally, we discuss how a fluid, and especially a stiff fluid or massless scalar field, affects the physics of the generation of spikes.

Estimating system parameters for solvent-water and plant cuticle-water using quantum chemically estimated Abraham solute parameters.

PubMed

Liang, Yuzhen; Torralba-Sanchez, Tifany L; Di Toro, Dominic M

2018-04-18

Polyparameter Linear Free Energy Relationships (pp-LFERs) using Abraham system parameters have many useful applications. However, developing the Abraham system parameters depends on the availability and quality of the Abraham solute parameters. Using Quantum Chemically estimated Abraham solute Parameters (QCAP) is shown to produce pp-LFERs that have lower root mean square errors (RMSEs) of predictions for solvent-water partition coefficients than parameters that are estimated using other presently available methods. pp-LFERs system parameters are estimated for solvent-water, plant cuticle-water systems, and for novel compounds using QCAP solute parameters and experimental partition coefficients. Refitting the system parameter improves the calculation accuracy and eliminates the bias. Refitted models for solvent-water partition coefficients using QCAP solute parameters give better results (RMSE = 0.278 to 0.506 log units for 24 systems) than those based on ABSOLV (0.326 to 0.618) and QSPR (0.294 to 0.700) solute parameters. For munition constituents and munition-like compounds not included in the calibration of the refitted model, QCAP solute parameters produce pp-LFER models with much lower RMSEs for solvent-water partition coefficients (RMSE = 0.734 and 0.664 for original and refitted model, respectively) than ABSOLV (4.46 and 5.98) and QSPR (2.838 and 2.723). Refitting plant cuticle-water pp-LFER including munition constituents using QCAP solute parameters also results in lower RMSE (RMSE = 0.386) than that using ABSOLV (0.778) and QSPR (0.512) solute parameters. Therefore, for fitting a model in situations for which experimental data exist and system parameters can be re-estimated, or for which system parameters do not exist and need to be developed, QCAP is the quantum chemical method of choice.

Improved biochemical preservation of heart slices during cold storage.

PubMed

Bull, D A; Reid, B B; Connors, R C; Albanil, A; Stringham, J C; Karwande, S V

2000-01-01

Development of myocardial preservation solutions requires the use of whole organ models which are animal and labor intensive. These models rely on physiologic rather than biochemical endpoints, making accurate comparison of the relative efficacy of individual solution components difficult. We hypothesized that myocardial slices could be used to assess preservation of biochemical function during cold storage. Whole rat hearts were precision cut into slices with a thickness of 200 microm and preserved at 4 degrees C in one of the following solutions: Columbia University (CU), University of Wisconsin (UW), D5 0.2% normal saline with 20 meq/l KCL (QNS), normal saline (NS), or a novel cardiac preservation solution (NPS) developed using this model. Myocardial biochemical function was assessed by ATP content (etamoles ATP/mg wet weight) and capacity for protein synthesis (counts per minute (cpm)/mg protein) immediately following slicing (0 hours), and at 6, 12, 18, and 24 hours of cold storage. Six slices were assayed at each time point for each solution. The data were analyzed using analysis of variance and are presented as the mean +/- standard deviation. ATP content was higher in the heart slices stored in the NPS compared to all other solutions at 6, 12, 18 and 24 hours of cold storage (p < 0.05). Capacity for protein synthesis was higher in the heart slices stored in the NPS compared to all other solutions at 6, 12, and 18 hours of cold storage (p < 0.05). CONCLUSIONS This myocardial slice model allows the rapid and efficient screening of cardiac preservation solutions and their components using quantifiable biochemical endpoints. Using this model, we have developed a novel preservation solution which improves the biochemical function of myocardial slices during cold storage.

Analytical model for advective-dispersive transport involving flexible boundary inputs, initial distributions and zero-order productions

NASA Astrophysics Data System (ADS)

Chen, Jui-Sheng; Li, Loretta Y.; Lai, Keng-Hsin; Liang, Ching-Ping

2017-11-01

A novel solution method is presented which leads to an analytical model for the advective-dispersive transport in a semi-infinite domain involving a wide spectrum of boundary inputs, initial distributions, and zero-order productions. The novel solution method applies the Laplace transform in combination with the generalized integral transform technique (GITT) to obtain the generalized analytical solution. Based on this generalized analytical expression, we derive a comprehensive set of special-case solutions for some time-dependent boundary distributions and zero-order productions, described by the Dirac delta, constant, Heaviside, exponentially-decaying, or periodically sinusoidal functions as well as some position-dependent initial conditions and zero-order productions specified by the Dirac delta, constant, Heaviside, or exponentially-decaying functions. The developed solutions are tested against an analytical solution from the literature. The excellent agreement between the analytical solutions confirms that the new model can serve as an effective tool for investigating transport behaviors under different scenarios. Several examples of applications, are given to explore transport behaviors which are rarely noted in the literature. The results show that the concentration waves resulting from the periodically sinusoidal input are sensitive to dispersion coefficient. The implication of this new finding is that a tracer test with a periodic input may provide additional information when for identifying the dispersion coefficients. Moreover, the solution strategy presented in this study can be extended to derive analytical models for handling more complicated problems of solute transport in multi-dimensional media subjected to sequential decay chain reactions, for which analytical solutions are not currently available.

An asymptotic solution to a passive biped walker model

NASA Astrophysics Data System (ADS)

Yudaev, Sergey A.; Rachinskii, Dmitrii; Sobolev, Vladimir A.

2017-02-01

We consider a simple model of a passive dynamic biped robot walker with point feet and legs without knee. The model is a switched system, which includes an inverted double pendulum. Robot’s gait and its stability depend on parameters such as the slope of the ramp, the length of robot’s legs, and the mass distribution along the legs. We present an asymptotic solution of the model. The first correction to the zero order approximation is shown to agree with the numerical solution for a limited parameter range.

Common quandaries and their practical solutions in Bayesian network modeling

Treesearch

Bruce G. Marcot

2017-01-01

Use and popularity of Bayesian network (BN) modeling has greatly expanded in recent years, but many common problems remain. Here, I summarize key problems in BN model construction and interpretation,along with suggested practical solutions. Problems in BN model construction include parameterizing probability values, variable definition, complex network structures,...

Linear discrete systems with memory: a generalization of the Langmuir model

NASA Astrophysics Data System (ADS)

Băleanu, Dumitru; Nigmatullin, Raoul R.

2013-10-01

In this manuscript we analyzed a general solution of the linear nonlocal Langmuir model within time scale calculus. Several generalizations of the Langmuir model are presented together with their exact corresponding solutions. The physical meaning of the proposed models are investigated and their corresponding geometries are reported.

Homoclinic accretion solutions in the Schwarzschild-anti-de Sitter space-time

NASA Astrophysics Data System (ADS)

Mach, Patryk

2015-04-01

The aim of this paper is to clarify the distinction between homoclinic and standard (global) Bondi-type accretion solutions in the Schwarzschild-anti-de Sitter space-time. The homoclinic solutions have recently been discovered numerically for polytropic equations of state. Here I show that they exist also for certain isothermal (linear) equations of state, and an analytic solution of this type is obtained. It is argued that the existence of such solutions is generic, although for sufficiently relativistic matter models (photon gas, ultrahard equation of state) there exist global solutions that can be continued to infinity, similarly to standard Michel's solutions in the Schwarzschild space-time. In contrast to that global solutions should not exist for matter models with a nonvanishing rest-mass component, and this is demonstrated for polytropes. For homoclinic isothermal solutions I derive an upper bound on the mass of the black hole for which stationary transonic accretion is allowed.

Finite Element Modeling of the Buckling Response of Sandwich Panels

NASA Technical Reports Server (NTRS)

Rose, Cheryl A.; Moore, David F.; Knight, Norman F., Jr.; Rankin, Charles C.

2002-01-01

A comparative study of different modeling approaches for predicting sandwich panel buckling response is described. The study considers sandwich panels with anisotropic face sheets and a very thick core. Results from conventional analytical solutions for sandwich panel overall buckling and face-sheet-wrinkling type modes are compared with solutions obtained using different finite element modeling approaches. Finite element solutions are obtained using layered shell element models, with and without transverse shear flexibility, layered shell/solid element models, with shell elements for the face sheets and solid elements for the core, and sandwich models using a recently developed specialty sandwich element. Convergence characteristics of the shell/solid and sandwich element modeling approaches with respect to in-plane and through-the-thickness discretization, are demonstrated. Results of the study indicate that the specialty sandwich element provides an accurate and effective modeling approach for predicting both overall and localized sandwich panel buckling response. Furthermore, results indicate that anisotropy of the face sheets, along with the ratio of principle elastic moduli, affect the buckling response and these effects may not be represented accurately by analytical solutions. Modeling recommendations are also provided.

Mathematical model formulation and validation of water and solute transport in whole hamster pancreatic islets.

PubMed

Benson, James D; Benson, Charles T; Critser, John K

2014-08-01

Optimization of cryopreservation protocols for cells and tissues requires accurate models of heat and mass transport. Model selection often depends on the configuration of the tissue. Here, a mathematical and conceptual model of water and solute transport for whole hamster pancreatic islets has been developed and experimentally validated incorporating fundamental biophysical data from previous studies on individual hamster islet cells while retaining whole-islet structural information. It describes coupled transport of water and solutes through the islet by three methods: intracellularly, intercellularly, and in combination. In particular we use domain decomposition techniques to couple a transmembrane flux model with an interstitial mass transfer model. The only significant undetermined variable is the cellular surface area which is in contact with the intercellularly transported solutes, Ais. The model was validated and Ais determined using a 3×3 factorial experimental design blocked for experimental day. Whole islet physical experiments were compared with model predictions at three temperatures, three perfusing solutions, and three islet size groups. A mean of 4.4 islets were compared at each of the 27 experimental conditions and found to correlate with a coefficient of determination of 0.87±0.06 (mean ± SD). Only the treatment variable of perfusing solution was found to be significant (p<0.05). We have devised a model that retains much of the intrinsic geometric configuration of the system, and thus fewer laboratory experiments are needed to determine model parameters and thus to develop new optimized cryopreservation protocols. Additionally, extensions to ovarian follicles and other concentric tissue structures may be made. Copyright © 2014 Elsevier Inc. All rights reserved.

A Mathematical Model of Solute Coupled Water Transport in Toad Intestine Incorporating Recirculation of the Actively Transported Solute

PubMed Central

Larsen, Erik Hviid; Sørensen, Jakob Balslev; Sørensen, Jens Nørkær

2000-01-01

A mathematical model of an absorbing leaky epithelium is developed for analysis of solute coupled water transport. The non-charged driving solute diffuses into cells and is pumped from cells into the lateral intercellular space (lis). All membranes contain water channels with the solute passing those of tight junction and interspace basement membrane by convection-diffusion. With solute permeability of paracellular pathway large relative to paracellular water flow, the paracellular flux ratio of the solute (influx/outflux) is small (2–4) in agreement with experiments. The virtual solute concentration of fluid emerging from lis is then significantly larger than the concentration in lis. Thus, in absence of external driving forces the model generates isotonic transport provided a component of the solute flux emerging downstream lis is taken up by cells through the serosal membrane and pumped back into lis, i.e., the solute would have to be recirculated. With input variables from toad intestine (Nedergaard, S., E.H. Larsen, and H.H. Ussing, J. Membr. Biol. 168:241–251), computations predict that 60–80% of the pumped flux stems from serosal bath in agreement with the experimental estimate of the recirculation flux. Robust solutions are obtained with realistic concentrations and pressures of lis, and with the following features. Rate of fluid absorption is governed by the solute permeability of mucosal membrane. Maximum fluid flow is governed by density of pumps on lis-membranes. Energetic efficiency increases with hydraulic conductance of the pathway carrying water from mucosal solution into lis. Uphill water transport is accomplished, but with high hydraulic conductance of cell membranes strength of transport is obscured by water flow through cells. Anomalous solvent drag occurs when back flux of water through cells exceeds inward water flux between cells. Molecules moving along the paracellular pathway are driven by a translateral flow of water, i.e., the model generates pseudo-solvent drag. The associated flux-ratio equation is derived. PMID:10919860

Universal solvation model based on solute electron density and on a continuum model of the solvent defined by the bulk dielectric constant and atomic surface tensions.

PubMed

Marenich, Aleksandr V; Cramer, Christopher J; Truhlar, Donald G

2009-05-07

We present a new continuum solvation model based on the quantum mechanical charge density of a solute molecule interacting with a continuum description of the solvent. The model is called SMD, where the "D" stands for "density" to denote that the full solute electron density is used without defining partial atomic charges. "Continuum" denotes that the solvent is not represented explicitly but rather as a dielectric medium with surface tension at the solute-solvent boundary. SMD is a universal solvation model, where "universal" denotes its applicability to any charged or uncharged solute in any solvent or liquid medium for which a few key descriptors are known (in particular, dielectric constant, refractive index, bulk surface tension, and acidity and basicity parameters). The model separates the observable solvation free energy into two main components. The first component is the bulk electrostatic contribution arising from a self-consistent reaction field treatment that involves the solution of the nonhomogeneous Poisson equation for electrostatics in terms of the integral-equation-formalism polarizable continuum model (IEF-PCM). The cavities for the bulk electrostatic calculation are defined by superpositions of nuclear-centered spheres. The second component is called the cavity-dispersion-solvent-structure term and is the contribution arising from short-range interactions between the solute and solvent molecules in the first solvation shell. This contribution is a sum of terms that are proportional (with geometry-dependent proportionality constants called atomic surface tensions) to the solvent-accessible surface areas of the individual atoms of the solute. The SMD model has been parametrized with a training set of 2821 solvation data including 112 aqueous ionic solvation free energies, 220 solvation free energies for 166 ions in acetonitrile, methanol, and dimethyl sulfoxide, 2346 solvation free energies for 318 neutral solutes in 91 solvents (90 nonaqueous organic solvents and water), and 143 transfer free energies for 93 neutral solutes between water and 15 organic solvents. The elements present in the solutes are H, C, N, O, F, Si, P, S, Cl, and Br. The SMD model employs a single set of parameters (intrinsic atomic Coulomb radii and atomic surface tension coefficients) optimized over six electronic structure methods: M05-2X/MIDI!6D, M05-2X/6-31G, M05-2X/6-31+G, M05-2X/cc-pVTZ, B3LYP/6-31G, and HF/6-31G. Although the SMD model has been parametrized using the IEF-PCM protocol for bulk electrostatics, it may also be employed with other algorithms for solving the nonhomogeneous Poisson equation for continuum solvation calculations in which the solute is represented by its electron density in real space. This includes, for example, the conductor-like screening algorithm. With the 6-31G basis set, the SMD model achieves mean unsigned errors of 0.6-1.0 kcal/mol in the solvation free energies of tested neutrals and mean unsigned errors of 4 kcal/mol on average for ions with either Gaussian03 or GAMESS.

Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions

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

Marenich, Aleksandr; Cramer, Christopher J; Truhlar, Donald G

2009-04-30

We present a new continuum solvation model based on the quantum mechanical charge density of a solute molecule interacting with a continuum description of the solvent. The model is called SMD, where the “D” stands for “density” to denote that the full solute electron density is used without defining partial atomic charges. “Continuum” denotes that the solvent is not represented explicitly but rather as a dielectric medium with surface tension at the solute-solvent boundary. SMD is a universal solvation model, where “universal” denotes its applicability to any charged or uncharged solute in any solvent or liquid medium for which amore » few key descriptors are known (in particular, dielectric constant, refractive index, bulk surface tension, and acidity and basicity parameters). The model separates the observable solvation free energy into two main components. The first component is the bulk electrostatic contribution arising from a self-consistent reaction field treatment that involves the solution of the nonhomogeneous Poisson equation for electrostatics in terms of the integral-equation-formalism polarizable continuum model (IEF-PCM). The cavities for the bulk electrostatic calculation are defined by superpositions of nuclear-centered spheres. The second component is called the cavity-dispersion-solvent-structure term and is the contribution arising from short-range interactions between the solute and solvent molecules in the first solvation shell. This contribution is a sum of terms that are proportional (with geometry-dependent proportionality constants called atomic surface tensions) to the solvent-accessible surface areas of the individual atoms of the solute. The SMD model has been parametrized with a training set of 2821 solvation data including 112 aqueous ionic solvation free energies, 220 solvation free energies for 166 ions in acetonitrile, methanol, and dimethyl sulfoxide, 2346 solvation free energies for 318 neutral solutes in 91 solvents (90 nonaqueous organic solvents and water), and 143 transfer free energies for 93 neutral solutes between water and 15 organic solvents. The elements present in the solutes are H, C, N, O, F, Si, P, S, Cl, and Br. The SMD model employs a single set of parameters (intrinsic atomic Coulomb radii and atomic surface tension coefficients) optimized over six electronic structure methods: M05-2X/MIDI!6D, M05-2X/6-31G*, M05-2X/6-31+G**, M05-2X/cc-pVTZ, B3LYP/6-31G*, and HF/6-31G*. Although the SMD model has been parametrized using the IEF-PCM protocol for bulk electrostatics, it may also be employed with other algorithms for solving the nonhomogeneous Poisson equation for continuum solvation calculations in which the solute is represented by its electron density in real space. This includes, for example, the conductor-like screening algorithm. With the 6-31G* basis set, the SMD model achieves mean unsigned errors of 0.6-1.0 kcal/mol in the solvation free energies of tested neutrals and mean unsigned errors of 4 kcal/mol on average for ions with either Gaussian03 or GAMESS.« less

Metal Ion Speciation and Dissolved Organic Matter Composition in Soil Solutions

NASA Astrophysics Data System (ADS)

Benedetti, M. F.; Ren, Z. L.; Bravin, M.; Tella, M.; Dai, J.

2014-12-01

Knowledge of the speciation of heavy metals and the role of dissolved organic matter (DOM) in soil solution is a key to understand metal mobility and ecotoxicity. In this study, soil column-Donnan membrane technique (SC-DMT) was used to measure metal speciation of Cd, Cu, Ni, Pb, and Zn in eighteen soil solutions, covering a wide range of metal sources and concentrations. DOM composition in these soil solutions was also determined. Our results show that in soil solution Pb and Cu are dominant in complex form, whereas Cd, Ni and Zn mainly exist as free ions; for the whole range of soil solutions, only 26.2% of DOM is reactive and consists mainly of fulvic acid (FA). The metal speciation measured by SC-DMT was compared to the predicted ones obtained via the NICA-Donnan model using the measured FA concentrations. The free ion concentrations predicted by speciation modelling were in good agreement with the measurements. Diffusive gradients in thin-films gels (DGT) were also performed to quantify the labile metal species in the fluxes from solid phase to solution in fourteen soils. The concentrations of metal species detected by DGT were compared with the free ion concentrations measured by DMT and the maximum concentrations calculated based on the predicted metal speciation in SC-DMT soil solutions. It is concluded that both inorganic species and a fraction of FA bound species account for the amount of labile metals measured by DGT, consistent with the dynamic features of this technique. The comparisons between measurements using analytical techniques and mechanistic model predictions provided mutual validation in their performance. Moreover, we show that to make accurate modelling of metal speciation in soil solutions, the knowledge of DOM composition is the crucial information, especially for Cu; like in previous studies the modelling of Pb speciation is not optimal and an updated of Pb generic binding parameters is required to reduce model prediction uncertainties.

A 2D flood inundation model based on cellular automata approach

NASA Astrophysics Data System (ADS)

Dottori, Francesco; Todini, Ezio

2010-05-01

In the past years, the cellular automata approach has been successfully applied in two-dimensional modelling of flood events. When used in experimental applications, models based on such approach have provided good results, comparable to those obtained with more complex 2D models; moreover, CA models have proven significantly faster and easier to apply than most of existing models, and these features make them a valuable tool for flood analysis especially when dealing with large areas. However, to date the real degree of accuracy of such models has not been demonstrated, since they have been mainly used in experimental applications, while very few comparisons with theoretical solutions have been made. Also, the use of an explicit scheme of solution, which is inherent in cellular automata models, forces them to work only with small time steps, thus reducing model computation speed. The present work describes a cellular automata model based on the continuity and diffusive wave equations. Several model versions based on different solution schemes have been realized and tested in a number of numerical cases, both 1D and 2D, comparing the results with theoretical and numerical solutions. In all cases, the model performed well compared to the reference solutions, and proved to be both stable and accurate. Finally, the version providing the best results in terms of stability was tested in a real flood event and compared with different hydraulic models. Again, the cellular automata model provided very good results, both in term of computational speed and reproduction of the simulated event.

Some Considerations on the Partial Credit Model

ERIC Educational Resources Information Center

Verhelst, N. D.; Verstralen, H. H. F. M.

2008-01-01

The Partial Credit Model (PCM) is sometimes interpreted as a model for stepwise solution of polytomously scored items, where the item parameters are interpreted as difficulties of the steps. It is argued that this interpretation is not justified. A model for stepwise solution is discussed. It is shown that the PCM is suited to model sums of binary…

An approach of traffic signal control based on NLRSQP algorithm

NASA Astrophysics Data System (ADS)

Zou, Yuan-Yang; Hu, Yu

2017-11-01

This paper presents a linear program model with linear complementarity constraints (LPLCC) to solve traffic signal optimization problem. The objective function of the model is to obtain the minimization of total queue length with weight factors at the end of each cycle. Then, a combination algorithm based on the nonlinear least regression and sequence quadratic program (NLRSQP) is proposed, by which the local optimal solution can be obtained. Furthermore, four numerical experiments are proposed to study how to set the initial solution of the algorithm that can get a better local optimal solution more quickly. In particular, the results of numerical experiments show that: The model is effective for different arrival rates and weight factors; and the lower bound of the initial solution is, the better optimal solution can be obtained.

Anomaly General Circulation Models.

NASA Astrophysics Data System (ADS)

Navarra, Antonio

The feasibility of the anomaly model is assessed using barotropic and baroclinic models. In the barotropic case, both a stationary and a time-dependent model has been formulated and constructed, whereas only the stationary, linear case is considered in the baroclinic case. Results from the barotropic model indicate that a relation between the stationary solution and the time-averaged non-linear solution exists. The stationary linear baroclinic solution can therefore be considered with some confidence. The linear baroclinic anomaly model poses a formidable mathematical problem because it is necessary to solve a gigantic linear system to obtain the solution. A new method to find solution of large linear system, based on a projection on the Krylov subspace is shown to be successful when applied to the linearized baroclinic anomaly model. The scheme consists of projecting the original linear system on the Krylov subspace, thereby reducing the dimensionality of the matrix to be inverted to obtain the solution. With an appropriate setting of the damping parameters, the iterative Krylov method reaches a solution even using a Krylov subspace ten times smaller than the original space of the problem. This generality allows the treatment of the important problem of linear waves in the atmosphere. A larger class (nonzonally symmetric) of basic states can now be treated for the baroclinic primitive equations. These problem leads to large unsymmetrical linear systems of order 10000 and more which can now be successfully tackled by the Krylov method. The (R7) linear anomaly model is used to investigate extensively the linear response to equatorial and mid-latitude prescribed heating. The results indicate that the solution is deeply affected by the presence of the stationary waves in the basic state. The instability of the asymmetric flows, first pointed out by Simmons et al. (1983), is active also in the baroclinic case. However, the presence of baroclinic processes modifies the dominant response. The most sensitive areas are identified; they correspond to north Japan, the Pole and Greenland regions. A limited set of higher resolution (R15) experiments indicate that this situation is still present and enhanced at higher resolution. The linear anomaly model is also applied to a realistic case. (Abstract shortened with permission of author.).

Exact solutions in 3D gravity with torsion

NASA Astrophysics Data System (ADS)

González, P. A.; Vásquez, Yerko

2011-08-01

We study the three-dimensional gravity with torsion given by the Mielke-Baekler (MB) model coupled to gravitational Chern-Simons term, and that possess electric charge described by Maxwell-Chern-Simons electrodynamics. We find and discuss this theory's charged black holes solutions and uncharged solutions. We find that for vanishing torsion our solutions by means of a coordinate transformation can be written as three-dimensional Chern-Simons black holes. We also discuss a special case of this theory, Topologically Massive Gravity (TMG) at chiral point, and we show that the logarithmic solution of TMG is also a solution of the MB model at a fixed point in the space of parameters. Furthermore, we show that our solutions generalize Gödel type solutions in a particular case. Also, we recover BTZ black hole in Riemann-Cartan spacetime for vanishing charge.

Exact Riemann solutions of the Ripa model for flat and non-flat bottom topographies

NASA Astrophysics Data System (ADS)

Rehman, Asad; Ali, Ishtiaq; Qamar, Shamsul

2018-03-01

This article is concerned with the derivation of exact Riemann solutions for Ripa model considering flat and non-flat bottom topographies. The Ripa model is a system of shallow water equations accounting for horizontal temperature gradients. In the case of non-flat bottom topography, the mass, momentum and energy conservation principles are utilized to relate the left and right states across the step-type bottom topography. The resulting system of algebraic equations is solved iteratively. Different numerical case studies of physical interest are considered. The solutions obtained from developed exact Riemann solvers are compared with the approximate solutions of central upwind scheme.

A Modified Robinson-Stokes equation for describing the thermodynamic properties of aqueous solutions of 1-1 electrolytes

NASA Astrophysics Data System (ADS)

Rudakov, A. M.; Sergievskii, V. V.

2008-05-01

Equations relating osmotic, mean ionic activity, and water activity coefficients to electrolyte concentrations in binary aqueous solutions were substantiated within the framework of cluster concepts. The model includes the contribution to solution nonideality of electrostatic interactions in terms of the Debye-Hückel theory along with hydration and association of salts via relations containing hydration and association numbers in the standard states. According to the description of data on 54 aqueous solutions of 1-1 electrolytes, this model should be given preference compared with the most extensively used NRTL, NRTL-NRF, Wilson, and Pitzer models.

Study of galactic halo F(T,TG) wormhole solutions

NASA Astrophysics Data System (ADS)

Sharif, M.; Nazir, Kanwal

In this paper, we investigate static spherically symmetric wormhole solutions with galactic halo region in the background of F(T,TG) gravity. Here, T represents torsion scalar and TG is teleparallel equivalent Gauss-Bonnet term. For this purpose, we consider a diagonal tetrad and two specific F(T,TG) models. We analyze the wormhole structure through shape function graphically for both models. We also investigate the behavior of null/weak energy conditions. Finally, we evaluate the equilibrium condition to check stability of the wormhole solutions. It is concluded that there exists physically viable wormhole solution only for the first model that turns out to be stable.

Hopf solitons in the Nicole model

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

Gillard, Mike; Sutcliffe, Paul

2010-12-15

The Nicole model is a conformal field theory in a three-dimensional space. It has topological soliton solutions classified by the integer-valued Hopf charge, and all currently known solitons are axially symmetric. A volume-preserving flow is used to construct soliton solutions numerically for all Hopf charges from 1 to 8. It is found that the known axially symmetric solutions are unstable for Hopf charges greater than 2 and new lower energy solutions are obtained that include knots and links. A comparison with the Skyrme-Faddeev model suggests many universal features, though there are some differences in the link types obtained in themore » two theories.« less

The dynamics of a delayed predator-prey model with state dependent feedback control

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

Singh, Anuraj; Gakkhar, Sunita

2011-11-30

A delayed prey-predator model with state-dependent impulses is investigated. The sufficient conditions of existence and stability of semi-trivial solution and positive period-1 solution are obtained by using the Poincare map and analogue of the Poincare Criterion. The qualitative analysis shows that the positive period-one solution bifurcates from the semi-trivial solution through a fold bifurcation. The complex dynamics including chaos is obtained and numerical simulations substantiate the analytical results.

A simple model for electrical charge in globular macromolecules and linear polyelectrolytes in solution

NASA Astrophysics Data System (ADS)

Krishnan, M.

2017-05-01

We present a model for calculating the net and effective electrical charge of globular macromolecules and linear polyelectrolytes such as proteins and DNA, given the concentration of monovalent salt and pH in solution. The calculation is based on a numerical solution of the non-linear Poisson-Boltzmann equation using a finite element discretized continuum approach. The model simultaneously addresses the phenomena of charge regulation and renormalization, both of which underpin the electrostatics of biomolecules in solution. We show that while charge regulation addresses the true electrical charge of a molecule arising from the acid-base equilibria of its ionizable groups, charge renormalization finds relevance in the context of a molecule's interaction with another charged entity. Writing this electrostatic interaction free energy in terms of a local electrical potential, we obtain an "interaction charge" for the molecule which we demonstrate agrees closely with the "effective charge" discussed in charge renormalization and counterion-condensation theories. The predictions of this model agree well with direct high-precision measurements of effective electrical charge of polyelectrolytes such as nucleic acids and disordered proteins in solution, without tunable parameters. Including the effective interior dielectric constant for compactly folded molecules as a tunable parameter, the model captures measurements of effective charge as well as published trends of pKa shifts in globular proteins. Our results suggest a straightforward general framework to model electrostatics in biomolecules in solution. In offering a platform that directly links theory and experiment, these calculations could foster a systematic understanding of the interrelationship between molecular 3D structure and conformation, electrical charge and electrostatic interactions in solution. The model could find particular relevance in situations where molecular crystal structures are not available or rapid, reliable predictions are desired.

An image-based reaction field method for electrostatic interactions in molecular dynamics simulations of aqueous solutions

NASA Astrophysics Data System (ADS)

Lin, Yuchun; Baumketner, Andrij; Deng, Shaozhong; Xu, Zhenli; Jacobs, Donald; Cai, Wei

2009-10-01

In this paper, a new solvation model is proposed for simulations of biomolecules in aqueous solutions that combines the strengths of explicit and implicit solvent representations. Solute molecules are placed in a spherical cavity filled with explicit water, thus providing microscopic detail where it is most needed. Solvent outside of the cavity is modeled as a dielectric continuum whose effect on the solute is treated through the reaction field corrections. With this explicit/implicit model, the electrostatic potential represents a solute molecule in an infinite bath of solvent, thus avoiding unphysical interactions between periodic images of the solute commonly used in the lattice-sum explicit solvent simulations. For improved computational efficiency, our model employs an accurate and efficient multiple-image charge method to compute reaction fields together with the fast multipole method for the direct Coulomb interactions. To minimize the surface effects, periodic boundary conditions are employed for nonelectrostatic interactions. The proposed model is applied to study liquid water. The effect of model parameters, which include the size of the cavity, the number of image charges used to compute reaction field, and the thickness of the buffer layer, is investigated in comparison with the particle-mesh Ewald simulations as a reference. An optimal set of parameters is obtained that allows for a faithful representation of many structural, dielectric, and dynamic properties of the simulated water, while maintaining manageable computational cost. With controlled and adjustable accuracy of the multiple-image charge representation of the reaction field, it is concluded that the employed model achieves convergence with only one image charge in the case of pure water. Future applications to pKa calculations, conformational sampling of solvated biomolecules and electrolyte solutions are briefly discussed.

A 2D nonlinear multiring model for blood flow in large elastic arteries

NASA Astrophysics Data System (ADS)

Ghigo, Arthur R.; Fullana, Jose-Maria; Lagrée, Pierre-Yves

2017-12-01

In this paper, we propose a two-dimensional nonlinear ;multiring; model to compute blood flow in axisymmetric elastic arteries. This model is designed to overcome the numerical difficulties of three-dimensional fluid-structure interaction simulations of blood flow without using the over-simplifications necessary to obtain one-dimensional blood flow models. This multiring model is derived by integrating over concentric rings of fluid the simplified long-wave Navier-Stokes equations coupled to an elastic model of the arterial wall. The resulting system of balance laws provides a unified framework in which both the motion of the fluid and the displacement of the wall are dealt with simultaneously. The mathematical structure of the multiring model allows us to use a finite volume method that guarantees the conservation of mass and the positivity of the numerical solution and can deal with nonlinear flows and large deformations of the arterial wall. We show that the finite volume numerical solution of the multiring model provides at a reasonable computational cost an asymptotically valid description of blood flow velocity profiles and other averaged quantities (wall shear stress, flow rate, ...) in large elastic and quasi-rigid arteries. In particular, we validate the multiring model against well-known solutions such as the Womersley or the Poiseuille solutions as well as against steady boundary layer solutions in quasi-rigid constricted and expanded tubes.

Experimental testing and modeling analysis of solute mixing at water distribution pipe junctions.

PubMed

Shao, Yu; Jeffrey Yang, Y; Jiang, Lijie; Yu, Tingchao; Shen, Cheng

2014-06-01

Flow dynamics at a pipe junction controls particle trajectories, solute mixing and concentrations in downstream pipes. The effect can lead to different outcomes of water quality modeling and, hence, drinking water management in a distribution network. Here we have investigated solute mixing behavior in pipe junctions of five hydraulic types, for which flow distribution factors and analytical equations for network modeling are proposed. First, based on experiments, the degree of mixing at a cross is found to be a function of flow momentum ratio that defines a junction flow distribution pattern and the degree of departure from complete mixing. Corresponding analytical solutions are also validated using computational-fluid-dynamics (CFD) simulations. Second, the analytical mixing model is further extended to double-Tee junctions. Correspondingly the flow distribution factor is modified to account for hydraulic departure from a cross configuration. For a double-Tee(A) junction, CFD simulations show that the solute mixing depends on flow momentum ratio and connection pipe length, whereas the mixing at double-Tee(B) is well represented by two independent single-Tee junctions with a potential water stagnation zone in between. Notably, double-Tee junctions differ significantly from a cross in solute mixing and transport. However, it is noted that these pipe connections are widely, but incorrectly, simplified as cross junctions of assumed complete solute mixing in network skeletonization and water quality modeling. For the studied pipe junction types, analytical solutions are proposed to characterize the incomplete mixing and hence may allow better water quality simulation in a distribution network. Published by Elsevier Ltd.

Crystal Nucleation of Tolbutamide in Solution: Relationship to Solvent, Solute Conformation, and Solution Structure.

PubMed

Zeglinski, Jacek; Kuhs, Manuel; Khamar, Dikshitkumar; Hegarty, Avril C; Devi, Renuka K; Rasmuson, Åke C

2018-04-03

The influence of the solvent in nucleation of tolbutamide, a medium-sized, flexible and polymorphic organic molecule, has been explored by measuring nucleation induction times, estimating solvent-solute interaction enthalpies using molecular modelling and calorimetric data, probing interactions and clustering with spectroscopy, and modelling solvent-dependence of molecular conformation in solution. The nucleation driving force required to reach the same induction time is strongly solvent-dependent, increasing in the order: acetonitrile

Solubility of KF and NaCl in water by molecular simulation.

PubMed

Sanz, E; Vega, C

2007-01-07

The solubility of two ionic salts, namely, KF and NaCl, in water has been calculated by Monte Carlo molecular simulation. Water has been modeled with the extended simple point charge model (SPC/E), ions with the Tosi-Fumi model and the interaction between water and ions with the Smith-Dang model. The chemical potential of the solute in the solution has been computed as the derivative of the total free energy with respect to the number of solute particles. The chemical potential of the solute in the solid phase has been calculated by thermodynamic integration to an Einstein crystal. The solubility of the salt has been calculated as the concentration at which the chemical potential of the salt in the solution becomes identical to that of the pure solid. The methodology used in this work has been tested by reproducing the results for the solubility of KF determined previously by Ferrario et al. [J. Chem. Phys. 117, 4947 (2002)]. For KF, it was found that the solubility of the model is only in qualitative agreement with experiment. The variation of the solubility with temperature for KF has also been studied. For NaCl, the potential model used predicts a solubility in good agreement with the experimental value. The same is true for the hydration chemical potential at infinite dilution. Given the practical importance of solutions of NaCl in water the model used in this work, whereas simple, can be of interest for future studies.

Exact solutions and low-frequency instability of the adiabatic auroral arc model

NASA Technical Reports Server (NTRS)

Cornwall, John M.

1988-01-01

The adiabatic auroral arc model couples a kinetic theory parallel current driven by mirror forces to horizontal ionospheric currents; the resulting equations are nonlinear. Some exact stationary solutions to these equations, some of them based on the Liouville equation, are developed, with both latitudinal and longitudinal spatial variations. These Liouville equation exact solutions are related to stability boundaries of low-frequency instabilities such as Kelvin-Helmholtz, as shown by a study of a simplified model.

Multiphasic modeling of charged solute transport across articular cartilage: Application of multi-zone finite-bath model.

PubMed

Arbabi, Vahid; Pouran, Behdad; Weinans, Harrie; Zadpoor, Amir A

2016-06-14

Charged and uncharged solutes penetrate through cartilage to maintain the metabolic function of chondrocytes and to possibly restore or further breakdown the cartilage tissue in different stages of osteoarthritis. In this study the transport of charged solutes across the various zones of cartilage was quantified, taken into account the physicochemical interactions between the solute and the cartilage constituents. A multiphasic finite-bath finite element (FE) model was developed to simulate equine cartilage diffusion experiments that used a negatively charged contrast agent (ioxaglate) in combination with serial micro-computed tomography (micro-CT) to measure the diffusion. By comparing the FE model with the experimental data both the diffusion coefficient of ioxaglate and the fixed charge density (FCD) were obtained. In the multiphasic model, cartilage was divided into multiple (three) zones to help understand how diffusion coefficient and FCD vary across cartilage thickness. The direct effects of charged solute-FCD interaction on diffusion were investigated by comparing the diffusion coefficients derived from the multiphasic and biphasic-solute models. We found a relationship between the FCD obtained by the multiphasic model and ioxaglate partitioning obtained from micro-CT experiments. Using our multi-zone multiphasic model, diffusion coefficient of the superficial zone was up to ten-fold higher than that of the middle zone, while the FCD of the middle zone was up to almost two-fold higher than that of the superficial zone. In conclusion, the developed finite-bath multiphasic model provides us with a non-destructive method by which we could obtain both diffusion coefficient and FCD of different cartilage zones. The outcomes of the current work will also help understand how charge of the bath affects the diffusion of a charged molecule and also predict the diffusion behavior of a charged solute across articular cartilage. Copyright © 2016 Elsevier Ltd. All rights reserved.

Alternative solution model for the ternary carbonate system CaCO3 - MgCO3 - FeCO3 - II. Calibration of a combined ordering model and mixing model

USGS Publications Warehouse

McSwiggen, P.L.

1993-01-01

Earlier attempts at solution models for the ternary carbonate system have been unable to adequately accommodate the cation ordering which occurs in some of the carbonate phases. The carbonate solution model of this study combines a Margules type of interaction model with a Bragg-Williams type of ordering model. The ordering model determines the equilibrium state of order for a crystal, from which the cation distribution within the lattice can be obtained. The interaction model addresses the effect that mixing different cation species within a given cation layer has on the total free energy of the system. An ordering model was derived, based on the Bragg-Williams approach; it is applicable to ternary systems involving three cations substituting on two sites, and contains three ordering energy parameters (WCaMg, WCaFe, and WCaMgFe). The solution model of this study involves six Margules-type interaction parameters (W12, W21, W13, W31, W23, and W32). Values for the two sets of energy parameters were calculated from experimental data and from compositional relationships in natural assemblages. ?? 1993 Springer-Verlag.

Arbitrary Steady-State Solutions with the K-epsilon Model

NASA Technical Reports Server (NTRS)

Rumsey, Christopher L.; Pettersson Reif, B. A.; Gatski, Thomas B.

2006-01-01

Widely-used forms of the K-epsilon turbulence model are shown to yield arbitrary steady-state converged solutions that are highly dependent on numerical considerations such as initial conditions and solution procedure. These solutions contain pseudo-laminar regions of varying size. By applying a nullcline analysis to the equation set, it is possible to clearly demonstrate the reasons for the anomalous behavior. In summary, the degenerate solution acts as a stable fixed point under certain conditions, causing the numerical method to converge there. The analysis also suggests a methodology for preventing the anomalous behavior in steady-state computations.

Structure and anomalous solubility for hard spheres in an associating lattice gas model.

PubMed

Szortyka, Marcia M; Girardi, Mauricio; Henriques, Vera B; Barbosa, Marcia C

2012-08-14

In this paper we investigate the solubility of a hard-sphere gas in a solvent modeled as an associating lattice gas. The solution phase diagram for solute at 5% is compared with the phase diagram of the original solute free model. Model properties are investigated both through Monte Carlo simulations and a cluster approximation. The model solubility is computed via simulations and is shown to exhibit a minimum as a function of temperature. The line of minimum solubility (TmS) coincides with the line of maximum density (TMD) for different solvent chemical potentials, in accordance with the literature on continuous realistic models and on the "cavity" picture.

Exact Solutions for Wind-Driven Coastal Upwelling and Downwelling over Sloping Topography

NASA Astrophysics Data System (ADS)

Choboter, P.; Duke, D.; Horton, J.; Sinz, P.

2009-12-01

The dynamics of wind-driven coastal upwelling and downwelling are studied using a simplified dynamical model. Exact solutions are examined as a function of time and over a family of sloping topographies. Assumptions in the two-dimensional model include a frictionless ocean interior below the surface Ekman layer, and no alongshore dependence of the variables; however, dependence in the cross-shore and vertical directions is retained. Additionally, density and alongshore momentum are advected by the cross-shore velocity in order to maintain thermal wind. The time-dependent initial-value problem is solved with constant initial stratification and no initial alongshore flow. An alongshore pressure gradient is added to allow the cross-shore flow to be geostrophically balanced far from shore. Previously, this model has been used to study upwelling over flat-bottom and sloping topographies, but the novel feature in this work is the discovery of exact solutions for downwelling. These exact solutions are compared to numerical solutions from a primitive-equation ocean model, based on the Princeton Ocean Model, configured in a similar two-dimensional geometry. Many typical features of the evolution of density and velocity during downwelling are displayed by the analytical model.

Sequential-Optimization-Based Framework for Robust Modeling and Design of Heterogeneous Catalytic Systems

DOE PAGES

Rangarajan, Srinivas; Maravelias, Christos T.; Mavrikakis, Manos

2017-11-09

Here, we present a general optimization-based framework for (i) ab initio and experimental data driven mechanistic modeling and (ii) optimal catalyst design of heterogeneous catalytic systems. Both cases are formulated as a nonlinear optimization problem that is subject to a mean-field microkinetic model and thermodynamic consistency requirements as constraints, for which we seek sparse solutions through a ridge (L 2 regularization) penalty. The solution procedure involves an iterative sequence of forward simulation of the differential algebraic equations pertaining to the microkinetic model using a numerical tool capable of handling stiff systems, sensitivity calculations using linear algebra, and gradient-based nonlinear optimization.more » A multistart approach is used to explore the solution space, and a hierarchical clustering procedure is implemented for statistically classifying potentially competing solutions. An example of methanol synthesis through hydrogenation of CO and CO 2 on a Cu-based catalyst is used to illustrate the framework. The framework is fast, is robust, and can be used to comprehensively explore the model solution and design space of any heterogeneous catalytic system.« less

Sequential-Optimization-Based Framework for Robust Modeling and Design of Heterogeneous Catalytic Systems

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

Rangarajan, Srinivas; Maravelias, Christos T.; Mavrikakis, Manos

Here, we present a general optimization-based framework for (i) ab initio and experimental data driven mechanistic modeling and (ii) optimal catalyst design of heterogeneous catalytic systems. Both cases are formulated as a nonlinear optimization problem that is subject to a mean-field microkinetic model and thermodynamic consistency requirements as constraints, for which we seek sparse solutions through a ridge (L 2 regularization) penalty. The solution procedure involves an iterative sequence of forward simulation of the differential algebraic equations pertaining to the microkinetic model using a numerical tool capable of handling stiff systems, sensitivity calculations using linear algebra, and gradient-based nonlinear optimization.more » A multistart approach is used to explore the solution space, and a hierarchical clustering procedure is implemented for statistically classifying potentially competing solutions. An example of methanol synthesis through hydrogenation of CO and CO 2 on a Cu-based catalyst is used to illustrate the framework. The framework is fast, is robust, and can be used to comprehensively explore the model solution and design space of any heterogeneous catalytic system.« less

IMPROVED EXPERIMENTAL MODEL TO EVALUATE SUBMUCOSAL INJECTION SOLUTIONS FOR ENDOSCOPIC SUBMUCOSAL DISSECTION

PubMed Central

YAMAZAKI, Kendi; MALUF-FILHO, Fauze; da COSTA, Vitor Alves Pessoa; PESSORRUSSO, Fernanda Cristina Simões; HONDO, Fabio Yuji; SAKAI, Paulo; de FIGUEIREDO, Luis Francisco Poli

2015-01-01

Background : Endoscopic submucosal dissection carries an increased risk of bleeding and perforation. The creation of a long lasting submucosal cushion is essential for the safe and complete removal of the lesion. There is not a suitable experimental model for evaluation of the durability of the cushioning effect of different solutions. Aim : To describe an improved experimental model to evaluate submucosal injection solutions. Methods : A total of four domestic pigs were employed to evaluate two different submucosal fluid solutions in the gastric submucosa. After midline laparotomy, the anterior gastric wall was incised from the gastric body to the antrum and its mucosal surface was exposed by flipping inside out the incised gastric wall. Two different solutions (10% mannitol and normal saline) were injected in the submucosa of the anterior wall of the distal gastric body. All submucosal cushions were injected until they reach the same size, standardized as 1.0 cm in height and 2.0 cm in diameter. A caliper and a ruler were employed to guarantee accuracy of the measurements. Results : All four animal experiments were completed. All submucosal cushions had the exact same size measured with caliper and a ruler. By using the mannitol solution, the mean duration of the submucosal cushion was longer than the saline solution: 20 and 22 min (mean, 21 min) vs 5 and 6 min (mean, 5.5 min) Conclusions : This experimental model is simple and evaluate the duration, size, and effect of the submucosal cushion, making it more reliable than other models that employ resected porcine stomachs or endoscopic images in live porcine models. PMID:26734797

IMPROVED EXPERIMENTAL MODEL TO EVALUATE SUBMUCOSAL INJECTION SOLUTIONS FOR ENDOSCOPIC SUBMUCOSAL DISSECTION.

PubMed

Yamazaki, Kendi; Maluf-Filho, Fauze; da Costa, Vitor Alves Pessoa; Pessorrusso, Fernanda Cristina Simões; Hondo, Fabio Yuji; Sakai, Paulo; de Figueiredo, Luis Francisco Poli

2015-01-01

Endoscopic submucosal dissection carries an increased risk of bleeding and perforation. The creation of a long lasting submucosal cushion is essential for the safe and complete removal of the lesion. There is not a suitable experimental model for evaluation of the durability of the cushioning effect of different solutions. To describe an improved experimental model to evaluate submucosal injection solutions. A total of four domestic pigs were employed to evaluate two different submucosal fluid solutions in the gastric submucosa. After midline laparotomy, the anterior gastric wall was incised from the gastric body to the antrum and its mucosal surface was exposed by flipping inside out the incised gastric wall. Two different solutions (10% mannitol and normal saline) were injected in the submucosa of the anterior wall of the distal gastric body. All submucosal cushions were injected until they reach the same size, standardized as 1.0 cm in height and 2.0 cm in diameter. A caliper and a ruler were employed to guarantee accuracy of the measurements. All four animal experiments were completed. All submucosal cushions had the exact same size measured with caliper and a ruler. By using the mannitol solution, the mean duration of the submucosal cushion was longer than the saline solution: 20 and 22 min (mean, 21 min) vs 5 and 6 min (mean, 5.5 min) This experimental model is simple and evaluate the duration, size, and effect of the submucosal cushion, making it more reliable than other models that employ resected porcine stomachs or endoscopic images in live porcine models.

Dark-energy cosmological models in f(G) gravity

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

Shamir, M. F., E-mail: farasat.shamir@nu.edu.pk

We discuss dark-energy cosmological models in f(G) gravity. For this purpose, a locally rotationally symmetric Bianchi type I cosmological model is considered. First, exact solutions with a well-known form of the f(G) model are explored. One general solution is discussed using a power-law f(G) gravity model and physical quantities are calculated. In particular, Kasner’s universe is recovered and the corresponding f(G) gravity models are reported. Second, the energy conditions for the model under consideration are discussed using graphical analysis. It is concluded that solutions with f(G) = G{sup 5/6} support expansion of universe while those with f(G) = G{sup 1/2}more » do not favor the current expansion.« less

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

Choi, Jeong

The research program reported here is focused on critical issues that represent conspicuous gaps in current understanding of rapid solidification, limiting our ability to predict and control microstructural evolution (i.e. morphological dynamics and microsegregation) at high undercooling, where conditions depart significantly from local equilibrium. More specifically, through careful application of phase-field modeling, using appropriate thin-interface and anti-trapping corrections and addressing important details such as transient effects and a velocity-dependent (i.e. adaptive) numerics, the current analysis provides a reasonable simulation-based picture of non-equilibrium solute partitioning and the corresponding oscillatory dynamics associated with single-phase rapid solidification and show that this method ismore » a suitable means for a self-consistent simulation of transient behavior and operating point selection under rapid growth conditions. Moving beyond the limitations of conventional theoretical/analytical treatments of non-equilibrium solute partitioning, these results serve to substantiate recent experimental findings and analytical treatments for single-phase rapid solidification. The departure from the equilibrium solid concentration at the solid-liquid interface was often observed during rapid solidification, and the energetic associated non-equilibrium solute partitioning has been treated in detail, providing possible ranges of interface concentrations for a given growth condition. Use of these treatments for analytical description of specific single-phase dendritic and cellular operating point selection, however, requires a model for solute partitioning under a given set of growth conditions. Therefore, analytical solute trapping models which describe the chemical partitioning as a function of steady state interface velocities have been developed and widely utilized in most of the theoretical investigations of rapid solidification. However, these solute trapping models are not rigorously verified due to the difficulty in experimentally measuring under rapid growth conditions. Moreover, since these solute trapping models include kinetic parameters which are difficult to directly measure from experiments, application of the solute trapping models or the associated analytic rapid solidification model is limited. These theoretical models for steady state rapid solidification which incorporate the solute trapping models do not describe the interdependency of solute diffusion, interface kinetics, and alloy thermodynamics. The phase-field approach allows calculating, spontaneously, the non-equilibrium growth effects of alloys and the associated time-dependent growth dynamics, without making the assumptions that solute partitioning is an explicit function of velocity, as is the current convention. In the research described here, by utilizing the phase-field model in the thin-interface limit, incorporating the anti-trapping current term, more quantitatively valid interface kinetics and solute diffusion across the interface are calculated. In order to sufficiently resolve the physical length scales (i.e. interface thickness and diffusion boundary length), grid spacings are continually adjusted in calculations. The full trajectories of transient planar growth dynamics under rapid directional solidification conditions with different pulling velocities are described. As a validation of a model, the predicted steady state conditions are consistent with the analytic approach for rapid growth. It was confirmed that rapid interface dynamics exhibits the abrupt acceleration of the planar front when the effect of the non-equilibrium solute partitioning at the interface becomes signi ficant. This is consistent with the previous linear stability analysis for the non-equilibrium interface dynamics. With an appropriate growth condition, the continuous oscillation dynamics was able to be simulated using continually adjusting grid spacings. This oscillatory dynamics including instantaneous jump of interface velocities are consistent with a previous phenomenological model by and a numerical investigation, which may cause the formation of banded structures. Additionally, the selection of the steady state growth dynamics in the highly undercooled melt is demonstrated. The transition of the growth morphology, interface velocity selection, and solute trapping phenomenon with increasing melt supersaturations was described by the phase-field simulation. The tip selection for the dendritic growth was consistent with Ivantsov's function, and the non-equilibrium chemical partitioning behavior shows good qualitative agreement with the Aziz's solute trapping model even though the model parameter(V D) remains as an arbitrary constant. This work is able to show the possibility of comprehensive description of rapid alloy growth over the entire time-dependent non-equilibrium phenomenon.« less

Existence of global weak solution for a reduced gravity two and a half layer model

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

Guo, Zhenhua, E-mail: zhenhua.guo.math@gmail.com; Li, Zilai, E-mail: lizilai0917@163.com; Yao, Lei, E-mail: yaolei1056@hotmail.com

2013-12-15

We investigate the existence of global weak solution to a reduced gravity two and a half layer model in one-dimensional bounded spatial domain or periodic domain. Also, we show that any possible vacuum state has to vanish within finite time, then the weak solution becomes a unique strong one.

The Computation of Orthogonal Independent Cluster Solutions and Their Oblique Analogs in Factor Analysis.

ERIC Educational Resources Information Center

Hofmann, Richard J.

A very general model for the computation of independent cluster solutions in factor analysis is presented. The model is discussed as being either orthogonal or oblique. Furthermore, it is demonstrated that for every orthogonal independent cluster solution there is an oblique analog. Using three illustrative examples, certain generalities are made…

New integrable models and analytical solutions in f (R ) cosmology with an ideal gas

NASA Astrophysics Data System (ADS)

Papagiannopoulos, G.; Basilakos, Spyros; Barrow, John D.; Paliathanasis, Andronikos

2018-01-01

In the context of f (R ) gravity with a spatially flat FLRW metric containing an ideal fluid, we use the method of invariant transformations to specify families of models which are integrable. We find three families of f (R ) theories for which new analytical solutions are given and closed-form solutions are provided.

Balancing anisotropic curvature with gauge fields in a class of shear-free cosmological models

NASA Astrophysics Data System (ADS)

Thorsrud, Mikjel

2018-05-01

We present a complete list of general relativistic shear-free solutions in a class of anisotropic, spatially homogeneous and orthogonal cosmological models containing a collection of n independent p-form gauge fields, where p\\in\\{0, 1, 2, 3\\} , in addition to standard ΛCDM matter fields modelled as perfect fluids. Here a (collection of) gauge field(s) balances anisotropic spatial curvature on the right-hand side of the shear propagation equation. The result is a class of solutions dynamically equivalent to standard FLRW cosmologies, with an effective curvature constant Keff that depends both on spatial curvature and the energy density of the gauge field(s). In the case of a single gauge field (n  =  1) we show that the only spacetimes that admit such solutions are the LRS Bianchi type III, Bianchi type VI0 and Kantowski–Sachs metric, which are dynamically equivalent to open (Keff<0 ), flat (Keff=0 ) and closed (Keff>0 ) FLRW models, respectively. With a collection of gauge fields (n  >  1) also Bianchi type II admits a shear-free solution (Keff>0 ). We identify the LRS Bianchi type III solution to be the unique shear-free solution with a gauge field Hamiltonian bounded from below in the entire class of models.

Factor Structure of the Psychopathic Personality Inventory (PPI): Findings from a Large Incarcerated Sample

PubMed Central

Neumann, Craig S.; Malterer, Melanie B.; Newman, Joseph P.

2010-01-01

Recent exploratory factor analysis (EFA) of the Psychopathic Personality Inventory (PPI; Lilienfeld, 1990) with a community sample suggested that the PPI subscales may be comprised of two higher-order factors (Benning et al., 2003). However, little research has examined the PPI structure in offenders. The current study attempted to replicate the Benning et al. two-factor solution using a large (N=1224) incarcerated male sample. Confirmatory factor analysis (CFA) of this model with the full sample resulted in poor model fit. Next, to identify a factor solution that would summarize the offender data, EFA was conducted using a split-half of the total sample, followed by an attempt to replicate the EFA solution via CFA with the other split-half sample. Using the recommendations of Prooijen and van der Kloot (2001) for recovering EFA solutions, model fit results provided some evidence that the EFA solution could be recovered via CFA. However, this model involved extensive cross-loadings of the subscales across three factors, suggesting item overlap across PPI subscales. In sum, the two-factor solution reported by Benning et al. (2003) was not a viable model for the current sample of offenders, and additional research is needed to elucidate the latent structure of the PPI. PMID:18557694

Influence of dissolved organic matter and manganese oxides on metal speciation in soil solution: A modelling approach.

PubMed

Schneider, Arnaud R; Ponthieu, Marie; Cancès, Benjamin; Conreux, Alexandra; Morvan, Xavier; Gommeaux, Maxime; Marin, Béatrice; Benedetti, Marc F

2016-06-01

Trace element (TE) speciation modelling in soil solution is controlled by the assumptions made about the soil solution composition. To evaluate this influence, different assumptions using Visual MINTEQ were tested and compared to measurements of free TE concentrations. The soil column Donnan membrane technique (SC-DMT) was used to estimate the free TE (Cd, Cu, Ni, Pb and Zn) concentrations in six acidic soil solutions. A batch technique using DAX-8 resin was used to fractionate the dissolved organic matter (DOM) into four fractions: humic acids (HA), fulvic acids (FA), hydrophilic acids (Hy) and hydrophobic neutral organic matter (HON). To model TE speciation, particular attention was focused on the hydrous manganese oxides (HMO) and the Hy fraction, ligands not considered in most of the TE speciation modelling studies in soil solution. In this work, the model predictions of free ion activities agree with the experimental results. The knowledge of the FA fraction seems to be very useful, especially in the case of high DOM content, for more accurately representing experimental data. Finally, the role of the manganese oxides and of the Hy fraction on TE speciation was identified and, depending on the physicochemical conditions of the soil solution, should be considered in future studies. Copyright © 2016 Elsevier Ltd. All rights reserved.

Upscaling of Solute Transport in Heterogeneous Media with Non-uniform Flow and Dispersion Fields

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

Xu, Zhijie; Meakin, Paul

2013-10-01

An analytical and computational model for non-reactive solute transport in periodic heterogeneous media with arbitrary non-uniform flow and dispersion fields within the unit cell of length ε is described. The model lumps the effect of non-uniform flow and dispersion into an effective advection velocity Ve and an effective dispersion coefficient De. It is shown that both Ve and De are scale-dependent (dependent on the length scale of the microscopic heterogeneity, ε), dependent on the Péclet number Pe, and on a dimensionless parameter α that represents the effects of microscopic heterogeneity. The parameter α, confined to the range of [-0.5, 0.5]more » for the numerical example presented, depends on the flow direction and non-uniform flow and dispersion fields. Effective advection velocity Ve and dispersion coefficient De can be derived for any given flow and dispersion fields, and . Homogenized solutions describing the macroscopic variations can be obtained from the effective model. Solutions with sub-unit-cell accuracy can be constructed by homogenized solutions and its spatial derivatives. A numerical implementation of the model compared with direct numerical solutions using a fine grid, demonstrated that the new method was in good agreement with direct solutions, but with significant computational savings.« less

Cellulose Nanofibrils and Mechanism of their Mineralization in Biomimetic Synthesis of Hydroxyapatite/Native Bacterial Cellulose Nanocomposites: Molecular Dynamics Simulations.

PubMed

Lukasheva, N V; Tolmachev, D A

2016-01-12

Molecular dynamics (MD) simulation of a nanofibril of native bacterial cellulose (BC) in solutions of mineral ions is presented. The supersaturated calcium-phosphate (CP) solution with the ionic composition of hydroxyapatite and CaCl2 solutions with the concentrations below, equal to, and above the solubility limits are simulated. The influence of solvation models (TIP3P and TIP4P-ew water models) on structural characteristics of the simulated nanofibril and on the crystal nucleation process is assessed. The structural characteristics of cellulose nanofibrils (in particular, of the surface layer) are found to be nearly independent of the solvation models used in the simulation and on the presence of ions in the solutions. It is shown that ionic clusters are formed in the solution rather than on the fibril surface. The cluster sizes are slightly different for the two water models. The effect of the ion-ion interaction parameters on the results is discussed. The main conclusion is that the activity of hydroxyl groups on the BC fibril surface is not high enough to cause adsorption of Ca(2+) ions from the solution. Therefore, the nucleation of CP crystals takes place initially in solution, and then the crystallites formed can be adsorbed on BC nanofibril surfaces.

Reference Solutions for Benchmark Turbulent Flows in Three Dimensions

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.; Pandya, Mohagna J.; Rumsey, Christopher L.

2016-01-01

A grid convergence study is performed to establish benchmark solutions for turbulent flows in three dimensions (3D) in support of turbulence-model verification campaign at the Turbulence Modeling Resource (TMR) website. The three benchmark cases are subsonic flows around a 3D bump and a hemisphere-cylinder configuration and a supersonic internal flow through a square duct. Reference solutions are computed for Reynolds Averaged Navier Stokes equations with the Spalart-Allmaras turbulence model using a linear eddy-viscosity model for the external flows and a nonlinear eddy-viscosity model based on a quadratic constitutive relation for the internal flow. The study involves three widely-used practical computational fluid dynamics codes developed and supported at NASA Langley Research Center: FUN3D, USM3D, and CFL3D. Reference steady-state solutions computed with these three codes on families of consistently refined grids are presented. Grid-to-grid and code-to-code variations are described in detail.

Advanced scatter search approach and its application in a sequencing problem of mixed-model assembly lines in a case company

NASA Astrophysics Data System (ADS)

Liu, Qiong; Wang, Wen-xi; Zhu, Ke-ren; Zhang, Chao-yong; Rao, Yun-qing

2014-11-01

Mixed-model assembly line sequencing is significant in reducing the production time and overall cost of production. To improve production efficiency, a mathematical model aiming simultaneously to minimize overtime, idle time and total set-up costs is developed. To obtain high-quality and stable solutions, an advanced scatter search approach is proposed. In the proposed algorithm, a new diversification generation method based on a genetic algorithm is presented to generate a set of potentially diverse and high-quality initial solutions. Many methods, including reference set update, subset generation, solution combination and improvement methods, are designed to maintain the diversification of populations and to obtain high-quality ideal solutions. The proposed model and algorithm are applied and validated in a case company. The results indicate that the proposed advanced scatter search approach is significant for mixed-model assembly line sequencing in this company.

Numerical Modeling of Ablation Heat Transfer

NASA Technical Reports Server (NTRS)

Ewing, Mark E.; Laker, Travis S.; Walker, David T.

2013-01-01

A unique numerical method has been developed for solving one-dimensional ablation heat transfer problems. This paper provides a comprehensive description of the method, along with detailed derivations of the governing equations. This methodology supports solutions for traditional ablation modeling including such effects as heat transfer, material decomposition, pyrolysis gas permeation and heat exchange, and thermochemical surface erosion. The numerical scheme utilizes a control-volume approach with a variable grid to account for surface movement. This method directly supports implementation of nontraditional models such as material swelling and mechanical erosion, extending capabilities for modeling complex ablation phenomena. Verifications of the numerical implementation are provided using analytical solutions, code comparisons, and the method of manufactured solutions. These verifications are used to demonstrate solution accuracy and proper error convergence rates. A simple demonstration of a mechanical erosion (spallation) model is also provided to illustrate the unique capabilities of the method.

Comparative study on ATR-FTIR calibration models for monitoring solution concentration in cooling crystallization

NASA Astrophysics Data System (ADS)

Zhang, Fangkun; Liu, Tao; Wang, Xue Z.; Liu, Jingxiang; Jiang, Xiaobin

2017-02-01

In this paper calibration model building based on using an ATR-FTIR spectroscopy is investigated for in-situ measurement of the solution concentration during a cooling crystallization process. The cooling crystallization of L-glutamic Acid (LGA) as a case is studied here. It was found that using the metastable zone (MSZ) data for model calibration can guarantee the prediction accuracy for monitoring the operating window of cooling crystallization, compared to the usage of undersaturated zone (USZ) spectra for model building as traditionally practiced. Calibration experiments were made for LGA solution under different concentrations. Four candidate calibration models were established using different zone data for comparison, by using a multivariate partial least-squares (PLS) regression algorithm for the collected spectra together with the corresponding temperature values. Experiments under different process conditions including the changes of solution concentration and operating temperature were conducted. The results indicate that using the MSZ spectra for model calibration can give more accurate prediction of the solution concentration during the crystallization process, while maintaining accuracy in changing the operating temperature. The primary reason of prediction error was clarified as spectral nonlinearity for in-situ measurement between USZ and MSZ. In addition, an LGA cooling crystallization experiment was performed to verify the sensitivity of these calibration models for monitoring the crystal growth process.

Alternative solution model for the ternary carbonate system CaCO3 - MgCO3 - FeCO3 - I. A ternary Bragg-Williams ordering model

USGS Publications Warehouse

McSwiggen, P.L.

1993-01-01

The minerals of the ternary carbonate system CaCO3 - MgCO3 - FeCO3 represent a complex series of solid solutions and ordering states. An understanding of those complexities requires a solution model that can both duplicate the subsolidus phase relationships and generate correct values for the activities. Such a solution model must account for the changes in the total energy of the system resulting from a change in the ordering state of the individual constituents. Various ordering models have been applied to binary carbonate systems, but no attempts have previously been made to model the ordering in the ternary system. This study derives a new set of equations that allow for the equilibrium degree of order to be calculated for a system involving three cations mixing on two sites, as in the case of the ternary carbonates. The method is based on the Bragg-Williams approach. From the degree of order, the mole fractions of the three cations in each of the two sites can be determined. Once the site occupancies have been established, a Margules-type mixing model can be used to determine the free energy of mixing in the solid solution and therefore the activities of the various components. ?? 1993 Springer-Verlag.

Experimental validation of the influence of white matter anisotropy on the intracranial EEG forward solution

PubMed Central

Schomer, Donald L.; Dehghani, Nima; Ulbert, Istvan; Cash, Sydney; Papavasiliou, Steve; Eisenberg, Solomon R.; Dale, Anders M.; Halgren, Eric

2010-01-01

Forward solutions with different levels of complexity are employed for localization of current generators, which are responsible for the electric and magnetic fields measured from the human brain. The influence of brain anisotropy on the forward solution is poorly understood. The goal of this study is to validate an anisotropic model for the intracranial electric forward solution by comparing with the directly measured ‘gold standard’. Dipolar sources are created at known locations in the brain and intracranial electroencephalogram (EEG) is recorded simultaneously. Isotropic models with increasing level of complexity are generated along with anisotropic models based on Diffusion tensor imaging (DTI). A Finite Element Method based forward solution is calculated and validated using the measured data. Major findings are (1) An anisotropic model with a linear scaling between the eigenvalues of the electrical conductivity tensor and water self-diffusion tensor in brain tissue is validated. The greatest improvement was obtained when the stimulation site is close to a region of high anisotropy. The model with a global anisotropic ratio of 10:1 between the eigenvalues (parallel: tangential to the fiber direction) has the worst performance of all the anisotropic models. (2) Inclusion of cerebrospinal fluid as well as brain anisotropy in the forward model is necessary for an accurate description of the electric field inside the skull. The results indicate that an anisotropic model based on the DTI can be constructed non-invasively and shows an improved performance when compared to the isotropic models for the calculation of the intracranial EEG forward solution. Electronic supplementary material The online version of this article (doi:10.1007/s10827-009-0205-z) contains supplementary material, which is available to authorized users. PMID:20063051

Drude-jellium model for the microwave conductivity of electrolyte solutions

NASA Astrophysics Data System (ADS)

Nhan, Tran Thi; Theu, Luong Thi; Tuan, Le; Viet, Nguyen Ai

2018-05-01

The microwave conductivity characteristics of electrolyte solutions have attracted much interest of researchers because a good understanding of their properties plays a key role to study fundamental processes in biology and chemistry. In this work, we consider the solution of sodium chloride as a plasma consisting of ions with water background. Its plasmon frequency is calculated by the jellium theory. The linear dependence of the microwave conductivity on the ion concentration of the electrolyte solutions is explained by a microscopic approach and described by a combination of this plasmon relationship and the simplified Drude formula for dielectric constant. Furthermore, the dependence of the microwave conductivity on the frequency of the salt solution is also examined. We suggest that it obeys the logistic distribution. We found a good agreement between theoretical calculations and experimental data. The values of the damping coefficient γ for the conductive solutions at low frequencies and the cutting frequency are estimated. The linear dependence of the diffusion coefficient on the temperature of the salt solution is also shown, in similarity with the result in the other model. The application of the Drude-jellium model could be done for the other electrolyte solutions in order to study theirs electro-dynamic properties.

Approximate Solutions for Ideal Dam-Break Sediment-Laden Flows on Uniform Slopes

NASA Astrophysics Data System (ADS)

Ni, Yufang; Cao, Zhixian; Borthwick, Alistair; Liu, Qingquan

2018-04-01

Shallow water hydro-sediment-morphodynamic (SHSM) models have been applied increasingly widely in hydraulic engineering and geomorphological studies over the past few decades. Analytical and approximate solutions are usually sought to verify such models and therefore confirm their credibility. Dam-break flows are often evoked because such flows normally feature shock waves and contact discontinuities that warrant refined numerical schemes to solve. While analytical and approximate solutions to clear-water dam-break flows have been available for some time, such solutions are rare for sediment transport in dam-break flows. Here we aim to derive approximate solutions for ideal dam-break sediment-laden flows resulting from the sudden release of a finite volume of frictionless, incompressible water-sediment mixture on a uniform slope. The approximate solutions are presented for three typical sediment transport scenarios, i.e., pure advection, pure sedimentation, and concurrent entrainment and deposition. Although the cases considered in this paper are not real, the approximate solutions derived facilitate suitable benchmark tests for evaluating SHSM models, especially presently when shock waves can be numerically resolved accurately with a suite of finite volume methods, while the accuracy of the numerical solutions of contact discontinuities in sediment transport remains generally poorer.

Homogenization Theory for the Prediction of Obstructed Solute Diffusivity in Macromolecular Solutions.

PubMed

Donovan, Preston; Chehreghanianzabi, Yasaman; Rathinam, Muruhan; Zustiak, Silviya Petrova

2016-01-01

The study of diffusion in macromolecular solutions is important in many biomedical applications such as separations, drug delivery, and cell encapsulation, and key for many biological processes such as protein assembly and interstitial transport. Not surprisingly, multiple models for the a-priori prediction of diffusion in macromolecular environments have been proposed. However, most models include parameters that are not readily measurable, are specific to the polymer-solute-solvent system, or are fitted and do not have a physical meaning. Here, for the first time, we develop a homogenization theory framework for the prediction of effective solute diffusivity in macromolecular environments based on physical parameters that are easily measurable and not specific to the macromolecule-solute-solvent system. Homogenization theory is useful for situations where knowledge of fine-scale parameters is used to predict bulk system behavior. As a first approximation, we focus on a model where the solute is subjected to obstructed diffusion via stationary spherical obstacles. We find that the homogenization theory results agree well with computationally more expensive Monte Carlo simulations. Moreover, the homogenization theory agrees with effective diffusivities of a solute in dilute and semi-dilute polymer solutions measured using fluorescence correlation spectroscopy. Lastly, we provide a mathematical formula for the effective diffusivity in terms of a non-dimensional and easily measurable geometric system parameter.

An analytic, approximate method for modeling steady, three-dimensional flow to partially penetrating wells

NASA Astrophysics Data System (ADS)

Bakker, Mark

2001-05-01

An analytic, approximate solution is derived for the modeling of three-dimensional flow to partially penetrating wells. The solution is written in terms of a correction on the solution for a fully penetrating well and is obtained by dividing the aquifer up, locally, in a number of aquifer layers. The resulting system of differential equations is solved by application of the theory for multiaquifer flow. The presented approach has three major benefits. First, the solution may be applied to any groundwater model that can simulate flow to a fully penetrating well; the solution may be superimposed onto the solution for the fully penetrating well to simulate the local three-dimensional drawdown and flow field. Second, the approach is applicable to isotropic, anisotropic, and stratified aquifers and to both confined and unconfined flow. Third, the solution extends over a small area around the well only; outside this area the three-dimensional effect of the partially penetrating well is negligible, and no correction to the fully penetrating well is needed. A number of comparisons are made to existing three-dimensional, analytic solutions, including radial confined and unconfined flow and a well in a uniform flow field. It is shown that a subdivision in three layers is accurate for many practical cases; very accurate solutions are obtained with more layers.

Absence of solute drag in solidification

NASA Astrophysics Data System (ADS)

Kittl, J. A.; Aziz, M. J.; Brunco, D. P.; Thompson, M. O.

1994-05-01

The interface response functions for alloy solidification were measured in the nondegenerate regime of partial solute trapping. We used a new technique to measure temperatures and velocities simultaneously during rapid solidification of Si-As alloys induced by pulsed laser melting. In addition, partition coefficients were determined using Rutherford backscattering. The results are in good agreement with predictions of the Continuous Growth Model without solute drag of M. J. Aziz and T. Kaplan [Acta Metall. 36, 1335 (1988)] and are inconsistent with all solute drag models.

Unsteady solute-transport simulation in streamflow using a finite-difference model

USGS Publications Warehouse

Land, Larry F.

1978-01-01

This report documents a rather simple, general purpose, one-dimensional, one-parameter, mass-transport model for field use. The model assumes a well-mixed conservative solute that may be coming from an unsteady source and is moving in unsteady streamflow. The quantity of solute being transported is in the units of concentration. Results are reported as such. An implicit finite-difference technique is used to solve the mass transport equation. It consists of creating a tridiagonal matrix and using the Thomas algorithm to solve the matrix for the unknown concentrations at the new time step. The computer program pesented is designed to compute the concentration of a water-quality constituent at any point and at any preselected time in a one-dimensional stream. The model is driven by the inflowing concentration of solute at the upstream boundary and is influenced by the solute entering the stream from tributaries and lateral ground-water inflow and from a source or sink. (Woodard-USGS)

Numerical modeling of subsurface radioactive solute transport from waste seepage ponds at the Idaho National Engineering Laboratory

USGS Publications Warehouse

Robertson, John B.

1976-01-01

Aqueous chemical and low-level radioactive effluents have been disposed to seepage ponds since 1952 at the Idaho National Engineering Laboratory. The solutions percolate toward the Snake River Plain aquifer (135 m below) through interlayered basalts and unconsolidated sediments and an extensive zone of ground water perched on a sedimentary layer about 40 m beneath the ponds. A three-segment numerical model was developed to simulate the system, including effects of convection, hydrodynamic dispersion, radioactive decay, and adsorption. Simulated hydraulics and solute migration patterns for all segments agree adequately with the available field data. The model can be used to project subsurface distributions of waste solutes under a variety of assumed conditions for the future. Although chloride and tritium reached the aquifer several years ago, the model analysis suggests that the more easily sorbed solutes, such as cesium-137 and strontium-90, would not reach the aquifer in detectable concentrations within 150 years for the conditions assumed. (Woodard-USGS)

Exact solutions of the Navier-Stokes equations generalized for flow in porous media

NASA Astrophysics Data System (ADS)

Daly, Edoardo; Basser, Hossein; Rudman, Murray

2018-05-01

Flow of Newtonian fluids in porous media is often modelled using a generalized version of the full non-linear Navier-Stokes equations that include additional terms describing the resistance to flow due to the porous matrix. Because this formulation is becoming increasingly popular in numerical models, exact solutions are required as a benchmark of numerical codes. The contribution of this study is to provide a number of non-trivial exact solutions of the generalized form of the Navier-Stokes equations for parallel flow in porous media. Steady-state solutions are derived in the case of flows in a medium with constant permeability along the main direction of flow and a constant cross-stream velocity in the case of both linear and non-linear drag. Solutions are also presented for cases in which the permeability changes in the direction normal to the main flow. An unsteady solution for a flow with velocity driven by a time-periodic pressure gradient is also derived. These solutions form a basis for validating computational models across a wide range of Reynolds and Darcy numbers.

Survey of Turbulence Models for the Computation of Turbulent Jet Flow and Noise

NASA Technical Reports Server (NTRS)

Nallasamy, N.

1999-01-01

The report presents an overview of jet noise computation utilizing the computational fluid dynamic solution of the turbulent jet flow field. The jet flow solution obtained with an appropriate turbulence model provides the turbulence characteristics needed for the computation of jet mixing noise. A brief account of turbulence models that are relevant for the jet noise computation is presented. The jet flow solutions that have been directly used to calculate jet noise are first reviewed. Then, the turbulent jet flow studies that compute the turbulence characteristics that may be used for noise calculations are summarized. In particular, flow solutions obtained with the k-e model, algebraic Reynolds stress model, and Reynolds stress transport equation model are reviewed. Since, the small scale jet mixing noise predictions can be improved by utilizing anisotropic turbulence characteristics, turbulence models that can provide the Reynolds stress components must now be considered for jet flow computations. In this regard, algebraic stress models and Reynolds stress transport models are good candidates. Reynolds stress transport models involve more modeling and computational effort and time compared to algebraic stress models. Hence, it is recommended that an algebraic Reynolds stress model (ASM) be implemented in flow solvers to compute the Reynolds stress components.

Consequences of energy conservation violation: late time solutions of Λ (T) CDM subclass of f(R,T) gravity using dynamical system approach

NASA Astrophysics Data System (ADS)

Shabani, Hamid; Ziaie, Amir Hadi

2017-05-01

Very recently, Josset and Perez (Phys. Rev. Lett. 118:021102, 2017) have shown that a violation of the energy-momentum tensor ( EMT) could result in an accelerated expansion state via the appearance of an effective cosmological constant, in the context of unimodular gravity. Inspired by this outcome, in this paper we investigate cosmological consequences of a violation of the EMT conservation in a particular class of f(R,T) gravity when only the pressure-less fluid is present. In this respect, we focus on the late time solutions of models of the type f(R,T)=R+β Λ (-T). As the first task, we study the solutions when the conservation of EMT is respected, and then we proceed with those in which violation occurs. We have found, provided that the EMT conservation is violated, that there generally exist two accelerated expansion solutions of which the stability properties depend on the underlying model. More exactly, we obtain a dark energy solution for which the effective equation of state depends on the model parameters and a de Sitter solution. We present a method to parametrize the Λ (-T) function, which is useful in a dynamical system approach and has been employed in the model. Also, we discuss the cosmological solutions for models with Λ (-T)=8π G(-T)^{α } in the presence of ultra-relativistic matter.

Advanced Technology for Portable Personal Visualization

DTIC Science & Technology

1991-03-01

walking. The building model is created using AutoCAD. Realism is enhanced by calculating a radiosity solution for the lighting model. This has an added...lighting, color combinations and decor. Due to the computationally intensive nature of the radiosity solution, modeling changes cannot be made on-line

Holomorphic solutions of the susy Grassmannian σ-model and gauge invariance

NASA Astrophysics Data System (ADS)

Hussin, V.; Lafrance, M.; Yurduşen, İ.; Zakrzewski, W. J.

2018-05-01

We study the gauge invariance of the supersymmetric Grassmannian sigma model . It is richer then its purely bosonic submodel and we show how to use it in order to reduce some constant curvature holomorphic solutions of the model into simpler expressions.

Modeling the Quiet Time Outflow Solution in the Polar Cap

NASA Technical Reports Server (NTRS)

Glocer, Alex

2011-01-01

We use the Polar Wind Outflow Model (PWOM) to study the geomagnetically quiet conditions in the polar cap during solar maximum, The PWOM solves the gyrotropic transport equations for O(+), H(+), and He(+) along several magnetic field lines in the polar region in order to reconstruct the full 3D solution. We directly compare our simulation results to the data based empirical model of Kitamura et al. [2011] of electron density, which is based on 63 months of Akebono satellite observations. The modeled ion and electron temperatures are also compared with a statistical compilation of quiet time data obtained by the EISCAT Svalbard Radar (ESR) and Intercosmos Satellites (Kitamura et al. [2011]). The data and model agree reasonably well. This study shows that photoelectrons play an important role in explaining the differences between sunlit and dark results, ion composition, as well as ion and electron temperatures of the quiet time polar wind solution. Moreover, these results provide validation of the PWOM's ability to model the quiet time ((background" solution.

Soliton stability in some knot soliton models

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

Adam, C.; Sanchez-Guillen, J.; Wereszczynski, A.

2007-02-15

We study the issue of stability of static solitonlike solutions in some nonlinear field theories which allow for knotted field configurations. Concretely, we investigate the Aratyn-Ferreira-Zimerman model [Phys. Lett. B 456, 162 (1999); Phys. Rev. Lett. 83, 1723 (1999)], based on a Lagrangian quartic in first derivatives with infinitely many conserved currents, for which infinitely many soliton solutions are known analytically. For this model we find that sectors with different (integer) topological charges (Hopf index) are not separated by an infinite energy barrier. Further, if variations which change the topological charge are allowed, then the static solutions are not evenmore » critical points of the energy functional. We also explain why soliton solutions can exist at all, in spite of these facts. In addition, we briefly discuss the Nicole model [J. Phys. G 4, 1363 (1978)], which is based on a sigma-model-type Lagrangian. For the Nicole model we find that different topological sectors are separated by an infinite energy barrier.« less

Synchronization Experiments With A Global Coupled Model of Intermediate Complexity

NASA Astrophysics Data System (ADS)

Selten, Frank; Hiemstra, Paul; Shen, Mao-Lin

2013-04-01

In the super modeling approach an ensemble of imperfect models are connected through nudging terms that nudge the solution of each model to the solution of all other models in the ensemble. The goal is to obtain a synchronized state through a proper choice of connection strengths that closely tracks the trajectory of the true system. For the super modeling approach to be successful, the connections should be dense and strong enough for synchronization to occur. In this study we analyze the behavior of an ensemble of connected global atmosphere-ocean models of intermediate complexity. All atmosphere models are connected to the same ocean model through the surface fluxes of heat, water and momentum, the ocean is integrated using weighted averaged surface fluxes. In particular we analyze the degree of synchronization between the atmosphere models and the characteristics of the ensemble mean solution. The results are interpreted using a low order atmosphere-ocean toy model.

Simulation of water-quality data at selected stream sites in the Missouri River Basin, Montana

USGS Publications Warehouse

Knapton, J.R.; Jacobson, M.A.

1980-01-01

Modification of sampling programs at some water-quality stations in the Missouri River basin in Montana has eliminated the means by which solute loads have been directly obtained in past years. To compensate for this loss, water-quality and streamflow data were statistically analyzed and solute loads were simulated using computer techniques.Functional relationships existing between specific conductance and solute concentration for monthly samples were used to develop linear regression models. The models were then used to simulate daily solute concentrations using daily specific conductance as the independent variable. Once simulated, the solute concentrations, in milligrams per liter, were transformed into daily solute loads, in tons, using mean daily streamflow records.Computer output was formatted into tables listing simulated mean monthly solute concentrations, in milligrams per liter, and the monthly and annual solute loads, in tons, for water years 1975-78.

Modeling preferential water flow and solute transport in unsaturated soil using the active region model

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

Sheng, F.; Wang, K.; Zhang, R.

2009-03-15

Preferential flow and solute transport are common processes in the unsaturated soil, in which distributions of soil water content and solute concentrations are often characterized as fractal patterns. An active region model (ARM) was recently proposed to describe the preferential flow and transport patterns. In this study, ARM governing equations were derived to model the preferential soil water flow and solute transport processes. To evaluate the ARM equations, dye infiltration experiments were conducted, in which distributions of soil water content and Cl{sup -} concentration were measured. Predicted results using the ARM and the mobile-immobile region model (MIM) were compared withmore » the measured distributions of soil water content and Cl{sup -} concentration. Although both the ARM and the MIM are two-region models, they are fundamental different in terms of treatments of the flow region. The models were evaluated based on the modeling efficiency (ME). The MIM provided relatively poor prediction results of the preferential flow and transport with negative ME values or positive ME values less than 0.4. On the contrary, predicted distributions of soil water content and Cl- concentration using the ARM agreed reasonably well with the experimental data with ME values higher than 0.8. The results indicated that the ARM successfully captured the macroscopic behavior of preferential flow and solute transport in the unsaturated soil.« less

Panel summary report

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

Gutjahr, A.L.; Kincaid, C.T.; Mercer, J.W.

1987-04-01

The objective of this report is to summarize the various modeling approaches that were used to simulate solute transport in a variably saturated emission. In particular, the technical strengths and weaknesses of each approach are discussed, and conclusions and recommendations for future studies are made. Five models are considered: (1) one-dimensional analytical and semianalytical solutions of the classical deterministic convection-dispersion equation (van Genuchten, Parker, and Kool, this report ); (2) one-dimensional simulation using a continuous-time Markov process (Knighton and Wagenet, this report); (3) one-dimensional simulation using the time domain method and the frequency domain method (Duffy and Al-Hassan, this report);more » (4) one-dimensional numerical approach that combines a solution of the classical deterministic convection-dispersion equation with a chemical equilibrium speciation model (Cederberg, this report); and (5) three-dimensional numerical solution of the classical deterministic convection-dispersion equation (Huyakorn, Jones, Parker, Wadsworth, and White, this report). As part of the discussion, the input data and modeling results are summarized. The models were used in a data analysis mode, as opposed to a predictive mode. Thus, the following discussion will concentrate on the data analysis aspects of model use. Also, all the approaches were similar in that they were based on a convection-dispersion model of solute transport. Each discussion addresses the modeling approaches in the order listed above.« less

Two cation exchange models for direct and inverse modelling of solution major cation composition in equilibrium with illite surfaces

NASA Astrophysics Data System (ADS)

Tournassat, Christophe; Gailhanou, Hélène; Crouzet, Catherine; Braibant, Gilles; Gautier, Anne; Lassin, Arnault; Blanc, Philippe; Gaucher, Eric C.

2007-03-01

Na/K, Na/Ca and Na/Mg exchange isotherms were performed on the fine fraction (<2 μm) of Imt-2 illite samples at a total normality of about 0.005 mol/L in anionic chloride medium. The derived selectivity coefficients for Na/K, Na/Ca and Na/Mg were found to vary as a function of the exchanger composition and compared well with the data collected in the literature for similar experimental conditions. Two models were built to reproduce the data: the first was a multi(2)-site model with constant Gaines and Thomas selectivity coefficients; the second was a one-site model taking into account surface species activity coefficients. The results of the models were in rather good agreement with both our data and literature data. The multi-site model proved to be efficient in predicting the exchanger composition as a function of the Na/Ca/Mg/K concentrations in solution, whereas the one-site model proved to be a better approach to derive the Na/Ca/Mg/K concentrations in solution based on the knowledge of the exchanger composition and the total normality of the solution. The interest of this approach is illustrated by the need for major cation solute concentration predictions in compacted clay for the characterization of nuclear deep disposal host rock repositories.

Transport and concentration controls for chloride, strontium, potassium and lead in Uvas Creek, a small cobble-bed stream in Santa Clara County, California, U.S.A. 2. Mathematical modeling

USGS Publications Warehouse

Jackman, A.P.; Walters, R.A.; Kennedy, V.C.

1984-01-01

Three models describing solute transport of conservative ion species and another describing transport of species which adsorb linearly and reversibly on bed sediments are developed and tested. The conservative models are based on three different conceptual models of the transient storage of solute in the bed. One model assumes the bed to be a well-mixed zone with flux of solute into the bed proportional to the difference between stream concentration and bed concentration. The second model assumes solute in the bed is transported by a vertical diffusion process described by Fick's law. The third model assumes that convection occurs in a selected portion of the bed while the mechanism of the first model functions everywhere. The model for adsorbing species assumes that the bed consists of particles of uniform size with the rate of uptake controlled by an intraparticle diffusion process. All models are tested using data collected before, during and after a 24-hr. pulse injection of chloride, strontium, potassium and lead ions into Uvas Creek near Morgan Hill, California, U.S.A. All three conservative models accurately predict chloride ion concentrations in the stream. The model employing the diffusion mechanism for bed transport predicts better than the others. The adsorption model predicts both strontium and potassium ion concentrations well during the injection of the pulse but somewhat overestimates the observed concentrations after the injection ceases. The overestimation may be due to the convection of solute deep into the bed where it is retained longer than the 3-week post-injection observation period. The model, when calibrated for strontium, predicts potassium equally well when the adsorption equilibrium constant for strontium is replaced by that for potassium. ?? 1984.

On the Solution of the Three-Dimensional Flowfield About a Flow-Through Nacelle. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Compton, William Bernard

1985-01-01

The solution of the three dimensional flow field for a flow through nacelle was studied. Both inviscid and viscous inviscid interacting solutions were examined. Inviscid solutions were obtained with two different computational procedures for solving the three dimensional Euler equations. The first procedure employs an alternating direction implicit numerical algorithm, and required the development of a complete computational model for the nacelle problem. The second computational technique employs a fourth order Runge-Kutta numerical algorithm which was modified to fit the nacelle problem. Viscous effects on the flow field were evaluated with a viscous inviscid interacting computational model. This model was constructed by coupling the explicit Euler solution procedure with a flag entrainment boundary layer solution procedure in a global iteration scheme. The computational techniques were used to compute the flow field for a long duct turbofan engine nacelle at free stream Mach numbers of 0.80 and 0.94 and angles of attack of 0 and 4 deg.

Analysis of stability and bifurcations of fixed points and periodic solutions of a lumped model of neocortex with two delays

PubMed Central

2012-01-01

A lumped model of neural activity in neocortex is studied to identify regions of multi-stability of both steady states and periodic solutions. Presence of both steady states and periodic solutions is considered to correspond with epileptogenesis. The model, which consists of two delay differential equations with two fixed time lags is mainly studied for its dependency on varying connection strength between populations. Equilibria are identified, and using linear stability analysis, all transitions are determined under which both trivial and non-trivial fixed points lose stability. Periodic solutions arising at some of these bifurcations are numerically studied with a two-parameter bifurcation analysis. PMID:22655859

Shape determination and control for large space structures

NASA Technical Reports Server (NTRS)

Weeks, C. J.

1981-01-01

An integral operator approach is used to derive solutions to static shape determination and control problems associated with large space structures. Problem assumptions include a linear self-adjoint system model, observations and control forces at discrete points, and performance criteria for the comparison of estimates or control forms. Results are illustrated by simulations in the one dimensional case with a flexible beam model, and in the multidimensional case with a finite model of a large space antenna. Modal expansions for terms in the solution algorithms are presented, using modes from the static or associated dynamic mode. These expansions provide approximated solutions in the event that a used form analytical solution to the system boundary value problem is not available.

Uncovering Implicit Assumptions: A Large-Scale Study on Students' Mental Models of Diffusion

ERIC Educational Resources Information Center

Stains, Marilyne; Sevian, Hannah

2015-01-01

Students' mental models of diffusion in a gas phase solution were studied through the use of the Structure and Motion of Matter (SAMM) survey. This survey permits identification of categories of ways students think about the structure of the gaseous solute and solvent, the origin of motion of gas particles, and trajectories of solute particles in…

Developing semi-analytical solution for multiple-zone transient storage model with spatially non-uniform storage

NASA Astrophysics Data System (ADS)

Deng, Baoqing; Si, Yinbing; Wang, Jia

2017-12-01

Transient storages may vary along the stream due to stream hydraulic conditions and the characteristics of storage. Analytical solutions of transient storage models in literature didn't cover the spatially non-uniform storage. A novel integral transform strategy is presented that simultaneously performs integral transforms to the concentrations in the stream and in storage zones by using the single set of eigenfunctions derived from the advection-diffusion equation of the stream. The semi-analytical solution of the multiple-zone transient storage model with the spatially non-uniform storage is obtained by applying the generalized integral transform technique to all partial differential equations in the multiple-zone transient storage model. The derived semi-analytical solution is validated against the field data in literature. Good agreement between the computed data and the field data is obtained. Some illustrative examples are formulated to demonstrate the applications of the present solution. It is shown that solute transport can be greatly affected by the variation of mass exchange coefficient and the ratio of cross-sectional areas. When the ratio of cross-sectional areas is big or the mass exchange coefficient is small, more reaches are recommended to calibrate the parameter.

Influence of Anti-inflammatory Drugs on the Rheological Properties of Synovial Fluid and Its Components

NASA Astrophysics Data System (ADS)

Krause, Wendy E.; Klossner, Rebecca R.; Liang, Jing; Colby, Ralph H.

2006-03-01

The polyelectrolyte hyaluronic acid (HA, hyaluronan), its interactions with anti-inflammatory drugs and other biopolymers, and its role in synovial fluid are being studied. We are investigating the rheological properties of sodium hyaluronate (NaHA) solutions and an experimental model of synovial fluid (comprised of NaHA, and the plasma proteins albumin and γ-globulins). Steady shear measurements on bovine synovial fluid, the synovial fluid model, and plasma protein solutions indicate that the fluids are rheopectic (stress increases with time under steady shear). In addition, the influence of anti-inflammatory agents on these solutions is being explored. Initial results indicate that D-penicillamine and hydroxychloroquine (HCQ) affect the rheology of the synovial fluid model and its components. While HCQ has no effect on the viscosity of NaHA solutions, it inhibits/suppresses the observed rheopexy of the synovial fluid model and plasma protein solutions. In contrast, D-penicillamine has a complex, time dependent effect on the viscosity of NaHA solutions,---reducing the zero shear rate viscosity of a 3 mg/mL NaHA (in phosphate buffered saline) by ca. 40% after 44 days. The potential implications of these results will be discussed.

On the Liouville 2D dilaton gravity models with sinh-Gordon matter

NASA Astrophysics Data System (ADS)

Frolov, Valeri P.; Zelnikov, Andrei

2018-02-01

We study 1 + 1 dimensional dilaton gravity models which take into account backreaction of the sinh-Gordon matter field. We found a wide class of exact solutions which generalizes black hole solutions of the Jackiw-Teitelboim gravity model and its hyperbolic deformation.

Modelling Difficulties and Their Overcoming Strategies in the Solution of a Modelling Problem

ERIC Educational Resources Information Center

Dede, Ayse Tekin

2016-01-01

The purpose of the study is to reveal the elementary mathematics student teachers' difficulties encountered in the solution of a modelling problem, the strategies to overcome those difficulties and whether the strategies worked or not. Nineteen student teachers solved the modelling problem in their four or five-person groups, and the video records…

On the accuracy of analytical models of impurity segregation during directional melt crystallization and their applicability for quantitative calculations

NASA Astrophysics Data System (ADS)

Voloshin, A. E.; Prostomolotov, A. I.; Verezub, N. A.

2016-11-01

The paper deals with the analysis of the accuracy of some one-dimensional (1D) analytical models of the axial distribution of impurities in the crystal grown from a melt. The models proposed by Burton-Prim-Slichter, Ostrogorsky-Muller and Garandet with co-authors are considered, these models are compared to the results of a two-dimensional (2D) numerical simulation. Stationary solutions as well as solutions for the initial transient regime obtained using these models are considered. The sources of errors are analyzed, a conclusion is made about the applicability of 1D analytical models for quantitative estimates of impurity incorporation into the crystal sample as well as for the solution of the inverse problems.

Joint global optimization of tomographic data based on particle swarm optimization and decision theory

NASA Astrophysics Data System (ADS)

Paasche, H.; Tronicke, J.

2012-04-01

In many near surface geophysical applications multiple tomographic data sets are routinely acquired to explore subsurface structures and parameters. Linking the model generation process of multi-method geophysical data sets can significantly reduce ambiguities in geophysical data analysis and model interpretation. Most geophysical inversion approaches rely on local search optimization methods used to find an optimal model in the vicinity of a user-given starting model. The final solution may critically depend on the initial model. Alternatively, global optimization (GO) methods have been used to invert geophysical data. They explore the solution space in more detail and determine the optimal model independently from the starting model. Additionally, they can be used to find sets of optimal models allowing a further analysis of model parameter uncertainties. Here we employ particle swarm optimization (PSO) to realize the global optimization of tomographic data. PSO is an emergent methods based on swarm intelligence characterized by fast and robust convergence towards optimal solutions. The fundamental principle of PSO is inspired by nature, since the algorithm mimics the behavior of a flock of birds searching food in a search space. In PSO, a number of particles cruise a multi-dimensional solution space striving to find optimal model solutions explaining the acquired data. The particles communicate their positions and success and direct their movement according to the position of the currently most successful particle of the swarm. The success of a particle, i.e. the quality of the currently found model by a particle, must be uniquely quantifiable to identify the swarm leader. When jointly inverting disparate data sets, the optimization solution has to satisfy multiple optimization objectives, at least one for each data set. Unique determination of the most successful particle currently leading the swarm is not possible. Instead, only statements about the Pareto optimality of the found solutions can be made. Identification of the leading particle traditionally requires a costly combination of ranking and niching techniques. In our approach, we use a decision rule under uncertainty to identify the currently leading particle of the swarm. In doing so, we consider the different objectives of our optimization problem as competing agents with partially conflicting interests. Analysis of the maximin fitness function allows for robust and cheap identification of the currently leading particle. The final optimization result comprises a set of possible models spread along the Pareto front. For convex Pareto fronts, solution density is expected to be maximal in the region ideally compromising all objectives, i.e. the region of highest curvature.

Peritoneal fluid transport in CAPD patients with different transport rates of small solutes.

PubMed

Sobiecka, Danuta; Waniewski, Jacek; Weryński, Andrzej; Lindholm, Bengt

2004-01-01

Continuous ambulatory peritoneal dialysis (CAPD) patients with high peritoneal solute transport rate often have inadequate peritoneal fluid transport. It is not known whether this inadequate fluid transport is due solely to a too rapid fall of osmotic pressure, or if the decreased effectiveness of fluid transport is also a contributing factor. To analyze fluid transport parameters and the effectiveness of dialysis fluid osmotic pressure in the induction of fluid flow in CAPD patients with different small solute transport rates. 44 CAPD patients were placed in low (n = 6), low-average (n = 13), high-average (n = 19), and high (n = 6) transport groups according to a modified peritoneal equilibration test (PET). The study involved a 6-hour peritoneal dialysis dwell with 2 L 3.86% glucose dialysis fluid for each patient. Radioisotopically labeled serum albumin was added as a volume marker.The fluid transport parameters (osmotic conductance and fluid absorption rate) were estimated using three mathematical models of fluid transport: (1) Pyle model (model P), which describes ultrafiltration rate as an exponential function of time; (2) model OS, which is based on the linear relationship of ultrafiltration rate and overall osmolality gradient between dialysis fluid and blood; and (3) model G, which is based on the linear relationship between ultrafiltration rate and glucose concentration gradient between dialysis fluid and blood. Diffusive mass transport coefficients (K(BD)) for glucose, urea, creatinine, potassium, and sodium were estimated using the modified Babb-Randerson-Farrell model. The high transport group had significantly lower dialysate volume and glucose and osmolality gradients between dialysate and blood, but significantly higher K(BD) for small solutes compared with the other transport groups. Osmotic conductance, fluid absorption rate, and initial ultrafiltration rate did not differ among the transport groups for model OS and model P. Model G yielded unrealistic values of fluid transport parameters that differed from those estimated by models OS and P. The K(BD) values for small solutes were significantly different among the groups, and did not correlate with fluid transport parameters for model OS. The difference in fluid transport between the different transport groups was due only to the differences in the rate of disappearance of the overall osmotic pressure of the dialysate, which was a combined result of the transport rate of glucose and other small solutes. Although the glucose gradient is the major factor influencing ultrafiltration rate, other solutes, such as urea, are also of importance. The counteractive effect of plasma small solutes on transcapillary ultrafiltration was found to be especially notable in low transport patients. Thus, glucose gradient alone should not be considered the only force that shapes the ultrafiltration profile during peritoneal dialysis. We did not find any correlations between diffusive mass transport coefficients for small solutes and fluid transport parameters such as osmotic conductance or fluid and volume marker absorption. We may thus conclude that the pathway(s) for fluid transport appears to be partly independent from the pathway(s) for small solute transport, which supports the hypothesis of different pore types for fluid and solute transport.

Mechanism for suppression of radiation-induced segregation by oversized solute addition in austenitic stainless steel

NASA Astrophysics Data System (ADS)

Hackett, Micah Jeremiah

The objective of this thesis is to quantify the effect of oversized solutes on radiation-induced segregation in austenitic stainless steels and to determine the mechanism of this effect. Zr or Hf additions to austenitic stainless steels demonstrated a reduction in radiation-induced segregation of Cr and Ni at the grain boundary after proton irradiation at 400°C and 500°C to low doses, but the solute effect disappeared at higher doses. Rate theory modeling of RIS was extended to incorporate a solute-vacancy trapping mechanism to predict the effect of solutes on RIS. The model showed that RIS is most sensitive to the solute-vacancy binding energy. First principles calculations were used to determine a binding energy of 1.08 eV for Zr and 0.71 eV for Hf. Model and experiment agreed in showing suppression of Cr depletion at doses of 3 dpa at 400°C and 1 dpa at 500°C, and experimental results were consistent with the model in showing greater effectiveness of Zr relative to Hf due to a larger binding energy. The dislocation loop microstructure was measured at 400°C, 3 and 7 dpa, and a significant decrease in loop density and total loop line length in the oversized solute alloys relative to the reference alloys. The loop microstructure results were consistent with RIS results by confirming enhanced recombination of point defects by solute-vacancy trapping. Increases in RIS with dose indicated a loss of solute effectiveness, which was consistent with an observed increase in loop line length from 3 to 7 dpa. The loss of solute effectiveness at high dose is attributed to a loss of oversized solute from the matrix due to coarsening of carbide precipitates. X-ray diffraction identified a microstructure with ZrC or HfC precipitates prior to irradiation. Precipitate coarsening was identified as the most likely mechanism for the loss of solute effectiveness on RIS by the following: (1) diffusion analysis suggested significant solute diffusion by the vacancy flux to precipitate surfaces on the time scales of proton irradiations, and (2) atom probe measurements confirmed the loss of oversized solute in solution as a function of irradiation dose. RIS measurements and subsequent analyses were consistent with the solute-vacancy trapping process as the mechanism for enhanced recombination and suppression of RIS.

The screening Horndeski cosmologies

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

Starobinsky, Alexei A.; Department of General Relativity and Gravitation, Institute of Physics,Kazan Federal University,Kremlevskaya street 18, 420008 Kazan; Sushkov, Sergey V.

2016-06-06

We present a systematic analysis of homogeneous and isotropic cosmologies in a particular Horndeski model with Galileon shift symmetry, containing also a Λ-term and a matter. The model, sometimes called Fab Five, admits a rich spectrum of solutions. Some of them describe the standard late time cosmological dynamic dominated by the Λ-term and matter, while at the early times the universe expands with a constant Hubble rate determined by the value of the scalar kinetic coupling. For other solutions the Λ-term and matter are screened at all times but there are nevertheless the early and late accelerating phases. The modelmore » also admits bounces, as well as peculiar solutions describing “the emergence of time”. Most of these solutions contain ghosts in the scalar and tensor sectors. However, a careful analysis reveals three different branches of ghost-free solutions, all showing a late time acceleration phase. We analyse the dynamical stability of these solutions and find that all of them are stable in the future, since all their perturbations stay bounded at late times. However, they all turn out to be unstable in the past, as their perturbations grow violently when one approaches the initial spacetime singularity. We therefore conclude that the model has no viable solutions describing the whole of the cosmological history, although it may describe the current acceleration phase. We also check that the flat space solution is ghost-free in the model, but it may acquire ghost in more general versions of the Horndeski theory.« less

Applications of IBSOM and ETEM for solving the nonlinear chains of atoms with long-range interactions

NASA Astrophysics Data System (ADS)

Foroutan, Mohammadreza; Zamanpour, Isa; Manafian, Jalil

2017-10-01

This paper presents a number of new solutions obtained for solving a complex nonlinear equation describing dynamics of nonlinear chains of atoms via the improved Bernoulli sub-ODE method (IBSOM) and the extended trial equation method (ETEM). The proposed solutions are kink solitons, anti-kink solitons, soliton solutions, hyperbolic solutions, trigonometric solutions, and bellshaped soliton solutions. Then our new results are compared with the well-known results. The methods used here are very simple and succinct and can be also applied to other nonlinear models. The balance number of these methods is not constant contrary to other methods. The proposed methods also allow us to establish many new types of exact solutions. By utilizing the Maple software package, we show that all obtained solutions satisfy the conditions of the studied model. More importantly, the solutions found in this work can have significant applications in Hamilton's equations and generalized momentum where solitons are used for long-range interactions.

FAST TRACK COMMUNICATION: Regularized Kerr-Newman solution as a gravitating soliton

NASA Astrophysics Data System (ADS)

Burinskii, Alexander

2010-10-01

The charged, spinning and gravitating soliton is realized as a regular solution of the Kerr-Newman (KN) field coupled with a chiral Higgs model. A regular core of the solution is formed by a domain wall bubble interpolating between the external KN solution and a flat superconducting interior. An internal electromagnetic (em) field is expelled to the boundary of the bubble by the Higgs field. The solution reveals two new peculiarities: (i) the Higgs field is oscillating, similar to the known oscillon models; (ii) the em field forms on the edge of the bubble a Wilson loop, resulting in quantization of the total angular momentum.

From 'solution shop' model to 'focused factory' in hospital surgery: increasing care value and predictability.

PubMed

Cook, David; Thompson, Jeffrey E; Habermann, Elizabeth B; Visscher, Sue L; Dearani, Joseph A; Roger, Veronique L; Borah, Bijan J

2014-05-01

The full-service US hospital has been described organizationally as a "solution shop," in which medical problems are assumed to be unstructured and to require expert physicians to determine each course of care. If universally applied, this model contributes to unwarranted variation in care, which leads to lower quality and higher costs. We purposely disrupted the adult cardiac surgical practice that we led at Mayo Clinic, in Rochester, Minnesota, by creating a "focused factory" model (characterized by a uniform approach to delivering a limited set of high-quality products) within the practice's solution shop. Key elements of implementing the new model were mapping the care process, segmenting the patient population, using information technology to communicate clearly defined expectations, and empowering nonphysician providers at the bedside. Using a set of criteria, we determined that the focused-factory model was appropriate for 67 percent of cardiac surgical patients. We found that implementation of the model reduced resource use, length-of-stay, and cost. Variation was markedly reduced, and outcomes were improved. Assigning patients to different care models increases care value and the predictability of care process, outcomes, and costs while preserving (in a lesser clinical footprint) the strengths of the solution shop. We conclude that creating a focused-factory model within a solution shop, by applying industrial engineering principles and health information technology tools and changing the model of work, is very effective in both improving quality and reducing costs.

A model for managing sources of groundwater pollution

USGS Publications Warehouse

Gorelick, Steven M.

1982-01-01

The waste disposal capacity of a groundwater system can be maximized while maintaining water quality at specified locations by using a groundwater pollutant source management model that is based upon linear programing and numerical simulation. The decision variables of the management model are solute waste disposal rates at various facilities distributed over space. A concentration response matrix is used in the management model to describe transient solute transport and is developed using the U.S. Geological Survey solute transport simulation model. The management model was applied to a complex hypothetical groundwater system. Large-scale management models were formulated as dual linear programing problems to reduce numerical difficulties and computation time. Linear programing problems were solved using a numerically stable, available code. Optimal solutions to problems with successively longer management time horizons indicated that disposal schedules at some sites are relatively independent of the number of disposal periods. Optimal waste disposal schedules exhibited pulsing rather than constant disposal rates. Sensitivity analysis using parametric linear programing showed that a sharp reduction in total waste disposal potential occurs if disposal rates at any site are increased beyond their optimal values.

Solitons, τ-functions and hamiltonian reduction for non-Abelian conformal affine Toda theories

NASA Astrophysics Data System (ADS)

Ferreira, L. A.; Miramontes, J. Luis; Guillén, Joaquín Sánchez

1995-02-01

We consider the Hamiltonian reduction of the "two-loop" Wess-Zumino-Novikov-Witten model (WZNW) based on an untwisted affine Kac-Moody algebra G. The resulting reduced models, called Generalized Non-Abelian Conformal Affine Toda (G-CAT), are conformally invariant and a wide class of them possesses soliton solutions; these models constitute non-Abelian generalizations of the conformal affine Toda models. Their general solution is constructed by the Leznov-Saveliev method. Moreover, the dressing transformations leading to the solutions in the orbit of the vacuum are considered in detail, as well as the τ-functions, which are defined for any integrable highest weight representation of G, irrespectively of its particular realization. When the conformal symmetry is spontaneously broken, the G-CAT model becomes a generalized affine Toda model, whose soliton solutions are constructed. Their masses are obtained exploring the spontaneous breakdown of the conformal symmetry, and their relation to the fundamental particle masses is discussed. We also introduce what we call the two-loop Virasoro algebra, describing extended symmetries of the two-loop WZNW models.

A scaled-ionic-charge simulation model that reproduces enhanced and suppressed water diffusion in aqueous salt solutions.

PubMed

Kann, Z R; Skinner, J L

2014-09-14

Non-polarizable models for ions and water quantitatively and qualitatively misrepresent the salt concentration dependence of water diffusion in electrolyte solutions. In particular, experiment shows that the water diffusion coefficient increases in the presence of salts of low charge density (e.g., CsI), whereas the results of simulations with non-polarizable models show a decrease of the water diffusion coefficient in all alkali halide solutions. We present a simple charge-scaling method based on the ratio of the solvent dielectric constants from simulation and experiment. Using an ion model that was developed independently of a solvent, i.e., in the crystalline solid, this method improves the water diffusion trends across a range of water models. When used with a good-quality water model, e.g., TIP4P/2005 or E3B, this method recovers the qualitative behaviour of the water diffusion trends. The model and method used were also shown to give good results for other structural and dynamic properties including solution density, radial distribution functions, and ion diffusion coefficients.

A trade-off solution between model resolution and covariance in surface-wave inversion

USGS Publications Warehouse

Xia, J.; Xu, Y.; Miller, R.D.; Zeng, C.

2010-01-01

Regularization is necessary for inversion of ill-posed geophysical problems. Appraisal of inverse models is essential for meaningful interpretation of these models. Because uncertainties are associated with regularization parameters, extra conditions are usually required to determine proper parameters for assessing inverse models. Commonly used techniques for assessment of a geophysical inverse model derived (generally iteratively) from a linear system are based on calculating the model resolution and the model covariance matrices. Because the model resolution and the model covariance matrices of the regularized solutions are controlled by the regularization parameter, direct assessment of inverse models using only the covariance matrix may provide incorrect results. To assess an inverted model, we use the concept of a trade-off between model resolution and covariance to find a proper regularization parameter with singular values calculated in the last iteration. We plot the singular values from large to small to form a singular value plot. A proper regularization parameter is normally the first singular value that approaches zero in the plot. With this regularization parameter, we obtain a trade-off solution between model resolution and model covariance in the vicinity of a regularized solution. The unit covariance matrix can then be used to calculate error bars of the inverse model at a resolution level determined by the regularization parameter. We demonstrate this approach with both synthetic and real surface-wave data. ?? 2010 Birkh??user / Springer Basel AG.

Comparing the Caputo, Caputo-Fabrizio and Atangana-Baleanu derivative with fractional order: Fractional cubic isothermal auto-catalytic chemical system

NASA Astrophysics Data System (ADS)

Saad, K. M.

2018-03-01

In this work we extend the standard model for a cubic isothermal auto-catalytic chemical system (CIACS) to a new model of a fractional cubic isothermal auto-catalytic chemical system (FCIACS) based on Caputo (C), Caputo-Fabrizio (CF) and Atangana-Baleanu in the Liouville-Caputo sense (ABC) fractional time derivatives, respectively. We present approximate solutions for these extended models using the q -homotopy analysis transform method ( q -HATM). We solve the FCIACS with the C derivative and compare our results with those obtained using the CF and ABC derivatives. The ranges of convergence of the solutions are found and the optimal values of h , the auxiliary parameter, are derived. Finally, these solutions are compared with numerical solutions of the various models obtained using finite differences and excellent agreement is found.

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

Brihaye, Yves; Delsate, Terence; Kodama, Yuta

We consider a six-dimensional brane world model, where the brane is described by a localized solution to the baby-Skyrme model extending in the extra dimensions. The branes have a cosmological constant modeled by inflating four-dimensional slices, and we further consider a bulk cosmological constant. We construct solutions numerically and present evidence that the solutions cease to exist for large values of the brane cosmological constant in some particular case. Then we study the stability of the model by considering perturbation of the gravitational part (resp. baby Skyrmion) with fixed matter fields (resp. gravitational background). Our results indicate that the perturbationmore » equations do not admit localized solutions for certain type of perturbation. The stability analysis can be alternatively seen as leading to a particle spectrum; we give mass estimations for the baby-Skyrme perturbation and for the graviton.« less

Spatial model of convective solute transport in brain extracellular space does not support a “glymphatic” mechanism

PubMed Central

Jin, Byung-Ju; Smith, Alex J.

2016-01-01

A “glymphatic system,” which involves convective fluid transport from para-arterial to paravenous cerebrospinal fluid through brain extracellular space (ECS), has been proposed to account for solute clearance in brain, and aquaporin-4 water channels in astrocyte endfeet may have a role in this process. Here, we investigate the major predictions of the glymphatic mechanism by modeling diffusive and convective transport in brain ECS and by solving the Navier–Stokes and convection–diffusion equations, using realistic ECS geometry for short-range transport between para-arterial and paravenous spaces. Major model parameters include para-arterial and paravenous pressures, ECS volume fraction, solute diffusion coefficient, and astrocyte foot-process water permeability. The model predicts solute accumulation and clearance from the ECS after a step change in solute concentration in para-arterial fluid. The principal and robust conclusions of the model are as follows: (a) significant convective transport requires a sustained pressure difference of several mmHg between the para-arterial and paravenous fluid and is not affected by pulsatile pressure fluctuations; (b) astrocyte endfoot water permeability does not substantially alter the rate of convective transport in ECS as the resistance to flow across endfeet is far greater than in the gaps surrounding them; and (c) diffusion (without convection) in the ECS is adequate to account for experimental transport studies in brain parenchyma. Therefore, our modeling results do not support a physiologically important role for local parenchymal convective flow in solute transport through brain ECS. PMID:27836940

Real-solution stability diagrams: A thermodynamic tool for modeling corrosion in wide temperature and concentration ranges

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

Anderko, A.; Sanders, S.J.; Young, R.D.

1997-01-01

A method was developed for construction of stability diagrams for metals in the presence of realistically modeled aqueous solutions. The method was based on a comprehensive thermodynamic model that combines the Helgeson-Kirkham-Flowers (HKF) equation of state for standard-state properties with a solution nonideality model based on the activity coefficient expressions developed by Bromley and Pitzer. Composition-dependent nonideality effects were incorporated into the calculation of predominance areas for dissolved and solid species. Using the combined thermodynamic model, stability diagrams can be computed for systems involving concentrated solutions (i.e., with molalities up to 30 mol/kg) at temperatures up to 573 K andmore » pressures up to 100 MPa. Since the diagrams are based on a realistic thermodynamic model for the aqueous phase, they are referred to as real-solution stability diagrams. In addition to customary potential (E) and pH variables, concentrations of various active species (e.g., complexing agents) can be used as independent variables, making it possible to analyze effects of various compounds that promote or inhibit corrosion. Usefulness of the methodology was demonstrated by generating real-solution stability diagrams for five representative systems (i.e., sulfur-water [S-H{sub 2}O], copper-ammonia-water [Cu-NH{sub 3}-H{sub 2}O], titanium-chlorine-calcium-water [Ti-Cl-Ca-H{sub 2}O], iron-sulfur-water [Fe-S-H{sub 2}O], and zinc-water [Zn-H{sub 2}O]).« less

Spatial model of convective solute transport in brain extracellular space does not support a "glymphatic" mechanism.

PubMed

Jin, Byung-Ju; Smith, Alex J; Verkman, Alan S

2016-12-01

A "glymphatic system," which involves convective fluid transport from para-arterial to paravenous cerebrospinal fluid through brain extracellular space (ECS), has been proposed to account for solute clearance in brain, and aquaporin-4 water channels in astrocyte endfeet may have a role in this process. Here, we investigate the major predictions of the glymphatic mechanism by modeling diffusive and convective transport in brain ECS and by solving the Navier-Stokes and convection-diffusion equations, using realistic ECS geometry for short-range transport between para-arterial and paravenous spaces. Major model parameters include para-arterial and paravenous pressures, ECS volume fraction, solute diffusion coefficient, and astrocyte foot-process water permeability. The model predicts solute accumulation and clearance from the ECS after a step change in solute concentration in para-arterial fluid. The principal and robust conclusions of the model are as follows: (a) significant convective transport requires a sustained pressure difference of several mmHg between the para-arterial and paravenous fluid and is not affected by pulsatile pressure fluctuations; (b) astrocyte endfoot water permeability does not substantially alter the rate of convective transport in ECS as the resistance to flow across endfeet is far greater than in the gaps surrounding them; and (c) diffusion (without convection) in the ECS is adequate to account for experimental transport studies in brain parenchyma. Therefore, our modeling results do not support a physiologically important role for local parenchymal convective flow in solute transport through brain ECS. © 2016 Jin et al.

Analytical solutions for a soil vapor extraction model that incorporates gas phase dispersion and molecular diffusion

NASA Astrophysics Data System (ADS)

Huang, Junqi; Goltz, Mark N.

2017-06-01

To greatly simplify their solution, the equations describing radial advective/dispersive transport to an extraction well in a porous medium typically neglect molecular diffusion. While this simplification is appropriate to simulate transport in the saturated zone, it can result in significant errors when modeling gas phase transport in the vadose zone, as might be applied when simulating a soil vapor extraction (SVE) system to remediate vadose zone contamination. A new analytical solution for the equations describing radial gas phase transport of a sorbing contaminant to an extraction well is presented. The equations model advection, dispersion (including both mechanical dispersion and molecular diffusion), and rate-limited mass transfer of dissolved, separate phase, and sorbed contaminants into the gas phase. The model equations are analytically solved by using the Laplace transform with respect to time. The solutions are represented by confluent hypergeometric functions in the Laplace domain. The Laplace domain solutions are then evaluated using a numerical Laplace inversion algorithm. The solutions can be used to simulate the spatial distribution and the temporal evolution of contaminant concentrations during operation of a soil vapor extraction well. Results of model simulations show that the effect of gas phase molecular diffusion upon concentrations at the extraction well is relatively small, although the effect upon the distribution of concentrations in space is significant. This study provides a tool that can be useful in designing SVE remediation strategies, as well as verifying numerical models used to simulate SVE system performance.

Nonminimal coupling for the gravitational and electromagnetic fields: Black hole solutions and solitons

NASA Astrophysics Data System (ADS)

Balakin, Alexander B.; Bochkarev, Vladimir V.; Lemos, José P. S.

2008-04-01

Using a Lagrangian formalism, a three-parameter nonminimal Einstein-Maxwell theory is established. The three parameters q1, q2, and q3 characterize the cross-terms in the Lagrangian, between the Maxwell field and terms linear in the Ricci scalar, Ricci tensor, and Riemann tensor, respectively. Static spherically symmetric equations are set up, and the three parameters are interrelated and chosen so that effectively the system reduces to a one parameter only, q. Specific black hole and other type of one-parameter solutions are studied. First, as a preparation, the Reissner-Nordström solution, with q1=q2=q3=0, is displayed. Then, we search for solutions in which the electric field is regular everywhere as well as asymptotically Coulombian, and the metric potentials are regular at the center as well as asymptotically flat. In this context, the one-parameter model with q1≡-q, q2=2q, q3=-q, called the Gauss-Bonnet model, is analyzed in detail. The study is done through the solution of the Abel equation (the key equation), and the dynamical system associated with the model. There is extra focus on an exact solution of the model and its critical properties. Finally, an exactly integrable one-parameter model, with q1≡-q, q2=q, q3=0, is considered also in detail. A special submodel, in which the Fibonacci number appears naturally, of this one-parameter model is shown, and the corresponding exact solution is presented. Interestingly enough, it is a soliton of the theory, the Fibonacci soliton, without horizons and with a mild conical singularity at the center.

Numerical Solution of the Extended Nernst-Planck Model.

PubMed

Samson; Marchand

1999-07-01

The main features of a numerical model aiming at predicting the drift of ions in an electrolytic solution upon a chemical potential gradient are presented. The mechanisms of ionic diffusion are described by solving the extended Nernst-Planck system of equations. The electrical coupling between the various ionic fluxes is accounted for by the Poisson equation. Furthermore, chemical activity effects are considered in the model. The whole system of nonlinear equations is solved using the finite-element method. Results yielded by the model for simple test cases are compared to those obtained using an analytical solution. Applications of the model to more complex problems are also presented and discussed. Copyright 1999 Academic Press.

Numerical model for the uptake of groundwater contaminants by phreatophytes

USGS Publications Warehouse

Widdowson, M.A.; El-Sayed, A.; Landmeyer, J.E.

2008-01-01

Conventional solute transport models do not adequately account for the effects of phreatophytic plant systems on contaminant concentrations in shallow groundwater systems. A numerical model was developed and tested to simulate threedimensional reactive solute transport in a heterogeneous porous medium. Advective-dispersive transport is coupled to biodegradation, sorption, and plantbased attenuation processes including plant uptake and sorption by plant roots. The latter effects are a function of the physical-chemical properties of the individual solutes and plant species. Models for plant uptake were tested and evaluated using the experimental data collected at a field site comprised of hybrid poplar trees. A non-linear equilibrium isotherm model best represented site conditions.

Hierarchic plate and shell models based on p-extension

NASA Technical Reports Server (NTRS)

Szabo, Barna A.; Sahrmann, Glenn J.

1988-01-01

Formulations of finite element models for beams, arches, plates and shells based on the principle of virtual work was studied. The focus is on computer implementation of hierarchic sequences of finite element models suitable for numerical solution of a large variety of practical problems which may concurrently contain thin and thick plates and shells, stiffeners, and regions where three dimensional representation is required. The approximate solutions corresponding to the hierarchic sequence of models converge to the exact solution of the fully three dimensional model. The stopping criterion is based on: (1) estimation of the relative error in energy norm; (2) equilibrium tests, and (3) observation of the convergence of quantities of interest.

Aqueous Solution Vessel Thermal Model Development II

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

Buechler, Cynthia Eileen

2015-10-28

The work presented in this report is a continuation of the work described in the May 2015 report, “Aqueous Solution Vessel Thermal Model Development”. This computational fluid dynamics (CFD) model aims to predict the temperature and bubble volume fraction in an aqueous solution of uranium. These values affect the reactivity of the fissile solution, so it is important to be able to calculate them and determine their effects on the reaction. Part A of this report describes some of the parameter comparisons performed on the CFD model using Fluent. Part B describes the coupling of the Fluent model with amore » Monte-Carlo N-Particle (MCNP) neutron transport model. The fuel tank geometry is the same as it was in the May 2015 report, annular with a thickness-to-height ratio of 0.16. An accelerator-driven neutron source provides the excitation for the reaction, and internal and external water cooling channels remove the heat. The model used in this work incorporates the Eulerian multiphase model with lift, wall lubrication, turbulent dispersion and turbulence interaction. The buoyancy-driven flow is modeled using the Boussinesq approximation, and the flow turbulence is determined using the k-ω Shear-Stress-Transport (SST) model. The dispersed turbulence multiphase model is employed to capture the multiphase turbulence effects.« less

Scaffolding Mathematical Modelling with a Solution Plan

ERIC Educational Resources Information Center

Schukajlow, Stanislaw; Kolter, Jana; Blum, Werner

2015-01-01

In the study presented in this paper, we examined the possibility to scaffold mathematical modelling with strategies. The strategies were prompted using an instrument called "solution plan" as a scaffold. The effects of this step by step instrument on mathematical modelling competency and on self-reported strategies were tested using…

Predicting membrane flux decline from complex mixtures using flow-field flow fractionation measurements and semi-empirical theory.

PubMed

Pellegrino, J; Wright, S; Ranvill, J; Amy, G

2005-01-01

Flow-Field Flow Fractionation (FI-FFF) is an idealization of the cross flow membrane filtration process in that, (1) the filtration flux and crossflow velocity are constant from beginning to end of the device, (2) the process is a relatively well-defined laminar-flow hydrodynamic condition, and (3) the solutes are introduced as a pulse-input that spreads due to interactions with each other and the membrane in the dilute-solution limit. We have investigated the potential for relating FI-FFF measurements to membrane fouling. An advection-dispersion transport model was used to provide 'ideal' (defined as spherical, non-interacting solutes) solute residence time distributions (RTDs) for comparison with 'real' RTDs obtained experimentally at different cross-field velocities and solution ionic strength. An RTD moment analysis based on a particle diameter probability density function was used to extract "effective" characteristic properties, rather than uniquely defined characteristics, of the standard solute mixture. A semi-empirical unsteady-state, flux decline model was developed that uses solute property parameters. Three modes of flux decline are included: (1) concentration polarization, (2) cake buildup, and (3) adsorption on/in pores, We have used this model to test the hypothesis-that an analysis of a residence time distribution using FI-FFF can describe 'effective' solute properties or indices that can be related to membrane flux decline in crossflow membrane filtration. Constant flux filtration studies included the changes of transport hydrodynamics (solvent flux to solute back diffusion (J/k) ratios), solution ionic strength, and feed water composition for filtration using a regenerated cellulose ultrafiltration membrane. Tests of the modeling hypothesis were compared with experimental results from the filtration measurements using several correction parameters based on the mean and variance of the solute RTDs. The corrections used to modify the boundary layer mass transfer coefficient and the specific resistance of cake or adsorption layers demonstrated that RTD analysis is potentially useful technique to describe colloid properties but requires improvements.

Using the Domenico Solution to Teach Contaminant Transport Modeling

ERIC Educational Resources Information Center

Devlin, J. F.; Brookfield, A.; Huang, B.; Schillig, P. C.

2012-01-01

The Domenico solution is a heuristic simplification of a solution to the transport equation. Although there is a growing consensus that the Domenico solution is undesirable for use in professional and research applications due to departures from exact solutions under certain conditions, it behaves well under conditions suitable for instruction.…

Biocompatibility assessment of peritoneal dialysis solutions with a new in vitro model of preconditioned human HL60 cells.

PubMed

Koball, Sebastian; Korten, Gero; Stange, Jan; Schmidt, Reinhard; Mitzner, Steffen

2009-07-01

The purposes of this study were to test the human promyelocytic cell line HL60 for its usability as a new cell model for the immune barrier of the peritoneum, and to investigate the impact of different peritoneal dialysis (PD) solutions in the model. HL60 cells were stimulated by retinoic acid and recombinant human granulocyte and macrophage colony-stimulating factor to differentiate into neutrophilic granulocytes. Cells were incubated in different commercially available PD solutions. After a 4-h incubation, functional (chemiluminescence phagocytosis) and viability tests (Live-Dead, XTT) were performed. High glucose concentrations (>1.36%) and low pH values (<7.0) appeared to be detrimental for neutrophil functions and for neutrophil viability. There is a quantitative correlation between glucose concentration and the cytotoxicity of standard PD solutions (PD 1.36% glucose shows 42.6% higher chemiluminescence than PD 3.86% glucose [P < 0.05]). PD solution containing icodextrin shows 74.3% higher chemiluminescence than PD 3.86% glucose, and PD solution with amino acids shows 52.4% higher chemiluminescence than PD 3.86% glucose which is a sign for better biocompatibility in these tests (P < 0.05). The test system is useful for biocompatibility investigations of PD solutions and their effect on immune cells, for example, neutrophil granulocytes. It does not depend on donor variability and availability in comparison to models based on primary isolated leukocytes.

Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations

NASA Astrophysics Data System (ADS)

Arqub, Omar Abu; El-Ajou, Ahmad; Momani, Shaher

2015-07-01

Building fractional mathematical models for specific phenomena and developing numerical or analytical solutions for these fractional mathematical models are crucial issues in mathematics, physics, and engineering. In this work, a new analytical technique for constructing and predicting solitary pattern solutions of time-fractional dispersive partial differential equations is proposed based on the generalized Taylor series formula and residual error function. The new approach provides solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software. For method evaluation and validation, the proposed technique was applied to three different models and compared with some of the well-known methods. The resultant simulations clearly demonstrate the superiority and potentiality of the proposed technique in terms of the quality performance and accuracy of substructure preservation in the construct, as well as the prediction of solitary pattern solutions for time-fractional dispersive partial differential equations.

Salty popcorn in a homogeneous low-dimensional toy model of holographic QCD

NASA Astrophysics Data System (ADS)

Elliot-Ripley, Matthew

2017-04-01

Recently, a homogeneous ansatz has been used to study cold dense nuclear matter in the Sakai-Sugimoto model of holographic QCD. To justify this homogeneous approximation we here investigate a homogeneous ansatz within a low-dimensional toy version of Sakai-Sugimoto to study finite baryon density configurations and compare it to full numerical solutions. We find the ansatz corresponds to enforcing a dyon salt arrangement in which the soliton solutions are split into half-soliton layers. Within this ansatz we find analogues of the proposed baryonic popcorn transitions, in which solutions split into multiple layers in the holographic direction. The homogeneous results are found to qualitatively match the full numerical solutions, lending confidence to the homogeneous approximations of the full Sakai-Sugimoto model. In addition, we find exact compact solutions in the high density, flat space limit which demonstrate the existence of further popcorn transitions to three layers and beyond.

Tikekar superdense stars in electric fields

NASA Astrophysics Data System (ADS)

Komathiraj, K.; Maharaj, S. D.

2007-04-01

We present exact solutions to the Einstein-Maxwell system of equations with a specified form of the electric field intensity by assuming that the hypersurface {t=constant} are spheroidal. The solution of the Einstein-Maxwell system is reduced to a recurrence relation with variable rational coefficients which can be solved in general using mathematical induction. New classes of solutions of linearly independent functions are obtained by restricting the spheroidal parameter K and the electric field intensity parameter α. Consequently, it is possible to find exact solutions in terms of elementary functions, namely, polynomials and algebraic functions. Our result contains models found previously including the superdense Tikekar neutron star model [J. Math. Phys. 31, 2454 (1990)] when K=-7 and α=0. Our class of charged spheroidal models generalize the uncharged isotropic Maharaj and Leach solutions [J. Math. Phys. 37, 430 (1996)]. In particular, we find an explicit relationship directly relating the spheroidal parameter K to the electromagnetic field.

Hydration of nonelectrolytes in binary aqueous solutions

NASA Astrophysics Data System (ADS)

Rudakov, A. M.; Sergievskii, V. V.

2010-10-01

Literature data on the thermodynamic properties of binary aqueous solutions of nonelectrolytes that show negative deviations from Raoult's law due largely to the contribution of the hydration of the solute are briefly surveyed. Attention is focused on simulating the thermodynamic properties of solutions using equations of the cluster model. It is shown that the model is based on the assumption that there exists a distribution of stoichiometric hydrates over hydration numbers. In terms of the theory of ideal associated solutions, the equations for activity coefficients, osmotic coefficients, vapor pressure, and excess thermodynamic functions (volume, Gibbs energy, enthalpy, entropy) are obtained in analytical form. Basic parameters in the equations are the hydration numbers of the nonelectrolyte (the mathematical expectation of the distribution of hydrates) and the dispersions of the distribution. It is concluded that the model equations adequately describe the thermodynamic properties of a wide range of nonelectrolytes partly or completely soluble in water.

Mass Transport through Nanostructured Membranes: Towards a Predictive Tool

PubMed Central

Darvishmanesh, Siavash; Van der Bruggen, Bart

2016-01-01

This study proposes a new mechanism to understand the transport of solvents through nanostructured membranes from a fundamental point of view. The findings are used to develop readily applicable mathematical models to predict solvent fluxes and solute rejections through solvent resistant membranes used for nanofiltration. The new model was developed based on a pore-flow type of transport. New parameters found to be of fundamental importance were introduced to the equation, i.e., the affinity of the solute and the solvent for the membrane expressed as the hydrogen-bonding contribution of the solubility parameter for the solute, solvent and membrane. A graphical map was constructed to predict the solute rejection based on the hydrogen-bonding contribution of the solubility parameter. The model was evaluated with performance data from the literature. Both the solvent flux and the solute rejection calculated with the new approach were similar to values reported in the literature. PMID:27918434

Unique heating curves generated by radiofrequency electric-field interactions with semi-aqueous solutions

NASA Astrophysics Data System (ADS)

Lara, Nadia C.; Haider, Asad A.; Wilson, Lon J.; Curley, Steven A.; Corr, Stuart J.

2017-01-01

Aqueous and nanoparticle-based solutions have been reported to heat when exposed to an alternating radiofrequency (RF) electric-field. Although the theoretical models have been developed to accurately model such a behavior given the solution composition as well as the geometrical constraints of the sample holder, these models have not been investigated across a wide-range of solutions where the dielectric properties differ, especially with regard to the real permittivity. In this work, we investigate the RF heating properties of non-aqueous solutions composed of ethanol, propylene glycol, and glycine betaine with and without varying amounts of NaCl and LiCl. This allowed us to modulate the real permittivity across the range 25-132, as well as the imaginary permittivity across the range 37-177. Our results are in excellent agreement with the previously developed theoretical models. We have shown that different materials generate unique RF heating curves that differ from the standard aqueous heating curves. The theoretical model previously described is robust and accounts for the RF heating behavior of materials with a variety of dielectric properties, which may provide applications in non-invasive RF cancer hyperthermia.

An accurate coarse-grained model for chitosan polysaccharides in aqueous solution.

PubMed

Tsereteli, Levan; Grafmüller, Andrea

2017-01-01

Computational models can provide detailed information about molecular conformations and interactions in solution, which is currently inaccessible by other means in many cases. Here we describe an efficient and precise coarse-grained model for long polysaccharides in aqueous solution at different physico-chemical conditions such as pH and ionic strength. The Model is carefully constructed based on all-atom simulations of small saccharides and metadynamics sampling of the dihedral angles in the glycosidic links, which represent the most flexible degrees of freedom of the polysaccharides. The model is validated against experimental data for Chitosan molecules in solution with various degree of deacetylation, and is shown to closely reproduce the available experimental data. For long polymers, subtle differences of the free energy maps of the glycosidic links are found to significantly affect the measurable polymer properties. Therefore, for titratable monomers the free energy maps of the corresponding links are updated according to the current charge of the monomers. We then characterize the microscopic and mesoscopic structural properties of large chitosan polysaccharides in solution for a wide range of solvent pH and ionic strength, and investigate the effect of polymer length and degree and pattern of deacetylation on the polymer properties.

An accurate coarse-grained model for chitosan polysaccharides in aqueous solution

PubMed Central

Tsereteli, Levan

2017-01-01

Computational models can provide detailed information about molecular conformations and interactions in solution, which is currently inaccessible by other means in many cases. Here we describe an efficient and precise coarse-grained model for long polysaccharides in aqueous solution at different physico-chemical conditions such as pH and ionic strength. The Model is carefully constructed based on all-atom simulations of small saccharides and metadynamics sampling of the dihedral angles in the glycosidic links, which represent the most flexible degrees of freedom of the polysaccharides. The model is validated against experimental data for Chitosan molecules in solution with various degree of deacetylation, and is shown to closely reproduce the available experimental data. For long polymers, subtle differences of the free energy maps of the glycosidic links are found to significantly affect the measurable polymer properties. Therefore, for titratable monomers the free energy maps of the corresponding links are updated according to the current charge of the monomers. We then characterize the microscopic and mesoscopic structural properties of large chitosan polysaccharides in solution for a wide range of solvent pH and ionic strength, and investigate the effect of polymer length and degree and pattern of deacetylation on the polymer properties. PMID:28732036

A new and inexpensive non-bit-for-bit solution reproducibility test based on time step convergence (TSC1.0)

NASA Astrophysics Data System (ADS)

Wan, Hui; Zhang, Kai; Rasch, Philip J.; Singh, Balwinder; Chen, Xingyuan; Edwards, Jim

2017-02-01

A test procedure is proposed for identifying numerically significant solution changes in evolution equations used in atmospheric models. The test issues a fail signal when any code modifications or computing environment changes lead to solution differences that exceed the known time step sensitivity of the reference model. Initial evidence is provided using the Community Atmosphere Model (CAM) version 5.3 that the proposed procedure can be used to distinguish rounding-level solution changes from impacts of compiler optimization or parameter perturbation, which are known to cause substantial differences in the simulated climate. The test is not exhaustive since it does not detect issues associated with diagnostic calculations that do not feedback to the model state variables. Nevertheless, it provides a practical and objective way to assess the significance of solution changes. The short simulation length implies low computational cost. The independence between ensemble members allows for parallel execution of all simulations, thus facilitating fast turnaround. The new method is simple to implement since it does not require any code modifications. We expect that the same methodology can be used for any geophysical model to which the concept of time step convergence is applicable.

Transport of fluid and solutes in the body II. Model validation and implications.

PubMed

Gyenge, C C; Bowen, B D; Reed, R K; Bert, J L

1999-09-01

A mathematical model of short-term whole body fluid, protein, and ion distribution and transport developed earlier [see companion paper: C. C. Gyenge, B. D. Bowen, R. K. Reed, and J. L. Bert. Am. J. Physiol. 277 (Heart Circ. Physiol. 46): H1215-H1227, 1999] is validated using experimental data available in the literature. The model was tested against data measured for the following three types of experimental infusions: 1) hyperosmolar saline solutions with an osmolarity in the range of 2,000-2,400 mosmol/l, 2) saline solutions with an osmolarity of approximately 270 mosmol/l and composition comparable with Ringer solution, and 3) an isosmotic NaCl solution with an osmolarity of approximately 300 mosmol/l. Good agreement between the model predictions and the experimental data was obtained with respect to the trends and magnitudes of fluid shifts between the intra- and extracellular compartments, extracellular ion and protein contents, and hematocrit values. The model is also able to yield information about inaccessible or difficult-to-measure system variables such as intracellular ion contents, cellular volumes, and fluid fluxes across the vascular capillary membrane, data that can be used to help interpret the behavior of the system.

VAVUQ, Python and Matlab freeware for Verification and Validation, Uncertainty Quantification

NASA Astrophysics Data System (ADS)

Courtney, J. E.; Zamani, K.; Bombardelli, F. A.; Fleenor, W. E.

2015-12-01

A package of scripts is presented for automated Verification and Validation (V&V) and Uncertainty Quantification (UQ) for engineering codes that approximate Partial Differential Equations (PDFs). The code post-processes model results to produce V&V and UQ information. This information can be used to assess model performance. Automated information on code performance can allow for a systematic methodology to assess the quality of model approximations. The software implements common and accepted code verification schemes. The software uses the Method of Manufactured Solutions (MMS), the Method of Exact Solution (MES), Cross-Code Verification, and Richardson Extrapolation (RE) for solution (calculation) verification. It also includes common statistical measures that can be used for model skill assessment. Complete RE can be conducted for complex geometries by implementing high-order non-oscillating numerical interpolation schemes within the software. Model approximation uncertainty is quantified by calculating lower and upper bounds of numerical error from the RE results. The software is also able to calculate the Grid Convergence Index (GCI), and to handle adaptive meshes and models that implement mixed order schemes. Four examples are provided to demonstrate the use of the software for code and solution verification, model validation and uncertainty quantification. The software is used for code verification of a mixed-order compact difference heat transport solver; the solution verification of a 2D shallow-water-wave solver for tidal flow modeling in estuaries; the model validation of a two-phase flow computation in a hydraulic jump compared to experimental data; and numerical uncertainty quantification for 3D CFD modeling of the flow patterns in a Gust erosion chamber.

Numerical Modelling of Foundation Slabs with use of Schur Complement Method

NASA Astrophysics Data System (ADS)

Koktan, Jiří; Brožovský, Jiří

2017-10-01

The paper discusses numerical modelling of foundation slabs with use of advanced numerical approaches, which are suitable for parallel processing. The solution is based on the Finite Element Method with the slab-type elements. The subsoil is modelled with use of Winklertype contact model (as an alternative a multi-parameter model can be used). The proposed modelling approach uses the Schur Complement method to speed-up the computations of the problem. The method is based on a special division of the analyzed model to several substructures. It adds some complexity to the numerical procedures, especially when subsoil models are used inside the finite element method solution. In other hand, this method makes possible a fast solution of large models but it introduces further problems to the process. Thus, the main aim of this paper is to verify that such method can be successfully used for this type of problem. The most suitable finite elements will be discussed, there will be also discussion related to finite element mesh and limitations of its construction for such problem. The core approaches of the implementation of the Schur Complement Method for this type of the problem will be also presented. The proposed approach was implemented in the form of a computer program, which will be also briefly introduced. There will be also presented results of example computations, which prove the speed-up of the solution - there will be shown important speed-up of solution even in the case of on-parallel processing and the ability of bypass size limitations of numerical models with use of the discussed approach.

Numerical Solutions for Nonlinear High Damping Rubber Bearing Isolators: Newmark's Method with Netwon-Raphson Iteration Revisited

NASA Astrophysics Data System (ADS)

Markou, A. A.; Manolis, G. D.

2018-03-01

Numerical methods for the solution of dynamical problems in engineering go back to 1950. The most famous and widely-used time stepping algorithm was developed by Newmark in 1959. In the present study, for the first time, the Newmark algorithm is developed for the case of the trilinear hysteretic model, a model that was used to describe the shear behaviour of high damping rubber bearings. This model is calibrated against free-vibration field tests implemented on a hybrid base isolated building, namely the Solarino project in Italy, as well as against laboratory experiments. A single-degree-of-freedom system is used to describe the behaviour of a low-rise building isolated with a hybrid system comprising high damping rubber bearings and low friction sliding bearings. The behaviour of the high damping rubber bearings is simulated by the trilinear hysteretic model, while the description of the behaviour of the low friction sliding bearings is modeled by a linear Coulomb friction model. In order to prove the effectiveness of the numerical method we compare the analytically solved trilinear hysteretic model calibrated from free-vibration field tests (Solarino project) against the same model solved with the Newmark method with Netwon-Raphson iteration. Almost perfect agreement is observed between the semi-analytical solution and the fully numerical solution with Newmark's time integration algorithm. This will allow for extension of the trilinear mechanical models to bidirectional horizontal motion, to time-varying vertical loads, to multi-degree-of-freedom-systems, as well to generalized models connected in parallel, where only numerical solutions are possible.

Homogenization Theory for the Prediction of Obstructed Solute Diffusivity in Macromolecular Solutions

PubMed Central

Donovan, Preston; Chehreghanianzabi, Yasaman; Rathinam, Muruhan; Zustiak, Silviya Petrova

2016-01-01

The study of diffusion in macromolecular solutions is important in many biomedical applications such as separations, drug delivery, and cell encapsulation, and key for many biological processes such as protein assembly and interstitial transport. Not surprisingly, multiple models for the a-priori prediction of diffusion in macromolecular environments have been proposed. However, most models include parameters that are not readily measurable, are specific to the polymer-solute-solvent system, or are fitted and do not have a physical meaning. Here, for the first time, we develop a homogenization theory framework for the prediction of effective solute diffusivity in macromolecular environments based on physical parameters that are easily measurable and not specific to the macromolecule-solute-solvent system. Homogenization theory is useful for situations where knowledge of fine-scale parameters is used to predict bulk system behavior. As a first approximation, we focus on a model where the solute is subjected to obstructed diffusion via stationary spherical obstacles. We find that the homogenization theory results agree well with computationally more expensive Monte Carlo simulations. Moreover, the homogenization theory agrees with effective diffusivities of a solute in dilute and semi-dilute polymer solutions measured using fluorescence correlation spectroscopy. Lastly, we provide a mathematical formula for the effective diffusivity in terms of a non-dimensional and easily measurable geometric system parameter. PMID:26731550

Thermodynamic properties of potassium chloride aqueous solutions

NASA Astrophysics Data System (ADS)

Zezin, Denis; Driesner, Thomas

2017-04-01

Potassium chloride is a ubiquitous salt in natural fluids, being the second most abundant dissolved salt in many geological aqueous solutions after sodium chloride. It is a simple solute and strong electrolyte easily dissociating in water, however the thermodynamic properties of KCl aqueous solutions were never correlated with sufficient accuracy for a wide range of physicochemical conditions. In this communication we propose a set of parameters for a Pitzer-type model which allows calculation of all necessary thermodynamic properties of KCl solution, namely excess Gibbs free energy and derived activity coefficient, apparent molar enthalpy, heat capacity and volume, as well as osmotic coefficient and activity of water in solutions. The system KCl-water is one of the best studied aqueous systems containing electrolytes. Although extensive experimental data were collected for thermodynamic properties of these solutions over the years, the accurate volumetric data became available only recently, thus making possible a complete thermodynamic formulation including a pressure dependence of excess Gibbs free energy and derived properties of the KCl-water liquids. Our proposed model is intended for calculation of major thermodynamic properties of KCl aqueous solutions at temperatures ranging from freezing point of a solution to 623 K, pressures ranging from saturated water vapor up to 150 MPa, and concentrations up to the salt saturation. This parameterized model will be further implemented in geochemical software packages and can facilitate the calculation of aqueous equilibrium for reactive transport codes.

Periodic Solution and Stationary Distribution of Stochastic Predator-Prey Models with Higher-Order Perturbation

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing

2018-04-01

In this paper, two stochastic predator-prey models with general functional response and higher-order perturbation are proposed and investigated. For the nonautonomous periodic case of the system, by using Khasminskii's theory of periodic solution, we show that the system admits a nontrivial positive T-periodic solution. For the system disturbed by both white and telegraph noises, sufficient conditions for positive recurrence and the existence of an ergodic stationary distribution to the solutions are established. The existence of stationary distribution implies stochastic weak stability to some extent.

On non-exponential cosmological solutions with two factor spaces of dimensions m and 1 in the Einstein-Gauss-Bonnet model with a Λ-term

NASA Astrophysics Data System (ADS)

Ernazarov, K. K.

2017-12-01

We consider a (m + 2)-dimensional Einstein-Gauss-Bonnet (EGB) model with the cosmological Λ-term. We restrict the metrics to be diagonal ones and find for certain Λ = Λ(m) class of cosmological solutions with non-exponential time dependence of two scale factors of dimensions m > 2 and 1. Any solution from this class describes an accelerated expansion of m-dimensional subspace and tends asymptotically to isotropic solution with exponential dependence of scale factors.

SAXS-WAXS studies of the low-resolution structure in solution of xylose/glucose isomerase from Streptomyces rubiginosus

NASA Astrophysics Data System (ADS)

Kozak, Maciej; Taube, Michał

2009-10-01

The structure and conformation of molecule of xylose/glucose isomerase from Streptomyces rubiginosus in solution (at pH 6 and 7.6; with and without the substrate) has been studied by small- and wide-angle scattering of synchrotron radiation (SAXS-WAXS). On the basis of the SAXS-WAXS data, the low-resolution structure in solution has been reconstructed using ab inito methods. A comparison of the models of glucose isomerase shows only small differences between the model in solution and the crystal structure.

Electronic business in the home medical equipment industry.

PubMed

Wei, June; Graham, Michael J; Liu, Lai C

2011-01-01

This paper aims at developing electronic business solutions to increase value for the home medical equipment industry. First, an electronic strategic value chain model was developed for the home medical equipment industry. Second, electronic business solutions were mapped from this model. Third, the top 20 dominant companies in the home medical equipment industry were investigated to see the current adoption patterns of these electronic business solutions. The solutions will be beneficial to decision-makers in the information technology adoptions in the home medical equipment industry to increase the business values.

Finite Element Modeling of Scattering from Underwater Proud and Buried Military Munitions

DTIC Science & Technology

2017-02-28

FINAL REPORT Finite Element Modeling of Scattering from Underwater Proud and Buried Military Munitions SERDP Project MR-2408 JULY 2017...solution and the red dash-dot line repre- sents the coupled finite -boundary element solution. . . . . . . . . . . . . . . . . . 11 3 The scattering...dot line represents the coupled finite -boundary element solution. . . . . . . . 11 i 4 The scattering amplitude as a function of the receiver angle for

Periodic solution for a stochastic non-autonomous competitive Lotka-Volterra model in a polluted environment

NASA Astrophysics Data System (ADS)

Jiang, Daqing; Zhang, Qiumei; Hayat, Tasawar; Alsaedi, Ahmed

2017-04-01

In this paper, we consider a stochastic non-autonomous competitive Lotka-Volterra model in a polluted environment. We derive sufficient criteria for the existence and global attractivity of the boundary periodic solutions. Furthermore, we obtain conditions for the existence and global attractivity of a nontrivial positive periodic solution. Finally we make simulations to illustrate our analytical results.

Interpreting Degenerate Solutions in Unfolding by Use of the Vector Model and the Compensatory Distance Model

ERIC Educational Resources Information Center

Van Deun, K.; Groenen, P. J. F.; Heiser, W. J.; Busing, F. M. T. A.; Delbeke, L.

2005-01-01

In this paper, we reconsider the merits of unfolding solutions based on loss functions involving a normalization on the variance per subject. In the literature, solutions based on Stress-2 are often diagnosed to be degenerate in the majority of cases. Here, the focus lies on two frequently occurring types of degeneracies. The first type typically…

Fluid transition layer between rigid solute and liquid solvent: is there depletion or enrichment?

PubMed

Djikaev, Yuri S; Ruckenstein, Eli

2016-03-21

The fluid layer between solute and liquid solvent is studied by combining the density functional theory with the probabilistic hydrogen bond model. This combination allows one to obtain the equilibrium distribution of fluid molecules, taking into account the hydrogen bond contribution to the external potential whereto they are subjected near the solute. One can find the effective width of the fluid solvent-solute transition layer and fluid average density in that layer, and determine their dependence on temperature, solvent-solute affinity, vicinal hydrogen bond (hb) energy alteration ratio, and solute radius. Numerical calculations are performed for the solvation of a plate and spherical solutes of four different radii in two model solvents (associated liquid and non-associated one) in the temperature range from 293 K to 333 K for various solvent-solute affinities and hydrogen bond energy alteration ratios. The predictions of our model for the effective width and average density of the transition layer are consistent with experiments and simulations. The small-to-large crossover lengthscale for hydrophobic hydration is expected to be about 3-5 nm. Remarkably, characterizing the transition layer with the average density, one can observe that for small hydrophobes, the transition layer becomes enriched with rather than depleted of fluid when the solvent-solute affinity and hb-energy alteration ratio become large enough. The boundary values of solvent-solute affinity and hb-energy alteration ratio, needed for the "depletion-to-enrichment" crossover (in the smoothed density sense), are predicted to decrease with increasing temperature.

Considering Decision Variable Diversity in Multi-Objective Optimization: Application in Hydrologic Model Calibration

NASA Astrophysics Data System (ADS)

Sahraei, S.; Asadzadeh, M.

2017-12-01

Any modern multi-objective global optimization algorithm should be able to archive a well-distributed set of solutions. While the solution diversity in the objective space has been explored extensively in the literature, little attention has been given to the solution diversity in the decision space. Selection metrics such as the hypervolume contribution and crowding distance calculated in the objective space would guide the search toward solutions that are well-distributed across the objective space. In this study, the diversity of solutions in the decision-space is used as the main selection criteria beside the dominance check in multi-objective optimization. To this end, currently archived solutions are clustered in the decision space and the ones in less crowded clusters are given more chance to be selected for generating new solution. The proposed approach is first tested on benchmark mathematical test problems. Second, it is applied to a hydrologic model calibration problem with more than three objective functions. Results show that the chance of finding more sparse set of high-quality solutions increases, and therefore the analyst would receive a well-diverse set of options with maximum amount of information. Pareto Archived-Dynamically Dimensioned Search, which is an efficient and parsimonious multi-objective optimization algorithm for model calibration, is utilized in this study.

Modelling of interaction of the large disrupted meteoroid with the Earth atmosphere

NASA Astrophysics Data System (ADS)

Brykina, Irina G.

2018-05-01

The model of atmospheric fragmentation of large meteoroids to the cloud of fragments is proposed. The comparison with similar models used in the literature is made. The approximate analytical solution of meteor physics equations is obtained for the mass loss of the disrupted meteoroid, the energy deposition and for the light curve normalized to the maximum brightness. This solution is applied to modelling of interaction of the Chelyabinsk meteoroid with the atmosphere. The influence of uncertainty of initial parameters of the meteoroid on characteristics of its interaction with the atmosphere is estimated. Comparison of the analytical solution with the observational data is made.

Using Micromechanical Resonators to Measure Rheological Properties and Alcohol Content of Model Solutions and Commercial Beverages

PubMed Central

Paxman, Rosemary; Stinson, Jake; Dejardin, Anna; McKendry, Rachel A.; Hoogenboom, Bart W.

2012-01-01

Micromechanic resonators provide a small-volume and potentially high-throughput method to determine rheological properties of fluids. Here we explore the accuracy in measuring mass density and viscosity of ethanol-water and glycerol-water model solutions, using a simple and easily implemented model to deduce the hydrodynamic effects on resonating cantilevers of various length-to-width aspect ratios. We next show that these measurements can be extended to determine the alcohol percentage of both model solutions and commercial beverages such as beer, wine and liquor. This demonstrates how micromechanical resonators can be used for quality control of every-day drinks. PMID:22778654

ANALYZING NUMERICAL ERRORS IN DOMAIN HEAT TRANSPORT MODELS USING THE CVBEM.

USGS Publications Warehouse

Hromadka, T.V.

1987-01-01

Besides providing an exact solution for steady-state heat conduction processes (Laplace-Poisson equations), the CVBEM (complex variable boundary element method) can be used for the numerical error analysis of domain model solutions. For problems where soil-water phase change latent heat effects dominate the thermal regime, heat transport can be approximately modeled as a time-stepped steady-state condition in the thawed and frozen regions, respectively. The CVBEM provides an exact solution of the two-dimensional steady-state heat transport problem, and also provides the error in matching the prescribed boundary conditions by the development of a modeling error distribution or an approximate boundary generation.

An open-source model and solution method to predict co-contraction in the finger.

PubMed

MacIntosh, Alexander R; Keir, Peter J

2017-10-01

A novel open-source biomechanical model of the index finger with an electromyography (EMG)-constrained static optimization solution method are developed with the goal of improving co-contraction estimates and providing means to assess tendon tension distribution through the finger. The Intrinsic model has four degrees of freedom and seven muscles (with a 14 component extensor mechanism). A novel plugin developed for the OpenSim modelling software applied the EMG-constrained static optimization solution method. Ten participants performed static pressing in three finger postures and five dynamic free motion tasks. Index finger 3D kinematics, force (5, 15, 30 N), and EMG (4 extrinsic muscles and first dorsal interosseous) were used in the analysis. The Intrinsic model predicted co-contraction increased by 29% during static pressing over the existing model. Further, tendon tension distribution patterns and forces, known to be essential to produce finger action, were determined by the model across all postures. The Intrinsic model and custom solution method improved co-contraction estimates to facilitate force propagation through the finger. These tools improve our interpretation of loads in the finger to develop better rehabilitation and workplace injury risk reduction strategies.

Correspondence between discrete and continuous models of excitable media: trigger waves

NASA Technical Reports Server (NTRS)

Chernyak, Y. B.; Feldman, A. B.; Cohen, R. J.

1997-01-01

We present a theoretical framework for relating continuous partial differential equation (PDE) models of excitable media to discrete cellular automata (CA) models on a randomized lattice. These relations establish a quantitative link between the CA model and the specific physical system under study. We derive expressions for the CA model's plane wave speed, critical curvature, and effective diffusion constant in terms of the model's internal parameters (the interaction radius, excitation threshold, and time step). We then equate these expressions to the corresponding quantities obtained from solution of the PDEs (for a fixed excitability). This yields a set of coupled equations with a unique solution for the required CA parameter values. Here we restrict our analysis to "trigger" wave solutions obtained in the limiting case of a two-dimensional excitable medium with no recovery processes. We tested the correspondence between our CA model and two PDE models (the FitzHugh-Nagumo medium and a medium with a "sawtooth" nonlinear reaction source) and found good agreement with the numerical solutions of the PDEs. Our results suggest that the behavior of trigger waves is actually controlled by a small number of parameters.

Transitions of stationary to pulsating solutions in the complex cubic-quintic Ginzburg-Landau equation under the influence of nonlinear gain and higher-order effects

NASA Astrophysics Data System (ADS)

Uzunov, Ivan M.; Georgiev, Zhivko D.; Arabadzhiev, Todor N.

2018-05-01

In this paper we study the transitions of stationary to pulsating solutions in the complex cubic-quintic Ginzburg-Landau equation (CCQGLE) under the influence of nonlinear gain, its saturation, and higher-order effects: self-steepening, third-order of dispersion, and intrapulse Raman scattering in the anomalous dispersion region. The variation method and the method of moments are applied in order to obtain the dynamic models with finite degrees of freedom for the description of stationary and pulsating solutions. Having applied the first model and its bifurcation analysis we have discovered the existence of families of subcritical Poincaré-Andronov-Hopf bifurcations due to the intrapulse Raman scattering, as well as some small nonlinear gain and the saturation of the nonlinear gain. A phenomenon of nonlinear stability has been studied and it has been shown that long living pulsating solutions with relatively small fluctuations of amplitude and frequencies exist at the bifurcation point. The numerical analysis of the second model has revealed the existence of Poincaré-Andronov-Hopf bifurcations of Raman dissipative soliton under the influence of the self-steepening effect and large nonlinear gain. All our theoretical predictions have been confirmed by the direct numerical solution of the full perturbed CCQGLE. The detailed comparison between the results obtained by both dynamic models and the direct numerical solution of the perturbed CCQGLE has proved the applicability of the proposed models in the investigation of the solutions of the perturbed CCQGLE.

Value increasing business model for e-hospital.

PubMed

Null, Robert; Wei, June

2009-01-01

This paper developed a business value increasing model for electronic hospital (e-hospital) based on electronic value chain analysis. From this model, 58 hospital electronic business (e-business) solutions were developed. Additionally, this paper investigated the adoption patterns of these 58 e-business solutions within six US leading hospitals. The findings show that only 36 of 58 or 62% of the e-business solutions are fully or partially implemented within the six hospitals. Ultimately, the research results will be beneficial to managers and executives for accelerating e-business adoptions for e-hospital.

Application of regular associated solution model to the liquidus curves of the Sn-Te and Sn-SnS systems

NASA Astrophysics Data System (ADS)

Eric, H.

1982-12-01

The liquidus curves of the Sn-Te and Sn-SnS systems were evaluated by the regular associated solution model (RAS). The main assumption of this theory is the existence of species A, B and associated complexes AB in the liquid phase. Thermodynamic properties of the binary A-B system are derived by ternary regular solution equations. Calculations based on this model for the Sn-Te and Sn-SnS systems are in agreement with published data.

Calculation of amorphous silica solubilities at 25° to 300°C and apparent cation hydration numbers in aqueous salt solutions using the concept of effective density of water

USGS Publications Warehouse

Fournier, Robert O.; Williams, Marshall L.

1983-01-01

The solubility of amorphous silica in aqueous salt solutions at 25° to 300°C can be calculated using information on its solubility in pure water and a model in which the activity of water in the salt solution is defined to equal the effective density. pe, of “free” water in that solution. At temperatures of 100°C and above, pe closely equals the product of the density of the solution times the weight fraction of water in the solution. At 25°C, a correction parameter must be applied to pe that incorporates a term called the apparent cation hydration number, h. Because of the many assumptions and other uncertainties involved in determining values of h, by the model used here, the reported numbers are not necessarily real hydration numbers even though they do agree with some published values determined by activity and diffusion methods. Whether or not h is a real hydration number, it would appear to be useful in its inclusion within a more extensive activity coefficient term that describes the departure of silica solubilities in concentrated salt solutions from expected behavior according to the model presented here. Values of h can be calculated from measured amorphous silica solubilities in salt solutions at 25°C provided there is no complexing of dissolved silica with the dissolved salt, or if the degree of complexing is known. The previously postulated aqueous silica-sulfate complexing in aqueous Na2SO4 solutions is supported by results of the present effective density of water model

Breeding novel solutions in the brain: a model of Darwinian neurodynamics.

PubMed

Szilágyi, András; Zachar, István; Fedor, Anna; de Vladar, Harold P; Szathmáry, Eörs

2016-01-01

Background : The fact that surplus connections and neurons are pruned during development is well established. We complement this selectionist picture by a proof-of-principle model of evolutionary search in the brain, that accounts for new variations in theory space. We present a model for Darwinian evolutionary search for candidate solutions in the brain. Methods : We combine known components of the brain - recurrent neural networks (acting as attractors), the action selection loop and implicit working memory - to provide the appropriate Darwinian architecture. We employ a population of attractor networks with palimpsest memory. The action selection loop is employed with winners-share-all dynamics to select for candidate solutions that are transiently stored in implicit working memory. Results : We document two processes: selection of stored solutions and evolutionary search for novel solutions. During the replication of candidate solutions attractor networks occasionally produce recombinant patterns, increasing variation on which selection can act. Combinatorial search acts on multiplying units (activity patterns) with hereditary variation and novel variants appear due to (i) noisy recall of patterns from the attractor networks, (ii) noise during transmission of candidate solutions as messages between networks, and, (iii) spontaneously generated, untrained patterns in spurious attractors. Conclusions : Attractor dynamics of recurrent neural networks can be used to model Darwinian search. The proposed architecture can be used for fast search among stored solutions (by selection) and for evolutionary search when novel candidate solutions are generated in successive iterations. Since all the suggested components are present in advanced nervous systems, we hypothesize that the brain could implement a truly evolutionary combinatorial search system, capable of generating novel variants.

Winnerless competition principle and prediction of the transient dynamics in a Lotka-Volterra model

NASA Astrophysics Data System (ADS)

Afraimovich, Valentin; Tristan, Irma; Huerta, Ramon; Rabinovich, Mikhail I.

2008-12-01

Predicting the evolution of multispecies ecological systems is an intriguing problem. A sufficiently complex model with the necessary predicting power requires solutions that are structurally stable. Small variations of the system parameters should not qualitatively perturb its solutions. When one is interested in just asymptotic results of evolution (as time goes to infinity), then the problem has a straightforward mathematical image involving simple attractors (fixed points or limit cycles) of a dynamical system. However, for an accurate prediction of evolution, the analysis of transient solutions is critical. In this paper, in the framework of the traditional Lotka-Volterra model (generalized in some sense), we show that the transient solution representing multispecies sequential competition can be reproducible and predictable with high probability.

Winnerless competition principle and prediction of the transient dynamics in a Lotka-Volterra model.

PubMed

Afraimovich, Valentin; Tristan, Irma; Huerta, Ramon; Rabinovich, Mikhail I

2008-12-01

Predicting the evolution of multispecies ecological systems is an intriguing problem. A sufficiently complex model with the necessary predicting power requires solutions that are structurally stable. Small variations of the system parameters should not qualitatively perturb its solutions. When one is interested in just asymptotic results of evolution (as time goes to infinity), then the problem has a straightforward mathematical image involving simple attractors (fixed points or limit cycles) of a dynamical system. However, for an accurate prediction of evolution, the analysis of transient solutions is critical. In this paper, in the framework of the traditional Lotka-Volterra model (generalized in some sense), we show that the transient solution representing multispecies sequential competition can be reproducible and predictable with high probability.

Functional test of pedotransfer functions to predict water flow and solute transport with the dual-permeability model MACRO

NASA Astrophysics Data System (ADS)

Moeys, J.; Larsbo, M.; Bergström, L.; Brown, C. D.; Coquet, Y.; Jarvis, N. J.

2012-07-01

Estimating pesticide leaching risks at the regional scale requires the ability to completely parameterise a pesticide fate model using only survey data, such as soil and land-use maps. Such parameterisations usually rely on a set of lookup tables and (pedo)transfer functions, relating elementary soil and site properties to model parameters. The aim of this paper is to describe and test a complete set of parameter estimation algorithms developed for the pesticide fate model MACRO, which accounts for preferential flow in soil macropores. We used tracer monitoring data from 16 lysimeter studies, carried out in three European countries, to evaluate the ability of MACRO and this "blind parameterisation" scheme to reproduce measured solute leaching at the base of each lysimeter. We focused on the prediction of early tracer breakthrough due to preferential flow, because this is critical for pesticide leaching. We then calibrated a selected number of parameters in order to assess to what extent the prediction of water and solute leaching could be improved. Our results show that water flow was generally reasonably well predicted (median model efficiency, ME, of 0.42). Although the general pattern of solute leaching was reproduced well by the model, the overall model efficiency was low (median ME = -0.26) due to errors in the timing and magnitude of some peaks. Preferential solute leaching at early pore volumes was also systematically underestimated. Nonetheless, the ranking of soils according to solute loads at early pore volumes was reasonably well estimated (concordance correlation coefficient, CCC, between 0.54 and 0.72). Moreover, we also found that ignoring macropore flow leads to a significant deterioration in the ability of the model to reproduce the observed leaching pattern, and especially the early breakthrough in some soils. Finally, the calibration procedure showed that improving the estimation of solute transport parameters is probably more important than the estimation of water flow parameters. Overall, the results are encouraging for the use of this modelling set-up to estimate pesticide leaching risks at the regional-scale, especially where the objective is to identify vulnerable soils and "source" areas of contamination.

Implementation of Solute Transport in the Vadose Zone into the `HYDRUS Package for MODFLOW'

NASA Astrophysics Data System (ADS)

Simunek, J.; Beegum, S.; Szymkiewicz, A.; Sudheer, K. P.

2017-12-01

The 'HYDRUS package for MODFLOW' was developed by Seo et al. (2007) and Twarakavi et al. (2008) to simultaneously evaluate transient water flow in both unsaturated and saturated zones. The package, which is based on the HYDRUS-1D model (Šimůnek et al., 2016) simulating unsaturated water flow in the vadose zone, was incorporated into MODFLOW (Harbaugh et al., 2000) simulating saturated groundwater flow. The HYDRUS package in the coupled model can be used to represent the effects of various unsaturated zone processes, including infiltration, evaporation, root water uptake, capillary rise, and recharge in homogeneous or layered soil profiles. The coupled model is effective in addressing spatially-variable saturated-unsaturated hydrological processes at the regional scale, allowing for complex layering in the unsaturated zone, spatially and temporarily variable water fluxes at the soil surface and in the root zone, and with alternating recharge and discharge fluxes (Twarakavi et al., 2008). One of the major limitations of the coupled model was that it could not be used to simulate at the same time solute transport. However, solute transport is highly dependent on water table fluctuations due to temporal and spatial variations in groundwater recharge. This is an important concern when the coupled model is used for analyzing groundwater contamination due to transport through the unsaturated zone. The objective of this study is to integrate the solute transport model (the solute transport part of HYDRUS-1D for the unsaturated zone and MT3DMS (Zheng and Wang, 1999; Zheng, 2009) for the saturated zone) into an existing coupled water flow model. The unsaturated zone component of the coupled model can consider solute transport involving many biogeochemical processes and reactions, including first-order degradation, volatilization, linear or nonlinear sorption, one-site kinetic sorption, two-site sorption, and two-kinetic sites sorption (Šimůnek and van Genuchten, 2008). Due to complex interactions at the groundwater table, certain modifications of the pressure head (compared to the original coupling) and solute concentration profiles were incorporated into the HYDRUS package. The developed integrated model is verified using HYDRUS-2D and analyzed for its computational time requirements.

Kinks in higher derivative scalar field theory

NASA Astrophysics Data System (ADS)

Zhong, Yuan; Guo, Rong-Zhen; Fu, Chun-E.; Liu, Yu-Xiao

2018-07-01

We study static kink configurations in a type of two-dimensional higher derivative scalar field theory whose Lagrangian contains second-order derivative terms of the field. The linear fluctuation around arbitrary static kink solutions is analyzed. We find that, the linear spectrum can be described by a supersymmetric quantum mechanics problem, and the criteria for stable static solutions can be given analytically. We also construct a superpotential formalism for finding analytical static kink solutions. Using this formalism we first reproduce some existed solutions and then offer a new solution. The properties of our solution is studied and compared with those preexisted. We also show the possibility in constructing twinlike model in the higher derivative theory, and give the consistency conditions for twinlike models corresponding to the canonical scalar field theory.

A non-local free boundary problem arising in a theory of financial bubbles

PubMed Central

Berestycki, Henri; Monneau, Regis; Scheinkman, José A.

2014-01-01

We consider an evolution non-local free boundary problem that arises in the modelling of speculative bubbles. The solution of the model is the speculative component in the price of an asset. In the framework of viscosity solutions, we show the existence and uniqueness of the solution. We also show that the solution is convex in space, and establish several monotonicity properties of the solution and of the free boundary with respect to parameters of the problem. To study the free boundary, we use, in particular, the fact that the odd part of the solution solves a more standard obstacle problem. We show that the free boundary is and describe the asymptotics of the free boundary as c, the cost of transacting the asset, goes to zero. PMID:25288815

Two-Dimensional Model for Reactive-Sorption Columns of Cylindrical Geometry: Analytical Solutions and Moment Analysis.

PubMed

Khan, Farman U; Qamar, Shamsul

2017-05-01

A set of analytical solutions are presented for a model describing the transport of a solute in a fixed-bed reactor of cylindrical geometry subjected to the first (Dirichlet) and third (Danckwerts) type inlet boundary conditions. Linear sorption kinetic process and first-order decay are considered. Cylindrical geometry allows the use of large columns to investigate dispersion, adsorption/desorption and reaction kinetic mechanisms. The finite Hankel and Laplace transform techniques are adopted to solve the model equations. For further analysis, statistical temporal moments are derived from the Laplace-transformed solutions. The developed analytical solutions are compared with the numerical solutions of high-resolution finite volume scheme. Different case studies are presented and discussed for a series of numerical values corresponding to a wide range of mass transfer and reaction kinetics. A good agreement was observed in the analytical and numerical concentration profiles and moments. The developed solutions are efficient tools for analyzing numerical algorithms, sensitivity analysis and simultaneous determination of the longitudinal and transverse dispersion coefficients from a laboratory-scale radial column experiment. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

The potential application of the blackboard model of problem solving to multidisciplinary design

NASA Technical Reports Server (NTRS)

Rogers, James L.

1989-01-01

The potential application of the blackboard model of problem solving to multidisciplinary design is discussed. Multidisciplinary design problems are complex, poorly structured, and lack a predetermined decision path from the initial starting point to the final solution. The final solution is achieved using data from different engineering disciplines. Ideally, for the final solution to be the optimum solution, there must be a significant amount of communication among the different disciplines plus intradisciplinary and interdisciplinary optimization. In reality, this is not what happens in today's sequential approach to multidisciplinary design. Therefore it is highly unlikely that the final solution is the true optimum solution from an interdisciplinary optimization standpoint. A multilevel decomposition approach is suggested as a technique to overcome the problems associated with the sequential approach, but no tool currently exists with which to fully implement this technique. A system based on the blackboard model of problem solving appears to be an ideal tool for implementing this technique because it offers an incremental problem solving approach that requires no a priori determined reasoning path. Thus it has the potential of finding a more optimum solution for the multidisciplinary design problems found in today's aerospace industries.

Approaches to stream solute load estimation for solutes with varying dynamics from five diverse small watershed

USGS Publications Warehouse

Aulenbach, Brent T.; Burns, Douglas A.; Shanley, James B.; Yanai, Ruth D.; Bae, Kikang; Wild, Adam; Yang, Yang; Yi, Dong

2016-01-01

Estimating streamwater solute loads is a central objective of many water-quality monitoring and research studies, as loads are used to compare with atmospheric inputs, to infer biogeochemical processes, and to assess whether water quality is improving or degrading. In this study, we evaluate loads and associated errors to determine the best load estimation technique among three methods (a period-weighted approach, the regression-model method, and the composite method) based on a solute's concentration dynamics and sampling frequency. We evaluated a broad range of varying concentration dynamics with stream flow and season using four dissolved solutes (sulfate, silica, nitrate, and dissolved organic carbon) at five diverse small watersheds (Sleepers River Research Watershed, VT; Hubbard Brook Experimental Forest, NH; Biscuit Brook Watershed, NY; Panola Mountain Research Watershed, GA; and Río Mameyes Watershed, PR) with fairly high-frequency sampling during a 10- to 11-yr period. Data sets with three different sampling frequencies were derived from the full data set at each site (weekly plus storm/snowmelt events, weekly, and monthly) and errors in loads were assessed for the study period, annually, and monthly. For solutes that had a moderate to strong concentration–discharge relation, the composite method performed best, unless the autocorrelation of the model residuals was <0.2, in which case the regression-model method was most appropriate. For solutes that had a nonexistent or weak concentration–discharge relation (modelR2 < about 0.3), the period-weighted approach was most appropriate. The lowest errors in loads were achieved for solutes with the strongest concentration–discharge relations. Sample and regression model diagnostics could be used to approximate overall accuracies and annual precisions. For the period-weighed approach, errors were lower when the variance in concentrations was lower, the degree of autocorrelation in the concentrations was higher, and sampling frequency was higher. The period-weighted approach was most sensitive to sampling frequency. For the regression-model and composite methods, errors were lower when the variance in model residuals was lower. For the composite method, errors were lower when the autocorrelation in the residuals was higher. Guidelines to determine the best load estimation method based on solute concentration–discharge dynamics and diagnostics are presented, and should be applicable to other studies.

Mathematical programming formulations for satellite synthesis

NASA Technical Reports Server (NTRS)

Bhasin, Puneet; Reilly, Charles H.

1987-01-01

The problem of satellite synthesis can be described as optimally allotting locations and sometimes frequencies and polarizations, to communication satellites so that interference from unwanted satellite signals does not exceed a specified threshold. In this report, mathematical programming models and optimization methods are used to solve satellite synthesis problems. A nonlinear programming formulation which is solved using Zoutendijk's method and a gradient search method is described. Nine mixed integer programming models are considered. Results of computer runs with these nine models and five geographically compatible scenarios are presented and evaluated. A heuristic solution procedure is also used to solve two of the models studied. Heuristic solutions to three large synthesis problems are presented. The results of our analysis show that the heuristic performs very well, both in terms of solution quality and solution time, on the two models to which it was applied. It is concluded that the heuristic procedure is the best of the methods considered for solving satellite synthesis problems.

Hydrodynamics beyond Navier-Stokes: the slip flow model.

PubMed

Yudistiawan, Wahyu P; Ansumali, Santosh; Karlin, Iliya V

2008-07-01

Recently, analytical solutions for the nonlinear Couette flow demonstrated the relevance of the lattice Boltzmann (LB) models to hydrodynamics beyond the continuum limit [S. Ansumali, Phys. Rev. Lett. 98, 124502 (2007)]. In this paper, we present a systematic study of the simplest LB kinetic equation-the nine-bit model in two dimensions--in order to quantify it as a slip flow approximation. Details of the aforementioned analytical solution are presented, and results are extended to include a general shear- and force-driven unidirectional flow in confined geometry. Exact solutions for the velocity, as well as for pertinent higher-order moments of the distribution functions, are obtained in both Couette and Poiseuille steady-state flows for all values of rarefaction parameter (Knudsen number). Results are compared with the slip flow solution by Cercignani, and a good quantitative agreement is found for both flow situations. Thus, the standard nine-bit LB model is characterized as a valid and self-consistent slip flow model for simulations beyond the Navier-Stokes approximation.

Magnetically-driven medical robots: An analytical magnetic model for endoscopic capsules design

NASA Astrophysics Data System (ADS)

Li, Jing; Barjuei, Erfan Shojaei; Ciuti, Gastone; Hao, Yang; Zhang, Peisen; Menciassi, Arianna; Huang, Qiang; Dario, Paolo

2018-04-01

Magnetic-based approaches are highly promising to provide innovative solutions for the design of medical devices for diagnostic and therapeutic procedures, such as in the endoluminal districts. Due to the intrinsic magnetic properties (no current needed) and the high strength-to-size ratio compared with electromagnetic solutions, permanent magnets are usually embedded in medical devices. In this paper, a set of analytical formulas have been derived to model the magnetic forces and torques which are exerted by an arbitrary external magnetic field on a permanent magnetic source embedded in a medical robot. In particular, the authors modelled cylindrical permanent magnets as general solution often used and embedded in magnetically-driven medical devices. The analytical model can be applied to axially and diametrically magnetized, solid and annular cylindrical permanent magnets in the absence of the severe calculation complexity. Using a cylindrical permanent magnet as a selected solution, the model has been applied to a robotic endoscopic capsule as a pilot study in the design of magnetically-driven robots.

Generalized analytic solutions and response characteristics of magnetotelluric fields on anisotropic infinite faults

NASA Astrophysics Data System (ADS)

Bing, Xue; Yicai, Ji

2018-06-01

In order to understand directly and analyze accurately the detected magnetotelluric (MT) data on anisotropic infinite faults, two-dimensional partial differential equations of MT fields are used to establish a model of anisotropic infinite faults using the Fourier transform method. A multi-fault model is developed to expand the one-fault model. The transverse electric mode and transverse magnetic mode analytic solutions are derived using two-infinite-fault models. The infinite integral terms of the quasi-analytic solutions are discussed. The dual-fault model is computed using the finite element method to verify the correctness of the solutions. The MT responses of isotropic and anisotropic media are calculated to analyze the response functions by different anisotropic conductivity structures. The thickness and conductivity of the media, influencing MT responses, are discussed. The analytic principles are also given. The analysis results are significant to how MT responses are perceived and to the data interpretation of the complex anisotropic infinite faults.

A multiple indicator solution approach to endogeneity in discrete-choice models for environmental valuation.

PubMed

Mariel, Petr; Hoyos, David; Artabe, Alaitz; Guevara, C Angelo

2018-08-15

Endogeneity is an often neglected issue in empirical applications of discrete choice modelling despite its severe consequences in terms of inconsistent parameter estimation and biased welfare measures. This article analyses the performance of the multiple indicator solution method to deal with endogeneity arising from omitted explanatory variables in discrete choice models for environmental valuation. We also propose and illustrate a factor analysis procedure for the selection of the indicators in practice. Additionally, the performance of this method is compared with the recently proposed hybrid choice modelling framework. In an empirical application we find that the multiple indicator solution method and the hybrid model approach provide similar results in terms of welfare estimates, although the multiple indicator solution method is more parsimonious and notably easier to implement. The empirical results open a path to explore the performance of this method when endogeneity is thought to have a different cause or under a different set of indicators. Copyright © 2018 Elsevier B.V. All rights reserved.

Delay induced stability switch, multitype bistability and chaos in an intraguild predation model.

PubMed

Shu, Hongying; Hu, Xi; Wang, Lin; Watmough, James

2015-12-01

In many predator-prey models, delay has a destabilizing effect and induces oscillations; while in many competition models, delay does not induce oscillations. By analyzing a rather simple delayed intraguild predation model, which combines both the predator-prey relation and competition, we show that delay in intraguild predation models promotes very complex dynamics. The delay can induce stability switches exhibiting a destabilizing role as well as a stabilizing role. It is shown that three types of bistability are possible: one stable equilibrium coexists with another stable equilibrium (node-node bistability); one stable equilibrium coexists with a stable periodic solution (node-cycle bistability); one stable periodic solution coexists with another stable periodic solution (cycle-cycle bistability). Numerical simulations suggest that delay can also induce chaos in intraguild predation models.

Documentation for the MODFLOW 6 framework

USGS Publications Warehouse

Hughes, Joseph D.; Langevin, Christian D.; Banta, Edward R.

2017-08-10

MODFLOW is a popular open-source groundwater flow model distributed by the U.S. Geological Survey. Growing interest in surface and groundwater interactions, local refinement with nested and unstructured grids, karst groundwater flow, solute transport, and saltwater intrusion, has led to the development of numerous MODFLOW versions. Often times, there are incompatibilities between these different MODFLOW versions. The report describes a new MODFLOW framework called MODFLOW 6 that is designed to support multiple models and multiple types of models. The framework is written in Fortran using a modular object-oriented design. The primary framework components include the simulation (or main program), Timing Module, Solutions, Models, Exchanges, and Utilities. The first version of the framework focuses on numerical solutions, numerical models, and numerical exchanges. This focus on numerical models allows multiple numerical models to be tightly coupled at the matrix level.

Solid/liquid interfacial free energies in binary systems

NASA Technical Reports Server (NTRS)

Nason, D.; Tiller, W. A.

1973-01-01

Description of a semiquantitative technique for predicting the segregation characteristics of smooth interfaces between binary solid and liquid solutions in terms of readily available thermodynamic parameters of the bulk solutions. A lattice-liquid interfacial model and a pair-bonded regular solution model are employed in the treatment with an accommodation for liquid interfacial entropy. The method is used to calculate the interfacial segregation and the free energy of segregation for solid-liquid interfaces between binary solutions for the (111) boundary of fcc crystals. The zone of compositional transition across the interface is shown to be on the order of a few atomic layers in width, being moderately narrower for ideal solutions. The free energy of the segregated interface depends primarily upon the solid composition and the heats of fusion of the component atoms, the composition difference of the solutions, and the difference of the heats of mixing of the solutions.

Large time behavior of entropy solutions to one-dimensional unipolar hydrodynamic model for semiconductor devices

NASA Astrophysics Data System (ADS)

Huang, Feimin; Li, Tianhong; Yu, Huimin; Yuan, Difan

2018-06-01

We are concerned with the global existence and large time behavior of entropy solutions to the one-dimensional unipolar hydrodynamic model for semiconductors in the form of Euler-Poisson equations in a bounded interval. In this paper, we first prove the global existence of entropy solution by vanishing viscosity and compensated compactness framework. In particular, the solutions are uniformly bounded with respect to space and time variables by introducing modified Riemann invariants and the theory of invariant region. Based on the uniform estimates of density, we further show that the entropy solution converges to the corresponding unique stationary solution exponentially in time. No any smallness condition is assumed on the initial data and doping profile. Moreover, the novelty in this paper is about the unform bound with respect to time for the weak solutions of the isentropic Euler-Poisson system.

Umami compounds enhance the intensity of retronasal sensation of aromas from model chicken soups.

PubMed

Nishimura, Toshihide; Goto, Shingo; Miura, Kyo; Takakura, Yukiko; Egusa, Ai S; Wakabayashi, Hidehiko

2016-04-01

We examined the influence of taste compounds on retronasal aroma sensation using a model chicken soup. The aroma intensity of a reconstituted flavour solution from which glutamic acid (Glu), inosine 5'-monophosphate (IMP), or phosphate was omitted was significantly lower (p<0.05) than that of the model soup. The aroma intensity of 0.4% NaCl solution containing the aroma chicken model (ACM) with added Glu and IMP was significantly higher (p<0.05) than that of 0.4% NaCl solution containing only ACM. The quantitative analyses showed that adding monosodium glutamate (MSG) to aqueous aroma solution containing only ACM enhanced the intensity of retronasal aroma sensation by 2.5-folds with increasing MSG concentration from 0% to 0.3%. Sensation intensity using an umami solution with added MSG and IMP was significantly higher than that with only MSG when the MSG concentration was 0.05%, 0.075%, or 0.1%. However, it plateaued when MSG concentration was beyond 0.3%. Copyright © 2015 Elsevier Ltd. All rights reserved.

The processing of the Viking Orbiter range data and its contribution to Mars gravity solutions

NASA Technical Reports Server (NTRS)

Lemoine, Frank G.; Rosborough, George W.; Smith, David E.

1992-01-01

The processing of Doppler data has been the primary method for deriving models of the Mars gravity field. Since the Mariner 9 and Viking spacecraft were placed in orbit about Mars, many models from degree and order 6 to degree and order 50 have been developed. However, during the Viking mission, some 26,000 range measurements to the two Viking Orbiters were also obtained. These data have not previously been used in the derivation of Mars gravity models. A portion of these range data have been processed simultaneously with the Doppler data. Normal equations were generated for both sets of data and were used to create two solutions complete to degree and order 30: a nominal solution including both the range and the Doppler data (MGM-R100), and another solution including only the Doppler data (MGM-R101). Tests with the covariances of these solutions, as well as with orbit overlap tests indicate that the interplanetary range data can be used to improve the modeling of the Mars gravity field.

Bifurcation structure of a wind-driven shallow water model with layer-outcropping

NASA Astrophysics Data System (ADS)

Primeau, François W.; Newman, David

The steady state bifurcation structure of the double-gyre wind-driven ocean circulation is examined in a shallow water model where the upper layer is allowed to outcrop at the sea surface. In addition to the classical jet-up and jet-down multiple equilibria, we find a new regime in which one of the equilibrium solutions has a large outcropping region in the subpolar gyre. Time dependent simulations show that the outcropping solution equilibrates to a stable periodic orbit with a period of 8 months. Co-existing with the periodic solution is a stable steady state solution without outcropping. A numerical scheme that has the unique advantage of being differentiable while still allowing layers to outcrop at the sea surface is used for the analysis. In contrast, standard schemes for solving layered models with outcropping are non-differentiable and have an ill-defined Jacobian making them unsuitable for solution using Newton's method. As such, our new scheme expands the applicability of numerical bifurcation techniques to an important class of ocean models whose bifurcation structure had hitherto remained unexplored.

Semianalytical solutions for transport in aquifer and fractured clay matrix system

NASA Astrophysics Data System (ADS)

Huang, Junqi; Goltz, Mark N.

2015-09-01

A three-dimensional mathematical model that describes transport of contaminant in a horizontal aquifer with simultaneous diffusion into a fractured clay formation is proposed. A group of semianalytical solutions is derived based on specific initial and boundary conditions as well as various source functions. The analytical model solutions are evaluated by numerical Laplace inverse transformation and analytical Fourier inverse transformation. The model solutions can be used to study the fate and transport in a three-dimensional spatial domain in which a nonaqueous phase liquid exists as a pool atop a fractured low-permeability clay layer. The nonaqueous phase liquid gradually dissolves into the groundwater flowing past the pool, while simultaneously diffusing into the fractured clay formation below the aquifer. Mass transfer of the contaminant into the clay formation is demonstrated to be significantly enhanced by the existence of the fractures, even though the volume of fractures is relatively small compared to the volume of the clay matrix. The model solution is a useful tool in assessing contaminant attenuation processes in a confined aquifer underlain by a fractured clay formation.

Capacitive Deionization of High-Salinity Solutions

DOE PAGES

Sharma, Ketki; Gabitto, Jorge; Mayes, Richard T.; ...

2014-12-22

Desalination of high salinity solutions has been studied using a novel experimental technique and a theoretical model. Neutron imaging has been employed to visualize lithium ions in mesoporous carbon materials, which are used as electrodes in capacitive deionization for water desalination. Experiments were conducted with a flow-through capacitive deionization cell designed for neutron imaging and with lithium chloride ( 6LiCl) as the electrolyte. Sequences of neutron images have been obtained at a relatively high concentration of lithium chloride ( 6LiCl) solution to provide information on the transport of ions within the electrodes. A new model that computes the individual ionicmore » concentration profiles inside mesoporous carbon electrodes has been used to simulate the capacitive deionization process. Modifications have also been introduced into the simulation model to calculate results at high electrolyte concentrations. Experimental data and simulation results provide insight into why capacitive deionization is not effective for desalination of high ionic-strength solutions. The combination of experimental information, obtained through neutron imaging, with the theoretical model will help in the design of capacitive deionization devices, which can improve the process for high ionic-strength solutions.« less

Finite Element Analysis of Magnetic Damping Effects on G-Jitter Induced Fluid Flow

NASA Technical Reports Server (NTRS)

Pan, Bo; Li, Ben Q.; deGroh, Henry C., III

1997-01-01

This paper reports some interim results on numerical modeling and analyses of magnetic damping of g-jitter driven fluid flow in microgravity. A finite element model is developed to represent the fluid flow, thermal and solute transport phenomena in a 2-D cavity under g-jitter conditions with and without an applied magnetic field. The numerical model is checked by comparing with analytical solutions obtained for a simple parallel plate channel flow driven by g-jitter in a transverse magnetic field. The model is then applied to study the effect of steady state g-jitter induced oscillation and on the solute redistribution in the liquid that bears direct relevance to the Bridgman-Stockbarger single crystal growth processes. A selection of computed results is presented and the results indicate that an applied magnetic field can effectively damp the velocity caused by g-jitter and help to reduce the time variation of solute redistribution.

Solving bi-level optimization problems in engineering design using kriging models

NASA Astrophysics Data System (ADS)

Xia, Yi; Liu, Xiaojie; Du, Gang

2018-05-01

Stackelberg game-theoretic approaches are applied extensively in engineering design to handle distributed collaboration decisions. Bi-level genetic algorithms (BLGAs) and response surfaces have been used to solve the corresponding bi-level programming models. However, the computational costs for BLGAs often increase rapidly with the complexity of lower-level programs, and optimal solution functions sometimes cannot be approximated by response surfaces. This article proposes a new method, namely the optimal solution function approximation by kriging model (OSFAKM), in which kriging models are used to approximate the optimal solution functions. A detailed example demonstrates that OSFAKM can obtain better solutions than BLGAs and response surface-based methods, and at the same time reduce the workload of computation remarkably. Five benchmark problems and a case study of the optimal design of a thin-walled pressure vessel are also presented to illustrate the feasibility and potential of the proposed method for bi-level optimization in engineering design.

Analytical theory of the hydrophobic effect of solutes in water.

PubMed

Urbic, Tomaz; Dill, Ken A

2017-09-01

We develop an analytical statistical-mechanical model for hydrophobic solvation in water. In this three-dimensional Mercedes-Benz-like model, two neighboring waters have three possible interaction states: a radial van der Waals interaction, a tetrahedral orientation-dependent hydrogen-bonding interaction, or no interaction. Nonpolar solutes are modeled as van der Waals particles of different radii. The model is sufficiently simple that we can calculate the partition function and thermal and volumetric properties of solvation versus temperature, pressure, and solute radius. Predictions are in good agreement with results of Monte Carlo simulations. And their trends agree with experiments on hydrophobic solute insertion. The theory shows that first-shell waters are more highly structured than bulk waters, because of hydrogen bonding, and that that structure melts out faster with temperature than it does in bulk waters. Because the theory is analytical, it can explore a broad range of solvation properties and anomalies of water, at minimal computational expense.

Measurement and modeling of diameter distributions of particulate matter in terrestrial solutions

NASA Astrophysics Data System (ADS)

Levia, Delphis F.; Michalzik, Beate; Bischoff, Sebastian; NäThe, Kerstin; Legates, David R.; Gruselle, Marie-Cecile; Richter, Susanne

2013-04-01

Particulate matter (PM) plays an important role in biogeosciences, affecting biosphere-atmosphere interactions and ecosystem health. This is the first known study to quantify and model PM diameter distributions of bulk precipitation, throughfall, stemflow, and organic layer (Oa) solution. Solutions were collected from a European beech (Fagus sylvatica L.) forest during leafed and leafless periods. Following scanning electron microscopy and image analysis, PM distributions were quantified and then modeled with the Box-Cox transformation. Based on an analysis of 43,278 individual particulates, median PM diameter of all solutions was around 3.0 µm. All PM diameter frequency distributions were skewed significantly to the right. Optimal power transformations of PM diameter distributions were between -1.00 and -1.56. The utility of this model reconstruction would be that large samples having a similar probability density function can be developed for similar forests. Further work on the shape and chemical composition of particulates is warranted.

Numerical Simulation of Droplet Breakup and Collision in the Solution Precursor Plasma Spraying

NASA Astrophysics Data System (ADS)

Shan, Y.; Coyle, T. W.; Mostaghimi, J.

2007-12-01

Finely structured ceramic coatings can be obtained by solution precursor plasma spraying. The final structure of the coating highly depends on the droplet size and velocity distribution at the injection, the evolution of the spray in the jet, and droplet breakup and collision within the spray. This article describes a 3D model to simulate the transport phenomena and the trajectory and heating of the solution spray in the process. O’Rourke’s droplet collision model is used to take into account the influence of droplet collision. The influence of droplet breakup is also considered by implementing TAB droplet breakup models into the plasma jet model. The effects of droplet collisions and breakup on the droplet size, velocity, and temperature distribution of the solution spray are investigated. The results indicate that droplet breakup and collision play an important role in determining the final particle size and velocity distributions on the substrate.

Stationary spiral flow in polytropic stellar models

PubMed Central

Pekeris, C. L.

1980-01-01

It is shown that, in addition to the static Emden solution, a self-gravitating polytropic gas has a dynamic option in which there is stationary flow along spiral trajectories wound around the surfaces of concentric tori. The motion is obtained as a solution of a partial differential equation which is satisfied by the meridional stream function, coupled with Poisson's equation and a Bernoulli-type equation for the pressure (density). The pressure is affected by the whole of the Bernoulli term rather than by the centrifugal part only, which acts for a rotating model, and it may be reduced down to zero at the center. The spiral type of flow is illustrated for an incompressible fluid (n = 0), for which an exact solution is obtained. The features of the dynamic constant-density model are discussed as a basis for future comparison with the solution for compressible models. PMID:16592825

Analytical theory of the hydrophobic effect of solutes in water

NASA Astrophysics Data System (ADS)

Urbic, Tomaz; Dill, Ken A.

2017-09-01

We develop an analytical statistical-mechanical model for hydrophobic solvation in water. In this three-dimensional Mercedes-Benz-like model, two neighboring waters have three possible interaction states: a radial van der Waals interaction, a tetrahedral orientation-dependent hydrogen-bonding interaction, or no interaction. Nonpolar solutes are modeled as van der Waals particles of different radii. The model is sufficiently simple that we can calculate the partition function and thermal and volumetric properties of solvation versus temperature, pressure, and solute radius. Predictions are in good agreement with results of Monte Carlo simulations. And their trends agree with experiments on hydrophobic solute insertion. The theory shows that first-shell waters are more highly structured than bulk waters, because of hydrogen bonding, and that that structure melts out faster with temperature than it does in bulk waters. Because the theory is analytical, it can explore a broad range of solvation properties and anomalies of water, at minimal computational expense.

A well-behaved class of charged analogue of Durgapal solution

NASA Astrophysics Data System (ADS)

Mehta, R. N.; Pant, Neeraj; Mahto, Dipo; Jha, J. S.

2013-02-01

We present a well behaved class of charged analogue of M.C. Durgapal (J. Phys. A, Math. Gen. 15:2637, 1982) solution. This solution describes charged fluid balls with positively finite central pressure, positively finite central density; their ratio is less than one and causality condition is obeyed at the centre. The outmarch of pressure, density, pressure-density ratio and the adiabatic speed of sound is monotonically decreasing, however, the electric intensity is monotonically increasing in nature. This solution gives us wide range of parameter for every positive value of n for which the solution is well behaved hence, suitable for modeling of super dense stars. Keeping in view of well behaved nature of this solution, one new class of solution is being studied extensively. Moreover, this class of solution gives us wide range of constant K (0≤ K≤2.2) for which the solution is well behaved hence, suitable for modeling of super dense stars like strange quark stars, neutron stars and pulsars. For this class of solution the mass of a star is maximized with all degree of suitability, compatible with quark stars, neutron stars and pulsars. By assuming the surface density ρ b =2×1014 g/cm3 (like, Brecher and Capocaso, Nature 259:377, 1976), corresponding to K=0 with X=0..235, the resulting well behaved model has the mass M=4.03 M Θ , radius r b =19.53 km and moment of inertia I=1.213×1046 g cm2; for K=1.5 with X=0.235, the resulting well behaved model has the mass M=4.43 M Θ , radius r b =18.04 km and moment of inertia I=1.136×1046 g cm2; for K=2.2 with X=0.235, the resulting well behaved model has the mass M=4.56 M Θ , radius r b =17.30 km and moment of inertia I=1.076×1046 g cm2. These values of masses and moment of inertia are found to be consistent with the crab pulsars.

Vibrational spectra of water solutions of azoles from QM/MM calculations: effects of solvation.

PubMed

Tanzi, Luana; Ramondo, Fabio; Guidoni, Leonardo

2012-10-18

Using microsolvation models and mixed quantum/classical ab initio molecular dynamics simulations, we investigate the vibrational properties of two azoles in water solution: pyrazole and oxazole. The effects of the water-azole hydrogen bonding are rationalized by an extensive comparison between structural parameters and harmonic frequencies obtained by microsolvation models. Following the effective normal-mode analysis introduced by Martinez et al. [Martinez et al., J. Chem. Phys. 2006, 125, 144106], we identify the vibrational frequencies of the solutes using the decomposition of the vibrational density of states of the gas phase and solution dynamics. The calculated shifts from gas phase to solution are fairly in agreement with the available experimental data.

Rogue waves: from nonlinear Schrödinger breather solutions to sea-keeping test.

PubMed

Onorato, Miguel; Proment, Davide; Clauss, Günther; Klein, Marco

2013-01-01

Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by the one-dimensional nonlinear Schrödinger equation. Besides traveling wave solutions like solitons, this model admits also breather solutions that are now considered as prototypes of rogue waves in ocean. We propose a novel technique to study the interaction between waves and ships/structures during extreme ocean conditions using such breather solutions. In particular, we discuss a state of the art sea-keeping test in a 90-meter long wave tank by creating a Peregrine breather solution hitting a scaled chemical tanker and we discuss its potential devastating effects on the ship.

Rogue Waves: From Nonlinear Schrödinger Breather Solutions to Sea-Keeping Test

PubMed Central

Onorato, Miguel; Proment, Davide; Clauss, Günther; Klein, Marco

2013-01-01

Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by the one-dimensional nonlinear Schrödinger equation. Besides traveling wave solutions like solitons, this model admits also breather solutions that are now considered as prototypes of rogue waves in ocean. We propose a novel technique to study the interaction between waves and ships/structures during extreme ocean conditions using such breather solutions. In particular, we discuss a state of the art sea-keeping test in a 90-meter long wave tank by creating a Peregrine breather solution hitting a scaled chemical tanker and we discuss its potential devastating effects on the ship. PMID:23405086

Solute load concentrations in some streams in the Upper Osun and Owena drainage basins, central western Nigeria

NASA Astrophysics Data System (ADS)

Jeje, L. K.; Ogunkoya, O. O.; Oluwatimilehin, J. M.

1999-12-01

The solute load dynamics of 12 third-order streams in central western Nigeria are presented, during storm and non-storm runoff events. The relevance of the Walling and Foster model for explaining storm period solute load dynamics in the humid tropical environment was assessed and it was found that this model was generally applicable to the study area. Exceptions appear to be streams draining settlements and/or farms where fertilizers are applied heavily. The solute load ranged from 5 mg l -1 to 580 mg l -1 with streams draining basins with tree-crop plantations ( Theobroma cacao, Cola sp.) as the dominant land cover having the highest solute load.

Application of thermodynamics to silicate crystalline solutions

NASA Technical Reports Server (NTRS)

Saxena, S. K.

1972-01-01

A review of thermodynamic relations is presented, describing Guggenheim's regular solution models, the simple mixture, the zeroth approximation, and the quasi-chemical model. The possibilities of retrieving useful thermodynamic quantities from phase equilibrium studies are discussed. Such quantities include the activity-composition relations and the free energy of mixing in crystalline solutions. Theory and results of the study of partitioning of elements in coexisting minerals are briefly reviewed. A thermodynamic study of the intercrystalline and intracrystalline ion exchange relations gives useful information on the thermodynamic behavior of the crystalline solutions involved. Such information is necessary for the solution of most petrogenic problems and for geothermometry. Thermodynamic quantities for tungstates (CaWO4-SrWO4) are calculated.

Analytical solution to the fractional polytropic gas spheres

NASA Astrophysics Data System (ADS)

Nouh, Mohamed I.; Abdel-Salam, Emad A.-B.

2018-04-01

The Lane-Emden equation can be used to model stellar interiors, star clusters and many configurations in astrophysics. Unfortunately, there is an exact solution only for the polytropic indices n = 0, 1 and 5. In the present paper, a series solution for the fractional Lane-Emden equation is presented. The solution is performed in the frame of modified Rienmann Liouville derivatives. The obtained results recover the well-known series solutions when α =1. The fractional model of n = 3 is calculated and the mass-radius relation, density ratio, pressure ratio and temperature ratio are investigated. The fractional star appears much different than the integer star, as it is denser, more stressed and hotter than the integer star.

On stable exponential cosmological solutions with non-static volume factor in the Einstein-Gauss-Bonnet model

NASA Astrophysics Data System (ADS)

Ivashchuk, V. D.; Ernazarov, K. K.

2017-01-01

A (n + 1)-dimensional gravitational model with cosmological constant and Gauss-Bonnet term is studied. The ansatz with diagonal cosmological metrics is adopted and solutions with exponential dependence of scale factors: ai ˜ exp (vit), i = 1, …, n, are considered. The stability analysis of the solutions with non-static volume factor is presented. We show that the solutions with v 1 = v 2 = v 3 = H > 0 and small enough variation of the effective gravitational constant G are stable if certain restriction on (vi ) is obeyed. New examples of stable exponential solutions with zero variation of G in dimensions D = 1 + m + 2 with m > 2 are presented.

Transitions amongst synchronous solutions in the stochastic Kuramoto model

NASA Astrophysics Data System (ADS)

DeVille, Lee

2012-05-01

We consider the Kuramoto model of coupled oscillators with nearest-neighbour coupling and additive white noise. We show that synchronous solutions which are stable without the addition of noise become metastable and that we have transitions amongst synchronous solutions on long timescales. We compute these timescales and, moreover, compute the most likely path in phase space that transitions will follow. We show that these transition timescales do not increase as the number of oscillators in the system increases, and are roughly constant in the system size. Finally, we show that the transitions correspond to a splitting of one synchronous solution into two communities which move independently for some time and which rejoin to form a different synchronous solution.

Exact solution for the time evolution of network rewiring models

NASA Astrophysics Data System (ADS)

Evans, T. S.; Plato, A. D. K.

2007-05-01

We consider the rewiring of a bipartite graph using a mixture of random and preferential attachment. The full mean-field equations for the degree distribution and its generating function are given. The exact solution of these equations for all finite parameter values at any time is found in terms of standard functions. It is demonstrated that these solutions are an excellent fit to numerical simulations of the model. We discuss the relationship between our model and several others in the literature, including examples of urn, backgammon, and balls-in-boxes models, the Watts and Strogatz rewiring problem, and some models of zero range processes. Our model is also equivalent to those used in various applications including cultural transmission, family name and gene frequencies, glasses, and wealth distributions. Finally some Voter models and an example of a minority game also show features described by our model.

Validation of Groundwater Models: Meaningful or Meaningless?

NASA Astrophysics Data System (ADS)

Konikow, L. F.

2003-12-01

Although numerical simulation models are valuable tools for analyzing groundwater systems, their predictive accuracy is limited. People who apply groundwater flow or solute-transport models, as well as those who make decisions based on model results, naturally want assurance that a model is "valid." To many people, model validation implies some authentication of the truth or accuracy of the model. History matching is often presented as the basis for model validation. Although such model calibration is a necessary modeling step, it is simply insufficient for model validation. Because of parameter uncertainty and solution non-uniqueness, declarations of validation (or verification) of a model are not meaningful. Post-audits represent a useful means to assess the predictive accuracy of a site-specific model, but they require the existence of long-term monitoring data. Model testing may yield invalidation, but that is an opportunity to learn and to improve the conceptual and numerical models. Examples of post-audits and of the application of a solute-transport model to a radioactive waste disposal site illustrate deficiencies in model calibration, prediction, and validation.

Solutions to the Problem of Disproportionality: A Discussion of the Models.

ERIC Educational Resources Information Center

Newman, Isadore; Oravecz, Michael T.

The major concern for any research model, whether disproportionate or not, is the research question and how well that question is reflected by the model. Three "exact solutions" for disproportional situations, the hierarchial, unadjusted main effects, and fitting constant methods, are discussed in terms of the research question that each…

Cerebellum-inspired neural network solution of the inverse kinematics problem.

PubMed

Asadi-Eydivand, Mitra; Ebadzadeh, Mohammad Mehdi; Solati-Hashjin, Mehran; Darlot, Christian; Abu Osman, Noor Azuan

2015-12-01

The demand today for more complex robots that have manipulators with higher degrees of freedom is increasing because of technological advances. Obtaining the precise movement for a desired trajectory or a sequence of arm and positions requires the computation of the inverse kinematic (IK) function, which is a major problem in robotics. The solution of the IK problem leads robots to the precise position and orientation of their end-effector. We developed a bioinspired solution comparable with the cerebellar anatomy and function to solve the said problem. The proposed model is stable under all conditions merely by parameter determination, in contrast to recursive model-based solutions, which remain stable only under certain conditions. We modified the proposed model for the simple two-segmented arm to prove the feasibility of the model under a basic condition. A fuzzy neural network through its learning method was used to compute the parameters of the system. Simulation results show the practical feasibility and efficiency of the proposed model in robotics. The main advantage of the proposed model is its generalizability and potential use in any robot.

Assessment of IT solutions used in the Hungarian income tax microsimulation system

NASA Astrophysics Data System (ADS)

Molnar, I.; Hardhienata, S.

2017-01-01

This paper focuses on the use of information technology (IT) in diverse microsimulation studies and presents state-of-the-art solutions in the traditional application field of personal income tax simulation. The aim of the paper is to promote solutions, which can improve the efficiency and quality of microsimulation model implementation, assess their applicability and help to shift attention from microsimulation model implementation and data analysis towards experiment design and model use. First, the authors shortly discuss the relevant characteristics of the microsimulation application field and the managerial decision-making problem. After examination of the salient problems, advanced IT solutions, such as meta-database and service-oriented architecture are presented. The authors show how selected technologies can be applied to support both data- and behavior-driven and even agent-based personal income tax microsimulation model development. Finally, examples are presented and references made to the Hungarian Income Tax Simulator (HITS) models and their results. The paper concludes with a summary of the IT assessment and application-related author remarks dedicated to an Indonesian Income Tax Microsimulation Model.

Nonlocal electron transport: direct and Greens function solution and comparison of our model with the SNB model

NASA Astrophysics Data System (ADS)

Colombant, Denis; Manheimer, Wallace; Schmitt, Andrew J.

2013-10-01

At least two models, ours and SNB (Schurtz-Nicolai-Busquet), and two methods of solution, direct numerical solution (DS) and Greens function (GF) are being used in multi-dimensional radiation hydrodynamics codes. We present results of a laser target implosion using both methods of solution. Although our model and SNB differ in some physical content, direct comparisons have been non-existent up to now. However a paper by Marocchino et al. has recently presented the results of two nanosecond-time-scale test problems, showing that the preheat calculated by the two models are different by about three orders of magnitude. We have rerun these problems and we find much less difference between the two than they do. One can show analytically that the results should be quite similar and are about an order of magnitude less than the maximum, and two orders of magnitude more than the minimum preheating in. We have been able to trace the somewhat different results back to the different physical assumptions made in each model. Work supported by DoE-NNSA and ONR.

Boric acid permeation in forward osmosis membrane processes: modeling, experiments, and implications.

PubMed

Jin, Xue; Tang, Chuyang Y; Gu, Yangshuo; She, Qianhong; Qi, Saren

2011-03-15

Forward osmosis (FO) is attracting increasing interest for its potential applications in desalination. In FO, permeation of contaminants from feed solution into draw solution through the semipermeable membrane can take place simultaneously with water diffusion. Understanding the contaminants transport through and rejection by FO membrane has significant technical implications in the way to separate clean water from the diluted draw solution. In this study, a model was developed to predict boron flux in FO operation. A strong agreement between modeling results and experimental data indicates that the model developed in this study can accurately predict the boron transport through FO membranes. Furthermore, the model can guide the fabrication of improved FO membranes with decreased boron permeability and structural parameter to minimize boron flux. Both theoretical model and experimental results demonstrated that when membrane active layer was facing draw solution, boron flux was substantially greater compared to the other membrane orientation due to more severe internal concentration polarization. In this investigation, for the first time, rejection of contaminants was defined in FO processes. This is critical to compare the membrane performance between different membranes and experimental conditions.

Gravity Models from CHAMP and other Satellite Data

NASA Technical Reports Server (NTRS)

Lemoime, Frank G.; Cox, C. M.; Chinn, D. S.; Zelensky, N. P.; Thompson, B. F.; Rowlands, D. D.; Luthdke, S. B.; Nerem, R. S.

2003-01-01

CHAMP spacecraft is the first of a series of new spacecraft missions that are revolutionizing our ability to model the Earth's geopotential. We report on the analysis of over 100 days of CHAMP data in 2001 and 2002, merged with tracking data of other satellites such as Jason, Topex, GFO, Starlette, Stella, Spot-2, as well as satellite altimetry. We find that the CHAMP-only component of these solutions is a significant improvement over pre-CHAMP satellite only models with respect to the high degree information expressed by the geopotential model coefficients. For example, the variance of the differences with altimeter-derived anomalies through degree 70 is 2.80 mGal(sup 2) for the CHAMP-only solution based on 87 days of data vs. 10.19 mGal(sup 2) for EGM96S. Nonetheless, in order to model properly the various resonances to which different satellites are sensitive, we must include other satellite data. We evaluate the performance of these new CHAMP derived solutions with EGM96 and the EIGEN series of solutions. We review carefully the performance of these models for altimetric satellites.

Nonlinear feedback control for high alpha flight

NASA Technical Reports Server (NTRS)

Stalford, Harold

1990-01-01

Analytical aerodynamic models are derived from a high alpha 6 DOF wind tunnel model. One detail model requires some interpolation between nonlinear functions of alpha. One analytical model requires no interpolation and as such is a completely continuous model. Flight path optimization is conducted on the basic maneuvers: half-loop, 90 degree pitch-up, and level turn. The optimal control analysis uses the derived analytical model in the equations of motion and is based on both moment and force equations. The maximum principle solution for the half-loop is poststall trajectory performing the half-loop in 13.6 seconds. The agility induced by thrust vectoring capability provided a minimum effect on reducing the maneuver time. By means of thrust vectoring control the 90 degrees pitch-up maneuver can be executed in a small place over a short time interval. The agility capability of thrust vectoring is quite beneficial for pitch-up maneuvers. The level turn results are based currently on only outer layer solutions of singular perturbation. Poststall solutions provide high turn rates but generate higher losses of energy than that of classical sustained solutions.

Washout and non-washout solutions of a system describing microbial fermentation process under the influence of growth inhibitions and maximal concentration of yeast cells.

PubMed

Kasbawati; Gunawan, Agus Yodi; Sidarto, Kuntjoro Adjie

2017-07-01

An unstructured model for the growth of yeast cell on glucose due to growth inhibitions by substrate, products, and cell density is discussed. The proposed model describes the dynamical behavior of fermentation system that shows multiple steady states for a certain regime of operating parameters such as inlet glucose and dilution rate. Two types of steady state solutions are found, namely washout and non-washout solutions. Furthermore, different numerical impositions to the two parameters put in evidence three results regarding non-washout solution: a unique locally stable non-washout solution, a unique locally stable non-washout solution towards which other nearby solutions exhibit damped oscillations, and multiple non-washout solutions where one is locally stable while the other is unstable. It is also found an optimal inlet glucose which produces the highest cell and ethanol concentration. Copyright © 2017 Elsevier Inc. All rights reserved.

Quantum decay model with exact explicit analytical solution

NASA Astrophysics Data System (ADS)

Marchewka, Avi; Granot, Er'El

2009-01-01

A simple decay model is introduced. The model comprises a point potential well, which experiences an abrupt change. Due to the temporal variation, the initial quantum state can either escape from the well or stay localized as a new bound state. The model allows for an exact analytical solution while having the necessary features of a decay process. The results show that the decay is never exponential, as classical dynamics predicts. Moreover, at short times the decay has a fractional power law, which differs from perturbation quantum method predictions. At long times the decay includes oscillations with an envelope that decays algebraically. This is a model where the final state can be either continuous or localized, and that has an exact analytical solution.

Solute drag in polycrystalline materials: Derivation and numerical analysis of a variational model for the effect of solute on the motion of boundaries and junctions during coarsening

NASA Astrophysics Data System (ADS)

Wilson, Seth Robert

A mathematical model that results in an expression for the local acceleration of a network of sharp interfaces interacting with an ambient solute field is proposed. This expression comprises a first-order differential equation for the local velocity that, given the appropriate initial conditions, may be used to predict the subsequent time evolution of the system, including non-steady state absorption and desorption of solute. Evolution equations for both interfaces and the junction of interfaces are derived by maximizing a functional approximating the rate at which the local Gibbs free energy density decreases, as a function of the local solute content and the instantaneous velocity. The model has been formulated in three dimensions, and non-equilibrium effects such as grain boundary diffusion, solute gradients, and time-dependant segregation are taken into account. As a consequence of this model, it is shown that both interfaces and the junctions between interfaces obey evolution equations that closely resemble Newton's second law. In particular, the concept of "thrust" in variable-mass systems is shown to have a direct analog in solute-interface interaction. Numerical analysis of the equations that result reveals that a double cusp catastrophe governs the behavior of the solute-interface system, for which trajectories that include hysteresis, slip-stick motion, and jerky motion are all conceivable. The geometry of the cusp catastrophe is quantified, and a number of relations between physical parameters and system behavior are consequently predicted.

Upscaling heterogeneity in aquifer reactivity via exposure-time concept: forward model.

PubMed

Seeboonruang, Uma; Ginn, Timothy R

2006-03-20

Reactive properties of aquifer solid phase materials play an important role in solute fate and transport in the natural subsurface on time scales ranging from years in contaminant remediation to millennia in dynamics of aqueous geochemistry. Quantitative tools for dealing with the impact of natural heterogeneity in solid phase reactivity on solute fate and transport are limited. Here we describe the use of a structural variable to keep track of solute flux exposure to reactive surfaces. With this approach, we develop a non-reactive tracer model that is useful for determining the signature of multi-scale reactive solid heterogeneity in terms of solute flux distributions at the field scale, given realizations of three-dimensional reactive site density fields. First, a governing Eulerian equation for the non-reactive tracer model is determined by an upscaling technique in which it is found that the exposure time of solution to reactive surface areas evolves via both a macroscopic velocity and a macroscopic dispersion in the artificial dimension of exposure time. Second, we focus on the Lagrangian approach in the context of a streamtube ensemble and demonstrate the use of the distribution of solute flux over the exposure time dimension in modeling two-dimensional transport of a solute undergoing simplified linear reversible reactions, in hypothetical conditions following prior laboratory experiments. The distribution of solute flux over exposure time in a given case is a signature of the impact of heterogeneous aquifer reactivity coupled with a particular physical heterogeneity, boundary conditions, and hydraulic gradient. Rigorous application of this approach in a simulation sense is limited here to linear kinetically controlled reactions.

Addressing subjective decision-making inherent in GLUE-based multi-criteria rainfall-runoff model calibration

NASA Astrophysics Data System (ADS)

Shafii, Mahyar; Tolson, Bryan; Shawn Matott, L.

2015-04-01

GLUE is one of the most commonly used informal methodologies for uncertainty estimation in hydrological modelling. Despite the ease-of-use of GLUE, it involves a number of subjective decisions such as the strategy for identifying the behavioural solutions. This study evaluates the impact of behavioural solution identification strategies in GLUE on the quality of model output uncertainty. Moreover, two new strategies are developed to objectively identify behavioural solutions. The first strategy considers Pareto-based ranking of parameter sets, while the second one is based on ranking the parameter sets based on an aggregated criterion. The proposed strategies, as well as the traditional strategies in the literature, are evaluated with respect to reliability (coverage of observations by the envelope of model outcomes) and sharpness (width of the envelope of model outcomes) in different numerical experiments. These experiments include multi-criteria calibration and uncertainty estimation of three rainfall-runoff models with different number of parameters. To demonstrate the importance of behavioural solution identification strategy more appropriately, GLUE is also compared with two other informal multi-criteria calibration and uncertainty estimation methods (Pareto optimization and DDS-AU). The results show that the model output uncertainty varies with the behavioural solution identification strategy, and furthermore, a robust GLUE implementation would require considering multiple behavioural solution identification strategies and choosing the one that generates the desired balance between sharpness and reliability. The proposed objective strategies prove to be the best options in most of the case studies investigated in this research. Implementing such an approach for a high-dimensional calibration problem enables GLUE to generate robust results in comparison with Pareto optimization and DDS-AU.

Stability of subsystem solutions in agent-based models

NASA Astrophysics Data System (ADS)

Perc, Matjaž

2018-01-01

The fact that relatively simple entities, such as particles or neurons, or even ants or bees or humans, give rise to fascinatingly complex behaviour when interacting in large numbers is the hallmark of complex systems science. Agent-based models are frequently employed for modelling and obtaining a predictive understanding of complex systems. Since the sheer number of equations that describe the behaviour of an entire agent-based model often makes it impossible to solve such models exactly, Monte Carlo simulation methods must be used for the analysis. However, unlike pairwise interactions among particles that typically govern solid-state physics systems, interactions among agents that describe systems in biology, sociology or the humanities often involve group interactions, and they also involve a larger number of possible states even for the most simplified description of reality. This begets the question: when can we be certain that an observed simulation outcome of an agent-based model is actually stable and valid in the large system-size limit? The latter is key for the correct determination of phase transitions between different stable solutions, and for the understanding of the underlying microscopic processes that led to these phase transitions. We show that a satisfactory answer can only be obtained by means of a complete stability analysis of subsystem solutions. A subsystem solution can be formed by any subset of all possible agent states. The winner between two subsystem solutions can be determined by the average moving direction of the invasion front that separates them, yet it is crucial that the competing subsystem solutions are characterised by a proper composition and spatiotemporal structure before the competition starts. We use the spatial public goods game with diverse tolerance as an example, but the approach has relevance for a wide variety of agent-based models.

Asteroid shape and spin statistics from convex models

NASA Astrophysics Data System (ADS)

Torppa, J.; Hentunen, V.-P.; Pääkkönen, P.; Kehusmaa, P.; Muinonen, K.

2008-11-01

We introduce techniques for characterizing convex shape models of asteroids with a small number of parameters, and apply these techniques to a set of 87 models from convex inversion. We present three different approaches for determining the overall dimensions of an asteroid. With the first technique, we measured the dimensions of the shapes in the direction of the rotation axis and in the equatorial plane and with the two other techniques, we derived the best-fit ellipsoid. We also computed the inertia matrix of the model shape to test how well it represents the target asteroid, i.e., to find indications of possible non-convex features or albedo variegation, which the convex shape model cannot reproduce. We used shape models for 87 asteroids to perform statistical analyses and to study dependencies between shape and rotation period, size, and taxonomic type. We detected correlations, but more data are required, especially on small and large objects, as well as slow and fast rotators, to reach a more thorough understanding about the dependencies. Results show, e.g., that convex models of asteroids are not that far from ellipsoids in root-mean-square sense, even though clearly irregular features are present. We also present new spin and shape solutions for Asteroids (31) Euphrosyne, (54) Alexandra, (79) Eurynome, (93) Minerva, (130) Elektra, (376) Geometria, (471) Papagena, and (776) Berbericia. We used a so-called semi-statistical approach to obtain a set of possible spin state solutions. The number of solutions depends on the abundancy of the data, which for Eurynome, Elektra, and Geometria was extensive enough for determining an unambiguous spin and shape solution. Data of Euphrosyne, on the other hand, provided a wide distribution of possible spin solutions, whereas the rest of the targets have two or three possible solutions.

Modeling variably saturated subsurface solute transport with MODFLOW-UZF and MT3DMS

USGS Publications Warehouse

Morway, Eric D.; Niswonger, Richard G.; Langevin, Christian D.; Bailey, Ryan T.; Healy, Richard W.

2013-01-01

The MT3DMS groundwater solute transport model was modified to simulate solute transport in the unsaturated zone by incorporating the unsaturated-zone flow (UZF1) package developed for MODFLOW. The modified MT3DMS code uses a volume-averaged approach in which Lagrangian-based UZF1 fluid fluxes and storage changes are mapped onto a fixed grid. Referred to as UZF-MT3DMS, the linked model was tested against published benchmarks solved analytically as well as against other published codes, most frequently the U.S. Geological Survey's Variably-Saturated Two-Dimensional Flow and Transport Model. Results from a suite of test cases demonstrate that the modified code accurately simulates solute advection, dispersion, and reaction in the unsaturated zone. Two- and three-dimensional simulations also were investigated to ensure unsaturated-saturated zone interaction was simulated correctly. Because the UZF1 solution is analytical, large-scale flow and transport investigations can be performed free from the computational and data burdens required by numerical solutions to Richards' equation. Results demonstrate that significant simulation runtime savings can be achieved with UZF-MT3DMS, an important development when hundreds or thousands of model runs are required during parameter estimation and uncertainty analysis. Three-dimensional variably saturated flow and transport simulations revealed UZF-MT3DMS to have runtimes that are less than one tenth of the time required by models that rely on Richards' equation. Given its accuracy and efficiency, and the wide-spread use of both MODFLOW and MT3DMS, the added capability of unsaturated-zone transport in this familiar modeling framework stands to benefit a broad user-ship.

Modeling variably saturated subsurface solute transport with MODFLOW-UZF and MT3DMS.

PubMed

Morway, Eric D; Niswonger, Richard G; Langevin, Christian D; Bailey, Ryan T; Healy, Richard W

2013-03-01

The MT3DMS groundwater solute transport model was modified to simulate solute transport in the unsaturated zone by incorporating the unsaturated-zone flow (UZF1) package developed for MODFLOW. The modified MT3DMS code uses a volume-averaged approach in which Lagrangian-based UZF1 fluid fluxes and storage changes are mapped onto a fixed grid. Referred to as UZF-MT3DMS, the linked model was tested against published benchmarks solved analytically as well as against other published codes, most frequently the U.S. Geological Survey's Variably-Saturated Two-Dimensional Flow and Transport Model. Results from a suite of test cases demonstrate that the modified code accurately simulates solute advection, dispersion, and reaction in the unsaturated zone. Two- and three-dimensional simulations also were investigated to ensure unsaturated-saturated zone interaction was simulated correctly. Because the UZF1 solution is analytical, large-scale flow and transport investigations can be performed free from the computational and data burdens required by numerical solutions to Richards' equation. Results demonstrate that significant simulation runtime savings can be achieved with UZF-MT3DMS, an important development when hundreds or thousands of model runs are required during parameter estimation and uncertainty analysis. Three-dimensional variably saturated flow and transport simulations revealed UZF-MT3DMS to have runtimes that are less than one tenth of the time required by models that rely on Richards' equation. Given its accuracy and efficiency, and the wide-spread use of both MODFLOW and MT3DMS, the added capability of unsaturated-zone transport in this familiar modeling framework stands to benefit a broad user-ship. Published 2012. This article is a U.S. Government work and is in the public domain in the USA.

Multisite Ion Model in Concentrated Solutions of Divalent Cations (MgCl2 and CaCl2): Osmotic Pressure Calculations

PubMed Central

2015-01-01

Accurate force field parameters for ions are essential for meaningful simulation studies of proteins and nucleic acids. Currently accepted models of ions, especially for divalent ions, do not necessarily reproduce the right physiological behavior of Ca2+ and Mg2+ ions. Saxena and Sept (J. Chem. Theor. Comput.2013, 9, 3538–3542) described a model, called the multisite-ion model, where instead of treating the ions as an isolated sphere, the charge was split into multiple sites with partial charge. This model provided accurate inner shell coordination of the ion with biomolecules and predicted better free energies for proteins and nucleic acids. Here, we expand and refine the multisite model to describe the behavior of divalent ions in concentrated MgCl2 and CaCl2 electrolyte solutions, eliminating the unusual ion–ion pairing and clustering of ions which occurred in the original model. We calibrate and improve the parameters of the multisite model by matching the osmotic pressure of concentrated solutions of MgCl2 to the experimental values and then use these parameters to test the behavior of CaCl2 solutions. We find that the concentrated solutions of both divalent ions exhibit the experimentally observed behavior with correct osmotic pressure, the presence of solvent separated ion pairs instead of direct ion pairs, and no aggregation of ions. The improved multisite model for (Mg2+ and Ca2+) can be used in classical simulations of biomolecules at physiologically relevant salt concentrations. PMID:25482831

Two Novel Methods and Multi-Mode Periodic Solutions for the Fermi-Pasta-Ulam Model

NASA Astrophysics Data System (ADS)

Arioli, Gianni; Koch, Hans; Terracini, Susanna

2005-04-01

We introduce two novel methods for studying periodic solutions of the FPU β-model, both numerically and rigorously. One is a variational approach, based on the dual formulation of the problem, and the other involves computer-assisted proofs. These methods are used e.g. to construct a new type of solutions, whose energy is spread among several modes, associated with closely spaced resonances.

Adiabatic model of field reversal by fast ions in an axisymmetric open trap

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

Tsidulko, Yu. A., E-mail: tsidulko@mail.ru

2016-06-15

A model of field reversal by fast ions has been developed under the assumption of preservation of fast-ion adiabatic invariants. Analytical solutions obtained in the approximation of a narrow fast-ion layer and numerical solutions to the evolutionary problem are presented. The solutions demonstrate the process of formation of a field reversed configuration with parameters close to those of the planned experiment.

Numerical simulations to the nonlinear model of interpersonal relationships with time fractional derivative

NASA Astrophysics Data System (ADS)

Gencoglu, Muharrem Tuncay; Baskonus, Haci Mehmet; Bulut, Hasan

2017-01-01

The main aim of this manuscript is to obtain numerical solutions for the nonlinear model of interpersonal relationships with time fractional derivative. The variational iteration method is theoretically implemented and numerically conducted only to yield the desired solutions. Numerical simulations of desired solutions are plotted by using Wolfram Mathematica 9. The authors would like to thank the reviewers for their comments that help improve the manuscript.

Approximate solutions of acoustic 3D integral equation and their application to seismic modeling and full-waveform inversion

NASA Astrophysics Data System (ADS)

Malovichko, M.; Khokhlov, N.; Yavich, N.; Zhdanov, M.

2017-10-01

Over the recent decades, a number of fast approximate solutions of Lippmann-Schwinger equation, which are more accurate than classic Born and Rytov approximations, were proposed in the field of electromagnetic modeling. Those developments could be naturally extended to acoustic and elastic fields; however, until recently, they were almost unknown in seismology. This paper presents several solutions of this kind applied to acoustic modeling for both lossy and lossless media. We evaluated the numerical merits of those methods and provide an estimation of their numerical complexity. In our numerical realization we use the matrix-free implementation of the corresponding integral operator. We study the accuracy of those approximate solutions and demonstrate, that the quasi-analytical approximation is more accurate, than the Born approximation. Further, we apply the quasi-analytical approximation to the solution of the inverse problem. It is demonstrated that, this approach improves the estimation of the data gradient, comparing to the Born approximation. The developed inversion algorithm is based on the conjugate-gradient type optimization. Numerical model study demonstrates that the quasi-analytical solution significantly reduces computation time of the seismic full-waveform inversion. We also show how the quasi-analytical approximation can be extended to the case of elastic wavefield.

Dealing with Multiple Solutions in Structural Vector Autoregressive Models.

PubMed

Beltz, Adriene M; Molenaar, Peter C M

2016-01-01

Structural vector autoregressive models (VARs) hold great potential for psychological science, particularly for time series data analysis. They capture the magnitude, direction of influence, and temporal (lagged and contemporaneous) nature of relations among variables. Unified structural equation modeling (uSEM) is an optimal structural VAR instantiation, according to large-scale simulation studies, and it is implemented within an SEM framework. However, little is known about the uniqueness of uSEM results. Thus, the goal of this study was to investigate whether multiple solutions result from uSEM analysis and, if so, to demonstrate ways to select an optimal solution. This was accomplished with two simulated data sets, an empirical data set concerning children's dyadic play, and modifications to the group iterative multiple model estimation (GIMME) program, which implements uSEMs with group- and individual-level relations in a data-driven manner. Results revealed multiple solutions when there were large contemporaneous relations among variables. Results also verified several ways to select the correct solution when the complete solution set was generated, such as the use of cross-validation, maximum standardized residuals, and information criteria. This work has immediate and direct implications for the analysis of time series data and for the inferences drawn from those data concerning human behavior.

One-Dimensional Transport with Inflow and Storage (OTIS): A Solute Transport Model for Streams and Rivers

USGS Publications Warehouse

Runkel, Robert L.

1998-01-01

OTIS is a mathematical simulation model used to characterize the fate and transport of water-borne solutes in streams and rivers. The governing equation underlying the model is the advection-dispersion equation with additional terms to account for transient storage, lateral inflow, first-order decay, and sorption. This equation and the associated equations describing transient storage and sorption are solved using a Crank-Nicolson finite-difference solution. OTIS may be used in conjunction with data from field-scale tracer experiments to quantify the hydrologic parameters affecting solute transport. This application typically involves a trial-and-error approach wherein parameter estimates are adjusted to obtain an acceptable match between simulated and observed tracer concentrations. Additional applications include analyses of nonconservative solutes that are subject to sorption processes or first-order decay. OTIS-P, a modified version of OTIS, couples the solution of the governing equation with a nonlinear regression package. OTIS-P determines an optimal set of parameter estimates that minimize the squared differences between the simulated and observed concentrations, thereby automating the parameter estimation process. This report details the development and application of OTIS and OTIS-P. Sections of the report describe model theory, input/output specifications, sample applications, and installation instructions.

Predicting the Activity Coefficients of Free-Solvent for Concentrated Globular Protein Solutions Using Independently Determined Physical Parameters

PubMed Central

McBride, Devin W.; Rodgers, Victor G. J.

2013-01-01

The activity coefficient is largely considered an empirical parameter that was traditionally introduced to correct the non-ideality observed in thermodynamic systems such as osmotic pressure. Here, the activity coefficient of free-solvent is related to physically realistic parameters and a mathematical expression is developed to directly predict the activity coefficients of free-solvent, for aqueous protein solutions up to near-saturation concentrations. The model is based on the free-solvent model, which has previously been shown to provide excellent prediction of the osmotic pressure of concentrated and crowded globular proteins in aqueous solutions up to near-saturation concentrations. Thus, this model uses only the independently determined, physically realizable quantities: mole fraction, solvent accessible surface area, and ion binding, in its prediction. Predictions are presented for the activity coefficients of free-solvent for near-saturated protein solutions containing either bovine serum albumin or hemoglobin. As a verification step, the predictability of the model for the activity coefficient of sucrose solutions was evaluated. The predicted activity coefficients of free-solvent are compared to the calculated activity coefficients of free-solvent based on osmotic pressure data. It is observed that the predicted activity coefficients are increasingly dependent on the solute-solvent parameters as the protein concentration increases to near-saturation concentrations. PMID:24324733

Research of Radionuclides Migrating in Porous Media Allowing for the "Solution-Rock" Interaction

NASA Astrophysics Data System (ADS)

Drozhko, E.; Aleksakhin, A. I.; Samsanova, L.; Kotchergina, N.; Zinin, A.

2001-12-01

Industrial solutions from the surface storage of liquid radioactive waste in Lake Karachay, near the Mayak Production Association in Russia, enter groundwaters through the reservoir loamy bed and have formed a contaminated groundwater plume. In order to predict radionuclide migration with the groundwater flow in porous unconsolidated rocks and to assess the protective mechanism of the natural environment, it is necessary to allow for the "solution-rock" physical and chemical interaction described by the distribution factor (Kd). In order to study radionuclide distribution in porous media, a numerical model was developed which models stontium-90 migration in a uniform unit of loams typical for the Karachay Lake bed. For the migration to be calculated, the results of the in situ and laboratory reasearch on strontium-90 sorption and desorption were used in the code, as well as strontium-90 dependance on sodium nitrate concentration in the solution. The code uses various models of the "solution-rock" interaction, taking into account both sorption/desorption and diffusion processes. Numerical research of strontium-90 migration resulted in data on strontium-90 distribution in solid and liquid phases of the porous loam unit over different time periods. Various models of the "solution-rock" interaction affecting strontium-90 migration are demonstrated.

The Green's functions for peridynamic non-local diffusion.

PubMed

Wang, L J; Xu, J F; Wang, J X

2016-09-01

In this work, we develop the Green's function method for the solution of the peridynamic non-local diffusion model in which the spatial gradient of the generalized potential in the classical theory is replaced by an integral of a generalized response function in a horizon. We first show that the general solutions of the peridynamic non-local diffusion model can be expressed as functionals of the corresponding Green's functions for point sources, along with volume constraints for non-local diffusion. Then, we obtain the Green's functions by the Fourier transform method for unsteady and steady diffusions in infinite domains. We also demonstrate that the peridynamic non-local solutions converge to the classical differential solutions when the non-local length approaches zero. Finally, the peridynamic analytical solutions are applied to an infinite plate heated by a Gauss source, and the predicted variations of temperature are compared with the classical local solutions. The peridynamic non-local diffusion model predicts a lower rate of variation of the field quantities than that of the classical theory, which is consistent with experimental observations. The developed method is applicable to general diffusion-type problems.

A new modal-based approach for modelling the bump foil structure in the simultaneous solution of foil-air bearing rotor dynamic problems

NASA Astrophysics Data System (ADS)

Bin Hassan, M. F.; Bonello, P.

2017-05-01

Recently-proposed techniques for the simultaneous solution of foil-air bearing (FAB) rotor dynamic problems have been limited to a simple bump foil model in which the individual bumps were modelled as independent spring-damper (ISD) subsystems. The present paper addresses this limitation by introducing a modal model of the bump foil structure into the simultaneous solution scheme. The dynamics of the corrugated bump foil structure are first studied using the finite element (FE) technique. This study is experimentally validated using a purpose-made corrugated foil structure. Based on the findings of this study, it is proposed that the dynamics of the full foil structure, including bump interaction and foil inertia, can be represented by a modal model comprising a limited number of modes. This full foil structure modal model (FFSMM) is then adapted into the rotordynamic FAB problem solution scheme, instead of the ISD model. Preliminary results using the FFSMM under static and unbalance excitation conditions are proven to be reliable by comparison against the corresponding ISD foil model results and by cross-correlating different methods for computing the deflection of the full foil structure. The rotor-bearing model is also validated against experimental and theoretical results in the literature.

Fluid and Electrolyte Balance model (FEB)

NASA Technical Reports Server (NTRS)

Fitzjerrell, D. G.

1973-01-01

The effects of various oral input water loads on solute and water distribution throughout the body are presented in the form of a model. The model was a three compartment model; the three compartments being plasma, interstitial fluid and cellular fluid. Sodium, potassium, chloride and urea were the only major solutes considered explicitly. The control of body water and electrolyte distribution was affected via drinking and hormone levels.

Delineating pMDI model reactions with loblolly pine via solution-state NMR spectroscopy. Part 1, Catalyzed reactions with wood models and wood polymers

Treesearch

Daniel J. Yelle; John Ralph; Charles R. Frihart

2011-01-01

To better understand adhesive interactions with wood, reactions between model compounds of wood and a model compound of polymeric methylene diphenyl diisocyanate (pMDI) were characterized by solution-state NMR spectroscopy. For comparison, finely ground loblolly pine sapwood, milled-wood lignin and holocellulose from the same wood were isolated and derivatized with...

Bianchi class A models in Sàez-Ballester's theory

NASA Astrophysics Data System (ADS)

Socorro, J.; Espinoza-García, Abraham

2012-08-01

We apply the Sàez-Ballester (SB) theory to Bianchi class A models, with a barotropic perfect fluid in a stiff matter epoch. We obtain exact classical solutions à la Hamilton for Bianchi type I, II and VIh=-1 models. We also find exact quantum solutions to all Bianchi Class A models employing a particular ansatz for the wave function of the universe.

Structure and aggregation in model tetramethylurea solutions

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

Gupta, Rini; Patey, G. N., E-mail: patey@chem.ubc.ca

The structure of model aqueous tetramethylurea (TMU) solutions is investigated employing large-scale (32 000, 64 000 particles) molecular dynamics simulations. Results are reported for TMU mole fractions, X{sub t}, ranging from infinite dilution up to 0.07, and for two temperatures, 300 and 330 K. Two existing force fields for TMU-water solutions are considered. These are the GROMOS 53A6 united-atom TMU model combined with SPC/E water [TMU(GROMOS-UA)/W(SPC/E)], and the more frequently employed AMBER03 all-atom force field for TMU combined with the TIP3P water model [TMU(AMBER-AA)/W(TIP3P)]. It is shown that TMU has a tendency towards aggregation for both models considered, but the tendency ismore » significantly stronger for the [TMU(AMBER-AA)/W(TIP3P)] force field. For this model signs of aggregation are detected at X{sub t} = 0.005, aggregation is a well established feature of the solution at X{sub t} = 0.02, and the aggregates increase further in size with increasing concentration. This is in agreement with at least some experimental studies, which report signals of aggregation in the low concentration regime. The TMU aggregates exhibit little structure and are simply loosely ordered, TMU-rich regions of solution. The [TMU(GROMOS-UA)/W(SPC/E)] model shows strong signs of aggregation only at higher concentrations (X{sub t} ≳ 0.04), and the aggregates appear more loosely ordered, and less well-defined than those occurring in the [TMU(AMBER-AA)/W(TIP3P)] system. For both models, TMU aggregation increases when the temperature is increased from 300 to 330 K, consistent with an underlying entropy driven, hydrophobic interaction mechanism. At X{sub t} = 0.07, the extra-molecular correlation length expected for microheterogeneous solutions has become comparable with the size of the simulation cell for both models considered, indicating that even the systems simulated here are sufficiently large only at low concentrations.« less

Bi-objective integer programming for RNA secondary structure prediction with pseudoknots.

PubMed

Legendre, Audrey; Angel, Eric; Tahi, Fariza

2018-01-15

RNA structure prediction is an important field in bioinformatics, and numerous methods and tools have been proposed. Pseudoknots are specific motifs of RNA secondary structures that are difficult to predict. Almost all existing methods are based on a single model and return one solution, often missing the real structure. An alternative approach would be to combine different models and return a (small) set of solutions, maximizing its quality and diversity in order to increase the probability that it contains the real structure. We propose here an original method for predicting RNA secondary structures with pseudoknots, based on integer programming. We developed a generic bi-objective integer programming algorithm allowing to return optimal and sub-optimal solutions optimizing simultaneously two models. This algorithm was then applied to the combination of two known models of RNA secondary structure prediction, namely MEA and MFE. The resulting tool, called BiokoP, is compared with the other methods in the literature. The results show that the best solution (structure with the highest F 1 -score) is, in most cases, given by BiokoP. Moreover, the results of BiokoP are homogeneous, regardless of the pseudoknot type or the presence or not of pseudoknots. Indeed, the F 1 -scores are always higher than 70% for any number of solutions returned. The results obtained by BiokoP show that combining the MEA and the MFE models, as well as returning several optimal and several sub-optimal solutions, allow to improve the prediction of secondary structures. One perspective of our work is to combine better mono-criterion models, in particular to combine a model based on the comparative approach with the MEA and the MFE models. This leads to develop in the future a new multi-objective algorithm to combine more than two models. BiokoP is available on the EvryRNA platform: https://EvryRNA.ibisc.univ-evry.fr .

The uniqueness of the solution of cone-like inversion models for halo CMEs

NASA Astrophysics Data System (ADS)

Zhao, X. P.

2006-12-01

Most of elliptic halo CMEs are believed to be formed by the Thompson scattering of the photospheric light by the 3-D cone-like shell of the CME plasma. To obtain the real propagation direction and angular width of the halo CMEs, such cone-like inversion models as the circular cone, the elliptic cone and the ice-cream cone models have been suggested recently. Because the number of given parameters that are used to characterize 2-D elliptic halo CMEs observed by one spacecraft are less than the number of unknown parameters that are used to characterize the 3-D elliptic cone model, the solution of the elliptic cone model is not unique. Since it is difficult to determine whether or not an observed halo CME is formed by an circular cone or elliptic cone shell, the solution of circular cone model may often be not unique too. To fix the problem of the uniqueness of the solution of various 3-D cone-like inversion models, this work tries to develop the algorithm for using the data from multi-spacecraft, such as the STEREO A and B, and the Solar Sentinels.

Modelling solute dispersion in periodic heterogeneous porous media: Model benchmarking against intermediate scale experiments

NASA Astrophysics Data System (ADS)

Majdalani, Samer; Guinot, Vincent; Delenne, Carole; Gebran, Hicham

2018-06-01

This paper is devoted to theoretical and experimental investigations of solute dispersion in heterogeneous porous media. Dispersion in heterogenous porous media has been reported to be scale-dependent, a likely indication that the proposed dispersion models are incompletely formulated. A high quality experimental data set of breakthrough curves in periodic model heterogeneous porous media is presented. In contrast with most previously published experiments, the present experiments involve numerous replicates. This allows the statistical variability of experimental data to be accounted for. Several models are benchmarked against the data set: the Fickian-based advection-dispersion, mobile-immobile, multirate, multiple region advection dispersion models, and a newly proposed transport model based on pure advection. A salient property of the latter model is that its solutions exhibit a ballistic behaviour for small times, while tending to the Fickian behaviour for large time scales. Model performance is assessed using a novel objective function accounting for the statistical variability of the experimental data set, while putting equal emphasis on both small and large time scale behaviours. Besides being as accurate as the other models, the new purely advective model has the advantages that (i) it does not exhibit the undesirable effects associated with the usual Fickian operator (namely the infinite solute front propagation speed), and (ii) it allows dispersive transport to be simulated on every heterogeneity scale using scale-independent parameters.

Effects of dialysate flow configurations in continuous renal replacement therapy on solute removal: computational modeling.

PubMed

Kim, Jeong Chul; Cruz, Dinna; Garzotto, Francesco; Kaushik, Manish; Teixeria, Catarina; Baldwin, Marie; Baldwin, Ian; Nalesso, Federico; Kim, Ji Hyun; Kang, Eungtaek; Kim, Hee Chan; Ronco, Claudio

2013-01-01

Continuous renal replacement therapy (CRRT) is commonly used for critically ill patients with acute kidney injury. During treatment, a slow dialysate flow rate can be applied to enhance diffusive solute removal. However, due to the lack of the rationale of the dialysate flow configuration (countercurrent or concurrent to blood flow), in clinical practice, the connection settings of a hemodiafilter are done depending on nurse preference or at random. In this study, we investigated the effects of flow configurations in a hemodiafilter during continuous venovenous hemodialysis on solute removal and fluid transport using computational fluid dynamic modeling. We solved the momentum equation coupling solute transport to predict quantitative diffusion and convection phenomena in a simplified hemodiafilter model. Computational modeling results showed superior solute removal (clearance of urea: 67.8 vs. 45.1 ml/min) and convection (filtration volume: 29.0 vs. 25.7 ml/min) performances for the countercurrent flow configuration. Countercurrent flow configuration enhances convection and diffusion compared to concurrent flow configuration by increasing filtration volume and equilibrium concentration in the proximal part of a hemodiafilter and backfiltration of pure dialysate in the distal part. In clinical practice, the countercurrent dialysate flow configuration of a hemodiafilter could increase solute removal in CRRT. Nevertheless, while this configuration may become mandatory for high-efficiency treatments, the impact of differences in solute removal observed in slow continuous therapies may be less important. Under these circumstances, if continuous therapies are prescribed, some of the advantages of the concurrent configuration in terms of simpler circuit layout and simpler machine design may overcome the advantages in terms of solute clearance. Different dialysate flow configurations influence solute clearance and change major solute removal mechanisms in the proximal and distal parts of a hemodiafilter. Advantages of each configuration should be balanced against the overall performance of the treatment and its simplicity in terms of treatment delivery and circuit handling procedures. Copyright © 2013 S. Karger AG, Basel.

[Analysis of parameters of serum concentration and pharmacokinetic of liposome and aqueous solution of toatal ginsenoside of ginseng stems and leaves in rats].

PubMed

Zha, Lin; Zhao, Yan; Zhu, Hong-Yan; Cai, En-Bo; Liu, Shuang-Li; Yang, He; Zhao, Ying; Gao, Yu-Gang; Zhang, Lian-Xue

2017-05-01

The experiment was aimed to investigate the difference of plasma concentration and pharmacokinetic parameters between liposome and aqueous solution of toatal ginsenoside of ginseng stems and leaves in rats, such as ginsenosides Rg₁, Re, Rf, Rb₁, Rg₂, Rc, Rb₂, Rb₃, Rd. After intravenous injection of liposome and aqueous solution in rats, the blood was taken from the femoral vein to detect the plasma concentration of the above 9 ginsenoside monomers in different time points by using HPLC. The concentration-time curve was obtained and 3p97 pharmacokinetic software was used to get the pharmacokinetic parameters. After the intravenous injection of ginsenosides to rats, nine ginsenosides were detected in plasma. In general, among these ginsenosides, the peak time of the aqueous solution was between 0.05 to 0.083 3 h, and the serum concentration peak of liposome usually appeared after 0.5 h. After software fitting, the aqueous solution of ginsenoside monomers Rg₁, Re, Rf, Rg₂, Rc, Rd, Rb₃ was two-compartment model, and the liposomes were one-compartment model; aqueous solution and liposome of ginsenoside monomers Rb₁ were three-compartment model; aqueous solution of ginsenoside monomers Rb₂ was three-compartment model, and its liposome was one-compartment model. Area under the drug time curve (AUC) of these 9 kinds of saponin liposomes was larger than that of aqueous solution, and the retention time of the liposomes was longer than that of the aqueous solution; the removal rate was slower than that of the aqueous solution, and the half-life was longer than that of the water solution. The results from the experiment showed that by intravenous administration, the pharmacokinetic parameters of two formulations were significantly different from each other; the liposomes could not only remain the drug for a longer time in vivo, but also reduce the elimination rate and increase the treatment efficacy. As compared with the traditional dosage forms, the total ginsenoside of ginseng stems and leaves can improve the sustained release of the drug, which is of great significance for the research and development of new dosage forms of ginsenosides in the future. Copyright© by the Chinese Pharmaceutical Association.

Study on the influence of stochastic properties of correction terms on the reliability of instantaneous network RTK

NASA Astrophysics Data System (ADS)

Próchniewicz, Dominik

2014-03-01

The reliability of precision GNSS positioning primarily depends on correct carrier-phase ambiguity resolution. An optimal estimation and correct validation of ambiguities necessitates a proper definition of mathematical positioning model. Of particular importance in the model definition is the taking into account of the atmospheric errors (ionospheric and tropospheric refraction) as well as orbital errors. The use of the network of reference stations in kinematic positioning, known as Network-based Real-Time Kinematic (Network RTK) solution, facilitates the modeling of such errors and their incorporation, in the form of correction terms, into the functional description of positioning model. Lowered accuracy of corrections, especially during atmospheric disturbances, results in the occurrence of unaccounted biases, the so-called residual errors. The taking into account of such errors in Network RTK positioning model is possible by incorporating the accuracy characteristics of the correction terms into the stochastic model of observations. In this paper we investigate the impact of the expansion of the stochastic model to include correction term variances on the reliability of the model solution. In particular the results of instantaneous solution that only utilizes a single epoch of GPS observations, is analyzed. Such a solution mode due to the low number of degrees of freedom is very sensitive to an inappropriate mathematical model definition. Thus the high level of the solution reliability is very difficult to achieve. Numerical tests performed for a test network located in mountain area during ionospheric disturbances allows to verify the described method for the poor measurement conditions. The results of the ambiguity resolution as well as the rover positioning accuracy shows that the proposed method of stochastic modeling can increase the reliability of instantaneous Network RTK performance.

Comments on the Synergism Between the Analytic Planetary Boundary-Layer Model and Remote Sensing Data

NASA Astrophysics Data System (ADS)

Brown, R. A.

2005-08-01

This paper is adapted from a presentation at the session of the European Geophysical Society meeting in 2002 honouring Joost Businger. It documents the interaction of the non-linear planetary boundary-layer (PBL) model (UW-PBL) and satellite remote sensing of marine surface winds from verification and calibration studies for the sensor model function to the current state of verification of the model by satellite data. It is also a personal history where Joost Businger had seminal input to this research at several critical junctures. The first scatterometer in space was on SeaSat in 1978, while currently in orbit there are the QuikSCAT and ERS-2 scatterometers and the WindSat radiometer. The volume and detail of data from the scatterometers during the past decade are unprecedented, though the value of these data depends on a careful interpretation of the PBL dynamics. The model functions (algorithms) that relate surface wind to sensor signal have evolved from straight empirical correlation with simple surface-layer 10-m winds to satellite sensor model functions for surface pressure fields. A surface stress model function is also available. The validation data for the satellite model functions depended crucially on the PBL solution. The non-linear solution for the flow of fluid in the boundary layer of a rotating coordinate system was completed in 1969. The implications for traditional ways of measuring and modelling the PBL were huge and continue to this day. Unfortunately, this solution replaced an elegant one by Ekman with a stability/finite perturbation equilibrium solution. Consequently, there has been great reluctance to accept this solution. The verification of model predictions has been obtained from the satellite data.

Statically determined slip-line field solution for the axial forming force estimation in the radial-axial ring rolling process

NASA Astrophysics Data System (ADS)

Quagliato, Luca; Berti, Guido A.

2017-10-01

In this paper, a statically determined slip-line solution algorithm is proposed for the calculation of the axial forming force in the radial-axial ring rolling process of flat rings. The developed solution is implemented in an Excel spreadsheet for the construction of the slip-line field and the calculation of the pressure factor to be used in the force model. The comparison between analytical solution and authors' FE simulation allows stating that the developed model supersedes the previous literature ones and proves the reliability of the proposed approach.

CFD Script for Rapid TPS Damage Assessment

NASA Technical Reports Server (NTRS)

McCloud, Peter

2013-01-01

This grid generation script creates unstructured CFD grids for rapid thermal protection system (TPS) damage aeroheating assessments. The existing manual solution is cumbersome, open to errors, and slow. The invention takes a large-scale geometry grid and its large-scale CFD solution, and creates a unstructured patch grid that models the TPS damage. The flow field boundary condition for the patch grid is then interpolated from the large-scale CFD solution. It speeds up the generation of CFD grids and solutions in the modeling of TPS damages and their aeroheating assessment. This process was successfully utilized during STS-134.

An exact solution of a simplified two-phase plume model. [for solid propellant rocket

NASA Technical Reports Server (NTRS)

Wang, S.-Y.; Roberts, B. B.

1974-01-01

An exact solution of a simplified two-phase, gas-particle, rocket exhaust plume model is presented. It may be used to make the upper-bound estimation of the heat flux and pressure loads due to particle impingement on the objects existing in the rocket exhaust plume. By including the correction factors to be determined experimentally, the present technique will provide realistic data concerning the heat and aerodynamic loads on these objects for design purposes. Excellent agreement in trend between the best available computer solution and the present exact solution is shown.

Monte Carlo exploration of Mikheyev-Smirnov-Wolfenstein solutions to the solar neutrino problem

NASA Technical Reports Server (NTRS)

Shi, X.; Schramm, D. N.; Bahcall, J. N.

1992-01-01

The paper explores the impact of astrophysical uncertainties on the Mikheyev-Smirnov-Wolfenstein (MSW) solution by calculating the allowed MSW solutions for 1000 different solar models with a Monte Carlo selection of solar model input parameters, assuming a full three-family MSW mixing. Applications are made to the chlorine, gallium, Kamiokande, and Borexino experiments. The initial GALLEX result limits the mixing parameters to the upper diagonal and the vertical regions of the MSW triangle. The expected event rates in the Borexino experiment are also calculated, assuming the MSW solutions implied by GALLEX.

Modelling the spread of Ebola virus with Atangana-Baleanu fractional operators

NASA Astrophysics Data System (ADS)

Koca, Ilknur

2018-03-01

The model of Ebola spread within a targeted population is extended to the concept of fractional differentiation and integration with non-local and non-singular fading memory introduced by Atangana and Baleanu. It is expected that the proposed model will show better approximation than the models established before. The existence and uniqueness of solutions for the spread of Ebola disease model is given via the Picard-Lindelof method. Finally, numerical solutions for the model are given by using different parameter values.

Application of the θ-method to a telegraphic model of fluid flow in a dual-porosity medium

NASA Astrophysics Data System (ADS)

González-Calderón, Alfredo; Vivas-Cruz, Luis X.; Herrera-Hernández, Erik César

2018-01-01

This work focuses mainly on the study of numerical solutions, which are obtained using the θ-method, of a generalized Warren and Root model that includes a second-order wave-like equation in its formulation. The solutions approximately describe the single-phase hydraulic head in fractures by considering the finite velocity of propagation by means of a Cattaneo-like equation. The corresponding discretized model is obtained by utilizing a non-uniform grid and a non-uniform time step. A simple relationship is proposed to give the time-step distribution. Convergence is analyzed by comparing results from explicit, fully implicit, and Crank-Nicolson schemes with exact solutions: a telegraphic model of fluid flow in a single-porosity reservoir with relaxation dynamics, the Warren and Root model, and our studied model, which is solved with the inverse Laplace transform. We find that the flux and the hydraulic head have spurious oscillations that most often appear in small-time solutions but are attenuated as the solution time progresses. Furthermore, we show that the finite difference method is unable to reproduce the exact flux at time zero. Obtaining results for oilfield production times, which are in the order of months in real units, is only feasible using parallel implicit schemes. In addition, we propose simple parallel algorithms for the memory flux and for the explicit scheme.

Analytical solutions of one-dimensional multispecies reactive transport in a permeable reactive barrier-aquifer system

NASA Astrophysics Data System (ADS)

Mieles, John; Zhan, Hongbin

2012-06-01

The permeable reactive barrier (PRB) remediation technology has proven to be more cost-effective than conventional pump-and-treat systems, and has demonstrated the ability to rapidly reduce the concentrations of specific chemicals of concern (COCs) by up to several orders of magnitude in some scenarios. This study derives new steady-state analytical solutions to multispecies reactive transport in a PRB-aquifer (dual domain) system. The advantage of the dual domain model is that it can account for the potential existence of natural degradation in the aquifer, when designing the required PRB thickness. The study focuses primarily on the steady-state analytical solutions of the tetrachloroethene (PCE) serial degradation pathway and secondly on the analytical solutions of the parallel degradation pathway. The solutions in this study can also be applied to other types of dual domain systems with distinct flow and transport properties. The steady-state analytical solutions are shown to be accurate and the numerical program RT3D is selected for comparison. The results of this study are novel in that the solutions provide improved modeling flexibility including: 1) every species can have unique first-order reaction rates and unique retardation factors, and 2) daughter species can be modeled with their individual input concentrations or solely as byproducts of the parent species. The steady-state analytical solutions exhibit a limitation that occurs when interspecies reaction rate factors equal each other, which result in undefined solutions. Excel spreadsheet programs were created to facilitate prompt application of the steady-state analytical solutions, for both the serial and parallel degradation pathways.

Modelling the effect of intervillous flow on solute transfer based on 3D imaging of the human placental microstructure.

PubMed

Perazzolo, S; Lewis, R M; Sengers, B G

2017-12-01

A healthy pregnancy depends on placental transfer from mother to fetus. Placental transfer takes place at the micro scale across the placental villi. Solutes from the maternal blood are taken up by placental villi and enter the fetal capillaries. This study investigated the effect of maternal blood flow on solute uptake at the micro scale. A 3D image based modelling approach of the placental microstructures was undertaken. Solute transport in the intervillous space was modelled explicitly and solute uptake with respect to different maternal blood flow rates was estimated. Fetal capillary flow was not modelled and treated as a perfect sink. For a freely diffusing small solute, the flow of maternal blood through the intervillous space was found to be limiting the transfer. Ignoring the effects of maternal flow resulted in a 2.4 ± 0.4 fold over-prediction of transfer by simple diffusion, in absence of binding. Villous morphology affected the efficiency of solute transfer due to concentration depleted zones. Interestingly, less dense microvilli had lower surface area available for uptake which was compensated by increased flow due to their higher permeability. At super-physiological pressures, maternal flow was not limiting, however the efficiency of uptake decreased. This study suggests that the interplay between maternal flow and villous structure affects the efficiency of placental transfer but predicted that flow rate will be the major determinant of transfer. Copyright © 2017 Elsevier Ltd. All rights reserved.

The mathematical properties of the quasi-chemical model for microorganism growth-death kinetics in foods.

PubMed

Ross, E W; Taub, I A; Doona, C J; Feeherry, F E; Kustin, K

2005-03-15

Knowledge of the mathematical properties of the quasi-chemical model [Taub, Feeherry, Ross, Kustin, Doona, 2003. A quasi-chemical kinetics model for the growth and death of Staphylococcus aureus in intermediate moisture bread. J. Food Sci. 68 (8), 2530-2537], which is used to characterize and predict microbial growth-death kinetics in foods, is important for its applications in predictive microbiology. The model consists of a system of four ordinary differential equations (ODEs), which govern the temporal dependence of the bacterial life cycle (the lag, exponential growth, stationary, and death phases, respectively). The ODE system derives from a hypothetical four-step reaction scheme that postulates the activity of a critical intermediate as an antagonist to growth (perhaps through a quorum sensing biomechanism). The general behavior of the solutions to the ODEs is illustrated by several examples. In instances when explicit mathematical solutions to these ODEs are not obtainable, mathematical approximations are used to find solutions that are helpful in evaluating growth in the early stages and again near the end of the process. Useful solutions for the ODE system are also obtained in the case where the rate of antagonist formation is small. The examples and the approximate solutions provide guidance in the parameter estimation that must be done when fitting the model to data. The general behavior of the solutions is illustrated by examples, and the MATLAB programs with worked examples are included in the appendices for use by predictive microbiologists for data collected independently.

Possible evolution of a bouncing universe in cosmological models with non-minimally coupled scalar fields

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

Pozdeeva, Ekaterina O.; Vernov, Sergey Yu.; Skugoreva, Maria A.

2016-12-01

We explore dynamics of cosmological models with bounce solutions evolving on a spatially flat Friedmann-Lemaître-Robertson-Walker background. We consider cosmological models that contain the Hilbert-Einstein curvature term, the induced gravity term with a negative coupled constant, and even polynomial potentials of the scalar field. Bounce solutions with non-monotonic Hubble parameters have been obtained and analyzed. The case when the scalar field has the conformal coupling and the Higgs-like potential with an opposite sign is studied in detail. In this model the evolution of the Hubble parameter of the bounce solution essentially depends on the sign of the cosmological constant.

Eigen model with general fitness functions and degradation rates

NASA Astrophysics Data System (ADS)

Hu, Chin-Kun; Saakian, David B.

2006-03-01

We present an exact solution of Eigen's quasispecies model with a general degradation rate and fitness functions, including a square root decrease of fitness with increasing Hamming distance from the wild type. The found behavior of the model with a degradation rate is analogous to a viral quasi-species under attack by the immune system of the host. Our exact solutions also revise the known results of neutral networks in quasispecies theory. To explain the existence of mutants with large Hamming distances from the wild type, we propose three different modifications of the Eigen model: mutation landscape, multiple adjacent mutations, and frequency-dependent fitness in which the steady state solution shows a multi-center behavior.

Advection modes by optimal mass transfer

NASA Astrophysics Data System (ADS)

Iollo, Angelo; Lombardi, Damiano

2014-02-01

Classical model reduction techniques approximate the solution of a physical model by a limited number of global modes. These modes are usually determined by variants of principal component analysis. Global modes can lead to reduced models that perform well in terms of stability and accuracy. However, when the physics of the model is mainly characterized by advection, the nonlocal representation of the solution by global modes essentially reduces to a Fourier expansion. In this paper we describe a method to determine a low-order representation of advection. This method is based on the solution of Monge-Kantorovich mass transfer problems. Examples of application to point vortex scattering, Korteweg-de Vries equation, and hurricane Dean advection are discussed.

A mathematical framework for yield (vs. rate) optimization in constraint-based modeling and applications in metabolic engineering.

PubMed

Klamt, Steffen; Müller, Stefan; Regensburger, Georg; Zanghellini, Jürgen

2018-05-01

The optimization of metabolic rates (as linear objective functions) represents the methodical core of flux-balance analysis techniques which have become a standard tool for the study of genome-scale metabolic models. Besides (growth and synthesis) rates, metabolic yields are key parameters for the characterization of biochemical transformation processes, especially in the context of biotechnological applications. However, yields are ratios of rates, and hence the optimization of yields (as nonlinear objective functions) under arbitrary linear constraints is not possible with current flux-balance analysis techniques. Despite the fundamental importance of yields in constraint-based modeling, a comprehensive mathematical framework for yield optimization is still missing. We present a mathematical theory that allows one to systematically compute and analyze yield-optimal solutions of metabolic models under arbitrary linear constraints. In particular, we formulate yield optimization as a linear-fractional program. For practical computations, we transform the linear-fractional yield optimization problem to a (higher-dimensional) linear problem. Its solutions determine the solutions of the original problem and can be used to predict yield-optimal flux distributions in genome-scale metabolic models. For the theoretical analysis, we consider the linear-fractional problem directly. Most importantly, we show that the yield-optimal solution set (like the rate-optimal solution set) is determined by (yield-optimal) elementary flux vectors of the underlying metabolic model. However, yield- and rate-optimal solutions may differ from each other, and hence optimal (biomass or product) yields are not necessarily obtained at solutions with optimal (growth or synthesis) rates. Moreover, we discuss phase planes/production envelopes and yield spaces, in particular, we prove that yield spaces are convex and provide algorithms for their computation. We illustrate our findings by a small example and demonstrate their relevance for metabolic engineering with realistic models of E. coli. We develop a comprehensive mathematical framework for yield optimization in metabolic models. Our theory is particularly useful for the study and rational modification of cell factories designed under given yield and/or rate requirements. Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.

Dynamic of solitary wave solutions in some nonlinear pseudoparabolic models and Dodd-Bullough-Mikhailov equation

NASA Astrophysics Data System (ADS)

Ilhan, O. A.; Bulut, H.; Sulaiman, T. A.; Baskonus, H. M.

2018-02-01

In this study, the modified exp ( - Φ (η )) -expansion function method is used in constructing some solitary wave solutions to the Oskolkov-Benjamin-Bona-Mahony-Burgers, one-dimensional Oskolkov equations and the Dodd-Bullough-Mikhailov equation. We successfully construct some singular solitons and singular periodic waves solutions with the hyperbolic, trigonometric and exponential function structures to these three nonlinear models. Under the choice of some suitable values of the parameters involved, we plot the 2D and 3D graphics to some of the obtained solutions in this study. All the obtained solutions in this study verify their corresponding equation. We perform all the computations in this study with the help of the Wolfram Mathematica software. The obtained solutions in this study may be helpful in explaining some practical physical problems.

Osmotic water transport in aquaporins: evidence for a stochastic mechanism

PubMed Central

Zeuthen, Thomas; Alsterfjord, Magnus; Beitz, Eric; MacAulay, Nanna

2013-01-01

We test a novel, stochastic model of osmotic water transport in aquaporins. A solute molecule present at the pore mouth can either be reflected or permeate the pore. We assume that only reflected solute molecules induce osmotic transport of water through the pore, while permeating solute molecules give rise to no water transport. Accordingly, the rate of water transport is proportional to the reflection coefficient σ, while the solute permeability, PS, is proportional to 1 –σ. The model was tested in aquaporins heterologously expressed in Xenopus oocytes. A variety of aquaporin channel sizes and geometries were obtained with the two aquaporins AQP1 and AQP9 and mutant versions of these. Osmotic water transport was generated by adding 20 mm of a range of different-sized osmolytes to the outer solution. The osmotic water permeability and the reflection coefficient were measured optically at high resolution and compared to the solute permeability obtained from short-term uptake of radio-labelled solute under isotonic conditions. For each type of aquaporin there was a linear relationship between solute permeability and reflection coefficient, in accordance with the model. We found no evidence for coupling between water and solute fluxes in the pore. In confirmation of molecular dynamic simulations, we conclude that the magnitude of the osmotic water permeability and the reflection coefficient are determined by processes at the arginine selectivity filter located at the outward-facing end of the pore. PMID:23959676

Multiple steady states in atmospheric chemistry

NASA Technical Reports Server (NTRS)

Stewart, Richard W.

1993-01-01

The equations describing the distributions and concentrations of trace species are nonlinear and may thus possess more than one solution. This paper develops methods for searching for multiple physical solutions to chemical continuity equations and applies these to subsets of equations describing tropospheric chemistry. The calculations are carried out with a box model and use two basic strategies. The first strategy is a 'search' method. This involves fixing model parameters at specified values, choosing a wide range of initial guesses at a solution, and using a Newton-Raphson technique to determine if different initial points converge to different solutions. The second strategy involves a set of techniques known as homotopy methods. These do not require an initial guess, are globally convergent, and are guaranteed, in principle, to find all solutions of the continuity equations. The first method is efficient but essentially 'hit or miss' in the sense that it cannot guarantee that all solutions which may exist will be found. The second method is computationally burdensome but can, in principle, determine all the solutions of a photochemical system. Multiple solutions have been found for models that contain a basic complement of photochemical reactions involving O(x), HO(x), NO(x), and CH4. In the present calculations, transitions occur between stable branches of a multiple solution set as a control parameter is varied. These transitions are manifestations of hysteresis phenomena in the photochemical system and may be triggered by increasing the NO flux or decreasing the CH4 flux from current mean tropospheric levels.

Models for the dynamics of dust-like matter in the self-gravity field: The method of hydrodynamic substitutions

NASA Astrophysics Data System (ADS)

Zhuravlev, V. M.

2017-09-01

Models for the dynamics of a dust-like medium in the self-gravity field are investigated. Solutions of the corresponding problems are constructed by the method of hydrodynamic substitutions generalizing the Cole-Hopf substitutions. The method is extended to multidimensional ideal and viscous fluid flows with cylindrical and spherical symmetries for which exact solutions are constructed. Solutions for the dynamics of self-gravitating dust with arbitrary initial distributions of both fluid density and velocity are constructed using special coordinate transformations. In particular, the problem of cosmological expansion is considered in terms of Newton's gravity theory. Models of a one-dimensional viscous dust fluid flow and some problems of gas hydrodynamics are considered. Examples of exact solutions and their brief analysis are provided.

Preprocessing Inconsistent Linear System for a Meaningful Least Squares Solution

NASA Technical Reports Server (NTRS)

Sen, Syamal K.; Shaykhian, Gholam Ali

2011-01-01

Mathematical models of many physical/statistical problems are systems of linear equations. Due to measurement and possible human errors/mistakes in modeling/data, as well as due to certain assumptions to reduce complexity, inconsistency (contradiction) is injected into the model, viz. the linear system. While any inconsistent system irrespective of the degree of inconsistency has always a least-squares solution, one needs to check whether an equation is too much inconsistent or, equivalently too much contradictory. Such an equation will affect/distort the least-squares solution to such an extent that renders it unacceptable/unfit to be used in a real-world application. We propose an algorithm which (i) prunes numerically redundant linear equations from the system as these do not add any new information to the model, (ii) detects contradictory linear equations along with their degree of contradiction (inconsistency index), (iii) removes those equations presumed to be too contradictory, and then (iv) obtain the minimum norm least-squares solution of the acceptably inconsistent reduced linear system. The algorithm presented in Matlab reduces the computational and storage complexities and also improves the accuracy of the solution. It also provides the necessary warning about the existence of too much contradiction in the model. In addition, we suggest a thorough relook into the mathematical modeling to determine the reason why unacceptable contradiction has occurred thus prompting us to make necessary corrections/modifications to the models - both mathematical and, if necessary, physical.

Preprocessing in Matlab Inconsistent Linear System for a Meaningful Least Squares Solution

NASA Technical Reports Server (NTRS)

Sen, Symal K.; Shaykhian, Gholam Ali

2011-01-01

Mathematical models of many physical/statistical problems are systems of linear equations Due to measurement and possible human errors/mistakes in modeling/data, as well as due to certain assumptions to reduce complexity, inconsistency (contradiction) is injected into the model, viz. the linear system. While any inconsistent system irrespective of the degree of inconsistency has always a least-squares solution, one needs to check whether an equation is too much inconsistent or, equivalently too much contradictory. Such an equation will affect/distort the least-squares solution to such an extent that renders it unacceptable/unfit to be used in a real-world application. We propose an algorithm which (i) prunes numerically redundant linear equations from the system as these do not add any new information to the model, (ii) detects contradictory linear equations along with their degree of contradiction (inconsistency index), (iii) removes those equations presumed to be too contradictory, and then (iv) obtain the . minimum norm least-squares solution of the acceptably inconsistent reduced linear system. The algorithm presented in Matlab reduces the computational and storage complexities and also improves the accuracy of the solution. It also provides the necessary warning about the existence of too much contradiction in the model. In addition, we suggest a thorough relook into the mathematical modeling to determine the reason why unacceptable contradiction has occurred thus prompting us to make necessary corrections/modifications to the models - both mathematical and, if necessary, physical.

Dimension reduction method for SPH equations

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

Tartakovsky, Alexandre M.; Scheibe, Timothy D.

2011-08-26

Smoothed Particle Hydrodynamics model of a complex multiscale processe often results in a system of ODEs with an enormous number of unknowns. Furthermore, a time integration of the SPH equations usually requires time steps that are smaller than the observation time by many orders of magnitude. A direct solution of these ODEs can be extremely expensive. Here we propose a novel dimension reduction method that gives an approximate solution of the SPH ODEs and provides an accurate prediction of the average behavior of the modeled system. The method consists of two main elements. First, effective equationss for evolution of averagemore » variables (e.g. average velocity, concentration and mass of a mineral precipitate) are obtained by averaging the SPH ODEs over the entire computational domain. These effective ODEs contain non-local terms in the form of volume integrals of functions of the SPH variables. Second, a computational closure is used to close the system of the effective equations. The computational closure is achieved via short bursts of the SPH model. The dimension reduction model is used to simulate flow and transport with mixing controlled reactions and mineral precipitation. An SPH model is used model transport at the porescale. Good agreement between direct solutions of the SPH equations and solutions obtained with the dimension reduction method for different boundary conditions confirms the accuracy and computational efficiency of the dimension reduction model. The method significantly accelerates SPH simulations, while providing accurate approximation of the solution and accurate prediction of the average behavior of the system.« less

ANALYZING NUMERICAL ERRORS IN DOMAIN HEAT TRANSPORT MODELS USING THE CVBEM.

USGS Publications Warehouse

Hromadka, T.V.; ,

1985-01-01

Besides providing an exact solution for steady-state heat conduction processes (Laplace Poisson equations), the CVBEM (complex variable boundary element method) can be used for the numerical error analysis of domain model solutions. For problems where soil water phase change latent heat effects dominate the thermal regime, heat transport can be approximately modeled as a time-stepped steady-state condition in the thawed and frozen regions, respectively. The CVBEM provides an exact solution of the two-dimensional steady-state heat transport problem, and also provides the error in matching the prescribed boundary conditions by the development of a modeling error distribution or an approximative boundary generation. This error evaluation can be used to develop highly accurate CVBEM models of the heat transport process, and the resulting model can be used as a test case for evaluating the precision of domain models based on finite elements or finite differences.

MT3DMS: Model use, calibration, and validation

USGS Publications Warehouse

Zheng, C.; Hill, Mary C.; Cao, G.; Ma, R.

2012-01-01

MT3DMS is a three-dimensional multi-species solute transport model for solving advection, dispersion, and chemical reactions of contaminants in saturated groundwater flow systems. MT3DMS interfaces directly with the U.S. Geological Survey finite-difference groundwater flow model MODFLOW for the flow solution and supports the hydrologic and discretization features of MODFLOW. MT3DMS contains multiple transport solution techniques in one code, which can often be important, including in model calibration. Since its first release in 1990 as MT3D for single-species mass transport modeling, MT3DMS has been widely used in research projects and practical field applications. This article provides a brief introduction to MT3DMS and presents recommendations about calibration and validation procedures for field applications of MT3DMS. The examples presented suggest the need to consider alternative processes as models are calibrated and suggest opportunities and difficulties associated with using groundwater age in transport model calibration.

Effects of oversized solutes on radiation-induced segregation in austenitic stainless steels

NASA Astrophysics Data System (ADS)

Hackett, M. J.; Busby, J. T.; Miller, M. K.; Was, G. S.

2009-06-01

Zirconium or hafnium additions to austenitic stainless steels caused a reduction in grain boundary Cr depletion after proton irradiations for up to 3 dpa at 400 °C and 1 dpa at 500 °C. The predictions of a radiation-induced segregation (RIS) model were also consistent with experiments in showing greater effectiveness of Zr relative to Hf due to a larger binding energy. However, the experiments showed that the effectiveness of the solute additions disappeared above 3 dpa at 400 °C and above 1 dpa at 500 °C. The loss of solute effectiveness with increasing dose is attributed to a reduction in the amount of oversized solute from the matrix due to growth of carbide precipitates. Atom probe tomography measurements indicated a reduction in amount of oversized solute in solution as a function of irradiation dose. The observations were supported by diffusion analysis suggesting that significant solute diffusion by the vacancy flux to precipitate surfaces occurs on the time scales of proton irradiations. With a decrease in available solute in solution, improved agreement between the predictions of the RIS model and measurements were consistent with the solute-vacancy trapping process, as the mechanism for enhanced recombination and suppression of RIS.

Application of geometric approximation to the CPMG experiment: Two- and three-site exchange.

PubMed

Chao, Fa-An; Byrd, R Andrew

2017-04-01

The Carr-Purcell-Meiboom-Gill (CPMG) experiment is one of the most classical and well-known relaxation dispersion experiments in NMR spectroscopy, and it has been successfully applied to characterize biologically relevant conformational dynamics in many cases. Although the data analysis of the CPMG experiment for the 2-site exchange model can be facilitated by analytical solutions, the data analysis in a more complex exchange model generally requires computationally-intensive numerical analysis. Recently, a powerful computational strategy, geometric approximation, has been proposed to provide approximate numerical solutions for the adiabatic relaxation dispersion experiments where analytical solutions are neither available nor feasible. Here, we demonstrate the general potential of geometric approximation by providing a data analysis solution of the CPMG experiment for both the traditional 2-site model and a linear 3-site exchange model. The approximate numerical solution deviates less than 0.5% from the numerical solution on average, and the new approach is computationally 60,000-fold more efficient than the numerical approach. Moreover, we find that accurate dynamic parameters can be determined in most cases, and, for a range of experimental conditions, the relaxation can be assumed to follow mono-exponential decay. The method is general and applicable to any CPMG RD experiment (e.g. N, C', C α , H α , etc.) The approach forms a foundation of building solution surfaces to analyze the CPMG experiment for different models of 3-site exchange. Thus, the geometric approximation is a general strategy to analyze relaxation dispersion data in any system (biological or chemical) if the appropriate library can be built in a physically meaningful domain. Published by Elsevier Inc.

Aqueous Binary Lanthanide(III) Nitrate Ln(NO3)3 Electrolytes Revisited: Extended Pitzer and Bromley Treatments

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

Chatterjee, Sayandev; Campbell, Emily L.; Neiner, Doinita

To date, only limited thermodynamic models describing activity coefficients of the aqueous solutions of lanthanide ions are available. This work expands the existing experimental osmotic coefficient data obtained by classical isopiestic technique for the aqueous binary trivalent lanthanide nitrate Ln(NO3)3 solutions using a combination of water activity and vapor pressure osmometry measurements. The combined osmotic coefficient database for each aqueous lanthanide nitrate at 25°C, consisting of literature available data as well as data obtained in this work, was used to test the validity of Pitzer and Bromley thermodynamic models for the accurate prediction of mean molal activity coefficients of themore » Ln(NO3)3 solutions in wide concentration ranges. The new and improved Pitzer and Bromley parameters were calculated. It was established that the Ln(NO3)3 activity coefficients in the solutions with ionic strength up to 12 mol kg-1 can be estimated by both Pitzer and single-parameter Bromley models, even though the latter provides for more accurate prediction, particularly in the lower ionic strength regime (up to 6 mol kg-1). On the other hand for the concentrated solutions, the extended three-parameter Bromley model can be employed to predict the Ln(NO3)3 activity coefficients with remarkable accuracy. The accuracy of the extended Bromley model in predicting the activity coefficients was greater than ~95% and ~90% for all solutions with the ionic strength up to 12 mol kg-1 and and 20 mol kg-1, respectively. This is the first time that the activity coefficients for concentrated lanthanide solutions have been predicted with such a remarkable accuracy.« less

How Long is my Toilet Roll?--A Simple Exercise in Mathematical Modelling

ERIC Educational Resources Information Center

Johnston, Peter R.

2013-01-01

The simple question of how much paper is left on my toilet roll is studied from a mathematical modelling perspective. As is typical with applied mathematics, models of increasing complexity are introduced and solved. Solutions produced at each step are compared with the solution from the previous step. This process exposes students to the typical…

Bifurcation structure of positive stationary solutions for a Lotka-Volterra competition model with diffusion I

NASA Astrophysics Data System (ADS)

Kan-On, Yukio

2007-04-01

This paper is concerned with the bifurcation structure of positive stationary solutions for a generalized Lotka-Volterra competition model with diffusion. To establish the structure, the bifurcation theory and the interval arithmetic are employed.

Modeling of dispersed-drug delivery from planar polymeric systems: optimizing analytical solutions.

PubMed

Helbling, Ignacio M; Ibarra, Juan C D; Luna, Julio A; Cabrera, María I; Grau, Ricardo J A

2010-11-15

Analytical solutions for the case of controlled dispersed-drug release from planar non-erodible polymeric matrices, based on Refined Integral Method, are presented. A new adjusting equation is used for the dissolved drug concentration profile in the depletion zone. The set of equations match the available exact solution. In order to illustrate the usefulness of this model, comparisons with experimental profiles reported in the literature are presented. The obtained results show that the model can be employed in a broad range of applicability. Copyright © 2010 Elsevier B.V. All rights reserved.

Stability of stationary solutions for inflow problem on the micropolar fluid model

NASA Astrophysics Data System (ADS)

Yin, Haiyan

2017-04-01

In this paper, we study the asymptotic behavior of solutions to the initial boundary value problem for the micropolar fluid model in a half-line R+:=(0,∞). We prove that the corresponding stationary solutions of the small amplitude to the inflow problem for the micropolar fluid model are time asymptotically stable under small H1 perturbations in both the subsonic and degenerate cases. The microrotation velocity brings us some additional troubles compared with Navier-Stokes equations in the absence of the microrotation velocity. The proof of asymptotic stability is based on the basic energy method.

The solubility and activity coefficient of oxygen in salt solutions and brines

NASA Astrophysics Data System (ADS)

Clegg, Simon L.; Brimblecombe, Peter

1990-12-01

Molal oxygen activity coefficients ( γO2) in aqueous salt solutions from 0-100°C have been calculated from O 2 solubility data and established Henry's law constants. Pitzer specific interaction model parameters λO2c, λO2a and ζO2ca have been determined for the following ions: H +, NH +4 Li +, Na +, Rb +, Cs +, Mg 2+, Ca 2+, Ba 2+, Al 3+, OH -, Cl -, Br -, I -, NO -3, SO 2-3, SO 2-4, HCO 3-, CO 32- and PO 3-4. Results confirm that the effect of individual ions on In ( γO2) is additive. Model calculations of γO2 in seawater agree with experimentally derived values at normal salinities to within 0.2% at 298 K and 0.65% at 273 K. Additional data for brines of seawater composition enable the model to be used to represent γO2 empirically to a salinity of 255 S%. The model has thus far only been parameterised from measurements for single salt solutions. Comparisons with experimental data for brines suggest that additional model parameters, obtained from ternary solution data, will be required for accurate representation of γO2 in mixed salt solutions above about 5 mol kg -1 total ion concentration.

A new and inexpensive non-bit-for-bit solution reproducibility test based on time step convergence (TSC1.0)

DOE PAGES

Wan, Hui; Zhang, Kai; Rasch, Philip J.; ...

2017-02-03

A test procedure is proposed for identifying numerically significant solution changes in evolution equations used in atmospheric models. The test issues a fail signal when any code modifications or computing environment changes lead to solution differences that exceed the known time step sensitivity of the reference model. Initial evidence is provided using the Community Atmosphere Model (CAM) version 5.3 that the proposed procedure can be used to distinguish rounding-level solution changes from impacts of compiler optimization or parameter perturbation, which are known to cause substantial differences in the simulated climate. The test is not exhaustive since it does not detect issues associatedmore » with diagnostic calculations that do not feedback to the model state variables. Nevertheless, it provides a practical and objective way to assess the significance of solution changes. The short simulation length implies low computational cost. The independence between ensemble members allows for parallel execution of all simulations, thus facilitating fast turnaround. The new method is simple to implement since it does not require any code modifications. We expect that the same methodology can be used for any geophysical model to which the concept of time step  convergence is applicable.« less

Water age and stream solute dynamics at the Hubbard Brook Experimental Forest (US)

NASA Astrophysics Data System (ADS)

Botter, Gianluca; Benettin, Paolo; McGuire, Kevin; Rinaldo, Andrea

2016-04-01

The contribution discusses experimental and modeling results from a headwater catchment at the Hubbard Brook Experimental Forest (New Hampshire, USA) to explore the link between stream solute dynamics and water age. A theoretical framework based on water age dynamics, which represents a general basis for characterizing solute transport at the catchment scale, is used to model both conservative and weathering-derived solutes. Based on the available information about the hydrology of the site, an integrated transport model was developed and used to estimate the relevant hydrochemical fluxes. The model was designed to reproduce the deuterium content of streamflow and allowed for the estimate of catchment water storage and dynamic travel time distributions (TTDs). Within this framework, dissolved silicon and sodium concentration in streamflow were simulated by implementing first-order chemical kinetics based explicitly on dynamic TTD, thus upscaling local geochemical processes to catchment scale. Our results highlight the key role of water stored within the subsoil glacial material in both the short-term and long-term solute circulation at Hubbard Brook. The analysis of the results provided by the calibrated model allowed a robust estimate of the emerging concentration-discharge relationship, streamflow age distributions (including the fraction of event water) and storage size, and their evolution in time due to hydrologic variability.

The construction of sparse models of Mars' crustal magnetic field

NASA Astrophysics Data System (ADS)

Moore, Kimberly; Bloxham, Jeremy

2017-04-01

The crustal magnetic field of Mars is a key constraint on Martian geophysical history, especially the timing of the dynamo shutoff. Maps of the crustal magnetic field of Mars show wide variations in the intensity of magnetization, with most of the Northern hemisphere only weakly magnetized. Previous methods of analysis tend to favor smooth solutions for the crustal magnetic field of Mars, making use of techniques such as L2 norms. Here we utilize inversion methods designed for sparse models, to see how much of the surface area of Mars must be magnetized in order to fit available spacecraft magnetic field data. We solve for the crustal magnetic field at 10,000 individual magnetic pixels on the surface of Mars. We employ an L1 regularization, and solve for models where each magnetic pixel is identically zero, unless required otherwise by the data. We find solutions with an adequate fit to the data with over 90% sparsity (90% of magnetic pixels having a field value of exactly 0). We contrast these solutions with L2-based solutions, as well as an elastic net model (combination of L1 and L2). We find our sparse solutions look dramatically different from previous models in the literature, but still give a physically reasonable history of the dynamo (shutting off around 4.1 Ga).

Theoretical Modeling of Hydrogen Bonding in omolecular Solutions: The Combination of Quantum Mechanics and Molecular Mechanics

NASA Astrophysics Data System (ADS)

Ma, Jing; Jiang, Nan; Li, Hui

Hydrogen bonding interaction takes an important position in solutions. The non-classic nature of hydrogen bonding requires the resource-demanding quantum mechanical (QM) calculations. The molecular mechanics (MM) method, with much lower computational load, is applicable to the large-sized system. The combination of QM and MM is an efficient way in the treatment of solution. Taking advantage of the low-cost energy-based fragmentation QM approach (in which the o-molecule is divided into several subsystems, and QM calculation is carried out on each subsystem that is embedded in the environment of background charges of distant parts), the fragmentation-based QM/MM and polarization models have been implemented for the modeling of o-molecule in aqueous solutions, respectively. Within the framework of the fragmentation-based QM/MM hybrid model, the solute is treated by the fragmentation QM calculation while the numerous solvent molecules are described by MM. In the polarization model, the polarizability is considered by allowing the partial charges and fragment-centered dipole moments to be variables, with values coming from the energy-based fragmentation QM calculations. Applications of these two methods to the solvated long oligomers and cyclic peptides have demonstrated that the hydrogen bonding interaction affects the dynamic change in chain conformations of backbone.

Existence and global attractivity of unique positive periodic solution for a model of hematopoiesis

NASA Astrophysics Data System (ADS)

Liu, Guirong; Yan, Jurang; Zhang, Fengqin

2007-10-01

In this paper, we consider the generalized model of hematopoiesis By using a fixed point theorem, some criteria are established for the existence of the unique positive [omega]-periodic solution of the above equation. In particular, we not only give the conclusion of convergence of xk to , where {xk} is a successive sequence, but also show that is a global attractor of all other positive solutions.

Microwave Dielectric Constant Dependence on Soil Tension.

DTIC Science & Technology

1983-10-01

water to be only a single monolayer thick .1 (OA) with Ice-like dielectric properties EWS = (3.15, JO). The first approach apportions the soil solution Into...mixing model that accounts explicitly for the presence of a hydrationU layer of bound water adjacent to hydrophilic soil particle surfaces. The soil ... solution is differentiated Into (1) a bound, ice-like component and (2) a bulk solution component, by a physical soil model dependent upon either soil

2-Dimensional B-Spline Algorithms with Applications to Ray Tracing in Media of Spatially-Varying Refractive Index

DTIC Science & Technology

2007-08-01

In the approach, photon trajectories are computed using a solution of the Eikonal equation (ray-tracing methods) rather than linear trajectories. The...coupling the radiative transport solution into heat transfer and damage models. 15. SUBJECT TERMS: B-Splines, Ray-Tracing, Eikonal Equation...multi-layer biological tissue model. In the approach, photon trajectories are computed using a solution of the Eikonal equation (ray-tracing methods

Probability density function of non-reactive solute concentration in heterogeneous porous formations.

PubMed

Bellin, Alberto; Tonina, Daniele

2007-10-30

Available models of solute transport in heterogeneous formations lack in providing complete characterization of the predicted concentration. This is a serious drawback especially in risk analysis where confidence intervals and probability of exceeding threshold values are required. Our contribution to fill this gap of knowledge is a probability distribution model for the local concentration of conservative tracers migrating in heterogeneous aquifers. Our model accounts for dilution, mechanical mixing within the sampling volume and spreading due to formation heterogeneity. It is developed by modeling local concentration dynamics with an Ito Stochastic Differential Equation (SDE) that under the hypothesis of statistical stationarity leads to the Beta probability distribution function (pdf) for the solute concentration. This model shows large flexibility in capturing the smoothing effect of the sampling volume and the associated reduction of the probability of exceeding large concentrations. Furthermore, it is fully characterized by the first two moments of the solute concentration, and these are the same pieces of information required for standard geostatistical techniques employing Normal or Log-Normal distributions. Additionally, we show that in the absence of pore-scale dispersion and for point concentrations the pdf model converges to the binary distribution of [Dagan, G., 1982. Stochastic modeling of groundwater flow by unconditional and conditional probabilities, 2, The solute transport. Water Resour. Res. 18 (4), 835-848.], while it approaches the Normal distribution for sampling volumes much larger than the characteristic scale of the aquifer heterogeneity. Furthermore, we demonstrate that the same model with the spatial moments replacing the statistical moments can be applied to estimate the proportion of the plume volume where solute concentrations are above or below critical thresholds. Application of this model to point and vertically averaged bromide concentrations from the first Cape Cod tracer test and to a set of numerical simulations confirms the above findings and for the first time it shows the superiority of the Beta model to both Normal and Log-Normal models in interpreting field data. Furthermore, we show that assuming a-priori that local concentrations are normally or log-normally distributed may result in a severe underestimate of the probability of exceeding large concentrations.

Effects of Electronic-State-Dependent Solute Polarizability: Application to Solute-Pump/Solvent-Probe Spectra.

PubMed

Sun, Xiang; Ladanyi, Branka M; Stratt, Richard M

2015-07-23

Experimental studies of solvation dynamics in liquids invariably ask how changing a solute from its electronic ground state to an electronically excited state affects a solution's dynamics. With traditional time-dependent-fluorescence experiments, that means looking for the dynamical consequences of the concomitant change in solute-solvent potential energy. But if one follows the shift in the dynamics through its effects on the macroscopic polarizability, as recent solute-pump/solvent-probe spectra do, there is another effect of the electronic excitation that should be considered: the jump in the solute's own polarizability. We examine the spectroscopic consequences of this solute polarizability change in the classic example of the solvation dye coumarin 153 dissolved in acetonitrile. After demonstrating that standard quantum chemical methods can be used to construct accurate multisite models for the polarizabilities of ground- and excited-state solvation dyes, we show via simulation that this polarizability change acts as a contrast agent, significantly enhancing the observable differences in optical-Kerr spectra between ground- and excited-state solutions. A comparison of our results with experimental solute-pump/solvent-probe spectra supports our interpretation and modeling of this spectroscopy. We predict, in particular, that solute-pump/solvent-probe spectra should be sensitive to changes in both the solvent dynamics near the solute and the electronic-state-dependence of the solute's own rotational dynamics.

Reflection K-matrices for a nineteen vertex model with Uq [ osp (2 | 2) (2) ] symmetry

NASA Astrophysics Data System (ADS)

Vieira, R. S.; Lima Santos, A.

2017-09-01

We derive the solutions of the boundary Yang-Baxter equation associated with a supersymmetric nineteen vertex model constructed from the three-dimensional representation of the twisted quantum affine Lie superalgebra Uq [ osp (2 | 2) (2) ]. We found three classes of solutions. The type I solution is characterized by three boundary free-parameters and all elements of the corresponding reflection K-matrix are different from zero. In the type II solution, the reflection K-matrix is even (every element of the K-matrix with an odd parity is null) and it has only one boundary free-parameter. Finally, the type III solution corresponds to a diagonal reflection K-matrix with two boundary free-parameters.

Investigation of the effects of radiolytic-gas bubbles on the long-term operation of solution reactors for medical-isotope production

NASA Astrophysics Data System (ADS)

Souto Mantecon, Francisco Javier

One of the most common and important medical radioisotopes is 99Mo, which is currently produced using the target irradiation technology in heterogeneous nuclear reactors. The medical isotope 99Mo can also be produced from uranium fission using aqueous homogeneous solution reactors. In solution reactors, 99Mo is generated directly in the fuel solution, resulting in potential advantages when compared with the target irradiation process in heterogeneous reactors, such as lower reactor power, less waste heat, and reduction by a factor of about 100 in the generation of spent fuel. The commercial production of medical isotopes in solution reactors requires steady-state operation at about 200 kW. At this power regime, the formation of radiolytic-gas bubbles creates a void volume in the fuel solution that introduces a negative coefficient of reactivity, resulting in power reduction and instabilities that may impede reactor operation for medical-isotope production. A model has been developed considering that reactivity effects are due to the increase in the fuel-solution temperature and the formation of radiolytic-gas bubbles. The model has been validated against experimental results from the Los Alamos National Laboratory uranyl fluoride Solution High-Energy Burst Assembly (SHEBA), and the SILENE uranyl nitrate solution reactor, commissioned at the Commissariat a l'Energie Atomique, in Valduc, France. The model shows the feasibility of solution reactors for the commercial production of medical isotopes and reveals some of the important parameters to consider in their design, including the fuel-solution type, 235U enrichment, uranium concentration, reactor vessel geometry, and neutron reflectors surrounding the reactor vessel. The work presented herein indicates that steady-state operation at 200 kW can be achieved with a solution reactor consisting of 120 L of uranyl nitrate solution enriched up to 20% with 235U and a uranium concentration of 145 kg/m3 in a graphite-reflected cylindrical geometry.

Finite-difference model for 3-D flow in bays and estuaries

USGS Publications Warehouse

Smith, Peter E.; Larock, Bruce E.; ,

1993-01-01

This paper describes a semi-implicit finite-difference model for the numerical solution of three-dimensional flow in bays and estuaries. The model treats the gravity wave and vertical diffusion terms in the governing equations implicitly, and other terms explicitly. The model achieves essentially second-order accurate and stable solutions in strongly nonlinear problems by using a three-time-level leapfrog-trapezoidal scheme for the time integration.

The art of fault-tolerant system reliability modeling

NASA Technical Reports Server (NTRS)

Butler, Ricky W.; Johnson, Sally C.

1990-01-01

A step-by-step tutorial of the methods and tools used for the reliability analysis of fault-tolerant systems is presented. Emphasis is on the representation of architectural features in mathematical models. Details of the mathematical solution of complex reliability models are not presented. Instead the use of several recently developed computer programs--SURE, ASSIST, STEM, PAWS--which automate the generation and solution of these models is described.

A simple model of fluid flow and electrolyte balance in the body

NASA Technical Reports Server (NTRS)

White, R. J.; Neal, L.

1973-01-01

The model is basically a three-compartment model, the three compartments being the plasma, interstitial fluid and cellular fluid. Sodium, potassium, chloride and urea are the only major solutes considered explicitly. The control of body water and electrolyte distribution is affected via drinking and hormone levels. Basically, the model follows the effect of various oral input water loads on solute and water distribution throughout the body.

Modification of a method-of-characteristics solute-transport model to incorporate decay and equilibrium-controlled sorption or ion exchange

USGS Publications Warehouse

Goode, D.J.; Konikow, Leonard F.

1989-01-01

The U.S. Geological Survey computer model of two-dimensional solute transport and dispersion in ground water (Konikow and Bredehoeft, 1978) has been modified to incorporate the following types of chemical reactions: (1) first-order irreversible rate-reaction, such as radioactive decay; (2) reversible equilibrium-controlled sorption with linear, Freundlich, or Langmuir isotherms; and (3) reversible equilibrium-controlled ion exchange for monovalent or divalent ions. Numerical procedures are developed to incorporate these processes in the general solution scheme that uses method-of- characteristics with particle tracking for advection and finite-difference methods for dispersion. The first type of reaction is accounted for by an exponential decay term applied directly to the particle concentration. The second and third types of reactions are incorporated through a retardation factor, which is a function of concentration for nonlinear cases. The model is evaluated and verified by comparison with analytical solutions for linear sorption and decay, and by comparison with other numerical solutions for nonlinear sorption and ion exchange.

Automated structure solution, density modification and model building.

PubMed

Terwilliger, Thomas C

2002-11-01

The approaches that form the basis of automated structure solution in SOLVE and RESOLVE are described. The use of a scoring scheme to convert decision making in macromolecular structure solution to an optimization problem has proven very useful and in many cases a single clear heavy-atom solution can be obtained and used for phasing. Statistical density modification is well suited to an automated approach to structure solution because the method is relatively insensitive to choices of numbers of cycles and solvent content. The detection of non-crystallographic symmetry (NCS) in heavy-atom sites and checking of potential NCS operations against the electron-density map has proven to be a reliable method for identification of NCS in most cases. Automated model building beginning with an FFT-based search for helices and sheets has been successful in automated model building for maps with resolutions as low as 3 A. The entire process can be carried out in a fully automatic fashion in many cases.

Modulation stability and optical soliton solutions of nonlinear Schrödinger equation with higher order dispersion and nonlinear terms and its applications

NASA Astrophysics Data System (ADS)

Arshad, Muhammad; Seadawy, Aly R.; Lu, Dianchen

2017-12-01

In optical fibers, the higher order non-linear Schrödinger equation (NLSE) with cubic quintic nonlinearity describes the propagation of extremely short pulses. We constructed bright and dark solitons, solitary wave and periodic solitary wave solutions of generalized higher order NLSE in cubic quintic non Kerr medium by applying proposed modified extended mapping method. These obtained solutions have key applications in physics and mathematics. Moreover, we have also presented the formation conditions on solitary wave parameters in which dark and bright solitons can exist for this media. We also gave graphically the movement of constructed solitary wave and soliton solutions, that helps to realize the physical phenomena's of this model. The stability of the model in normal dispersion and anomalous regime is discussed by using the modulation instability analysis, which confirms that all constructed solutions are exact and stable. Many other such types of models arising in applied sciences can also be solved by this reliable, powerful and effective method.

Phase transition solutions in geometrically constrained magnetic domain wall models

NASA Astrophysics Data System (ADS)

Chen, Shouxin; Yang, Yisong

2010-02-01

Recent work on magnetic phase transition in nanoscale systems indicates that new physical phenomena, in particular, the Bloch wall width narrowing, arise as a consequence of geometrical confinement of magnetization and leads to the introduction of geometrically constrained domain wall models. In this paper, we present a systematic mathematical analysis on the existence of the solutions of the basic governing equations in such domain wall models. We show that, when the cross section of the geometric constriction is a simple step function, the solutions may be obtained by minimizing the domain wall energy over the constriction and solving the Bogomol'nyi equation outside the constriction. When the cross section and potential density are both even, we establish the existence of an odd domain wall solution realizing the phase transition process between two adjacent domain phases. When the cross section satisfies a certain integrability condition, we prove that a domain wall solution always exists which links two arbitrarily designated domain phases.

Absolute instabilities of travelling wave solutions in a Keller-Segel model

NASA Astrophysics Data System (ADS)

Davis, P. N.; van Heijster, P.; Marangell, R.

2017-11-01

We investigate the spectral stability of travelling wave solutions in a Keller-Segel model of bacterial chemotaxis with a logarithmic chemosensitivity function and a constant, sublinear, and linear consumption rate. Linearising around the travelling wave solutions, we locate the essential and absolute spectrum of the associated linear operators and find that all travelling wave solutions have parts of the essential spectrum in the right half plane. However, we show that in the case of constant or sublinear consumption there exists a range of parameters such that the absolute spectrum is contained in the open left half plane and the essential spectrum can thus be weighted into the open left half plane. For the constant and sublinear consumption rate models we also determine critical parameter values for which the absolute spectrum crosses into the right half plane, indicating the onset of an absolute instability of the travelling wave solution. We observe that this crossing always occurs off of the real axis.

Agile Implementation: A Blueprint for Implementing Evidence-Based Healthcare Solutions.

PubMed

Boustani, Malaz; Alder, Catherine A; Solid, Craig A

2018-03-07

To describe the essential components of an Agile Implementation (AI) process, which rapidly and effectively implements evidence-based healthcare solutions, and present a case study demonstrating its utility. Case demonstration study. Integrated, safety net healthcare delivery system in Indianapolis. Interdisciplinary team of clinicians and administrators. Reduction in dementia symptoms and caregiver burden; inpatient and outpatient care expenditures. Implementation scientists were able to implement a collaborative care model for dementia care and sustain it for more than 9 years. The model was implemented and sustained by using the elements of the AI process: proactive surveillance and confirmation of clinical opportunities, selection of the right evidence-based healthcare solution, localization (i.e., tailoring to the local environment) of the selected solution, development of an evaluation plan and performance feedback loop, development of a minimally standardized operation manual, and updating such manual annually. The AI process provides an effective model to implement and sustain evidence-based healthcare solutions. © 2018, Copyright the Authors Journal compilation © 2018, The American Geriatrics Society.

Quasielastic small-angle neutron scattering from heavy water solutions of cyclodextrins

NASA Astrophysics Data System (ADS)

Kusmin, André; Lechner, Ruep E.; Saenger, Wolfram

2011-01-01

We present a model for quasielastic neutron scattering (QENS) by an aqueous solution of compact and inflexible molecules. This model accounts for time-dependent spatial pair correlations between the atoms of the same as well as of distinct molecules and includes all coherent and incoherent neutron scattering contributions. The extension of the static theory of the excluded volume effect [A. K. Soper, J. Phys.: Condens. Matter 9, 2399 (1997)] to the time-dependent (dynamic) case allows us to obtain simplified model expressions for QENS spectra in the low Q region in the uniform fluid approximation. The resulting expressions describe the quasielastic small-angle neutron scattering (QESANS) spectra of D _2O solutions of native and methylated cyclodextrins well, yielding in particular translational and rotational diffusion coefficients of these compounds in aqueous solution. Finally, we discuss the full potential of the QESANS analysis (that is, beyond the uniform fluid approximation), in particular, the information on solute-solvent interactions (e.g., hydration shell properties) that such an analysis can provide, in principle.

Effect of heat/pressure on cyanidin-3-glucoside ethanol model solutions

NASA Astrophysics Data System (ADS)

Corrales, M.; Lindauer, R.; Butz, P.; Tauscher, B.

2008-07-01

The stability of cyanidin-3-glucoside (Cy3gl) in 50% ethanol model solutions under heat/pressure treatments was investigated. Cy3gl was rapidly degraded when solutions were subjected to a heat/pressure treatment. The higher the pressure and the temperature used, the higher the degradation. Moreover, the degradation was increased according to increasing holding times. Parallel to the degradation of Cy3gl several hydrolytic products were formed and identified by LC-DAD/ESI-MS. The degradation of Cy3gl was well fitted to a first order reaction (R=0.99). This study pointed out the rate of susceptibility of Cy3gl in model solutions to degrade when exposed to a heat/pressure treatment and the trigger effect of high hydrostatic pressure to hydrolyse Cy3gl. By contrast, the degradation of anthocyanins in a food matrix (red grape extract solutions) was negligible after a heat/pressure process at 600MPa, 70°C during 1h (P >0.05).

Thermal Stability of Nanocrystalline Alloys by Solute Additions and A Thermodynamic Modeling

NASA Astrophysics Data System (ADS)

Saber, Mostafa

Nanocrystalline alloys show superior properties due to their exceptional microstructure. Thermal stability of these materials is a critical aspect. It is well known that grain boundaries in nanocrystalline microstructures cause a significant increase in the total free energy of the system. A driving force provided to reduce this excess free energy can cause grain growth. The presence of a solute addition within a nanocrystalline alloy can lead to the thermal stability. Kinetic and thermodynamic stabilization are the two basic mechanisms with which stability of a nanoscale grain size can be achieved at high temperatures. The basis of this thesis is to study the effect of solute addition on thermal stability of nanocrystalline alloys. The objective is to determine the effect of Zr addition on the thermal stability of mechanically alloyed nanocrysatillne Fe-Cr and Fe-Ni alloys. In Fe-Cr-Zr alloy system, nanoscale grain size stabilization was maintained up to 900 °C by adding 2 at% Zr. Kinetic pinning by intermetallic particles in the nanoscale range was identified as a primary mechanism of thermal stabilization. In addition to the grain size strengthening, intermetallic particles also contribute to strengthening mechanisms. The analysis of microhardness, XRD data, and measured grain sizes from TEM micrographs suggested that both thermodynamic and kinetic mechanisms are possible mechanisms. It was found that alpha → gamma phase transformation in Fe-Cr-Zr system does not influence the grain size stabilization. In the Fe-Ni-Zr alloy system, it was shown that the grain growth in Fe-8Ni-1Zr alloy is much less than that of pure Fe and Fe-8Ni alloy at elevated temperatures. The microstructure of the ternary Fe-8Ni-1Zr alloy remains in the nanoscale range up to 700 °C. Using an in-situ TEM study, it was determined that drastic grain growth occurs when the alpha → gamma phase transformation occurs. Accordingly, there can be a synergistic relationship between grain growth and alpha → gamma phase transformation in Fe-Ni-Zr alloys. In addition to the experimental study of thermal stabilization of nanocrystalline Fe-Cr-Zr or Fe-Ni-Zr alloys, the thesis presented here developed a new predictive model, applicable to strongly segregating solutes, for thermodynamic stabilization of binary alloys. This model can serve as a benchmark for selecting solute and evaluating the possible contribution of stabilization. Following a regular solution model, both the chemical and elastic strain energy contributions are combined to obtain the mixing enthalpy. The total Gibbs free energy of mixing is then minimized with respect to simultaneous variations in the grain boundary volume fraction and the solute concentration in the grain boundary and the grain interior. The Lagrange multiplier method was used to obtained numerical solutions. Application are given for the temperature dependence of the grain size and the grain boundary solute excess for selected binary system where experimental results imply that thermodynamic stabilization could be operative. This thesis also extends the binary model to a new model for thermodynamic stabilization of ternary nanocrystalline alloys. It is applicable to strongly segregating size-misfit solutes and uses input data available in the literature. In a same manner as the binary model, this model is based on a regular solution approach such that the chemical and elastic strain energy contributions are incorporated into the mixing enthalpy DeltaHmix, and the mixing entropy DeltaSmix is obtained using the ideal solution approximation. The Gibbs mixing free energy Delta Gmix is then minimized with respect to simultaneous variations in grain growth and solute segregation parameters. The Lagrange multiplier method is similarly used to obtain numerical solutions for the minimum Delta Gmix. The temperature dependence of the nanocrystalline grain size and interfacial solute excess can be obtained for selected ternary systems. As an example, model predictions are compared to experimental results for Fe-Cr-Zr and Fe-Ni-Zr alloy systems. Consistency between the experimental results and the present model predictions provide a more rigorous criterion for investigating thermal stabilization. However, other possible contributions for grain growth stabilization should still be considered.

Contribution of the GOCE gradiometer components to regional gravity solutions

NASA Astrophysics Data System (ADS)

Naeimi, Majid; Bouman, Johannes

2017-05-01

The contribution of the GOCE gravity gradients to regional gravity field solutions is investigated in this study. We employ radial basis functions to recover the gravity field on regional scales over Amazon and Himalayas as our test regions. In the first step, four individual solutions based on the more accurate gravity gradient components Txx, Tyy, Tzz and Txz are derived. The Tzz component gives better solution than the other single-component solutions despite the less accuracy of Tzz compared to Txx and Tyy. Furthermore, we determine five more solutions based on several selected combinations of the gravity gradient components including a combined solution using the four gradient components. The Tzz and Tyy components are shown to be the main contributors in all combined solutions whereas the Txz adds the least value to the regional gravity solutions. We also investigate the contribution of the regularization term. We show that the contribution of the regularization significantly decreases as more gravity gradients are included. For the solution using all gravity gradients, regularization term contributes to about 5 per cent of the total solution. Finally, we demonstrate that in our test areas, regional gravity modelling based on GOCE data provide more reliable gravity signal in medium wavelengths as compared to pre-GOCE global gravity field models such as the EGM2008.

The removal of chloramphenicol from water through adsorption on activated carbon

NASA Astrophysics Data System (ADS)

Lach, Joanna; Ociepa-Kubicka, Agnieszka

2017-10-01

The presented research investigated the removal of chloramphenicol from water solutions on selected activated carbon available in three grades with different porous structure and surface chemical composition. Two models of adsorption kinetics were examined, i.e. the pseudo-first order and the pseudo-second order models. For all examined cases, the results of tests with higher value of coefficient R2 were described by the equation for pseudo-second order kinetics. The adsorption kinetics was also investigated on the activated carbons modified with ozone. The measurements were taken from the solutions with pH values of 2 and 7. Chloramphenicol was the most efficiently adsorbed on the activated carbon F-300 from the solutions with pH=7, and on the activated carbon ROW 08 Supra from the solutions with pH=2. The adsorption of this antibiotic was in the majority of cases higher from the solutions with pH=2 than pH=7. The modification of the activated carbons with ozone enhanced their adsorption capacities for chloramphenicol. The adsorption is influenced by the modification method of activated carbon (i.e. the duration of ozonation of the activated carbon solution and the solution temperature). The results were described with the Freundlich and Langmuir adsorption isotherm equations. Both models well described the obtained results (high R2 values).

Prediction of local concentration statistics in variably saturated soils: Influence of observation scale and comparison with field data

NASA Astrophysics Data System (ADS)

Graham, Wendy; Destouni, Georgia; Demmy, George; Foussereau, Xavier

1998-07-01

The methodology developed in Destouni and Graham [Destouni, G., Graham, W.D., 1997. The influence of observation method on local concentration statistics in the subsurface. Water Resour. Res. 33 (4) 663-676.] for predicting locally measured concentration statistics for solute transport in heterogeneous porous media under saturated flow conditions is applied to the prediction of conservative nonreactive solute transport in the vadose zone where observations are obtained by soil coring. Exact analytical solutions are developed for both the mean and variance of solute concentrations measured in discrete soil cores using a simplified physical model for vadose-zone flow and solute transport. Theoretical results show that while the ensemble mean concentration is relatively insensitive to the length-scale of the measurement, predictions of the concentration variance are significantly impacted by the sampling interval. Results also show that accounting for vertical heterogeneity in the soil profile results in significantly less spreading in the mean and variance of the measured solute breakthrough curves, indicating that it is important to account for vertical heterogeneity even for relatively small travel distances. Model predictions for both the mean and variance of locally measured solute concentration, based on independently estimated model parameters, agree well with data from a field tracer test conducted in Manatee County, Florida.

Real-time and rapid GNSS solutions from the M8.2 September 2017 Tehuantepec Earthquake and implications for Earthquake and Tsunami Early Warning Systems

NASA Astrophysics Data System (ADS)

Mencin, D.; Hodgkinson, K. M.; Mattioli, G. S.

2017-12-01

In support of hazard research and Earthquake Early Warning (EEW) Systems UNAVCO operates approximately 800 RT-GNSS stations throughout western North America and Alaska (EarthScope Plate Boundary Observatory), Mexico (TLALOCNet), and the pan-Caribbean region (COCONet). Our system produces and distributes raw data (BINEX and RTCM3) and real-time Precise Point Positions via the Trimble PIVOT Platform (RTX). The 2017-09-08 earthquake M8.2 located 98 km SSW of Tres Picos, Mexico is the first great earthquake to occur within the UNAVCO RT-GNSS footprint, which allows for a rigorous analysis of our dynamic and static processing methods. The need for rapid geodetic solutions ranges from seconds (EEW systems) to several minutes (Tsunami Warning and NEIC moment tensor and finite fault models). Here, we compare and quantify the relative processing strategies for producing static offsets, moment tensors and geodetically determined finite fault models using data recorded during this event. We also compare the geodetic solutions with the USGS NEIC seismically derived moment tensors and finite fault models, including displacement waveforms generated from these models. We define kinematic post-processed solutions from GIPSY-OASISII (v6.4) with final orbits and clocks as a "best" case reference to evaluate the performance of our different processing strategies. We find that static displacements of a few centimeters or less are difficult to resolve in the real-time GNSS position estimates. The standard daily 24-hour solutions provide the highest-quality data-set to determine coseismic offsets, but these solutions are delayed by at least 48 hours after the event. Dynamic displacements, estimated in real-time, however, show reasonable agreement with final, post-processed position estimates, and while individual position estimates have large errors, the real-time solutions offer an excellent operational option for EEW systems, including the use of estimated peak-ground displacements or directly inverting for finite-fault solutions. In the near-field, we find that the geodetically-derived moment tensors and finite fault models differ significantly with seismically-derived models, highlighting the utility of using geodetic data in hazard applications.

Intercomparison of 3D pore-scale flow and solute transport simulation methods

DOE PAGES

Mehmani, Yashar; Schoenherr, Martin; Pasquali, Andrea; ...

2015-09-28

Multiple numerical approaches have been developed to simulate porous media fluid flow and solute transport at the pore scale. These include 1) methods that explicitly model the three-dimensional geometry of pore spaces and 2) methods that conceptualize the pore space as a topologically consistent set of stylized pore bodies and pore throats. In previous work we validated a model of the first type, using computational fluid dynamics (CFD) codes employing a standard finite volume method (FVM), against magnetic resonance velocimetry (MRV) measurements of pore-scale velocities. Here we expand that validation to include additional models of the first type based onmore » the lattice Boltzmann method (LBM) and smoothed particle hydrodynamics (SPH), as well as a model of the second type, a pore-network model (PNM). The PNM approach used in the current study was recently improved and demonstrated to accurately simulate solute transport in a two-dimensional experiment. While the PNM approach is computationally much less demanding than direct numerical simulation methods, the effect of conceptualizing complex three-dimensional pore geometries on solute transport in the manner of PNMs has not been fully determined. We apply all four approaches (FVM-based CFD, LBM, SPH and PNM) to simulate pore-scale velocity distributions and (for capable codes) nonreactive solute transport, and intercompare the model results. Comparisons are drawn both in terms of macroscopic variables (e.g., permeability, solute breakthrough curves) and microscopic variables (e.g., local velocities and concentrations). Generally good agreement was achieved among the various approaches, but some differences were observed depending on the model context. The intercomparison work was challenging because of variable capabilities of the codes, and inspired some code enhancements to allow consistent comparison of flow and transport simulations across the full suite of methods. This paper provides support for confidence in a variety of pore-scale modeling methods and motivates further development and application of pore-scale simulation methods.« less

Intercomparison of 3D pore-scale flow and solute transport simulation methods

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

Yang, Xiaofan; Mehmani, Yashar; Perkins, William A.

2016-09-01

Multiple numerical approaches have been developed to simulate porous media fluid flow and solute transport at the pore scale. These include 1) methods that explicitly model the three-dimensional geometry of pore spaces and 2) methods that conceptualize the pore space as a topologically consistent set of stylized pore bodies and pore throats. In previous work we validated a model of the first type, using computational fluid dynamics (CFD) codes employing a standard finite volume method (FVM), against magnetic resonance velocimetry (MRV) measurements of pore-scale velocities. Here we expand that validation to include additional models of the first type based onmore » the lattice Boltzmann method (LBM) and smoothed particle hydrodynamics (SPH), as well as a model of the second type, a pore-network model (PNM). The PNM approach used in the current study was recently improved and demonstrated to accurately simulate solute transport in a two-dimensional experiment. While the PNM approach is computationally much less demanding than direct numerical simulation methods, the effect of conceptualizing complex three-dimensional pore geometries on solute transport in the manner of PNMs has not been fully determined. We apply all four approaches (FVM-based CFD, LBM, SPH and PNM) to simulate pore-scale velocity distributions and (for capable codes) nonreactive solute transport, and intercompare the model results. Comparisons are drawn both in terms of macroscopic variables (e.g., permeability, solute breakthrough curves) and microscopic variables (e.g., local velocities and concentrations). Generally good agreement was achieved among the various approaches, but some differences were observed depending on the model context. The intercomparison work was challenging because of variable capabilities of the codes, and inspired some code enhancements to allow consistent comparison of flow and transport simulations across the full suite of methods. This study provides support for confidence in a variety of pore-scale modeling methods and motivates further development and application of pore-scale simulation methods.« less

Water and solute transport parameterization form a soil of semi-arid region of northeast of Brazil

NASA Astrophysics Data System (ADS)

Netto, A. M.; Antonino, A. C. D.; Lima, L. J. S.; Angulo-Jaramillo, R.; Montenegro, S. M. G.

2003-04-01

Water and solute transfer modeling needs the transport parameters as input data. Classical theory, Fickian advection-dispersion, is not successfully applied to account for solute transport along with preferential flow pathways. This transport may be operating at scales smaller than spatial discretization used in a field scale numerical model. An axisymetric infiltration using a single ring infiltrometer along with a conservative tracer (Cl^-) is an efficient and easy method to use in fields tools. Two experiments were accomplished on a Yellow Oxissol in a 4,0 ha area in Centro de Ciências Agrárias, UFPB, Areia City, Paraíba State, Brazil (6^o 58'S, 35o 41'W and 645 m), in a 50 × 50 m grid (16 points): a) cultivated with beans (Vigna Unguinculata (L.) Walp.), and b) bare soil after harvest. The unsaturated hydraulic conductivity K and sorptivity S were estimated from short time or long time analysis of cumulative three dimensional infiltration. Single tracer technique was used for the calculation of mobile water fraction f by measuring the solute concentration underneath the ring infiltrometer, at the end of infiltration. A solute transfer numerical model, based on the mobile-immobile water concept, was used for the determination of the solute transport parameters. The mobile water fraction f, the dispersion coefficient D, and the mass transfer coefficient α, were estimated from both the measured infiltration depth and concentration profile underneath the ring infiltrometer. The presence of preferential flow was due to the soil nature (aggregated soil, macropores, flux instabilities and heterogeneity). The lateral solute transfer is not only diffusive but also convective. The parameters deduced from the numerical model associated to the solute profile concentration are representative of this phenomenon.

Water and Solute Flux Simulation Using Hydropedology Survey Data in South African Catchments

NASA Astrophysics Data System (ADS)

Lorentz, Simon; van Tol, Johan; le Roux, Pieter

2017-04-01

Hydropedology surveys include linking soil profile information in hillslope transects in order to define dominant subsurface flow mechanisms and pathways. This information is useful for deriving hillslope response functions, which aid storage and travel time estimates of water and solute movement in the sub-surface. In this way, the "soft" data of the hydropedological survey can be included in simple hydrological models, where detailed modelling of processes and pathways is prohibitive. Hydropedology surveys were conducted in two catchments and the information used to improve the prediction of water and solute responses. Typical hillslope response functions are then derived using a 2-D finite element model of the hydropedological features. Similar response types are mapped. These mapped response units are invoked in a simple SCS based, hydrological and solute transport model to yield water and solute fluxes at the catchment outlets. The first catchment (1.6 km2) comprises commercial forestry in a sedimentary geology of sandstone and mudstone formation while the second catchment (6.1 km2) includes mine waste impoundments in a granitic geology. In this paper, we demonstrate the method of combining hydropedological interpretation with catchment hydrology and solute transport simulation. The forested catchment, with three dominant hillslope response types, have solute response times in excess of 90 days, whereas the granitic responses occur within 10 days. The use of the hydropedological data improves the solute distribution response and storage simulation, compared to simulations without the hydropedology interpretation. The hydrological responses are similar, with and without the use of the hydropedology data, but the simulated distribution of water in the catchment is improved using the techniques demonstrated.

Aerosol hygroscopic growth parameterization based on a solute specific coefficient

NASA Astrophysics Data System (ADS)

Metzger, S.; Steil, B.; Xu, L.; Penner, J. E.; Lelieveld, J.

2011-09-01

Water is a main component of atmospheric aerosols and its amount depends on the particle chemical composition. We introduce a new parameterization for the aerosol hygroscopic growth factor (HGF), based on an empirical relation between water activity (aw) and solute molality (μs) through a single solute specific coefficient νi. Three main advantages are: (1) wide applicability, (2) simplicity and (3) analytical nature. (1) Our approach considers the Kelvin effect and covers ideal solutions at large relative humidity (RH), including CCN activation, as well as concentrated solutions with high ionic strength at low RH such as the relative humidity of deliquescence (RHD). (2) A single νi coefficient suffices to parameterize the HGF for a wide range of particle sizes, from nanometer nucleation mode to micrometer coarse mode particles. (3) In contrast to previous methods, our analytical aw parameterization depends not only on a linear correction factor for the solute molality, instead νi also appears in the exponent in form x · ax. According to our findings, νi can be assumed constant for the entire aw range (0-1). Thus, the νi based method is computationally efficient. In this work we focus on single solute solutions, where νi is pre-determined with the bisection method from our analytical equations using RHD measurements and the saturation molality μssat. The computed aerosol HGF and supersaturation (Köhler-theory) compare well with the results of the thermodynamic reference model E-AIM for the key compounds NaCl and (NH4)2SO4 relevant for CCN modeling and calibration studies. The equations introduced here provide the basis of our revised gas-liquid-solid partitioning model, i.e. version 4 of the EQuilibrium Simplified Aerosol Model (EQSAM4), described in a companion paper.

A review on symmetries for certain Aedes aegypti models

NASA Astrophysics Data System (ADS)

Freire, Igor Leite; Torrisi, Mariano

2015-04-01

We summarize our results related with mathematical modeling of Aedes aegypti and its Lie symmetries. Moreover, some explicit, group-invariant solutions are also shown. Weak equivalence transformations of more general reaction diffusion systems are also considered. New classes of solutions are obtained.

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 ...

Water movement through plant roots - exact solutions of the water flow equation in roots with linear or exponential piecewise hydraulic properties

NASA Astrophysics Data System (ADS)

Meunier, Félicien; Couvreur, Valentin; Draye, Xavier; Zarebanadkouki, Mohsen; Vanderborght, Jan; Javaux, Mathieu

2017-12-01

In 1978, Landsberg and Fowkes presented a solution of the water flow equation inside a root with uniform hydraulic properties. These properties are root radial conductivity and axial conductance, which control, respectively, the radial water flow between the root surface and xylem and the axial flow within the xylem. From the solution for the xylem water potential, functions that describe the radial and axial flow along the root axis were derived. These solutions can also be used to derive root macroscopic parameters that are potential input parameters of hydrological and crop models. In this paper, novel analytical solutions of the water flow equation are developed for roots whose hydraulic properties vary along their axis, which is the case for most plants. We derived solutions for single roots with linear or exponential variations of hydraulic properties with distance to root tip. These solutions were subsequently combined to construct single roots with complex hydraulic property profiles. The analytical solutions allow one to verify numerical solutions and to get a generalization of the hydric behaviour with the main influencing parameters of the solutions. The resulting flow distributions in heterogeneous roots differed from those in uniform roots and simulations led to more regular, less abrupt variations of xylem suction or radial flux along root axes. The model could successfully be applied to maize effective root conductance measurements to derive radial and axial hydraulic properties. We also show that very contrasted root water uptake patterns arise when using either uniform or heterogeneous root hydraulic properties in a soil-root model. The optimal root radius that maximizes water uptake under a carbon cost constraint was also studied. The optimal radius was shown to be highly dependent on the root hydraulic properties and close to observed properties in maize roots. We finally used the obtained functions for evaluating the impact of root maturation versus root growth on water uptake. Very diverse uptake strategies arise from the analysis. These solutions open new avenues to investigate for optimal genotype-environment-management interactions by optimization, for example, of plant-scale macroscopic hydraulic parameters used in ecohydrogolocial models.

Source of solutes to the coastal sabkha of Abu Dhabi

USGS Publications Warehouse

Wood, W.W.; Sanford, W.E.; Al Habshi, A.R.S.

2002-01-01

An ascending-brine model is proposed to address the observed isotope geochemistry, solute composition, and solute and water fluxes in the coastal sabkha of the Emirate of Abu Dhabi. Mass-balance measurements document that >95% of the solutes are derived from ascending continental brines; minor amounts are derived from rainfall and from groundwater entering from upgradient areas. Nearly 100% of the annual water loss is from evaporation and not lateral discharge. Direct rainfall on the sabkha and subsequent recharge to the underlying aquifer account for ~ 90% of the annual water input to the system; the remaining 10% comes from both lateral and ascending groundwater flow. Thus, the water and solutes in this system are from different sources. Solute concentrations of conservative (i.e., nonreactive) elements in the coastal, sabkha-covered aquifer are consistent with the fluid pore volumes of ascending brine calculated from hydrologic properties. Calcium to sulfate ratios and sulfur isotopes are consistent with this source of solute from the underlying Tertiary formations. Recharging rainwater dissolves halite and other soluble minerals on the surface, causing the solution to become more dense and sink to the bottom of the aquifer where it vertically mixes with less dense ascending brines. Solutes are returned to the surface by capillary forces and recycled or lost from the system by eolian or fluvial processes. Thus, the system becomes vertically mixed, consistent with the presence of tritium throughout the aquifer; but there is essentially no horizontal mixing of seawater with groundwater. The observed seawater solutes in the supratidal zone come from interstitial seawater trapped by the rapid progradation of the sediments into the Arabian Gulf and are not refluxed or laterally mixed. The ascending-brine model contrasts significantly with both the seawater-flooding and evaporative-pumping models previously proposed as a source of solutes to the coastal sabkha of the Emirate of Abu Dhabi. Use of these earlier models leads to incorrect conclusions and raises serious questions about their applicability in the evaluation of sabkhat in the geologic record.

Thermodynamically accurate modeling of the catalytic cycle of photosynthetic oxygen evolution: a mathematical solution to asymmetric Markov chains.

PubMed

Vinyard, David J; Zachary, Chase E; Ananyev, Gennady; Dismukes, G Charles

2013-07-01

Forty-three years ago, Kok and coworkers introduced a phenomenological model describing period-four oscillations in O2 flash yields during photosynthetic water oxidation (WOC), which had been first reported by Joliot and coworkers. The original two-parameter Kok model was subsequently extended in its level of complexity to better simulate diverse data sets, including intact cells and isolated PSII-WOCs, but at the expense of introducing physically unrealistic assumptions necessary to enable numerical solutions. To date, analytical solutions have been found only for symmetric Kok models (inefficiencies are equally probable for all intermediates, called "S-states"). However, it is widely accepted that S-state reaction steps are not identical and some are not reversible (by thermodynamic restraints) thereby causing asymmetric cycles. We have developed a mathematically more rigorous foundation that eliminates unphysical assumptions known to be in conflict with experiments and adopts a new experimental constraint on solutions. This new algorithm termed STEAMM for S-state Transition Eigenvalues of Asymmetric Markov Models enables solutions to models having fewer adjustable parameters and uses automated fitting to experimental data sets, yielding higher accuracy and precision than the classic Kok or extended Kok models. This new tool provides a general mathematical framework for analyzing damped oscillations arising from any cycle period using any appropriate Markov model, regardless of symmetry. We illustrate applications of STEAMM that better describe the intrinsic inefficiencies for photon-to-charge conversion within PSII-WOCs that are responsible for damped period-four and period-two oscillations of flash O2 yields across diverse species, while using simpler Markov models free from unrealistic assumptions. Copyright © 2013 Elsevier B.V. All rights reserved.

Establishment of a Physical Model for Solute Diffusion in Hydrogel: Understanding the Diffusion of Proteins in Poly(sulfobetaine methacrylate) Hydrogel.

PubMed

Zhou, Yuhang; Li, Junjie; Zhang, Ying; Dong, Dianyu; Zhang, Ershuai; Ji, Feng; Qin, Zhihui; Yang, Jun; Yao, Fanglian

2017-02-02

Prediction of the diffusion coefficient of solute, especially bioactive molecules, in hydrogel is significant in the biomedical field. Considering the randomness of solute movement in a hydrogel network, a physical diffusion RMP-1 model based on obstruction theory was established in this study. The physical properties of the solute and the polymer chain and their interactions were introduced into this model. Furthermore, models RMP-2 and RMP-3 were established to understand and predict the diffusion behaviors of proteins in hydrogel. In addition, zwitterionic poly(sulfobetaine methacrylate) (PSBMA) hydrogels with wide range and fine adjustable mesh sizes were prepared and used as efficient experimental platforms for model validation. The Flory characteristic ratios, Flory-Huggins parameter, mesh size, and polymer chain radii of PSBMA hydrogels were determined. The diffusion coefficients of the proteins (bovine serum albumin, immunoglobulin G, and lysozyme) in PSBMA hydrogels were studied by the fluorescence recovery after photobleaching technique. The measured diffusion coefficients were compared with the predictions of obstruction models, and it was found that our model presented an excellent predictive ability. Furthermore, the assessment of our model revealed that protein diffusion in PSBMA hydrogel would be affected by the physical properties of the protein and the PSBMA network. It was also confirmed that the diffusion behaviors of protein in zwitterionic hydrogels can be adjusted by changing the cross-linking density of the hydrogel and the ionic strength of the swelling medium. Our model is expected to possess accurate predictive ability for the diffusion coefficient of solute in hydrogel, which will be widely used in the biomedical field.

CFD Code Validation of Wall Heat Fluxes for a G02/GH2 Single Element Combustor

NASA Technical Reports Server (NTRS)

Lin, Jeff; West, Jeff S.; Williams, Robert W.; Tucker, P. Kevin

2005-01-01

This paper puts forth the case for the need for improved injector design tools to meet NASA s Vision for Space Exploration goals. Requirements for this improved tool are outlined and discussed. The potential for Computational Fluid Dynamics (CFD) to meet these requirements is noted along with its current shortcomings, especially relative to demonstrated solution accuracy. The concept of verification and validation is introduced as the primary process for building and quantifying the confidence necessary for CFD to be useful as an injector design tool. The verification and validation process is considered in the context of the Marshall Space Flight Center (MSFC) Combustion Devices CFD Simulation Capability Roadmap via the Simulation Readiness Level (SRL) concept. The portion of the validation process which demonstrates the ability of a CFD code to simulate heat fluxes to a rocket engine combustor wall is the focus of the current effort. The FDNS and Loci-CHEM codes are used to simulate a shear coaxial single element G02/GH2 injector experiment. The experiment was conducted a t a chamber pressure of 750 psia using hot propellants from preburners. A measured wall temperature profile is used as a boundary condition to facilitate the calculations. Converged solutions, obtained from both codes by using wall functions with the K-E turbulence model and integrating to the wall using Mentor s baseline turbulence model, are compared to the experimental data. The initial solutions from both codes revealed significant issues with the wall function implementation associated with the recirculation zone between the shear coaxial jet and the chamber wall. The FDNS solution with a corrected implementation shows marked improvement in overall character and level of comparison to the data. With the FDNS code, integrating to the wall with Mentor s baseline turbulence model actually produce a degraded solution when compared to the wall function solution with the K--E model. The Loci-CHEM solution, produced by integrating to the wall with Mentor s baseline turbulence model, matches both the heat flux rise rate in the near injector region and the peak heat flux level very well. However, it moderately over predicts the heat fluxes downstream of the reattachment point. The Loci-CHEM solution achieved by integrating to the wall with Mentor s baseline turbulence model was clearly superior to the other solutions produced in this effort.

Large Black Holes in the Randall-Sundrum II Model

NASA Astrophysics Data System (ADS)

Yaghoobpour Tari, Shima

The Einstein equation with a negative cosmological constant ! in the five dimensions for the Randall-Sundrum II model, which includes a black hole, has been solved numerically. We have constructed an AdS5-CFT 4 solution numerically, using a spectral method to minimize the integral of the square of the error of the Einstein equation, with 210 parameters to be determined by optimization. This metric is conformal to the Schwarzschild metric at an AdS5 boundary with an infinite scale factor. So, we consider this solution as an infinite-mass black hole solution. We have rewritten the infinite-mass black hole in the Fefferman-Graham form and obtained the numerical components of the CFT energy-momentum tensor. Using them, we have perturbed the metric to relocate the brane from infinity and obtained a large static black hole solution for the Randall- Sundrum II model. The changes of mass, entropy, temperature and area of the large black hole from the Schwarzschild metric are studied up to the first order for the perturbation parameter 1/(-Λ5M 2). The Hawking temperature and entropy for our large black hole have the same values as the Schwarzschild metric with the same mass, but the horizon area is increased by about 4.7/(-Λ5). Figueras, Lucietti, and Wiseman found an AdS5-CFT4 solution using an independent and different method from us, called the Ricci-DeTurck-flow method. Then, Figueras and Wiseman perturbed this solution in a same way as we have done and obtained the solution for the large black hole in the Randall-Sundrum II model. These two numerical solutions are the first mathematical proofs for having a large black hole in the Randall-Sundrum II. We have compared their results with ours for the CFT energy-momentum tensor components and the perturbed metric. We have shown that the results are closely in agreement, which can be considered as evidence that the solution for the large black hole in the Randall-Sundrum II model exists.