An approach to derive some simple empirical equations to calibrate nuclear and acoustic well logging tools.

PubMed

Mohammad Al Alfy, Ibrahim

2018-01-01

A set of three pads was constructed from primary materials (sand, gravel and cement) to calibrate the gamma-gamma density tool. A simple equation was devised to convert the qualitative cps values to quantitative g/cc values. The neutron-neutron porosity tool measures the qualitative cps porosity values. A direct equation was derived to calculate the porosity percentage from the cps porosity values. Cement-bond log illustrates the cement quantities, which surround well pipes. This log needs a difficult process due to the existence of various parameters, such as: drilling well diameter as well as internal diameter, thickness and type of well pipes. An equation was invented to calculate the cement percentage at standard conditions. This equation can be modified according to varying conditions. Copyright © 2017 Elsevier Ltd. All rights reserved.

TEACHING PHYSICS: Biking around a hollow sphere

NASA Astrophysics Data System (ADS)

Mak, Se-yuen; Yip, Din-yan

1999-11-01

The conditions required for a cyclist riding a motorbike in a horizontal circle on or above the equator of a hollow sphere are derived using concepts of equilibrium and the condition for uniform circular motion. The result is compared with an empirical analysis based on a video show. Some special cases of interest derived from the general solution are elaborated.

Network Reconstruction From High-Dimensional Ordinary Differential Equations.

PubMed

Chen, Shizhe; Shojaie, Ali; Witten, Daniela M

2017-01-01

We consider the task of learning a dynamical system from high-dimensional time-course data. For instance, we might wish to estimate a gene regulatory network from gene expression data measured at discrete time points. We model the dynamical system nonparametrically as a system of additive ordinary differential equations. Most existing methods for parameter estimation in ordinary differential equations estimate the derivatives from noisy observations. This is known to be challenging and inefficient. We propose a novel approach that does not involve derivative estimation. We show that the proposed method can consistently recover the true network structure even in high dimensions, and we demonstrate empirical improvement over competing approaches. Supplementary materials for this article are available online.

Empirical relations between large wood transport and catchment characteristics

NASA Astrophysics Data System (ADS)

Steeb, Nicolas; Rickenmann, Dieter; Rickli, Christian; Badoux, Alexandre

2017-04-01

The transport of vast amounts of large wood (LW) in water courses can considerably aggravate hazardous situations during flood events, and often strongly affects resulting flood damage. Large wood recruitment and transport are controlled by various factors which are difficult to assess and the prediction of transported LW volumes is difficult. Such information are, however, important for engineers and river managers to adequately dimension retention structures or to identify critical stream cross-sections. In this context, empirical formulas have been developed to estimate the volume of transported LW during a flood event (Rickenmann, 1997; Steeb et al., 2017). The data base of existing empirical wood load equations is, however, limited. The objective of the present study is to test and refine existing empirical equations, and to derive new relationships to reveal trends in wood loading. Data have been collected for flood events with LW occurrence in Swiss catchments of various sizes. This extended data set allows us to derive statistically more significant results. LW volumes were found to be related to catchment and transport characteristics, such as catchment size, forested area, forested stream length, water discharge, sediment load, or Melton ratio. Both the potential wood load and the fraction that is effectively mobilized during a flood event (effective wood load) are estimated. The difference of potential and effective wood load allows us to derive typical reduction coefficients that can be used to refine spatially explicit GIS models for potential LW recruitment.

Conservational PDF Equations of Turbulence

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Liu, Nan-Suey

2010-01-01

Recently we have revisited the traditional probability density function (PDF) equations for the velocity and species in turbulent incompressible flows. They are all unclosed due to the appearance of various conditional means which are modeled empirically. However, we have observed that it is possible to establish a closed velocity PDF equation and a closed joint velocity and species PDF equation through conditions derived from the integral form of the Navier-Stokes equations. Although, in theory, the resulted PDF equations are neither general nor unique, they nevertheless lead to the exact transport equations for the first moment as well as all higher order moments. We refer these PDF equations as the conservational PDF equations. This observation is worth further exploration for its validity and CFD application

Burst and inter-burst duration statistics as empirical test of long-range memory in the financial markets

NASA Astrophysics Data System (ADS)

Gontis, V.; Kononovicius, A.

2017-10-01

We address the problem of long-range memory in the financial markets. There are two conceptually different ways to reproduce power-law decay of auto-correlation function: using fractional Brownian motion as well as non-linear stochastic differential equations. In this contribution we address this problem by analyzing empirical return and trading activity time series from the Forex. From the empirical time series we obtain probability density functions of burst and inter-burst duration. Our analysis reveals that the power-law exponents of the obtained probability density functions are close to 3 / 2, which is a characteristic feature of the one-dimensional stochastic processes. This is in a good agreement with earlier proposed model of absolute return based on the non-linear stochastic differential equations derived from the agent-based herding model.

PolyWaTT: A polynomial water travel time estimator based on Derivative Dynamic Time Warping and Perceptually Important Points

NASA Astrophysics Data System (ADS)

Claure, Yuri Navarro; Matsubara, Edson Takashi; Padovani, Carlos; Prati, Ronaldo Cristiano

2018-03-01

Traditional methods for estimating timing parameters in hydrological science require a rigorous study of the relations of flow resistance, slope, flow regime, watershed size, water velocity, and other local variables. These studies are mostly based on empirical observations, where the timing parameter is estimated using empirically derived formulas. The application of these studies to other locations is not always direct. The locations in which equations are used should have comparable characteristics to the locations from which such equations have been derived. To overcome this barrier, in this work, we developed a data-driven approach to estimate timing parameters such as travel time. Our proposal estimates timing parameters using historical data of the location without the need of adapting or using empirical formulas from other locations. The proposal only uses one variable measured at two different locations on the same river (for instance, two river-level measurements, one upstream and the other downstream on the same river). The recorded data from each location generates two time series. Our method aligns these two time series using derivative dynamic time warping (DDTW) and perceptually important points (PIP). Using data from timing parameters, a polynomial function generalizes the data by inducing a polynomial water travel time estimator, called PolyWaTT. To evaluate the potential of our proposal, we applied PolyWaTT to three different watersheds: a floodplain ecosystem located in the part of Brazil known as Pantanal, the world's largest tropical wetland area; and the Missouri River and the Pearl River, in United States of America. We compared our proposal with empirical formulas and a data-driven state-of-the-art method. The experimental results demonstrate that PolyWaTT showed a lower mean absolute error than all other methods tested in this study, and for longer distances the mean absolute error achieved by PolyWaTT is three times smaller than empirical formulas.

Regionally Adaptable Ground Motion Prediction Equation (GMPE) from Empirical Models of Fourier and Duration of Ground Motion

NASA Astrophysics Data System (ADS)

Bora, Sanjay; Scherbaum, Frank; Kuehn, Nicolas; Stafford, Peter; Edwards, Benjamin

2016-04-01

The current practice of deriving empirical ground motion prediction equations (GMPEs) involves using ground motions recorded at multiple sites. However, in applications like site-specific (e.g., critical facility) hazard ground motions obtained from the GMPEs are need to be adjusted/corrected to a particular site/site-condition under investigation. This study presents a complete framework for developing a response spectral GMPE, within which the issue of adjustment of ground motions is addressed in a manner consistent with the linear system framework. The present approach is a two-step process in which the first step consists of deriving two separate empirical models, one for Fourier amplitude spectra (FAS) and the other for a random vibration theory (RVT) optimized duration (Drvto) of ground motion. In the second step the two models are combined within the RVT framework to obtain full response spectral amplitudes. Additionally, the framework also involves a stochastic model based extrapolation of individual Fourier spectra to extend the useable frequency limit of the empirically derived FAS model. The stochastic model parameters were determined by inverting the Fourier spectral data using an approach similar to the one as described in Edwards and Faeh (2013). Comparison of median predicted response spectra from present approach with those from other regional GMPEs indicates that the present approach can also be used as a stand-alone model. The dataset used for the presented analysis is a subset of the recently compiled database RESORCE-2012 across Europe, the Middle East and the Mediterranean region.

Simulating sunflower canopy temperatures to infer root-zone soil water potential

NASA Technical Reports Server (NTRS)

Choudhury, B. J.; Idso, S. B.

1983-01-01

A soil-plant-atmosphere model for sunflower (Helianthus annuus L.), together with clear sky weather data for several days, is used to study the relationship between canopy temperature and root-zone soil water potential. Considering the empirical dependence of stomatal resistance on insolation, air temperature and leaf water potential, a continuity equation for water flux in the soil-plant-atmosphere system is solved for the leaf water potential. The transpirational flux is calculated using Monteith's combination equation, while the canopy temperature is calculated from the energy balance equation. The simulation shows that, at high soil water potentials, canopy temperature is determined primarily by air and dew point temperatures. These results agree with an empirically derived linear regression equation relating canopy-air temperature differential to air vapor pressure deficit. The model predictions of leaf water potential are also in agreement with observations, indicating that measurements of canopy temperature together with a knowledge of air and dew point temperatures can provide a reliable estimate of the root-zone soil water potential.

Equation of state for dense nucleonic matter from metamodeling. I. Foundational aspects

NASA Astrophysics Data System (ADS)

Margueron, Jérôme; Hoffmann Casali, Rudiney; Gulminelli, Francesca

2018-02-01

Metamodeling for the nucleonic equation of state (EOS), inspired from a Taylor expansion around the saturation density of symmetric nuclear matter, is proposed and parameterized in terms of the empirical parameters. The present knowledge of nuclear empirical parameters is first reviewed in order to estimate their average values and associated uncertainties, and thus defining the parameter space of the metamodeling. They are divided into isoscalar and isovector types, and ordered according to their power in the density expansion. The goodness of the metamodeling is analyzed against the predictions of the original models. In addition, since no correlation among the empirical parameters is assumed a priori, all arbitrary density dependences can be explored, which might not be accessible in existing functionals. Spurious correlations due to the assumed functional form are also removed. This meta-EOS allows direct relations between the uncertainties on the empirical parameters and the density dependence of the nuclear equation of state and its derivatives, and the mapping between the two can be done with standard Bayesian techniques. A sensitivity analysis shows that the more influential empirical parameters are the isovector parameters Lsym and Ksym, and that laboratory constraints at supersaturation densities are essential to reduce the present uncertainties. The present metamodeling for the EOS for nuclear matter is proposed for further applications in neutron stars and supernova matter.

Derivation of the Boltzmann Equation for Financial Brownian Motion: Direct Observation of the Collective Motion of High-Frequency Traders.

PubMed

Kanazawa, Kiyoshi; Sueshige, Takumi; Takayasu, Hideki; Takayasu, Misako

2018-03-30

A microscopic model is established for financial Brownian motion from the direct observation of the dynamics of high-frequency traders (HFTs) in a foreign exchange market. Furthermore, a theoretical framework parallel to molecular kinetic theory is developed for the systematic description of the financial market from microscopic dynamics of HFTs. We report first on a microscopic empirical law of traders' trend-following behavior by tracking the trajectories of all individuals, which quantifies the collective motion of HFTs but has not been captured in conventional order-book models. We next introduce the corresponding microscopic model of HFTs and present its theoretical solution paralleling molecular kinetic theory: Boltzmann-like and Langevin-like equations are derived from the microscopic dynamics via the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy. Our model is the first microscopic model that has been directly validated through data analysis of the microscopic dynamics, exhibiting quantitative agreements with mesoscopic and macroscopic empirical results.

Derivation of the Boltzmann Equation for Financial Brownian Motion: Direct Observation of the Collective Motion of High-Frequency Traders

NASA Astrophysics Data System (ADS)

Kanazawa, Kiyoshi; Sueshige, Takumi; Takayasu, Hideki; Takayasu, Misako

2018-03-01

A microscopic model is established for financial Brownian motion from the direct observation of the dynamics of high-frequency traders (HFTs) in a foreign exchange market. Furthermore, a theoretical framework parallel to molecular kinetic theory is developed for the systematic description of the financial market from microscopic dynamics of HFTs. We report first on a microscopic empirical law of traders' trend-following behavior by tracking the trajectories of all individuals, which quantifies the collective motion of HFTs but has not been captured in conventional order-book models. We next introduce the corresponding microscopic model of HFTs and present its theoretical solution paralleling molecular kinetic theory: Boltzmann-like and Langevin-like equations are derived from the microscopic dynamics via the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy. Our model is the first microscopic model that has been directly validated through data analysis of the microscopic dynamics, exhibiting quantitative agreements with mesoscopic and macroscopic empirical results.

Dynamics of osmosis in a porous medium.

PubMed

Cardoso, Silvana S S; Cartwright, Julyan H E

2014-11-01

We derive from kinetic theory, fluid mechanics and thermodynamics the minimal continuum-level equations governing the flow of a binary, non-electrolytic mixture in an isotropic porous medium with osmotic effects. For dilute mixtures, these equations are linear and in this limit provide a theoretical basis for the widely used semi-empirical relations of Kedem & Katchalsky (Kedem & Katchalsky 1958 Biochim. Biophys. Acta 27, 229-246 (doi:10.1016/0006-3002(58)90330-5), which have hitherto been validated experimentally but not theoretically. The above linearity between the fluxes and the driving forces breaks down for concentrated or non-ideal mixtures, for which our equations go beyond the Kedem-Katchalsky formulation. We show that the heretofore empirical solute permeability coefficient reflects the momentum transfer between the solute molecules that are rejected at a pore entrance and the solvent molecules entering the pore space; it can be related to the inefficiency of a Maxwellian demi-demon.

A model of rotationally-sampled wind turbulence for predicting fatigue loads in wind turbines

NASA Technical Reports Server (NTRS)

Spera, David A.

1995-01-01

Empirical equations are presented with which to model rotationally-sampled (R-S) turbulence for input to structural-dynamic computer codes and the calculation of wind turbine fatigue loads. These equations are derived from R-S turbulence data which were measured at the vertical-plane array in Clayton, New Mexico. For validation, the equations are applied to the calculation of cyclic flapwise blade loads for the NASA/DOE Mod-2 2.5-MW experimental HAWT's (horizontal-axis wind turbines), and the results compared to measured cyclic loads. Good correlation is achieved, indicating that the R-S turbulence model developed in this study contains the characteristics of the wind which produce many of the fatigue loads sustained by wind turbines. Empirical factors are included which permit the prediction of load levels at specified percentiles of occurrence, which is required for the generation of fatigue load spectra and the prediction of the fatigue lifetime of structures.

Design guidelines for an umbilical cord blood stem cell therapy quality assessment model

NASA Astrophysics Data System (ADS)

Januszewski, Witold S.; Michałek, Krzysztof; Yagensky, Oleksandr; Wardzińska, Marta

The paper enlists the pivotal guidelines for producing an empirical umbilical cord blood stem cell therapy quality assessment model. The methodology adapted was single equation linear model with domain knowledge derived from MEDAFAR classification. The resulting model is ready for therapeutical application.

Refractive Index of Alkali Halides and Its Wavelength and Temperature Derivatives.

DTIC Science & Technology

1975-05-01

of CoBr . . . .......... 236 82. Comparison of Dispersion Equations Proposed for CsBr ... . 237 83. Recommmded Values on the Refractive Index and Its... discovery of empirical relationships which enable us to calculate dn/dT data at 293 K for some ma- terials on which no data are available. In the data...or in handbooks. In the present work, however, this problem 160 was solved by our empirical discoveries by which the unknown parameters of Eq. (19) for

Derivation of Hodgkin-Huxley equations for a Na+ channel from a master equation for coupled activation and inactivation

NASA Astrophysics Data System (ADS)

Vaccaro, S. R.

2016-11-01

The Na+ current in nerve and muscle membranes may be described in terms of the activation variable m (t ) and the inactivation variable h (t ) , which are dependent on the transitions of S4 sensors of each of the Na+ channel domains DI to DIV. The time-dependence of the Na+ current and the rate equations satisfied by m (t ) and h (t ) may be derived from the solution to a master equation that describes the coupling between two or three activation sensors regulating the Na+ channel conductance and a two-stage inactivation process. If the inactivation rate from the closed or open states increases as the S4 sensors activate, a more general form of the Hodgkin-Huxley expression for the open-state probability may be derived where m (t ) is dependent on both activation and inactivation processes. The voltage dependence of the rate functions for inactivation and recovery from inactivation are consistent with the empirically determined expressions and exhibit saturation for both depolarized and hyperpolarized clamp potentials.

An Alternative to the Stay/Switch Equation Assessed When Using a Changeover-Delay

PubMed Central

MacDonall, James S.

2015-01-01

An alternative to the generalized matching equation for understanding concurrent performances is the stay/switch model. For the stay/switch model, the important events are the contingencies and behaviors at each alternative. The current experiment compares the descriptions by two stay/switch equations, the original, empirically derived stay/switch equation and a more theoretically derived equation based on ratios of stay to switch responses matching ratios of stay to switch reinforcers. The present experiment compared descriptions by the original stay/switch equation when using and not using a changeover delay. It also compared descriptions by the more theoretical equation with and without a changeover delay. Finally, it compared descriptions of the concurrent performances by these two equations. Rats were trained in 15 conditions on identical concurrent random-interval schedules in each component of a multiple schedule. A COD operated in only one component. There were no consistent differences in the variance accounted for by each equation of concurrent performances whether or not a COD was used. The simpler equation found greater sensitivity to stay than to switch reinforcers. It also found a COD eliminated the influence of switch reinforcers. Because estimates of parameters were more meaningful when using the more theoretical stay/switch equation it is preferred. PMID:26299548

An alternative to the stay/switch equation assessed when using a changeover-delay.

PubMed

MacDonall, James S

2015-11-01

An alternative to the generalized matching equation for understanding concurrent performances is the stay/switch model. For the stay/switch model, the important events are the contingencies and behaviors at each alternative. The current experiment compares the descriptions by two stay/switch equations, the original, empirically derived stay/switch equation and a more theoretically derived equation based on ratios of stay to switch responses matching ratios of stay to switch reinforcers. The present experiment compared descriptions by the original stay/switch equation when using and not using a changeover delay. It also compared descriptions by the more theoretical equation with and without a changeover delay. Finally, it compared descriptions of the concurrent performances by these two equations. Rats were trained in 15 conditions on identical concurrent random-interval schedules in each component of a multiple schedule. A COD operated in only one component. There were no consistent differences in the variance accounted for by each equation of concurrent performances whether or not a COD was used. The simpler equation found greater sensitivity to stay than to switch reinforcers. It also found a COD eliminated the influence of switch reinforcers. Because estimates of parameters were more meaningful when using the more theoretical stay/switch equation it is preferred. Copyright © 2015 Elsevier B.V. All rights reserved.

Modeling of Inverted Annular Film Boiling using an integral method

NASA Astrophysics Data System (ADS)

Sridharan, Arunkumar

In modeling Inverted Annular Film Boiling (IAFB), several important phenomena such as interaction between the liquid and the vapor phases and irregular nature of the interface, which greatly influence the momentum and heat transfer at the interface, need to be accounted for. However, due to the complexity of these phenomena, they were not modeled in previous studies. Since two-phase heat transfer equations and relationships rely heavily on experimental data, many closure relationships that were used in previous studies to solve the problem are empirical in nature. Also, in deriving the relationships, the experimental data were often extrapolated beyond the intended range of conditions, causing errors in predictions. In some cases, empirical correlations that were derived from situations other than IAFB, and whose applicability to IAFB was questionable, were used. Moreover, arbitrary constants were introduced in the model developed in previous studies to provide good fit to the experimental data. These constants have no physical basis, thereby leading to questionable accuracy in the model predictions. In the present work, modeling of Inverted Annular Film Boiling (IAFB) is done using Integral Method. Two-dimensional formulation of IAFB is presented. Separate equations for the conservation of mass, momentum and energy are derived from first principles, for the vapor film and the liquid core. Turbulence is incorporated in the formulation. The system of second-order partial differential equations is integrated over the radial direction to obtain a system of integral differential equations. In order to solve the system of equations, second order polynomial profiles are used to describe the nondimensional velocity and temperatures. The unknown coefficients in the profiles are functions of the axial direction alone. Using the boundary conditions that govern the physical problem, equations for the unknown coefficients are derived in terms of the primary dependent variables: wall shear stress, interfacial shear stress, film thickness, pressure, wall temperature and the mass transfer rate due to evaporation. A system of non-linear first order coupled ordinary differential equations is obtained. Due to the inherent mathematical complexity of the system of equations, simplifying assumptions are made to obtain a numerical solution. The system of equations is solved numerically to obtain values of the unknown quantities at each subsequent axial location. Derived quantities like void fraction and heat transfer coefficient are calculated at each axial location. The calculation is terminated when the void fraction reaches a value of 0.6, the upper limit of IAFB. The results obtained agree with the experimental trends observed. Void fraction increases along the heated length, while the heat transfer coefficient drops due to the increased resistance of the vapor film as expected.

Quantitative reconstruction of cross-sectional dimensions and hydrological parameters of gravelly fluvial channels developed in a forearc basin setting under a temperate climatic condition, central Japan

NASA Astrophysics Data System (ADS)

Shibata, Kenichiro; Adhiperdana, Billy G.; Ito, Makoto

2018-01-01

Reconstructions of the dimensions and hydrological features of ancient fluvial channels, such as bankfull depth, bankfull width, and water discharges, have used empirical equations developed from compiled data-sets, mainly from modern meandering rivers, in various tectonic and climatic settings. However, the application of the proposed empirical equations to an ancient fluvial succession should be carefully examined with respect to the tectonic and climatic settings of the objective deposits. In this study, we developed empirical relationships among the mean bankfull channel depth, bankfull channel depth, drainage area, bankfull channel width, mean discharge, and bankfull discharge using data from 24 observation sites of modern gravelly rivers in the Kanto region, central Japan. Some of the equations among these parameters are different from those proposed by previous studies. The discrepancies are considered to reflect tectonic and climatic settings of the present river systems, which are characterized by relatively steeper valley slope, active supply of volcaniclastic sediments, and seasonal precipitation in the Kanto region. The empirical relationships derived from the present study can be applied to modern and ancient gravelly fluvial channels with multiple and alternate bars, developed in convergent margin settings under a temperate climatic condition. The developed empirical equations were applied to a transgressive gravelly fluvial succession of the Paleogene Iwaki Formation, Northeast Japan as a case study. Stratigraphic thicknesses of bar deposits were used for estimation of the bankfull channel depth. In addition, some other geomorphological and hydrological parameters were calculated using the empirical equations developed by the present study. The results indicate that the Iwaki Formation fluvial deposits were formed by a fluvial system that was represented by the dimensions and discharges of channels similar to those of the middle to lower reaches of the modern Kuji River, northern Kanto region. In addition, no distinct temporal changes in paleochannel dimensions and discharges were observed in an overall transgressive Iwaki Formation fluvial system. This implies that a rise in relative sea level did not affect the paleochannel dimensions within a sequence stratigraphic framework.

Spatial and Temporal Evaluation of Soil Erosion with RUSLE: A Case Study in an Olive Orchard Microcathment in Spain

EPA Science Inventory

Soil loss is commonly estimated using the Revised Universal Soil Loss Equation (RUSLE). Since RUSLE is an empirically based soil loss model derived from surveys on plots, the high spatial and temporal variability of erosion in Mediterranean environments and scale effects provoke...

Spatial and Temporal Evaluation of Soil Erosion with RUSLE: A case Study in an Olive Orchard Microcathment in Spain

EPA Science Inventory

Soil loss is commonly estimated using the Revised Universal Soil Loss Equation (RUSLE). Since RUSLE is an empirically based soil loss model derived from surveys on plots, the high spatial and temporal variability of erosion in Mediterranean environments and scale effects provo...

Sea Ice Freeboard and Thickness from the 2013 IceBridge ATM and DMS Data in Ross Sea, Antarctica

NASA Astrophysics Data System (ADS)

Xie, H.; Tian, L.; Tang, J.; Ackley, S. F.

2016-12-01

In November (20, 21, 27, and 28) 2013, NASA's IceBridge mission flew over the Ross Sea, Antarctica and collected important sea ice data with the ATM and DMS for the first time. We will present our methods to derive the local sea level and total freeboard for ice thickness retrieval from these two datasets. The methods include (1) leads classification from DMS data using an automated lead detection method, (2) potential leads from the reflectance of less than 0.25 from the ATM laser shots of L1B data, (3) local sea level retrieval based on these qualified ATM laser shots (L1B) within the DMS-derived leads (after outliers removal from the mean ± 2 standard deviation of these ATM elevations), (4) establishment of an empirical equation of local sea level as a function of distance from the starting point of each IceBridge flight, (5) total freeboard retrieval from the ATM L2 elevations by subtracting the local sea level derived from the empirical equation, and (6) ice thickness retrieval. The ice thickness derived from this method will be analyzed and compared with ICESat data (2003-2009) and other available data for the same region at the similar time period. Possible change and potential reasons will be identified and discussed.

The rate of bubble growth in a superheated liquid in pool boiling

NASA Astrophysics Data System (ADS)

Abdollahi, Mohammad Reza; Jafarian, Mehdi; Jamialahmadi, Mohammad

2017-12-01

A semi-empirical model for the estimation of the rate of bubble growth in nucleate pool boiling is presented, considering a new equation to estimate the temperature history of the bubble in the bulk of liquid. The conservation equations of energy, mass and momentum have been firstly derived and solved analytically. The present analytical model of the bubble growth predicts that the radius of the bubble grows as a function of √{t}.{\\operatorname{erf}}( N√{t}) , while so far the bubble growth rate has been mainly correlated to √{t} in the previous studies. In the next step, the analytical solutions were used to develop a new semi-empirical equation. To achieve this, firstly the analytical solution were non-dimensionalised and then the experimental data, available in the literature, were applied to tune the dimensionless coefficients appeared in the dimensionless equation. Finally, the reliability of the proposed semi-empirical model was assessed through comparison of the model predictions with the available experimental data in the literature, which were not applied in the tuning of the dimensionless parameters of the model. The comparison of the model predictions with other proposed models in the literature was also performed. These comparisons show that this model enables more accurate predictions than previously proposed models with a deviation of less than 10% in a wide range of operating conditions.

Body composition of Colombian women.

PubMed

Spurr, G B; Reina, J C; Li, S J; de Orozco, B; Dufour, D L

1994-08-01

Measurements of anthropometry and total body water (TBW) were made in 99 women 19-44 y of age living in socioeconomically deprived circumstances in Cali, Colombia. TBW was measured by dilution of deuterium oxide. An empirical equation for estimating lean body mass (LBM) was derived and applied satisfactorily to an independent study group. Comparisons were also made with body-composition values obtained by the Durnin and Womersley equations and an equation derived from rural women living in Guatemala. Neither set of equations was suitable for use with the Colombian subjects because both significantly overestimated LBM and therefore underestimated body fat. Lower values of standing height in older women suggest that they may have been subjected to more severe undernutrition during their growth than the younger subjects. When compared with a group of US women, Colombian subjects were less physically fit and had greater subcutaneous-fat deposits, which were distributed over the trunk and limbs, whereas body mass indexes and waist-hip ratios were not significantly different.

Renormalization of the fragmentation equation: exact self-similar solutions and turbulent cascades.

PubMed

Saveliev, V L; Gorokhovski, M A

2012-12-01

Using an approach developed earlier for renormalization of the Boltzmann collision integral [Saveliev and Nanbu, Phys. Rev. E 65, 051205 (2002)], we derive an exact divergence form for the fragmentation operator. Then we reduce the fragmentation equation to the continuity equation in size space, with the flux given explicitly. This allows us to obtain self-similar solutions and to find the integral of motion for these solutions (we call it the bare flux). We show how these solutions can be applied as a description of cascade processes in three- and two-dimensional turbulence. We also suggested an empirical cascade model of impact fragmentation of brittle materials.

Universal equation for estimating ideal body weight and body weight at any BMI1

PubMed Central

Peterson, Courtney M; Thomas, Diana M; Blackburn, George L; Heymsfield, Steven B

2016-01-01

Background: Ideal body weight (IBW) equations and body mass index (BMI) ranges have both been used to delineate healthy or normal weight ranges, although these 2 different approaches are at odds with each other. In particular, past IBW equations are misaligned with BMI values, and unlike BMI, the equations have failed to recognize that there is a range of ideal or target body weights. Objective: For the first time, to our knowledge, we merged the concepts of a linear IBW equation and of defining target body weights in terms of BMI. Design: With the use of calculus and approximations, we derived an easy-to-use linear equation that clinicians can use to calculate both IBW and body weight at any target BMI value. We measured the empirical accuracy of the equation with the use of NHANES data and performed a comparative analysis with past IBW equations. Results: Our linear equation allowed us to calculate body weights for any BMI and height with a mean empirical accuracy of 0.5–0.7% on the basis of NHANES data. Moreover, we showed that our body weight equation directly aligns with BMI values for both men and women, which avoids the overestimation and underestimation problems at the upper and lower ends of the height spectrum that have plagued past IBW equations. Conclusions: Our linear equation increases the sophistication of IBW equations by replacing them with a single universal equation that calculates both IBW and body weight at any target BMI and height. Therefore, our equation is compatible with BMI and can be applied with the use of mental math or a calculator without the need for an app, which makes it a useful tool for both health practitioners and the general public. PMID:27030535

Universal equation for estimating ideal body weight and body weight at any BMI.

PubMed

Peterson, Courtney M; Thomas, Diana M; Blackburn, George L; Heymsfield, Steven B

2016-05-01

Ideal body weight (IBW) equations and body mass index (BMI) ranges have both been used to delineate healthy or normal weight ranges, although these 2 different approaches are at odds with each other. In particular, past IBW equations are misaligned with BMI values, and unlike BMI, the equations have failed to recognize that there is a range of ideal or target body weights. For the first time, to our knowledge, we merged the concepts of a linear IBW equation and of defining target body weights in terms of BMI. With the use of calculus and approximations, we derived an easy-to-use linear equation that clinicians can use to calculate both IBW and body weight at any target BMI value. We measured the empirical accuracy of the equation with the use of NHANES data and performed a comparative analysis with past IBW equations. Our linear equation allowed us to calculate body weights for any BMI and height with a mean empirical accuracy of 0.5-0.7% on the basis of NHANES data. Moreover, we showed that our body weight equation directly aligns with BMI values for both men and women, which avoids the overestimation and underestimation problems at the upper and lower ends of the height spectrum that have plagued past IBW equations. Our linear equation increases the sophistication of IBW equations by replacing them with a single universal equation that calculates both IBW and body weight at any target BMI and height. Therefore, our equation is compatible with BMI and can be applied with the use of mental math or a calculator without the need for an app, which makes it a useful tool for both health practitioners and the general public. © 2016 American Society for Nutrition.

Advancing individual tree biomass prediction: assessment and alternatives to the component ratio method

Treesearch

Aaron Weiskittel; Jereme Frank; David Walker; Phil Radtke; David Macfarlane; James Westfall

2015-01-01

Prediction of forest biomass and carbon is becoming important issues in the United States. However, estimating forest biomass and carbon is difficult and relies on empirically-derived regression equations. Based on recent findings from a national gap analysis and comprehensive assessment of the USDA Forest Service Forest Inventory and Analysis (USFS-FIA) component...

Use of NMR logging to obtain estimates of hydraulic conductivity in the High Plains aquifer, Nebraska, USA

USGS Publications Warehouse

Dlubac, Katherine; Knight, Rosemary; Song, Yi-Qiao; Bachman, Nate; Grau, Ben; Cannia, Jim; Williams, John

2013-01-01

Hydraulic conductivity (K) is one of the most important parameters of interest in groundwater applications because it quantifies the ease with which water can flow through an aquifer material. Hydraulic conductivity is typically measured by conducting aquifer tests or wellbore flow (WBF) logging. Of interest in our research is the use of proton nuclear magnetic resonance (NMR) logging to obtain information about water-filled porosity and pore space geometry, the combination of which can be used to estimate K. In this study, we acquired a suite of advanced geophysical logs, aquifer tests, WBF logs, and sidewall cores at the field site in Lexington, Nebraska, which is underlain by the High Plains aquifer. We first used two empirical equations developed for petroleum applications to predict K from NMR logging data: the Schlumberger Doll Research equation (KSDR) and the Timur-Coates equation (KT-C), with the standard empirical constants determined for consolidated materials. We upscaled our NMR-derived K estimates to the scale of the WBF-logging K(KWBF-logging) estimates for comparison. All the upscaled KT-C estimates were within an order of magnitude of KWBF-logging and all of the upscaled KSDR estimates were within 2 orders of magnitude of KWBF-logging. We optimized the fit between the upscaled NMR-derived K and KWBF-logging estimates to determine a set of site-specific empirical constants for the unconsolidated materials at our field site. We conclude that reliable estimates of K can be obtained from NMR logging data, thus providing an alternate method for obtaining estimates of K at high levels of vertical resolution.

Quasi-two-layer morphodynamic model for bedload-dominated problems: bed slope-induced morphological diffusion

NASA Astrophysics Data System (ADS)

Maldonado, Sergio; Borthwick, Alistair G. L.

2018-02-01

We derive a two-layer depth-averaged model of sediment transport and morphological evolution for application to bedload-dominated problems. The near-bed transport region is represented by the lower (bedload) layer which has an arbitrarily constant, vanishing thickness (of approx. 10 times the sediment particle diameter), and whose average sediment concentration is free to vary. Sediment is allowed to enter the upper layer, and hence the total load may also be simulated, provided that concentrations of suspended sediment remain low. The model conforms with established theories of bedload, and is validated satisfactorily against empirical expressions for sediment transport rates and the morphodynamic experiment of a migrating mining pit by Lee et al. (1993 J. Hydraul. Eng. 119, 64-80 (doi:10.1061/(ASCE)0733-9429(1993)119:1(64))). Investigation into the effect of a local bed gradient on bedload leads to derivation of an analytical, physically meaningful expression for morphological diffusion induced by a non-zero local bed slope. Incorporation of the proposed morphological diffusion into a conventional morphodynamic model (defined as a coupling between the shallow water equations, Exner equation and an empirical formula for bedload) improves model predictions when applied to the evolution of a mining pit, without the need either to resort to special numerical treatment of the equations or to use additional tuning parameters.

Quasi-two-layer morphodynamic model for bedload-dominated problems: bed slope-induced morphological diffusion.

PubMed

Maldonado, Sergio; Borthwick, Alistair G L

2018-02-01

We derive a two-layer depth-averaged model of sediment transport and morphological evolution for application to bedload-dominated problems. The near-bed transport region is represented by the lower (bedload) layer which has an arbitrarily constant, vanishing thickness (of approx. 10 times the sediment particle diameter), and whose average sediment concentration is free to vary. Sediment is allowed to enter the upper layer, and hence the total load may also be simulated, provided that concentrations of suspended sediment remain low. The model conforms with established theories of bedload, and is validated satisfactorily against empirical expressions for sediment transport rates and the morphodynamic experiment of a migrating mining pit by Lee et al. (1993 J. Hydraul. Eng. 119 , 64-80 (doi:10.1061/(ASCE)0733-9429(1993)119:1(64))). Investigation into the effect of a local bed gradient on bedload leads to derivation of an analytical, physically meaningful expression for morphological diffusion induced by a non-zero local bed slope. Incorporation of the proposed morphological diffusion into a conventional morphodynamic model (defined as a coupling between the shallow water equations, Exner equation and an empirical formula for bedload) improves model predictions when applied to the evolution of a mining pit, without the need either to resort to special numerical treatment of the equations or to use additional tuning parameters.

Ozone generation by negative direct current corona discharges in dry air fed coaxial wire-cylinder reactors

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

Yehia, Ashraf; Mizuno, Akira

An analytical study was made in this paper for calculating the ozone generation by negative dc corona discharges. The corona discharges were formed in a coaxial wire-cylinder reactor. The reactor was fed by dry air flowing with constant rates at atmospheric pressure and room temperature, and stressed by a negative dc voltage. The current-voltage characteristics of the negative dc corona discharges formed inside the reactor were measured in parallel with concentration of the generated ozone under different operating conditions. An empirical equation was derived from the experimental results for calculating the ozone concentration generated inside the reactor. The results, thatmore » have been recalculated by using the derived equation, have agreed with the experimental results over the whole range of the investigated parameters, except in the saturation range for the ozone concentration. Therefore, the derived equation represents a suitable criterion for expecting the ozone concentration generated by negative dc corona discharges in dry air fed coaxial wire-cylinder reactors under any operating conditions in range of the investigated parameters.« less

On the effects of nonlinear boundary conditions in diffusive logistic equations on bounded domains

NASA Astrophysics Data System (ADS)

Cantrell, Robert Stephen; Cosner, Chris

We study a diffusive logistic equation with nonlinear boundary conditions. The equation arises as a model for a population that grows logistically inside a patch and crosses the patch boundary at a rate that depends on the population density. Specifically, the rate at which the population crosses the boundary is assumed to decrease as the density of the population increases. The model is motivated by empirical work on the Glanville fritillary butterfly. We derive local and global bifurcation results which show that the model can have multiple equilibria and in some parameter ranges can support Allee effects. The analysis leads to eigenvalue problems with nonstandard boundary conditions.

Renormalization of the fragmentation equation: Exact self-similar solutions and turbulent cascades

NASA Astrophysics Data System (ADS)

Saveliev, V. L.; Gorokhovski, M. A.

2012-12-01

Using an approach developed earlier for renormalization of the Boltzmann collision integral [Saveliev and Nanbu, Phys. Rev. E1539-375510.1103/PhysRevE.65.051205 65, 051205 (2002)], we derive an exact divergence form for the fragmentation operator. Then we reduce the fragmentation equation to the continuity equation in size space, with the flux given explicitly. This allows us to obtain self-similar solutions and to find the integral of motion for these solutions (we call it the bare flux). We show how these solutions can be applied as a description of cascade processes in three- and two-dimensional turbulence. We also suggested an empirical cascade model of impact fragmentation of brittle materials.

The Rayleigh-Taylor instability in a self-gravitating two-layer viscous sphere

NASA Astrophysics Data System (ADS)

Mondal, Puskar; Korenaga, Jun

2018-03-01

The dispersion relation of the Rayleigh-Taylor instability in the spherical geometry is of profound importance in the context of the Earth's core formation. Here we present a complete derivation of this dispersion relation for a self-gravitating two-layer viscous sphere. Such relation is, however, obtained through the solution of a complex transcendental equation, and it is difficult to gain physical insights directly from the transcendental equation itself. We thus also derive an empirical formula to compute the growth rate, by combining the Monte Carlo sampling of the relevant model parameter space with linear regression. Our analysis indicates that the growth rate of Rayleigh-Taylor instability is most sensitive to the viscosity of inner layer in a physical setting that is most relevant to the core formation.

Statistical Mechanical Model for Adsorption Coupled with SAFT-VR Mie Equation of State.

PubMed

Franco, Luís F M; Economou, Ioannis G; Castier, Marcelo

2017-10-24

We extend the SAFT-VR Mie equation of state to calculate adsorption isotherms by considering explicitly the residual energy due to the confinement effect. Assuming a square-well potential for the fluid-solid interactions, the structure imposed by the fluid-solid interface is calculated using two different approaches: an empirical expression proposed by Travalloni et al. ( Chem. Eng. Sci. 65 , 3088 - 3099 , 2010 ), and a new theoretical expression derived by applying the mean value theorem. Adopting the SAFT-VR Mie ( Lafitte et al. J. Chem. Phys. , 139 , 154504 , 2013 ) equation of state to describe the fluid-fluid interactions, and solving the phase equilibrium criteria, we calculate adsorption isotherms for light hydrocarbons adsorbed in a carbon molecular sieve and for carbon dioxide, nitrogen, and water adsorbed in a zeolite. Good results are obtained from the model using either approach. Nonetheless, the theoretical expression seems to correlate better the experimental data than the empirical one, possibly implying that a more reliable way to describe the structure ensures a better description of the thermodynamic behavior.

An empirically derived basis for calculating the area, rate, and distribution of water-drop impingement on airfoils

NASA Technical Reports Server (NTRS)

Bergrun, Norman R

1952-01-01

An empirically derived basis for predicting the area, rate, and distribution of water-drop impingement on airfoils of arbitrary section is presented. The concepts involved represent an initial step toward the development of a calculation technique which is generally applicable to the design of thermal ice-prevention equipment for airplane wing and tail surfaces. It is shown that sufficiently accurate estimates, for the purpose of heated-wing design, can be obtained by a few numerical computations once the velocity distribution over the airfoil has been determined. The calculation technique presented is based on results of extensive water-drop trajectory computations for five airfoil cases which consisted of 15-percent-thick airfoils encompassing a moderate lift-coefficient range. The differential equations pertaining to the paths of the drops were solved by a differential analyzer.

Dynamical Stochastic Processes of Returns in Financial Markets

NASA Astrophysics Data System (ADS)

Kim, Kyungsik; Kim, Soo Yong; Lim, Gyuchang; Zhou, Junyuan; Yoon, Seung-Min

2006-03-01

We show how the evolution of probability distribution functions of the returns from the tick data of the Korean treasury bond futures (KTB) and the S&P 500 stock index can be described by means of the Fokker-Planck equation. We derive the Fokker- Planck equation from the estimated Kramers-Moyal coefficients estimated directly from the empirical data. By analyzing the statistics of the returns, we present the quantitative deterministic and random influences on both financial time series, for which we can give a simple physical interpretation. Finally, we remark that the diffusion coefficient should be significantly considered to make a portfolio.

Stochastic modelling of non-stationary financial assets

NASA Astrophysics Data System (ADS)

Estevens, Joana; Rocha, Paulo; Boto, João P.; Lind, Pedro G.

2017-11-01

We model non-stationary volume-price distributions with a log-normal distribution and collect the time series of its two parameters. The time series of the two parameters are shown to be stationary and Markov-like and consequently can be modelled with Langevin equations, which are derived directly from their series of values. Having the evolution equations of the log-normal parameters, we reconstruct the statistics of the first moments of volume-price distributions which fit well the empirical data. Finally, the proposed framework is general enough to study other non-stationary stochastic variables in other research fields, namely, biology, medicine, and geology.

Full nonlinear treatment of the global thermospheric wind system. Part 1: Mathematical method and analysis of forces

NASA Technical Reports Server (NTRS)

Blum, P. W.; Harris, I.

1973-01-01

The equations of horizontal motion of the neutral atmosphere between 120 and 500 km are integrated with the inclusion of all the nonlinear terms of the convective derivative and the viscous forces due to vertical and horizontal velocity gradients. Empirical models of the distribution of neutral and charged particles are assumed to be known. The model of velocities developed is a steady state model. In part 1 the mathematical method used in the integration of the Navier-Stokes equations is described and the various forces are analysed.

Development of Semi-Empirical Damping Equation for Baffled Tank with Oblate Spheroidal Dome

NASA Technical Reports Server (NTRS)

Yang, H. Q.; West, Jeff; Brodnick, Jacob; Eberhart, Chad

2016-01-01

Propellant slosh is a potential source of disturbance that can significantly impact the stability of space vehicles. The slosh dynamics are typically represented by a mechanical model of a spring-mass-damper. This mechanical model is then included in the equation of motion of the entire vehicle for Guidance, Navigation and Control analysis. The typical parameters required by the mechanical model include natural frequency of the slosh, slosh mass, slosh mass center location, and the critical damping ratio. A fundamental study has been undertaken at NASA MSFC to understand the fluid damping physics from a ring baffle in the barrel section of a propellant tank. An asymptotic damping equation and CFD blended equation have been derived by NASA MSFC team to complement the popularly used Miles equation at different flow regimes. The new development has found success in providing a nonlinear damping model for the Space Launch System. The purpose of this study is to further extend the semi-empirical damping equations into the oblate spheroidal dome section of the propellant tanks. First, previous experimental data from the spherical baffled tank are collected and analyzed. Several methods of taking the dome curvature effect, including a generalized Miles equation, area projection method, and equalized fill height method, are assessed. CFD simulation is used to shed light on the interaction of vorticity around the baffle with the locally curved wall and liquid-gas interface. The final damping equation will be validated by a recent subscale test with an oblate spheroidal dome conducted at NASA MSFC.

Regressed relations for forced convection heat transfer in a direct injection stratified charge rotary engine

NASA Technical Reports Server (NTRS)

Lee, Chi M.; Schock, Harold J.

1988-01-01

Currently, the heat transfer equation used in the rotary combustion engine (RCE) simulation model is taken from piston engine studies. These relations have been empirically developed by the experimental input coming from piston engines whose geometry differs considerably from that of the RCE. The objective of this work was to derive equations to estimate heat transfer coefficients in the combustion chamber of an RCE. This was accomplished by making detailed temperature and pressure measurements in a direct injection stratified charge (DISC) RCE under a range of conditions. For each specific measurement point, the local gas velocity was assumed equal to the local rotor tip speed. Local physical properties of the fluids were then calculated. Two types of correlation equations were derived and are described in this paper. The first correlation expresses the Nusselt number as a function of the Prandtl number, Reynolds number, and characteristic temperature ratio; the second correlation expresses the forced convection heat transfer coefficient as a function of fluid temperature, pressure and velocity.

Prediction of the Dynamic Yield Strength of Metals Using Two Structural-Temporal Parameters

NASA Astrophysics Data System (ADS)

Selyutina, N. S.; Petrov, Yu. V.

2018-02-01

The behavior of the yield strength of steel and a number of aluminum alloys is investigated in a wide range of strain rates, based on the incubation time criterion of yield and the empirical models of Johnson-Cook and Cowper-Symonds. In this paper, expressions for the parameters of the empirical models are derived through the characteristics of the incubation time criterion; a satisfactory agreement of these data and experimental results is obtained. The parameters of the empirical models can depend on some strain rate. The independence of the characteristics of the incubation time criterion of yield from the loading history and their connection with the structural and temporal features of the plastic deformation process give advantage of the approach based on the concept of incubation time with respect to empirical models and an effective and convenient equation for determining the yield strength in a wider range of strain rates.

A five-step procedure for the clinical use of the MPD in neuropsychological assessment of children.

PubMed

Wallbrown, F H; Fuller, G B

1984-01-01

Described a five-step procedure that can be used to detect organicity on the basis of children's performance on the Minnesota Percepto Diagnostic Test (MPD). The first step consists of examining the T score for rotations to determine whether it is below the cut-off score, which has been established empirically as an indicator of organicity. The second step consists of matching the examinee's configuration of error scores, separation of circle-diamond (SpCD), distortion of circle-diamond (DCD), and distortion of dots (DD), with empirically derived tables. The third step consists of considering the T score for rotations and error configuration jointly. The fourth step consists of using empirically established discriminant equations, and the fifth step involves using data from limits testing and other data sources. The clinical and empirical bases for the five-step procedure also are discussed.

Effect of quantity and composition of waste on the prediction of annual methane potential from landfills.

PubMed

Cho, Han Sang; Moon, Hee Sun; Kim, Jae Young

2012-04-01

A study was conducted to investigate the effect of waste composition change on the methane production in landfills. An empirical equation for the methane potential of the mixed waste is derived based on the methane potential values of individual waste components and the compositional ratio of waste components. A correction factor was introduced in the equation and was determined from the BMP and lysimeter tests. The equation and LandGEM were applied for a full size landfill and the annual methane potential was estimated. Results showed that the changes in quantity of waste affected the annual methane potential from the landfill more than the changes of waste composition. Copyright © 2012 Elsevier Ltd. All rights reserved.

Effect of collision energy optimization on the measurement of peptides by selected reaction monitoring (SRM) mass spectrometry.

PubMed

Maclean, Brendan; Tomazela, Daniela M; Abbatiello, Susan E; Zhang, Shucha; Whiteaker, Jeffrey R; Paulovich, Amanda G; Carr, Steven A; Maccoss, Michael J

2010-12-15

Proteomics experiments based on Selected Reaction Monitoring (SRM, also referred to as Multiple Reaction Monitoring or MRM) are being used to target large numbers of protein candidates in complex mixtures. At present, instrument parameters are often optimized for each peptide, a time and resource intensive process. Large SRM experiments are greatly facilitated by having the ability to predict MS instrument parameters that work well with the broad diversity of peptides they target. For this reason, we investigated the impact of using simple linear equations to predict the collision energy (CE) on peptide signal intensity and compared it with the empirical optimization of the CE for each peptide and transition individually. Using optimized linear equations, the difference between predicted and empirically derived CE values was found to be an average gain of only 7.8% of total peak area. We also found that existing commonly used linear equations fall short of their potential, and should be recalculated for each charge state and when introducing new instrument platforms. We provide a fully automated pipeline for calculating these equations and individually optimizing CE of each transition on SRM instruments from Agilent, Applied Biosystems, Thermo-Scientific and Waters in the open source Skyline software tool ( http://proteome.gs.washington.edu/software/skyline ).

Heavy use of equations impedes communication among biologists.

PubMed

Fawcett, Tim W; Higginson, Andrew D

2012-07-17

Most research in biology is empirical, yet empirical studies rely fundamentally on theoretical work for generating testable predictions and interpreting observations. Despite this interdependence, many empirical studies build largely on other empirical studies with little direct reference to relevant theory, suggesting a failure of communication that may hinder scientific progress. To investigate the extent of this problem, we analyzed how the use of mathematical equations affects the scientific impact of studies in ecology and evolution. The density of equations in an article has a significant negative impact on citation rates, with papers receiving 28% fewer citations overall for each additional equation per page in the main text. Long, equation-dense papers tend to be more frequently cited by other theoretical papers, but this increase is outweighed by a sharp drop in citations from nontheoretical papers (35% fewer citations for each additional equation per page in the main text). In contrast, equations presented in an accompanying appendix do not lessen a paper's impact. Our analysis suggests possible strategies for enhancing the presentation of mathematical models to facilitate progress in disciplines that rely on the tight integration of theoretical and empirical work.

Errors in calculated oncotic pressure of dog plasma.

PubMed

Gabel, J C; Scott, R L; Adair, T H; Drake, R E; Traber, D L

1980-12-01

Several equations to calculate plasma oncotic pressure (pi) from the total protein concentration (C) have been previously described. These equations were derived empirically from samples with a wide range of C obtained by diluting or concentrating normal plasma samples. To test these equations over a range of naturally occurring C, we measured C and pi of plasma samples from 40 dogs. C ranged from 5.3 to 8.7 g/dl and averaged 6.5 +/- 0.1 (mean +/- SE) and pi averaged 17.9 +/- 0.3 mmHg. The regression equation was pi = 78.14 + 1.67 C (r = 0.74). pi increased with C much less than predicted with the commonly used equations. The albumin-to-globulin concentration ratios (A/G), determined in 27 of the dogs, decreased with increasing C (A/G = 1.56-0.128 C, r = 0.62). The lower A/G at the higher C's could cause the lower than predicted increase in pi with C, because the equations were developed from data in which A/G was constant.

Semiempirical Two-Dimensional Magnetohydrodynamic Model of the Solar Corona and Interplanetary Medium

NASA Technical Reports Server (NTRS)

Sittler, Edward C., Jr.; Guhathakurta, Madhulika

1999-01-01

We have developed a two-dimensional semiempirical MHD model of the solar corona and solar wind. The model uses empirically derived electron density profiles from white-light coronagraph data measured during the Skylub period and an empirically derived model of the magnetic field which is fitted to observed streamer topologies, which also come from the white-light coronagraph data The electron density model comes from that developed by Guhathakurta and coworkers. The electron density model is extended into interplanetary space by using electron densities derived from the Ulysses plasma instrument. The model also requires an estimate of the solar wind velocity as a function of heliographic latitude and radial component of the magnetic field at 1 AU, both of which can be provided by the Ulysses spacecraft. The model makes estimates as a function of radial distance and latitude of various fluid parameters of the plasma such as flow velocity V, effective temperature T(sub eff), and effective heat flux q(sub eff), which are derived from the equations of conservation of mass, momentum, and energy, respectively. The term effective indicates that wave contributions could be present. The model naturally provides the spiral pattern of the magnetic field far from the Sun and an estimate of the large-scale surface magnetic field at the Sun, which we estimate to be approx. 12 - 15 G. The magnetic field model shows that the large-scale surface magnetic field is dominated by an octupole term. The model is a steady state calculation which makes the assumption of azimuthal symmetry and solves the various conservation equations in the rotating frame of the Sun. The conservation equations are integrated along the magnetic field direction in the rotating frame of the Sun, thus providing a nearly self-consistent calculation of the fluid parameters. The model makes a minimum number of assumptions about the physics of the solar corona and solar wind and should provide a very accurate empirical description of the solar corona and solar wind Once estimates of mass density rho, flow velocity V, effective temperature T(sub eff), effective heat flux q(sub eff), and magnetic field B are computed from the model and waves are assumed unimportant, all other plasma parameters such as Mach number, Alfven speed, gyrofrequency, etc. can be derived as a function of radial distance and latitude from the Sun. The model can be used as a planning tool for such missions as Slar Probe and provide an empirical framework for theoretical models of the solar corona and solar wind The model will be used to construct a semiempirical MHD description of the steady state solar corona and solar wind using the SOHO Large Angle Spectrometric Coronagraph (LASCO) polarized brightness white-light coronagraph data, SOHO Extreme Ultraviolet Imaging Telescope data, and Ulysses plasma data.

Electrochemical carbon dioxide concentrator: Math model

NASA Technical Reports Server (NTRS)

Marshall, R. D.; Schubert, F. H.; Carlson, J. N.

1973-01-01

A steady state computer simulation model of an Electrochemical Depolarized Carbon Dioxide Concentrator (EDC) has been developed. The mathematical model combines EDC heat and mass balance equations with empirical correlations derived from experimental data to describe EDC performance as a function of the operating parameters involved. The model is capable of accurately predicting performance over EDC operating ranges. Model simulation results agree with the experimental data obtained over the prediction range.

Design optimization of a brush turbine with a cleaner/water based solution

NASA Technical Reports Server (NTRS)

Kim, Rhyn H.

1995-01-01

Recently, a turbine-brush was analyzed based on the energy conservation and the force momentum equation with an empirical relationship of the drag coefficient. An equation was derived to predict the rotational speed of the turbine-brush in terms of the blade angle, number of blades, rest of geometries of the turbine-brush and the incoming velocity. Using the observed flow conditions, drag coefficients were determined. Based on the experimental values as boundary conditions, the turbine-brush flows were numerically simulated to understand first the nature of the flows, and to extend the observed drag coefficient to a flow without holding the turbine-brush.

Estimation of instantaneous heat transfer coefficients for a direct-injection stratified-charge rotary engine

NASA Technical Reports Server (NTRS)

Lee, C. M.; Addy, H. E.; Bond, T. H.; Chun, K. S.; Lu, C. Y.

1987-01-01

The main objective of this report was to derive equations to estimate heat transfer coefficients in both the combustion chamber and coolant pasage of a rotary engine. This was accomplished by making detailed temperature and pressure measurements in a direct-injection stratified-charge rotary engine under a range of conditions. For each sppecific measurement point, the local physical properties of the fluids were calculated. Then an empirical correlation of the coefficients was derived by using a multiple regression program. This correlation expresses the Nusselt number as a function of the Prandtl number and Reynolds number.

The basic science and mathematics of random mutation and natural selection.

PubMed

Kleinman, Alan

2014-12-20

The mutation and natural selection phenomenon can and often does cause the failure of antimicrobial, herbicidal, pesticide and cancer treatments selection pressures. This phenomenon operates in a mathematically predictable behavior, which when understood leads to approaches to reduce and prevent the failure of the use of these selection pressures. The mathematical behavior of mutation and selection is derived using the principles given by probability theory. The derivation of the equations describing the mutation and selection phenomenon is carried out in the context of an empirical example. Copyright © 2014 John Wiley & Sons, Ltd.

Study on the Optimization and Process Modeling of the Rotary Ultrasonic Machining of Zerodur Glass-Ceramic

NASA Astrophysics Data System (ADS)

Pitts, James Daniel

Rotary ultrasonic machining (RUM), a hybrid process combining ultrasonic machining and diamond grinding, was created to increase material removal rates for the fabrication of hard and brittle workpieces. The objective of this research was to experimentally derive empirical equations for the prediction of multiple machined surface roughness parameters for helically pocketed rotary ultrasonic machined Zerodur glass-ceramic workpieces by means of a systematic statistical experimental approach. A Taguchi parametric screening design of experiments was employed to systematically determine the RUM process parameters with the largest effect on mean surface roughness. Next empirically determined equations for the seven common surface quality metrics were developed via Box-Behnken surface response experimental trials. Validation trials were conducted resulting in predicted and experimental surface roughness in varying levels of agreement. The reductions in cutting force and tool wear associated with RUM, reported by previous researchers, was experimentally verified to also extended to helical pocketing of Zerodur glass-ceramic.

Positive direct current corona discharges in single wire-duct electrostatic precipitators

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

Yehia, Ashraf, E-mail: yehia30161@yahoo.com; Department of Physics, Faculty of Science, Assiut University, Assiut 71516, Arab Republic of Egypt; Abdel-Fattah, E.

This paper is aimed to study the characteristics of the positive dc corona discharges in single wire-duct electrostatic precipitators. Therefore, the corona discharges were formed inside dry air fed single wire-duct reactor under positive dc voltage at the normal atmospheric conditions. The corona current-voltage characteristics curves have been measured in parallel with the ozone concentration generated inside the reactor under different discharge conditions. The corona current-voltage characteristics curves have agreed with a semi empirical equation derived from the previous studies. The experimental results of the ozone concentration generated inside the reactor were formulated in the form of an empirical equationmore » included the different parameters that were studied experimentally. The obtained equations are valid to expect both the current-voltage characteristics curves and the corresponding ozone concentration that generates with the positive dc corona discharges inside single wire-duct electrostatic precipitators under any operating conditions in the same range of the present study.« less

Impact of the Equation of State in Models for Surfactant Spreading Experiments

NASA Astrophysics Data System (ADS)

Levy, Rachel

2014-11-01

Pulmonary surfactant spreading models often rely on an equation of state relating surfactant concentration to surface tension. Mathematically, these models have been analyzed with simple functional relationships. However, to model an experiment with a given fluid and surfactant, a physically meaningful equation of state can be derived from experimentally obtained isotherms. We discuss the comparison between model and experiment for NBD-PC lipid (surfactant) spreading on glycerol for an empirically-determined equation of state, and compare those results to simulations with traditionally employed functional forms. In particular we compare the timescales by tracking the leading edge of surfactant, the central fluid height and dynamics of the Marangoni ridge. We consider both outward spreading of a disk-shaped region of surfactant and the hole-closure problem in which a disk-shaped surfactant-free region self-heals. Support from NSF-DMS-FRG 0968154, RCSA-CCS-19788, and HHMI.

Uncertainty in Measurement: A Review of Monte Carlo Simulation Using Microsoft Excel for the Calculation of Uncertainties Through Functional Relationships, Including Uncertainties in Empirically Derived Constants

PubMed Central

Farrance, Ian; Frenkel, Robert

2014-01-01

The Guide to the Expression of Uncertainty in Measurement (usually referred to as the GUM) provides the basic framework for evaluating uncertainty in measurement. The GUM however does not always provide clearly identifiable procedures suitable for medical laboratory applications, particularly when internal quality control (IQC) is used to derive most of the uncertainty estimates. The GUM modelling approach requires advanced mathematical skills for many of its procedures, but Monte Carlo simulation (MCS) can be used as an alternative for many medical laboratory applications. In particular, calculations for determining how uncertainties in the input quantities to a functional relationship propagate through to the output can be accomplished using a readily available spreadsheet such as Microsoft Excel. The MCS procedure uses algorithmically generated pseudo-random numbers which are then forced to follow a prescribed probability distribution. When IQC data provide the uncertainty estimates the normal (Gaussian) distribution is generally considered appropriate, but MCS is by no means restricted to this particular case. With input variations simulated by random numbers, the functional relationship then provides the corresponding variations in the output in a manner which also provides its probability distribution. The MCS procedure thus provides output uncertainty estimates without the need for the differential equations associated with GUM modelling. The aim of this article is to demonstrate the ease with which Microsoft Excel (or a similar spreadsheet) can be used to provide an uncertainty estimate for measurands derived through a functional relationship. In addition, we also consider the relatively common situation where an empirically derived formula includes one or more ‘constants’, each of which has an empirically derived numerical value. Such empirically derived ‘constants’ must also have associated uncertainties which propagate through the functional relationship and contribute to the combined standard uncertainty of the measurand. PMID:24659835

Uncertainty in measurement: a review of monte carlo simulation using microsoft excel for the calculation of uncertainties through functional relationships, including uncertainties in empirically derived constants.

PubMed

Farrance, Ian; Frenkel, Robert

2014-02-01

The Guide to the Expression of Uncertainty in Measurement (usually referred to as the GUM) provides the basic framework for evaluating uncertainty in measurement. The GUM however does not always provide clearly identifiable procedures suitable for medical laboratory applications, particularly when internal quality control (IQC) is used to derive most of the uncertainty estimates. The GUM modelling approach requires advanced mathematical skills for many of its procedures, but Monte Carlo simulation (MCS) can be used as an alternative for many medical laboratory applications. In particular, calculations for determining how uncertainties in the input quantities to a functional relationship propagate through to the output can be accomplished using a readily available spreadsheet such as Microsoft Excel. The MCS procedure uses algorithmically generated pseudo-random numbers which are then forced to follow a prescribed probability distribution. When IQC data provide the uncertainty estimates the normal (Gaussian) distribution is generally considered appropriate, but MCS is by no means restricted to this particular case. With input variations simulated by random numbers, the functional relationship then provides the corresponding variations in the output in a manner which also provides its probability distribution. The MCS procedure thus provides output uncertainty estimates without the need for the differential equations associated with GUM modelling. The aim of this article is to demonstrate the ease with which Microsoft Excel (or a similar spreadsheet) can be used to provide an uncertainty estimate for measurands derived through a functional relationship. In addition, we also consider the relatively common situation where an empirically derived formula includes one or more 'constants', each of which has an empirically derived numerical value. Such empirically derived 'constants' must also have associated uncertainties which propagate through the functional relationship and contribute to the combined standard uncertainty of the measurand.

A possible closure relation for heat transport in the solar wind

NASA Technical Reports Server (NTRS)

Feldman, W. C.; Asbridge, J. R.; Bame, S. J.; Gosling, J. T.; Lemons, D. S.

1979-01-01

The objective of the present paper is to search for an empirical closure relation for solar wind heat transport that applies to a microscopic scale. This task is approached by using the quasi-linear wave-particle formalism proposed by Perkins (1973) as a guide to derive an equation relating the relative drift speed between core-electron and proton populations to local bulk flow conditions. The resulting relationship, containing one free parameter, is found to provide a good characterization of Los Alamos Imp electron data measuring during the period from March 1971 through August 1974. An empirical closure relation is implied by this result because of the observed proportionality between heat flux and relative drift speed.

Analysis of the Effects of Thermal Environment on Optical Systems for Navigation Guidance and Control in Supersonic Aircraft Based on Empirical Equations

PubMed Central

Cheng, Xuemin; Yang, Yikang; Hao, Qun

2016-01-01

The thermal environment is an important factor in the design of optical systems. This study investigated the thermal analysis technology of optical systems for navigation guidance and control in supersonic aircraft by developing empirical equations for the front temperature gradient and rear thermal diffusion distance, and for basic factors such as flying parameters and the structure of the optical system. Finite element analysis (FEA) was used to study the relationship between flying and front dome parameters and the system temperature field. Systematic deduction was then conducted based on the effects of the temperature field on the physical geometry and ray tracing performance of the front dome and rear optical lenses, by deriving the relational expressions between the system temperature field and the spot size and positioning precision of the rear optical lens. The optical systems used for navigation guidance and control in supersonic aircraft when the flight speed is in the range of 1–5 Ma were analysed using the derived equations. Using this new method it was possible to control the precision within 10% when considering the light spot received by the four-quadrant detector, and computation time was reduced compared with the traditional method of separately analysing the temperature field of the front dome and rear optical lens using FEA. Thus, the method can effectively increase the efficiency of parameter analysis and computation in an airborne optical system, facilitating the systematic, effective and integrated thermal analysis of airborne optical systems for navigation guidance and control. PMID:27763515

Equation of state of dense nuclear matter and neutron star structure from nuclear chiral interactions

NASA Astrophysics Data System (ADS)

Bombaci, Ignazio; Logoteta, Domenico

2018-02-01

Aims: We report a new microscopic equation of state (EOS) of dense symmetric nuclear matter, pure neutron matter, and asymmetric and β-stable nuclear matter at zero temperature using recent realistic two-body and three-body nuclear interactions derived in the framework of chiral perturbation theory (ChPT) and including the Δ(1232) isobar intermediate state. This EOS is provided in tabular form and in parametrized form ready for use in numerical general relativity simulations of binary neutron star merging. Here we use our new EOS for β-stable nuclear matter to compute various structural properties of non-rotating neutron stars. Methods: The EOS is derived using the Brueckner-Bethe-Goldstone quantum many-body theory in the Brueckner-Hartree-Fock approximation. Neutron star properties are next computed solving numerically the Tolman-Oppenheimer-Volkov structure equations. Results: Our EOS models are able to reproduce the empirical saturation point of symmetric nuclear matter, the symmetry energy Esym, and its slope parameter L at the empirical saturation density n0. In addition, our EOS models are compatible with experimental data from collisions between heavy nuclei at energies ranging from a few tens of MeV up to several hundreds of MeV per nucleon. These experiments provide a selective test for constraining the nuclear EOS up to 4n0. Our EOS models are consistent with present measured neutron star masses and particularly with the mass M = 2.01 ± 0.04 M⊙ of the neutron stars in PSR J0348+0432.

Analysis of the Effects of Thermal Environment on Optical Systems for Navigation Guidance and Control in Supersonic Aircraft Based on Empirical Equations.

PubMed

Cheng, Xuemin; Yang, Yikang; Hao, Qun

2016-10-17

The thermal environment is an important factor in the design of optical systems. This study investigated the thermal analysis technology of optical systems for navigation guidance and control in supersonic aircraft by developing empirical equations for the front temperature gradient and rear thermal diffusion distance, and for basic factors such as flying parameters and the structure of the optical system. Finite element analysis (FEA) was used to study the relationship between flying and front dome parameters and the system temperature field. Systematic deduction was then conducted based on the effects of the temperature field on the physical geometry and ray tracing performance of the front dome and rear optical lenses, by deriving the relational expressions between the system temperature field and the spot size and positioning precision of the rear optical lens. The optical systems used for navigation guidance and control in supersonic aircraft when the flight speed is in the range of 1-5 Ma were analysed using the derived equations. Using this new method it was possible to control the precision within 10% when considering the light spot received by the four-quadrant detector, and computation time was reduced compared with the traditional method of separately analysing the temperature field of the front dome and rear optical lens using FEA. Thus, the method can effectively increase the efficiency of parameter analysis and computation in an airborne optical system, facilitating the systematic, effective and integrated thermal analysis of airborne optical systems for navigation guidance and control.

Measuring the effects of heat wave episodes on the human body's thermal balance

NASA Astrophysics Data System (ADS)

Katavoutas, George; Theoharatos, George; Flocas, Helena A.; Asimakopoulos, Dimosthenis N.

2009-03-01

During the peak of an extensive heat wave episode on 23-25 July 2007, simultaneous thermophysiological measurements were made in two non-acclimated healthy adults of different sex in a suburban area of Greater Athens, Greece. Based on experimental measurements of mean skin temperature and metabolic heat production, heat fluxes to and from the human body were calculated, and the biometeorological index heat load (HL) produced was determined according to the heat balance equation. Comparing experimental values with those derived from theoretical estimates revealed a great heat stress for both individuals, especially the male, while theoretical values underestimated heat stress. The study also revealed that thermophysiological factors, such as mean skin temperature and metabolic heat production, play an important role in determining heat fluxes patterns in the heat balance equation. The theoretical values of mean skin temperature as derived from an empirical equation may not be appropriate to describe the changes that take place in a non-acclimated individual. Furthermore, the changes in metabolic heat production were significant even for standard activity.

Use of a Spreadsheet to Help Students Understand the Origin of the Empirical Equation that Allows Estimation of the Extinction Coefficients of Proteins

ERIC Educational Resources Information Center

Sims, Paul A.

2012-01-01

A brief history of the development of the empirical equation that is used by prominent, Internet-based programs to estimate (or calculate) the extinction coefficients of proteins is presented. In addition, an overview of a series of related assignments designed to help students understand the origin of the empirical equation is provided. The…

A Comparison of Two-Stage Approaches for Fitting Nonlinear Ordinary Differential Equation (ODE) Models with Mixed Effects

PubMed Central

Chow, Sy-Miin; Bendezú, Jason J.; Cole, Pamela M.; Ram, Nilam

2016-01-01

Several approaches currently exist for estimating the derivatives of observed data for model exploration purposes, including functional data analysis (FDA), generalized local linear approximation (GLLA), and generalized orthogonal local derivative approximation (GOLD). These derivative estimation procedures can be used in a two-stage process to fit mixed effects ordinary differential equation (ODE) models. While the performance and utility of these routines for estimating linear ODEs have been established, they have not yet been evaluated in the context of nonlinear ODEs with mixed effects. We compared properties of the GLLA and GOLD to an FDA-based two-stage approach denoted herein as functional ordinary differential equation with mixed effects (FODEmixed) in a Monte Carlo study using a nonlinear coupled oscillators model with mixed effects. Simulation results showed that overall, the FODEmixed outperformed both the GLLA and GOLD across all the embedding dimensions considered, but a novel use of a fourth-order GLLA approach combined with very high embedding dimensions yielded estimation results that almost paralleled those from the FODEmixed. We discuss the strengths and limitations of each approach and demonstrate how output from each stage of FODEmixed may be used to inform empirical modeling of young children’s self-regulation. PMID:27391255

A Comparison of Two-Stage Approaches for Fitting Nonlinear Ordinary Differential Equation Models with Mixed Effects.

PubMed

Chow, Sy-Miin; Bendezú, Jason J; Cole, Pamela M; Ram, Nilam

2016-01-01

Several approaches exist for estimating the derivatives of observed data for model exploration purposes, including functional data analysis (FDA; Ramsay & Silverman, 2005 ), generalized local linear approximation (GLLA; Boker, Deboeck, Edler, & Peel, 2010 ), and generalized orthogonal local derivative approximation (GOLD; Deboeck, 2010 ). These derivative estimation procedures can be used in a two-stage process to fit mixed effects ordinary differential equation (ODE) models. While the performance and utility of these routines for estimating linear ODEs have been established, they have not yet been evaluated in the context of nonlinear ODEs with mixed effects. We compared properties of the GLLA and GOLD to an FDA-based two-stage approach denoted herein as functional ordinary differential equation with mixed effects (FODEmixed) in a Monte Carlo (MC) study using a nonlinear coupled oscillators model with mixed effects. Simulation results showed that overall, the FODEmixed outperformed both the GLLA and GOLD across all the embedding dimensions considered, but a novel use of a fourth-order GLLA approach combined with very high embedding dimensions yielded estimation results that almost paralleled those from the FODEmixed. We discuss the strengths and limitations of each approach and demonstrate how output from each stage of FODEmixed may be used to inform empirical modeling of young children's self-regulation.

A comparison between two powder compaction parameters of plasticity: the effective medium A parameter and the Heckel 1/K parameter.

PubMed

Mahmoodi, Foad; Klevan, Ingvild; Nordström, Josefina; Alderborn, Göran; Frenning, Göran

2013-09-10

The purpose of the research was to introduce a procedure to derive a powder compression parameter (EM A) representing particle yield stress using an effective medium equation and to compare the EM A parameter with the Heckel compression parameter (1/K). 16 pharmaceutical powders, including drugs and excipients, were compressed in a materials testing instrument and powder compression profiles were derived using the EM and Heckel equations. The compression profiles thus obtained could be sub-divided into regions among which one region was approximately linear and from this region, the compression parameters EM A and 1/K were calculated. A linear relationship between the EM A parameter and the 1/K parameter was obtained with a strong correlation. The slope of the plot was close to 1 (0.84) and the intercept of the plot was small in comparison to the range of parameter values obtained. The relationship between the theoretical EM A parameter and the 1/K parameter supports the interpretation of the empirical Heckel parameter as being a measure of yield stress. It is concluded that the combination of Heckel and EM equations represents a suitable procedure to derive a value of particle plasticity from powder compression data. Copyright © 2013 Elsevier B.V. All rights reserved.

Empirical equations for viscosity and specific heat capacity determination of paraffin PCM and fatty acid PCM

NASA Astrophysics Data System (ADS)

Barreneche, C.; Ferrer, G.; Palacios, A.; Solé, A.; Inés Fernández, A.; Cabeza, L. F.

2017-10-01

Phase change materials (PCM) used in thermal energy storage (TES) systems have been presented, over recent years, as one of the most effective options in energy storage. Paraffin and fatty acids are some of the most used PCM in TES systems, as they have high phase change enthalpy and in addition they do not present subcooling nor hysteresis and have proper cycling stability. The simulations and design of TES systems require the knowledge of the thermophysical properties of PCM. Thermal conductivity, viscosity, specific heat capacity (Cp) can be experimentally determined, but these are material and time consuming tasks. To avoid or to reduce them, and to have reliable data without the need of experimentation, thermal properties can be calculated by empirical equations. In this study, five different equations are given to calculate the viscosity and specific heat capacity of fatty acid PCM and paraffin PCM. Two of these equations concern, respectively, the empirical calculation of the viscosity and liquid Cp of the whole paraffin PCM family, while the other three equations presented are for the corresponding calculation of viscosity, solid Cp, liquid Cp of the whole fatty acid family of PCM. Therefore, this study summarize the work performed to obtain the main empirical equations to measure the above mentioned properties for whole fatty acid PCM family and whole paraffin PCM family. Moreover, empirical equations have been obtained to calculate these properties for other materials of these PCM groups and these empirical equations can be extrapolated for PCM with higher or lower phase change temperatures within a lower relative error 4%.

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

Sorin Zaharia; C.Z. Cheng

In this paper, we study whether the magnetic field of the T96 empirical model can be in force balance with an isotropic plasma pressure distribution. Using the field of T96, we obtain values for the pressure P by solving a Poisson-type equation {del}{sup 2}P = {del} {center_dot} (J x B) in the equatorial plane, and 1-D profiles on the Sun-Earth axis by integrating {del}P = J x B. We work in a flux coordinate system in which the magnetic field is expressed in terms of Euler potentials. Our results lead to the conclusion that the T96 model field cannot bemore » in equilibrium with an isotropic pressure. We also analyze in detail the computation of Birkeland currents using the Vasyliunas relation and the T96 field, which yields unphysical results, again indicating the lack of force balance in the empirical model. The underlying reason for the force imbalance is likely the fact that the derivatives of the least-square fitted model B are not accurate predictions of the actual magnetospheric field derivatives. Finally, we discuss a possible solution to the problem of lack of force balance in empirical field models.« less

Modeling of outgassing and matrix decomposition in carbon-phenolic composites

NASA Technical Reports Server (NTRS)

Mcmanus, Hugh L.

1993-01-01

A new release rate equation to model the phase change of water to steam in composite materials was derived from the theory of molecular diffusion and equilibrium moisture concentration. The new model is dependent on internal pressure, the microstructure of the voids and channels in the composite materials, and the diffusion properties of the matrix material. Hence, it is more fundamental and accurate than the empirical Arrhenius rate equation currently in use. The model was mathematically formalized and integrated into the thermostructural analysis code CHAR. Parametric studies on variation of several parameters have been done. Comparisons to Arrhenius and straight-line models show that the new model produces physically realistic results under all conditions.

High Reynolds number turbulence model of rotating shear flows

NASA Astrophysics Data System (ADS)

Masuda, S.; Ariga, I.; Koyama, H. S.

1983-09-01

A Reynolds stress closure model for rotating turbulent shear flows is developed. Special attention is paid to keeping the model constants independent of rotation. First, general forms of the model of a Reynolds stress equation and a dissipation rate equation are derived, the only restrictions of which are high Reynolds number and incompressibility. The model equations are then applied to two-dimensional equilibrium boundary layers and the effects of Coriolis acceleration on turbulence structures are discussed. Comparisons with the experimental data and with previous results in other external force fields show that there exists a very close analogy between centrifugal, buoyancy and Coriolis force fields. Finally, the model is applied to predict the two-dimensional boundary layers on rotating plane walls. Comparisons with existing data confirmed its capability of predicting mean and turbulent quantities without employing any empirical relations in rotating fields.

Physics, stability, and dynamics of supply networks

NASA Astrophysics Data System (ADS)

Helbing, Dirk; Lämmer, Stefan; Seidel, Thomas; Šeba, Pétr; Płatkowski, Tadeusz

2004-12-01

We show how to treat supply networks as physical transport problems governed by balance equations and equations for the adaptation of production speeds. Although the nonlinear behavior is different, the linearized set of coupled differential equations is formally related to those of mechanical or electrical oscillator networks. Supply networks possess interesting features due to their complex topology and directed links. We derive analytical conditions for absolute and convective instabilities. The empirically observed “bullwhip effect” in supply chains is explained as a form of convective instability based on resonance effects. Moreover, it is generalized to arbitrary supply networks. Their related eigenvalues are usually complex, depending on the network structure (even without loops). Therefore, their generic behavior is characterized by damped or growing oscillations. We also show that regular distribution networks possess two negative eigenvalues only, but perturbations generate a spectrum of complex eigenvalues.

Gibbs Sampler-Based λ-Dynamics and Rao-Blackwell Estimator for Alchemical Free Energy Calculation.

PubMed

Ding, Xinqiang; Vilseck, Jonah Z; Hayes, Ryan L; Brooks, Charles L

2017-06-13

λ-dynamics is a generalized ensemble method for alchemical free energy calculations. In traditional λ-dynamics, the alchemical switch variable λ is treated as a continuous variable ranging from 0 to 1 and an empirical estimator is utilized to approximate the free energy. In the present article, we describe an alternative formulation of λ-dynamics that utilizes the Gibbs sampler framework, which we call Gibbs sampler-based λ-dynamics (GSLD). GSLD, like traditional λ-dynamics, can be readily extended to calculate free energy differences between multiple ligands in one simulation. We also introduce a new free energy estimator, the Rao-Blackwell estimator (RBE), for use in conjunction with GSLD. Compared with the current empirical estimator, the advantage of RBE is that RBE is an unbiased estimator and its variance is usually smaller than the current empirical estimator. We also show that the multistate Bennett acceptance ratio equation or the unbinned weighted histogram analysis method equation can be derived using the RBE. We illustrate the use and performance of this new free energy computational framework by application to a simple harmonic system as well as relevant calculations of small molecule relative free energies of solvation and binding to a protein receptor. Our findings demonstrate consistent and improved performance compared with conventional alchemical free energy methods.

Stochastic theory of fatigue corrosion

NASA Astrophysics Data System (ADS)

Hu, Haiyun

1999-10-01

A stochastic theory of corrosion has been constructed. The stochastic equations are described giving the transportation corrosion rate and fluctuation corrosion coefficient. In addition the pit diameter distribution function, the average pit diameter and the most probable pit diameter including other related empirical formula have been derived. In order to clarify the effect of stress range on the initiation and growth behaviour of pitting corrosion, round smooth specimen were tested under cyclic loading in 3.5% NaCl solution.

Radar-aeolian roughness project

NASA Technical Reports Server (NTRS)

Greeley, Ronald; Dobrovolskis, A.; Gaddis, L.; Iversen, J. D.; Lancaster, N.; Leach, Rodman N.; Rasnussen, K.; Saunders, S.; Vanzyl, J.; Wall, S.

1991-01-01

The objective is to establish an empirical relationship between measurements of radar, aeolian, and surface roughness on a variety of natural surfaces and to understand the underlying physical causes. This relationship will form the basis for developing a predictive equation to derive aeolian roughness from radar backscatter. Results are given from investigations carried out in 1989 on the principal elements of the project, with separate sections on field studies, radar data analysis, laboratory simulations, and development of theory for planetary applications.

A Computer Model for Evaluating the Effects on Fighting Vehicle Crewmembers of Exposure to Carbon Monoxide Emissions.

DTIC Science & Technology

1980-01-01

SUPPLEMENTARY NOTES Is. KEY WORDS (Continue on reverse ede If neceseay id Identify by block number) Carbon Monoxide (CO) Computer Program Carboxyhemoglobin ...several researchers, which predicts the instantaneous amount of carboxyhemoglobin (COHb) in the blood of a person based upon the amount of carbon monoxide...developed from an empirical equation (derived from reference I and detailed in reference 3) which predicts the amount of carboxyhemoglobin (COHb) in

Relationship between the Kubelka-Munk scattering and radiative transfer coefficients.

PubMed

Thennadil, Suresh N

2008-07-01

The relationship between the Kubelka-Munk (K-M) and the transport scattering coefficient is obtained through a semi-empirical approach. This approach gives the same result as that given by Gate [Appl. Opt.13, 236 (1974)] when the incident beam is diffuse. This result and those given by Star et al. [Phys. Med. Biol.33, 437 (1988)] and Brinkworth [Appl. Opt.11, 1434 (1972)] are compared with the exact solution of the radiative transfer equation over a large range of optical properties. It is found that the latter expressions, which include an absorption component, do not give accurate results over the range considered. Using the semi-empirical approach, the relationship between the K-M and the transport scattering coefficient is derived for the case where the incident light is collimated. It is shown that although the K-M equation is derived based on diffuse incident light, it can also represent very well the reflectance from a slab of infinite thickness when the incident light is collimated. However, in this case the relationship between the coefficients has to include a function that is dependent on the anisotropy factor. Analysis indicates that the K-M transform achieves the objective of obtaining a measure that gives the ratio of absorption to scattering effects for both diffuse and collimated incident beams over a large range of optical properties.

Single wall penetration equations

NASA Technical Reports Server (NTRS)

Hayashida, K. B.; Robinson, J. H.

1991-01-01

Five single plate penetration equations are compared for accuracy and effectiveness. These five equations are two well-known equations (Fish-Summers and Schmidt-Holsapple), two equations developed by the Apollo project (Rockwell and Johnson Space Center (JSC), and one recently revised from JSC (Cour-Palais). They were derived from test results, with velocities ranging up to 8 km/s. Microsoft Excel software was used to construct a spreadsheet to calculate the diameters and masses of projectiles for various velocities, varying the material properties of both projectile and target for the five single plate penetration equations. The results were plotted on diameter versus velocity graphs for ballistic and spallation limits using Cricket Graph software, for velocities ranging from 2 to 15 km/s defined for the orbital debris. First, these equations were compared to each other, then each equation was compared with various aluminum projectile densities. Finally, these equations were compared with test results performed at JSC for the Marshall Space Flight Center. These equations predict a wide variety of projectile diameters at a given velocity. Thus, it is very difficult to choose the 'right' prediction equation. The thickness of a single plate could have a large variation by choosing a different penetration equation. Even though all five equations are empirically developed with various materials, especially for aluminum alloys, one cannot be confident in the shield design with the predictions obtained by the penetration equations without verifying by tests.

New Equations for the Sublimation Pressure and Melting Pressure of H2O Ice Ih

NASA Astrophysics Data System (ADS)

Wagner, Wolfgang; Riethmann, Thomas; Feistel, Rainer; Harvey, Allan H.

2011-12-01

New reference equations, adopted by the International Association for the Properties of Water and Steam (IAPWS), are presented for the sublimation pressure and melting pressure of ice Ih as a function of temperature. These equations are based on input values derived from the phase-equilibrium condition between the IAPWS-95 scientific standard for thermodynamic properties of fluid H2O and the equation of state of H2O ice Ih adopted by IAPWS in 2006, making them thermodynamically consistent with the bulk-phase properties. Compared to the previous IAPWS formulations, which were empirical fits to experimental data, the new equations have significantly less uncertainty. The sublimation-pressure equation covers the temperature range from 50 K to the vapor-liquid-solid triple point at 273.16 K. The ice Ih melting-pressure equation describes the entire melting curve from 273.16 K to the ice Ih-ice III-liquid triple point at 251.165 K. For completeness, we also give the IAPWS melting-pressure equation for ice III, which is slightly adjusted to agree with the ice Ih melting-pressure equation at the corresponding triple point, and the unchanged IAPWS melting-pressure equations for ice V, ice VI, and ice VII.

Correlation of plume opacity with particles and sulfates from boilers

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

Lou, J.C.; Lee, M.; Chen, K.S.

1997-07-01

The effects of emission concentrations of particulate matters and sulfates on plume opacity are investigated by in situ measurements. The studies are conducted for three processes of two coal-fired plants and one oil-fired that are all equipped with electrostatic precipitators. Flue-gas sampling and analysis include the concentrations of particles and total water soluble sulfates, particle size distribution, and flue-gas composition; while in-stack and out-of-stack opacities are determined by a transmissometer and certified smoke inspectors, respectively. Experimental results show that plume opacity outside the stack linearly correlates well with the in-stack opacity. The mixing of hot flue gas with cold ambientmore » air would result in the condensation of hygroscopic sulfuric acid aerosols and an increase about 1.6% out of typical 15--25% measured opacity. An empirical equation similar to the Beer-Lambert-Bouger form is derived for predicting the plume opacity in terms of the stack diameter and the concentrations of particles and total water soluble sulfates. Good comparisons are achieved between predictions by the empirical equation and other available field data.« less

Charge Transport in Nonaqueous Liquid Electrolytes: A Paradigm Shift

DTIC Science & Technology

2015-05-18

that provide inadequate descriptions of experimental data, often using empirical equations whose fitting parameters have no physical significance...provide inadequate descriptions of experimental data, often using empirical equations whose fitting parameters have no physical significance...Ea The hydrodynamic model, utilizing the Stokes equation describes isothermal conductivity, self-diffusion coefficient, and the dielectric

Generalized master equations for non-Poisson dynamics on networks.

PubMed

Hoffmann, Till; Porter, Mason A; Lambiotte, Renaud

2012-10-01

The traditional way of studying temporal networks is to aggregate the dynamics of the edges to create a static weighted network. This implicitly assumes that the edges are governed by Poisson processes, which is not typically the case in empirical temporal networks. Accordingly, we examine the effects of non-Poisson inter-event statistics on the dynamics of edges, and we apply the concept of a generalized master equation to the study of continuous-time random walks on networks. We show that this equation reduces to the standard rate equations when the underlying process is Poissonian and that its stationary solution is determined by an effective transition matrix whose leading eigenvector is easy to calculate. We conduct numerical simulations and also derive analytical results for the stationary solution under the assumption that all edges have the same waiting-time distribution. We discuss the implications of our work for dynamical processes on temporal networks and for the construction of network diagnostics that take into account their nontrivial stochastic nature.

Generalized master equations for non-Poisson dynamics on networks

NASA Astrophysics Data System (ADS)

Hoffmann, Till; Porter, Mason A.; Lambiotte, Renaud

2012-10-01

The traditional way of studying temporal networks is to aggregate the dynamics of the edges to create a static weighted network. This implicitly assumes that the edges are governed by Poisson processes, which is not typically the case in empirical temporal networks. Accordingly, we examine the effects of non-Poisson inter-event statistics on the dynamics of edges, and we apply the concept of a generalized master equation to the study of continuous-time random walks on networks. We show that this equation reduces to the standard rate equations when the underlying process is Poissonian and that its stationary solution is determined by an effective transition matrix whose leading eigenvector is easy to calculate. We conduct numerical simulations and also derive analytical results for the stationary solution under the assumption that all edges have the same waiting-time distribution. We discuss the implications of our work for dynamical processes on temporal networks and for the construction of network diagnostics that take into account their nontrivial stochastic nature.

Non-Linear Steady State Vibrations of Beams Excited by Vortex Shedding

NASA Astrophysics Data System (ADS)

LEWANDOWSKI, R.

2002-05-01

In this paper the non-linear vibrations of beams excited by vortex-shedding are considered. In particular, the steady state responses of beams near the synchronization region are taken into account. The main aerodynamic properties of wind are described by using the semi-empirical model proposed by Hartlen and Currie. The finite element method and the strip method are used to formulate the equation of motion of the system treated. The harmonic balance method is adopted to derive the amplitude equations. These equations are solved with the help of the continuation method which is very convenient to perform the parametric studies of the problem and to determine the response curve in the synchronization region. Moreover, the equations of motion are also integrated using the Newmark method. The results of calculations of several example problems are also shown to confirm the efficiency and accuracy of the presented method. The results obtained by the harmonic balance method and by the Newmark methods are in good agreement with each other.

Is Directivity Still Effective in a PSHA Framework?

NASA Astrophysics Data System (ADS)

Spagnuolo, E.; Herrero, A.; Cultrera, G.

2008-12-01

Source rupture parameters, like directivity, modulate the energy release causing variations in the radiated signal amplitude. Thus they affect the empirical predictive equations and as a consequence the seismic hazard assessment. Classical probabilistic hazard evaluations, e.g. Cornell (1968), use very simple predictive equations only based on magnitude and distance which do not account for variables concerning the rupture process. However nowadays, a few predictive equations (e.g. Somerville 1997, Spudich and Chiou 2008) take into account for rupture directivity. Also few implementations have been made in a PSHA framework (e.g. Convertito et al. 2006, Rowshandel 2006). In practice, these new empirical predictive models incorporate quantitatively the rupture propagation effects through the introduction of variables like rake, azimuth, rupture velocity and laterality. The contribution of all these variables is summarized in corrective factors derived from measuring differences between the real data and the predicted ones Therefore, it's possible to keep the older computation, making use of a simple predictive model, and besides, to incorporate the directivity effect through the corrective factors. Any single supplementary variable meaning a new integral in the parametric space. However the difficulty consists of the constraints on parameter distribution functions. We present the preliminary result for ad hoc distributions (Gaussian, uniform distributions) in order to test the impact of incorporating directivity into PSHA models. We demonstrate that incorporating directivity in PSHA by means of the new predictive equations may lead to strong percentage variations in the hazard assessment.

Synoptic, Global Mhd Model For The Solar Corona

NASA Astrophysics Data System (ADS)

Cohen, Ofer; Sokolov, I. V.; Roussev, I. I.; Gombosi, T. I.

2007-05-01

The common techniques for mimic the solar corona heating and the solar wind acceleration in global MHD models are as follow. 1) Additional terms in the momentum and energy equations derived from the WKB approximation for the Alfv’en wave turbulence; 2) some empirical heat source in the energy equation; 3) a non-uniform distribution of the polytropic index, γ, used in the energy equation. In our model, we choose the latter approach. However, in order to get a more realistic distribution of γ, we use the empirical Wang-Sheeley-Arge (WSA) model to constrain the MHD solution. The WSA model provides the distribution of the asymptotic solar wind speed from the potential field approximation; therefore it also provides the distribution of the kinetic energy. Assuming that far from the Sun the total energy is dominated by the energy of the bulk motion and assuming the conservation of the Bernoulli integral, we can trace the total energy along a magnetic field line to the solar surface. On the surface the gravity is known and the kinetic energy is negligible. Therefore, we can get the surface distribution of γ as a function of the final speed originating from this point. By interpolation γ to spherically uniform value on the source surface, we use this spatial distribution of γ in the energy equation to obtain a self-consistent, steady state MHD solution for the solar corona. We present the model result for different Carrington Rotations.

Modeling interfacial area transport in multi-fluid systems

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

Yarbro, Stephen Lee

1996-11-01

Many typical chemical engineering operations are multi-fluid systems. They are carried out in distillation columns (vapor/liquid), liquid-liquid contactors (liquid/liquid) and other similar devices. An important parameter is interfacial area concentration, which determines the rate of interfluid heat, mass and momentum transfer and ultimately, the overall performance of the equipment. In many cases, the models for determining interfacial area concentration are empirical and can only describe the cases for which there is experimental data. In an effort to understand multiphase reactors and the mixing process better, a multi-fluid model has been developed as part of a research effort to calculate interfacialmore » area transport in several different types of in-line static mixers. For this work, the ensemble-averaged property conservation equations have been derived for each fluid and for the mixture. These equations were then combined to derive a transport equation for the interfacial area concentration. The final, one-dimensional model was compared to interfacial area concentration data from two sizes of Kenics in-line mixer, two sizes of concurrent jet and a Tee mixer. In all cases, the calculated and experimental data compared well with the highest scatter being with the Tee mixer comparison.« less

Frequency equation for the submicron CMOS ring oscillator using the first order characterization

NASA Astrophysics Data System (ADS)

Koithyar, Aravinda; Ramesh, T. K.

2018-05-01

By utilizing the first order behavior of the device, an equation for the frequency of operation of the submicron CMOS ring oscillator is presented. A 5-stage ring oscillator is utilized as the initial design, with different Beta ratios, for the computation of the operating frequency. Later on, the circuit simulation is performed from 5-stage till 23-stage, with the range of oscillating frequency being 3.0817 and 0.6705 GHz respectively. It is noted that the output frequency is inversely proportional to the square of the device length, and when the value of Beta ratio is used as 2.3, a difference of 3.64% is observed on an average, in between the computed and the simulated values of frequency. As an outcome, the derived equation can be utilized, with the inclusion of an empirical constant in general, for arriving at the ring oscillator circuit’s output frequency.

Modeling duckweed growth in wastewater treatment systems

USGS Publications Warehouse

Landesman, L.; Parker, N.C.; Fedler, C.B.; Konikoff, M.

2005-01-01

Species of the genera Lemnaceae, or duckweeds, are floating aquatic plants that show great promise for both wastewater treatment and livestock feed production. Research conducted in the Southern High Plains of Texas has shown that Lemna obscura grew well in cattle feedlot runoff water and produced leaf tissue with a high protein content. A model or mathematical expression derived from duckweed growth data was used to fit data from experiments conducted in a greenhouse in Lubbock, Texas. The relationship between duckweed growth and the total nitrogen concentration in the mediium follows the Mitscherlich Function and is similar to that of other plants. Empirically derived model equations have successfully predicted the growth response of Lemna obscura.

The amorphous state: first-principles derivation of the Gordon-Taylor equation for direct prediction of the glass transition temperature of mixtures; estimation of the crossover temperature of fragile glass formers; physical basis of the "Rule of 2/3".

PubMed

Skrdla, Peter J; Floyd, Philip D; Dell'Orco, Philip C

2017-08-09

Predicting the glass transition temperature (T g ) of mixtures has applications that span across industries and scientific disciplines. By plotting experimentally determined T g values as a function of the glass composition, one can usually apply the Gordon-Taylor (G-T) equation to determine the slope, k, which subsequently can be used in T g predictions. Traditionally viewed as a phenomenological/empirical model, this work proposes a physical basis for the G-T equation. The proposed equations allow for the calculation of k directly and, hence, they determine/predict the T g values of mixtures algebraically. Two derivations for k are provided, one for strong glass-formers and the other for fragile mixtures, with the modeled trehalose-water and naproxen-indomethacin systems serving as examples of each. Separately, a new equation is described for the first time that allows for the direct determination of the crossover temperature, T x , for fragile glass-formers. Lastly, the so-called "Rule of 2/3", which is commonly used to estimate the T g of a pure amorphous phase based solely on the fusion/melting temperature, T f , of the corresponding crystalline phase, is shown to be underpinned by the heat capacity ratio of the two phases referenced to a common temperature, as evidenced by the calculations put forth for indomethacin and felodipine.

Comparison of artificial intelligence methods and empirical equations to estimate daily solar radiation

NASA Astrophysics Data System (ADS)

Mehdizadeh, Saeid; Behmanesh, Javad; Khalili, Keivan

2016-08-01

In the present research, three artificial intelligence methods including Gene Expression Programming (GEP), Artificial Neural Networks (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) as well as, 48 empirical equations (10, 12 and 26 equations were temperature-based, sunshine-based and meteorological parameters-based, respectively) were used to estimate daily solar radiation in Kerman, Iran in the period of 1992-2009. To develop the GEP, ANN and ANFIS models, depending on the used empirical equations, various combinations of minimum air temperature, maximum air temperature, mean air temperature, extraterrestrial radiation, actual sunshine duration, maximum possible sunshine duration, sunshine duration ratio, relative humidity and precipitation were considered as inputs in the mentioned intelligent methods. To compare the accuracy of empirical equations and intelligent models, root mean square error (RMSE), mean absolute error (MAE), mean absolute relative error (MARE) and determination coefficient (R2) indices were used. The results showed that in general, sunshine-based and meteorological parameters-based scenarios in ANN and ANFIS models presented high accuracy than mentioned empirical equations. Moreover, the most accurate method in the studied region was ANN11 scenario with five inputs. The values of RMSE, MAE, MARE and R2 indices for the mentioned model were 1.850 MJ m-2 day-1, 1.184 MJ m-2 day-1, 9.58% and 0.935, respectively.

Modeling NAPL dissolution from pendular rings in idealized porous media

NASA Astrophysics Data System (ADS)

Huang, Junqi; Christ, John A.; Goltz, Mark N.; Demond, Avery H.

2015-10-01

The dissolution rate of nonaqueous phase liquid (NAPL) often governs the remediation time frame at subsurface hazardous waste sites. Most formulations for estimating this rate are empirical and assume that the NAPL is the nonwetting fluid. However, field evidence suggests that some waste sites might be organic wet. Thus, formulations that assume the NAPL is nonwetting may be inappropriate for estimating the rates of NAPL dissolution. An exact solution to the Young-Laplace equation, assuming NAPL resides as pendular rings around the contact points of porous media idealized as spherical particles in a hexagonal close packing arrangement, is presented in this work to provide a theoretical prediction for NAPL-water interfacial area. This analytic expression for interfacial area is then coupled with an exact solution to the advection-diffusion equation in a capillary tube assuming Hagen-Poiseuille flow to provide a theoretical means of calculating the mass transfer rate coefficient for dissolution at the NAPL-water interface in an organic-wet system. A comparison of the predictions from this theoretical model with predictions from empirically derived formulations from the literature for water-wet systems showed a consistent range of values for the mass transfer rate coefficient, despite the significant differences in model foundations (water wetting versus NAPL wetting, theoretical versus empirical). This finding implies that, under these system conditions, the important parameter is interfacial area, with a lesser role played by NAPL configuration.

Pauling's electronegativity equation and a new corollary accurately predict bond dissociation enthalpies and enhance current understanding of the nature of the chemical bond.

PubMed

Matsunaga, Nikita; Rogers, Donald W; Zavitsas, Andreas A

2003-04-18

Contrary to other recent reports, Pauling's original electronegativity equation, applied as Pauling specified, describes quite accurately homolytic bond dissociation enthalpies of common covalent bonds, including highly polar ones, with an average deviation of +/-1.5 kcal mol(-1) from literature values for 117 such bonds. Dissociation enthalpies are presented for more than 250 bonds, including 79 for which experimental values are not available. Some previous evaluations of accuracy gave misleadingly poor results by applying the equation to cases for which it was not derived and for which it should not reproduce experimental values. Properly interpreted, the results of the equation provide new and quantitative insights into many facets of chemistry such as radical stabilities, factors influencing reactivity in electrophilic aromatic substitutions, the magnitude of steric effects, conjugative stabilization in unsaturated systems, rotational barriers, molecular and electronic structure, and aspects of autoxidation. A new corollary of the original equation expands its applicability and provides a rationale for previously observed empirical correlations. The equation raises doubts about a new bonding theory. Hydrogen is unique in that its electronegativity is not constant.

Theoretical Foundation of Zisman's Empirical Equation for Wetting of Liquids on Solid Surfaces

ERIC Educational Resources Information Center

Zhu, Ruzeng; Cui, Shuwen; Wang, Xiaosong

2010-01-01

Theories of wetting of liquids on solid surfaces under the condition that van der Waals force is dominant are briefly reviewed. We show theoretically that Zisman's empirical equation for wetting of liquids on solid surfaces is a linear approximation of the Young-van der Waals equation in the wetting region, and we express the two parameters in…

Recalibrated Equations for Determining Effect of Oil Filtration on Rolling Bearing Life

NASA Technical Reports Server (NTRS)

Needelman, William M.; Zaretsky, Erwin V.

2014-01-01

In 1991, Needelman and Zaretsky presented a set of empirically derived equations for bearing fatigue life (adjustment) factors (LFs) as a function of oil filter ratings. These equations for life factors were incorporated into the reference book, "STLE Life Factors for Rolling Bearings." These equations were normalized (LF = 1) to a 10-micrometer filter rating at Beta(sub x) = 200 (normal cleanliness) as it was then defined. Over the past 20 years, these life factors based on oil filtration have been used in conjunction with ANSI/ABMA standards and bearing computer codes to predict rolling bearing life. Also, additional experimental studies have been made by other investigators into the relationship between rolling bearing life and the size, number, and type of particle contamination. During this time period filter ratings have also been revised and improved, and they now use particle counting calibrated to a new National Institute of Standards and Technology (NIST) reference material, NIST SRM 2806, 1997. This paper reviews the relevant bearing life studies and describes the new filter ratings. New filter ratings, Beta(sub x(c)) = 200 and Beta(sub x(c)) = 1000, are benchmarked to old filter ratings, Beta(sub x) = 200, and vice versa. Two separate sets of filter LF values were derived based on the new filter ratings for roller bearings and ball bearings, respectively. Filter LFs can be calculated for the new filter ratings.

Simulation studies of chemical erosion on carbon based materials at elevated temperatures

NASA Astrophysics Data System (ADS)

Kenmotsu, T.; Kawamura, T.; Li, Zhijie; Ono, T.; Yamamura, Y.

1999-06-01

We simulated the fluence dependence of methane reaction yield in carbon with hydrogen bombardment using the ACAT-DIFFUSE code. The ACAT-DIFFUSE code is a simulation code based on a Monte Carlo method with a binary collision approximation and on solving diffusion equations. The chemical reaction model in carbon was studied by Roth or other researchers. Roth's model is suitable for the steady state methane reaction. But this model cannot estimate the fluence dependence of the methane reaction. Then, we derived an empirical formula based on Roth's model for methane reaction. In this empirical formula, we assumed the reaction region where chemical sputtering due to methane formation takes place. The reaction region corresponds to the peak range of incident hydrogen distribution in the target material. We adopted this empirical formula to the ACAT-DIFFUSE code. The simulation results indicate the similar fluence dependence compared with the experiment result. But, the fluence to achieve the steady state are different between experiment and simulation results.

Systems of frequency distributions for water and environmental engineering

NASA Astrophysics Data System (ADS)

Singh, Vijay P.

2018-09-01

A wide spectrum of frequency distributions are used in hydrologic, hydraulic, environmental and water resources engineering. These distributions may have different origins, are based on different hypotheses, and belong to different generating systems. Review of literature suggests that different systems of frequency distributions employed in science and engineering in general and environmental and water engineering in particular have been derived using different approaches which include (1) differential equations, (2) distribution elasticity, (3) genetic theory, (4) generating functions, (5) transformations, (6) Bessel function, (7) expansions, and (8) entropy maximization. This paper revisits these systems of distributions and discusses the hypotheses that are used for deriving these systems. It also proposes, based on empirical evidence, another general system of distributions and derives a number of distributions from this general system that are used in environmental and water engineering.

Excitation, response, and fatigue life estimation methods for the structural design of externally blown flaps

NASA Technical Reports Server (NTRS)

Ungar, E. E.; Chandiramani, K. L.; Barger, J. E.

1972-01-01

Means for predicting the fluctuating pressures acting on externally blown flap surfaces are developed on the basis of generalizations derived from non-dimensionalized empirical data. Approaches for estimation of the fatigue lives of skin-stringer and honeycomb-core sandwich flap structures are derived from vibration response analyses and panel fatigue data. Approximate expressions for fluctuating pressures, structural response, and fatigue life are combined to reveal the important parametric dependences. The two-dimensional equations of motion of multi-element flap systems are derived in general form, so that they can be specialized readily for any particular system. An introduction is presented of an approach to characterizing the excitation pressures and structural responses which makes use of space-time spectral concepts and promises to provide useful insights, as well as experimental and analytical savings.

Kinetic Glomerular Filtration Rate Equation Can Accommodate a Changing Body Volume: Derivation and Usage of the Formula.

PubMed

Chen, Sheldon

2018-05-22

Ascertaining a patient's kidney function is more difficult to do when the serum creatinine is changing than when it is stable. To accomplish the task, various kinetic clearance equations have been developed. To date, however, none of them have allowed for ongoing changes to the creatinine's volume of distribution. These diluting or concentrating effects on the [creatinine] can greatly impact the accuracy of kidney function assessment. Described herein is a model of creatinine kinetics that also accommodates volume changes. The differential equation is solved for the kinetic glomerular filtration rate (GFR), which is helpful information to the physician. Some of the equation's discontinuities, such as from dividing by a volume rate of zero, can be resolved by using limits. Being "volume-capable," the new kinetic equation reveals how a changing volume influences the maximum rate of rise in [creatinine], a parameter that heretofore was chosen empirically. To show the advantages of incorporating volume, the new and old kinetic equations are applied to a clinical case of overzealous fluid resuscitation. Appropriately, when the volume gain's dilution of [creatinine] is taken into account, the creatinine clearance is calculated to be substantially lower. In conclusion, the kinetic GFR equation has been upgraded to handle volume changes simultaneously with [creatinine] changes. Copyright © 2018. Published by Elsevier Inc.

Extending Maxwell's equations for dielectric materials using analytical principles from viscoelasticity based on the fractional calculus

NASA Astrophysics Data System (ADS)

Wharmby, Andrew William

Existing fractional calculus models having a non-empirical basis used to describe constitutive relationships between stress and strain in viscoelastic materials are modified to employ all orders of fractional derivatives between zero and one. Parallels between viscoelastic and dielectric theory are drawn so that these modified fractional calculus based models for viscoelastic materials may be used to describe relationships between electric flux density and electric field intensity in dielectric materials. The resulting fractional calculus based dielectric relaxation model is tested using existing complex permittivity data in the radio-frequency bandwidth of a wide variety of homogeneous materials. The consequences that the application of this newly developed fractional calculus based dielectric relaxation model has on Maxwell's equations are also examined through the effects of dielectric dissipation and dispersion.

Modeling techniques for quantum cascade lasers

NASA Astrophysics Data System (ADS)

Jirauschek, Christian; Kubis, Tillmann

2014-03-01

Quantum cascade lasers are unipolar semiconductor lasers covering a wide range of the infrared and terahertz spectrum. Lasing action is achieved by using optical intersubband transitions between quantized states in specifically designed multiple-quantum-well heterostructures. A systematic improvement of quantum cascade lasers with respect to operating temperature, efficiency, and spectral range requires detailed modeling of the underlying physical processes in these structures. Moreover, the quantum cascade laser constitutes a versatile model device for the development and improvement of simulation techniques in nano- and optoelectronics. This review provides a comprehensive survey and discussion of the modeling techniques used for the simulation of quantum cascade lasers. The main focus is on the modeling of carrier transport in the nanostructured gain medium, while the simulation of the optical cavity is covered at a more basic level. Specifically, the transfer matrix and finite difference methods for solving the one-dimensional Schrödinger equation and Schrödinger-Poisson system are discussed, providing the quantized states in the multiple-quantum-well active region. The modeling of the optical cavity is covered with a focus on basic waveguide resonator structures. Furthermore, various carrier transport simulation methods are discussed, ranging from basic empirical approaches to advanced self-consistent techniques. The methods include empirical rate equation and related Maxwell-Bloch equation approaches, self-consistent rate equation and ensemble Monte Carlo methods, as well as quantum transport approaches, in particular the density matrix and non-equilibrium Green's function formalism. The derived scattering rates and self-energies are generally valid for n-type devices based on one-dimensional quantum confinement, such as quantum well structures.

Bernoulli-Langevin Wind Speed Model for Simulation of Storm Events

NASA Astrophysics Data System (ADS)

Fürstenau, Norbert; Mittendorf, Monika

2016-12-01

We present a simple nonlinear dynamics Langevin model for predicting the instationary wind speed profile during storm events typically accompanying extreme low-pressure situations. It is based on a second-degree Bernoulli equation with δ-correlated Gaussian noise and may complement stationary stochastic wind models. Transition between increasing and decreasing wind speed and (quasi) stationary normal wind and storm states are induced by the sign change of the controlling time-dependent rate parameter k(t). This approach corresponds to the simplified nonlinear laser dynamics for the incoherent to coherent transition of light emission that can be understood by a phase transition analogy within equilibrium thermodynamics [H. Haken, Synergetics, 3rd ed., Springer, Berlin, Heidelberg, New York 1983/2004.]. Evidence for the nonlinear dynamics two-state approach is generated by fitting of two historical wind speed profiles (low-pressure situations "Xaver" and "Christian", 2013) taken from Meteorological Terminal Air Report weather data, with a logistic approximation (i.e. constant rate coefficients k) to the solution of our dynamical model using a sum of sigmoid functions. The analytical solution of our dynamical two-state Bernoulli equation as obtained with a sinusoidal rate ansatz k(t) of period T (=storm duration) exhibits reasonable agreement with the logistic fit to the empirical data. Noise parameter estimates of speed fluctuations are derived from empirical fit residuals and by means of a stationary solution of the corresponding Fokker-Planck equation. Numerical simulations with the Bernoulli-Langevin equation demonstrate the potential for stochastic wind speed profile modeling and predictive filtering under extreme storm events that is suggested for applications in anticipative air traffic management.

Modeling techniques for quantum cascade lasers

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

Jirauschek, Christian; Kubis, Tillmann

2014-03-15

Quantum cascade lasers are unipolar semiconductor lasers covering a wide range of the infrared and terahertz spectrum. Lasing action is achieved by using optical intersubband transitions between quantized states in specifically designed multiple-quantum-well heterostructures. A systematic improvement of quantum cascade lasers with respect to operating temperature, efficiency, and spectral range requires detailed modeling of the underlying physical processes in these structures. Moreover, the quantum cascade laser constitutes a versatile model device for the development and improvement of simulation techniques in nano- and optoelectronics. This review provides a comprehensive survey and discussion of the modeling techniques used for the simulation ofmore » quantum cascade lasers. The main focus is on the modeling of carrier transport in the nanostructured gain medium, while the simulation of the optical cavity is covered at a more basic level. Specifically, the transfer matrix and finite difference methods for solving the one-dimensional Schrödinger equation and Schrödinger-Poisson system are discussed, providing the quantized states in the multiple-quantum-well active region. The modeling of the optical cavity is covered with a focus on basic waveguide resonator structures. Furthermore, various carrier transport simulation methods are discussed, ranging from basic empirical approaches to advanced self-consistent techniques. The methods include empirical rate equation and related Maxwell-Bloch equation approaches, self-consistent rate equation and ensemble Monte Carlo methods, as well as quantum transport approaches, in particular the density matrix and non-equilibrium Green's function formalism. The derived scattering rates and self-energies are generally valid for n-type devices based on one-dimensional quantum confinement, such as quantum well structures.« less

Empirical Equation Based Chirality (n, m) Assignment of Semiconducting Single Wall Carbon Nanotubes from Resonant Raman Scattering Data

PubMed Central

Arefin, Md Shamsul

2012-01-01

This work presents a technique for the chirality (n, m) assignment of semiconducting single wall carbon nanotubes by solving a set of empirical equations of the tight binding model parameters. The empirical equations of the nearest neighbor hopping parameters, relating the term (2n− m) with the first and second optical transition energies of the semiconducting single wall carbon nanotubes, are also proposed. They provide almost the same level of accuracy for lower and higher diameter nanotubes. An algorithm is presented to determine the chiral index (n, m) of any unknown semiconducting tube by solving these empirical equations using values of radial breathing mode frequency and the first or second optical transition energy from resonant Raman spectroscopy. In this paper, the chirality of 55 semiconducting nanotubes is assigned using the first and second optical transition energies. Unlike the existing methods of chirality assignment, this technique does not require graphical comparison or pattern recognition between existing experimental and theoretical Kataura plot. PMID:28348319

Surface albedo from bidirectional reflectance

NASA Technical Reports Server (NTRS)

Ranson, K. J.; Irons, J. R.; Daughtry, C. S. T.

1991-01-01

The validity of integrating over discrete wavelength bands is examined to estimate total shortwave bidirectional reflectance of vegetated and bare soil surfaces. Methods for estimating albedo from multiple angle, discrete wavelength band radiometer measurements are studied. These methods include a numerical integration technique and the integration of an empirically derived equation for bidirectional reflectance. It is concluded that shortwave albedos estimated through both techniques agree favorably with the independent pyranometer measurements. Absolute rms errors are found to be 0.5 percent or less for both grass sod and bare soil surfaces.

A novel approach for estimating sugar and alcohol concentrations in wines using refractometer and hydrometer.

PubMed

Son, H S; Hong, Y S; Park, W M; Yu, M A; Lee, C H

2009-03-01

To estimate true Brix and alcoholic strength of must and wines without distillation, a novel approach using a refractometer and a hydrometer was developed. Initial Brix (I.B.), apparent refractometer Brix (A.R.), and apparent hydrometer Brix (A.H.) of must were measured by refractometer and hydrometer, respectively. Alcohol content (A) was determined with a hydrometer after distillation and true Brix (T.B.) was measured in distilled wines using a refractometer. Strong proportional correlations among A.R., A.H., T.B., and A in sugar solutions containing varying alcohol concentrations were observed in preliminary experiments. Similar proportional relationships among the parameters were also observed in must, which is a far more complex system than the sugar solution. To estimate T.B. and A of must during alcoholic fermentation, a total of 6 planar equations were empirically derived from the relationships among the experimental parameters. The empirical equations were then tested to estimate T.B. and A in 17 wine products, and resulted in good estimations of both quality factors. This novel approach was rapid, easy, and practical for use in routine analyses or for monitoring quality of must during fermentation and final wine products in a winery and/or laboratory.

Empirical prediction of peak pressure levels in anthropogenic impulsive noise. Part I: Airgun arrays signals.

PubMed

Galindo-Romero, Marta; Lippert, Tristan; Gavrilov, Alexander

2015-12-01

This paper presents an empirical linear equation to predict peak pressure level of anthropogenic impulsive signals based on its correlation with the sound exposure level. The regression coefficients are shown to be weakly dependent on the environmental characteristics but governed by the source type and parameters. The equation can be applied to values of the sound exposure level predicted with a numerical model, which provides a significant improvement in the prediction of the peak pressure level. Part I presents the analysis for airgun arrays signals, and Part II considers the application of the empirical equation to offshore impact piling noise.

Lifespan estimation of seal welded super stainless steels for water condenser of nuclear power plants

NASA Astrophysics Data System (ADS)

Kim, Young Sik; Park, Sujin; Chang, Hyun Young

2014-01-01

When sea water was used as cooling water for water condenser of nuclear power plants, commercial stainless steels can not be applied because chloride concentration exceeds 20,000 ppm. There are many opinions for the materials selection of tube and tube sheets of a condenser. This work reviewed the application guide line of stainless steels for sea-water facilities and the estimation equations of lifespan were proposed from the analyses of both field data for sea water condenser and experimental results of corrosion. Empirical equations for lifespan estimation were derived from the pit initiation time and re-tubing time of stainless steel tubing in sea water condenser of nuclear power plants. The lifespan of seal-welded super austenitic stainless steel tube/tube sheet was calculated from these equations. Critical pitting temperature of seal-welded PRE 50 grade super stainless steel was evaluated as 60 °C. Using the proposed equation in engineering aspect, tube pitting corrosion time of seal-welded tube/tube sheet was calculated as 69.8 years and re-tubing time was estimated as 82.0 years.

Stochastic model of financial markets reproducing scaling and memory in volatility return intervals

NASA Astrophysics Data System (ADS)

Gontis, V.; Havlin, S.; Kononovicius, A.; Podobnik, B.; Stanley, H. E.

2016-11-01

We investigate the volatility return intervals in the NYSE and FOREX markets. We explain previous empirical findings using a model based on the interacting agent hypothesis instead of the widely-used efficient market hypothesis. We derive macroscopic equations based on the microscopic herding interactions of agents and find that they are able to reproduce various stylized facts of different markets and different assets with the same set of model parameters. We show that the power-law properties and the scaling of return intervals and other financial variables have a similar origin and could be a result of a general class of non-linear stochastic differential equations derived from a master equation of an agent system that is coupled by herding interactions. Specifically, we find that this approach enables us to recover the volatility return interval statistics as well as volatility probability and spectral densities for the NYSE and FOREX markets, for different assets, and for different time-scales. We find also that the historical S&P500 monthly series exhibits the same volatility return interval properties recovered by our proposed model. Our statistical results suggest that human herding is so strong that it persists even when other evolving fluctuations perturbate the financial system.

General slip regime permeability model for gas flow through porous media

NASA Astrophysics Data System (ADS)

Zhou, Bo; Jiang, Peixue; Xu, Ruina; Ouyang, Xiaolong

2016-07-01

A theoretical effective gas permeability model was developed for rarefied gas flow in porous media, which holds over the entire slip regime with the permeability derived as a function of the Knudsen number. This general slip regime model (GSR model) is derived from the pore-scale Navier-Stokes equations subject to the first-order wall slip boundary condition using the volume-averaging method. The local closure problem for the volume-averaged equations is studied analytically and numerically using a periodic sphere array geometry. The GSR model includes a rational fraction function of the Knudsen number which leads to a limit effective permeability as the Knudsen number increases. The mechanism for this behavior is the viscous fluid inner friction caused by converging-diverging flow channels in porous media. A linearization of the GSR model leads to the Klinkenberg equation for slightly rarefied gas flows. Finite element simulations show that the Klinkenberg model overestimates the effective permeability by as much as 33% when a flow approaches the transition regime. The GSR model reduces to the unified permeability model [F. Civan, "Effective correlation of apparent gas permeability in tight porous media," Transp. Porous Media 82, 375 (2010)] for the flow in the slip regime and clarifies the physical significance of the empirical parameter b in the unified model.

Equation of State for Detonation Product Gases

NASA Astrophysics Data System (ADS)

Nagayama, Kunihito; Kubota, Shiro

2013-06-01

Based on the empirical linear relationship between detonation velocity and loading density, an approximate description for the Chapman-Jouguet state for detonation product gases of solid phase high explosives has been developed. Provided that the Grüneisen parameter is a function only of volume, systematic and closed system of equations for the Grüneisen parameter and CJ volume have been formulated. These equations were obtained by combining this approximation with the Jones-Stanyukovich-Manson relation together with JWL isentrope for detonation of crystal density PETN. A thermodynamic identity between the Grüneisen parameter and another non-dimensional material parameter introduced by Wu and Jing can be used to derive the enthalpy-pressure-volume equation of state for detonation gases. This Wu-Jing parameter is found to be the ratio of the Grüneisen parameter and the adiabatic index. Behavior of this parameter as a function of pressure was calculated and revealed that their change with pressure is very gradual. By using this equation of state, several isentropes down from the Chapman-Jouguet states reached by four different lower initial density PETN have been calculated and compared with available cylinder expansion tests.

Development of an analytical solution for the Budyko watershed parameter in terms of catchment physical features

NASA Astrophysics Data System (ADS)

Reaver, N.; Kaplan, D. A.; Jawitz, J. W.

2017-12-01

The Budyko hypothesis states that a catchment's long-term water and energy balances are dependent on two relatively easy to measure quantities: rainfall depth and potential evaporation. This hypothesis is expressed as a simple function, the Budyko equation, which allows for the prediction of a catchment's actual evapotranspiration and discharge from measured rainfall depth and potential evaporation, data which are widely available. However, the two main analytically derived forms of the Budyko equation contain a single unknown watershed parameter, whose value varies across catchments; variation in this parameter has been used to explain the hydrological behavior of different catchments. The watershed parameter is generally thought of as a lumped quantity that represents the influence of all catchment biophysical features (e.g. soil type and depth, vegetation type, timing of rainfall, etc). Previous work has shown that the parameter is statistically correlated with catchment properties, but an explicit expression has been elusive. While the watershed parameter can be determined empirically by fitting the Budyko equation to measured data in gauged catchments where actual evapotranspiration can be estimated, this limits the utility of the framework for predicting impacts to catchment hydrology due to changing climate and land use. In this study, we developed an analytical solution for the lumped catchment parameter for both forms of the Budyko equation. We combined these solutions with a statistical soil moisture model to obtain analytical solutions for the Budyko equation parameter as a function of measurable catchment physical features, including rooting depth, soil porosity, and soil wilting point. We tested the predictive power of these solutions using the U.S. catchments in the MOPEX database. We also compared the Budyko equation parameter estimates generated from our analytical solutions (i.e. predicted parameters) with those obtained through the calibration of the Budyko equation to discharge data (i.e. empirical parameters), and found good agreement. These results suggest that it is possible to predict the Budyko equation watershed parameter directly from physical features, even for ungauged catchments.

Intermittency in small-scale turbulence: a velocity gradient approach

NASA Astrophysics Data System (ADS)

Meneveau, Charles; Johnson, Perry

2017-11-01

Intermittency of small-scale motions is an ubiquitous facet of turbulent flows, and predicting this phenomenon based on reduced models derived from first principles remains an important open problem. Here, a multiple-time scale stochastic model is introduced for the Lagrangian evolution of the full velocity gradient tensor in fluid turbulence at arbitrarily high Reynolds numbers. This low-dimensional model differs fundamentally from prior shell models and other empirically-motivated models of intermittency because the nonlinear gradient self-stretching and rotation A2 term vital to the energy cascade and intermittency development is represented exactly from the Navier-Stokes equations. With only one adjustable parameter needed to determine the model's effective Reynolds number, numerical solutions of the resulting set of stochastic differential equations show that the model predicts anomalous scaling for moments of the velocity gradient components and negative derivative skewness. It also predicts signature topological features of the velocity gradient tensor such as vorticity alignment trends with the eigen-directions of the strain-rate. This research was made possible by a graduate Fellowship from the National Science Foundation and by a Grant from The Gulf of Mexico Research Initiative.

Providing the physical basis of SCS curve number method and its proportionality relationship from Richards' equation

NASA Astrophysics Data System (ADS)

Hooshyar, M.; Wang, D.

2016-12-01

The empirical proportionality relationship, which indicates that the ratio of cumulative surface runoff and infiltration to their corresponding potentials are equal, is the basis of the extensively used Soil Conservation Service Curve Number (SCS-CN) method. The objective of this paper is to provide the physical basis of the SCS-CN method and its proportionality hypothesis from the infiltration excess runoff generation perspective. To achieve this purpose, an analytical solution of Richards' equation is derived for ponded infiltration in shallow water table environment under the following boundary conditions: 1) the soil is saturated at the land surface; and 2) there is a no-flux boundary which moves downward. The solution is established based on the assumptions of negligible gravitational effect, constant soil water diffusivity, and hydrostatic soil moisture profile between the no-flux boundary and water table. Based on the derived analytical solution, the proportionality hypothesis is a reasonable approximation for rainfall partitioning at the early stage of ponded infiltration in areas with a shallow water table for coarse textured soils.

An analytical solution of Richards' equation providing the physical basis of SCS curve number method and its proportionality relationship

NASA Astrophysics Data System (ADS)

Hooshyar, Milad; Wang, Dingbao

2016-08-01

The empirical proportionality relationship, which indicates that the ratio of cumulative surface runoff and infiltration to their corresponding potentials are equal, is the basis of the extensively used Soil Conservation Service Curve Number (SCS-CN) method. The objective of this paper is to provide the physical basis of the SCS-CN method and its proportionality hypothesis from the infiltration excess runoff generation perspective. To achieve this purpose, an analytical solution of Richards' equation is derived for ponded infiltration in shallow water table environment under the following boundary conditions: (1) the soil is saturated at the land surface; and (2) there is a no-flux boundary which moves downward. The solution is established based on the assumptions of negligible gravitational effect, constant soil water diffusivity, and hydrostatic soil moisture profile between the no-flux boundary and water table. Based on the derived analytical solution, the proportionality hypothesis is a reasonable approximation for rainfall partitioning at the early stage of ponded infiltration in areas with a shallow water table for coarse textured soils.

Regionalisation of low flow frequency curves for the Peninsular Malaysia

NASA Astrophysics Data System (ADS)

Mamun, Abdullah A.; Hashim, Alias; Daoud, Jamal I.

2010-02-01

SUMMARYRegional maps and equations for the magnitude and frequency of 1, 7 and 30-day low flows were derived and are presented in this paper. The river gauging stations of neighbouring catchments that produced similar low flow frequency curves were grouped together. As such, the Peninsular Malaysia was divided into seven low flow regions. Regional equations were developed using the multivariate regression technique. An empirical relationship was developed for mean annual minimum flow as a function of catchment area, mean annual rainfall and mean annual evaporation. The regional equations exhibited good coefficient of determination ( R2 > 0.90). Three low flow frequency curves showing the low, mean and high limits for each region were proposed based on a graphical best-fit technique. Knowing the catchment area, mean annual rainfall and evaporation in the region, design low flows of different durations can be easily estimated for the ungauged catchments. This procedure is expected to overcome the problem of data unavailability in estimating low flows in the Peninsular Malaysia.

Proposed Framework for Determining Added Mass of Orion Drogue Parachutes

NASA Technical Reports Server (NTRS)

Fraire, Usbaldo, Jr.; Dearman, James; Morris, Aaron

2011-01-01

The Crew Exploration Vehicle (CEV) Parachute Assembly System (CPAS) project is executing a program to qualify a parachute system for a next generation human spacecraft. Part of the qualification process involves predicting parachute riser tension during system descent with flight simulations. Human rating the CPAS hardware requires a high degree of confidence in the simulation models used to predict parachute loads. However, uncertainty exists in the heritage added mass models used for loads predictions due to a lack of supporting documentation and data. Even though CPAS anchors flight simulation loads predictions to flight tests, extrapolation of these models outside the test regime carries the risk of producing non-bounding loads. A set of equations based on empirically derived functions of skirt radius is recommended as the simplest and most viable method to test and derive an enhanced added mass model for an inflating parachute. This will increase confidence in the capability to predict parachute loads. The selected equations are based on those published in A Simplified Dynamic Model of Parachute Inflation by Dean Wolf. An Ames 80x120 wind tunnel test campaign is recommended to acquire the reefing line tension and canopy photogrammetric data needed to quantify the terms in the Wolf equations and reduce uncertainties in parachute loads predictions. Once the campaign is completed, the Wolf equations can be used to predict loads in a typical CPAS Drogue Flight test. Comprehensive descriptions of added mass test techniques from the Apollo Era to the current CPAS project are included for reference.

Saturation behavior: a general relationship described by a simple second-order differential equation.

PubMed

Kepner, Gordon R

2010-04-13

The numerous natural phenomena that exhibit saturation behavior, e.g., ligand binding and enzyme kinetics, have been approached, to date, via empirical and particular analyses. This paper presents a mechanism-free, and assumption-free, second-order differential equation, designed only to describe a typical relationship between the variables governing these phenomena. It develops a mathematical model for this relation, based solely on the analysis of the typical experimental data plot and its saturation characteristics. Its utility complements the traditional empirical approaches. For the general saturation curve, described in terms of its independent (x) and dependent (y) variables, a second-order differential equation is obtained that applies to any saturation phenomena. It shows that the driving factor for the basic saturation behavior is the probability of the interactive site being free, which is described quantitatively. Solving the equation relates the variables in terms of the two empirical constants common to all these phenomena, the initial slope of the data plot and the limiting value at saturation. A first-order differential equation for the slope emerged that led to the concept of the effective binding rate at the active site and its dependence on the calculable probability the interactive site is free. These results are illustrated using specific cases, including ligand binding and enzyme kinetics. This leads to a revised understanding of how to interpret the empirical constants, in terms of the variables pertinent to the phenomenon under study. The second-order differential equation revealed the basic underlying relations that describe these saturation phenomena, and the basic mathematical properties of the standard experimental data plot. It was shown how to integrate this differential equation, and define the common basic properties of these phenomena. The results regarding the importance of the slope and the new perspectives on the empirical constants governing the behavior of these phenomena led to an alternative perspective on saturation behavior kinetics. Their essential commonality was revealed by this analysis, based on the second-order differential equation.

Measurement and correlation of the solubility of gossypol acetic acid and gossypol acetic acid of optical activity in different solvents

NASA Astrophysics Data System (ADS)

Zhang, B.; Tang, H.; Liu, X. Y.; Zhai, X.; Yao, X. C.

2018-01-01

The equilibrium method was used to measure the solubility of gossypol acetic acid and gossypol acetic acid of optical activity in isopropyl alcohol, ethanol, acetic acid and ethyl acetate at temperature from 288.15 to 315.15. The Empirical equation and the Apelblat equation model were adopted to correlate the experimental data. For gossypol acetic acid, the root-mean-square deviations (RMSD) were observed in the range of 0.023-4.979 and 0.0112-0.614 for the Empirical equation and the Apelblat equation, respectively. For gossypol acetic acid of optical activity, the RMSD were observed in the range of 0.021-2.211 and 0.021-2.243 for the Empirical equation and the Apelblat equation, individually. And the maximum relative average deviation was 7.5%. Both equations offered an accurate mathematical expression of the experimental results. The calculated solubility showed a good relationship with the experimental solubility for most of solvents. This study provided valuable datas not only for optimizing the process of purification of gossypol acetic acid of optical activity in industry but also for further theoretical studies.

Hypervelocity impact on shielded plates

NASA Technical Reports Server (NTRS)

Smith, James P.

1993-01-01

A ballistic limit equation for hypervelocity impact on thin plates is derived analytically. This equation applies to cases of impulsive impact on a plate that is protected by a multi-shock shield, and it is valid in the range of velocity above 6 km/s. Experimental tests were conducted at the NASA Johnson Space Center on square aluminum plates. Comparing the center deflections of these plates with the theoretical deflections of a rigid-plastic plate subjected to a blast load, one determines the dynamic yield strength of the plate material. The analysis is based on a theory for the expansion of the fragmented projectile and on a simple failure criterion. Curves are presented for the critical projectile radius versus the projectile velocity, and for the critical plate thickness versus the velocity. These curves are in good agreement with curves that have been generated empirically.

Physical properties, vitrinite reflectance, and microstructure of coal, Taiyuan Formation, Qinshui Basin, China

NASA Astrophysics Data System (ADS)

Li, Qiong; Chen, Jie; He, Jian-Jun

2017-12-01

In this study, we experimentally established the relationship between physical properties, vitrinite reflectance, and microstructure of coal, Taiyuan Formation, Qinshui Basin, China using representative coal samples collected from three different mines via the rock mechanics testing system (MTS). We analyzed the organic macerals, vitrinite reflectance, and microstructure of 11 coal samples using petrography and scanning electron microscopy (SEM). The experimental results suggest that (1) the elastic parameters can be described by linear equations, (2) both P-and S-wave velocities display anisotropy, (3) the anisotropy negatively correlates with vitrinite reflectance, and (4) the acoustic velocities and Young's modulus are negatively correlated with the volume of micropores. The derived empirical equations can be used in the forward modeling and seismic inversion of physical properties of coal for improving the coal-bed methane (CBM) reservoir characterization.

Do dual-route models accurately predict reading and spelling performance in individuals with acquired alexia and agraphia?

PubMed

Rapcsak, Steven Z; Henry, Maya L; Teague, Sommer L; Carnahan, Susan D; Beeson, Pélagie M

2007-06-18

Coltheart and co-workers [Castles, A., Bates, T. C., & Coltheart, M. (2006). John Marshall and the developmental dyslexias. Aphasiology, 20, 871-892; Coltheart, M., Rastle, K., Perry, C., Langdon, R., & Ziegler, J. (2001). DRC: A dual route cascaded model of visual word recognition and reading aloud. Psychological Review, 108, 204-256] have demonstrated that an equation derived from dual-route theory accurately predicts reading performance in young normal readers and in children with reading impairment due to developmental dyslexia or stroke. In this paper, we present evidence that the dual-route equation and a related multiple regression model also accurately predict both reading and spelling performance in adult neurological patients with acquired alexia and agraphia. These findings provide empirical support for dual-route theories of written language processing.

Thermospheric winds and exospheric temperatures from incoherent scatter radar measurements in four seasons

NASA Technical Reports Server (NTRS)

Antoniadis, D. A.

1976-01-01

The time-dependent equations of neutral air motion are solved subject to three constraints: two of them are the usual upper and lower boundary conditions and the third is the value of the wind-induced ion drift at any given height. Using incoherent radar data, this procedure leads to a fast, direct numerical integration of the two coupled differential equations describing the horizontal wind components and yields time dependent wind profiles and meridional exospheric neutral temperature gradients. The diurnal behavior of the neutral wind system and of the exospheric temperature is presented for two solstice and two equinox days. The data used were obtained by the St. Santin and the Millstone Hill incoherent scatter radars. The derived geographic distributions of the exospheric temperatures are compared with those predicted by the OGO-6 empirical thermospheric model.

A weakly nonlinear model with exact coefficients for the fluttering and spiraling motions of buoyancy-driven bodies

NASA Astrophysics Data System (ADS)

Magnaudet, Jacques; Tchoufag, Joel; Fabre, David

2015-11-01

Gravity/buoyancy-driven bodies moving in a slightly viscous fluid frequently follow fluttering or helical paths. Current models of such systems are largely empirical and fail to predict several of the key features of their evolution, especially close to the onset of path instability. Using a weakly nonlinear expansion of the full set of governing equations, we derive a new generic reduced-order model of this class of phenomena based on a pair of amplitude equations with exact coefficients that drive the evolution of the first pair of unstable modes. We show that the predictions of this model for the style (eg. fluttering or spiraling) and characteristics (eg. frequency and maximum inclination angle) of path oscillations compare well with various recent data for both solid disks and air bubbles.

Petrophysical approach for S-wave velocity prediction based on brittleness index and total organic carbon of shale gas reservoir: A case study from Horn River Basin, Canada

NASA Astrophysics Data System (ADS)

Kim, Taeyoun; Hwang, Seho; Jang, Seonghyung

2017-01-01

When finding the "sweet spot" of a shale gas reservoir, it is essential to estimate the brittleness index (BI) and total organic carbon (TOC) of the formation. Particularly, the BI is one of the key factors in determining the crack propagation and crushing efficiency for hydraulic fracturing. There are several methods for estimating the BI of a formation, but most of them are empirical equations that are specific to particular rock types. We estimated the mineralogical BI based on elemental capture spectroscopy (ECS) log and elastic BI based on well log data, and we propose a new method for predicting S-wave velocity (VS) using mineralogical BI and elastic BI. The TOC is related to the gas content of shale gas reservoirs. Since it is difficult to perform core analysis for all intervals of shale gas reservoirs, we make empirical equations for the Horn River Basin, Canada, as well as TOC log using a linear relation between core-tested TOC and well log data. In addition, two empirical equations have been suggested for VS prediction based on density and gamma ray log used for TOC analysis. By applying the empirical equations proposed from the perspective of BI and TOC to another well log data and then comparing predicted VS log with real VS log, the validity of empirical equations suggested in this paper has been tested.

Geometrically constrained kinematic global navigation satellite systems positioning: Implementation and performance

NASA Astrophysics Data System (ADS)

Asgari, Jamal; Mohammadloo, Tannaz H.; Amiri-Simkooei, Ali Reza

2015-09-01

GNSS kinematic techniques are capable of providing precise coordinates in extremely short observation time-span. These methods usually determine the coordinates of an unknown station with respect to a reference one. To enhance the precision, accuracy, reliability and integrity of the estimated unknown parameters, GNSS kinematic equations are to be augmented by possible constraints. Such constraints could be derived from the geometric relation of the receiver positions in motion. This contribution presents the formulation of the constrained kinematic global navigation satellite systems positioning. Constraints effectively restrict the definition domain of the unknown parameters from the three-dimensional space to a subspace defined by the equation of motion. To test the concept of the constrained kinematic positioning method, the equation of a circle is employed as a constraint. A device capable of moving on a circle was made and the observations from 11 positions on the circle were analyzed. Relative positioning was conducted by considering the center of the circle as the reference station. The equation of the receiver's motion was rewritten in the ECEF coordinates system. A special attention is drawn onto how a constraint is applied to kinematic positioning. Implementing the constraint in the positioning process provides much more precise results compared to the unconstrained case. This has been verified based on the results obtained from the covariance matrix of the estimated parameters and the empirical results using kinematic positioning samples as well. The theoretical standard deviations of the horizontal components are reduced by a factor ranging from 1.24 to 2.64. The improvement on the empirical standard deviation of the horizontal components ranges from 1.08 to 2.2.

Optical and Thermo-optical Properties of Polyimide-Single-Walled Carbon Nanotube Films: Experimental Results and Empirical Equations

NASA Technical Reports Server (NTRS)

Smith, Joseph G., Jr.; Connell, John W.; Watson, Kent A.; Danehy, Paul M.

2005-01-01

The incorporation of single-walled carbon nanotubes (SWNTs) into the bulk of space environmentally durable polymers at loading levels greater than or equal to 0.05 wt % has afforded thin films with surface and volume resistivities sufficient for electrostatic charge mitigation. However, the optical transparency at 500 nm decreased and the thermo-optical properties (solar absorptivity and thermal emissivity) increased with increaed SWNT loading. These properties were also dependent on film thickness. The absorbance characteristics of the films as a function of SWNT loading and film thickness were measured and determined to follow the classical Beer-Lambert law. Based on these results, an empirical relationship was derived and molar absorptivities determined for both the SWNTs and polymer matrix to provide a predictive approximation of these properties. The molar absorptivity determined for SWNTs dispersed in the polymer was comparable to reported solution determined values for HiPco SWNTs.

Sediment composition for the assessment of water erosion and nonpoint source pollution in natural and fire-affected landscapes.

PubMed

Carkovic, Athena B; Pastén, Pablo A; Bonilla, Carlos A

2015-04-15

Water erosion is a leading cause of soil degradation and a major nonpoint source pollution problem. Many efforts have been undertaken to estimate the amount and size distribution of the sediment leaving the field. Multi-size class water erosion models subdivide eroded soil into different sizes and estimate the aggregate's composition based on empirical equations derived from agricultural soils. The objective of this study was to evaluate these equations on soil samples collected from natural landscapes (uncultivated) and fire-affected soils. Chemical, physical, and soil fractions and aggregate composition analyses were performed on samples collected in the Chilean Patagonia and later compared with the equations' estimates. The results showed that the empirical equations were not suitable for predicting the sediment fractions. Fine particles, including primary clay, primary silt, and small aggregates (<53 μm) were over-estimated, and large aggregates (>53 μm) and primary sand were under-estimated. The uncultivated and fire-affected soils showed a reduced fraction of fine particles in the sediment, as clay and silt were mostly in the form of large aggregates. Thus, a new set of equations was developed for these soils, where small aggregates were defined as particles with sizes between 53 μm and 250 μm and large aggregates as particles>250 μm. With r(2) values between 0.47 and 0.98, the new equations provided better estimates for primary sand and large aggregates. The aggregate's composition was also well predicted, especially the silt and clay fractions in the large aggregates from uncultivated soils (r(2)=0.63 and 0.83, respectively) and the fractions of silt in the small aggregates (r(2)=0.84) and clay in the large aggregates (r(2)=0.78) from fire-affected soils. Overall, these new equations proved to be better predictors for the sediment and aggregate's composition in uncultivated and fire-affected soils, and they reduce the error when estimating soil loss in natural landscapes. Copyright © 2015 Elsevier B.V. All rights reserved.

Empirical Ground Motion Characterization of Induced Seismicity in Alberta and Oklahoma

NASA Astrophysics Data System (ADS)

Novakovic, M.; Atkinson, G. M.; Assatourians, K.

2017-12-01

We develop empirical ground-motion prediction equations (GMPEs) for ground motions from induced earthquakes in Alberta and Oklahoma following the stochastic-model-based method of Atkinson et al. (2015 BSSA). The Oklahoma ground-motion database is compiled from over 13,000 small to moderate seismic events (M 1 to 5.8) recorded at 1600 seismic stations, at distances from 1 to 750 km. The Alberta database is compiled from over 200 small to moderate seismic events (M 1 to 4.2) recorded at 50 regional stations, at distances from 30 to 500 km. A generalized inversion is used to solve for regional source, attenuation and site parameters. The obtained parameters describe the regional attenuation, stress parameter and site amplification. Resolving these parameters allows for the derivation of regionally-calibrated GMPEs that can be used to compare ground motion observations between waste water injection (Oklahoma) and hydraulic fracture induced events (Alberta), and further compare induced observations with ground motions resulting from natural sources (California, NGAWest2). The derived GMPEs have applications for the evaluation of hazards from induced seismicity and can be used to track amplitudes across the regions in real time, which is useful for ground-motion-based alerting systems and traffic light protocols.

Semi-empirical models of the wind in cool supergiant stars

NASA Technical Reports Server (NTRS)

Kuin, N. P. M.; Ahmad, Imad A.

1988-01-01

A self-consistent semi-empirical model for the wind of the supergiant in zeta Aurigae type systems is proposed. The damping of the Alfven waves which are assumed to drive the wind is derived from the observed velocity profile. Solution of the ionization balance and energy equation gives the temperature structure for given stellar magnetic field and wave flux. Physically acceptable solutions of the temperature structure place limits on the stellar magnetic field. A crude formula for a critical mass loss rate is derived. For a mass loss rate below the critical value the wind cannot be cool. Comparison between the observed and the critical mass loss rate suggests that the proposed theory may provide an explanation for the coronal dividing line in the Hertzsprung-Russell diagram. The physical explanation may be that the atmosphere has a cool wind, unless it is physically impossible to have one. Stars which cannot have a cool wind release their nonthermal energy in an outer atmosphere at coronal temperatures. It is possible that in the absence of a substantial stellar wind the magnetic field has less incentive to extend radially outward, and coronal loop structures may become more dominant.

What makes people leave their food? The interaction of personal and situational factors leading to plate leftovers in canteens.

PubMed

Lorenz, Bettina Anne-Sophie; Hartmann, Monika; Langen, Nina

2017-09-01

In order to provide a basis for the reduction of food losses, our study analyzes individual food choice, eating and leftover behavior in a university canteen by consideration of personal, social and environmental determinants. Based on an extended literature review, a structural equation model is derived and empirically tested for a sample of 343 students. The empirical estimates support the derived model with a good overall model fit and sufficient R 2 values for dependent variables. Hence, our results provide evidence for a general significant impact of behavioral intention and related personal and social determinants as well as for the relevance of environmental/situational determinants such as portion sizes and palatability of food for plate leftovers. Moreover, we find that environmental and personal determinants are interrelated and that the impact of different determinants is relative to perceived time constraints during a visit of the university canteen. Accordingly, we conclude that simple measures to decrease avoidable food waste may take effects via complex and interrelated behavioral structures and that future research should focus on these effects to understand and change food leftover behavior. Copyright © 2017 Elsevier Ltd. All rights reserved.

Petrophysics of low-permeability medina sandstone, northwestern Pennsylvania, Appalachian Basin

USGS Publications Warehouse

Castle, J.W.; Byrnes, A.P.

1998-01-01

Petrophysical core testing combined with geophysical log analysis of low-permeability, Lower Silurian sandstones of the Appalachian basin provides guidelines and equations for predicting gas producibility. Permeability values are predictable from the borehole logs by applying empirically derived equations based on correlation between in-situ porosity and in-situ effective gas permeability. An Archie-form equation provides reasonable accuracy of log-derived water saturations because of saturated brine salinities and low clay content in the sands. Although measured porosity and permeability average less than 6% and 0.1 mD, infrequent values as high as 18% and 1,048 mD occur. Values of effective gas permeability at irreducible water saturation (Swi) range from 60% to 99% of routine values for the highest permeability rocks to several orders of magnitude less for the lowest permeability rocks. Sandstones having porosity greater than 6% and effective gas permeability greater than 0.01 mD exhibit Swi less than 20%. With decreasing porosity, Swi sharply increases to values near 40% at 3 porosity%. Analysis of cumulative storage and flow capacity indicates zones with porosity greater than 6% generally contain over 90% of flow capacity and hold a major portion of storage capacity. For rocks with Swi < 20%, gas relative permeabilities exceed 45%. Gas relative permeability and hydrocarbon volume decrease rapidly with increasing Swi as porosity drops below 6%. At Swi above 40%, gas relative permeabilities are less than approximately 10%.

Scaling of mean inertia and theoretical basis for a log law in turbulent boundary layers

NASA Astrophysics Data System (ADS)

Philip, Jimmy; Morrill-Winter, Caleb; Klewicki, Joseph

2017-11-01

Log law in the mean streamwise velocity (U) for pipes/channels is well accepted based on the derivation from the mean momentum balance (MMB) equation and support from experimental data. For flat plate turbulent boundary layers (TBLs), however, there is only empirical evidence and a theoretical underpinning of the kind available for pipes/channels in lacking. The main difficultly is the mean inertia (MI) term in the MMB equation, which, unlike in pipes/channels, is not a constant in TBLs. We present results from our paper (JFM `` 2017, Vol 813, pp 594-617), where the MI term for TBL is transformed so as to render it invariant in the outer region, corroborated with high Re (δ+) data from Melbourne Wind Tunnel and New Hampshire Flow Physics Facility. The transformation is possible because the MI term in the TBL has a `shape' which becomes invariant with increasing δ+ and a `magnitude' which is proportional to 1 /δ+ . The transformed equation is then employed to derive a log law for U with κ an order one (von-Karman) constant. We also show that the log law begins at y+ =C1√{δ+} , and the peak location of the Reynolds shear stress, ym+ =C2√{δ+} , where, C1 3.6 and C2 2.17 are from high Re data. Australian Research Council and the US National Science Foundation.

Effect of casing yield stress on bomb blast impulse

NASA Astrophysics Data System (ADS)

Hutchinson, M. D.

2012-08-01

An equation to predict blast effects from cased charges was first proposed by U. Fano in 1944 and revised by E.M. Fisher in 1953 [1]. Fisher's revision provides much better matches to available blast impulse data, but still requires empirical parameter adjustments. A new derivation [2], based on the work of R.W. Gurney [3] and G.I. Taylor [4], has resulted in an equation which nearly matches experimental data. This new analytical model is also capable of being extended, through the incorporation of additional physics, such as the effects of early case fracture, finite casing thickness, casing metal strain energy dissipation, explosive gas escape through casing fractures and the comparative dynamics of blast wave and metal fragment impacts. This paper will focus on the choice of relevant case fracture strain criterion, as it will be shown that this allows the explicit inclusion of the dynamic properties of the explosive and casing metal. It will include a review and critique of the most significant earlier work on this topic, contained in a paper by Hoggatt and Recht [5]. Using this extended analytical model, good matches can readily be made to available free-field blast impulse data, without any empirical adjustments being needed. Further work will be required to apply this model to aluminised and other highly oxygen-deficient explosives.

A comparison/validation of a fractional derivative model with an empirical model of non-linear shock waves in swelling shales

NASA Astrophysics Data System (ADS)

Droghei, Riccardo; Salusti, Ettore

2013-04-01

Control of drilling parameters, as fluid pressure, mud weight, salt concentration is essential to avoid instabilities when drilling through shale sections. To investigate shale deformation, fundamental for deep oil drilling and hydraulic fracturing for gas extraction ("fracking"), a non-linear model of mechanic and chemo-poroelastic interactions among fluid, solute and the solid matrix is here discussed. The two equations of this model describe the isothermal evolution of fluid pressure and solute density in a fluid saturated porous rock. Their solutions are quick non-linear Burger's solitary waves, potentially destructive for deep operations. In such analysis the effect of diffusion, that can play a particular role in fracking, is investigated. Then, following Civan (1998), both diffusive and shock waves are applied to fine particles filtration due to such quick transients , their effect on the adjacent rocks and the resulting time-delayed evolution. Notice how time delays in simple porous media dynamics have recently been analyzed using a fractional derivative approach. To make a tentative comparison of these two deeply different methods,in our model we insert fractional time derivatives, i.e. a kind of time-average of the fluid-rocks interactions. Then the delaying effects of fine particles filtration is compared with fractional model time delays. All this can be seen as an empirical check of these fractional models.

Ground-motion prediction equations for the average horizontal component of PGA, PGV, and 5%-damped PSA at spectral periods between 0.01 s and 10.0 s

USGS Publications Warehouse

Boore, D.M.; Atkinson, G.M.

2008-01-01

This paper contains ground-motion prediction equations (GMPEs) for average horizontal-component ground motions as a function of earthquake magnitude, distance from source to site, local average shear-wave velocity, and fault type. Our equations are for peak ground acceleration (PGA), peak ground velocity (PGV), and 5%-damped pseudo-absolute-acceleration spectra (PSA) at periods between 0.01 s and 10 s. They were derived by empirical regression of an extensive strong-motion database compiled by the 'PEER NGA' (Pacific Earthquake Engineering Research Center's Next Generation Attenuation) project. For periods less than 1 s, the analysis used 1,574 records from 58 mainshocks in the distance range from 0 km to 400 km (the number of available data decreased as period increased). The primary predictor variables are moment magnitude (M), closest horizontal distance to the surface projection of the fault plane (RJB), and the time-averaged shear-wave velocity from the surface to 30 m (VS30). The equations are applicable for M=5-8, RJB<200 km, and VS30= 180-1300 m/s. ?? 2008, Earthquake Engineering Research Institute.

Decomposition of hydroxy amino acids in foraminiferal tests; kinetics, mechanism and geochronological implications

USGS Publications Warehouse

Bada, J.L.; Shou, M.-Y.; Man, E.H.; Schroeder, R.A.

1978-01-01

The diagenesis of the hydroxy amino acids serine and threonine in foraminiferal tests has been investigated. The decomposition pathways of these amino acids are complex; the principal reactions appear to be dehydration, aldol cleavage and decarboxylation. Stereochemical studies indicate that the ??-amino-n-butyric acid (ABA) detected in foraminiferal tests is the end product of threonine dehydration pathway. Decomposition of serine and threonine in foraminiferal tests from two well-dated Caribbean deep-sea cores, P6304-8 and -9, has been found to follow irreversible first-order kinetics. Three empirical equations were derived for the disappearance of serine and threonine and the appearance of ABA. These equations can be used as a new geochronological method for dating foraminiferal tests from other deep-sea sediments. Preliminary results suggest that ages deduced from the ABA kinetics equation are most reliable because "species effect" and contamination problems are not important for this nonbiological amino acid. Because of the variable serine and threonine contents of modern foraminiferal species, it is likely that the accurate age estimates can be obtained from the serine and threonine decomposition equations only if a homogeneous species assemblage or single species sample isolated from mixed natural assemblages is used. ?? 1978.

The study and development of the empirical correlations equation of natural convection heat transfer on vertical rectangular sub-channels

NASA Astrophysics Data System (ADS)

Kamajaya, Ketut; Umar, Efrizon; Sudjatmi, K. S.

2012-06-01

This study focused on natural convection heat transfer using a vertical rectangular sub-channel and water as the coolant fluid. To conduct this study has been made pipe heaters are equipped with thermocouples. Each heater is equipped with five thermocouples along the heating pipes. The diameter of each heater is 2.54 cm and 45 cm in length. The distance between the central heating and the pitch is 29.5 cm. Test equipment is equipped with a primary cooling system, a secondary cooling system and a heat exchanger. The purpose of this study is to obtain new empirical correlations equations of the vertical rectangular sub-channel, especially for the natural convection heat transfer within a bundle of vertical cylinders rectangular arrangement sub-channels. The empirical correlation equation can support the thermo-hydraulic analysis of research nuclear reactors that utilize cylindrical fuel rods, and also can be used in designing of baffle-free vertical shell and tube heat exchangers. The results of this study that the empirical correlation equations of natural convection heat transfer coefficients with rectangular arrangement is Nu = 6.3357 (Ra.Dh/x)0.0740.

Deriving Equations of State for Specific Lakes and Inland Seas from Laboratory Measurements

NASA Astrophysics Data System (ADS)

Andrulionis, Natalia; Zavialov, Ivan; Zavialov, Peter; Osadchiev, Alexander; Kolokolova, Alexandra; Alukaeva, Alevtina; Izhitskiy, Alexander; Izhitskaya, Elena

2017-04-01

The equation of state is the dependence of water density on temperature, salinity, and pressure. It is important in many respects, in particular, for numerical modeling of marine systems. The widely used UNESCO equation of state, as well as the more recent and general TEOS-10 equation, are intended for the ocean waters. Hence, they are confined to salinities below 40 ‰ and, even more restrictively, valid only for ionic salt composition characteristic for the ocean. Both conditions do not hold for many lakes. Moreover, significant deviations of the ionic composition from the oceanic one have been documented for coastal zones, especially those exposed to river discharges. Therefore, the objective of this study was to find equations of state for areas or water bodies with non-oceanic ionic salt composition. In order to obtain the required equations, we analyzed water samples obtained in expeditions of 2014-2016 from the Black Sea, the Aral Sea, Lake Issyk-Kul and Caspian Sea. The filtered samples were submitted to high accuracy (up to 0.00001 g/cm3) density measurements in laboratory using the Anton Paar DMA 5000M in the temperature range from 1 to 29°C. The absolute salinity values of the initial samples were obtained through the dry residue method. Further, we diluted the samples by purified deionized water to produce different salinities. To control the accuracy of the dilution process, we used a reference sample of standard IAPSO-certified seawater at 35‰. The density versus salinity and temperature data obtained thereby were then approximated by a best fitting 2-order polynomial surface using the least squares method. This procedure yielded the approximate empirical equations of state for the selected marine areas (the Russian Black Sea shelf) and inland water bodies (the Aral Sea, the Lake Issyk-Kul, the Caspian Sea). The newly derived equations - even the one for the Black Sea shelf - are different from the oceanic equation significantly within the confidence intervals. We also analyzed the salt content in all samples using the ionic chromotography method and the potentiometric titration method and discussed the relations between the ionic composition on the one hand and density on the other.

Towards a universal model for carbon dioxide uptake by plants

DOE PAGES

Wang, Han; Prentice, I. Colin; Keenan, Trevor F.; ...

2017-09-04

Gross primary production (GPP) - the uptake of carbon dioxide (CO 2) by leaves, and its conversion to sugars by photosynthesis - is the basis for life on land. Earth System Models (ESMs) incorporating the interactions of land ecosystems and climate are used to predict the future of the terrestrial sink for anthropogenic CO 2. ESMs require accurate representation of GPP. However, current ESMs disagree on how GPP responds to environmental variations, suggesting a need for a more robust theoretical framework for modelling. Here in this work, we focus on a key quantity for GPP, the ratio of leaf internalmore » to external CO 2 (χ). χ is tightly regulated and depends on environmental conditions, but is represented empirically and incompletely in today's models. We show that a simple evolutionary optimality hypothesis predicts specific quantitative dependencies of χ on temperature, vapour pressure deficit and elevation; and that these same dependencies emerge from an independent analysis of empirical χ values, derived from a worldwide dataset of >3,500 leaf stable carbon isotope measurements. A single global equation embodying these relationships then unifies the empirical light-use efficiency model with the standard model of C 3 photosynthesis, and successfully predicts GPP measured at eddy-covariance flux sites. This success is notable given the equation's simplicity and broad applicability across biomes and plant functional types. Finally, it provides a theoretical underpinning for the analysis of plant functional coordination across species and emergent properties of ecosystems, and a potential basis for the reformulation of the controls of GPP in next-generation ESMs.« less

Towards a universal model for carbon dioxide uptake by plants

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

Wang, Han; Prentice, I. Colin; Keenan, Trevor F.

Gross primary production (GPP) - the uptake of carbon dioxide (CO 2) by leaves, and its conversion to sugars by photosynthesis - is the basis for life on land. Earth System Models (ESMs) incorporating the interactions of land ecosystems and climate are used to predict the future of the terrestrial sink for anthropogenic CO 2. ESMs require accurate representation of GPP. However, current ESMs disagree on how GPP responds to environmental variations, suggesting a need for a more robust theoretical framework for modelling. Here in this work, we focus on a key quantity for GPP, the ratio of leaf internalmore » to external CO 2 (χ). χ is tightly regulated and depends on environmental conditions, but is represented empirically and incompletely in today's models. We show that a simple evolutionary optimality hypothesis predicts specific quantitative dependencies of χ on temperature, vapour pressure deficit and elevation; and that these same dependencies emerge from an independent analysis of empirical χ values, derived from a worldwide dataset of >3,500 leaf stable carbon isotope measurements. A single global equation embodying these relationships then unifies the empirical light-use efficiency model with the standard model of C 3 photosynthesis, and successfully predicts GPP measured at eddy-covariance flux sites. This success is notable given the equation's simplicity and broad applicability across biomes and plant functional types. Finally, it provides a theoretical underpinning for the analysis of plant functional coordination across species and emergent properties of ecosystems, and a potential basis for the reformulation of the controls of GPP in next-generation ESMs.« less

Assessing Chaos in Sickle Cell Anemia Crises

NASA Astrophysics Data System (ADS)

Harris, Wesley; Le Floch, Francois

2006-11-01

Recent developments in sickle cell research and blood flow modeling allow for new interpretations of the sickle cell crises. With an appropriate set of theoretical and empirical equations describing the dynamics of the red cells in their environment, and the response of the capillaries to major changes in the rheology, a complete mathematical system has been derived. This system of equations is believed to be of major importance to provide new and significant insight into the causes of the disease and related crises. With simulations, it has been proven that the system transition from a periodic solution to a chaotic one, which illustrates the onset of crises from a regular blood flow synchronized with the heart beat. Moreover, the analysis of the effects of various physiological parameters exposes the potential to control chaotic solutions, which, in turn, could lead to the creation of new and more effective treatments for sickle cell anemia. .

Deterministic multidimensional nonuniform gap sampling.

PubMed

Worley, Bradley; Powers, Robert

2015-12-01

Born from empirical observations in nonuniformly sampled multidimensional NMR data relating to gaps between sampled points, the Poisson-gap sampling method has enjoyed widespread use in biomolecular NMR. While the majority of nonuniform sampling schemes are fully randomly drawn from probability densities that vary over a Nyquist grid, the Poisson-gap scheme employs constrained random deviates to minimize the gaps between sampled grid points. We describe a deterministic gap sampling method, based on the average behavior of Poisson-gap sampling, which performs comparably to its random counterpart with the additional benefit of completely deterministic behavior. We also introduce a general algorithm for multidimensional nonuniform sampling based on a gap equation, and apply it to yield a deterministic sampling scheme that combines burst-mode sampling features with those of Poisson-gap schemes. Finally, we derive a relationship between stochastic gap equations and the expectation value of their sampling probability densities. Copyright © 2015 Elsevier Inc. All rights reserved.

Comparative study of three-nucleon potentials in nuclear matter

NASA Astrophysics Data System (ADS)

Lovato, Alessandro; Benhar, Omar; Fantoni, Stefano; Schmidt, Kevin E.

2012-02-01

A new generation of local three-body potentials providing an excellent description of the properties of light nuclei, as well as of the neutron-deuteron doublet scattering length, has been recently derived. We have performed a comparative analysis of the equations of state of both pure neutron matter (PNM) and symmetric nuclear matter (SNM) at zero temperature obtained using these models of three-nucleon forces. In particular, we have carried out both variational and auxiliary field diffusion Monte Carlo calculations of the equation of state of PNM, while in the case of SNM we have only the variational approach has been considered. None of the considered potentials simultaneously explains the empirical equilibrium density and binding energy of symmetric nuclear matter. However, two of them provide reasonable values of the saturation density. The ambiguity concerning the treatment of the contact term of the chiral inspired potentials is discussed.

Full non-linear treatment of the global thermospheric wind system. I - Mathematical method and analysis of forces. II - Results and comparison with observations

NASA Technical Reports Server (NTRS)

Blum, P. W.; Harris, I.

1975-01-01

The equations of horizontal motion of the neutral atmosphere between 120 and 500 km are integrated with the inclusion of all nonlinear terms of the convective derivative and the viscous forces due to vertical and horizontal velocity gradients. Empirical models of the distribution of neutral and charged particles are assumed to be known. The model of velocities developed is a steady state model. In Part I the mathematical method used in the integration of the Navier-Stokes equations is described and the various forces are analyzed. Results of the method given in Part I are presented with comparison with previous calculations and observations of upper atmospheric winds. Conclusions are that nonlinear effects are only significant in the equatorial region, especially at solstice conditions and that nonlinear effects do not produce any superrotation.

Data-Driven H∞ Control for Nonlinear Distributed Parameter Systems.

PubMed

Luo, Biao; Huang, Tingwen; Wu, Huai-Ning; Yang, Xiong

2015-11-01

The data-driven H∞ control problem of nonlinear distributed parameter systems is considered in this paper. An off-policy learning method is developed to learn the H∞ control policy from real system data rather than the mathematical model. First, Karhunen-Loève decomposition is used to compute the empirical eigenfunctions, which are then employed to derive a reduced-order model (ROM) of slow subsystem based on the singular perturbation theory. The H∞ control problem is reformulated based on the ROM, which can be transformed to solve the Hamilton-Jacobi-Isaacs (HJI) equation, theoretically. To learn the solution of the HJI equation from real system data, a data-driven off-policy learning approach is proposed based on the simultaneous policy update algorithm and its convergence is proved. For implementation purpose, a neural network (NN)- based action-critic structure is developed, where a critic NN and two action NNs are employed to approximate the value function, control, and disturbance policies, respectively. Subsequently, a least-square NN weight-tuning rule is derived with the method of weighted residuals. Finally, the developed data-driven off-policy learning approach is applied to a nonlinear diffusion-reaction process, and the obtained results demonstrate its effectiveness.

BODYFIT-1FE: a computer code for three-dimensional steady-state/transient single-phase rod-bundle thermal-hydraulic analysis. Draft report

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

Chen, B.C.J.; Sha, W.T.; Doria, M.L.

1980-11-01

The governing equations, i.e., conservation equations for mass, momentum, and energy, are solved as a boundary-value problem in space and an initial-value problem in time. BODYFIT-1FE code uses the technique of boundary-fitted coordinate systems where all the physical boundaries are transformed to be coincident with constant coordinate lines in the transformed space. By using this technique, one can prescribe boundary conditions accurately without interpolation. The transformed governing equations in terms of the boundary-fitted coordinates are then solved by using implicit cell-by-cell procedure with a choice of either central or upwind convective derivatives. It is a true benchmark rod-bundle code withoutmore » invoking any assumptions in the case of laminar flow. However, for turbulent flow, some empiricism must be employed due to the closure problem of turbulence modeling. The detailed velocity and temperature distributions calculated from the code can be used to benchmark and calibrate empirical coefficients employed in subchannel codes and porous-medium analyses.« less

New dimension analyses with error analysis for quaking aspen and black spruce

NASA Technical Reports Server (NTRS)

Woods, K. D.; Botkin, D. B.; Feiveson, A. H.

1987-01-01

Dimension analysis for black spruce in wetland stands and trembling aspen are reported, including new approaches in error analysis. Biomass estimates for sacrificed trees have standard errors of 1 to 3%; standard errors for leaf areas are 10 to 20%. Bole biomass estimation accounts for most of the error for biomass, while estimation of branch characteristics and area/weight ratios accounts for the leaf area error. Error analysis provides insight for cost effective design of future analyses. Predictive equations for biomass and leaf area, with empirically derived estimators of prediction error, are given. Systematic prediction errors for small aspen trees and for leaf area of spruce from different site-types suggest a need for different predictive models within species. Predictive equations are compared with published equations; significant differences may be due to species responses to regional or site differences. Proportional contributions of component biomass in aspen change in ways related to tree size and stand development. Spruce maintains comparatively constant proportions with size, but shows changes corresponding to site. This suggests greater morphological plasticity of aspen and significance for spruce of nutrient conditions.

Local Linear Observed-Score Equating

ERIC Educational Resources Information Center

Wiberg, Marie; van der Linden, Wim J.

2011-01-01

Two methods of local linear observed-score equating for use with anchor-test and single-group designs are introduced. In an empirical study, the two methods were compared with the current traditional linear methods for observed-score equating. As a criterion, the bias in the equated scores relative to true equating based on Lord's (1980)…

Semi-empirical equation of limiting current for cobalt electrodeposition in the presence of magnetic field and additive electrolyte

NASA Astrophysics Data System (ADS)

Sudibyo, Aziz, N.

2016-02-01

One of the available methods to solve a roughening in cobalt electrodeposition is magneto electrodeposition (MED) in the presence of additive electrolyte. Semi-empirical equation of limiting current under a magnetic field for cobalt MED in the presence of boric acid as an additive electrolyte was successfully developed. This semi empirical equation shows the effects of the electrode area (A), the concentration of the electro active species (C), the diffusion coefficient of the electro active species (D), the kinematic viscosity of the electrolyte (v), magnetic strength (B) and the number of electrons involved in the redox process (n). The presence of boric acid led to decrease in the limiting current, but the acid was found useful as a buffer to avoid the local pH rise caused by parallel hydrogen evolution reaction (HER).

Calibration of an M L scale for South Africa using tectonic earthquake data recorded by the South African National Seismograph Network: 2006 to 2009

NASA Astrophysics Data System (ADS)

Saunders, Ian; Ottemöller, Lars; Brandt, Martin B. C.; Fourie, Christoffel J. S.

2013-04-01

A relation to determine local magnitude ( M L) based on the original Richter definition is empirically derived from synthetic Wood-Anderson seismograms recorded by the South African National Seismograph Network. In total, 263 earthquakes in the distance range 10 to 1,000 km, representing 1,681 trace amplitudes measured in nanometers from synthesized Wood-Anderson records on the vertical channel were considered to derive an attenuation relation appropriate for South Africa through multiple regression analysis. Additionally, station corrections were determined for 26 stations during the regression analysis resulting in values ranging between -0.31 and 0.50. The most appropriate M L scale for South Africa from this study satisfies the equation: {M_{{{L}}}} = {{lo}}{{{g}}_{{10}}}(A) + 1.149{{lo}}{{{g}}_{{10}}}(R) + 0.00063R + 2.04 - S The anelastic attenuation term derived from this study indicates that ground motion attenuation is significantly different from Southern California but comparable with stable continental regions.

Small-Sample Equating with Prior Information. Research Report. ETS RR-09-25

ERIC Educational Resources Information Center

Livingston, Samuel A.; Lewis, Charles

2009-01-01

This report proposes an empirical Bayes approach to the problem of equating scores on test forms taken by very small numbers of test takers. The equated score is estimated separately at each score point, making it unnecessary to model either the score distribution or the equating transformation. Prior information comes from equatings of other…

Constitutive Equation with Varying Parameters for Superplastic Flow Behavior

NASA Astrophysics Data System (ADS)

Guan, Zhiping; Ren, Mingwen; Jia, Hongjie; Zhao, Po; Ma, Pinkui

2014-03-01

In this study, constitutive equations for superplastic materials with an extra large elongation were investigated through mechanical analysis. From the view of phenomenology, firstly, some traditional empirical constitutive relations were standardized by restricting some strain paths and parameter conditions, and the coefficients in these relations were strictly given new mechanical definitions. Subsequently, a new, general constitutive equation with varying parameters was theoretically deduced based on the general mechanical equation of state. The superplastic tension test data of Zn-5%Al alloy at 340 °C under strain rates, velocities, and loads were employed for building a new constitutive equation and examining its validity. Analysis results indicated that the constitutive equation with varying parameters could characterize superplastic flow behavior in practical superplastic forming with high prediction accuracy and without any restriction of strain path or deformation condition, showing good industrial or scientific interest. On the contrary, those empirical equations have low prediction capabilities due to constant parameters and poor applicability because of the limit of special strain path or parameter conditions based on strict phenomenology.

Review of Thawing Time Prediction Models Depending
on Process Conditions and Product Characteristics

PubMed Central

Kluza, Franciszek; Spiess, Walter E. L.; Kozłowicz, Katarzyna

2016-01-01

Summary Determining thawing times of frozen foods is a challenging problem as the thermophysical properties of the product change during thawing. A number of calculation models and solutions have been developed. The proposed solutions range from relatively simple analytical equations based on a number of assumptions to a group of empirical approaches that sometimes require complex calculations. In this paper analytical, empirical and graphical models are presented and critically reviewed. The conditions of solution, limitations and possible applications of the models are discussed. The graphical and semi--graphical models are derived from numerical methods. Using the numerical methods is not always possible as running calculations takes time, whereas the specialized software and equipment are not always cheap. For these reasons, the application of analytical-empirical models is more useful for engineering. It is demonstrated that there is no simple, accurate and feasible analytical method for thawing time prediction. Consequently, simplified methods are needed for thawing time estimation of agricultural and food products. The review reveals the need for further improvement of the existing solutions or development of new ones that will enable accurate determination of thawing time within a wide range of practical conditions of heat transfer during processing. PMID:27904387

An Empirical Study of Atmospheric Correction Procedures for Regional Infrasound Amplitudes with Ground Truth.

NASA Astrophysics Data System (ADS)

Howard, J. E.

2014-12-01

This study focusses on improving methods of accounting for atmospheric effects on infrasound amplitudes observed on arrays at regional distances in the southwestern United States. Recordings at ranges of 150 to nearly 300 km from a repeating ground truth source of small HE explosions are used. The explosions range in actual weight from approximately 2000-4000 lbs. and are detonated year-round which provides signals for a wide range of atmospheric conditions. Three methods of correcting the observed amplitudes for atmospheric effects are investigated with the data set. The first corrects amplitudes for upper stratospheric wind as developed by Mutschlecner and Whitaker (1999) and uses the average wind speed between 45-55 km altitudes in the direction of propagation to derive an empirical correction formula. This approach was developed using large chemical and nuclear explosions and is tested with the smaller explosions for which shorter wavelengths cause the energy to be scattered by the smaller scale structure of the atmosphere. The second approach isa semi-empirical method using ray tracing to determine wind speed at ray turning heights where the wind estimates replace the wind values in the existing formula. Finally, parabolic equation (PE) modeling is used to predict the amplitudes at the arrays at 1 Hz. The PE amplitudes are compared to the observed amplitudes with a narrow band filter centered at 1 Hz. An analysis is performed of the conditions under which the empirical and semi-empirical methods fail and full wave methods must be used.

A physically-based Mie–Gruneisen equation of state to determine hot spot temperature distributions

DOE PAGES

Kittell, David Erik; Yarrington, Cole Davis

2016-07-14

Here, a physically-based form of the Mie–Grüneisen equation of state (EOS) is derived for calculating 1d planar shock temperatures, as well as hot spot temperature distributions from heterogeneous impact simulations. This form utilises a multi-term Einstein oscillator model for specific heat, and is completely algebraic in terms of temperature, volume, an integrating factor, and the cold curve energy. Moreover, any empirical relation for the reference pressure and energy may be substituted into the equations via the use of a generalised reference function. The complete EOS is then applied to calculations of the Hugoniot temperature and simulation of hydrodynamic pore collapsemore » using data for the secondary explosive, hexanitrostilbene (HNS). From these results, it is shown that the choice of EOS is even more significant for determining hot spot temperature distributions than planar shock states. The complete EOS is also compared to an alternative derivation assuming that specific heat is a function of temperature alone, i.e. cv(T). Temperature discrepancies on the order of 100–600 K were observed corresponding to the shock pressures required to initiate HNS (near 10 GPa). Overall, the results of this work will improve confidence in temperature predictions. By adopting this EOS, future work may be able to assign physical meaning to other thermally sensitive constitutive model parameters necessary to predict the shock initiation and detonation of heterogeneous explosives.« less

Ballistic Limit Equation for Single Wall Titanium

NASA Technical Reports Server (NTRS)

Ratliff, J. M.; Christiansen, Eric L.; Bryant, C.

2009-01-01

Hypervelocity impact tests and hydrocode simulations were used to determine the ballistic limit equation (BLE) for perforation of a titanium wall, as a function of wall thickness. Two titanium alloys were considered, and separate BLEs were derived for each. Tested wall thicknesses ranged from 0.5mm to 2.0mm. The single-wall damage equation of Cour-Palais [ref. 1] was used to analyze the Ti wall's shielding effectiveness. It was concluded that the Cour-Palais single-wall equation produced a non-conservative prediction of the ballistic limit for the Ti shield. The inaccurate prediction was not a particularly surprising result; the Cour-Palais single-wall BLE contains shield material properties as parameters, but it was formulated only from tests of different aluminum alloys. Single-wall Ti shield tests were run (thicknesses of 2.0 mm, 1.5 mm, 1.0 mm, and 0.5 mm) on Ti 15-3-3-3 material custom cut from rod stock. Hypervelocity impact (HVI) tests were used to establish the failure threshold empirically, using the additional constraint that the damage scales with impact energy, as was indicated by hydrocode simulations. The criterion for shield failure was defined as no detached spall from the shield back surface during HVI. Based on the test results, which confirmed an approximately energy-dependent shield effectiveness, the Cour-Palais equation was modified.

Large wood influence on stream metabolism at a reach-scale in the Assabet River, Massachusetts

NASA Astrophysics Data System (ADS)

David, G. C. L.; Snyder, N. P.; Rosario, G. M.

2016-12-01

Total stream metabolism (TSM) represents the transfer of carbon through a channel by both primary production and respiration, and thus represents the movement of energy through a watershed. Large wood (LW) creates geomorphically complex channels by diverting flows, altering shear stresses on the channel bed and banks, and pool development. The increase in habitat complexity around LW is expected to increase TSM, but this change has not been directly measured. In this study, we measured changes in TSM around a LW jam in a Massachusetts river. Dissolved oxygen (DO) time series data are used to quantify gross primary production (GPP), ecosystem respiration (ER), which equal TSM when summed. Two primary objectives of this study are to (1) assess changes in TSM around LW and (2) compare empirical methods of deriving TSM to Grace et al.'s (2015) BASE model. We hypothesized that LW would increase TSM by providing larger pools, increasing coverage for fish and macroinvertebrates, increasing organic matter accumulation, and providing a place for primary producers to anchor and grow. The Assabet River is a 78 km2 drainage basin in central Massachusetts that provides public water supply to 7 towns. A change in TSM over a reach-scale was assessed using two YSI 6-Series Multiparameter Water Quality sondes over a 140 m long pool-riffle open meadow section. The reach included 6 pools and one LW jam. Every two weeks from July to November 2015, the sondes were moved to different pools. The sondes collected DO, temperature, depth, pH, salinity, light intensity, and turbidity at 15-minute intervals. Velocity (V) and discharge (Q) were measured weekly around the sondes and at established cross sections. Instantaneous V and Q were calculated for each sonde by modeling flows in HEC-RAS. Overall, TSM was heavily influenced by the pool size and indirectly to the LW jam which was associated with the largest pool. The largest error in TSM calculations is related to the empirically calculated reaeration flux (k), which represents oxygen inputs from the atmosphere. We used two well-established empirical equations to compare k values to the BASE model. The model agreed with empirically derived values during intermediate and high Q. Modeled GPP and ER diverged, sometimes by an order of magnitude, from the empirically derived results during the lowest flows.

Development of Response Spectral Ground Motion Prediction Equations from Empirical Models for Fourier Spectra and Duration of Ground Motion

NASA Astrophysics Data System (ADS)

Bora, S. S.; Scherbaum, F.; Kuehn, N. M.; Stafford, P.; Edwards, B.

2014-12-01

In a probabilistic seismic hazard assessment (PSHA) framework, it still remains a challenge to adjust ground motion prediction equations (GMPEs) for application in different seismological environments. In this context, this study presents a complete framework for the development of a response spectral GMPE easily adjustable to different seismological conditions; and which does not suffer from the technical problems associated with the adjustment in response spectral domain. Essentially, the approach consists of an empirical FAS (Fourier Amplitude Spectrum) model and a duration model for ground motion which are combined within the random vibration theory (RVT) framework to obtain the full response spectral ordinates. Additionally, FAS corresponding to individual acceleration records are extrapolated beyond the frequency range defined by the data using the stochastic FAS model, obtained by inversion as described in Edwards & Faeh, (2013). To that end, an empirical model for a duration, which is tuned to optimize the fit between RVT based and observed response spectral ordinate, at each oscillator frequency is derived. Although, the main motive of the presented approach was to address the adjustability issues of response spectral GMPEs; comparison, of median predicted response spectra with the other regional models indicate that presented approach can also be used as a stand-alone model. Besides that, a significantly lower aleatory variability (σ<0.5 in log units) in comparison to other regional models, at shorter periods brands it to a potentially viable alternative to the classical regression (on response spectral ordinates) based GMPEs for seismic hazard studies in the near future. The dataset used for the presented analysis is a subset of the recently compiled database RESORCE-2012 across Europe, Middle East and the Mediterranean region.

Analytical Modeling of Pressure Wall Hole Size and Maximum Tip-to-Tip Crack Length for Perforating Normal and Oblique Orbital Debris Impacts

NASA Technical Reports Server (NTRS)

Schonberg, William P.; Mohamed, Essam

1997-01-01

This report presents the results of a study whose objective was to develop first-principles-based models of hole size and maximum tip-to-tip crack length for a spacecraft module pressure wall that has been perforated in an orbital debris particle impact. The hole size and crack length models are developed by sequentially characterizing the phenomena comprising the orbital debris impact event, including the initial impact, the creation and motion of a debris cloud within the dual-wall system, the impact of the debris cloud on the pressure wall, the deformation of the pressure wall due to debris cloud impact loading prior to crack formation, pressure wall crack initiation, propagation, and arrest, and finally pressure wall deformation following crack initiation and growth. The model development has been accomplished through the application of elementary shock physics and thermodynamic theory, as well as the principles of mass, momentum, and energy conservation. The predictions of the model developed herein are compared against the predictions of empirically-based equations for hole diameters and maximum tip-to-tip crack length for three International Space Station wall configurations. The ISS wall systems considered are the baseline U.S. Lab Cylinder, the enhanced U.S. Lab Cylinder, and the U.S. Lab Endcone. The empirical predictor equations were derived from experimentally obtained hole diameters and crack length data. The original model predictions did not compare favorably with the experimental data, especially for cases in which pressure wall petalling did not occur. Several modifications were made to the original model to bring its predictions closer in line with the experimental results. Following the adjustment of several empirical constants, the predictions of the modified analytical model were in much closer agreement with the experimental results.

Study of clad ballooning and rupture behaviour of Indian PHWR fuel pins under transient heating condition in steam environment

NASA Astrophysics Data System (ADS)

Sawarn, Tapan K.; Banerjee, Suparna; Sheelvantra, Smita S.; Singh, J. L.; Bhasin, Vivek

2017-11-01

This paper presents the results of the investigation on the deformation and rupture characteristics of Indian pressurized heavy water reactor (IPHWR) fuel pins under simulated loss of coolant accident (LOCA) condition in steam environment. Transient heating experiments were carried out on single fuel pin internally pressurized with argon gas in the range 3-70 bar. Effect of internal pressure on burst temperature, influence of burst temperature on the circumferential strain and rupture opening area were also studied. Two circumferential strain maxima at the burst temperatures of 740 & ∼979 °C and a minimum at the burst temperature of ∼868 °C were observed. It was found that oxidation had considerable effect on the burst behavior. Test data were used to derive a direct empirical correlation for burst stress exclusively as a function of temperature. The ballooning and rupture behaviours in steam and argon environments have been compared. Experimental data were examined against various correlations using Erbacher equation and author's previous correlation in argon. A second burst correlation has also been developed combining the equation in argon from the previous work of the authors and an exponential factor with oxygen content as a parameter assuming the burst stress to be a function of both temperature and oxygen concentration. The burst temperatures predicted by this empirical correlation are in good agreement with the test data.

The physics behind Van der Burgh's empirical equation, providing a new predictive equation for salinity intrusion in estuaries

NASA Astrophysics Data System (ADS)

Zhang, Zhilin; Savenije, Hubert H. G.

2017-07-01

The practical value of the surprisingly simple Van der Burgh equation in predicting saline water intrusion in alluvial estuaries is well documented, but the physical foundation of the equation is still weak. In this paper we provide a connection between the empirical equation and the theoretical literature, leading to a theoretical range of Van der Burgh's coefficient of 1/2 < K < 2/3 for density-driven mixing which falls within the feasible range of 0 < K < 1. In addition, we developed a one-dimensional predictive equation for the dispersion of salinity as a function of local hydraulic parameters that can vary along the estuary axis, including mixing due to tide-driven residual circulation. This type of mixing is relevant in the wider part of alluvial estuaries where preferential ebb and flood channels appear. Subsequently, this dispersion equation is combined with the salt balance equation to obtain a new predictive analytical equation for the longitudinal salinity distribution. Finally, the new equation was tested and applied to a large database of observations in alluvial estuaries, whereby the calibrated K values appeared to correspond well to the theoretical range.

A reduced-order model from high-dimensional frictional hysteresis

PubMed Central

Biswas, Saurabh; Chatterjee, Anindya

2014-01-01

Hysteresis in material behaviour includes both signum nonlinearities as well as high dimensionality. Available models for component-level hysteretic behaviour are empirical. Here, we derive a low-order model for rate-independent hysteresis from a high-dimensional massless frictional system. The original system, being given in terms of signs of velocities, is first solved incrementally using a linear complementarity problem formulation. From this numerical solution, to develop a reduced-order model, basis vectors are chosen using the singular value decomposition. The slip direction in generalized coordinates is identified as the minimizer of a dissipation-related function. That function includes terms for frictional dissipation through signum nonlinearities at many friction sites. Luckily, it allows a convenient analytical approximation. Upon solution of the approximated minimization problem, the slip direction is found. A final evolution equation for a few states is then obtained that gives a good match with the full solution. The model obtained here may lead to new insights into hysteresis as well as better empirical modelling thereof. PMID:24910522

Equating Scores from Adaptive to Linear Tests

ERIC Educational Resources Information Center

van der Linden, Wim J.

2006-01-01

Two local methods for observed-score equating are applied to the problem of equating an adaptive test to a linear test. In an empirical study, the methods were evaluated against a method based on the test characteristic function (TCF) of the linear test and traditional equipercentile equating applied to the ability estimates on the adaptive test…

Unified Theory for Decoding the Signals from X-Ray Florescence and X-Ray Diffraction of Mixtures.

PubMed

Chung, Frank H

2017-05-01

For research and development or for solving technical problems, we often need to know the chemical composition of an unknown mixture, which is coded and stored in the signals of its X-ray fluorescence (XRF) and X-ray diffraction (XRD). X-ray fluorescence gives chemical elements, whereas XRD gives chemical compounds. The major problem in XRF and XRD analyses is the complex matrix effect. The conventional technique to deal with the matrix effect is to construct empirical calibration lines with standards for each element or compound sought, which is tedious and time-consuming. A unified theory of quantitative XRF analysis is presented here. The idea is to cancel the matrix effect mathematically. It turns out that the decoding equation for quantitative XRF analysis is identical to that for quantitative XRD analysis although the physics of XRD and XRF are fundamentally different. The XRD work has been published and practiced worldwide. The unified theory derives a new intensity-concentration equation of XRF, which is free from the matrix effect and valid for a wide range of concentrations. The linear decoding equation establishes a constant slope for each element sought, hence eliminating the work on calibration lines. The simple linear decoding equation has been verified by 18 experiments.

Auto-Bäcklund transformations for a matrix partial differential equation

NASA Astrophysics Data System (ADS)

Gordoa, P. R.; Pickering, A.

2018-07-01

We derive auto-Bäcklund transformations, analogous to those of the matrix second Painlevé equation, for a matrix partial differential equation. We also then use these auto-Bäcklund transformations to derive matrix equations involving shifts in a discrete variable, a process analogous to the use of the auto-Bäcklund transformations of the matrix second Painlevé equation to derive a discrete matrix first Painlevé equation. The equations thus derived then include amongst other examples a semidiscrete matrix equation which can be considered to be an extension of this discrete matrix first Painlevé equation. The application of this technique to the auto-Bäcklund transformations of the scalar case of our partial differential equation has not been considered before, and so the results obtained here in this scalar case are also new. Other equations obtained here using this technique include a scalar semidiscrete equation which arises in the case of the second Painlevé equation, and which does not seem to have been thus derived previously.

Magnetic minerals' classification for sources of magnetic anomalies

NASA Astrophysics Data System (ADS)

Kletetschka, G.; Wieczorek, M. A.

2016-12-01

Our analysis allows interpretation of magnetic anomalies detected in meteorites, on Mars and Moon, and other bodies where the sources of magnetic field can be assumed to be thermoremanent magnetization (Mtr). We show how the specific approach allows reconsideration of the major magnetic carriers on Moon and Mars. Furthermore we are deriving a generalized equation for iron concentration estimate from magnetizations derived from crustal magnetic anomalies on the Moon. There is fundamental linear relation between the magnetic efficiency of thermoremanent magnetization Mtr measured at room temperature and level of the ambient field present at the time of acquisition. We used experimental data for derivation of the empirical constants for paleofield estimate equations. Specific magnetic mineral carriers from single domain (SD) through pseudosingle domain (PSD) to multidomain (MD) states include iron, meteoritic iron, magnetite, maghemite, pyrrhotite, and hematite. The Mtr/Msr is linearly proportional to the product of the magnetizing field and saturation remanence, while the proportionality constant is independent of magnetic mineralogy, domain state, or composition. We show that the level of magnetic paleofield record relates to two types of demagnetizing field that act as a barrier against the domain wall pinning during the magnetic acquisition. The first type of demagnetizing field relates to saturation magnetization constant derived from the distribution of Bohr's magnetons within the crystal lattice. The second type of demagnetizing field originates from the effect of shape of the magnetic minerals. Knowledge of the character of these demagnetizing fields is a prerequisite for paleofield estimates from rocks containing known magnetic mineralogy and magnetic shape anisotropy.

Two-population dynamics in a growing network model

NASA Astrophysics Data System (ADS)

Ivanova, Kristinka; Iordanov, Ivan

2012-02-01

We introduce a growing network evolution model with nodal attributes. The model describes the interactions between potentially violent V and non-violent N agents who have different affinities in establishing connections within their own population versus between the populations. The model is able to generate all stable triads observed in real social systems. In the framework of rate equations theory, we employ the mean-field approximation to derive analytical expressions of the degree distribution and the local clustering coefficient for each type of nodes. Analytical derivations agree well with numerical simulation results. The assortativity of the potentially violent network qualitatively resembles the connectivity pattern in terrorist networks that was recently reported. The assortativity of the network driven by aggression shows clearly different behavior than the assortativity of the networks with connections of non-aggressive nature in agreement with recent empirical results of an online social system.

The effects of trace impurities in coal-derived liquid fuels on deposition and accelerated high temperature corrosion of cast superalloys

NASA Technical Reports Server (NTRS)

Lowell, C. E.; Deadmore, D. J.; Santoro, G. J.; Kohl, F. J.

1981-01-01

The effects of trace metal impurities in coal-derived liquids on deposition, high temperature corrosion and fouling were examined. Alloys were burner rig tested from 800 to 1100 C and corrosion was evaluated as a function of potential impurities. Actual and doped fuel test were used to define an empirical life prediction equation. An evaluation of inhibitors to reduce or eliminate accelerated corrosion was made. Barium and strontium were found to limit attack. Intermittent application of the inhibitors or silicon additions were found to be effective techniques for controlling deposition without losing the inhibitor benefits. A computer program was used to predict the dew points and compositions of deposits. These predictions were confirmed in deposition test. The potential for such deposits to plug cooling holes of turbine airfoils was evaluated. Tests indicated that, while a potential problem exists, it strongly depended on minor impurity variations.

Jet Aeroacoustics: Noise Generation Mechanism and Prediction

NASA Technical Reports Server (NTRS)

Tam, Christopher

1998-01-01

This report covers the third year research effort of the project. The research work focussed on the fine scale mixing noise of both subsonic and supersonic jets and the effects of nozzle geometry and tabs on subsonic jet noise. In publication 1, a new semi-empirical theory of jet mixing noise from fine scale turbulence is developed. By an analogy to gas kinetic theory, it is shown that the source of noise is related to the time fluctuations of the turbulence kinetic theory. On starting with the Reynolds Averaged Navier-Stokes equations, a formula for the radiated noise is derived. An empirical model of the space-time correlation function of the turbulence kinetic energy is adopted. The form of the model is in good agreement with the space-time two-point velocity correlation function measured by Davies and coworkers. The parameters of the correlation are related to the parameters of the k-epsilon turbulence model. Thus the theory is self-contained. Extensive comparisons between the computed noise spectrum of the theory and experimental measured have been carried out. The parameters include jet Mach number from 0.3 to 2.0 and temperature ratio from 1.0 to 4.8. Excellent agreements are found in the spectrum shape, noise intensity and directivity. It is envisaged that the theory would supercede all semi-empirical and totally empirical jet noise prediction methods in current use.

Standard Errors of Equating for the Percentile Rank-Based Equipercentile Equating with Log-Linear Presmoothing

ERIC Educational Resources Information Center

Wang, Tianyou

2009-01-01

Holland and colleagues derived a formula for analytical standard error of equating using the delta-method for the kernel equating method. Extending their derivation, this article derives an analytical standard error of equating procedure for the conventional percentile rank-based equipercentile equating with log-linear smoothing. This procedure is…

Further Evaluation of an Emperical Equation for Annual Total Evaporation

NASA Technical Reports Server (NTRS)

Choudhury, Bhaskar J.

1999-01-01

An empirical equation for annual total evaporation based on annual precipitation and net radiation was found to provide evaporation within 10% of the observed values at seven locations within temperate and tropical regions, but it overestimated evaporation by 90% at one location within the tundra region. A synthesis of observations at two other locations within the tundra region gives overestimates of about 65%. A general analysis of observed precipitation, net radiation, and runoff within the tundra region shows that the empirical equation is generally biased to overestimate annual evaporation within the tundra region. A theoretical analysis is being done to understand the reason behind this bias.

Concentration Dependences of the Surface Tension and Density of Solutions of Acetone-Ethanol-Water Systems at 293 K

NASA Astrophysics Data System (ADS)

Dadashev, R. Kh.; Dzhambulatov, R. S.; Mezhidov, V. Kh.; Elimkhanov, D. Z.

2018-05-01

Concentration dependences of the surface tension and density of solutions of three-component acetone-ethanol-water systems and the bounding binary systems at 273 K are studied. The molar volume, adsorption, and composition of surface layers are calculated. Experimental data and calculations show that three-component solutions are close to ideal ones. The surface tensions of these solutions are calculated using semi-empirical and theoretical equations. Theoretical equations qualitatively convey the concentration dependence of surface tension. A semi-empirical method based on the Köhler equation allows us to predict the concentration dependence of surface tension within the experimental error.

Empirical equation for predicting the surface tension of some liquid metals at their melting point

NASA Astrophysics Data System (ADS)

Ceotto, D.

2014-07-01

A new empirical equation is proposed for predicting the surface tension of some pure metals at their melting point. The investigation has been conducted adopting a statistical approach using some of the most accredited data available in literature. It is found that for Ag, Al, Au, Co, Cu, Fe, Ni, and Pb the surface tension can be conveniently expressed in function of the latent heat of fusion and of the geometrical parameters of an ideal liquid spherical drop. The equation proposed has been compared also with the model proposed by Lu and Jiang giving satisfactory agreement for the metals considered.

Receptor binding kinetics equations: Derivation using the Laplace transform method.

PubMed

Hoare, Sam R J

Measuring unlabeled ligand receptor binding kinetics is valuable in optimizing and understanding drug action. Unfortunately, deriving equations for estimating kinetic parameters is challenging because it involves calculus; integration can be a frustrating barrier to the pharmacologist seeking to measure simple rate parameters. Here, a well-known tool for simplifying the derivation, the Laplace transform, is applied to models of receptor-ligand interaction. The method transforms differential equations to a form in which simple algebra can be applied to solve for the variable of interest, for example the concentration of ligand-bound receptor. The goal is to provide instruction using familiar examples, to enable investigators familiar with handling equilibrium binding equations to derive kinetic equations for receptor-ligand interaction. First, the Laplace transform is used to derive the equations for association and dissociation of labeled ligand binding. Next, its use for unlabeled ligand kinetic equations is exemplified by a full derivation of the kinetics of competitive binding equation. Finally, new unlabeled ligand equations are derived using the Laplace transform. These equations incorporate a pre-incubation step with unlabeled or labeled ligand. Four equations for measuring unlabeled ligand kinetics were compared and the two new equations verified by comparison with numerical solution. Importantly, the equations have not been verified with experimental data because no such experiments are evident in the literature. Equations were formatted for use in the curve-fitting program GraphPad Prism 6.0 and fitted to simulated data. This description of the Laplace transform method will enable pharmacologists to derive kinetic equations for their model or experimental paradigm under study. Application of the transform will expand the set of equations available for the pharmacologist to measure unlabeled ligand binding kinetics, and for other time-dependent pharmacological activities. Copyright © 2017 Elsevier Inc. All rights reserved.

Exact multisoliton solutions of general nonlinear Schrödinger equation with derivative.

PubMed

Li, Qi; Duan, Qiu-yuan; Zhang, Jian-bing

2014-01-01

Multisoliton solutions are derived for a general nonlinear Schrödinger equation with derivative by using Hirota's approach. The dynamics of one-soliton solution and two-soliton interactions are also illustrated. The considered equation can reduce to nonlinear Schrödinger equation with derivative as well as the solutions.

Kernel and Traditional Equipercentile Equating with Degrees of Presmoothing. Research Report. ETS RR-07-15

ERIC Educational Resources Information Center

Moses, Tim; Holland, Paul

2007-01-01

The purpose of this study was to empirically evaluate the impact of loglinear presmoothing accuracy on equating bias and variability across chained and post-stratification equating methods, kernel and percentile-rank continuization methods, and sample sizes. The results of evaluating presmoothing on equating accuracy generally agreed with those of…

A simple analytical model for dynamics of time-varying target leverage ratios

NASA Astrophysics Data System (ADS)

Lo, C. F.; Hui, C. H.

2012-03-01

In this paper we have formulated a simple theoretical model for the dynamics of the time-varying target leverage ratio of a firm under some assumptions based upon empirical observations. In our theoretical model the time evolution of the target leverage ratio of a firm can be derived self-consistently from a set of coupled Ito's stochastic differential equations governing the leverage ratios of an ensemble of firms by the nonlinear Fokker-Planck equation approach. The theoretically derived time paths of the target leverage ratio bear great resemblance to those used in the time-dependent stationary-leverage (TDSL) model [Hui et al., Int. Rev. Financ. Analy. 15, 220 (2006)]. Thus, our simple model is able to provide a theoretical foundation for the selected time paths of the target leverage ratio in the TDSL model. We also examine how the pace of the adjustment of a firm's target ratio, the volatility of the leverage ratio and the current leverage ratio affect the dynamics of the time-varying target leverage ratio. Hence, with the proposed dynamics of the time-dependent target leverage ratio, the TDSL model can be readily applied to generate the default probabilities of individual firms and to assess the default risk of the firms.

Empirical relationships between instrumental ground motions and observed intensities for two great Chilean subduction zone earthquakes

NASA Astrophysics Data System (ADS)

Cilia, M. G.; Baker, L. M.

2015-12-01

We determine empirical relationships between instrumental peak ground motions and observed intensities for two great Chilean subduction earthquakes: the 2010 Mw8.8 Maule earthquake and the 2014 Mw8.2 Iquique earthquake. Both occurred immediately offshore on the primary plate boundary interface between the Nazca and South America plates. They are among the largest earthquakes to be instrumentally recorded; the 2010 Maule event is the second largest earthquake to produce strong motion recordings. Ground motion to intensity conversion equations (GMICEs) are used to reconstruct the distribution of shaking for historical earthquakes by using intensities estimated from contemporary accounts. Most great (M>8) earthquakes, like these, occur within subduction zones, yet few GMICEs exist for subduction earthquakes. It is unclear whether GMICEs developed for active crustal regions, such as California, can be scaled up to the large M of subduction zone events, or if new data sets must be analyzed to develop separate subduction GMICEs. To address this question, we pair instrumental peak ground motions, both acceleration (PGA) and velocity (PGV), with intensities derived from onsite surveys of earthquake damage made in the weeks after the events and internet-derived felt reports. We fit a linear predictive equation between the geometric mean of the maximum PGA or PGV of the two horizontal components and intensity, using linear least squares. We use a weighting scheme to express the uncertainty of the pairings based on a station's proximity to the nearest intensity observation. The intensity data derived from the onsite surveys is a complete, high-quality investigation of the earthquake damage. We perform the computations using both the survey data and community decimal intensities (CDI) calculated from felt reports volunteered by citizens (USGS "Did You Feel It", DYFI) and compare the results. We compare the GMICEs we developed to the most widely used GMICEs from California and central US earthquakes, and global earthquakes. Existing GMICEs consistently over-predict intensity for these two subduction events. This may be a regional difference, or a magnitude-dependent effect. Currently, however, there is not enough data from these great subduction earthquakes to prefer one interpretation over the other.

Identification of unmeasured variables in the set of model constraints of the data reconciliation in a power unit

NASA Astrophysics Data System (ADS)

Szega, Marcin; Nowak, Grzegorz Tadeusz

2013-12-01

In generalized method of data reconciliation as equations of conditions beside substance and energy balances can be used equations which don't have precisely the status of conservation lows. Empirical coefficients in these equations are traded as unknowns' values. To this kind of equations, in application of the generalized method of data reconciliation in supercritical power unit, can be classified: steam flow capacity of a turbine for a group of stages, adiabatic internal efficiency of group of stages, equations for pressure drop in pipelines and equations for heat transfer in regeneration heat exchangers. Mathematical model of a power unit was developed in the code Thermoflex. Using this model the off-design calculation has been made in several points of loads for the power unit. Using these calculations identification of unknown values and empirical coefficients for generalized method of data reconciliation used in power unit has been made. Additional equations of conditions will be used in the generalized method of data reconciliation which will be used in optimization of measurement placement in redundant measurement system in power unit for new control systems

Equations of state of anhydrous AlF3 and AlI3: Modeling of extreme condition halide chemistry

NASA Astrophysics Data System (ADS)

Stavrou, Elissaios; Zaug, Joseph M.; Bastea, Sorin; Crowhurst, Jonathan C.; Goncharov, Alexander F.; Radousky, Harry B.; Armstrong, Michael R.; Roberts, Sarah K.; Plaue, Jonathan W.

2015-06-01

Pressure dependent angle-dispersive x-ray powder diffraction measurements of alpha-phase aluminum trifluoride (α-AlF3) and separately, aluminum triiodide (AlI3) were conducted using a diamond-anvil cell. Results at 295 K extend to 50 GPa. The equations of state of AlF3 and AlI3 were determined through refinements of collected x-ray diffraction patterns. The respective bulk moduli and corresponding pressure derivatives are reported for multiple orders of the Birch-Murnaghan (B-M), finite-strain (F-f), and higher pressure finite-strain (G-g) EOS analysis models. Aluminum trifluoride exhibits an apparent isostructural phase transition at approximately 12 GPa. Aluminum triiodide also undergoes a second-order atomic rearrangement: applied stress transformed a monoclinically distorted face centered cubic (fcc) structure into a standard fcc structural arrangement of iodine atoms. Results from semi-empirical thermochemical computations of energetic materials formulated with fluorine containing reactants were obtained with the aim of predicting the yield of halogenated products.

Electron-impact vibrational relaxation in high-temperature nitrogen

NASA Technical Reports Server (NTRS)

Lee, Jong-Hun

1992-01-01

Vibrational relaxation process of N2 molecules by electron-impact is examined for the future planetary entry environments. Multiple-quantum transitions from excited states to higher/lower states are considered for the electronic ground state of the nitrogen molecule N2 (X 1Sigma-g(+)). Vibrational excitation and deexcitation rate coefficients obtained by computational quantum chemistry are incorporated into the 'diffusion model' to evaluate the time variations of vibrational number densities of each energy state and total vibrational energy. Results show a non-Boltzmann distribution of number densities at the earlier stage of relaxation, which in turn suppresses the equilibrium process but affects little the time variation of total vibrational energy. An approximate rate equation and a corresponding relaxation time from the excited states, compatible with the system of flow conservation equations, are derived. The relaxation time from the excited states indicates the weak dependency of the initial vibrational temperature. The empirical curve-fit formula for the improved e-V relaxation time is obtained.

Turbulent flame propagation and combustion in spark ignition engines

NASA Technical Reports Server (NTRS)

Beretta, G. P.; Rashidi, M.; Keck, J. C.

1983-01-01

Pressure measurements synchronized with high-speed motion-picture records of flame propagation have been made in a transparent-piston engine. The data show that the initial expansion speed of the flame front is close to that of a laminar flame. As the flame expands, its speed rapidly accelerates to a quasi-steady value comparable with that of the turbulent velocity fluctuations in the unburned gas. During the quasi-steady propagation phase, a significant fraction of the gas behind the visible front is unburned. Final burnout of the charge may be approximated by an exponential decay in time. The data have been analyzed in a model-independent way to obtain a set of empirical equations for calculating mass burning rates in spark-ignition engines. The burning equations contain three parameters: the laminar burning speed, a characteristic speed (uT), and a characteristic length (lT). The laminar burning speed is known from laboratory measurements. Tentative correlations relating uT and lT to engine geometry and operating variables have been derived from the engine data.

A covariance correction that accounts for correlation estimation to improve finite-sample inference with generalized estimating equations: A study on its applicability with structured correlation matrices

PubMed Central

Westgate, Philip M.

2016-01-01

When generalized estimating equations (GEE) incorporate an unstructured working correlation matrix, the variances of regression parameter estimates can inflate due to the estimation of the correlation parameters. In previous work, an approximation for this inflation that results in a corrected version of the sandwich formula for the covariance matrix of regression parameter estimates was derived. Use of this correction for correlation structure selection also reduces the over-selection of the unstructured working correlation matrix. In this manuscript, we conduct a simulation study to demonstrate that an increase in variances of regression parameter estimates can occur when GEE incorporates structured working correlation matrices as well. Correspondingly, we show the ability of the corrected version of the sandwich formula to improve the validity of inference and correlation structure selection. We also study the relative influences of two popular corrections to a different source of bias in the empirical sandwich covariance estimator. PMID:27818539

A computer program for borehole compensation of dual-detector density well logs

USGS Publications Warehouse

Scott, James Henry

1978-01-01

The computer program described in this report was developed for applying a borehole-rugosity and mudcake compensation algorithm to dual-density logs using the following information: the water level in the drill hole, hole diameter (from a caliper log if available, or the nominal drill diameter if not), and the two gamma-ray count rate logs from the near and far detectors of the density probe. The equations that represent the compensation algorithm and the calibration of the two detectors (for converting countrate or density) were derived specifically for a probe manufactured by Comprobe Inc. (5.4 cm O.D. dual-density-caliper); they are not applicable to other probes. However, equivalent calibration and compensation equations can be empirically determined for any other similar two-detector density probes and substituted in the computer program listed in this report. * Use of brand names in this report does not necessarily constitute endorsement by the U.S. Geological Survey.

A covariance correction that accounts for correlation estimation to improve finite-sample inference with generalized estimating equations: A study on its applicability with structured correlation matrices.

PubMed

Westgate, Philip M

2016-01-01

When generalized estimating equations (GEE) incorporate an unstructured working correlation matrix, the variances of regression parameter estimates can inflate due to the estimation of the correlation parameters. In previous work, an approximation for this inflation that results in a corrected version of the sandwich formula for the covariance matrix of regression parameter estimates was derived. Use of this correction for correlation structure selection also reduces the over-selection of the unstructured working correlation matrix. In this manuscript, we conduct a simulation study to demonstrate that an increase in variances of regression parameter estimates can occur when GEE incorporates structured working correlation matrices as well. Correspondingly, we show the ability of the corrected version of the sandwich formula to improve the validity of inference and correlation structure selection. We also study the relative influences of two popular corrections to a different source of bias in the empirical sandwich covariance estimator.

Calculation of effective penetration depth in X-ray diffraction for pharmaceutical solids.

PubMed

Liu, Jodi; Saw, Robert E; Kiang, Y-H

2010-09-01

The use of the glancing incidence X-ray diffraction configuration to depth profile surface phase transformations is of interest to pharmaceutical scientists. The Parratt equation has been used to depth profile phase changes in pharmaceutical compacts. However, it was derived to calculate 1/e penetration at glancing incident angles slightly below the critical angle of condensed matter and is, therefore, applicable to surface studies of materials such as single crystalline nanorods and metal thin films. When the depth of interest is 50-200 microm into the surface, which is typical for pharmaceutical solids, the 1/e penetration depth, or skin depth, can be directly calculated from an exponential absorption law without utilizing the Parratt equation. In this work, we developed a more relevant method to define X-ray penetration depth based on the signal detection limits of the X-ray diffractometer. Our definition of effective penetration depth was empirically verified using bilayer compacts of varying known thicknesses of mannitol and lactose.

Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier–Stokes equations

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

Balajewicz, Maciej; Tezaur, Irina; Dowell, Earl

For a projection-based reduced order model (ROM) of a fluid flow to be stable and accurate, the dynamics of the truncated subspace must be taken into account. This paper proposes an approach for stabilizing and enhancing projection-based fluid ROMs in which truncated modes are accounted for a priori via a minimal rotation of the projection subspace. Attention is focused on the full non-linear compressible Navier–Stokes equations in specific volume form as a step toward a more general formulation for problems with generic non-linearities. Unlike traditional approaches, no empirical turbulence modeling terms are required, and consistency between the ROM and themore » Navier–Stokes equation from which the ROM is derived is maintained. Mathematically, the approach is formulated as a trace minimization problem on the Stiefel manifold. As a result, the reproductive as well as predictive capabilities of the method are evaluated on several compressible flow problems, including a problem involving laminar flow over an airfoil with a high angle of attack, and a channel-driven cavity flow problem.« less

Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier–Stokes equations

DOE PAGES

Balajewicz, Maciej; Tezaur, Irina; Dowell, Earl

2016-05-25

For a projection-based reduced order model (ROM) of a fluid flow to be stable and accurate, the dynamics of the truncated subspace must be taken into account. This paper proposes an approach for stabilizing and enhancing projection-based fluid ROMs in which truncated modes are accounted for a priori via a minimal rotation of the projection subspace. Attention is focused on the full non-linear compressible Navier–Stokes equations in specific volume form as a step toward a more general formulation for problems with generic non-linearities. Unlike traditional approaches, no empirical turbulence modeling terms are required, and consistency between the ROM and themore » Navier–Stokes equation from which the ROM is derived is maintained. Mathematically, the approach is formulated as a trace minimization problem on the Stiefel manifold. As a result, the reproductive as well as predictive capabilities of the method are evaluated on several compressible flow problems, including a problem involving laminar flow over an airfoil with a high angle of attack, and a channel-driven cavity flow problem.« less

An investigation of several factors involved in a finite difference procedure for analyzing the transonic flow about harmonically oscillating airfoils and wings

NASA Technical Reports Server (NTRS)

Ehlers, F. E.; Sebastian, J. D.; Weatherill, W. H.

1979-01-01

Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. Since sinusoidal motion is assumed, the unsteady equation is independent of time. Three finite difference investigations are discussed including a new operator for mesh points with supersonic flow, the effects on relaxation solution convergence of adding a viscosity term to the original differential equation, and an alternate and relatively simple downstream boundary condition. A method is developed which uses a finite difference procedure over a limited inner region and an approximate analytical procedure for the remaining outer region. Two investigations concerned with three-dimensional flow are presented. The first is the development of an oblique coordinate system for swept and tapered wings. The second derives the additional terms required to make row relaxation solutions converge when mixed flow is present. A finite span flutter analysis procedure is described using the two-dimensional unsteady transonic program with a full three-dimensional steady velocity potential.

Modeling the effect of topical oxygen therapy on wound healing

NASA Astrophysics Data System (ADS)

Agyingi, Ephraim; Ross, David; Maggelakis, Sophia

2011-11-01

Oxygen supply is a critical element for the healing of wounds. Clinical investigations have shown that topical oxygen therapy (TOT) increases the healing rate of wounds. The reason behind TOT increasing the healing rate of a wound remains unclear and hence current protocols are empirical. In this paper we present a mathematical model of wound healing that we use to simulate the application of TOT in the treatment of cutaneous wounds. At the core of our model is an account of the initiation of angiogenesis by macrophage-derived growth factors. The model is expressed as a system of reaction-diffusion equations. We present results of simulations for a version of the model with one spatial dimension.

Discharge in Long Air Gaps; Modelling and applications

NASA Astrophysics Data System (ADS)

Beroual, A.; Fofana, I.

2016-06-01

Discharge in Long Air Gaps: Modelling and applications presents self-consistent predictive dynamic models of positive and negative discharges in long air gaps. Equivalent models are also derived to predict lightning parameters based on the similarities between long air gap discharges and lightning flashes. Macroscopic air gap discharge parameters are calculated to solve electrical, empirical and physical equations, and comparisons between computed and experimental results for various test configurations are presented and discussed. This book is intended to provide a fresh perspective by contributing an innovative approach to this research domain, and universities with programs in high-voltage engineering will find this volume to be a working example of how to introduce the basics of electric discharge phenomena.

Derivation of kinetic equations from non-Wiener stochastic differential equations

NASA Astrophysics Data System (ADS)

Basharov, A. M.

2013-12-01

Kinetic differential-difference equations containing terms with fractional derivatives and describing α -stable Levy processes with 0 < α < 1 have been derived in a unified manner in terms of one-dimensional stochastic differential equations controlled merely by the Poisson processes.

Molecular Volumes and the Stokes-Einstein Equation

ERIC Educational Resources Information Center

Edward, John T.

1970-01-01

Examines the limitations of the Stokes-Einstein equation as it applies to small solute molecules. Discusses molecular volume determinations by atomic increments, molecular models, molar volumes of solids and liquids, and molal volumes. Presents an empirical correction factor for the equation which applies to molecular radii as small as 2 angstrom…

Empirical Likelihood in Nonignorable Covariate-Missing Data Problems.

PubMed

Xie, Yanmei; Zhang, Biao

2017-04-20

Missing covariate data occurs often in regression analysis, which frequently arises in the health and social sciences as well as in survey sampling. We study methods for the analysis of a nonignorable covariate-missing data problem in an assumed conditional mean function when some covariates are completely observed but other covariates are missing for some subjects. We adopt the semiparametric perspective of Bartlett et al. (Improving upon the efficiency of complete case analysis when covariates are MNAR. Biostatistics 2014;15:719-30) on regression analyses with nonignorable missing covariates, in which they have introduced the use of two working models, the working probability model of missingness and the working conditional score model. In this paper, we study an empirical likelihood approach to nonignorable covariate-missing data problems with the objective of effectively utilizing the two working models in the analysis of covariate-missing data. We propose a unified approach to constructing a system of unbiased estimating equations, where there are more equations than unknown parameters of interest. One useful feature of these unbiased estimating equations is that they naturally incorporate the incomplete data into the data analysis, making it possible to seek efficient estimation of the parameter of interest even when the working regression function is not specified to be the optimal regression function. We apply the general methodology of empirical likelihood to optimally combine these unbiased estimating equations. We propose three maximum empirical likelihood estimators of the underlying regression parameters and compare their efficiencies with other existing competitors. We present a simulation study to compare the finite-sample performance of various methods with respect to bias, efficiency, and robustness to model misspecification. The proposed empirical likelihood method is also illustrated by an analysis of a data set from the US National Health and Nutrition Examination Survey (NHANES).

Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives

NASA Technical Reports Server (NTRS)

Yan, Jue; Shu, Chi-Wang; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

In this paper we review the existing and develop new continuous Galerkin methods for solving time dependent partial differential equations with higher order derivatives in one and multiple space dimensions. We review local discontinuous Galerkin methods for convection diffusion equations involving second derivatives and for KdV type equations involving third derivatives. We then develop new local discontinuous Galerkin methods for the time dependent bi-harmonic type equations involving fourth derivatives, and partial differential equations involving fifth derivatives. For these new methods we present correct interface numerical fluxes and prove L(exp 2) stability for general nonlinear problems. Preliminary numerical examples are shown to illustrate these methods. Finally, we present new results on a post-processing technique, originally designed for methods with good negative-order error estimates, on the local discontinuous Galerkin methods applied to equations with higher derivatives. Numerical experiments show that this technique works as well for the new higher derivative cases, in effectively doubling the rate of convergence with negligible additional computational cost, for linear as well as some nonlinear problems, with a local uniform mesh.

Crash Padding Research : Volume II. Constitutive Equation Models.

DOT National Transportation Integrated Search

1986-08-01

Several simplified one-dimensional constitutive equations for viscoelastic materials are reviewed and found to be inadequate for representing the impact-response performance of strongly nonlinear materials. Two multi-parameter empirical models are de...

On the methods for determining the transverse dispersion coefficient in river mixing

NASA Astrophysics Data System (ADS)

Baek, Kyong Oh; Seo, Il Won

2016-04-01

In this study, the strengths and weaknesses of existing methods for determining the dispersion coefficient in the two-dimensional river mixing model were assessed based on hydraulic and tracer data sets acquired from experiments conducted on either laboratory channels or natural rivers. From the results of this study, it can be concluded that, when the longitudinal dispersion coefficient as well as the transverse dispersion coefficients must be determined in the transient concentration situation, the two-dimensional routing procedures, 2D RP and 2D STRP, can be employed to calculate dispersion coefficients among the observation methods. For the steady concentration situation, the STRP can be applied to calculate the transverse dispersion coefficient. When the tracer data are not available, either theoretical or empirical equations by the estimation method can be used to calculate the dispersion coefficient using the geometric and hydraulic data sets. Application of the theoretical and empirical equations to the laboratory channel showed that equations by Baek and Seo [[3], 2011] predicted reasonable values while equations by Fischer [23] and Boxwall and Guymer (2003) overestimated by factors of ten to one hundred. Among existing empirical equations, those by Jeon et al. [28] and Baek and Seo [6] gave the agreeable values of the transverse dispersion coefficient for most cases of natural rivers. Further, the theoretical equation by Baek and Seo [5] has the potential to be broadly applied to both laboratory and natural channels.

Numerical Limitations of 1D Hydraulic Models Using MIKE11 or HEC-RAS software - Case study of Baraolt River, Romania

NASA Astrophysics Data System (ADS)

Andrei, Armas; Robert, Beilicci; Erika, Beilicci

2017-10-01

MIKE 11 is an advanced hydroinformatic tool, a professional engineering software package for simulation of one-dimensional flows in estuaries, rivers, irrigation systems, channels and other water bodies. MIKE 11 is a 1-dimensional river model. It was developed by DHI Water · Environment · Health, Denmark. The basic computational procedure of HEC-RAS for steady flow is based on the solution of the one-dimensional energy equation. Energy losses are evaluated by friction and contraction / expansion. The momentum equation may be used in situations where the water surface profile is rapidly varied. These situations include hydraulic jumps, hydraulics of bridges, and evaluating profiles at river confluences. For unsteady flow, HEC-RAS solves the full, dynamic, 1-D Saint Venant Equation using an implicit, finite difference method. The unsteady flow equation solver was adapted from Dr. Robert L. Barkau’s UNET package. Fluid motion is controlled by the basic principles of conservation of mass, energy and momentum, which form the basis of fluid mechanics and hydraulic engineering. Complex flow situations must be solved using empirical approximations and numerical models, which are based on derivations of the basic principles (backwater equation, Navier-Stokes equation etc.). All numerical models are required to make some form of approximation to solve these principles, and consequently all have their limitations. The study of hydraulics and fluid mechanics is founded on the three basic principles of conservation of mass, energy and momentum. Real-life situations are frequently too complex to solve without the aid of numerical models. There is a tendency among some engineers to discard the basic principles taught at university and blindly assume that the results produced by the model are correct. Regardless of the complexity of models and despite the claims of their developers, all numerical models are required to make approximations. These may be related to geometric limitations, numerical simplification, or the use of empirical correlations. Some are obvious: one-dimensional models must average properties over the two remaining directions. It is the less obvious and poorly advertised approximations that pose the greatest threat to the novice user. Some of these, such as the inability of one-dimensional unsteady models to simulate supercritical flow can cause significant inaccuracy in the model predictions.

Derivation of the Schrodinger Equation from the Hamilton-Jacobi Equation in Feynman's Path Integral Formulation of Quantum Mechanics

ERIC Educational Resources Information Center

Field, J. H.

2011-01-01

It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…

EFFECTIVE USE OF SEDIMENT QUALITY GUIDELINES: WHICH GUIDELINE IS RIGHT FOR ME?

EPA Science Inventory

A bewildering array of sediment quality guidelines have been developed, but fortunately they mostly fall into two families: empirically-derived and theoretically-derived. The empirically-derived guidelines use large data bases of concurrent sediment chemistry and biological effe...

Topography and geology site effects from the intensity prediction model (ShakeMap) for Austria

NASA Astrophysics Data System (ADS)

del Puy Papí Isaba, María; Jia, Yan; Weginger, Stefan

2017-04-01

The seismicity in Austria can be categorized as moderated. Despite the fact that the hazard seems to be rather low, earthquakes can cause great damage and losses, specially in densely populated and industrialized areas. It is well known, that equations which predict intensity as a function of magnitude and distance, among other parameters, are useful tool for hazard and risk assessment. Therefore, this study aims to determine an empirical model of the ground shaking intensities (ShakeMap) of a series of earthquakes occurred in Austria between 1000 and 2014. Furthermore, the obtained empirical model will lead to further interpretation of both, contemporary and historical earthquakes. A total of 285 events, which epicenters were located in Austria, and a sum of 22.739 reported macreoseismic data points from Austria and adjoining countries, were used. These events are enclosed in the period 1000-2014 and characterized by having a local magnitude greater than 3. In the first state of the model development, the data was careful selected, e.g. solely intensities equal or greater than III were used. In a second state the data was adjusted to the selected empirical model. Finally, geology and topography corrections were obtained by means of the model residuals in order to derive intensity-based site amplification effects.

Canadian Field Soils IV: Modeling Thermal Conductivity at Dryness and Saturation

NASA Astrophysics Data System (ADS)

Tarnawski, V. R.; McCombie, M. L.; Leong, W. H.; Coppa, P.; Corasaniti, S.; Bovesecchi, G.

2018-03-01

The thermal conductivity data of 40 Canadian soils at dryness (λ _{dry}) and at full saturation (λ _{sat}) were used to verify 13 predictive models, i.e., four mechanistic, four semi-empirical and five empirical equations. The performance of each model, for λ _{dry} and λ _{sat}, was evaluated using a standard deviation ( SD) formula. Among the mechanistic models applied to dry soils, the closest λ _{dry} estimates were obtained by MaxRTCM (it{SD} = ± 0.018 Wm^{-1}\\cdot K^{-1}), followed by de Vries and a series-parallel model (S-{\\vert }{\\vert }). Among the semi-empirical equations (deVries-ave, Advanced Geometric Mean Model (A-GMM), Chaudhary and Bhandari (C-B) and Chen's equation), the closest λ _{dry} estimates were obtained by the C-B model (± 0.022 Wm^{-1}\\cdot K^{-1}). Among the empirical equations, the top λ _{dry} estimates were given by CDry-40 (± 0.021 Wm^{-1}\\cdot K^{-1} and ± 0.018 Wm^{-1}\\cdot K^{-1} for18-coarse and 22-fine soils, respectively). In addition, λ _{dry} and λ _{sat} models were applied to the λ _{sat} database of 21 other soils. From all the models tested, only the maxRTCM and the CDry-40 models provided the closest λ _{dry} estimates for the 40 Canadian soils as well as the 21 soils. The best λ _{sat} estimates for the 40-Canadian soils and the 21 soils were given by the A-GMM and the S-{\\vert }{\\vert } model.

An empirical relationship between mesoscale carbon monoxide concentrations and vehicular emission rates : final report.

DOT National Transportation Integrated Search

1979-01-01

Presented is a relatively simple empirical equation that reasonably approximates the relationship between mesoscale carbon monoxide (CO) concentrations, areal vehicular CO emission rates, and the meteorological factors of wind speed and mixing height...

Series expansion solutions for the multi-term time and space fractional partial differential equations in two- and three-dimensions

NASA Astrophysics Data System (ADS)

Ye, H.; Liu, F.; Turner, I.; Anh, V.; Burrage, K.

2013-09-01

Fractional partial differential equations with more than one fractional derivative in time describe some important physical phenomena, such as the telegraph equation, the power law wave equation, or the Szabo wave equation. In this paper, we consider two- and three-dimensional multi-term time and space fractional partial differential equations. The multi-term time-fractional derivative is defined in the Caputo sense, whose order belongs to the interval (1,2],(2,3],(3,4] or (0, m], and the space-fractional derivative is referred to as the fractional Laplacian form. We derive series expansion solutions based on a spectral representation of the Laplacian operator on a bounded region. Some applications are given for the two- and three-dimensional telegraph equation, power law wave equation and Szabo wave equation.

Thermodynamics Fundamental Equation of a "Non-Ideal" Rubber Band from Experiments

ERIC Educational Resources Information Center

Ritacco, Herna´n A.; Fortunatti, Juan C.; Devoto, Walter; Ferna´ndez-Miconi, Eugenio; Dominguez, Claudia; Sanchez, Miguel D.

2014-01-01

In this paper, we describe laboratory and classroom exercises designed to obtain the "fundamental" equation of a rubber band by combining experiments and theory. The procedure shows students how classical thermodynamics formalism can help to obtain empirical equations of state by constraining and guiding in the construction of the…

Empirical Sampling Distributions of Equating Coefficients for Graded and Nominal Response Instruments.

ERIC Educational Resources Information Center

Baker, Frank B.

1997-01-01

Examined the sampling distributions of equating coefficients produced by the characteristic curve method for tests using graded and nominal response scoring using simulated data. For both models and across all three equating situations, the sampling distributions were generally bell-shaped and peaked, and occasionally had a small degree of…

IR spectroscopy as a source of data on bond strengths

NASA Astrophysics Data System (ADS)

Finkelshtein, E. I.; Shamsiev, R. S.

2018-02-01

The aim of this work is the estimation of double bond strength, namely Cdbnd O bonds in ketones and aldehydes and Cdbnd C bonds in various compounds. By the breaking of these bonds one or both fragments formed are carbenes, for which experimental data on the enthalpies of formation (ΔHf298) are scarce. Thus for the estimation of ΔHf298 of the corresponding carbenes, the empirical equations were proposed based on different approximations. In addition, a quantum chemical calculations of the ΔHf298 values of carbenes were performed, and the data obtained were compared with experimental values and the results of earlier calculations. Equations for the calculation of Cdbnd O bond strengths of different ketones and aldehydes from the corresponding stretching frequencies ν(Cdbnd O) were derived. Using the proposed equations, the strengths of Cdbnd O bonds of 25 ketones and 12 conjugated aldehydes, as well as Cdbnd C bonds of 13 hydrocarbons and 7 conjugated aldehydes were estimated for the first time. Linear correlations of Cdbnd C and Cdbnd O bond strengths with the bond lengths were established, and the equations permitting the estimation of the double bond strengths and lengths with acceptable accuracy were obtained. Also, the strength of central Cdbnd C bond of stilbene was calculated for the first time. The uncertainty of the strengths of double bonds obtained may be regarded as accurate ±10-15 kJ/mol.

UDOT calibration of AASHTO's new prestress loss design equations.

DOT National Transportation Integrated Search

2009-07-01

In the next edition of the AASHTO LRFD Bridge Design Specifications the procedure to calculate prestress losses will change dramatically. The new equations are empirically based on high performance concrete from four states (Nebraska, New Hampshire, ...

UDOT's calibration of AASHTO's new prestress loss design equations.

DOT National Transportation Integrated Search

2009-07-01

In the next edition of the AASHTO LRFD Bridge Design Specifications the procedure to calculate prestress losses will change dramatically. The new equations are empirically based on high performance concrete from four states (Nebraska, New Hampshire, ...

Empirical Equations for Estimating Drying Times of Thick Rotary-Cut Veneer in Press and Jet Dryers.

DTIC Science & Technology

1985-05-01

producing veneer species. greater areas of effective contact in gluing. This paper describes the use of empirical equations for ’The use of trade, firm...grade logs have different volumes of knots from one area to another in the log, and because knots Of the three dryers, the roller unit has the lowest... areas of knotty veneer would be the same for chosen so that a smooth curve of MC over time could both. be obtained with about six passes per curve. All

Validity of bioelectrical impedance analysis in estimation of fat-free mass in colorectal cancer patients.

PubMed

Ræder, Hanna; Kværner, Ane Sørlie; Henriksen, Christine; Florholmen, Geir; Henriksen, Hege Berg; Bøhn, Siv Kjølsrud; Paur, Ingvild; Smeland, Sigbjørn; Blomhoff, Rune

2018-02-01

Bioelectrical impedance analysis (BIA) is an accessible and cheap method to measure fat-free mass (FFM). However, BIA estimates are subject to uncertainty in patient populations with altered body composition and hydration. The aim of the current study was to validate a whole-body and a segmental BIA device against dual-energy X-ray absorptiometry (DXA) in colorectal cancer (CRC) patients, and to investigate the ability of different empiric equations for BIA to predict DXA FFM (FFM DXA ). Forty-three non-metastatic CRC patients (aged 50-80 years) were enrolled in this study. Whole-body and segmental BIA FFM estimates (FFM whole-bodyBIA , FFM segmentalBIA ) were calculated using 14 empiric equations, including the equations from the manufacturers, before comparison to FFM DXA estimates. Strong linear relationships were observed between FFM BIA and FFM DXA estimates for all equations (R 2  = 0.94-0.98 for both devices). However, there were large discrepancies in FFM estimates depending on the equations used with mean differences in the ranges -6.5-6.8 kg and -11.0-3.4 kg for whole-body and segmental BIA, respectively. For whole-body BIA, 77% of BIA derived FFM estimates were significantly different from FFM DXA , whereas for segmental BIA, 85% were significantly different. For whole-body BIA, the Schols* equation gave the highest agreement with FFM DXA with mean difference ±SD of -0.16 ± 1.94 kg (p = 0.582). The manufacturer's equation gave a small overestimation of FFM with 1.46 ± 2.16 kg (p < 0.001) with a tendency towards proportional bias (r = 0.28, p = 0.066). For segmental BIA, the Heitmann* equation gave the highest agreement with FFM DXA (0.17 ± 1.83 kg (p = 0.546)). Using the manufacturer's equation, no difference in FFM estimates was observed (-0.34 ± 2.06 kg (p = 0.292)), however, a clear proportional bias was detected (r = 0.69, p < 0.001). Both devices demonstrated acceptable ability to detect low FFM compared to DXA using the optimal equation. In a population of non-metastatic CRC patients, mostly consisting of Caucasian adults and with a wide range of body composition measures, both the whole-body BIA and segmental BIA device provide FFM estimates that are comparable to FFM DXA on a group level when the appropriate equations are applied. At the individual level (i.e. in clinical practice) BIA may be a valuable tool to identify patients with low FFM as part of a malnutrition diagnosis. Copyright © 2017 The Author(s). Published by Elsevier Ltd.. All rights reserved.

Coupled rotor and fuselage equations of motion

NASA Technical Reports Server (NTRS)

Warmbrodt, W.

1979-01-01

The governing equations of motion of a helicopter rotor coupled to a rigid body fuselage are derived. A consistent formulation is used to derive nonlinear periodic coefficient equations of motion which are used to study coupled rotor/fuselage dynamics in forward flight. Rotor/fuselage coupling is documented and the importance of an ordering scheme in deriving nonlinear equations of motion is reviewed. The nature of the final equations and the use of multiblade coordinates are discussed.

More sound of church bells: Authors' correction

NASA Astrophysics Data System (ADS)

Vogt, Patrik; Kasper, Lutz; Burde, Jan-Philipp

2016-01-01

In the recently published article "The Sound of Church Bells: Tracking Down the Secret of a Traditional Arts and Crafts Trade," the bell frequencies have been erroneously oversimplified. The problem affects Eqs. (2) and (3), which were derived from the elementary "coffee mug model" and in which we used the speed of sound in air. However, this does not make sense from a physical point of view, since air only acts as a sound carrier, not as a sound source in the case of bells. Due to the excellent fit of the theoretical model with the empirical data, we unfortunately failed to notice this error before publication. However, all other equations, e.g., the introduction of the correction factor in Eq. (4) and the estimation of the mass in Eqs. (5) and (6) are not affected by this error, since they represent empirical models. However, it is unfortunate to introduce the speed of sound in air as a constant in Eqs. (4) and (6). Instead, we suggest the following simple rule of thumb for relating the radius of a church bell R to its humming frequency fhum:

Nonlinear acoustic wave equations with fractional loss operators.

PubMed

Prieur, Fabrice; Holm, Sverre

2011-09-01

Fractional derivatives are well suited to describe wave propagation in complex media. When introduced in classical wave equations, they allow a modeling of attenuation and dispersion that better describes sound propagation in biological tissues. Traditional constitutive equations from solid mechanics and heat conduction are modified using fractional derivatives. They are used to derive a nonlinear wave equation which describes attenuation and dispersion laws that match observations. This wave equation is a generalization of the Westervelt equation, and also leads to a fractional version of the Khokhlov-Zabolotskaya-Kuznetsov and Burgers' equations. © 2011 Acoustical Society of America

Clausius-Clapeyron Equation and Saturation Vapour Pressure: Simple Theory Reconciled with Practice

ERIC Educational Resources Information Center

Koutsoyiannis, Demetris

2012-01-01

While the Clausius-Clapeyron equation is very important as it determines the saturation vapour pressure, in practice it is replaced by empirical, typically Magnus-type, equations which are more accurate. It is shown that the reduced accuracy reflects an inconsistent assumption that the latent heat of vaporization is constant. Not only is this…

Representative equations for the thermodynamic and transport properties of fluids near the gas-liquid critical point

NASA Technical Reports Server (NTRS)

Sengers, J. V.; Basu, R. S.; Sengers, J. M. H. L.

1981-01-01

A survey is presented of representative equations for various thermophysical properties of fluids in the critical region. Representative equations for the transport properties are included. Semi-empirical modifications of the theoretically predicted asymtotic critical behavior that yield simple and practical representations of the fluid properties in the critical region are emphasized.

Collateral Information for Equating in Small Samples: A Preliminary Investigation

ERIC Educational Resources Information Center

Kim, Sooyeon; Livingston, Samuel A.; Lewis, Charles

2011-01-01

This article describes a preliminary investigation of an empirical Bayes (EB) procedure for using collateral information to improve equating of scores on test forms taken by small numbers of examinees. Resampling studies were done on two different forms of the same test. In each study, EB and non-EB versions of two equating methods--chained linear…

Derivation of Inviscid Quasi-geostrophic Equation from Rotational Compressible Magnetohydrodynamic Flows

NASA Astrophysics Data System (ADS)

Kwon, Young-Sam; Lin, Ying-Chieh; Su, Cheng-Fang

2018-04-01

In this paper, we consider the compressible models of magnetohydrodynamic flows giving rise to a variety of mathematical problems in many areas. We derive a rigorous quasi-geostrophic equation governed by magnetic field from the rotational compressible magnetohydrodynamic flows with the well-prepared initial data. It is a first derivation of quasi-geostrophic equation governed by the magnetic field, and the tool is based on the relative entropy method. This paper covers two results: the existence of the unique local strong solution of quasi-geostrophic equation with the good regularity and the derivation of a quasi-geostrophic equation.

Strong Asymmetric Limit of the Quasi-Potential of the Boundary Driven Weakly Asymmetric Exclusion Process

NASA Astrophysics Data System (ADS)

Bertini, Lorenzo; Gabrielli, Davide; Landim, Claudio

2009-07-01

We consider the weakly asymmetric exclusion process on a bounded interval with particles reservoirs at the endpoints. The hydrodynamic limit for the empirical density, obtained in the diffusive scaling, is given by the viscous Burgers equation with Dirichlet boundary conditions. In the case in which the bulk asymmetry is in the same direction as the drift due to the boundary reservoirs, we prove that the quasi-potential can be expressed in terms of the solution to a one-dimensional boundary value problem which has been introduced by Enaud and Derrida [16]. We consider the strong asymmetric limit of the quasi-potential and recover the functional derived by Derrida, Lebowitz, and Speer [15] for the asymmetric exclusion process.

Extracting and Converting Quantitative Data into Human Error Probabilities

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

Tuan Q. Tran; Ronald L. Boring; Jeffrey C. Joe

2007-08-01

This paper discusses a proposed method using a combination of advanced statistical approaches (e.g., meta-analysis, regression, structural equation modeling) that will not only convert different empirical results into a common metric for scaling individual PSFs effects, but will also examine the complex interrelationships among PSFs. Furthermore, the paper discusses how the derived statistical estimates (i.e., effect sizes) can be mapped onto a HRA method (e.g. SPAR-H) to generate HEPs that can then be use in probabilistic risk assessment (PRA). The paper concludes with a discussion of the benefits of using academic literature in assisting HRA analysts in generating sound HEPsmore » and HRA developers in validating current HRA models and formulating new HRA models.« less

Method and Apparatus for the Portable Identification Of Material Thickness And Defects Along Uneven Surfaces Using Spatially Controlled Heat Application

NASA Technical Reports Server (NTRS)

Reilly, Thomas L. (Inventor); Jacobstein, A. Ronald (Inventor); Cramer, K. Elliott (Inventor)

2006-01-01

A method and apparatus for testing a material such as the water-wall tubes in boilers includes the use of a portable thermal line heater having radiation shields to control the amount of thermal radiation that reaches a thermal imager. A procedure corrects for variations in the initial temperature of the material being inspected. A method of calibrating the testing device to determine an equation relating thickness of the material to temperatures created by the thermal line heater uses empirical data derived from tests performed on test specimens for each material type, geometry, density, specific heat, speed at which the line heater is moved across the material and heat intensity.

Solar array synthesis computer program

NASA Technical Reports Server (NTRS)

Faith, T. J.

1973-01-01

Photovoltaic characteristics have been measured on solar cells irradiated by 1 MeV electrons to fluences ranging from 1 x 10 to the 13th power e/sq cm to 1 x 10 to the 16th power e/sq cm, for cell temperatures ranging from 123 K to 473 K and for illumination intensities ranging from 5m W/sq cm to 1830m W/sq cm. Empirical equations have been derived from these measurements to describe the behavior of light generated current, open circuit voltage and I-V curve shape over various portions of these temperature/illumination ranges. Both 10 ohms/cm and 17 ohms/cm n-p silicon solar cells were tested, and similar analytical expressions were formulated for easy comparison between the two resistivities.

Aerosol correction for remotely sensed sea surface temperatures from the National Oceanic and Atmospheric Administration advanced very high resolution radiometer

NASA Astrophysics Data System (ADS)

Nalli, Nicholas R.; Stowe, Larry L.

2002-10-01

This research presents the first-phase derivation and implementation of daytime aerosol correction algorithms for remotely sensed sea surface temperature (SST) from the advanced very high resolution radiometer (AVHRR) instrument flown onboard NOAA polar orbiting satellites. To accomplish this, a long-term (1990-1998), global AVHRR-buoy match-up database was created by merging the NOAA/NASA Pathfinder Atmospheres and Pathfinder Oceans data sets. The merged data set is unique in that it includes daytime estimates of aerosol optical depth (AOD) derived from AVHRR channel 1 (0.63 μm) under global conditions of significant aerosol loading. Histograms of retrieved AOD reveal monomodal, lognormal distributions for both tropospheric and stratospheric aerosol modes. It is then shown empirically that the SST depression caused under each aerosol mode can be expressed as a linear function in two predictors, these being the slant path AOD retrieved from AVHRR channel 1 along with the ratio of channels 1 and 2 normalized reflectances. On the basis of these relationships, parametric equations are derived to provide an aerosol correction for retrievals from the daytime NOAA operational multichannel and nonlinear SST algorithms. Separate sets of coefficients are utilized for two aerosol modes: tropospheric (i.e., dust, smoke, haze) and stratospheric/tropospheric (i.e., following a major volcanic eruption). The equations are shown to significantly reduce retrieved SST bias using an independent set of match-ups. Eliminating aerosol-induced bias in both real-time and retrospective processing will enhance the utility of the AVHRR SST for the general user community and in climate research.

Moments of inertia for neutron and strange stars: Limits derived for the Crab pulsar

NASA Astrophysics Data System (ADS)

Bejger, M.; Haensel, P.

2002-12-01

Recent estimates of the properties of the Crab nebula are used to derive constraints on the moment of inertia, mass and radius of the pulsar. To this purpose, we employ an approximate formula combining these three parameters. Our ``empirical formula'' I =~ a(x) M R2, where x=(M/Msun) (km/R), is based on numerical results obtained for thirty theoretical equations of state of dense matter. The functions a(x) for neutron stars and strange stars are qualitatively different. For neutron stars aNS(x)=x/(0.1+2x) for x<=0.1 (valid for M>0.2 Msun) and aNS(x)={2/ 9}(1+5x) for x>0.1. For strange stars aSS(x)={2/ 5}(1+x) (not valid for strange stars with crust and M<0.1 Msun). We obtain also an approximate expression for the maximum moment of inertia Imax,45 =~ (-0.37 + 7.12* xmax) (Mmax/Msun)(RM_max/ {10 km})2, where I45 = I/1045 g* cm2, valid for both neutron stars and strange stars. Applying our formulae to the evaluated values of ICrab, we derive constraints on the mass and radius of the pulsar. { A very conservative evaluation of the expanding nebula mass, Mneb=2 Msun, yields MCrab>1.2 Msun and RCrab= 10-14 km. Setting the most recent evaluation (``central value'') Mneb=4.6 Msun rules out most of the existing equations of state, leaving only the stiffest ones: MCrab>1.9 Msun, RCrab= 14-15 km.

Empirical Allometric Models to Estimate Total Needle Biomass For Loblolly Pine

Treesearch

Hector M. de los Santos-Posadas; Bruce E. Borders

2002-01-01

Empirical geometric models based on the cone surface formula were adapted and used to estimate total dry needle biomass (TNB) and live branch basal area (LBBA). The results suggest that the empirical geometric equations produced good fit and stable parameters while estimating TNB and LBBA. The data used include trees form a spacing study of 12 years old and a set of...

Equation of state for dense nucleonic matter from metamodeling. II. Predictions for neutron star properties

NASA Astrophysics Data System (ADS)

Margueron, Jérôme; Hoffmann Casali, Rudiney; Gulminelli, Francesca

2018-02-01

Employing recently proposed metamodeling for the nucleonic matter equation of state, we analyze neutron star global properties such as masses, radii, momentum of inertia, and others. The impact of the uncertainty on empirical parameters on these global properties is analyzed in a Bayesian statistical approach. Physical constraints, such as causality and stability, are imposed on the equation of state and different hypotheses for the direct Urca (dUrca) process are investigated. In addition, only metamodels with maximum masses above 2 M⊙ are selected. Our main results are the following: the equation of state exhibits a universal behavior against the dUrca hypothesis under the condition of charge neutrality and β equilibrium; neutron stars, if composed exclusively of nucleons and leptons, have a radius of 12.7 ±0.4 km for masses ranging from 1 up to 2 M⊙ ; a small radius lower than 11 km is very marginally compatible with our present knowledge of the nuclear empirical parameters; and finally, the most important empirical parameters which are still affected by large uncertainties and play an important role in determining the radius of neutrons stars are the slope and curvature of the symmetry energy (Lsym and Ksym) and, to a lower extent, the skewness parameters (Qsat /sym).

Estimating Finite Rate of Population Increase for Sharks Based on Vital Parameters

PubMed Central

Liu, Kwang-Ming; Chin, Chien-Pang; Chen, Chun-Hui; Chang, Jui-Han

2015-01-01

The vital parameter data for 62 stocks, covering 38 species, collected from the literature, including parameters of age, growth, and reproduction, were log-transformed and analyzed using multivariate analyses. Three groups were identified and empirical equations were developed for each to describe the relationships between the predicted finite rates of population increase (λ’) and the vital parameters, maximum age (Tmax), age at maturity (Tm), annual fecundity (f/Rc)), size at birth (Lb), size at maturity (Lm), and asymptotic length (L∞). Group (1) included species with slow growth rates (0.034 yr-1 < k < 0.103 yr-1) and extended longevity (26 yr < Tmax < 81 yr), e.g., shortfin mako Isurus oxyrinchus, dusky shark Carcharhinus obscurus, etc.; Group (2) included species with fast growth rates (0.103 yr-1 < k < 0.358 yr-1) and short longevity (9 yr < Tmax < 26 yr), e.g., starspotted smoothhound Mustelus manazo, gray smoothhound M. californicus, etc.; Group (3) included late maturing species (Lm/L∞ ≧ 0.75) with moderate longevity (Tmax < 29 yr), e.g., pelagic thresher Alopias pelagicus, sevengill shark Notorynchus cepedianus. The empirical equation for all data pooled was also developed. The λ’ values estimated by these empirical equations showed good agreement with those calculated using conventional demographic analysis. The predictability was further validated by an independent data set of three species. The empirical equations developed in this study not only reduce the uncertainties in estimation but also account for the difference in life history among groups. This method therefore provides an efficient and effective approach to the implementation of precautionary shark management measures. PMID:26576058

Supplier-induced demand: re-examining identification and misspecification in cross-sectional analysis.

PubMed

Peacock, Stuart J; Richardson, Jeffrey R J

2007-09-01

This paper re-examines criticisms of cross-sectional methods used to test for supplier-induced demand (SID) and re-evaluates the empirical evidence using data from Australian medical services. Cross-sectional studies of SID have been criticised on two grounds. First, and most important, the inclusion of the doctor supply in the demand equation leads to an identification problem. This criticism is shown to be invalid, as the doctor supply variable is stochastic and depends upon a variety of other variables including the desirability of the location. Second, cross-sectional studies of SID fail diagnostic tests and produce artefactual findings due to model misspecification. Contrary to this, the re-evaluation of cross-sectional Australian data indicate that demand equations that do not include the doctor supply are misspecified. Empirical evidence from the re-evaluation of Australian medical services data supports the notion of SID. Demand and supply equations are well specified and have very good explanatory power. The demand equation is identified and the desirability of a location is an important predictor of the doctor supply. Results show an average price elasticity of demand of 0.22 and an average elasticity of demand with respect to the doctor supply of 0.46, with the impact of SID becoming stronger as the doctor supply rises. The conclusion we draw from this paper is that two of the main criticisms of the empirical evidence supporting the SID hypothesis have been inappropriately levelled at the methods used. More importantly, SID provides a satisfactory, and robust, explanation of the empirical data on the demand for medical services in Australia.

Variational Methods in Sensitivity Analysis and Optimization for Aerodynamic Applications

NASA Technical Reports Server (NTRS)

Ibrahim, A. H.; Hou, G. J.-W.; Tiwari, S. N. (Principal Investigator)

1996-01-01

Variational methods (VM) sensitivity analysis, which is the continuous alternative to the discrete sensitivity analysis, is employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The determination of the sensitivity derivatives of the performance index or functional entails the coupled solutions of the state and costate equations. As the stable and converged numerical solution of the costate equations with their boundary conditions are a priori unknown, numerical stability analysis is performed on both the state and costate equations. Thereafter, based on the amplification factors obtained by solving the generalized eigenvalue equations, the stability behavior of the costate equations is discussed and compared with the state (Euler) equations. The stability analysis of the costate equations suggests that the converged and stable solution of the costate equation is possible only if the computational domain of the costate equations is transformed to take into account the reverse flow nature of the costate equations. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.

Error simulation of paired-comparison-based scaling methods

NASA Astrophysics Data System (ADS)

Cui, Chengwu

2000-12-01

Subjective image quality measurement usually resorts to psycho physical scaling. However, it is difficult to evaluate the inherent precision of these scaling methods. Without knowing the potential errors of the measurement, subsequent use of the data can be misleading. In this paper, the errors on scaled values derived form paired comparison based scaling methods are simulated with randomly introduced proportion of choice errors that follow the binomial distribution. Simulation results are given for various combinations of the number of stimuli and the sampling size. The errors are presented in the form of average standard deviation of the scaled values and can be fitted reasonably well with an empirical equation that can be sued for scaling error estimation and measurement design. The simulation proves paired comparison based scaling methods can have large errors on the derived scaled values when the sampling size and the number of stimuli are small. Examples are also given to show the potential errors on actually scaled values of color image prints as measured by the method of paired comparison.

Voltage dependence of a stochastic model of activation of an alpha helical S4 sensor in a K channel membrane

NASA Astrophysics Data System (ADS)

Vaccaro, S. R.

2011-09-01

The voltage dependence of the ionic and gating currents of a K channel is dependent on the activation barriers of a voltage sensor with a potential function which may be derived from the principal electrostatic forces on an S4 segment in an inhomogeneous dielectric medium. By variation of the parameters of a voltage-sensing domain model, consistent with x-ray structures and biophysical data, the lowest frequency of the survival probability of each stationary state derived from a solution of the Smoluchowski equation provides a good fit to the voltage dependence of the slowest time constant of the ionic current in a depolarized membrane, and the gating current exhibits a rising phase that precedes an exponential relaxation. For each depolarizing potential, the calculated time dependence of the survival probabilities of the closed states of an alpha helical S4 sensor are in accord with an empirical model of the ionic and gating currents recorded during the activation process.

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

Kittell, David Erik; Yarrington, Cole Davis

Here, a physically-based form of the Mie–Grüneisen equation of state (EOS) is derived for calculating 1d planar shock temperatures, as well as hot spot temperature distributions from heterogeneous impact simulations. This form utilises a multi-term Einstein oscillator model for specific heat, and is completely algebraic in terms of temperature, volume, an integrating factor, and the cold curve energy. Moreover, any empirical relation for the reference pressure and energy may be substituted into the equations via the use of a generalised reference function. The complete EOS is then applied to calculations of the Hugoniot temperature and simulation of hydrodynamic pore collapsemore » using data for the secondary explosive, hexanitrostilbene (HNS). From these results, it is shown that the choice of EOS is even more significant for determining hot spot temperature distributions than planar shock states. The complete EOS is also compared to an alternative derivation assuming that specific heat is a function of temperature alone, i.e. cv(T). Temperature discrepancies on the order of 100–600 K were observed corresponding to the shock pressures required to initiate HNS (near 10 GPa). Overall, the results of this work will improve confidence in temperature predictions. By adopting this EOS, future work may be able to assign physical meaning to other thermally sensitive constitutive model parameters necessary to predict the shock initiation and detonation of heterogeneous explosives.« less

A hybrid method for flood simulation in small catchments combining hydrodynamic and hydrological techniques

NASA Astrophysics Data System (ADS)

Bellos, Vasilis; Tsakiris, George

2016-09-01

The study presents a new hybrid method for the simulation of flood events in small catchments. It combines a physically-based two-dimensional hydrodynamic model and the hydrological unit hydrograph theory. Unit hydrographs are derived using the FLOW-R2D model which is based on the full form of two-dimensional Shallow Water Equations, solved by a modified McCormack numerical scheme. The method is tested at a small catchment in a suburb of Athens-Greece for a storm event which occurred in February 2013. The catchment is divided into three friction zones and unit hydrographs of 15 and 30 min are produced. The infiltration process is simulated by the empirical Kostiakov equation and the Green-Ampt model. The results from the implementation of the proposed hybrid method are compared with recorded data at the hydrometric station at the outlet of the catchment and the results derived from the fully hydrodynamic model FLOW-R2D. It is concluded that for the case studied, the proposed hybrid method produces results close to those of the fully hydrodynamic simulation at substantially shorter computational time. This finding, if further verified in a variety of case studies, can be useful in devising effective hybrid tools for the two-dimensional flood simulations, which are lead to accurate and considerably faster results than those achieved by the fully hydrodynamic simulations.

Simple Derivation of the Lindblad Equation

ERIC Educational Resources Information Center

Pearle, Philip

2012-01-01

The Lindblad equation is an evolution equation for the density matrix in quantum theory. It is the general linear, Markovian, form which ensures that the density matrix is Hermitian, trace 1, positive and completely positive. Some elementary examples of the Lindblad equation are given. The derivation of the Lindblad equation presented here is…

Evaluation of the National Research Council (2001) dairy model and derivation of new prediction equations. 1. Digestibility of fiber, fat, protein, and nonfiber carbohydrate.

PubMed

White, R R; Roman-Garcia, Y; Firkins, J L; VandeHaar, M J; Armentano, L E; Weiss, W P; McGill, T; Garnett, R; Hanigan, M D

2017-05-01

Evaluation of ration balancing systems such as the National Research Council (NRC) Nutrient Requirements series is important for improving predictions of animal nutrient requirements and advancing feeding strategies. This work used a literature data set (n = 550) to evaluate predictions of total-tract digested neutral detergent fiber (NDF), fatty acid (FA), crude protein (CP), and nonfiber carbohydrate (NFC) estimated by the NRC (2001) dairy model. Mean biases suggested that the NRC (2001) lactating cow model overestimated true FA and CP digestibility by 26 and 7%, respectively, and under-predicted NDF digestibility by 16%. All NRC (2001) estimates had notable mean and slope biases and large root mean squared prediction error (RMSPE), and concordance (CCC) ranged from poor to good. Predicting NDF digestibility with independent equations for legumes, corn silage, other forages, and nonforage feeds improved CCC (0.85 vs. 0.76) compared with the re-derived NRC (2001) equation form (NRC equation with parameter estimates re-derived against this data set). Separate FA digestion coefficients were derived for different fat supplements (animal fats, oils, and other fat types) and for the basal diet. This equation returned improved (from 0.76 to 0.94) CCC compared with the re-derived NRC (2001) equation form. Unique CP digestibility equations were derived for forages, animal protein feeds, plant protein feeds, and other feeds, which improved CCC compared with the re-derived NRC (2001) equation form (0.74 to 0.85). New NFC digestibility coefficients were derived for grain-specific starch digestibilities, with residual organic matter assumed to be 98% digestible. A Monte Carlo cross-validation was performed to evaluate repeatability of model fit. In this procedure, data were randomly subsetted 500 times into derivation (60%) and evaluation (40%) data sets, and equations were derived using the derivation data and then evaluated against the independent evaluation data. Models derived with random study effects demonstrated poor repeatability of fit in independent evaluation. Similar equations derived without random study effects showed improved fit against independent data and little evidence of biased parameter estimates associated with failure to include study effects. The equations derived in this analysis provide interesting insight into how NDF, starch, FA, and CP digestibilities are affected by intake, feed type, and diet composition. The Authors. Published by the Federation of Animal Science Societies and Elsevier Inc. on behalf of the American Dairy Science Association®. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).

Cascades and Dissipative Anomalies in Compressible Fluid Turbulence

NASA Astrophysics Data System (ADS)

Eyink, Gregory L.; Drivas, Theodore D.

2018-02-01

We investigate dissipative anomalies in a turbulent fluid governed by the compressible Navier-Stokes equation. We follow an exact approach pioneered by Onsager, which we explain as a nonperturbative application of the principle of renormalization-group invariance. In the limit of high Reynolds and Péclet numbers, the flow realizations are found to be described as distributional or "coarse-grained" solutions of the compressible Euler equations, with standard conservation laws broken by turbulent anomalies. The anomalous dissipation of kinetic energy is shown to be due not only to local cascade but also to a distinct mechanism called pressure-work defect. Irreversible heating in stationary, planar shocks with an ideal-gas equation of state exemplifies the second mechanism. Entropy conservation anomalies are also found to occur via two mechanisms: an anomalous input of negative entropy (negentropy) by pressure work and a cascade of negentropy to small scales. We derive "4 /5 th-law"-type expressions for the anomalies, which allow us to characterize the singularities (structure-function scaling exponents) required to sustain the cascades. We compare our approach with alternative theories and empirical evidence. It is argued that the "Big Power Law in the Sky" observed in electron density scintillations in the interstellar medium is a manifestation of a forward negentropy cascade or an inverse cascade of usual thermodynamic entropy.

Semi-empirical correlation for binary interaction parameters of the Peng-Robinson equation of state with the van der Waals mixing rules for the prediction of high-pressure vapor-liquid equilibrium.

PubMed

Fateen, Seif-Eddeen K; Khalil, Menna M; Elnabawy, Ahmed O

2013-03-01

Peng-Robinson equation of state is widely used with the classical van der Waals mixing rules to predict vapor liquid equilibria for systems containing hydrocarbons and related compounds. This model requires good values of the binary interaction parameter kij . In this work, we developed a semi-empirical correlation for kij partly based on the Huron-Vidal mixing rules. We obtained values for the adjustable parameters of the developed formula for over 60 binary systems and over 10 categories of components. The predictions of the new equation system were slightly better than the constant-kij model in most cases, except for 10 systems whose predictions were considerably improved with the new correlation.

Brownian motion of classical spins: Anomalous dissipation and generalized Langevin equation

NASA Astrophysics Data System (ADS)

Bandyopadhyay, Malay; Jayannavar, A. M.

2017-10-01

In this work, we derive the Langevin equation (LE) of a classical spin interacting with a heat bath through momentum variables, starting from the fully dynamical Hamiltonian description. The derived LE with anomalous dissipation is analyzed in detail. The obtained LE is non-Markovian with multiplicative noise terms. The concomitant dissipative terms obey the fluctuation-dissipation theorem. The Markovian limit correctly produces the Kubo and Hashitsume equation. The perturbative treatment of our equations produces the Landau-Lifshitz equation and the Seshadri-Lindenberg equation. Then we derive the Fokker-Planck equation corresponding to LE and the concept of equilibrium probability distribution is analyzed.

The time-fractional radiative transport equation—Continuous-time random walk, diffusion approximation, and Legendre-polynomial expansion

NASA Astrophysics Data System (ADS)

Machida, Manabu

2017-01-01

We consider the radiative transport equation in which the time derivative is replaced by the Caputo derivative. Such fractional-order derivatives are related to anomalous transport and anomalous diffusion. In this paper we describe how the time-fractional radiative transport equation is obtained from continuous-time random walk and see how the equation is related to the time-fractional diffusion equation in the asymptotic limit. Then we solve the equation with Legendre-polynomial expansion.

Linear constraint relations in biochemical reaction systems: I. Classification of the calculability and the balanceability of conversion rates.

PubMed

van der Heijden, R T; Heijnen, J J; Hellinga, C; Romein, B; Luyben, K C

1994-01-05

Measurements provide the basis for process monitoring and control as well as for model development and validation. Systematic approaches to increase the accuracy and credibility of the empirical data set are therefore of great value. In (bio)chemical conversions, linear conservation relations such as the balance equations for charge, enthalpy, and/or chemical elements, can be employed to relate conversion rates. In a pactical situation, some of these rates will be measured (in effect, be calculated directly from primary measurements of, e.g., concentrations and flow rates), as others can or cannot be calculated from the measured ones. When certain measured rates can also be calculated from other measured rates, the set of equations, the accuracy and credibility of the measured rates can indeed be improved by, respectively, balancing and gross error diagnosis. The balanced conversion rates are more accurate, and form a consistent set of data, which is more suitable for further application (e.g., to calculate nonmeasured rates) than the raw measurements. Such an approach has drawn attention in previous studies. The current study deals mainly with the problem of mathematically classifying the conversion rates into balanceable and calculable rates, given the subset of measured rates. The significance of this problem is illustrated with some examples. It is shown that a simple matrix equation can be derived that contains the vector of measured conversion rates and the redundancy matrix R. Matrix R plays a predominant role in the classification problem. In supplementary articles, significance of the redundancy matrix R for an improved gross error diagnosis approach will be shown. In addition, efficient equations have been derived to calculate the balanceable and/or calculable rates. The method is completely based on matrix algebra (principally different from the graph-theoretical approach), and it is easily implemented into a computer program. (c) 1994 John Wiley & Sons, Inc.

Symmetry classification of time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Naeem, I.; Khan, M. D.

2017-01-01

In this article, a new approach is proposed to construct the symmetry groups for a class of fractional differential equations which are expressed in the modified Riemann-Liouville fractional derivative. We perform a complete group classification of a nonlinear fractional diffusion equation which arises in fractals, acoustics, control theory, signal processing and many other applications. Introducing the suitable transformations, the fractional derivatives are converted to integer order derivatives and in consequence the nonlinear fractional diffusion equation transforms to a partial differential equation (PDE). Then the Lie symmetries are computed for resulting PDE and using inverse transformations, we derive the symmetries for fractional diffusion equation. All cases are discussed in detail and results for symmetry properties are compared for different values of α. This study provides a new way of computing symmetries for a class of fractional differential equations.

Combined Effects Aluminized Explosives

DTIC Science & Technology

2010-07-01

1 4 5 AREA EXPANSIONS Figure 4 Cylinder velocities for PAX-3 (left) and an empirical PAX-30 JWL (right) THERMODYNAMIC EQUATIONS OF...STATE The JWLB and Jones-Wilkins-Lee ( JWL ) equations of state were parameterized for combined effects explosives using fairly conventional methodology...state. Such warning messages should be ignored when using these JWLB and JWL equations of state representing eigenvalue detonation behavior. Table 1

Analytical solution of the nonlinear diffusion equation

NASA Astrophysics Data System (ADS)

Shanker Dubey, Ravi; Goswami, Pranay

2018-05-01

In the present paper, we derive the solution of the nonlinear fractional partial differential equations using an efficient approach based on the q -homotopy analysis transform method ( q -HATM). The fractional diffusion equations derivatives are considered in Caputo sense. The derived results are graphically demonstrated as well.

Annual regression-based estimates of evapotranspiration for the contiguous United States based on climate, remote sensing, and stream gage data

NASA Astrophysics Data System (ADS)

Reitz, M. D.; Sanford, W. E.; Senay, G. B.; Cazenas, J.

2015-12-01

Evapotranspiration (ET) is a key quantity in the hydrologic cycle, accounting for ~70% of precipitation across the contiguous United States (CONUS). However, it is a challenge to estimate, due to difficulty in making direct measurements and gaps in our theoretical understanding. Here we present a new data-driven, ~1km2 resolution map of long-term average actual evapotranspiration rates across the CONUS. The new ET map is a function of the USGS Landsat-derived National Land Cover Database (NLCD), precipitation, temperature, and daily average temperature range (from the PRISM climate dataset), and is calibrated to long-term water balance data from 679 watersheds. It is unique from previously presented ET maps in that (1) it was co-developed with estimates of runoff and recharge; (2) the regression equation was chosen from among many tested, previously published and newly proposed functional forms for its optimal description of long-term water balance ET data; (3) it has values over open-water areas that are derived from separate mass-transfer and humidity equations; and (4) the data include additional precipitation representing amounts converted from 2005 USGS water-use census irrigation data. The regression equation is calibrated using data from 2000-2013, but can also be applied to individual years with their corresponding input datasets. Comparisons among this new map, the more detailed remote-sensing-based estimates of MOD16 and SSEBop, and AmeriFlux ET tower measurements shows encouraging consistency, and indicates that the empirical ET estimate approach presented here produces closer agreement with independent flux tower data for annual average actual ET than other more complex remote sensing approaches.

Predicting plot soil loss by empirical and process-oriented approaches: A review

USDA-ARS?s Scientific Manuscript database

Soil erosion directly affects the quality of the soil, its agricultural productivity and its biological diversity. Many mathematical models have been developed to estimate plot soil erosion at different temporal scales. At present, empirical soil loss equations and process-oriented models are consid...

Generalized Spencer-Lewis equation

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

Filippone, W.L.

The Spencer-Lewis equation, which describes electron transport in homogeneous media when continuous slowing down theory is valid, is derived from the Boltzmann equation. Also derived is a time-dependent generalized Spencer-Lewis equation valid for inhomogeneous media. An independent verification of this last equation is obtained for the one-dimensional case using particle balance considerations.

Mathematical modeling of PDC bit drilling process based on a single-cutter mechanics

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

Wojtanowicz, A.K.; Kuru, E.

1993-12-01

An analytical development of a new mechanistic drilling model for polycrystalline diamond compact (PDC) bits is presented. The derivation accounts for static balance of forces acting on a single PDC cutter and is based on assumed similarity between bit and cutter. The model is fully explicit with physical meanings given to all constants and functions. Three equations constitute the mathematical model: torque, drilling rate, and bit life. The equations comprise cutter`s geometry, rock properties drilling parameters, and four empirical constants. The constants are used to match the model to a PDC drilling process. Also presented are qualitative and predictive verificationsmore » of the model. Qualitative verification shows that the model`s response to drilling process variables is similar to the behavior of full-size PDC bits. However, accuracy of the model`s predictions of PDC bit performance is limited primarily by imprecision of bit-dull evaluation. The verification study is based upon the reported laboratory drilling and field drilling tests as well as field data collected by the authors.« less

A coarse-grained biophysical model of sequence evolution and the population size dependence of the speciation rate

PubMed Central

Khatri, Bhavin S.; Goldstein, Richard A.

2015-01-01

Speciation is fundamental to understanding the huge diversity of life on Earth. Although still controversial, empirical evidence suggests that the rate of speciation is larger for smaller populations. Here, we explore a biophysical model of speciation by developing a simple coarse-grained theory of transcription factor-DNA binding and how their co-evolution in two geographically isolated lineages leads to incompatibilities. To develop a tractable analytical theory, we derive a Smoluchowski equation for the dynamics of binding energy evolution that accounts for the fact that natural selection acts on phenotypes, but variation arises from mutations in sequences; the Smoluchowski equation includes selection due to both gradients in fitness and gradients in sequence entropy, which is the logarithm of the number of sequences that correspond to a particular binding energy. This simple consideration predicts that smaller populations develop incompatibilities more quickly in the weak mutation regime; this trend arises as sequence entropy poises smaller populations closer to incompatible regions of phenotype space. These results suggest a generic coarse-grained approach to evolutionary stochastic dynamics, allowing realistic modelling at the phenotypic level. PMID:25936759

Stochastic dynamic programming illuminates the link between environment, physiology, and evolution.

PubMed

Mangel, Marc

2015-05-01

I describe how stochastic dynamic programming (SDP), a method for stochastic optimization that evolved from the work of Hamilton and Jacobi on variational problems, allows us to connect the physiological state of organisms, the environment in which they live, and how evolution by natural selection acts on trade-offs that all organisms face. I first derive the two canonical equations of SDP. These are valuable because although they apply to no system in particular, they share commonalities with many systems (as do frictionless springs). After that, I show how we used SDP in insect behavioral ecology. I describe the puzzles that needed to be solved, the SDP equations we used to solve the puzzles, and the experiments that we used to test the predictions of the models. I then briefly describe two other applications of SDP in biology: first, understanding the developmental pathways followed by steelhead trout in California and second skipped spawning by Norwegian cod. In both cases, modeling and empirical work were closely connected. I close with lessons learned and advice for the young mathematical biologists.

Equations of state of anhydrous AlF 3 and AlI 3 : Modeling of extreme condition halide chemistry

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

Stavrou, Elissaios; Zaug, Joseph M.; Bastea, Sorin

Pressure dependent angle-dispersive x-ray powder diffraction measurements of alpha-phase aluminum trifluoride (α-AlF 3) and separately, aluminum triiodide (AlI 3) were conducted using a diamond-anvil cell. Results at 295 K extend to 50 GPa. The equations of state of AlF 3 and AlI 3 were determined through refinements of collected x-ray diffraction patterns. The respective bulk moduli and corresponding pressure derivatives are reported for multiple orders of the Birch-Murnaghan (B-M), finite-strain (F-f), and higher pressure finite-strain (G-g) EOS analysis models. Aluminum trifluoride exhibits an apparent isostructural phase transition at approximately 12 GPa. Aluminum triiodide also undergoes a second-order atomic rearrangement: appliedmore » stress transformed a monoclinically distorted face centered cubic (fcc) structure into a standard fcc structural arrangement of iodine atoms. In conclusion, results from semi-empirical thermochemical computations of energetic materials formulated with fluorine containing reactants were obtained with the aim of predicting the yield of halogenated products.« less

Equations of state of anhydrous AlF{sub 3} and AlI{sub 3}: Modeling of extreme condition halide chemistry

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

Stavrou, Elissaios, E-mail: stavrou1@llnl.gov; Lawrence Livermore National Laboratory, Physical and Life Sciences Directorate, P.O. Box 808 L-350, Livermore, California 94550; Zaug, Joseph M., E-mail: zaug1@llnl.gov

Pressure dependent angle-dispersive x-ray powder diffraction measurements of alpha-phase aluminum trifluoride (α-AlF{sub 3}) and separately, aluminum triiodide (AlI{sub 3}) were conducted using a diamond-anvil cell. Results at 295 K extend to 50 GPa. The equations of state of AlF{sub 3} and AlI{sub 3} were determined through refinements of collected x-ray diffraction patterns. The respective bulk moduli and corresponding pressure derivatives are reported for multiple orders of the Birch-Murnaghan (B-M), finite-strain (F-f), and higher pressure finite-strain (G-g) EOS analysis models. Aluminum trifluoride exhibits an apparent isostructural phase transition at approximately 12 GPa. Aluminum triiodide also undergoes a second-order atomic rearrangement: appliedmore » stress transformed a monoclinically distorted face centered cubic (fcc) structure into a standard fcc structural arrangement of iodine atoms. Results from semi-empirical thermochemical computations of energetic materials formulated with fluorine containing reactants were obtained with the aim of predicting the yield of halogenated products.« less

A New Approach for Alpha Radiography by Triple THGEM using Monte Carlo Simulation and Measurement

NASA Astrophysics Data System (ADS)

Khezripour, S.; Negarestani, A.; Rezaie, M. R.

2018-05-01

In this research, alpha imaging in Self Quenching Streamer (SQS) mode is investigated using a triple Thick Gas Electron Multiplier (THGEM) detector by Monte Carlo method and experimental data. First, a semi-empirical equation is derived to represent the relation between the SQS voltage and the alpha energy in every hole of the triple THGEM. The accuracy of this equation is tested and confirmed by a high degree of consistency. Secondly, the images of objects that are irradiated by Am-241 alpha source (5.49 MeV) are recorded by a CMOS camera using triple THGEM detector in the SQS mode. The resolution of images in this paper is a function of the exposure time. For an alpha source with 150 kBq activity, an optimal time interval for exposure is about 30 sec. For exposure time less or more than 30 sec, the images are incomplete and ambiguous, respectively. The overall objective of this work is to facilitate the alpha radiography in nuclear imaging through a triple THGEM without any amplifier or complicated electrical equipment.

Equations of state of anhydrous AlF 3 and AlI 3 : Modeling of extreme condition halide chemistry

DOE PAGES

Stavrou, Elissaios; Zaug, Joseph M.; Bastea, Sorin; ...

2015-06-04

Pressure dependent angle-dispersive x-ray powder diffraction measurements of alpha-phase aluminum trifluoride (α-AlF 3) and separately, aluminum triiodide (AlI 3) were conducted using a diamond-anvil cell. Results at 295 K extend to 50 GPa. The equations of state of AlF 3 and AlI 3 were determined through refinements of collected x-ray diffraction patterns. The respective bulk moduli and corresponding pressure derivatives are reported for multiple orders of the Birch-Murnaghan (B-M), finite-strain (F-f), and higher pressure finite-strain (G-g) EOS analysis models. Aluminum trifluoride exhibits an apparent isostructural phase transition at approximately 12 GPa. Aluminum triiodide also undergoes a second-order atomic rearrangement: appliedmore » stress transformed a monoclinically distorted face centered cubic (fcc) structure into a standard fcc structural arrangement of iodine atoms. In conclusion, results from semi-empirical thermochemical computations of energetic materials formulated with fluorine containing reactants were obtained with the aim of predicting the yield of halogenated products.« less

The validation of a human force model to predict dynamic forces resulting from multi-joint motions

NASA Technical Reports Server (NTRS)

Pandya, Abhilash K.; Maida, James C.; Aldridge, Ann M.; Hasson, Scott M.; Woolford, Barbara J.

1992-01-01

The development and validation is examined of a dynamic strength model for humans. This model is based on empirical data. The shoulder, elbow, and wrist joints were characterized in terms of maximum isolated torque, or position and velocity, in all rotational planes. This data was reduced by a least squares regression technique into a table of single variable second degree polynomial equations determining torque as a function of position and velocity. The isolated joint torque equations were then used to compute forces resulting from a composite motion, in this case, a ratchet wrench push and pull operation. A comparison of the predicted results of the model with the actual measured values for the composite motion indicates that forces derived from a composite motion of joints (ratcheting) can be predicted from isolated joint measures. Calculated T values comparing model versus measured values for 14 subjects were well within the statistically acceptable limits and regression analysis revealed coefficient of variation between actual and measured to be within 0.72 and 0.80.

Geophysical evaluation of sandstone aquifers in the Reconcavo-Tucano Basin, Bahia -- Brazil

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

Lima, O.A.L. de

1993-11-01

The upper clastic sediments in the Reconcavo-Tucano basin comprise a multilayer aquifer system of Jurassic age. Its groundwater is normally fresh down to depths of more than 1,000 m. Locally, however, there are zones producing high salinity or sulfur geothermal water. Analysis of electrical logs of more than 150 wells enabled the identification of the most typical sedimentary structures and the gross geometries for the sandstone units in selected areas of the basin. Based on this information, the thick sands are interpreted as coalescent point bars and the shales as flood plain deposits of a large fluvial environment. The resistivitymore » logs and core laboratory data are combined to develop empirical equations relating aquifer porosity and permeability to log-derived parameters such as formation factor and cementation exponent. Temperature logs of 15 wells were useful to quantify the water leakage through semiconfining shales. The groundwater quality was inferred from spontaneous potential (SP) log deflections under control of chemical analysis of water samples. An empirical chart is developed that relates the SP-derived water resistivity to the true water resistivity within the formations. The patterns of salinity variation with depth inferred from SP logs were helpful in identifying subsurface flows along major fault zones, where extensive mixing of water is taking place. A total of 49 vertical Schlumberger resistivity soundings aid in defining aquifer structures and in extrapolating the log derived results. Transition zones between fresh and saline waters have also been detected based on a combination of logging and surface sounding data. Ionic filtering by water leakage across regional shales, local convection and mixing along major faults and hydrodynamic dispersion away from lateral permeability contrasts are the main mechanisms controlling the observed distributions of salinity and temperature within the basin.« less

Gyrokinetic theory for particle and energy transport in fusion plasmas

NASA Astrophysics Data System (ADS)

Falessi, Matteo Valerio; Zonca, Fulvio

2018-03-01

A set of equations is derived describing the macroscopic transport of particles and energy in a thermonuclear plasma on the energy confinement time. The equations thus derived allow studying collisional and turbulent transport self-consistently, retaining the effect of magnetic field geometry without postulating any scale separation between the reference state and fluctuations. Previously, assuming scale separation, transport equations have been derived from kinetic equations by means of multiple-scale perturbation analysis and spatio-temporal averaging. In this work, the evolution equations for the moments of the distribution function are obtained following the standard approach; meanwhile, gyrokinetic theory has been used to explicitly express the fluctuation induced fluxes. In this way, equations for the transport of particles and energy up to the transport time scale can be derived using standard first order gyrokinetics.

Modelling and Computation in the Valuation of Carbon Derivatives with Stochastic Convenience Yields

PubMed Central

Chang, Shuhua; Wang, Xinyu

2015-01-01

The anthropogenic greenhouse gas (GHG) emission has risen dramatically during the last few decades, which mainstream researchers believe to be the main cause of climate change, especially the global warming. The mechanism of market-based carbon emission trading is regarded as a policy instrument to deal with global climate change. Although several empirical researches about the carbon allowance and its derivatives price have been made, theoretical results seem to be sparse. In this paper, we theoretically develop a mathematical model to price the CO2 emission allowance derivatives with stochastic convenience yields by the principle of absence of arbitrage opportunities. In the case of American options, we formulate the pricing problem to a linear parabolic variational inequality (VI) in two spatial dimensions and develop a power penalty method to solve it. Then, a fitted finite volume method is designed to solve the nonlinear partial differential equation (PDE) resulting from the power penalty method and governing the futures, European and American option valuation. Moreover, some numerical results are performed to illustrate the efficiency and usefulness of this method. We find that the stochastic convenience yield does effect the valuation of carbon emission derivatives. In addition, some sensitivity analyses are also made to examine the effects of some parameters on the valuation results. PMID:26010900

Modelling and computation in the valuation of carbon derivatives with stochastic convenience yields.

PubMed

Chang, Shuhua; Wang, Xinyu

2015-01-01

The anthropogenic greenhouse gas (GHG) emission has risen dramatically during the last few decades, which mainstream researchers believe to be the main cause of climate change, especially the global warming. The mechanism of market-based carbon emission trading is regarded as a policy instrument to deal with global climate change. Although several empirical researches about the carbon allowance and its derivatives price have been made, theoretical results seem to be sparse. In this paper, we theoretically develop a mathematical model to price the CO2 emission allowance derivatives with stochastic convenience yields by the principle of absence of arbitrage opportunities. In the case of American options, we formulate the pricing problem to a linear parabolic variational inequality (VI) in two spatial dimensions and develop a power penalty method to solve it. Then, a fitted finite volume method is designed to solve the nonlinear partial differential equation (PDE) resulting from the power penalty method and governing the futures, European and American option valuation. Moreover, some numerical results are performed to illustrate the efficiency and usefulness of this method. We find that the stochastic convenience yield does effect the valuation of carbon emission derivatives. In addition, some sensitivity analyses are also made to examine the effects of some parameters on the valuation results.

Direct coordinate-free derivation of the compatibility equation for finite strains

NASA Astrophysics Data System (ADS)

Ryzhak, E. I.

2014-07-01

The compatibility equation for the Cauchy-Green tensor field (squared tensor of pure extensionwith respect to the reference configuration) is directly derived from the well-known relation expressing this tensor via the vector field determining the mapping (transformation) of the reference configuration into the actual one. The derivation is based on the use of the apparatus of coordinatefree tensor calculus and does not apply any notions and relations of Riemannian geometry at all. The method is illustrated by deriving the well-known compatibility equation for small strains. It is shown that when the obtained compatibility equation for finite strains is linearized, it becomes the compatibility equation for small strains which indirectly confirms its correctness.

Educational Inequality and Income Inequality: An Empirical Study on China

ERIC Educational Resources Information Center

Yang, Jun; Huang, Xiao; Li, Xiaoyu

2009-01-01

Based on the endogenous growth theory, this paper uses the Gini coefficient to measure educational inequality and studies the empirical relationship between educational inequality and income inequality through a simultaneous equation model. The results show that: (1) Income inequality leads to educational inequality while the reduction of…

The mu-derivative and its applications to finding exact solutions of the Cahn-Hilliard, Korteveg-de Vries, and Burgers equations.

PubMed

Mitlin, Vlad

2005-10-15

A new transformation termed the mu-derivative is introduced. Applying it to the Cahn-Hilliard equation yields dynamical exact solutions. It is shown that the mu-transformed Cahn-Hilliard equation can be presented in a separable form. This transformation also yields dynamical exact solutions and separable forms for other nonlinear models such as the modified Korteveg-de Vries and the Burgers equations. The general structure of a nonlinear partial differential equation that becomes separable upon applying the mu-derivative is described.

SU-F-T-158: Experimental Characterization of Field Size Dependence of Dose and Lateral Beam Profiles of Scanning Proton and Carbon Ion Beams for Empirical Model in Air

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

Li, Y; Hsi, W; Zhao, J

2016-06-15

Purpose: The Gaussian model for the lateral profiles in air is crucial for an accurate treatment planning system. The field size dependence of dose and the lateral beam profiles of scanning proton and carbon ion beams are due mainly to particles undergoing multiple Coulomb scattering in the beam line components and secondary particles produced by nuclear interactions in the target, both of which depend upon the energy and species of the beam. In this work, lateral profile shape parameters were fitted to measurements of field size dependence dose at the center of field size in air. Methods: Previous studies havemore » employed empirical fits to measured profile data to significantly reduce the QA time required for measurements. From this approach to derive the weight and sigma of lateral profiles in air, empirical model formulations were simulated for three selected energies for both proton and carbon beams. Results: The 20%–80% lateral penumbras predicted by the double model for proton and single model for carbon with the error functions agreed with the measurements within 1 mm. The standard deviation between measured and fitted field size dependence of dose for empirical model in air has a maximum accuracy of 0.74% for proton with double Gaussian, and of 0.57% for carbon with single Gaussian. Conclusion: We have demonstrated that the double Gaussian model of lateral beam profiles is significantly better than the single Gaussian model for proton while a single Gaussian model is sufficient for carbon. The empirical equation may be used to double check the separately obtained model that is currently used by the planning system. The empirical model in air for dose of spot scanning proton and carbon ion beams cannot be directly used for irregular shaped patient fields, but can be to provide reference values for clinical use and quality assurance.« less

Understanding sport continuation: an integration of the theories of planned behaviour and basic psychological needs.

PubMed

Gucciardi, Daniel F; Jackson, Ben

2015-01-01

Fostering individuals' long-term participation in activities that promote positive development such as organised sport is an important agenda for research and practice. We integrated the theories of planned behaviour (TPB) and basic psychological needs (BPN) to identify factors associated with young adults' continuation in organised sport over a 12-month period. Prospective study, including an online psycho-social assessment at Time 1 and an assessment of continuation in sport approximately 12 months later. Participants (N=292) aged between 17 and 21 years (M=18.03; SD=1.29) completed an online survey assessing the theories of planned behaviour and basic psychological needs constructs. Bayesian structural equation modelling (BSEM) was employed to test the hypothesised theoretical sequence, using informative priors for structural relations based on empirical and theoretical expectations. The analyses revealed support for the robustness of the hypothesised theoretical model in terms of the pattern of relations as well as the direction and strength of associations among the constructs derived from quantitative summaries of existing research and theoretical expectations. The satisfaction of basic psychological needs was associated with more positive attitudes, higher levels of perceived behavioural control, and more favourable subjective norms; positive attitudes and perceived behavioural control were associated with higher behavioural intentions; and both intentions and perceived behavioural control predicted sport continuation. This study demonstrated the utility of Bayesian structural equation modelling for testing the robustness of an integrated theoretical model, which is informed by empirical evidence from meta-analyses and theoretical expectations, for understanding sport continuation. Crown Copyright © 2013. Published by Elsevier Ltd. All rights reserved.

Piezoviscosity In Lubrication Of Nonconformal Contacts

NASA Technical Reports Server (NTRS)

Jeng, Yeau-Ren; Hamrock, Bernard J.; Brewe, David E.

1988-01-01

Developments in theory of lubrication. Analysis of piezoviscous-rigid regime of lubrication of two ellipsoidal contacts. Begins with Reynolds equation for point contact. Equation nondimensionalized using Roelands empirical formula and Dowson and Higginson formula. Equation solved numerically. Solutions obtained for full spectrum of conditions to find effects of dimensionless load, speed, parameters of lubricated and lubricating materials, and angle between direction of rolling and direction of entrainment of lubricant.

THE FUNDAMENTAL SOLUTIONS FOR MULTI-TERM MODIFIED POWER LAW WAVE EQUATIONS IN A FINITE DOMAIN.

PubMed

Jiang, H; Liu, F; Meerschaert, M M; McGough, R J

2013-01-01

Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n ) ( n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko's Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi-term time-space fractional models including fractional Laplacian.

Derivation and computation of discrete-delay and continuous-delay SDEs in mathematical biology.

PubMed

Allen, Edward J

2014-06-01

Stochastic versions of several discrete-delay and continuous-delay differential equations, useful in mathematical biology, are derived from basic principles carefully taking into account the demographic, environmental, or physiological randomness in the dynamic processes. In particular, stochastic delay differential equation (SDDE) models are derived and studied for Nicholson's blowflies equation, Hutchinson's equation, an SIS epidemic model with delay, bacteria/phage dynamics, and glucose/insulin levels. Computational methods for approximating the SDDE models are described. Comparisons between computational solutions of the SDDEs and independently formulated Monte Carlo calculations support the accuracy of the derivations and of the computational methods.

Structural Equations and Causal Explanations: Some Challenges for Causal SEM

ERIC Educational Resources Information Center

Markus, Keith A.

2010-01-01

One common application of structural equation modeling (SEM) involves expressing and empirically investigating causal explanations. Nonetheless, several aspects of causal explanation that have an impact on behavioral science methodology remain poorly understood. It remains unclear whether applications of SEM should attempt to provide complete…

Analytical approach for the fractional differential equations by using the extended tanh method

NASA Astrophysics Data System (ADS)

Pandir, Yusuf; Yildirim, Ayse

2018-07-01

In this study, we consider analytical solutions of space-time fractional derivative foam drainage equation, the nonlinear Korteweg-de Vries equation with time and space-fractional derivatives and time-fractional reaction-diffusion equation by using the extended tanh method. The fractional derivatives are defined in the modified Riemann-Liouville context. As a result, various exact analytical solutions consisting of trigonometric function solutions, kink-shaped soliton solutions and new exact solitary wave solutions are obtained.

A more fundamental approach to the derivation of nonlinear acoustic wave equations with fractional loss operators (L).

PubMed

Prieur, Fabrice; Vilenskiy, Gregory; Holm, Sverre

2012-10-01

A corrected derivation of nonlinear wave propagation equations with fractional loss operators is presented. The fundamental approach is based on fractional formulations of the stress-strain and heat flux definitions but uses the energy equation and thermodynamic identities to link density and pressure instead of an erroneous fractional form of the entropy equation as done in Prieur and Holm ["Nonlinear acoustic wave equations with fractional loss operators," J. Acoust. Soc. Am. 130(3), 1125-1132 (2011)]. The loss operator of the obtained nonlinear wave equations differs from the previous derivations as well as the dispersion equation, but when approximating for low frequencies the expressions for the frequency dependent attenuation and velocity dispersion remain unchanged.

Empirical water depth predictions in Dublin Bay based on satellite EO multispectral imagery and multibeam data using spatially weighted geographical analysis

NASA Astrophysics Data System (ADS)

Monteys, Xavier; Harris, Paul; Caloca, Silvia

2014-05-01

The coastal shallow water zone can be a challenging and expensive environment within which to acquire bathymetry and other oceanographic data using traditional survey methods. Dangers and limited swath coverage make some of these areas unfeasible to survey using ship borne systems, and turbidity can preclude marine LIDAR. As a result, an extensive part of the coastline worldwide remains completely unmapped. Satellite EO multispectral data, after processing, allows timely, cost efficient and quality controlled information to be used for planning, monitoring, and regulating coastal environments. It has the potential to deliver repetitive derivation of medium resolution bathymetry, coastal water properties and seafloor characteristics in shallow waters. Over the last 30 years satellite passive imaging methods for bathymetry extraction, implementing analytical or empirical methods, have had a limited success predicting water depths. Different wavelengths of the solar light penetrate the water column to varying depths. They can provide acceptable results up to 20 m but become less accurate in deeper waters. The study area is located in the inner part of Dublin Bay, on the East coast of Ireland. The region investigated is a C-shaped inlet covering an area of 10 km long and 5 km wide with water depths ranging from 0 to 10 m. The methodology employed on this research uses a ratio of reflectance from SPOT 5 satellite bands, differing to standard linear transform algorithms. High accuracy water depths were derived using multibeam data. The final empirical model uses spatially weighted geographical tools to retrieve predicted depths. The results of this paper confirm that SPOT satellite scenes are suitable to predict depths using empirical models in very shallow embayments. Spatial regression models show better adjustments in the predictions over non-spatial models. The spatial regression equation used provides realistic results down to 6 m below the water surface, with reliable and error controlled depths. Bathymetric extraction approaches involving satellite imagery data are regarded as a fast, successful and economically advantageous solution to automatic water depth calculation in shallow and complex environments.

Arbitrary-order corrections for finite-time drift and diffusion coefficients

NASA Astrophysics Data System (ADS)

Anteneodo, C.; Riera, R.

2009-09-01

We address a standard class of diffusion processes with linear drift and quadratic diffusion coefficients. These contributions to dynamic equations can be directly drawn from data time series. However, real data are constrained to finite sampling rates and therefore it is crucial to establish a suitable mathematical description of the required finite-time corrections. Based on Itô-Taylor expansions, we present the exact corrections to the finite-time drift and diffusion coefficients. These results allow to reconstruct the real hidden coefficients from the empirical estimates. We also derive higher-order finite-time expressions for the third and fourth conditional moments that furnish extra theoretical checks for this class of diffusion models. The analytical predictions are compared with the numerical outcomes of representative artificial time series.

Nonlinear Waves in the Terrestrial Quasiparallel Foreshock.

PubMed

Hnat, B; Kolotkov, D Y; O'Connell, D; Nakariakov, V M; Rowlands, G

2016-12-02

We provide strongly conclusive evidence that the cubic nonlinearity plays an important part in the evolution of the large amplitude magnetic structures in the terrestrial foreshock. Large amplitude nonlinear wave trains at frequencies above the proton cyclotron frequency are identified after nonharmonic slow variations are filtered out by applying the empirical mode decomposition. Numerical solutions of the derivative nonlinear Schrödinger equation, predicted analytically by the use of a pseudopotential approach, are found to be consistent with the observed wave forms. The approximate phase speed of these nonlinear waves, indicated by the parameters of numerical solutions, is of the order of the local Alfvén speed. We suggest that the feedback of the large amplitude fluctuations on background plasma is reflected in the evolution of the pseudopotential.

Determination of errors in derived magnetic field directions in geosynchronous orbit: results from a statistical approach

NASA Astrophysics Data System (ADS)

Chen, Yue; Cunningham, Gregory; Henderson, Michael

2016-09-01

This study aims to statistically estimate the errors in local magnetic field directions that are derived from electron directional distributions measured by Los Alamos National Laboratory geosynchronous (LANL GEO) satellites. First, by comparing derived and measured magnetic field directions along the GEO orbit to those calculated from three selected empirical global magnetic field models (including a static Olson and Pfitzer 1977 quiet magnetic field model, a simple dynamic Tsyganenko 1989 model, and a sophisticated dynamic Tsyganenko 2001 storm model), it is shown that the errors in both derived and modeled directions are at least comparable. Second, using a newly developed proxy method as well as comparing results from empirical models, we are able to provide for the first time circumstantial evidence showing that derived magnetic field directions should statistically match the real magnetic directions better, with averaged errors < ˜ 2°, than those from the three empirical models with averaged errors > ˜ 5°. In addition, our results suggest that the errors in derived magnetic field directions do not depend much on magnetospheric activity, in contrast to the empirical field models. Finally, as applications of the above conclusions, we show examples of electron pitch angle distributions observed by LANL GEO and also take the derived magnetic field directions as the real ones so as to test the performance of empirical field models along the GEO orbits, with results suggesting dependence on solar cycles as well as satellite locations. This study demonstrates the validity and value of the method that infers local magnetic field directions from particle spin-resolved distributions.

Determination of errors in derived magnetic field directions in geosynchronous orbit: results from a statistical approach

DOE PAGES

Chen, Yue; Cunningham, Gregory; Henderson, Michael

2016-09-21

Our study aims to statistically estimate the errors in local magnetic field directions that are derived from electron directional distributions measured by Los Alamos National Laboratory geosynchronous (LANL GEO) satellites. First, by comparing derived and measured magnetic field directions along the GEO orbit to those calculated from three selected empirical global magnetic field models (including a static Olson and Pfitzer 1977 quiet magnetic field model, a simple dynamic Tsyganenko 1989 model, and a sophisticated dynamic Tsyganenko 2001 storm model), it is shown that the errors in both derived and modeled directions are at least comparable. Furthermore, using a newly developedmore » proxy method as well as comparing results from empirical models, we are able to provide for the first time circumstantial evidence showing that derived magnetic field directions should statistically match the real magnetic directions better, with averaged errors < ~2°, than those from the three empirical models with averaged errors > ~5°. In addition, our results suggest that the errors in derived magnetic field directions do not depend much on magnetospheric activity, in contrast to the empirical field models. Finally, as applications of the above conclusions, we show examples of electron pitch angle distributions observed by LANL GEO and also take the derived magnetic field directions as the real ones so as to test the performance of empirical field models along the GEO orbits, with results suggesting dependence on solar cycles as well as satellite locations. Finally, this study demonstrates the validity and value of the method that infers local magnetic field directions from particle spin-resolved distributions.« less

Determination of errors in derived magnetic field directions in geosynchronous orbit: results from a statistical approach

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

Chen, Yue; Cunningham, Gregory; Henderson, Michael

Our study aims to statistically estimate the errors in local magnetic field directions that are derived from electron directional distributions measured by Los Alamos National Laboratory geosynchronous (LANL GEO) satellites. First, by comparing derived and measured magnetic field directions along the GEO orbit to those calculated from three selected empirical global magnetic field models (including a static Olson and Pfitzer 1977 quiet magnetic field model, a simple dynamic Tsyganenko 1989 model, and a sophisticated dynamic Tsyganenko 2001 storm model), it is shown that the errors in both derived and modeled directions are at least comparable. Furthermore, using a newly developedmore » proxy method as well as comparing results from empirical models, we are able to provide for the first time circumstantial evidence showing that derived magnetic field directions should statistically match the real magnetic directions better, with averaged errors < ~2°, than those from the three empirical models with averaged errors > ~5°. In addition, our results suggest that the errors in derived magnetic field directions do not depend much on magnetospheric activity, in contrast to the empirical field models. Finally, as applications of the above conclusions, we show examples of electron pitch angle distributions observed by LANL GEO and also take the derived magnetic field directions as the real ones so as to test the performance of empirical field models along the GEO orbits, with results suggesting dependence on solar cycles as well as satellite locations. Finally, this study demonstrates the validity and value of the method that infers local magnetic field directions from particle spin-resolved distributions.« less

Finding the Equation for a Vibrating Car Antenna.

ERIC Educational Resources Information Center

Newburgh, Ronald; Newburgh, G. Alexander

2000-01-01

Presents the physical assumptions and mathematical expressions necessary to derive a fourth-order differential equation that describes the vibration of a particular car antenna. Contends that while students may not be able to derive or use the equation, they should be able to appreciate a guided derivation as an example of how physics is done.…

Semi-empirical model for prediction of unsteady forces on an airfoil with application to flutter

NASA Technical Reports Server (NTRS)

Mahajan, Aparajit J.; Kaza, Krishna Rao V.

1992-01-01

A semi-empirical model is described for predicting unsteady aerodynamic forces on arbitrary airfoils under mildly stalled and unstalled conditions. Aerodynamic forces are modeled using second order ordinary differential equations for lift and moment with airfoil motion as the input. This model is simultaneously integrated with structural dynamics equations to determine flutter characteristics for a two degrees-of-freedom system. Results for a number of cases are presented to demonstrate the suitability of this model to predict flutter. Comparison is made to the flutter characteristics determined by a Navier-Stokes solver and also the classical incompressible potential flow theory.

Semi-empirical model for prediction of unsteady forces on an airfoil with application to flutter

NASA Technical Reports Server (NTRS)

Mahajan, A. J.; Kaza, K. R. V.; Dowell, E. H.

1993-01-01

A semi-empirical model is described for predicting unsteady aerodynamic forces on arbitrary airfoils under mildly stalled and unstalled conditions. Aerodynamic forces are modeled using second order ordinary differential equations for lift and moment with airfoil motion as the input. This model is simultaneously integrated with structural dynamics equations to determine flutter characteristics for a two degrees-of-freedom system. Results for a number of cases are presented to demonstrate the suitability of this model to predict flutter. Comparison is made to the flutter characteristics determined by a Navier-Stokes solver and also the classical incompressible potential flow theory.

Lie symmetries and conservation laws for the time fractional Derrida-Lebowitz-Speer-Spohn equation

NASA Astrophysics Data System (ADS)

Rui, Wenjuan; Zhang, Xiangzhi

2016-05-01

This paper investigates the invariance properties of the time fractional Derrida-Lebowitz-Speer-Spohn (FDLSS) equation with Riemann-Liouville derivative. By using the Lie group analysis method of fractional differential equations, we derive Lie symmetries for the FDLSS equation. In a particular case of scaling transformations, we transform the FDLSS equation into a nonlinear ordinary fractional differential equation. Conservation laws for this equation are obtained with the aid of the new conservation theorem and the fractional generalization of the Noether operators.

Progressive wave expansions and open boundary problems

NASA Technical Reports Server (NTRS)

Hagstrom, T.; Hariharan, S. I.

1995-01-01

In this paper we construct progressive wave expansions and asymptotic boundary conditions for wave-like equations in exterior domains, including applications to electromagnetics, compressible flows and aero-acoustics. The development of the conditions will be discussed in two parts. The first part will include derivations of asymptotic conditions based on the well-known progressive wave expansions for the two-dimensional wave equations. A key feature in the derivations is that the resulting family of boundary conditions involves a single derivative in the direction normal to the open boundary. These conditions are easy to implement and an application in electromagnetics will be presented. The second part of the paper will discuss the theory for hyperbolic systems in two dimensions. Here, the focus will be to obtain the expansions in a general way and to use them to derive a class of boundary conditions that involve only time derivatives or time and tangential derivatives. Maxwell's equations and the compressible Euler equations are used as examples. Simulations with the linearized Euler equations are presented to validate the theory.

A Rapid Empirical Method for Estimating the Gross Takeoff Weight of a High Speed Civil Transport

NASA Technical Reports Server (NTRS)

Mack, Robert J.

1999-01-01

During the cruise segment of the flight mission, aircraft flying at supersonic speeds generate sonic booms that are usually maximum at the beginning of cruise. The pressure signature with the shocks causing these perceived booms can be predicted if the aircraft's geometry, Mach number, altitude, angle of attack, and cruise weight are known. Most methods for estimating aircraft weight, especially beginning-cruise weight, are empirical and based on least- square-fit equations that best represent a body of component weight data. The empirical method discussed in this report used simplified weight equations based on a study of performance and weight data from conceptual and real transport aircraft. Like other weight-estimation methods, weights were determined at several points in the mission. While these additional weights were found to be useful, it is the determination of beginning-cruise weight that is most important for the prediction of the aircraft's sonic-boom characteristics.

Analyzing Lie symmetry and constructing conservation laws for time-fractional Benny-Lin equation

NASA Astrophysics Data System (ADS)

Rashidi, Saeede; Hejazi, S. Reza

This paper investigates the invariance properties of the time fractional Benny-Lin equation with Riemann-Liouville and Caputo derivatives. This equation can be reduced to the Kawahara equation, fifth-order Kdv equation, the Kuramoto-Sivashinsky equation and Navier-Stokes equation. By using the Lie group analysis method of fractional differential equations (FDEs), we derive Lie symmetries for the Benny-Lin equation. Conservation laws for this equation are obtained with the aid of the concept of nonlinear self-adjointness and the fractional generalization of the Noether’s operators. Furthermore, by means of the invariant subspace method, exact solutions of the equation are also constructed.

Two-dimensional evolution equation of finite-amplitude internal gravity waves in a uniformly stratified fluid

PubMed

Kataoka; Tsutahara; Akuzawa

2000-02-14

We derive a fully nonlinear evolution equation that can describe the two-dimensional motion of finite-amplitude long internal waves in a uniformly stratified three-dimensional fluid of finite depth. The derived equation is the two-dimensional counterpart of the evolution equation obtained by Grimshaw and Yi [J. Fluid Mech. 229, 603 (1991)]. In the small-amplitude limit, our equation is reduced to the celebrated Kadomtsev-Petviashvili equation.

Preequating with Empirical Item Characteristic Curves: An Observed-Score Preequating Method

ERIC Educational Resources Information Center

Zu, Jiyun; Puhan, Gautam

2014-01-01

Preequating is in demand because it reduces score reporting time. In this article, we evaluated an observed-score preequating method: the empirical item characteristic curve (EICC) method, which makes preequating without item response theory (IRT) possible. EICC preequating results were compared with a criterion equating and with IRT true-score…

N-Loop Learning: Part II--An Empirical Investigation

ERIC Educational Resources Information Center

Simonin, Bernard L.

2017-01-01

Purpose: Through a survey of firm's experiences with strategic alliances and a structural equation modeling approach, the aim of this study is to stimulate further interest in modeling and empirical research in the area of N-loop learning. Although the concepts of single-loop and double-loop learning, in particular, are well established in the…

Empirical data and the variance-covariance matrix for the 1969 Smithsonian Standard Earth (2)

NASA Technical Reports Server (NTRS)

Gaposchkin, E. M.

1972-01-01

The empirical data used in the 1969 Smithsonian Standard Earth (2) are presented. The variance-covariance matrix, or the normal equations, used for correlation analysis, are considered. The format and contents of the matrix, available on magnetic tape, are described and a sample printout is given.

BOOK REVIEW: Statistical Mechanics of Turbulent Flows

NASA Astrophysics Data System (ADS)

Cambon, C.

2004-10-01

This is a handbook for a computational approach to reacting flows, including background material on statistical mechanics. In this sense, the title is somewhat misleading with respect to other books dedicated to the statistical theory of turbulence (e.g. Monin and Yaglom). In the present book, emphasis is placed on modelling (engineering closures) for computational fluid dynamics. The probabilistic (pdf) approach is applied to the local scalar field, motivated first by the nonlinearity of chemical source terms which appear in the transport equations of reacting species. The probabilistic and stochastic approaches are also used for the velocity field and particle position; nevertheless they are essentially limited to Lagrangian models for a local vector, with only single-point statistics, as for the scalar. Accordingly, conventional techniques, such as single-point closures for RANS (Reynolds-averaged Navier-Stokes) and subgrid-scale models for LES (large-eddy simulations), are described and in some cases reformulated using underlying Langevin models and filtered pdfs. Even if the theoretical approach to turbulence is not discussed in general, the essentials of probabilistic and stochastic-processes methods are described, with a useful reminder concerning statistics at the molecular level. The book comprises 7 chapters. Chapter 1 briefly states the goals and contents, with a very clear synoptic scheme on page 2. Chapter 2 presents definitions and examples of pdfs and related statistical moments. Chapter 3 deals with stochastic processes, pdf transport equations, from Kramer-Moyal to Fokker-Planck (for Markov processes), and moments equations. Stochastic differential equations are introduced and their relationship to pdfs described. This chapter ends with a discussion of stochastic modelling. The equations of fluid mechanics and thermodynamics are addressed in chapter 4. Classical conservation equations (mass, velocity, internal energy) are derived from their counterparts at the molecular level. In addition, equations are given for multicomponent reacting systems. The chapter ends with miscellaneous topics, including DNS, (idea of) the energy cascade, and RANS. Chapter 5 is devoted to stochastic models for the large scales of turbulence. Langevin-type models for velocity (and particle position) are presented, and their various consequences for second-order single-point corelations (Reynolds stress components, Kolmogorov constant) are discussed. These models are then presented for the scalar. The chapter ends with compressible high-speed flows and various models, ranging from k-epsilon to hybrid RANS-pdf. Stochastic models for small-scale turbulence are addressed in chapter 6. These models are based on the concept of a filter density function (FDF) for the scalar, and a more conventional SGS (sub-grid-scale model) for the velocity in LES. The final chapter, chapter 7, is entitled `The unification of turbulence models' and aims at reconciling large-scale and small-scale modelling. This book offers a timely survey of techniques in modern computational fluid mechanics for turbulent flows with reacting scalars. It should be of interest to engineers, while the discussion of the underlying tools, namely pdfs, stochastic and statistical equations should also be attractive to applied mathematicians and physicists. The book's emphasis on local pdfs and stochastic Langevin models gives a consistent structure to the book and allows the author to cover almost the whole spectrum of practical modelling in turbulent CFD. On the other hand, one might regret that non-local issues are not mentioned explicitly, or even briefly. These problems range from the presence of pressure-strain correlations in the Reynolds stress transport equations to the presence of two-point pdfs in the single-point pdf equation derived from the Navier--Stokes equations. (One may recall that, even without scalar transport, a general closure problem for turbulence statistics results from both non-linearity and non-locality of Navier-Stokes equations, the latter coming from, e.g., the nonlocal relationship of velocity and pressure in the quasi-incompressible case. These two aspects are often intricately linked. It is well known that non-linearity alone is not responsible for the `problem', as evidenced by 1D turbulence without pressure (`Burgulence' from the Burgers equation) and probably 3D (cosmological gas). A local description in terms of pdf for the velocity can resolve the `non-linear' problem, which instead yields an infinite hierarchy of equations in terms of moments. On the other hand, non-locality yields a hierarchy of unclosed equations, with the single-point pdf equation for velocity derived from NS incompressible equations involving a two-point pdf, and so on. The general relationship was given by Lundgren (1967, Phys. Fluids 10 (5), 969-975), with the equation for pdf at n points involving the pdf at n+1 points. The nonlocal problem appears in various statistical models which are not discussed in the book. The simplest example is full RST or ASM models, in which the closure of pressure-strain correlations is pivotal (their counterpart ought to be identified and discussed in equations (5-21) and the following ones). The book does not address more sophisticated non-local approaches, such as two-point (or spectral) non-linear closure theories and models, `rapid distortion theory' for linear regimes, not to mention scaling and intermittency based on two-point structure functions, etc. The book sometimes mixes theoretical modelling and pure empirical relationships, the empirical character coming from the lack of a nonlocal (two-point) approach.) In short, the book is orientated more towards applications than towards turbulence theory; it is written clearly and concisely and should be useful to a large community, interested either in the underlying stochastic formalism or in CFD applications.

Variational Methods in Design Optimization and Sensitivity Analysis for Two-Dimensional Euler Equations

NASA Technical Reports Server (NTRS)

Ibrahim, A. H.; Tiwari, S. N.; Smith, R. E.

1997-01-01

Variational methods (VM) sensitivity analysis employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.

Development and application of an observation-based light attenuation equation for northern Gulf of Mexico

EPA Science Inventory

Solar radiation is one of the main factors controlling the rate of primary production on the Louisiana Shelf in the northern Gulf of Mexico. This work seeks to improve on previously published empirical equations through the use of statistical data transformation and the incorpora...

Model development and applications at the USDA-ARS National Soil Erosion Research Laboratory

USDA-ARS?s Scientific Manuscript database

The United States Department of Agriculture (USDA) has a long history of development of soil erosion prediction technology, initially with empirical equations like the Universal Soil Loss Equation (USLE), and more recently with process-based models such as the Water Erosion Prediction Project (WEPP)...

Test Score Equating Using Discrete Anchor Items versus Passage-Based Anchor Items: A Case Study Using "SAT"® Data. Research Report. ETS RR-14-14

ERIC Educational Resources Information Center

Liu, Jinghua; Zu, Jiyun; Curley, Edward; Carey, Jill

2014-01-01

The purpose of this study is to investigate the impact of discrete anchor items versus passage-based anchor items on observed score equating using empirical data.This study compares an "SAT"® critical reading anchor that contains more discrete items proportionally, compared to the total tests to be equated, to another anchor that…

Unmitigated numerical solution to the diffraction term in the parabolic nonlinear ultrasound wave equation.

PubMed

Hasani, Mojtaba H; Gharibzadeh, Shahriar; Farjami, Yaghoub; Tavakkoli, Jahan

2013-09-01

Various numerical algorithms have been developed to solve the Khokhlov-Kuznetsov-Zabolotskaya (KZK) parabolic nonlinear wave equation. In this work, a generalized time-domain numerical algorithm is proposed to solve the diffraction term of the KZK equation. This algorithm solves the transverse Laplacian operator of the KZK equation in three-dimensional (3D) Cartesian coordinates using a finite-difference method based on the five-point implicit backward finite difference and the five-point Crank-Nicolson finite difference discretization techniques. This leads to a more uniform discretization of the Laplacian operator which in turn results in fewer calculation gridding nodes without compromising accuracy in the diffraction term. In addition, a new empirical algorithm based on the LU decomposition technique is proposed to solve the system of linear equations obtained from this discretization. The proposed empirical algorithm improves the calculation speed and memory usage, while the order of computational complexity remains linear in calculation of the diffraction term in the KZK equation. For evaluating the accuracy of the proposed algorithm, two previously published algorithms are used as comparison references: the conventional 2D Texas code and its generalization for 3D geometries. The results show that the accuracy/efficiency performance of the proposed algorithm is comparable with the established time-domain methods.

Symbolic computation of recurrence equations for the Chebyshev series solution of linear ODE's. [ordinary differential equations

NASA Technical Reports Server (NTRS)

Geddes, K. O.

1977-01-01

If a linear ordinary differential equation with polynomial coefficients is converted into integrated form then the formal substitution of a Chebyshev series leads to recurrence equations defining the Chebyshev coefficients of the solution function. An explicit formula is presented for the polynomial coefficients of the integrated form in terms of the polynomial coefficients of the differential form. The symmetries arising from multiplication and integration of Chebyshev polynomials are exploited in deriving a general recurrence equation from which can be derived all of the linear equations defining the Chebyshev coefficients. Procedures for deriving the general recurrence equation are specified in a precise algorithmic notation suitable for translation into any of the languages for symbolic computation. The method is algebraic and it can therefore be applied to differential equations containing indeterminates.

Evaluation of automated decisionmaking methodologies and development of an integrated robotic system simulation. Volume 2, Part 2: Appendixes B, C, D and E

NASA Technical Reports Server (NTRS)

Lowrie, J. W.; Fermelia, A. J.; Haley, D. C.; Gremban, K. D.; Vanbaalen, J.; Walsh, R. W.

1982-01-01

The derivation of the equations is presented, the rate control algorithm described, and simulation methodologies summarized. A set of dynamics equations that can be used recursively to calculate forces and torques acting at the joints of an n link manipulator given the manipulator joint rates are derived. The equations are valid for any n link manipulator system with any kind of joints connected in any sequence. The equations of motion for the class of manipulators consisting of n rigid links interconnected by rotary joints are derived. A technique is outlined for reducing the system of equations to eliminate contraint torques. The linearized dynamics equations for an n link manipulator system are derived. The general n link linearized equations are then applied to a two link configuration. The coordinated rate control algorithm used to compute individual joint rates when given end effector rates is described. A short discussion of simulation methodologies is presented.

Macroscopic constitutive equations of thermo-poroviscoelasticity derived using eigenstrains

NASA Astrophysics Data System (ADS)

Suvorov, A. P.; Selvadurai, A. P. S.

2010-10-01

Macroscopic constitutive equations for thermo-viscoelastic processes in a fully saturated porous medium are re-derived from basic principles of micromechanics applicable to solid multi-phase materials such as composites. Simple derivations of the constitutive relations and the void occupancy relationship are presented. The derivations use the notion of eigenstrain or, equivalently, eigenstress applied to the separate phases of a porous medium. Governing coupled equations for the displacement components and the fluid pressure are also obtained.

Algebro-geometric Solutions for the Derivative Burgers Hierarchy

NASA Astrophysics Data System (ADS)

Hou, Yu; Fan, Engui; Qiao, Zhijun; Wang, Zhong

2015-02-01

Though completely integrable Camassa-Holm (CH) equation and Degasperis-Procesi (DP) equation are cast in the same peakon family, they possess the second- and third-order Lax operators, respectively. From the viewpoint of algebro-geometrical study, this difference lies in hyper-elliptic and non-hyper-elliptic curves. The non-hyperelliptic curves lead to great difficulty in the construction of algebro-geometric solutions of the DP equation. In this paper, we study algebro-geometric solutions for the derivative Burgers (DB) equation, which is derived by Qiao and Li (2004) as a short wave model of the DP equation with the help of functional gradient and a pair of Lenard operators. Based on the characteristic polynomial of a Lax matrix for the DB equation, we introduce a third order algebraic curve with genus , from which the associated Baker-Akhiezer functions, meromorphic function, and Dubrovin-type equations are constructed. Furthermore, the theory of algebraic curve is applied to derive explicit representations of the theta function for the Baker-Akhiezer functions and the meromorphic function. In particular, the algebro-geometric solutions are obtained for all equations in the whole DB hierarchy.

Fractional Diffusion Processes: Probability Distributions and Continuous Time Random Walk

NASA Astrophysics Data System (ADS)

Gorenflo, R.; Mainardi, F.

A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By the space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order alpha in (0,2] and skewness theta (\\verttheta\\vertlemin \\{alpha ,2-alpha \\}), and the first-order time derivative with a Caputo derivative of order beta in (0,1] . The fundamental solution (for the Cauchy problem) of the fractional diffusion equation can be interpreted as a probability density evolving in time of a peculiar self-similar stochastic process. We view it as a generalized diffusion process that we call fractional diffusion process, and present an integral representation of the fundamental solution. A more general approach to anomalous diffusion is however known to be provided by the master equation for a continuous time random walk (CTRW). We show how this equation reduces to our fractional diffusion equation by a properly scaled passage to the limit of compressed waiting times and jump widths. Finally, we describe a method of simulation and display (via graphics) results of a few numerical case studies.

Dissolution of solid dosage form. II. Equations for the dissolution of nondisintegrating tablet under the sink condition.

PubMed

Yonezawa, Y; Shirakura, K; Otsuka, A; Sunada, H

1991-03-01

An equation for dissolution from the whole surface of a nondisintegrating single component tablet under the sink condition was derived. Also, equations for several dissolution manners of the tablet under the sink condition were derived in the postulation of the dominant dissolution rate constant which determines the dissolution manner. The applicability or validity of these equations were examined by the dissolution measurements with nondisintegrating single component tablets. About one-tenth the amount of the amount needed to saturate the solution was used to prepare a tablet, and dissolution measurements were carried out with the tablet whose flat or side surface was masked with an adhesive tape in accordance with the conditions for derivation of equations. Among the derived equations, dissolution from the whole surface of a tablet was expressed by a form similar to the cube root law equation for particles. Hence, a single component tablet compressed by the use of a suitable amount was thought to behave like a single crystal. Also, equations derived for several dissolution manners were thought to be applicable for the dissolution of a nonspherical particle and crystal concerning the crystal's habit and its dissolution property, and the extended applicability was examined by converting the crystal into a simplified or idealized form, i.e., rectangle or plate.

Equation-free modeling unravels the behavior of complex ecological systems

USGS Publications Warehouse

DeAngelis, Donald L.; Yurek, Simeon

2015-01-01

Ye et al. (1) address a critical problem confronting the management of natural ecosystems: How can we make forecasts of possible future changes in populations to help guide management actions? This problem is especially acute for marine and anadromous fisheries, where the large interannual fluctuations of populations, arising from complex nonlinear interactions among species and with varying environmental factors, have defied prediction over even short time scales. The empirical dynamic modeling (EDM) described in Ye et al.’s report, the latest in a series of papers by Sugihara and his colleagues, offers a promising quantitative approach to building models using time series to successfully project dynamics into the future. With the term “equation-free” in the article title, Ye et al. (1) are suggesting broader implications of their approach, considering the centrality of equations in modern science. From the 1700s on, nature has been increasingly described by mathematical equations, with differential or difference equations forming the basic framework for describing dynamics. The use of mathematical equations for ecological systems came much later, pioneered by Lotka and Volterra, who showed that population cycles might be described in terms of simple coupled nonlinear differential equations. It took decades for Lotka–Volterra-type models to become established, but the development of appropriate differential equations is now routine in modeling ecological dynamics. There is no question that the injection of mathematical equations, by forcing “clarity and precision into conjecture” (2), has led to increased understanding of population and community dynamics. As in science in general, in ecology equations are a key method of communication and of framing hypotheses. These equations serve as compact representations of an enormous amount of empirical data and can be analyzed by the powerful methods of mathematics.

Generalized fractional diffusion equations for subdiffusion in arbitrarily growing domains

NASA Astrophysics Data System (ADS)

Angstmann, C. N.; Henry, B. I.; McGann, A. V.

2017-10-01

The ubiquity of subdiffusive transport in physical and biological systems has led to intensive efforts to provide robust theoretical models for this phenomena. These models often involve fractional derivatives. The important physical extension of this work to processes occurring in growing materials has proven highly nontrivial. Here we derive evolution equations for modeling subdiffusive transport in a growing medium. The derivation is based on a continuous-time random walk. The concise formulation of these evolution equations requires the introduction of a new, comoving, fractional derivative. The implementation of the evolution equation is illustrated with a simple model of subdiffusing proteins in a growing membrane.

Body size and meta-community structure: the allometric scaling of parasitic worm communities in their mammalian hosts.

PubMed

DE Leo, Giulio A; Dobson, Andrew P; Gatto, Marino

2016-06-01

In this paper we derive from first principles the expected body sizes of the parasite communities that can coexist in a mammal of given body size. We use a mixture of mathematical models and known allometric relationships to examine whether host and parasite life histories constrain the diversity of parasite species that can coexist in the population of any host species. The model consists of one differential equation for each parasite species and a single density-dependent nonlinear equation for the affected host under the assumption of exploitation competition. We derive threshold conditions for the coexistence and competitive exclusion of parasite species using invasion criteria and stability analysis of the resulting equilibria. These results are then used to evaluate the range of parasites species that can invade and establish in a target host and identify the 'optimal' size of a parasite species for a host of a given body size; 'optimal' is defined as the body size of a parasite species that cannot be outcompeted by any other parasite species. The expected distributions of parasites body sizes in hosts of different sizes are then compared with those observed in empirical studies. Our analysis predicts the relative abundance of parasites of different size that establish in the host and suggests that increasing the ratio of parasite body size to host body size above a minimum threshold increases the persistence of the parasite population.

Understanding the physical basis of the salt dependence of the electrostatic binding free energy of mutated charged ligand-nucleic acid complexes.

PubMed

Harris, Robert C; Bredenberg, Johan H; Silalahi, Alexander R J; Boschitsch, Alexander H; Fenley, Marcia O

2011-06-01

The predictions of the derivative of the electrostatic binding free energy of a biomolecular complex, ΔG(el), with respect to the logarithm of the 1:1 salt concentration, d(ΔG(el))/d(ln[NaCl]), SK, by the Poisson-Boltzmann equation, PBE, are very similar to those of the simpler Debye-Hückel equation, DHE, because the terms in the PBE's predictions of SK that depend on the details of the dielectric interface are small compared to the contributions from long-range electrostatic interactions. These facts allow one to obtain predictions of SK using a simplified charge model along with the DHE that are highly correlated with both the PBE and experimental binding data. The DHE-based model developed here, which was derived from the generalized Born model, explains the lack of correlation between SK and ΔG(el) in the presence of a dielectric discontinuity, which conflicts with the popular use of this supposed correlation to parse experimental binding free energies into electrostatic and nonelectrostatic components. Moreover, the DHE model also provides a clear justification for the correlations between SK and various empirical quantities, like the number of ion pairs, the ligand charge on the interface, the Coulomb binding free energy, and the product of the charges on the complex's components, but these correlations are weak, questioning their usefulness. Copyright © 2011 Elsevier B.V. All rights reserved.

Macroscopic neural mass model constructed from a current-based network model of spiking neurons.

PubMed

Umehara, Hiroaki; Okada, Masato; Teramae, Jun-Nosuke; Naruse, Yasushi

2017-02-01

Neural mass models (NMMs) are efficient frameworks for describing macroscopic cortical dynamics including electroencephalogram and magnetoencephalogram signals. Originally, these models were formulated on an empirical basis of synaptic dynamics with relatively long time constants. By clarifying the relations between NMMs and the dynamics of microscopic structures such as neurons and synapses, we can better understand cortical and neural mechanisms from a multi-scale perspective. In a previous study, the NMMs were analytically derived by averaging the equations of synaptic dynamics over the neurons in the population and further averaging the equations of the membrane-potential dynamics. However, the averaging of synaptic current assumes that the neuron membrane potentials are nearly time invariant and that they remain at sub-threshold levels to retain the conductance-based model. This approximation limits the NMM to the non-firing state. In the present study, we newly propose a derivation of a NMM by alternatively approximating the synaptic current which is assumed to be independent of the membrane potential, thus adopting a current-based model. Our proposed model releases the constraint of the nearly constant membrane potential. We confirm that the obtained model is reducible to the previous model in the non-firing situation and that it reproduces the temporal mean values and relative power spectrum densities of the average membrane potentials for the spiking neurons. It is further ensured that the existing NMM properly models the averaged dynamics over individual neurons even if they are spiking in the populations.

Development of Quantum Chemical Method to Calculate Half Maximal Inhibitory Concentration (IC50 ).

PubMed

Bag, Arijit; Ghorai, Pradip Kr

2016-05-01

Till date theoretical calculation of the half maximal inhibitory concentration (IC50 ) of a compound is based on different Quantitative Structure Activity Relationship (QSAR) models which are empirical methods. By using the Cheng-Prusoff equation it may be possible to compute IC50 , but this will be computationally very expensive as it requires explicit calculation of binding free energy of an inhibitor with respective protein or enzyme. In this article, for the first time we report an ab initio method to compute IC50 of a compound based only on the inhibitor itself where the effect of the protein is reflected through a proportionality constant. By using basic enzyme inhibition kinetics and thermodynamic relations, we derive an expression of IC50 in terms of hydrophobicity, electric dipole moment (μ) and reactivity descriptor (ω) of an inhibitor. We implement this theory to compute IC50 of 15 HIV-1 capsid inhibitors and compared them with experimental results and available other QASR based empirical results. Calculated values using our method are in very good agreement with the experimental values compared to the values calculated using other methods. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Time Domain Strain/Stress Reconstruction Based on Empirical Mode Decomposition: Numerical Study and Experimental Validation.

PubMed

He, Jingjing; Zhou, Yibin; Guan, Xuefei; Zhang, Wei; Zhang, Weifang; Liu, Yongming

2016-08-16

Structural health monitoring has been studied by a number of researchers as well as various industries to keep up with the increasing demand for preventive maintenance routines. This work presents a novel method for reconstruct prompt, informed strain/stress responses at the hot spots of the structures based on strain measurements at remote locations. The structural responses measured from usage monitoring system at available locations are decomposed into modal responses using empirical mode decomposition. Transformation equations based on finite element modeling are derived to extrapolate the modal responses from the measured locations to critical locations where direct sensor measurements are not available. Then, two numerical examples (a two-span beam and a 19956-degree of freedom simplified airfoil) are used to demonstrate the overall reconstruction method. Finally, the present work investigates the effectiveness and accuracy of the method through a set of experiments conducted on an aluminium alloy cantilever beam commonly used in air vehicle and spacecraft. The experiments collect the vibration strain signals of the beam via optical fiber sensors. Reconstruction results are compared with theoretical solutions and a detailed error analysis is also provided.

Shear wave velocities of unconsolidated shallow sediments in the Gulf of Mexico

USGS Publications Warehouse

Lee, Myung W.

2013-01-01

Accurate shear-wave velocities for shallow sediments are important for a variety of seismic applications such as inver-sion and amplitude versus offset analysis. During the U.S. Department of Energy-sponsored Gas Hydrate Joint Industry Project Leg II, shear-wave velocities were measured at six wells in the Gulf of Mexico using the logging-while-drilling SonicScope acoustic tool. Because the tool measurement point was only 35 feet from the drill bit, the adverse effect of the borehole condition, which is severe for the shallow unconsolidated sediments in the Gulf of Mexico, was mini-mized and accurate shear-wave velocities of unconsolidated sediments were measured. Measured shear-wave velocities were compared with the shear-wave velocities predicted from the compressional-wave velocities using empirical formulas and the rock physics models based on the Biot-Gassmann theory, and the effectiveness of the two prediction methods was evaluated. Although the empirical equation derived from measured shear-wave data is accurate for predicting shear-wave velocities for depths greater than 500 feet in these wells, the three-phase Biot-Gassmann-theory -based theory appears to be optimum for predicting shear-wave velocities for shallow unconsolidated sediments in the Gulf of Mexico.

Heat-transfer processes in air-cooled engine cylinders

NASA Technical Reports Server (NTRS)

Pinkel, Benjamin

1938-01-01

From a consideration of heat-transfer theory, semi-empirical expressions are set up for the transfer of heat from the combustion gases to the cylinder of an air-cooled engine and from the cylinder to the cooling air. Simple equations for the average head and barrel temperatures as functions of the important engine and cooling variables are obtained from these expressions. The expressions involve a few empirical constants, which may be readily determined from engine tests. Numerical values for these constants were obtained from single-cylinder engine tests for cylinders of the Pratt & Whitney 1535 and 1340-h engines. The equations provide a means of calculating the effect of the various engine and cooling variables on the cylinder temperatures and also of correlating the results of engine cooling tests. An example is given of the application of the equations to the correlation of cooling-test data obtained in flight.

Linear force and moment equations for an annular smooth shaft seal perturbed both angularly and laterally

NASA Technical Reports Server (NTRS)

Fenwick, J.; Dijulio, R.; Ek, M. C.; Ehrgott, R.

1982-01-01

Coefficients are derived for equations expressing the lateral force and pitching moments associated with both planar translation and angular perturbations from a nominally centered rotating shaft with respect to a stationary seal. The coefficients for the lowest order and first derivative terms emerge as being significant and are of approximately the same order of magnitude as the fundamental coefficients derived by means of Black's equations. Second derivative, shear perturbation, and entrance coefficient variation effects are adjudged to be small.

A new (2+1) dimensional integrable evolution equation for an ion acoustic wave in a magnetized plasma

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

Mukherjee, Abhik, E-mail: abhik.mukherjee@saha.ac.in; Janaki, M. S., E-mail: ms.janaki@saha.ac.in; Kundu, Anjan, E-mail: anjan.kundu@saha.ac.in

2015-07-15

A new, completely integrable, two dimensional evolution equation is derived for an ion acoustic wave propagating in a magnetized, collisionless plasma. The equation is a multidimensional generalization of a modulated wavepacket with weak transverse propagation, which has resemblance to nonlinear Schrödinger (NLS) equation and has a connection to Kadomtsev-Petviashvili equation through a constraint relation. Higher soliton solutions of the equation are derived through Hirota bilinearization procedure, and an exact lump solution is calculated exhibiting 2D structure. Some mathematical properties demonstrating the completely integrable nature of this equation are described. Modulational instability using nonlinear frequency correction is derived, and the correspondingmore » growth rate is calculated, which shows the directional asymmetry of the system. The discovery of this novel (2+1) dimensional integrable NLS type equation for a magnetized plasma should pave a new direction of research in the field.« less

Evolution of basic equations for nearshore wave field

PubMed Central

ISOBE, Masahiko

2013-01-01

In this paper, a systematic, overall view of theories for periodic waves of permanent form, such as Stokes and cnoidal waves, is described first with their validity ranges. To deal with random waves, a method for estimating directional spectra is given. Then, various wave equations are introduced according to the assumptions included in their derivations. The mild-slope equation is derived for combined refraction and diffraction of linear periodic waves. Various parabolic approximations and time-dependent forms are proposed to include randomness and nonlinearity of waves as well as to simplify numerical calculation. Boussinesq equations are the equations developed for calculating nonlinear wave transformations in shallow water. Nonlinear mild-slope equations are derived as a set of wave equations to predict transformation of nonlinear random waves in the nearshore region. Finally, wave equations are classified systematically for a clear theoretical understanding and appropriate selection for specific applications. PMID:23318680

Admitting the Inadmissible: Adjoint Formulation for Incomplete Cost Functionals in Aerodynamic Optimization

NASA Technical Reports Server (NTRS)

Arian, Eyal; Salas, Manuel D.

1997-01-01

We derive the adjoint equations for problems in aerodynamic optimization which are improperly considered as "inadmissible." For example, a cost functional which depends on the density, rather than on the pressure, is considered "inadmissible" for an optimization problem governed by the Euler equations. We show that for such problems additional terms should be included in the Lagrangian functional when deriving the adjoint equations. These terms are obtained from the restriction of the interior PDE to the control surface. Demonstrations of the explicit derivation of the adjoint equations for "inadmissible" cost functionals are given for the potential, Euler, and Navier-Stokes equations.

Lie symmetry analysis, explicit solutions and conservation laws for the space-time fractional nonlinear evolution equations

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru

2018-04-01

This paper studies the symmetry analysis, explicit solutions, convergence analysis, and conservation laws (Cls) for two different space-time fractional nonlinear evolution equations with Riemann-Liouville (RL) derivative. The governing equations are reduced to nonlinear ordinary differential equation (ODE) of fractional order using their Lie point symmetries. In the reduced equations, the derivative is in Erdelyi-Kober (EK) sense, power series technique is applied to derive an explicit solutions for the reduced fractional ODEs. The convergence of the obtained power series solutions is also presented. Moreover, the new conservation theorem and the generalization of the Noether operators are developed to construct the nonlocal Cls for the equations . Some interesting figures for the obtained explicit solutions are presented.

A theoretical analysis of fluid flow and energy transport in hydrothermal systems

USGS Publications Warehouse

Faust, Charles R.; Mercer, James W.

1977-01-01

A mathematical derivation for fluid flow and energy transport in hydrothermal systems is presented. Specifically, the mathematical model describes the three-dimensional flow of both single- and two-phase, single-component water and the transport of heat in porous media. The derivation begins with the point balance equations for mass, momentum, and energy. These equations are then averaged over a finite volume to obtain the macroscopic balance equations for a porous medium. The macroscopic equations are combined by appropriate constitutive relationships to form two similified partial differential equations posed in terms of fluid pressure and enthalpy. A two-dimensional formulation of the simplified equations is also derived by partial integration in the vertical dimension. (Woodard-USGS)

Probabilistic inference of ecohydrological parameters using observations from point to satellite scales

NASA Astrophysics Data System (ADS)

Bassiouni, Maoya; Higgins, Chad W.; Still, Christopher J.; Good, Stephen P.

2018-06-01

Vegetation controls on soil moisture dynamics are challenging to measure and translate into scale- and site-specific ecohydrological parameters for simple soil water balance models. We hypothesize that empirical probability density functions (pdfs) of relative soil moisture or soil saturation encode sufficient information to determine these ecohydrological parameters. Further, these parameters can be estimated through inverse modeling of the analytical equation for soil saturation pdfs, derived from the commonly used stochastic soil water balance framework. We developed a generalizable Bayesian inference framework to estimate ecohydrological parameters consistent with empirical soil saturation pdfs derived from observations at point, footprint, and satellite scales. We applied the inference method to four sites with different land cover and climate assuming (i) an annual rainfall pattern and (ii) a wet season rainfall pattern with a dry season of negligible rainfall. The Nash-Sutcliffe efficiencies of the analytical model's fit to soil observations ranged from 0.89 to 0.99. The coefficient of variation of posterior parameter distributions ranged from < 1 to 15 %. The parameter identifiability was not significantly improved in the more complex seasonal model; however, small differences in parameter values indicate that the annual model may have absorbed dry season dynamics. Parameter estimates were most constrained for scales and locations at which soil water dynamics are more sensitive to the fitted ecohydrological parameters of interest. In these cases, model inversion converged more slowly but ultimately provided better goodness of fit and lower uncertainty. Results were robust using as few as 100 daily observations randomly sampled from the full records, demonstrating the advantage of analyzing soil saturation pdfs instead of time series to estimate ecohydrological parameters from sparse records. Our work combines modeling and empirical approaches in ecohydrology and provides a simple framework to obtain scale- and site-specific analytical descriptions of soil moisture dynamics consistent with soil moisture observations.

A methodology for airplane parameter estimation and confidence interval determination in nonlinear estimation problems. Ph.D. Thesis - George Washington Univ., Apr. 1985

NASA Technical Reports Server (NTRS)

Murphy, P. C.

1986-01-01

An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. With the fitted surface, sensitivity information can be updated at each iteration with less computational effort than that required by either a finite-difference method or integration of the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, and thus provides flexibility to use model equations in any convenient format. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. The degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels and to predict the degree of agreement between CR bounds and search estimates.

Field data-based mathematical modeling by Bode equations and vector fitting algorithm for renewable energy applications.

PubMed

Sabry, A H; W Hasan, W Z; Ab Kadir, M Z A; Radzi, M A M; Shafie, S

2018-01-01

The power system always has several variations in its profile due to random load changes or environmental effects such as device switching effects when generating further transients. Thus, an accurate mathematical model is important because most system parameters vary with time. Curve modeling of power generation is a significant tool for evaluating system performance, monitoring and forecasting. Several numerical techniques compete to fit the curves of empirical data such as wind, solar, and demand power rates. This paper proposes a new modified methodology presented as a parametric technique to determine the system's modeling equations based on the Bode plot equations and the vector fitting (VF) algorithm by fitting the experimental data points. The modification is derived from the familiar VF algorithm as a robust numerical method. This development increases the application range of the VF algorithm for modeling not only in the frequency domain but also for all power curves. Four case studies are addressed and compared with several common methods. From the minimal RMSE, the results show clear improvements in data fitting over other methods. The most powerful features of this method is the ability to model irregular or randomly shaped data and to be applied to any algorithms that estimating models using frequency-domain data to provide state-space or transfer function for the model.

Field data-based mathematical modeling by Bode equations and vector fitting algorithm for renewable energy applications

PubMed Central

W. Hasan, W. Z.

2018-01-01

The power system always has several variations in its profile due to random load changes or environmental effects such as device switching effects when generating further transients. Thus, an accurate mathematical model is important because most system parameters vary with time. Curve modeling of power generation is a significant tool for evaluating system performance, monitoring and forecasting. Several numerical techniques compete to fit the curves of empirical data such as wind, solar, and demand power rates. This paper proposes a new modified methodology presented as a parametric technique to determine the system’s modeling equations based on the Bode plot equations and the vector fitting (VF) algorithm by fitting the experimental data points. The modification is derived from the familiar VF algorithm as a robust numerical method. This development increases the application range of the VF algorithm for modeling not only in the frequency domain but also for all power curves. Four case studies are addressed and compared with several common methods. From the minimal RMSE, the results show clear improvements in data fitting over other methods. The most powerful features of this method is the ability to model irregular or randomly shaped data and to be applied to any algorithms that estimating models using frequency-domain data to provide state-space or transfer function for the model. PMID:29351554

Phase relations in the system NaCl-KCl-H2O. Part I: Differential thermal analysis of the NaCl-KCl liquidas at 1 atmosphere and 500, 1000, 1500, and 2000 bars

USGS Publications Warehouse

Chou, I.-Ming

1982-01-01

A simple differential thermal analysis (DTA) technique has been developed to study phase relations of various chemical systems at elevated pressures and temperatures. The DTA system has been calibrated against known melting temperatures in the system NaCl-KCl. Isobaric sections of the liquidus in the system NaCl-KCl have been determined at pressures of 1 atmosphere and 500, 1000, 1500, and 2000 bars. Using the least-squares method, the following equation was used to fit the experimental data: T(??C)= ??? i=0 6aiXiKCl where T is the liquidus temperature, XKCl is mole fraction of KCl, and ai (listed below) are the derived empirical constants. {A table is presented}. The liquidus temperatures estimated from these equations are within ??3??C of experimental values. The measured liquidus temperatures at 1 atmosphere agree with the best available data to within 5??C. The melting temperatures for pure end members at higher pressures agree with the values calculated from the Simon equation (Clark, 1959) to within 3??C. No previous melting data are available for the intermediate compositions at elevated pressures. Using the data in both heating and cooling scans, the minimum melting temperature at 1 atmosphere in the system was located at 658?? ?? 3??C where the sample has an equimolar composition. ?? 1982.

THE COSMIC RAY EQUATOR FROM DATA OF THE SECOND SOVIET EARTH SATELLITE

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

Savenko, I.A.; Shavrin, P.I.; Nesterov, V.Ye.

1962-11-01

Determination of the geographical position of the line of minimum intensity of primary cosmic radiation (cosmic ray equator) makes is possible to study the structure of the geomagnetic field and to check theoretical and empirical approximations to this field. The minima of cosmic radiation intensity were determined by the second Soviet spaceship for 22 latitude curves obtained from various crossings in the region of the geographical equator. (W.D.M.)

An Empirical Comparison of Methods for Equating with Randomly Equivalent Groups of 50 to 400 Test Takers. Research Report. ETS RR-10-05

ERIC Educational Resources Information Center

Livingston, Samuel A.; Kim, Sooyeon

2010-01-01

A series of resampling studies investigated the accuracy of equating by four different methods in a random groups equating design with samples of 400, 200, 100, and 50 test takers taking each form. Six pairs of forms were constructed. Each pair was constructed by assigning items from an existing test taken by 9,000 or more test takers. The…

Development of a simplified flexible pavement design protocol for New York State Department of Transportation based on the AASHTO mechanistic-empirical pavement design guide : final report.

DOT National Transportation Integrated Search

2017-01-01

The New York State Department of Transportation (NYSDOT) has used the AASHTO 1993 Design Guide for the design of new flexible pavement structures for more than two decades. The AASHTO 1993 Guide is based on the empirical design equations developed fr...

A Hybrid Ground-Motion Prediction Equation for Earthquakes in Western Alberta

NASA Astrophysics Data System (ADS)

Spriggs, N.; Yenier, E.; Law, A.; Moores, A. O.

2015-12-01

Estimation of ground-motion amplitudes that may be produced by future earthquakes constitutes the foundation of seismic hazard assessment and earthquake-resistant structural design. This is typically done by using a prediction equation that quantifies amplitudes as a function of key seismological variables such as magnitude, distance and site condition. In this study, we develop a hybrid empirical prediction equation for earthquakes in western Alberta, where evaluation of seismic hazard associated with induced seismicity is of particular interest. We use peak ground motions and response spectra from recorded seismic events to model the regional source and attenuation attributes. The available empirical data is limited in the magnitude range of engineering interest (M>4). Therefore, we combine empirical data with a simulation-based model in order to obtain seismologically informed predictions for moderate-to-large magnitude events. The methodology is two-fold. First, we investigate the shape of geometrical spreading in Alberta. We supplement the seismic data with ground motions obtained from mining/quarry blasts, in order to gain insights into the regional attenuation over a wide distance range. A comparison of ground-motion amplitudes for earthquakes and mining/quarry blasts show that both event types decay at similar rates with distance and demonstrate a significant Moho-bounce effect. In the second stage, we calibrate the source and attenuation parameters of a simulation-based prediction equation to match the available amplitude data from seismic events. We model the geometrical spreading using a trilinear function with attenuation rates obtained from the first stage, and calculate coefficients of anelastic attenuation and site amplification via regression analysis. This provides a hybrid ground-motion prediction equation that is calibrated for observed motions in western Alberta and is applicable to moderate-to-large magnitude events.

Τhe observational and empirical thermospheric CO2 and NO power do not exhibit power-law behavior; an indication of their reliability

NASA Astrophysics Data System (ADS)

Varotsos, C. A.; Efstathiou, M. N.

2018-03-01

In this paper we investigate the evolution of the energy emitted by CO2 and NO from the Earth's thermosphere on a global scale using both observational and empirically derived data. In the beginning, we analyze the daily power observations of CO2 and NO received from the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) equipment on the NASA Thermosphere-Ionosphere-Mesosphere Energetics and Dynamics (TIMED) satellite for the entire period 2002-2016. We then perform the same analysis on the empirical daily power emitted by CO2 and NO that were derived recently from the infrared energy budget of the thermosphere during 1947-2016. The tool used for the analysis of the observational and empirical datasets is the detrended fluctuation analysis, in order to investigate whether the power emitted by CO2 and by NO from the thermosphere exhibits power-law behavior. The results obtained from both observational and empirical data do not support the establishment of the power-law behavior. This conclusion reveals that the empirically derived data are characterized by the same intrinsic properties as those of the observational ones, thus enhancing the validity of their reliability.

Equations of motion for the variable mass flow-variable exhaust velocity rocket

NASA Technical Reports Server (NTRS)

Tempelman, W. H.

1972-01-01

An equation of motion for a one dimensional rocket is derived as a function of the mass flow rate into the acceleration chamber and the velocity distribution along the chamber, thereby including the transient flow changes in the chamber. The derivation of the mass density requires the introduction of the special time coordinate. The equation of motion is derived from both classical force and momentum approaches and is shown to be consistent with the standard equation expressed in terms of flow parameters at the exit to the acceleration chamber.

Travelling wave solutions and conservation laws for the Korteweg-de Vries-Bejamin-Bona-Mahony equation

NASA Astrophysics Data System (ADS)

Simbanefayi, Innocent; Khalique, Chaudry Masood

2018-03-01

In this work we study the Korteweg-de Vries-Benjamin-Bona-Mahony (KdV-BBM) equation, which describes the two-way propagation of waves. Using Lie symmetry method together with Jacobi elliptic function expansion and Kudryashov methods we construct its travelling wave solutions. Also, we derive conservation laws of the KdV-BBM equation using the variational derivative approach. In this method, we begin by computing second-order multipliers for the KdV-BBM equation followed by a derivation of the respective conservation laws for each multiplier.

Computation of the stability derivatives via CFD and the sensitivity equations

NASA Astrophysics Data System (ADS)

Lei, Guo-Dong; Ren, Yu-Xin

2011-04-01

The method to calculate the aerodynamic stability derivates of aircrafts by using the sensitivity equations is extended to flows with shock waves in this paper. Using the newly developed second-order cell-centered finite volume scheme on the unstructured-grid, the unsteady Euler equations and sensitivity equations are solved simultaneously in a non-inertial frame of reference, so that the aerodynamic stability derivatives can be calculated for aircrafts with complex geometries. Based on the numerical results, behavior of the aerodynamic sensitivity parameters near the shock wave is discussed. Furthermore, the stability derivatives are analyzed for supersonic and hypersonic flows. The numerical results of the stability derivatives are found in good agreement with theoretical results for supersonic flows, and variations of the aerodynamic force and moment predicted by the stability derivatives are very close to those obtained by CFD simulation for both supersonic and hypersonic flows.

An Application of Structural Equation Modeling for Developing Good Teaching Characteristics Ontology

ERIC Educational Resources Information Center

Phiakoksong, Somjin; Niwattanakul, Suphakit; Angskun, Thara

2013-01-01

Ontology is a knowledge representation technique which aims to make knowledge explicit by defining the core concepts and their relationships. The Structural Equation Modeling (SEM) is a statistical technique which aims to explore the core factors from empirical data and estimates the relationship between these factors. This article presents an…

Testing Mediation Using Multiple Regression and Structural Equation Modeling Analyses in Secondary Data

ERIC Educational Resources Information Center

Li, Spencer D.

2011-01-01

Mediation analysis in child and adolescent development research is possible using large secondary data sets. This article provides an overview of two statistical methods commonly used to test mediated effects in secondary analysis: multiple regression and structural equation modeling (SEM). Two empirical studies are presented to illustrate the…

Bootstrap Estimation of Sample Statistic Bias in Structural Equation Modeling.

ERIC Educational Resources Information Center

Thompson, Bruce; Fan, Xitao

This study empirically investigated bootstrap bias estimation in the area of structural equation modeling (SEM). Three correctly specified SEM models were used under four different sample size conditions. Monte Carlo experiments were carried out to generate the criteria against which bootstrap bias estimation should be judged. For SEM fit indices,…

Advancing Empirical Scholarship to Further Develop Evaluation Theory and Practice

ERIC Educational Resources Information Center

Christie, Christina A.

2011-01-01

Good theory development is grounded in empirical inquiry. In the context of educational evaluation, the development of empirically grounded theory has important benefits for the field and the practitioner. In particular, a shift to empirically derived theory will assist in advancing more systematic and contextually relevant evaluation practice, as…

Stress-intensity factor equations for cracks in three-dimensional finite bodies

NASA Technical Reports Server (NTRS)

Newman, J. C., Jr.; Raju, I. S.

1981-01-01

Empirical stress intensity factor equations are presented for embedded elliptical cracks, semi-elliptical surface cracks, quarter-elliptical corner cracks, semi-elliptical surface cracks at a hole, and quarter-elliptical corner cracks at a hole in finite plates. The plates were subjected to remote tensile loading. Equations give stress intensity factors as a function of parametric angle, crack depth, crack length, plate thickness, and where applicable, hole radius. The stress intensity factors used to develop the equations were obtained from three dimensional finite element analyses of these crack configurations.

Thermal Performance of Cryogenic Multilayer Insulation at Various Layer Spacings

NASA Technical Reports Server (NTRS)

Johnson, Wesley Louis

2010-01-01

Multilayer insulation (MLI) has been shown to be the best performing cryogenic insulation system at high vacuum (less that 10 (exp 3) torr), and is widely used on spaceflight vehicles. Over the past 50 years, many investigations into MLI have yielded a general understanding of the many variables that are associated with MLI. MLI has been shown to be a function of variables such as warm boundary temperature, the number of reflector layers, and the spacer material in between reflectors, the interstitial gas pressure and the interstitial gas. Since the conduction between reflectors increases with the thickness of the spacer material, yet the radiation heat transfer is inversely proportional to the number of layers, it stands to reason that the thermal performance of MLI is a function of the number of layers per thickness, or layer density. Empirical equations that were derived based on some of the early tests showed that the conduction term was proportional to the layer density to a power. This power depended on the material combination and was determined by empirical test data. Many authors have graphically shown such optimal layer density, but none have provided any data at such low densities, or any method of determining this density. Keller, Cunnington, and Glassford showed MLI thermal performance as a function of layer density of high layer densities, but they didn't show a minimal layer density or any data below the supposed optimal layer density. However, it was recently discovered that by manipulating the derived empirical equations and taking a derivative with respect to layer density yields a solution for on optimal layer density. Various manufacturers have begun manufacturing MLI at densities below the optimal density. They began this based on the theory that increasing the distance between layers lowered the conductive heat transfer and they had no limitations on volume. By modifying the circumference of these blankets, the layer density can easily be varied. The simplest method of determining the thermal performance of MLI at cryogenic temperature is by boil-off calorimetry. Several blankets were procured and tested at various layer densities at the Cryogenics Test Laboratory at Kennedy Space Center. The densities that the blankets were tested over covered a wide range of layer densities including the analytical minimum. Several of the blankets were tested at the same insulation thickness while changing the layer density (thus a different number of reflector layers). Optimizing the layer density of multilayer insulation systems for heat transfer would remove a layer density from the complex method of designing such insulation systems. Additional testing was performed at various warm boundary temperatures and pressures. The testing and analysis was performed to simplify the analysis of cryogenic thermal insulation systems. This research was funded by the National Aeronautics and Space Administration's Exploration Technology Development Program's Cryogenic Fluid Management Project

An empirical approach to estimate near-infra-red photon propagation and optically induced drug release in brain tissues

NASA Astrophysics Data System (ADS)

Prabhu Verleker, Akshay; Fang, Qianqian; Choi, Mi-Ran; Clare, Susan; Stantz, Keith M.

2015-03-01

The purpose of this study is to develop an alternate empirical approach to estimate near-infra-red (NIR) photon propagation and quantify optically induced drug release in brain metastasis, without relying on computationally expensive Monte Carlo techniques (gold standard). Targeted drug delivery with optically induced drug release is a noninvasive means to treat cancers and metastasis. This study is part of a larger project to treat brain metastasis by delivering lapatinib-drug-nanocomplexes and activating NIR-induced drug release. The empirical model was developed using a weighted approach to estimate photon scattering in tissues and calibrated using a GPU based 3D Monte Carlo. The empirical model was developed and tested against Monte Carlo in optical brain phantoms for pencil beams (width 1mm) and broad beams (width 10mm). The empirical algorithm was tested against the Monte Carlo for different albedos along with diffusion equation and in simulated brain phantoms resembling white-matter (μs'=8.25mm-1, μa=0.005mm-1) and gray-matter (μs'=2.45mm-1, μa=0.035mm-1) at wavelength 800nm. The goodness of fit between the two models was determined using coefficient of determination (R-squared analysis). Preliminary results show the Empirical algorithm matches Monte Carlo simulated fluence over a wide range of albedo (0.7 to 0.99), while the diffusion equation fails for lower albedo. The photon fluence generated by empirical code matched the Monte Carlo in homogeneous phantoms (R2=0.99). While GPU based Monte Carlo achieved 300X acceleration compared to earlier CPU based models, the empirical code is 700X faster than the Monte Carlo for a typical super-Gaussian laser beam.

Temperature, illumination, and fluence dependence of current and voltage in electron irradiated solar cells

NASA Technical Reports Server (NTRS)

Faith, T. J.; Obenschain, A. F.

1974-01-01

Empirical equations have been derived from measurements of solar cell photovoltaic characteristics relating light-generated current and open circuit voltage to cell temperature, intensity of illumination and 1-MeV electron fluence. Both 2-ohm-cm and 10-ohm-cm cells were tested over the temperature range from 120 to 470 K, the illumination intensity range from 5 to 1830 mW/sq cm, and the electron fluence range from 1 x 10 to the 13th to 1 x 10 to the 16th electrons/sq cm. The normalized temperature coefficient of the light generated current varies as the 0.18 power of the fluence for temperatures above approximately 273 K and is independent of fluence at lower temperatures. At 140 mW/sq cm, a power law expression was derived which shows that the light-generated current decreases at a rate proportional to the 0.153 power of the fluence for both resistivities. The coefficient of the expression is larger for 2-ohm-cm cells; consequently, the advantage for 10-ohm-cm cells increased with increasing fluence.

Analytical approach to impurity transport studies: Charge state dynamics in tokamak plasmas

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

Shurygin, V. A.

2006-08-15

Ionization and recombination of plasma impurities govern their charge state kinetics, which is imposed upon the dynamics of ions that implies a superposition of the appropriate probabilities and causes an impurity charge state dynamics. The latter is considered in terms of a vector field of conditional probabilities and presented by a vector charge state distribution function with coupled equations of the Kolmogorov type. Analytical solutions of a diffusion problem are derived with the basic spatial and temporal dimensionless parameters. Analysis shows that the empirical scaling D{sub A}{proportional_to}n{sub e}{sup -1} [K. Krieger, G. Fussmann, and the ASDEX Upgrade Team, Nucl. Fusionmore » 30, 2392 (1990)] can be explained by the ratio of the diffusive and kinetic terms, D{sub A}/(n{sub e}a{sup 2}), being used instead of diffusivity, D{sub A}. The derived time scales of charge state dynamics are given by a sum of the diffusive and kinetic times. Detailed simulations of charge state dynamics are performed for argon impurity and compared with the reference modeling.« less

Distribution theory for Schrödinger’s integral equation

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

Lange, Rutger-Jan, E-mail: rutger-jan.lange@cantab.net

2015-12-15

Much of the literature on point interactions in quantum mechanics has focused on the differential form of Schrödinger’s equation. This paper, in contrast, investigates the integral form of Schrödinger’s equation. While both forms are known to be equivalent for smooth potentials, this is not true for distributional potentials. Here, we assume that the potential is given by a distribution defined on the space of discontinuous test functions. First, by using Schrödinger’s integral equation, we confirm a seminal result by Kurasov, which was originally obtained in the context of Schrödinger’s differential equation. This hints at a possible deeper connection between bothmore » forms of the equation. We also sketch a generalisation of Kurasov’s [J. Math. Anal. Appl. 201(1), 297–323 (1996)] result to hypersurfaces. Second, we derive a new closed-form solution to Schrödinger’s integral equation with a delta prime potential. This potential has attracted considerable attention, including some controversy. Interestingly, the derived propagator satisfies boundary conditions that were previously derived using Schrödinger’s differential equation. Third, we derive boundary conditions for “super-singular” potentials given by higher-order derivatives of the delta potential. These boundary conditions cannot be incorporated into the normal framework of self-adjoint extensions. We show that the boundary conditions depend on the energy of the solution and that probability is conserved. This paper thereby confirms several seminal results and derives some new ones. In sum, it shows that Schrödinger’s integral equation is a viable tool for studying singular interactions in quantum mechanics.« less

Analyzing the uncertainties in use of forest-derived biomass equations for open-grown trees in agricultural land

Treesearch

Xinhua Zhou; Michele M. Schoeneberger; James R. Brandle; Tala N. Awada; Jianmin Chu; Derrel L. Martin; Jihong Li; Yuqiang Li; Carl W. Mize

2014-01-01

Quantifying carbon in agroforestry trees requires biomass equations that capture the growth differences (e.g., tree specific gravity and architecture) created in the more open canopies of agroforestry plantings compared with those generally encountered in forests. Whereas forest-derived equations are available, equations for open-grown trees are not. Data from...

Time of Concentration equations: the role of morphometric uncertainties in flood risk analysis and management

NASA Astrophysics Data System (ADS)

Martins, Luciano; Díez-Herrero, Andrés; Bodoque, Jose M.; Bateira, Carlos

2016-04-01

The perception of flood risk by the responsible authorities on the flood management disasters and mitigation strategies should be based on an overall evaluation of the uncertainties associated with the procedures for risk assessment and mapping production. This contribution presents the results of the development of mapping evaluation of the time of concentration (tc). This parameter reflects the time-space at which a watershed responds to rainfall events and is the most frequently utilized time parameter, and is of great importance in many hydrologic analysis. Accurate estimates of the tc are very important, for instance, if tc is under-estimated, the result is an over-estimated peak discharge and vice versa, resulting significant variations on the flooded areas, and could have important consequences in terms of the land use and occupation of territory, as management's own flood risk. The methology used evaluate 20 different empirical, semi-empirical and kinematics equations of tc calculation, due to different cartographic scales (1:200000; 1:100000; 1:25000; LIDAR 5x5m &1x1m) in in two hydrographic basins with distinct dimensions and geomorphological characteristics, located in the Gredos Mountain range (Spain). The results suggest that the changes in the cartographic scale, has not influence as significant as one might expect. The most important variations occur in the characteristics of the fequations, use different morphometricparameters in the calculations. Some just are based on geomorphological criteria and other magnify the hydraulic characteristics of the channels, resulting in very different tc values. However, we highlighting the role of cartographic scale particularly in the application of semi-empirical equations that take into account changes in land use and occupation. In this case, the determination of parameters, such as flow coefficient, curve number and roughness coefficient are very sensitive to cartographic scale. Sensitivity analysis demonstrates that the empirical equations are simpler (e.g Giandotti, Chow, Temez), since it is based only on the geometrical characteristics of the basin and therefore the results tend not to reflect the dynamic range leadings to worse results of tc.The application of these equations based on local parameters should not be applied to other regions that have distinct geomorphological and climatic characteristics, since greatly influences the results.The semi-empirical and kinematics equations (e.g SCS, Kinematic Wave) tc is reflected mainly in the form of the hydrograph, particularly in the Lag-time. Thats seems be an appropriate to the integrated analysis of hydrographic basins. Moreover, these methods are fundamental to understand spatio-temporal dynamics within the basin, even if some parameters are difficult to calculate. The best way to calibrate and evaluate the obtained concentration time values, should be based on known events, calibrated by rating curves records.

Deriving Multidimensional Poverty Indicators: Methodological Issues and an Empirical Analysis for Italy

ERIC Educational Resources Information Center

Coromaldi, Manuela; Zoli, Mariangela

2012-01-01

Theoretical and empirical studies have recently adopted a multidimensional concept of poverty. There is considerable debate about the most appropriate degree of multidimensionality to retain in the analysis. In this work we add to the received literature in two ways. First, we derive indicators of multiple deprivation by applying a particular…

Asymptotic Properties of the Sequential Empirical ROC, PPV and NPV Curves Under Case-Control Sampling.

PubMed

Koopmeiners, Joseph S; Feng, Ziding

2011-01-01

The receiver operating characteristic (ROC) curve, the positive predictive value (PPV) curve and the negative predictive value (NPV) curve are three measures of performance for a continuous diagnostic biomarker. The ROC, PPV and NPV curves are often estimated empirically to avoid assumptions about the distributional form of the biomarkers. Recently, there has been a push to incorporate group sequential methods into the design of diagnostic biomarker studies. A thorough understanding of the asymptotic properties of the sequential empirical ROC, PPV and NPV curves will provide more flexibility when designing group sequential diagnostic biomarker studies. In this paper we derive asymptotic theory for the sequential empirical ROC, PPV and NPV curves under case-control sampling using sequential empirical process theory. We show that the sequential empirical ROC, PPV and NPV curves converge to the sum of independent Kiefer processes and show how these results can be used to derive asymptotic results for summaries of the sequential empirical ROC, PPV and NPV curves.

Asymptotic Properties of the Sequential Empirical ROC, PPV and NPV Curves Under Case-Control Sampling

PubMed Central

Koopmeiners, Joseph S.; Feng, Ziding

2013-01-01

The receiver operating characteristic (ROC) curve, the positive predictive value (PPV) curve and the negative predictive value (NPV) curve are three measures of performance for a continuous diagnostic biomarker. The ROC, PPV and NPV curves are often estimated empirically to avoid assumptions about the distributional form of the biomarkers. Recently, there has been a push to incorporate group sequential methods into the design of diagnostic biomarker studies. A thorough understanding of the asymptotic properties of the sequential empirical ROC, PPV and NPV curves will provide more flexibility when designing group sequential diagnostic biomarker studies. In this paper we derive asymptotic theory for the sequential empirical ROC, PPV and NPV curves under case-control sampling using sequential empirical process theory. We show that the sequential empirical ROC, PPV and NPV curves converge to the sum of independent Kiefer processes and show how these results can be used to derive asymptotic results for summaries of the sequential empirical ROC, PPV and NPV curves. PMID:24039313

On the Yakhot-Orszag renormalization group method for deriving turbulence statistics and models

NASA Technical Reports Server (NTRS)

Smith, L. M.; Reynolds, W. C.

1992-01-01

An independent, comprehensive, critical review of the 'renormalization group' (RNG) theory of turbulence developed by Yakhot and Orszag (1986) is provided. Their basic theory for the Navier-Stokes equations is confirmed, and approximations in the scale removal procedure are discussed. The YO derivations of the velocity-derivative skewness and the transport equation for the energy dissipation rate are examined. An algebraic error in the derivation of the skewness is corrected. The corrected RNG skewness value of -0.59 is in agreement with experiments at moderate Reynolds numbers. Several problems are identified in the derivation of the energy dissipation rate equations which suggest that the derivation should be reformulated.

Global Langevin model of multidimensional biomolecular dynamics.

PubMed

Schaudinnus, Norbert; Lickert, Benjamin; Biswas, Mithun; Stock, Gerhard

2016-11-14

Molecular dynamics simulations of biomolecular processes are often discussed in terms of diffusive motion on a low-dimensional free energy landscape F(). To provide a theoretical basis for this interpretation, one may invoke the system-bath ansatz á la Zwanzig. That is, by assuming a time scale separation between the slow motion along the system coordinate x and the fast fluctuations of the bath, a memory-free Langevin equation can be derived that describes the system's motion on the free energy landscape F(), which is damped by a friction field and driven by a stochastic force that is related to the friction via the fluctuation-dissipation theorem. While the theoretical formulation of Zwanzig typically assumes a highly idealized form of the bath Hamiltonian and the system-bath coupling, one would like to extend the approach to realistic data-based biomolecular systems. Here a practical method is proposed to construct an analytically defined global model of structural dynamics. Given a molecular dynamics simulation and adequate collective coordinates, the approach employs an "empirical valence bond"-type model which is suitable to represent multidimensional free energy landscapes as well as an approximate description of the friction field. Adopting alanine dipeptide and a three-dimensional model of heptaalanine as simple examples, the resulting Langevin model is shown to reproduce the results of the underlying all-atom simulations. Because the Langevin equation can also be shown to satisfy the underlying assumptions of the theory (such as a delta-correlated Gaussian-distributed noise), the global model provides a correct, albeit empirical, realization of Zwanzig's formulation. As an application, the model can be used to investigate the dependence of the system on parameter changes and to predict the effect of site-selective mutations on the dynamics.

Moderators, mediators, and bidirectional relationships in the International Classification of Functioning, Disability and Health (ICF) framework: An empirical investigation using a longitudinal design and Structural Equation Modeling (SEM).

PubMed

Rouquette, Alexandra; Badley, Elizabeth M; Falissard, Bruno; Dub, Timothée; Leplege, Alain; Coste, Joël

2015-06-01

The International Classification of Functioning, Disability and Health (ICF) published in 2001 describes the consequences of health conditions with three components of impairments in body structures or functions, activity limitations and participation restrictions. Two of the new features of the conceptual model were the possibility of feedback effects between each ICF component and the introduction of contextual factors conceptualized as moderators of the relationship between the components. The aim of this longitudinal study is to provide empirical evidence of these two kinds of effect. Structural equation modeling was used to analyze data from a French population-based cohort of 548 patients with knee osteoarthritis recruited between April 2007 and March 2009 and followed for three years. Indicators of the body structure and function, activity and participation components of the ICF were derived from self-administered standardized instruments. The measurement model revealed four separate factors for body structures impairments, body functions impairments, activity limitations and participation restrictions. The classic sequence from body impairments to participation restrictions through activity limitations was found at each assessment time. Longitudinal study of the ICF component relationships showed a feedback pathway indicating that the level of participation restrictions at baseline was predictive of activity limitations three years later. Finally, the moderating role of personal (age, sex, mental health, etc.) and environmental factors (family relationships, mobility device use, etc.) was investigated. Three contextual factors (sex, family relationships and walking stick use) were found to be moderators for the relationship between the body impairments and the activity limitations components. Mental health was found to be a mediating factor of the effect of activity limitations on participation restrictions. Copyright © 2015 Elsevier Ltd. All rights reserved.

Global Langevin model of multidimensional biomolecular dynamics

NASA Astrophysics Data System (ADS)

Schaudinnus, Norbert; Lickert, Benjamin; Biswas, Mithun; Stock, Gerhard

2016-11-01

Molecular dynamics simulations of biomolecular processes are often discussed in terms of diffusive motion on a low-dimensional free energy landscape F ( 𝒙 ) . To provide a theoretical basis for this interpretation, one may invoke the system-bath ansatz á la Zwanzig. That is, by assuming a time scale separation between the slow motion along the system coordinate x and the fast fluctuations of the bath, a memory-free Langevin equation can be derived that describes the system's motion on the free energy landscape F ( 𝒙 ) , which is damped by a friction field and driven by a stochastic force that is related to the friction via the fluctuation-dissipation theorem. While the theoretical formulation of Zwanzig typically assumes a highly idealized form of the bath Hamiltonian and the system-bath coupling, one would like to extend the approach to realistic data-based biomolecular systems. Here a practical method is proposed to construct an analytically defined global model of structural dynamics. Given a molecular dynamics simulation and adequate collective coordinates, the approach employs an "empirical valence bond"-type model which is suitable to represent multidimensional free energy landscapes as well as an approximate description of the friction field. Adopting alanine dipeptide and a three-dimensional model of heptaalanine as simple examples, the resulting Langevin model is shown to reproduce the results of the underlying all-atom simulations. Because the Langevin equation can also be shown to satisfy the underlying assumptions of the theory (such as a delta-correlated Gaussian-distributed noise), the global model provides a correct, albeit empirical, realization of Zwanzig's formulation. As an application, the model can be used to investigate the dependence of the system on parameter changes and to predict the effect of site-selective mutations on the dynamics.

Dynamics and Control of Constrained Multibody Systems modeled with Maggi's equation: Application to Differential Mobile Robots Part I

NASA Astrophysics Data System (ADS)

Amengonu, Yawo H.; Kakad, Yogendra P.

2014-07-01

Quasivelocity techniques such as Maggi's and Boltzmann-Hamel's equations eliminate Lagrange multipliers from the beginning as opposed to the Euler-Lagrange method where one has to solve for the n configuration variables and the multipliers as functions of time when there are m nonholonomic constraints. Maggi's equation produces n second-order differential equations of which (n-m) are derived using (n-m) independent quasivelocities and the time derivative of the m kinematic constraints which add the remaining m second order differential equations. This technique is applied to derive the dynamics of a differential mobile robot and a controller which takes into account these dynamics is developed.

Determination of lateral-stability derivatives and transfer-function coefficients from frequency-response data for lateral motions

NASA Technical Reports Server (NTRS)

Donegan, James J; Robinson, Samuel W , Jr; Gates, Ordway, B , jr

1955-01-01

A method is presented for determining the lateral-stability derivatives, transfer-function coefficients, and the modes for lateral motion from frequency-response data for a rigid aircraft. The method is based on the application of the vector technique to the equations of lateral motion, so that the three equations of lateral motion can be separated into six equations. The method of least squares is then applied to the data for each of these equations to yield the coefficients of the equations of lateral motion from which the lateral-stability derivatives and lateral transfer-function coefficients are computed. Two numerical examples are given to demonstrate the use of the method.

Improvements in GRACE Gravity Field Determination through Stochastic Observation Modeling

NASA Astrophysics Data System (ADS)

McCullough, C.; Bettadpur, S. V.

2016-12-01

Current unconstrained Release 05 GRACE gravity field solutions from the Center for Space Research (CSR RL05) assume random observation errors following an independent multivariate Gaussian distribution. This modeling of observations, a simplifying assumption, fails to account for long period, correlated errors arising from inadequacies in the background force models. Fully modeling the errors inherent in the observation equations, through the use of a full observation covariance (modeling colored noise), enables optimal combination of GPS and inter-satellite range-rate data and obviates the need for estimating kinematic empirical parameters during the solution process. Most importantly, fully modeling the observation errors drastically improves formal error estimates of the spherical harmonic coefficients, potentially enabling improved uncertainty quantification of scientific results derived from GRACE and optimizing combinations of GRACE with independent data sets and a priori constraints.

AAPI college students' willingness to seek counseling: the role of culture, stigma, and attitudes.

PubMed

Choi, Na-Yeun; Miller, Matthew J

2014-07-01

This study tested 4 theoretically and empirically derived structural equation models of Asian, Asian American, and Pacific Islanders' willingness to seek counseling with a sample of 278 college students. The models represented competing hypotheses regarding the manner in which Asian cultural values, European American cultural values, public stigma, stigma by close others, self-stigma, and attitudes toward seeking professional help related to willingness to seek counseling. We found that Asian and European American cultural values differentially related to willingness to seek counseling indirectly through specific indirect pathways (public stigma, stigma by close others, self-stigma, and attitudes toward seeking professional help). Our results also showed that the magnitude of model-implied relationships did not vary as a function of generational status. Study limitations, future directions for research, and implications for counseling are discussed.

A Relationship Between the 2-body Energy of Kaxiras Pandey and Pearson Takai Halicioglu Tiller Potential Functions

NASA Astrophysics Data System (ADS)

Lim, Teik-Cheng

2004-01-01

A parametric relationship between the Pearson Takai Halicioglu Tiller (PTHT) and the Kaxiras Pandey (KP) empirical potential energy functions is developed for the case of 2-body interaction. The need for such relationship arises when preferred parametric data and adopted software correspond to different potential functions. The analytical relationship was obtained by equating the potential functions' derivatives at zeroth, first and second order with respect to the interatomic distance at the equilibrium bond length, followed by comparison of coefficients in the repulsive and attractive terms. Plots of non-dimensional 2-body energy versus the nondimensional interatomic distance verified the analytical relationships developed herein. The discrepancy revealed in theoretical plots suggests that the 2-body PTHT and KP potentials are more suitable for curve-fitting "softer" and "harder" bonds respectively.

Stochastic point-source modeling of ground motions in the Cascadia region

USGS Publications Warehouse

Atkinson, G.M.; Boore, D.M.

1997-01-01

A stochastic model is used to develop preliminary ground motion relations for the Cascadia region for rock sites. The model parameters are derived from empirical analyses of seismographic data from the Cascadia region. The model is based on a Brune point-source characterized by a stress parameter of 50 bars. The model predictions are compared to ground-motion data from the Cascadia region and to data from large earthquakes in other subduction zones. The point-source simulations match the observations from moderate events (M 100 km). The discrepancy at large magnitudes suggests further work on modeling finite-fault effects and regional attenuation is warranted. In the meantime, the preliminary equations are satisfactory for predicting motions from events of M < 7 and provide conservative estimates of motions from larger events at distances less than 100 km.

Conceptualising humiliation.

PubMed

Elshout, Maartje; Nelissen, Rob M A; van Beest, Ilja

2017-12-01

Humiliation lacks an empirically derived definition, sometimes simply being equated with shame. We approached the conceptualisation of humiliation from a prototype perspective, identifying 61 features of humiliation, some of which are more central to humiliation (e.g. losing self-esteem) than others (e.g. shyness). Prototypical humiliation involved feeling powerless, small, and inferior in a situation in which one was brought down and in which an audience was present, leading the person to appraise the situation as unfair and resulting in a mix of emotions, most notably disappointment, anger, and shame. Some of the features overlapped with those of shame (e.g. looking like a fool, losing self-esteem, presence of an audience) whereas other features overlapped with those of anger (e.g. being brought down, unfairness). Which specific features are present may determine whether the humiliation experience becomes more shame- or anger-like (or a combination thereof).

Higuchi equation: derivation, applications, use and misuse.

PubMed

Siepmann, Juergen; Peppas, Nicholas A

2011-10-10

Fifty years ago, the legendary Professor Takeru Higuchi published the derivation of an equation that allowed for the quantification of drug release from thin ointment films, containing finely dispersed drug into a perfect sink. This became the famous Higuchi equation whose fiftieth anniversary we celebrate this year. Despite the complexity of the involved mass transport processes, Higuchi derived a very simple equation, which is easy to use. Based on a pseudo-steady-state approach, a direct proportionality between the cumulative amount of drug released and the square root of time can be demonstrated. In contrast to various other "square root of time" release kinetics, the constant of proportionality in the classical Higuchi equation has a specific, physically realistic meaning. The major benefits of this equation include the possibility to: (i) facilitate device optimization, and (ii) to better understand the underlying drug release mechanisms. The equation can also be applied to other types of drug delivery systems than thin ointment films, e.g., controlled release transdermal patches or films for oral controlled drug delivery. Later, the equation was extended to other geometries and related theories have been proposed. The aim of this review is to highlight the assumptions the derivation of the classical Higuchi equation is based on and to give an overview on the use and potential misuse of this equation as well as of related theories. Copyright © 2011 Elsevier B.V. All rights reserved.

A Multi-Band Analytical Algorithm for Deriving Absorption and Backscattering Coefficients from Remote-Sensing Reflectance of Optically Deep Waters

NASA Technical Reports Server (NTRS)

Lee, Zhong-Ping; Carder, Kendall L.

2001-01-01

A multi-band analytical (MBA) algorithm is developed to retrieve absorption and backscattering coefficients for optically deep waters, which can be applied to data from past and current satellite sensors, as well as data from hyperspectral sensors. This MBA algorithm applies a remote-sensing reflectance model derived from the Radiative Transfer Equation, and values of absorption and backscattering coefficients are analytically calculated from values of remote-sensing reflectance. There are only limited empirical relationships involved in the algorithm, which implies that this MBA algorithm could be applied to a wide dynamic range of waters. Applying the algorithm to a simulated non-"Case 1" data set, which has no relation to the development of the algorithm, the percentage error for the total absorption coefficient at 440 nm a (sub 440) is approximately 12% for a range of 0.012 - 2.1 per meter (approximately 6% for a (sub 440) less than approximately 0.3 per meter), while a traditional band-ratio approach returns a percentage error of approximately 30%. Applying it to a field data set ranging from 0.025 to 2.0 per meter, the result for a (sub 440) is very close to that using a full spectrum optimization technique (9.6% difference). Compared to the optimization approach, the MBA algorithm cuts the computation time dramatically with only a small sacrifice in accuracy, making it suitable for processing large data sets such as satellite images. Significant improvements over empirical algorithms have also been achieved in retrieving the optical properties of optically deep waters.

NGA-West2 Empirical Fourier Model for Active Crustal Regions to Generate Regionally Adjustable Response Spectra

NASA Astrophysics Data System (ADS)

Bora, S. S.; Cotton, F.; Scherbaum, F.; Kuehn, N. M.

2016-12-01

Adjustment of median ground motion prediction equations (GMPEs) from data-rich (host) regions to data-poor regions (target) is one of major challenges that remains with the current practice of engineering seismology and seismic hazard analysis. Fourier spectral representation of ground motion provides a solution to address the problem of adjustment that is physically transparent and consistent with the concepts of linear system theory. Also, it provides a direct interface to appreciate the physically expected behavior of seismological parameters on ground motion. In the present study, we derive an empirical Fourier model for computing regionally adjustable response spectral ordinates based on random vibration theory (RVT) from shallow crustal earthquakes in active tectonic regions, following the approach of Bora et al. (2014, 2015). , For this purpose, we use an expanded NGA-West2 database with M 3.2—7.9 earthquakes at distances ranging from 0 to 300 km. A mixed-effects regression technique is employed to further explore various components of variability. The NGA-West2 database expanded over a wide magnitude range provides a better understanding (and constraint) of source scaling of ground motion. The large global volume of the database also allows investigating regional patterns in distance-dependent attenuation (i.e., geometrical spreading and inelastic attenuation) of ground motion as well as in the source parameters (e.g., magnitude and stress drop). Furthermore, event-wise variability and its correlation with stress parameter are investigated. Finally, application of the derived Fourier model in generating adjustable response spectra will be shown.

A tensor formulation of the equation of transfer for spherically symmetric flows. [radiative transfer in seven dimensional Riemannian space

NASA Technical Reports Server (NTRS)

Haisch, B. M.

1976-01-01

A tensor formulation of the equation of radiative transfer is derived in a seven-dimensional Riemannian space such that the resulting equation constitutes a divergence in any coordinate system. After being transformed to a spherically symmetric comoving coordinate system, the transfer equation contains partial derivatives in angle and frequency, as well as optical depth due to the effects of aberration and the Doppler shift. However, by virtue of the divergence form of this equation, the divergence theorem may be applied to yield a numerical differencing scheme which is expected to be stable and to conserve luminosity. It is shown that the equation of transfer derived by this method in a Lagrangian coordinate system may be reduced to that given by Castor (1972), although it is, of course, desirable to leave the equation in divergence form.

The Price Equation, Gradient Dynamics, and Continuous Trait Game Theory.

PubMed

Lehtonen, Jussi

2018-01-01

A recent article convincingly nominated the Price equation as the fundamental theorem of evolution and used it as a foundation to derive several other theorems. A major section of evolutionary theory that was not addressed is that of game theory and gradient dynamics of continuous traits with frequency-dependent fitness. Deriving fundamental results in these fields under the unifying framework of the Price equation illuminates similarities and differences between approaches and allows a simple, unified view of game-theoretical and dynamic concepts. Using Taylor polynomials and the Price equation, I derive a dynamic measure of evolutionary change, a condition for singular points, the convergence stability criterion, and an alternative interpretation of evolutionary stability. Furthermore, by applying the Price equation to a multivariable Taylor polynomial, the direct fitness approach to kin selection emerges. Finally, I compare these results to the mean gradient equation of quantitative genetics and the canonical equation of adaptive dynamics.

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

Rodigas, Timothy J.; Hinz, Philip M.; Malhotra, Renu, E-mail: rodigas@as.arizona.edu

Planets can affect debris disk structure by creating gaps, sharp edges, warps, and other potentially observable signatures. However, there is currently no simple way for observers to deduce a disk-shepherding planet's properties from the observed features of the disk. Here we present a single equation that relates a shepherding planet's maximum mass to the debris ring's observed width in scattered light, along with a procedure to estimate the planet's eccentricity and minimum semimajor axis. We accomplish this by performing dynamical N-body simulations of model systems containing a star, a single planet, and an exterior disk of parent bodies and dustmore » grains to determine the resulting debris disk properties over a wide range of input parameters. We find that the relationship between planet mass and debris disk width is linear, with increasing planet mass producing broader debris rings. We apply our methods to five imaged debris rings to constrain the putative planet masses and orbits in each system. Observers can use our empirically derived equation as a guide for future direct imaging searches for planets in debris disk systems. In the fortuitous case of an imaged planet orbiting interior to an imaged disk, the planet's maximum mass can be estimated independent of atmospheric models.« less

An equation of state for the financial markets: connecting order flow to price formation.

NASA Astrophysics Data System (ADS)

Gerig, Austin; Mike, Szabolcs; Doyne Farmer, J.

2006-03-01

Many of the peculiarities of price formation in the financial marketplace can be understood as the result of a few regularities in the placement and removal of trading orders. Based on a large data set from the London Stock Exchange we show that the distribution of prices where people place orders to buy or sell follows a surprisingly simple functional form that depends on the current best prices. In addition, whether or not an order is to buy or sell is described by a long-memory process, and the cancellation of orders can be described by a few simple rules. When these results are combined, simply by following the rules of the continuous double auction, the resulting simulation model produces good predictions for the distribution of price changes and transaction costs without any adjustment of parameters. We use the model to empirically derive equations of state relating order flow and the statistical properties of prices. In contrast to previous conjectures, our results demonstrate that these distributions are not universal, but rather depend on parameters of individual markets. They also show that factors other than supply and demand play an important role in price formation.

Dissipative Relativistic Fluid Dynamics: A New Way to Derive the Equations of Motion from Kinetic Theory

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

Denicol, G. S.; Koide, T.; Rischke, D. H.

2010-10-15

We rederive the equations of motion of dissipative relativistic fluid dynamics from kinetic theory. In contrast with the derivation of Israel and Stewart, which considered the second moment of the Boltzmann equation to obtain equations of motion for the dissipative currents, we directly use the latter's definition. Although the equations of motion obtained via the two approaches are formally identical, the coefficients are different. We show that, for the one-dimensional scaling expansion, our method is in better agreement with the solution obtained from the Boltzmann equation.

Eigenvalue sensitivity analysis of planar frames with variable joint and support locations

NASA Technical Reports Server (NTRS)

Chuang, Ching H.; Hou, Gene J. W.

1991-01-01

Two sensitivity equations are derived in this study based upon the continuum approach for eigenvalue sensitivity analysis of planar frame structures with variable joint and support locations. A variational form of an eigenvalue equation is first derived in which all of the quantities are expressed in the local coordinate system attached to each member. Material derivative of this variational equation is then sought to account for changes in member's length and orientation resulting form the perturbation of joint and support locations. Finally, eigenvalue sensitivity equations are formulated in either domain quantities (by the domain method) or boundary quantities (by the boundary method). It is concluded that the sensitivity equation derived by the boundary method is more efficient in computation but less accurate than that of the domain method. Nevertheless, both of them in terms of computational efficiency are superior to the conventional direct differentiation method and the finite difference method.

Item Selection and Pre-equating with Empirical Item Characteristic Curves.

ERIC Educational Resources Information Center

Livingston, Samuel A.

An empirical item characteristic curve shows the probability of a correct response as a function of the student's total test score. These curves can be estimated from large-scale pretest data. They enable test developers to select items that discriminate well in the score region where decisions are made. A similar set of curves can be used to…

On the integrable elliptic cylindrical Kadomtsev-Petviashvili equation.

PubMed

Khusnutdinova, K R; Klein, C; Matveev, V B; Smirnov, A O

2013-03-01

There exist two versions of the Kadomtsev-Petviashvili (KP) equation, related to the Cartesian and cylindrical geometries of the waves. In this paper, we derive and study a new version, related to the elliptic cylindrical geometry. The derivation is given in the context of surface waves, but the derived equation is a universal integrable model applicable to generic weakly nonlinear weakly dispersive waves. We also show that there exist nontrivial transformations between all three versions of the KP equation associated with the physical problem formulation, and use them to obtain new classes of approximate solutions for water waves.

Exact solutions of fractional mBBM equation and coupled system of fractional Boussinesq-Burgers

NASA Astrophysics Data System (ADS)

Javeed, Shumaila; Saif, Summaya; Waheed, Asif; Baleanu, Dumitru

2018-06-01

The new exact solutions of nonlinear fractional partial differential equations (FPDEs) are established by adopting first integral method (FIM). The Riemann-Liouville (R-L) derivative and the local conformable derivative definitions are used to deal with the fractional order derivatives. The proposed method is applied to get exact solutions for space-time fractional modified Benjamin-Bona-Mahony (mBBM) equation and coupled time-fractional Boussinesq-Burgers equation. The suggested technique is easily applicable and effectual which can be implemented successfully to obtain the solutions for different types of nonlinear FPDEs.

Modeling Explosive Cladding of Metallic Liners to Gun Tubes

DTIC Science & Technology

2010-01-01

a Jones Wilkins Lee ( JWL ) equation of state was parameterized using nonlinear optimization (ref. 8) and scaling the empirical v2£ for other volume...expansions based on TNT. The JWL equation of state is ( ,. A i -RiV* , GJE RiV* V IS./K v f +7~* (2) where P is pressure, V is

Prediction of Battery Life and Behavior from Analysis of Voltage Data

NASA Technical Reports Server (NTRS)

Mcdermott, P. P.

1984-01-01

A method for simulating charge and discharge characteristics of secondary batteries is discussed. The analysis utilizes a nonlinear regression technique where empirical data is computer fitted with a five coefficient nonlinear equation. The equations for charge and discharge voltage are identical except for a change of sign before the second and third terms.

Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: application to the theory of Neolithic transition.

PubMed

Vlad, Marcel Ovidiu; Ross, John

2002-12-01

We introduce a general method for the systematic derivation of nonlinear reaction-diffusion equations with distributed delays. We study the interactions among different types of moving individuals (atoms, molecules, quasiparticles, biological organisms, etc). The motion of each species is described by the continuous time random walk theory, analyzed in the literature for transport problems, whereas the interactions among the species are described by a set of transformation rates, which are nonlinear functions of the local concentrations of the different types of individuals. We use the time interval between two jumps (the transition time) as an additional state variable and obtain a set of evolution equations, which are local in time. In order to make a connection with the transport models used in the literature, we make transformations which eliminate the transition time and derive a set of nonlocal equations which are nonlinear generalizations of the so-called generalized master equations. The method leads under different specified conditions to various types of nonlocal transport equations including a nonlinear generalization of fractional diffusion equations, hyperbolic reaction-diffusion equations, and delay-differential reaction-diffusion equations. Thus in the analysis of a given problem we can fit to the data the type of reaction-diffusion equation and the corresponding physical and kinetic parameters. The method is illustrated, as a test case, by the study of the neolithic transition. We introduce a set of assumptions which makes it possible to describe the transition from hunting and gathering to agriculture economics by a differential delay reaction-diffusion equation for the population density. We derive a delay evolution equation for the rate of advance of agriculture, which illustrates an application of our analysis.

The chemical (not mechanical) paradigm of thermodynamics of colloid and interface science.

PubMed

Kaptay, George

2018-06-01

In the most influential monograph on colloid and interfacial science by Adamson three fundamental equations of "physical chemistry of surfaces" are identified: the Laplace equation, the Kelvin equation and the Gibbs adsorption equation, with a mechanical definition of surface tension by Young as a starting point. Three of them (Young, Laplace and Kelvin) are called here the "mechanical paradigm". In contrary it is shown here that there is only one fundamental equation of the thermodynamics of colloid and interface science and all the above (and other) equations of this field follow as its derivatives. This equation is due to chemical thermodynamics of Gibbs, called here the "chemical paradigm", leading to the definition of surface tension and to 5 rows of equations (see Graphical abstract). The first row is the general equation for interfacial forces, leading to the Young equation, to the Bakker equation and to the Laplace equation, etc. Although the principally wrong extension of the Laplace equation formally leads to the Kelvin equation, using the chemical paradigm it becomes clear that the Kelvin equation is generally incorrect, although it provides right results in special cases. The second row of equations provides equilibrium shapes and positions of phases, including sessile drops of Young, crystals of Wulff, liquids in capillaries, etc. The third row of equations leads to the size-dependent equations of molar Gibbs energies of nano-phases and chemical potentials of their components; from here the corrected versions of the Kelvin equation and its derivatives (the Gibbs-Thomson equation and the Freundlich-Ostwald equation) are derived, including equations for more complex problems. The fourth row of equations is the nucleation theory of Gibbs, also contradicting the Kelvin equation. The fifth row of equations is the adsorption equation of Gibbs, and also the definition of the partial surface tension, leading to the Butler equation and to its derivatives, including the Langmuir equation and the Szyszkowski equation. Positioning the single fundamental equation of Gibbs into the thermodynamic origin of colloid and interface science leads to a coherent set of correct equations of this field. The same provides the chemical (not mechanical) foundation of the chemical (not mechanical) discipline of colloid and interface science. Copyright © 2018 Elsevier B.V. All rights reserved.

On the Mo-Papas equation

NASA Astrophysics Data System (ADS)

Aguirregabiria, J. M.; Chamorro, A.; Valle, M. A.

1982-05-01

A new heuristic derivation of the Mo-Papas equation for charged particles is given. It is shown that this equation cannot be derived for a point particle by closely following Dirac's classical treatment of the problem. The Mo-Papas theory and the Bonnor-Rowe-Marx variable mass dynamics are not compatible.

Simplified Relativistic Force Transformation Equation.

ERIC Educational Resources Information Center

Stewart, Benjamin U.

1979-01-01

A simplified relativistic force transformation equation is derived and then used to obtain the equation for the electromagnetic forces on a charged particle, calculate the electromagnetic fields due to a point charge with constant velocity, transform electromagnetic fields in general, derive the Biot-Savart law, and relate it to Coulomb's law.…

Understanding differences between DELFT3D and empirical predictions of alongshore sediment transport gradients

USGS Publications Warehouse

List, Jeffrey; Benedet, Lindino; Hanes, Daniel M.; Ruggiero, Peter

2009-01-01

Predictions of alongshore transport gradients are critical for forecasting shoreline change. At the previous ICCE conference, it was demonstrated that alongshore transport gradients predicted by the empirical CERC equation can differ substantially from predictions made by the hydrodynamics-based model Delft3D in the case of a simulated borrow pit on the shoreface. Here we use the Delft3D momentum balance to examine the reason for this difference. Alongshore advective flow accelerations in our Delft3D simulation are mainly driven by pressure gradients resulting from alongshore variations in wave height and setup, and Delft3D transport gradients are controlled by these flow accelerations. The CERC equation does not take this process into account, and for this reason a second empirical transport term is sometimes added when alongshore gradients in wave height are thought to be significant. However, our test case indicates that this second term does not properly predict alongshore transport gradients.

Modeling self-consistent multi-class dynamic traffic flow

NASA Astrophysics Data System (ADS)

Cho, Hsun-Jung; Lo, Shih-Ching

2002-09-01

In this study, we present a systematic self-consistent multiclass multilane traffic model derived from the vehicular Boltzmann equation and the traffic dispersion model. The multilane domain is considered as a two-dimensional space and the interaction among vehicles in the domain is described by a dispersion model. The reason we consider a multilane domain as a two-dimensional space is that the driving behavior of road users may not be restricted by lanes, especially motorcyclists. The dispersion model, which is a nonlinear Poisson equation, is derived from the car-following theory and the equilibrium assumption. Under the concept that all kinds of users share the finite section, the density is distributed on a road by the dispersion model. In addition, the dynamic evolution of the traffic flow is determined by the systematic gas-kinetic model derived from the Boltzmann equation. Multiplying Boltzmann equation by the zeroth, first- and second-order moment functions, integrating both side of the equation and using chain rules, we can derive continuity, motion and variance equation, respectively. However, the second-order moment function, which is the square of the individual velocity, is employed by previous researches does not have physical meaning in traffic flow. Although the second-order expansion results in the velocity variance equation, additional terms may be generated. The velocity variance equation we propose is derived from multiplying Boltzmann equation by the individual velocity variance. It modifies the previous model and presents a new gas-kinetic traffic flow model. By coupling the gas-kinetic model and the dispersion model, a self-consistent system is presented.

Derivation of exact master equation with stochastic description: dissipative harmonic oscillator.

PubMed

Li, Haifeng; Shao, Jiushu; Wang, Shikuan

2011-11-01

A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of the bath-induced stochastic field is presented. The dynamics of the system is thereby fully described by a stochastic differential equation, and the desired master equation would be acquired with statistical averaging. It is shown that the existence of a closed-form master equation depends on the specificity of the system as well as the feature of the dissipation characterized by the spectral density function. For a dissipative harmonic oscillator it is observed that the correlation between the stochastic field due to the bath and the system can be decoupled, and the master equation naturally results. Such an equation possesses the Lindblad form in which time-dependent coefficients are determined by a set of integral equations. It is proved that the obtained master equation is equivalent to the well-known Hu-Paz-Zhang equation based on the path-integral technique. The procedure is also used to obtain the master equation of a dissipative harmonic oscillator in time-dependent fields.

Generalization of the lightning electromagnetic equations of Uman, McLain, and Krider based on Jefimenko equations

DOE PAGES

Shao, Xuan-Min

2016-04-12

The fundamental electromagnetic equations used by lightning researchers were introduced in a seminal paper by Uman, McLain, and Krider in 1975. However, these equations were derived for an infinitely thin, one-dimensional source current, and not for a general three-dimensional current distribution. In this paper, we introduce a corresponding pair of generalized equations that are determined from a three-dimensional, time-dependent current density distribution based on Jefimenko's original electric and magnetic equations. To do this, we derive the Jefimenko electric field equation into a new form that depends only on the time-dependent current density similar to that of Uman, McLain, and Krider,more » rather than on both the charge and current densities in its original form. The original Jefimenko magnetic field equation depends only on current, so no further derivation is needed. We show that the equations of Uman, McLain, and Krider can be readily obtained from the generalized equations if a one-dimensional source current is considered. For the purpose of practical applications, we discuss computational implementation of the new equations and present electric field calculations for a three-dimensional, conical-shape discharge.« less

Approach to first-order exact solutions of the Ablowitz-Ladik equation.

PubMed

Ankiewicz, Adrian; Akhmediev, Nail; Lederer, Falk

2011-05-01

We derive exact solutions of the Ablowitz-Ladik (A-L) equation using a special ansatz that linearly relates the real and imaginary parts of the complex function. This ansatz allows us to derive a family of first-order solutions of the A-L equation with two independent parameters. This novel technique shows that every exact solution of the A-L equation has a direct analog among first-order solutions of the nonlinear Schrödinger equation (NLSE). © 2011 American Physical Society

Einstein-Cartan Theory of Gravitation: Kinematical Parameters and Maxwell Equations

NASA Astrophysics Data System (ADS)

Katkar, L. N.

2015-03-01

In the space-time manifold of Einstein-Cartan Theory (ECT) of gravitation, the expressions for the time-like kinematical parameters are derived and the propagation equation for expansion is obtained.It has been observed that when the spin tensor is u-orthogonal the spin of the gravitating matter has no influence on the propagation equation of expansion while it has influence when it is not u-orthogonal. The usual formula for the curl of gradient of a scalar function is not zero in ECT. So is the case with the divergence of the curl of a vector.Their expressions on the space-time manifold of ECT are derived. A new derivative operator d ∗ is introduced to develop the calculus on space-time manifold of ECT. It is obtained by taking the covariant derivative of an associated tensor of a form with respect to an asymmetric connections. We have used this differential operator to obtain the form of the Maxwell's equations in the ECT of gravitation. Cartan's equations of structure are also derived through the new derivative operator. It has been shown that unlike the consequences of exterior derivative in Einstein space-time, the repetition of d ∗ on a form of any degree is not zero.

Increasing Functional Communication in Non-Speaking Preschool Children: Comparison of PECS and VOCA

ERIC Educational Resources Information Center

Bock, Stacey Jones; Stoner, Julia B.; Beck, Ann R.; Hanley, Laurie; Prochnow, Jessica

2005-01-01

For individuals who have complex communication needs and for the interventionists who work with them, the collection of empirically derived data that support the use of an intervention approach is critical. The purposes of this study were to continue building an empirically derived base of support for, and to compare the relative effectiveness of…

An Analytical Solution and Numerical Modeling Study of Gas Hydrate Saturation Effects on Porosity and Permeability of Porous Media

NASA Astrophysics Data System (ADS)

Zerpa, L.; Gao, F.; Wang, S.

2017-12-01

There are two major types of natural gas hydrate distributions in porous media: pore filling and contact cementing. The difference between these two distribution types is related to hydrate nucleation and growth processes. In the pore filling distribution, hydrate nucleates from a gas-dissolved aqueous phase at the grain boundary and grows away from grain contacts and surfaces into the pore space. In the contact cementing distribution, hydrate nucleates and grows at the gas-water interface and at intergranular contacts. Previous attempts to correlate changes on porosity and permeability during hydrate formation/dissociation were based on the length difference between the pore body and pore throat, and only considered contact cementing hydrate distribution. This work consists of a study of mathematical models of permeability and porosity as a function of gas hydrate saturation during formation and dissociation of gas hydrates in porous media. In this work, first we derive the permeability equation for the pore filling hydrate deposition as a function of hydrate saturation. Then, a more comprehensive model considering both types of gas hydrate deposition is developed to represent changes in permeability and porosity during hydrate formation and dissociation. This resulted in a model that combines pore filling and contact cementing deposition types in the same reservoir. Finally, the TOUGH+Hydrate numerical reservoir simulator was modified to include these models to analyze the response of production and saturation during a depressurization process, considering different combinations of pore filling and contact cementing hydrate distributions. The empirical exponent used in the permeability adjustment factor model influences both production profile and saturation results. This empirical factor describes the permeability dependence to changes in porosity caused by solid phase formation in the porous medium. The use of the permeability exponent decreases the permeability of the system for a given hydrate saturation, which affects the hydraulic performance of the system. However, from published experimental work, there is only a rough estimation of this permeability exponent. This factor could be represented with an empirical equation if more laboratory and field data becomes available.

SU-F-T-144: Analytical Closed Form Approximation for Carbon Ion Bragg Curves in Water

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

Tuomanen, S; Moskvin, V; Farr, J

2016-06-15

Purpose: Semi-empirical modeling is a powerful computational method in radiation dosimetry. A set of approximations exist for proton ion depth dose distribution (DDD) in water. However, the modeling is more complicated for carbon ions due to fragmentation. This study addresses this by providing and evaluating a new methodology for DDD modeling of carbon ions in water. Methods: The FLUKA, Monte Carlo (MC) general-purpose transport code was used for simulation of carbon DDDs for energies of 100–400 MeV in water as reference data model benchmarking. Based on Thomas Bortfeld’s closed form equation approximating proton Bragg Curves as a basis, we derivedmore » the critical constants for a beam of Carbon ions by applying models of radiation transport by Lee et. al. and Geiger to our simulated Carbon curves. We hypothesized that including a new exponential (κ) residual distance parameter to Bortfeld’s fluence reduction relation would improve DDD modeling for carbon ions. We are introducing an additional term to be added to Bortfeld’s equation to describe fragmentation tail. This term accounts for the pre-peak dose from nuclear fragments (NF). In the post peak region, the NF transport will be treated as new beams utilizing the Glauber model for interaction cross sections and the Abrasion- Ablation fragmentation model. Results: The carbon beam specific constants in the developed model were determined to be : p= 1.75, β=0.008 cm-1, γ=0.6, α=0.0007 cm MeV, σmono=0.08, and the new exponential parameter κ=0.55. This produced a close match for the plateau part of the curve (max deviation 6.37%). Conclusion: The derived semi-empirical model provides an accurate approximation of the MC simulated clinical carbon DDDs. This is the first direct semi-empirical simulation for the dosimetry of therapeutic carbon ions. The accurate modeling of the NF tail in the carbon DDD will provide key insight into distal edge dose deposition formation.« less

Plausibility check of a redesigned rain-on-snow simulator (RASA)

NASA Astrophysics Data System (ADS)

Rössler, Ole; Probst, Sabine; Weingartner, Rolf

2016-04-01

Rain-on-snow events are fascinating but still not completely understood processes. Although, several studies and equations have been published since decades that describe past events and theoretical descriptions, empirical data of what is happening in the snow cover is far less available. A way to fill this gap of empirical data, rain-on-snow-simulators might be of help. In 2013, Juras et al. published their inspiring idea of a portable rain-on-snow simulator. The huge advantage of this devise - in contrast to other purely field-based experiments - are their fixed, and mostly standardized conditions and the possibility to measure all required data to monitor the water fluxes and melting processes at a time. Mounted in a convenient location, a large number of experiments are relatively easy conductible. We applied and further developed the original device and plausified the results of this redesigned version, called RASA. The principal design was borrowed from the original version being a frame with a sprinkler on top and a snow sample in a box at the bottom, from which the outflow is measured with a tipping gauge. We added a moving sprinkling plate to ensure a uniform distribution of raindrops on the snow, and - most importantly - we suspended the watered snow sampled on weighting cells. The latter enables to continuous measurement of the snow sample throughout the experiment and thus the indirect quantification of liquid water saturation, water holding capacity, and snowmelt amount via balance equations. As it is remains unclear if this device is capable to reproduce known processes, a hypothesis based plausibility check was accomplished. Thus, eight hypothesizes were derived from literature and tested in 28 experiments with the RASA mounted at 2000 m elevation. In general, we were able to reproduce most of the hypotheses. The RASA proved to be a very valuable device that can generate suitable results and has the potential to extend the empirical-experimental data set on rain-on-snow events. Juras R., et al. (2013): A portable simulator for investigating rain-on-snow events, Zeitschrift für Geomorphologie, 57, Suppl.1, 73-89.

Empirical Correction to the Likelihood Ratio Statistic for Structural Equation Modeling with Many Variables.

PubMed

Yuan, Ke-Hai; Tian, Yubin; Yanagihara, Hirokazu

2015-06-01

Survey data typically contain many variables. Structural equation modeling (SEM) is commonly used in analyzing such data. The most widely used statistic for evaluating the adequacy of a SEM model is T ML, a slight modification to the likelihood ratio statistic. Under normality assumption, T ML approximately follows a chi-square distribution when the number of observations (N) is large and the number of items or variables (p) is small. However, in practice, p can be rather large while N is always limited due to not having enough participants. Even with a relatively large N, empirical results show that T ML rejects the correct model too often when p is not too small. Various corrections to T ML have been proposed, but they are mostly heuristic. Following the principle of the Bartlett correction, this paper proposes an empirical approach to correct T ML so that the mean of the resulting statistic approximately equals the degrees of freedom of the nominal chi-square distribution. Results show that empirically corrected statistics follow the nominal chi-square distribution much more closely than previously proposed corrections to T ML, and they control type I errors reasonably well whenever N ≥ max(50,2p). The formulations of the empirically corrected statistics are further used to predict type I errors of T ML as reported in the literature, and they perform well.

Non-classical and potential symmetry analysis of Richard's equation for moisture flow in soil

NASA Astrophysics Data System (ADS)

Wiltshire, Ron; El-Kafri, Manal

2004-01-01

This paper focuses upon the derivation of the non-classical symmetries of Bluman and Cole as they apply to Richard's equation for water flow in an unsaturated uniform soil. It is shown that the determining equations for the non-classical case lead to four highly non-linear equations which have been solved in five particular cases. In each case the corresponding similarity ansatz has been derived and Richard's equation is reduced to an ordinary differential equation. Explicit solutions are produced when possible. Richard's equation is also expressed as a potential system and in reviewing the classical Lie solutions a new symmetry is derived together with its similarity ansatz. Determining equations are then produced for the potential system using the non-classical algorithm. This results in an under-determined set of equations and an example symmetry that reveals a missing classical case is presented. An example of a classical and a non-classical symmetry reduction applied to the infiltration of moisture in soil is presented. The condition for surface invariance is used to demonstrate the equivalence of a classical Lie and a potential symmetry.

Quantum cluster theory for the polarizable continuum model. I. The CCSD level with analytical first and second derivatives.

PubMed

Cammi, R

2009-10-28

We present a general formulation of the coupled-cluster (CC) theory for a molecular solute described within the framework of the polarizable continuum model (PCM). The PCM-CC theory is derived in its complete form, called PTDE scheme, in which the correlated electronic density is used to have a self-consistent reaction field, and in an approximate form, called PTE scheme, in which the PCM-CC equations are solved assuming the fixed Hartree-Fock solvent reaction field. Explicit forms for the PCM-CC-PTDE equations are derived at the single and double (CCSD) excitation level of the cluster operator. At the same level, explicit equations for the analytical first derivatives of the PCM basic energy functional are presented, and analytical second derivatives are also discussed. The corresponding PCM-CCSD-PTE equations are given as a special case of the full theory.

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

Liemert, André, E-mail: andre.liemert@ilm.uni-ulm.de; Kienle, Alwin

Purpose: Explicit solutions of the monoenergetic radiative transport equation in the P{sub 3} approximation have been derived which can be evaluated with nearly the same computational effort as needed for solving the standard diffusion equation (DE). In detail, the authors considered the important case of a semi-infinite medium which is illuminated by a collimated beam of light. Methods: A combination of the classic spherical harmonics method and the recently developed method of rotated reference frames is used for solving the P{sub 3} equations in closed form. Results: The derived solutions are illustrated and compared to exact solutions of the radiativemore » transport equation obtained via the Monte Carlo (MC) method as well as with other approximated analytical solutions. It is shown that for the considered cases which are relevant for biomedical optics applications, the P{sub 3} approximation is close to the exact solution of the radiative transport equation. Conclusions: The authors derived exact analytical solutions of the P{sub 3} equations under consideration of boundary conditions for defining a semi-infinite medium. The good agreement to Monte Carlo simulations in the investigated domains, for example, in the steady-state and time domains, as well as the short evaluation time needed suggests that the derived equations can replace the often applied solutions of the diffusion equation for the homogeneous semi-infinite medium.« less

Numerical simulation of life cycles of advection warm fog

NASA Technical Reports Server (NTRS)

Hung, R. J.; Vaughan, O. H.

1977-01-01

The formation, development and dissipation of advection warm fog is investigated. The equations employed in the model include the equation of continuity, momentum and energy for the descriptions of density, wind component and potential temperature, respectively, together with two diffusion equations for the modification of water-vapor mixing ratio and liquid-water mixing ratios. A description of the vertical turbulent transfer of heat, moisture and momentum has been taken into consideration. The turbulent exchange coefficients adopted in the model are based on empirical flux-gradient relations.

Modeling extracellular electrical stimulation: I. Derivation and interpretation of neurite equations.

PubMed

Meffin, Hamish; Tahayori, Bahman; Grayden, David B; Burkitt, Anthony N

2012-12-01

Neuroprosthetic devices, such as cochlear and retinal implants, work by directly stimulating neurons with extracellular electrodes. This is commonly modeled using the cable equation with an applied extracellular voltage. In this paper a framework for modeling extracellular electrical stimulation is presented. To this end, a cylindrical neurite with confined extracellular space in the subthreshold regime is modeled in three-dimensional space. Through cylindrical harmonic expansion of Laplace's equation, we derive the spatio-temporal equations governing different modes of stimulation, referred to as longitudinal and transverse modes, under types of boundary conditions. The longitudinal mode is described by the well-known cable equation, however, the transverse modes are described by a novel ordinary differential equation. For the longitudinal mode, we find that different electrotonic length constants apply under the two different boundary conditions. Equations connecting current density to voltage boundary conditions are derived that are used to calculate the trans-impedance of the neurite-plus-thin-extracellular-sheath. A detailed explanation on depolarization mechanisms and the dominant current pathway under different modes of stimulation is provided. The analytic results derived here enable the estimation of a neurite's membrane potential under extracellular stimulation, hence bypassing the heavy computational cost of using numerical methods.

Interaction of Hurricane Katrina with Optically Complex Water in the Gulf of Mexico: Interpretation Using Satellite-Derived Inherent Optical Properties and Chlorophyll Concentration

DTIC Science & Technology

2009-04-01

Shelf, and into the Gulf of Mexico, empirically derived chl ; increases were observed in the Tortugas Gyre circulation feature, and in adjacent...Mexico, empirically derived chl a increases were observed in the Tortugas Gyre circulation feature, and in adjacent waters. Analy- sis of the...hurricane interaction also influenced the Tortugas Gyre, a recognized circulation feature in the southern Gulf of Mexico induced by the flow of the

Basic lubrication equations

NASA Technical Reports Server (NTRS)

Hamrock, B. J.; Dowson, D.

1981-01-01

Lubricants, usually Newtonian fluids, are assumed to experience laminar flow. The basic equations used to describe the flow are the Navier-Stokes equation of motion. The study of hydrodynamic lubrication is, from a mathematical standpoint, the application of a reduced form of these Navier-Stokes equations in association with the continuity equation. The Reynolds equation can also be derived from first principles, provided of course that the same basic assumptions are adopted in each case. Both methods are used in deriving the Reynolds equation, and the assumptions inherent in reducing the Navier-Stokes equations are specified. Because the Reynolds equation contains viscosity and density terms and these properties depend on temperature and pressure, it is often necessary to couple the Reynolds with energy equation. The lubricant properties and the energy equation are presented. Film thickness, a parameter of the Reynolds equation, is a function of the elastic behavior of the bearing surface. The governing elasticity equation is therefore presented.

Computing generalized Langevin equations and generalized Fokker-Planck equations.

PubMed

Darve, Eric; Solomon, Jose; Kia, Amirali

2009-07-07

The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.

Brans-Dicke Galileon and the variational principle

NASA Astrophysics Data System (ADS)

Quiros, Israel; García-Salcedo, Ricardo; Gonzalez, Tame; Horta-Rangel, F. Antonio; Saavedra, Joel

2016-09-01

This paper is aimed at a (mostly) pedagogical exposition of the derivation of the motion equations of certain modifications of general relativity. Here we derive in all detail the motion equations in the Brans-Dicke theory with cubic self-interaction. This is a modification of the Brans-Dicke theory by the addition of a term in the Lagrangian which is non-linear in the derivatives of the scalar field: it contains second-order derivatives. This is the basis of the so-called Brans-Dicke Galileon. We pay special attention to the variational principle and to the algebraic details of the derivation. It is shown how higher order derivatives of the fields appearing in the intermediate computations cancel out leading to second order motion equations. The reader will find useful tips for the derivation of the field equations of modifications of general relativity such as the scalar-tensor theories and f(R) theories, by means of the (stationary action) variational principle. The content of this paper is particularly recommended to those graduate and postgraduate students who are interested in the study of the mentioned modifications of general relativity.

Complex-valued derivative propagation method with approximate Bohmian trajectories: Application to electronic nonadiabatic dynamics

NASA Astrophysics Data System (ADS)

Wang, Yu; Chou, Chia-Chun

2018-05-01

The coupled complex quantum Hamilton-Jacobi equations for electronic nonadiabatic transitions are approximately solved by propagating individual quantum trajectories in real space. Equations of motion are derived through use of the derivative propagation method for the complex actions and their spatial derivatives for wave packets moving on each of the coupled electronic potential surfaces. These equations for two surfaces are converted into the moving frame with the same grid point velocities. Excellent wave functions can be obtained by making use of the superposition principle even when nodes develop in wave packet scattering.

Basic performance of a multilayer insulation system containing 20 to 160 layers. [thermal effectiveness of aluminized Mylar-silk net system

NASA Technical Reports Server (NTRS)

Stochl, R. J.

1974-01-01

An experimental investigation was conducted to determine the thermal effectiveness of an aluminized Mylar-silk net insulation system containing up to 160 layers. The experimentally measured heat flux was compared with results predicted by using (1) a previously developed semi-empirical equation and (2) an effective-thermal-conductivity value. All tests were conducted at a nominal hot-boundary temperature of 294 K (530 R) with liquid hydrogen as the heat sink. The experimental results show that the insulation performed as expected and that both the semi-empirical equation and effective thermal conductivity of a small number of layers were adequate in predicting the thermal performance of a large number of layers of insulation.

Development of an empirically based dynamic biomechanical strength model

NASA Technical Reports Server (NTRS)

Pandya, A.; Maida, J.; Aldridge, A.; Hasson, S.; Woolford, B.

1992-01-01

The focus here is on the development of a dynamic strength model for humans. Our model is based on empirical data. The shoulder, elbow, and wrist joints are characterized in terms of maximum isolated torque, position, and velocity in all rotational planes. This information is reduced by a least squares regression technique into a table of single variable second degree polynomial equations determining the torque as a function of position and velocity. The isolated joint torque equations are then used to compute forces resulting from a composite motion, which in this case is a ratchet wrench push and pull operation. What is presented here is a comparison of the computed or predicted results of the model with the actual measured values for the composite motion.

Analytic solutions for Long's equation and its generalization

NASA Astrophysics Data System (ADS)

Humi, Mayer

2017-12-01

Two-dimensional, steady-state, stratified, isothermal atmospheric flow over topography is governed by Long's equation. Numerical solutions of this equation were derived and used by several authors. In particular, these solutions were applied extensively to analyze the experimental observations of gravity waves. In the first part of this paper we derive an extension of this equation to non-isothermal flows. Then we devise a transformation that simplifies this equation. We show that this simplified equation admits solitonic-type solutions in addition to regular gravity waves. These new analytical solutions provide new insights into the propagation and amplitude of gravity waves over topography.

Conservation form of the equations of fluid dynamics in general nonsteady coordinates

NASA Astrophysics Data System (ADS)

Zhang, H.; Camarero, R.; Kahawita, R.

1985-11-01

Many of the differential equations arising in fluid dynamics may be stated in conservation-law form. A number of investigations have been conducted with the aim to derive the conservation-law form of the Navier-Stokes equations in general nonsteady coordinate systems. The present note has the objective to illustrate a mathematical methodology with which such forms of the equations may be derived in an easier and more general fashion. For numerical applications, the scalar form of the equations is eventually provided. Attention is given to the conservation form of equations in curvilinear coordinates and numerical considerations.

Gender disparity in BMD conversion: a comparison between Lunar and Hologic densitometers.

PubMed

Ganda, Kirtan; Nguyen, Tuan V; Pocock, Nicholas

2014-01-01

Female-derived inter-conversion and standardised BMD equations at the lumbar spine and hip have not been validated in men. This study of 110 male subjects scanned on Hologic and Lunar densitometers demonstrates that published equations may not applicable to men at the lumbar spine. Male inter-conversion equations have also been derived. Currently, available equations for inter-manufacturer conversion of bone mineral density (BMD) and calculation of standardised BMD (sBMD) are used in both males and females, despite being derived and validated only in women. Our aim was to test the validity of the published equations in men. One hundred ten men underwent lumbar spine (L2-4), femoral neck (FN) and total hip (TH) dual X-ray absorptiometry (DXA) using Hologic and Lunar scanners. Hologic BMD was converted to Lunar using published equations derived from women for L2-4 and FN. Actual Lunar BMD (A-Lunar) was compared to converted (Lunar equivalent) Hologic BMD values (H-Lunar). sBMD was calculated separately using Hologic (sBMD-H) and Lunar BMD (sBMD-L) at L2-4, FN and TH. Conversion equations in men for Hologic to Lunar BMD were derived using Deming regression analysis. There was a strong linear correlation between Lunar and Hologic BMD at all skeletal sites. A-Lunar BMD was however significantly higher than derived H-Lunar BMD (p < 0.001) at L2-L4 (mean difference, 0.07 g/cm(2)). There was no significant difference at the FN (mean difference, 0.01 g/cm(2)). sBMD-L at the spine was significantly higher than sBMD-H (mean difference, 0.06 g/cm(2), p < 0.001), whilst there was little difference at the FN and TH (mean difference, 0.01 g/cm(2)). Published conversion equations for Lunar BMD to Hologic BMD, and formulae for lumbar spine sBMD, derived in women may not be applicable to men.

Nonlocal electrical diffusion equation

NASA Astrophysics Data System (ADS)

Gómez-Aguilar, J. F.; Escobar-Jiménez, R. F.; Olivares-Peregrino, V. H.; Benavides-Cruz, M.; Calderón-Ramón, C.

2016-07-01

In this paper, we present an analysis and modeling of the electrical diffusion equation using the fractional calculus approach. This alternative representation for the current density is expressed in terms of the Caputo derivatives, the order for the space domain is 0<β≤1 and for the time domain is 0<γ≤2. We present solutions for the full fractional equation involving space and time fractional derivatives using numerical methods based on Fourier variable separation. The case with spatial fractional derivatives leads to Levy flight type phenomena, while the time fractional equation is related to sub- or super diffusion. We show that the mathematical concept of fractional derivatives can be useful to understand the behavior of semiconductors, the design of solar panels, electrochemical phenomena and the description of anomalous complex processes.

Maneuverability Estimation of High-Speed Craft

DTIC Science & Technology

2015-06-01

derived based on equations by Lewandowski and Denny- Hubble in order to find the fundamental maneuvering characteristics. The model is developed in...characteristic of high- speed craft. A mathematical model is derived based on equations by Lewandowski and Denny- Hubble in order to find the fundamental...33 C. EQUATIONS BY DENNY AND HUBBLE ................................................43 D. NOMOTO

Equations for the Filled Inelastic Membrane: A More General Derivation

ERIC Educational Resources Information Center

Deakin, Michael A. B.

2011-01-01

An earlier paper discussed the case of a flexible but inextensible membrane filled to capacity with incompressible fluid. It was found that the resulting shape satisfies a set of three simultaneous partial differential equations. This article gives a more general derivation of these equations and shows their form in an interesting special case.

Analytical study of fractional equations describing anomalous diffusion of energetic particles

NASA Astrophysics Data System (ADS)

Tawfik, A. M.; Fichtner, H.; Schlickeiser, R.; Elhanbaly, A.

2017-06-01

To present the main influence of anomalous diffusion on the energetic particle propagation, the fractional derivative model of transport is developed by deriving the fractional modified Telegraph and Rayleigh equations. Analytical solutions of the fractional modified Telegraph and the fractional Rayleigh equations, which are defined in terms of Caputo fractional derivatives, are obtained by using the Laplace transform and the Mittag-Leffler function method. The solutions of these fractional equations are given in terms of special functions like Fox’s H, Mittag-Leffler, Hermite and Hyper-geometric functions. The predicted travelling pulse solutions are discussed in each case for different values of fractional order.

A Comprehensive Review on the Predictive Performance of the Sheiner-Tozer and Derivative Equations for the Correction of Phenytoin Concentrations.

PubMed

Kiang, Tony K L; Ensom, Mary H H

2016-04-01

In settings where free phenytoin concentrations are not available, the Sheiner-Tozer equation-Corrected total phenytoin concentration = Observed total phenytoin concentration/[(0.2 × Albumin) + 0.1]; phenytoin in µg/mL, albumin in g/dL-and its derivative equations are commonly used to correct for altered phenytoin binding to albumin. The objective of this article was to provide a comprehensive and updated review on the predictive performance of these equations in various patient populations. A literature search of PubMed, EMBASE, and Google Scholar was conducted using combinations of the following terms: Sheiner-Tozer, Winter-Tozer, phenytoin, predictive equation, precision, bias, free fraction. All English-language articles up to November 2015 (excluding abstracts) were evaluated. This review shows the Sheiner-Tozer equation to be biased and imprecise in various critical care, head trauma, and general neurology patient populations. Factors contributing to bias and imprecision include the following: albumin concentration, free phenytoin assay temperature, experimental conditions (eg, timing of concentration sampling, steady-state dosing conditions), renal function, age, concomitant medications, and patient type. Although derivative equations using varying albumin coefficients have improved accuracy (without much improvement in precision) in intensive care and elderly patients, these equations still require further validation. Further experiments are also needed to yield derivative equations with good predictive performance in all populations as well as to validate the equations' impact on actual patient efficacy and toxicity outcomes. More complex, multivariate predictive equations may be required to capture all variables that can potentially affect phenytoin pharmacokinetics and clinical therapeutic outcomes. © The Author(s) 2016.

Thermodynamic Properties of Nitrogen Including Liquid and Vapor Phases from 63K to 2000K with Pressures to 10,000 Bar

NASA Technical Reports Server (NTRS)

Jacobsen, Richard T.; Stewart, Richard B.

1973-01-01

Tables of thermodynamic properties of nitrogen are presented for the liquid and vapor phases for temperatures from the freezing line to 2000K and pressures to 10,000 bar. The tables include values of density, internal energy, enthalpy, entropy, isochoric heat capacity, isobaric heat capacity velocity of sound, the isotherm derivative, and the isochor derivative. The thermodynamic property tables are based on an equation of state, P=P (p,T), which accurately represents liquid and gaseous nitrogen for the range of pressures and temperatures covered by the tables. Comparisons of property values calculated from the equation of state with measured values for P-p-T, heat capacity, enthalpy, latent heat, and velocity of sound are included to illustrate the agreement between the experimental data and the tables of properties presented here. The coefficients of the equation of state were determined by a weighted least squares fit to selected P-p-T data and, simultaneously, to isochoric heat capacity data determined by corresponding states analysis from oxygen data, and to data which define the phase equilibrium criteria for the saturated liquid and the saturated vapor. The vapor pressure equation, melting curve equation, and an equation to represent the ideal gas heat capacity are also presented. Estimates of the accuracy of the equation of state, the vapor pressure equation, and the ideal gas heat capacity equation are given. The equation of state, derivatives of the equation, and the integral functions for calculating derived thermodynamic properties are included.

An Empirically Derived Taxonomy for Personality Diagnosis: Bridging Science and Practice in Conceptualizing Personality

PubMed Central

Westen, Drew; Shedler, Jonathan; Bradley, Bekh; DeFife, Jared A.

2013-01-01

Objective The authors describe a system for diagnosing personality pathology that is empirically derived, clinically relevant, and practical for day-to-day use. Method A random national sample of psychiatrists and clinical psychologists (N=1,201) described a randomly selected current patient with any degree of personality dysfunction (from minimal to severe) using the descriptors in the Shedler-Westen Assessment Procedure–II and completed additional research forms. Results The authors applied factor analysis to identify naturally occurring diagnostic groupings within the patient sample. The analysis yielded 10 clinically coherent personality diagnoses organized into three higher-order clusters: internalizing, externalizing, and borderline-dysregulated. The authors selected the most highly rated descriptors to construct a diagnostic prototype for each personality syndrome. In a second, independent sample, research interviewers and patients’ treating clinicians were able to diagnose the personality syndromes with high agreement and minimal comorbidity among diagnoses. Conclusions The empirically derived personality prototypes described here provide a framework for personality diagnosis that is both empirically based and clinically relevant. PMID:22193534

A semi-empirical analysis of strong-motion peaks in terms of seismic source, propagation path, and local site conditions

NASA Astrophysics Data System (ADS)

Kamiyama, M.; Orourke, M. J.; Flores-Berrones, R.

1992-09-01

A new type of semi-empirical expression for scaling strong-motion peaks in terms of seismic source, propagation path, and local site conditions is derived. Peak acceleration, peak velocity, and peak displacement are analyzed in a similar fashion because they are interrelated. However, emphasis is placed on the peak velocity which is a key ground motion parameter for lifeline earthquake engineering studies. With the help of seismic source theories, the semi-empirical model is derived using strong motions obtained in Japan. In the derivation, statistical considerations are used in the selection of the model itself and the model parameters. Earthquake magnitude M and hypocentral distance r are selected as independent variables and the dummy variables are introduced to identify the amplification factor due to individual local site conditions. The resulting semi-empirical expressions for the peak acceleration, velocity, and displacement are then compared with strong-motion data observed during three earthquakes in the U.S. and Mexico.

Predicting Thermal Conductivity

NASA Technical Reports Server (NTRS)

Penn, B.; Ledbetter, F. E., III; Clemons, J.

1984-01-01

Empirical equation predicts thermal conductivity of composite insulators consisting of cellular, granular or fibrous material embedded in matrix of solid viscoelastic material. Application in designing custom insulators for particular environments.

New Intensity Attenuation in Georgia

NASA Astrophysics Data System (ADS)

Tsereteli, N. S.; Varazanashvili, O.; Tibaldi, A.; Bonali, F.; Gogoladze, Z.; Kvavadze, N.; Kvedelidze, I.

2016-12-01

In seismic-prone zones, increase of urbanization and infrastructures in turn produces increase of seismic risk that is mainly related to: the level of seismic hazard itself, the seismic resistance of dwelling houses, and many other factors. The relevant objectives of the present work is to improve the regional seismic hazard maps of Georgia, by implementing state-of-the art probabilistic seismic hazard assessment techniques and outputs from recent national and international collaborations. Seismic zoning is the identification of zones of similar levels of earthquake hazard. With reference to seismic zoning by ground motion assessment, the shaking intensity essentially depends on i) regional seismicity, ii) attenuation of ground motion with distance, iii) local site effects on ground motion. In the last decade, seismic hazard assessment is presented in terms of Peak Ground Acceleration (PGA), Peak Ground Velocity (PGV), or other recorded parameters. But there are very limited strong motion dataset in Georgia. Furthermore, vulnerability of buildings still is estimated for intensity, and there are no information about correlation between the distribution of ground motion recorded parameters and damage. So, macroseimic Intensity is still a very important parameter for strong ground motion evaluation. In the present work, we calibrated intensity prediction equations (IPE) for the Georgian dataset based on about 78 reviewed earthquakes. Metadata for Intensity (MSK 64 scale) were constrained and predictionequations for various types of distance (epicentral and hypocentral distance, Joyner-Boore distance, closest distance to the fault rupture plane) were calibrated. Relations between intensity and PGA values were derived. For this we used hybrid-empirical ground motion equation derived for Georgia and run scenario earthquakes for events with macroseismic data.

Development of a defect stream function, law of the wall/wake method for compressible turbulent boundary layers. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Wahls, Richard A.

1990-01-01

The method presented is designed to improve the accuracy and computational efficiency of existing numerical methods for the solution of flows with compressible turbulent boundary layers. A compressible defect stream function formulation of the governing equations assuming an arbitrary turbulence model is derived. This formulation is advantageous because it has a constrained zero-order approximation with respect to the wall shear stress and the tangential momentum equation has a first integral. Previous problems with this type of formulation near the wall are eliminated by using empirically based analytic expressions to define the flow near the wall. The van Driest law of the wall for velocity and the modified Crocco temperature-velocity relationship are used. The associated compressible law of the wake is determined and it extends the valid range of the analytical expressions beyond the logarithmic region of the boundary layer. The need for an inner-region eddy viscosity model is completely avoided. The near-wall analytic expressions are patched to numerically computed outer region solutions at a point determined during the computation. A new boundary condition on the normal derivative of the tangential velocity at the surface is presented; this condition replaces the no-slip condition and enables numerical integration to the surface with a relatively coarse grid using only an outer region turbulence model. The method was evaluated for incompressible and compressible equilibrium flows and was implemented into an existing Navier-Stokes code using the assumption of local equilibrium flow with respect to the patching. The method has proven to be accurate and efficient.

Equation of state for two-dimensional dusty plasma liquids and its applications

NASA Astrophysics Data System (ADS)

Feng, Yan

2017-10-01

Laboratory dusty plasma consists of free electrons, free ions, and micro-sized dust particles with thousands of negative elementary charges. Due to their extremely low charge-to-mass ratio, these dust particles are strongly coupled, arranging themselves like atoms in liquids or solids. Due to the shielding effects of electrons and ions, dust particles interact with each other through the Yukawa potential, so that simulations of Yukawa liquids or solids are used to study properties of dusty plasmas. In the past two decades, the properties of liquid 2D dusty plasmas have been widely studied from experiments to theories and simulations. However, from our literature search, we have not found a quantitative and comprehensive study of properties of 2D liquid dusty plasmas over a wide range of plasma conditions. Here, from molecular-dynamics simulations of Yukawa liquids, we have obtained a concise equation of state (EOS) for the 2D liquid dusty plasmas from empirical fitting, which contains three quantities of the internal pressure, the coupling parameter, and the screening parameter. From this EOS, different thermodynamical processes can be directly derived, such as isotherms, isobars and isochores. Also, various physical properties of 2D liquid dusty plasmas, like the bulk modulus of elasticity, can be analytically derived, so that the sound speeds can be obtained. Finally, an analytical expression of the specific heat for 2D liquid dusty plasmas has been achieved. Work supported by the National Natural Science Foundation of China under Grant No. 11505124, the 1000 Youth Talents Plan, and the startup funds from Soochow University.

Examining the Stability of "DSM-IV" and Empirically Derived Eating Disorder Classification: Implications for "DSM-5"

ERIC Educational Resources Information Center

Peterson, Carol B.; Crow, Scott J.; Swanson, Sonja A.; Crosby, Ross D.; Wonderlich, Stephen A.; Mitchell, James E.; Agras, W. Stewart; Halmi, Katherine A.

2011-01-01

Objective: The purpose of this investigation was to derive an empirical classification of eating disorder symptoms in a heterogeneous eating disorder sample using latent class analysis (LCA) and to examine the longitudinal stability of these latent classes (LCs) and the stability of DSM-IV eating disorder (ED) diagnoses. Method: A total of 429…

Student Response to Faculty Instruction (SRFI): An Empirically Derived Instrument to Measure Student Evaluations of Teaching

ERIC Educational Resources Information Center

Beitzel, Brian D.

2013-01-01

The Student Response to Faculty Instruction (SRFI) is an instrument designed to measure the student perspective on courses in higher education. The SRFI was derived from decades of empirical studies of student evaluations of teaching. This article describes the development of the SRFI and its psychometric attributes demonstrated in two pilot study…

An Empirical Comparison of Five Linear Equating Methods for the NEAT Design

ERIC Educational Resources Information Center

Suh, Youngsuk; Mroch, Andrew A.; Kane, Michael T.; Ripkey, Douglas R.

2009-01-01

In this study, a data base containing the responses of 40,000 candidates to 90 multiple-choice questions was used to mimic data sets for 50-item tests under the "nonequivalent groups with anchor test" (NEAT) design. Using these smaller data sets, we evaluated the performance of five linear equating methods for the NEAT design with five levels of…

Empirical tests of a theory of language, mathematics, and matter.

PubMed

Abler, William L

2008-01-01

In an earlier paper (Abler, 2006), I proposed a theory of language, especially sentences, based on the symmetrical structure of the equation. Here, I use the structure of equations to deduce neural structures (e.g., mirror neurons or intra-cellular macromolecules, or crystals, or resonations) that might generate them. Ultimately, the properties described are a consequence of dimensional properties of matter

Position-dependent effective masses in semiconductor theory. II

NASA Technical Reports Server (NTRS)

Von Roos, O.; Mavromatis, H.

1985-01-01

A compound semiconductor possessing a slowly varying position-dependent chemical composition is considered. An effective-mass equation governing the dynamics of electron (or hole) motion using the Kohn-Luttinger representation and canonical transformations is derived. It is shown that, as long as the variation in chemical composition may be treated as a perturbation, the effective masses become constant, position-independent quantities. The effective-mass equation derived here is identical to the effective-mass equation derived previously by von Roos (1983), using a Wannier representation.

Macroscopic constitutive equations of thermo-poroelasticity derived using eigenstrain-eigenstress approaches

NASA Astrophysics Data System (ADS)

Suvorov, Alexander P.; Selvadurai, A. P. S.

2011-06-01

Macroscopic constitutive equations for thermoelastic processes in a fluid-saturated porous medium are re-derived using the notion of eigenstrain or, equivalently, eigenstress. The eigenstrain-stress approach is frequently used in micromechanics of solid multi-phase materials, such as composites. Simple derivations of the stress-strain constitutive relations and the void occupancy relationship are presented for both fully saturated and partially saturated porous media. Governing coupled equations for the displacement components and the fluid pressure are also obtained.

Equivalence of quantum Boltzmann equation and Kubo formula for dc conductivity

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

Su, Z.B.; Chen, L.Y.

1990-02-01

This paper presents a derivation of the quantum Boltzmann equation for linear dc transport with a correction term to Mahan-Hansch's equations and derive a formal solution to it. Based on this formal solution, the authors find the electric conductivity can be expressed as the retarded current-current correlation. Therefore, the authors explicitly demonstrate the equivalence of the two most important theoretical methods: quantum Boltzmann equation and Kubo formula.

Prediction of blast fragmentation of underground stopes for in situ leaching

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

Stagg, M.S.; Otterness, R.E.; Djahanguiri, F.

1994-12-31

The US Bureau of Mines (USBM) evaluated empirical equations that predict fragmentation from underground stope rounds. Controlled blasting is necessary for creating leaching stopes that maximize the recovery and minimize backbreak of the perimeter wall. This paper presents the fragmentation results from one of the three drop-raise blasts used to develop a reduced-scale cylindrical stope, 1.8 m in diameter and 6 m in height. The stope is located in the Colorado School of Mines Experimental Mine (Edgar Mine) in Idaho Springs, Colorado. This stope is part of a USBM research effort to determine the feasibility of incorporating in situ leachingmore » of rubblized stopes into active underground metal and nonmetal mines. All the material from the first blast, 14 mtons was sieved. The resulting distribution was compared to the distribution predicted from empirical equations. The best fit was found with a USBM equation developed from over 50 sieved, reduced-scale (1- to 2-m) high wall blasts. Modifications to the equations were made to account for the observed differences due to breakout angle, shot geometry, initiation timing, decoupling, rock fracture toughness and explosive energy.« less

Sensitivity of viscosity Arrhenius parameters to polarity of liquids

NASA Astrophysics Data System (ADS)

Kacem, R. B. H.; Alzamel, N. O.; Ouerfelli, N.

2017-09-01

Several empirical and semi-empirical equations have been proposed in the literature to estimate the liquid viscosity upon temperature. In this context, this paper aims to study the effect of polarity of liquids on the modeling of the viscosity-temperature dependence, considering particularly the Arrhenius type equations. To achieve this purpose, the solvents are classified into three groups: nonpolar, borderline polar and polar solvents. Based on adequate statistical tests, we found that there is strong evidence that the polarity of solvents affects significantly the distribution of the Arrhenius-type equation parameters and consequently the modeling of the viscosity-temperature dependence. Thus, specific estimated values of parameters for each group of liquids are proposed in this paper. In addition, the comparison of the accuracy of approximation with and without classification of liquids, using the Wilcoxon signed-rank test, shows a significant discrepancy of the borderline polar solvents. For that, we suggested in this paper new specific coefficient values of the simplified Arrhenius-type equation for better estimation accuracy. This result is important given that the accuracy in the estimation of the viscosity-temperature dependence may affect considerably the design and the optimization of several industrial processes.

Momentum Maps and Stochastic Clebsch Action Principles

NASA Astrophysics Data System (ADS)

Cruzeiro, Ana Bela; Holm, Darryl D.; Ratiu, Tudor S.

2018-01-01

We derive stochastic differential equations whose solutions follow the flow of a stochastic nonlinear Lie algebra operation on a configuration manifold. For this purpose, we develop a stochastic Clebsch action principle, in which the noise couples to the phase space variables through a momentum map. This special coupling simplifies the structure of the resulting stochastic Hamilton equations for the momentum map. In particular, these stochastic Hamilton equations collectivize for Hamiltonians that depend only on the momentum map variable. The Stratonovich equations are derived from the Clebsch variational principle and then converted into Itô form. In comparing the Stratonovich and Itô forms of the stochastic dynamical equations governing the components of the momentum map, we find that the Itô contraction term turns out to be a double Poisson bracket. Finally, we present the stochastic Hamiltonian formulation of the collectivized momentum map dynamics and derive the corresponding Kolmogorov forward and backward equations.

Alternative stable qP wave equations in TTI media with their applications for reverse time migration

NASA Astrophysics Data System (ADS)

Zhou, Yang; Wang, Huazhong; Liu, Wenqing

2015-10-01

Numerical instabilities may arise if the spatial variation of symmetry axis is handled improperly when implementing P-wave modeling and reverse time migration in heterogeneous tilted transversely isotropic (TTI) media, especially in the cases where fast changes exist in TTI symmetry axis’ directions. Based on the pseudo-acoustic approximation to anisotropic elastic wave equations in Cartesian coordinates, alternative second order qP (quasi-P) wave equations in TTI media are derived in this paper. Compared with conventional stable qP wave equations, the proposed equations written in stress components contain only spatial derivatives of wavefield variables (stress components) and are free from spatial derivatives involving media parameters. These lead to an easy and efficient implementation for stable P-wave modeling and imaging. Numerical experiments demonstrate the stability and computational efficiency of the presented equations in complex TTI media.

Mechanical modeling for magnetorheological elastomer isolators based on constitutive equations and electromagnetic analysis

NASA Astrophysics Data System (ADS)

Wang, Qi; Dong, Xufeng; Li, Luyu; Ou, Jinping

2018-06-01

As constitutive models are too complicated and existing mechanical models lack universality, these models are beyond satisfaction for magnetorheological elastomer (MRE) devices. In this article, a novel universal method is proposed to build concise mechanical models. Constitutive model and electromagnetic analysis were applied in this method to ensure universality, while a series of derivations and simplifications were carried out to obtain a concise formulation. To illustrate the proposed modeling method, a conical MRE isolator was introduced. Its basic mechanical equations were built based on equilibrium, deformation compatibility, constitutive equations and electromagnetic analysis. An iteration model and a highly efficient differential equation editor based model were then derived to solve the basic mechanical equations. The final simplified mechanical equations were obtained by re-fitting the simulations with a novel optimal algorithm. In the end, verification test of the isolator has proved the accuracy of the derived mechanical model and the modeling method.

Covariant Conformal Decomposition of Einstein Equations

NASA Astrophysics Data System (ADS)

Gourgoulhon, E.; Novak, J.

It has been shown1,2 that the usual 3+1 form of Einstein's equations may be ill-posed. This result has been previously observed in numerical simulations3,4. We present a 3+1 type formalism inspired by these works to decompose Einstein's equations. This decomposition is motivated by the aim of stable numerical implementation and resolution of the equations. We introduce the conformal 3-``metric'' (scaled by the determinant of the usual 3-metric) which is a tensor density of weight -2/3. The Einstein equations are then derived in terms of this ``metric'', of the conformal extrinsic curvature and in terms of the associated derivative. We also introduce a flat 3-metric (the asymptotic metric for isolated systems) and the associated derivative. Finally, the generalized Dirac gauge (introduced by Smarr and York5) is used in this formalism and some examples of formulation of Einstein's equations are shown.

Gradients and Non-Adiabatic Derivative Coupling Terms for Spin-Orbit Wavefunctions

DTIC Science & Technology

2011-06-01

derivative, symmetric to the first time derivative. Solutions to the Dirac equation simultaneously satisfy the simple relativistic wave equation, the...For Pooki vi Acknowledgments I would like to thank the members of my committee for their time and...Theorem..............................................................................191 Appendix J. The Symmetric Group

A simple, direct derivation and proof of the validity of the SLLOD equations of motion for generalized homogeneous flows.

PubMed

Daivis, Peter J; Todd, B D

2006-05-21

We present a simple and direct derivation of the SLLOD equations of motion for molecular simulations of general homogeneous flows. We show that these equations of motion (1) generate the correct particle trajectories, (2) conserve the total thermal momentum without requiring the center of mass to be located at the origin, and (3) exactly generate the required energy dissipation. These equations of motion are compared with the g-SLLOD and p-SLLOD equations of motion, which are found to be deficient. Claims that the SLLOD equations of motion are incorrect for elongational flows are critically examined and found to be invalid. It is confirmed that the SLLOD equations are, in general, non-Hamiltonian. We derive a Hamiltonian from which they can be obtained in the special case of a symmetric velocity gradient tensor. In this case, it is possible to perform a canonical transformation that results in the well-known DOLLS tensor Hamiltonian.

General Tricomi-Rassias problem and oblique derivative problem for generalized Chaplygin equations

NASA Astrophysics Data System (ADS)

Wen, Guochun; Chen, Dechang; Cheng, Xiuzhen

2007-09-01

Many authors have discussed the Tricomi problem for some second order equations of mixed type, which has important applications in gas dynamics. In particular, Bers proposed the Tricomi problem for Chaplygin equations in multiply connected domains [L. Bers, Mathematical Aspects of Subsonic and Transonic Gas Dynamics, Wiley, New York, 1958]. And Rassias proposed the exterior Tricomi problem for mixed equations in a doubly connected domain and proved the uniqueness of solutions for the problem [J.M. Rassias, Lecture Notes on Mixed Type Partial Differential Equations, World Scientific, Singapore, 1990]. In the present paper, we discuss the general Tricomi-Rassias problem for generalized Chaplygin equations. This is one general oblique derivative problem that includes the exterior Tricomi problem as a special case. We first give the representation of solutions of the general Tricomi-Rassias problem, and then prove the uniqueness and existence of solutions for the problem by a new method. In this paper, we shall also discuss another general oblique derivative problem for generalized Chaplygin equations.

Cardiovascular risk prediction tools for populations in Asia.

PubMed

Barzi, F; Patel, A; Gu, D; Sritara, P; Lam, T H; Rodgers, A; Woodward, M

2007-02-01

Cardiovascular risk equations are traditionally derived from the Framingham Study. The accuracy of this approach in Asian populations, where resources for risk factor measurement may be limited, is unclear. To compare "low-information" equations (derived using only age, systolic blood pressure, total cholesterol and smoking status) derived from the Framingham Study with those derived from the Asian cohorts, on the accuracy of cardiovascular risk prediction. Separate equations to predict the 8-year risk of a cardiovascular event were derived from Asian and Framingham cohorts. The performance of these equations, and a subsequently "recalibrated" Framingham equation, were evaluated among participants from independent Chinese cohorts. Six cohort studies from Japan, Korea and Singapore (Asian cohorts); six cohort studies from China; the Framingham Study from the US. 172,077 participants from the Asian cohorts; 25,682 participants from Chinese cohorts and 6053 participants from the Framingham Study. In the Chinese cohorts, 542 cardiovascular events occurred during 8 years of follow-up. Both the Asian cohorts and the Framingham equations discriminated cardiovascular risk well in the Chinese cohorts; the area under the receiver-operator characteristic curve was at least 0.75 for men and women. However, the Framingham risk equation systematically overestimated risk in the Chinese cohorts by an average of 276% among men and 102% among women. The corresponding average overestimation using the Asian cohorts equation was 11% and 10%, respectively. Recalibrating the Framingham risk equation using cardiovascular disease incidence from the non-Chinese Asian cohorts led to an overestimation of risk by an average of 4% in women and underestimation of risk by an average of 2% in men. A low-information Framingham cardiovascular risk prediction tool, which, when recalibrated with contemporary data, is likely to estimate future cardiovascular risk with similar accuracy in Asian populations as tools developed from data on local cohorts.

Fluid equations with nonlinear wave-particle resonances^

NASA Astrophysics Data System (ADS)

Mattor, Nathan

1997-11-01

We have derived fluid equations that include linear and nonlinear wave-particle resonance effects. This greatly extends previous ``Landau-fluid'' closures, which include linear Landau damping. (G.W. Hammett and F.W. Perkins, Phys. Rev. Lett. 64,) 3019 (1990).^, (Z. Chang and J. D. Callen, Phys. Fluids B 4,) 1167 (1992). The new fluid equations are derived with no approximation regarding nonlinear kinetic interaction, and so additionally include numerous nonlinear kinetic effects. The derivation starts with the electrostatic drift kinetic equation for simplicity, with a Maxwellian distribution function. Fluid closure is accomplished through a simple integration trick applied to the drift kinetic equation, using the property that the nth moment of Maxwellian distribution is related to the nth derivative. The result is a compact closure term appearing in the highest moment equation, a term which involves a plasma dispersion function of the electrostatic field and its derivatives. The new term reduces to the linear closures in appropriate limits, so both approaches retain linear Landau damping. But the nonlinearly closed equations have additional desirable properties. Unlike linear closures, the nonlinear closure retains the time-reversibility of the original kinetic equation. We have shown directly that the nonlinear closure retains at least two nonlinear resonance effects: wave-particle trapping and Compton scattering. Other nonlinear kinetic effects are currently under investigation. The new equations correct two previous discrepancies between kinetic and Landau-fluid predictions, including a propagator discrepancy (N. Mattor, Phys. Fluids B 4,) 3952 (1992). and a numerical discrepancy for the 3-mode shearless bounded slab ITG problem. (S. E. Parker et al.), Phys. Plasmas 1, 1461 (1994). ^* In collaboration with S. E. Parker, Department of Physics, University of Colorado, Boulder. ^ Work performed at LLNL under DoE contract No. W7405-ENG-48.

Analytical solutions of the space-time fractional Telegraph and advection-diffusion equations

NASA Astrophysics Data System (ADS)

Tawfik, Ashraf M.; Fichtner, Horst; Schlickeiser, Reinhard; Elhanbaly, A.

2018-02-01

The aim of this paper is to develop a fractional derivative model of energetic particle transport for both uniform and non-uniform large-scale magnetic field by studying the fractional Telegraph equation and the fractional advection-diffusion equation. Analytical solutions of the space-time fractional Telegraph equation and space-time fractional advection-diffusion equation are obtained by use of the Caputo fractional derivative and the Laplace-Fourier technique. The solutions are given in terms of Fox's H function. As an illustration they are applied to the case of solar energetic particles.

Lie Symmetry Analysis, Analytical Solutions, and Conservation Laws of the Generalised Whitham-Broer-Kaup-Like Equations

NASA Astrophysics Data System (ADS)

Wang, Xiu-Bin; Tian, Shou-Fu; Qin, Chun-Yan; Zhang, Tian-Tian

2017-03-01

In this article, a generalised Whitham-Broer-Kaup-Like (WBKL) equations is investigated, which can describe the bidirectional propagation of long waves in shallow water. The equations can be reduced to the dispersive long wave equations, variant Boussinesq equations, Whitham-Broer-Kaup-Like equations, etc. The Lie symmetry analysis method is used to consider the vector fields and optimal system of the equations. The similarity reductions are given on the basic of the optimal system. Furthermore, the power series solutions are derived by using the power series theory. Finally, based on a new theorem of conservation laws, the conservation laws associated with symmetries of this equations are constructed with a detailed derivation.

Analysis of nonlocal neural fields for both general and gamma-distributed connectivities

NASA Astrophysics Data System (ADS)

Hutt, Axel; Atay, Fatihcan M.

2005-04-01

This work studies the stability of equilibria in spatially extended neuronal ensembles. We first derive the model equation from statistical properties of the neuron population. The obtained integro-differential equation includes synaptic and space-dependent transmission delay for both general and gamma-distributed synaptic connectivities. The latter connectivity type reveals infinite, finite, and vanishing self-connectivities. The work derives conditions for stationary and nonstationary instabilities for both kernel types. In addition, a nonlinear analysis for general kernels yields the order parameter equation of the Turing instability. To compare the results to findings for partial differential equations (PDEs), two typical PDE-types are derived from the examined model equation, namely the general reaction-diffusion equation and the Swift-Hohenberg equation. Hence, the discussed integro-differential equation generalizes these PDEs. In the case of the gamma-distributed kernels, the stability conditions are formulated in terms of the mean excitatory and inhibitory interaction ranges. As a novel finding, we obtain Turing instabilities in fields with local inhibition-lateral excitation, while wave instabilities occur in fields with local excitation and lateral inhibition. Numerical simulations support the analytical results.

Marangoni Flow Induced Evaporation Enhancement on Binary Sessile Drops.

PubMed

Chen, Pin; Harmand, Souad; Ouenzerfi, Safouene; Schiffler, Jesse

2017-06-15

The evaporation processes of pure water, pure 1-butanol, and 5% 1-butanol aqueous solution drops on heated hydrophobic substrates are investigated to determine the effect of temperature on the drop evaporation behavior. The evolution of the parameters (contact angle, diameter, and volume) during evaporation measured using a drop shape analyzer and the infrared thermal mapping of the drop surface recorded by an infrared camera were used in investigating the evaporation process. The pure 1-butanol drop does not show any thermal instability at different substrate temperatures, while the convection cells created by the thermal Marangoni effect appear on the surface of the pure water drop from 50 °C. Because 1-butanol and water have different surface tensions, the infrared video of the 5% 1-butanol aqueous solution drop shows that the convection cells are generated by the solutal Marangoni effect at any substrate temperature. Furthermore, when the substrate temperature exceeds 50 °C, coexistence of the thermal and solutal Marangoni flows is observed. By analyzing the relation between the ratio of the evaporation rate of pure water and 1-butanol aqueous solution drops and the Marangoni number, a series of empirical equations for predicting the evaporation rates of pure water and 1-butanol aqueous solution drops at the initial time as well as the equations for the evaporation rate of 1-butanol aqueous solution drop before the depletion of alcohol are derived. The results of these equations correspond fairly well to the experimental data.

River meanders and channel size

USGS Publications Warehouse

Williams, G.P.

1986-01-01

This study uses an enlarged data set to (1) compare measured meander geometry to that predicted by the Langbein and Leopold (1966) theory, (2) examine the frequency distribution of the ratio radius of curvature/channel width, and (3) derive 40 empirical equations (31 of which are original) involving meander and channel size features. The data set, part of which comes from publications by other authors, consists of 194 sites from a large variety of physiographic environments in various countries. The Langbein-Leopold sine-generated-curve theory for predicting radius of curvature agrees very well with the field data (78 sites). The ratio radius of curvature/channel width has a modal value in the range of 2 to 3, in accordance with earlier work; about one third of the 79 values is less than 2.0. The 40 empirical relations, most of which include only two variables, involve channel cross-section dimensions (bankfull area, width, and mean depth) and meander features (wavelength, bend length, radius of curvature, and belt width). These relations have very high correlation coefficients, most being in the range of 0.95-0.99. Although channel width traditionally has served as a scale indicator, bankfull cross-sectional area and mean depth also can be used for this purpose. ?? 1986.

Monastic incorporation of classical botanic medicines into the Renaissance pharmacopeia.

PubMed

Petrucelli, R J

1994-01-01

Ancient Greek physicians believed that health resulted from a balance of natural forces. Many, including Dioscorides, made compilations of plants and medicines derived from them, giving prominence to diuretics, cathartics and emetics. During the Roman Empire, although Greek physicians were highly valued, the Roman matron performed many medical functions and magic and astrology were increasingly used. In Judaic and later Christian societies disease was equated with divine disfavor. After the fall of Rome, the classical Greek medical texts were mainly preserved in Latin translation by the Benedictine monasteries, which were based around a patient infirmary, a herb garden and a library. Local plants were often substituted for the classical ones, however, and the compilations became confused and inaccurate. Greek medicine survived better in the remains of the Eastern Roman Empire, and benefitted from the influence of Arab medicine. Intellectual revival, when it came to Europe, did so on the fringes of the Moslem world, and Montpellier and Salerno were among the first of the new medical centers. Rather than relying on ancient experts, the new experimental method reported the tested effects of substances from identified plants. This advance was fostered by the foundation of universities and greatly aided by the later invention of the printing press, which also allowed wider dissemination of the classical texts.

The application of flow competence evaluations to the assessment of flood-flow velocities and stresses

NASA Technical Reports Server (NTRS)

Komar, Paul D.

1987-01-01

The concept of flow competence is generally employed to evaluate the velocities, discharges, and bottom stresses of river floods inferred from the size of the largest sediment particles transported. Flow competence has become an important tool for evaluating the hydraulics of exceptional floods on Earth, including those which eroded the Channeled Scabland of eastern Washington, and has potential for similar evaluations of the floods which carved the outflow channels on Mars. For the most part, flow-competence evaluations were empirical, based on data compiled from a variety of sources including major terrestrial floods caused by natural processes or dam failures. Such flow-competence relationships would appear to provide a straight-forward assessment of flood-flow stresses and velocities based on the maximum size of gravel and boulders transported. However, a re-examination of the data base and comparisons with measurements of selective entrainment and transport of gravel in rivers open to question such evaluations. Analyses of the forces acting on the grain during entrainment by pivoting, rolling, or sliding, an approach which focuses more on the physical processes than the purely empirical relationships can be demonstrated. These derived equations require further testing by flume and field measurements before being applied to flow-competence evaluations. Such tests are now underway.

Investigation of the Dirac Equation by Using the Conformable Fractional Derivative

NASA Astrophysics Data System (ADS)

Mozaffari, F. S.; Hassanabadi, H.; Sobhani, H.; Chung, W. S.

2018-05-01

In this paper,the Dirac equation is constructed using the conformable fractional derivative so that in its limit for the fractional parameter, the normal version is recovered. Then, the Cornell potential is considered as the interaction of the system. In this case, the wave function and the energy eigenvalue equation are derived with the aim of the bi-confluent Heun functions. use of the conformable fractional derivative is proven to lead to a branching treatment for the energy of the system. Such a treatment is obvious for small values of the fractional parameter, and a united value as the fractional parameter approaches unity.

Power-law spatial dispersion from fractional Liouville equation

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

Tarasov, Vasily E.

2013-10-15

A microscopic model in the framework of fractional kinetics to describe spatial dispersion of power-law type is suggested. The Liouville equation with the Caputo fractional derivatives is used to obtain the power-law dependence of the absolute permittivity on the wave vector. The fractional differential equations for electrostatic potential in the media with power-law spatial dispersion are derived. The particular solutions of these equations for the electric potential of point charge in this media are considered.

1/f Noise from nonlinear stochastic differential equations.

PubMed

Ruseckas, J; Kaulakys, B

2010-03-01

We consider a class of nonlinear stochastic differential equations, giving the power-law behavior of the power spectral density in any desirably wide range of frequency. Such equations were obtained starting from the point process models of 1/fbeta noise. In this article the power-law behavior of spectrum is derived directly from the stochastic differential equations, without using the point process models. The analysis reveals that the power spectrum may be represented as a sum of the Lorentzian spectra. Such a derivation provides additional justification of equations, expands the class of equations generating 1/fbeta noise, and provides further insights into the origin of 1/fbeta noise.

Exact solutions to the time-fractional differential equations via local fractional derivatives

NASA Astrophysics Data System (ADS)

Guner, Ozkan; Bekir, Ahmet

2018-01-01

This article utilizes the local fractional derivative and the exp-function method to construct the exact solutions of nonlinear time-fractional differential equations (FDEs). For illustrating the validity of the method, it is applied to the time-fractional Camassa-Holm equation and the time-fractional-generalized fifth-order KdV equation. Moreover, the exact solutions are obtained for the equations which are formed by different parameter values related to the time-fractional-generalized fifth-order KdV equation. This method is an reliable and efficient mathematical tool for solving FDEs and it can be applied to other non-linear FDEs.

How to Obtain the Covariant Form of Maxwell's Equations from the Continuity Equation

ERIC Educational Resources Information Center

Heras, Jose A.

2009-01-01

The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell's equations in which charge conservation is emphasized as the fundamental axiom underlying these equations.

Rapid inundation estimates at harbor scale using tsunami wave heights offshore simulation and Green's law approach

NASA Astrophysics Data System (ADS)

Gailler, Audrey; Hébert, Hélène; Loevenbruck, Anne

2013-04-01

Improvements in the availability of sea-level observations and advances in numerical modeling techniques are increasing the potential for tsunami warnings to be based on numerical model forecasts. Numerical tsunami propagation and inundation models are well developed and have now reached an impressive level of accuracy, especially in locations such as harbors where the tsunami waves are mostly amplified. In the framework of tsunami warning under real-time operational conditions, the main obstacle for the routine use of such numerical simulations remains the slowness of the numerical computation, which is strengthened when detailed grids are required for the precise modeling of the coastline response on the scale of an individual harbor. In fact, when facing the problem of the interaction of the tsunami wavefield with a shoreline, any numerical simulation must be performed over an increasingly fine grid, which in turn mandates a reduced time step, and the use of a fully non-linear code. Such calculations become then prohibitively time-consuming, which is clearly unacceptable in the framework of real-time warning. Thus only tsunami offshore propagation modeling tools using a single sparse bathymetric computation grid are presently included within the French Tsunami Warning Center (CENALT), providing rapid estimation of tsunami wave heights in high seas, and tsunami warning maps at western Mediterranean and NE Atlantic basins scale. We present here a preliminary work that performs quick estimates of the inundation at individual harbors from these deep wave heights simulations. The method involves an empirical correction relation derived from Green's law, expressing conservation of wave energy flux to extend the gridded wave field into the harbor with respect to the nearby deep-water grid node. The main limitation of this method is that its application to a given coastal area would require a large database of previous observations, in order to define the empirical parameters of the correction equation. As no such data (i.e., historical tide gage records of significant tsunamis) are available for the western Mediterranean and NE Atlantic basins, a set of synthetic mareograms is calculated for both fake and well-known historical tsunamigenic earthquakes in the area. This synthetic dataset is obtained through accurate numerical tsunami propagation and inundation modeling by using several nested bathymetric grids characterized by a coarse resolution over deep water regions and an increasingly fine resolution close to the shores (down to a grid cell size of 3m in some Mediterranean harbors). This synthetic dataset is then used to approximate the empirical parameters of the correction equation. Results of inundation estimates in several french Mediterranean harbors obtained with the fast "Green's law - derived" method are presented and compared with values given by time-consuming nested grids simulations.

Comparisons of ground motions from the 1999 Chi-Chi, earthquake with empirical predictions largely based on data from California

USGS Publications Warehouse

Boore, D.M.

2001-01-01

This article has the modest goal of comparing the ground motions recorded during the 1999 Chi-Chi, Taiwan, mainshock with predictions from four empirical-based equations commonly used for western North America; these empirical predictions are largely based on data from California. Comparisons are made for peak acceleration and 5%-damped response spectra at periods between 0.1 and 4 sec. The general finding is that the Chi-Chi ground motions are smaller than those predicted from the empirically based equations for periods less than about 1 sec by factors averaging about 0.4 but as small as 0.26 (depending on period, on which equation is used, and on whether the sites are assumed to be rock or soil). There is a trend for the observed motions to approach or even exceed the predicted motions for longer periods. Motions at similar distances (30-60 km) to the east and to the west of the fault differ dramatically at periods between about 2 and 20 sec: Long-duration wave trains are present on the motions to the west, and when normalized to similar amplitudes at short periods, the response spectra of the motions at the western stations are as much as five times larger than those of motions from eastern stations. The explanation for the difference is probably related to site and propagation effects; the western stations are on the Coastal Plain, whereas the eastern stations are at the foot of young and steep mountains, either in the relatively narrow Longitudinal Valley or along the eastern coast-the sediments underlying the eastern stations are probably shallower and have higher velocity than those under the western stations.

Predicting the particle size distribution of eroded sediment using artificial neural networks.

PubMed

Lagos-Avid, María Paz; Bonilla, Carlos A

2017-03-01

Water erosion causes soil degradation and nonpoint pollution. Pollutants are primarily transported on the surfaces of fine soil and sediment particles. Several soil loss models and empirical equations have been developed for the size distribution estimation of the sediment leaving the field, including the physically-based models and empirical equations. Usually, physically-based models require a large amount of data, sometimes exceeding the amount of available data in the modeled area. Conversely, empirical equations do not always predict the sediment composition associated with individual events and may require data that are not always available. Therefore, the objective of this study was to develop a model to predict the particle size distribution (PSD) of eroded soil. A total of 41 erosion events from 21 soils were used. These data were compiled from previous studies. Correlation and multiple regression analyses were used to identify the main variables controlling sediment PSD. These variables were the particle size distribution in the soil matrix, the antecedent soil moisture condition, soil erodibility, and hillslope geometry. With these variables, an artificial neural network was calibrated using data from 29 events (r 2 =0.98, 0.97, and 0.86; for sand, silt, and clay in the sediment, respectively) and then validated and tested on 12 events (r 2 =0.74, 0.85, and 0.75; for sand, silt, and clay in the sediment, respectively). The artificial neural network was compared with three empirical models. The network presented better performance in predicting sediment PSD and differentiating rain-runoff events in the same soil. In addition to the quality of the particle distribution estimates, this model requires a small number of easily obtained variables, providing a convenient routine for predicting PSD in eroded sediment in other pollutant transport models. Copyright © 2017 Elsevier B.V. All rights reserved.

On the Lennard-Jones and Devonshire theory for solid state thermodynamics

NASA Astrophysics Data System (ADS)

Lustig, Rolf

2017-06-01

The Lennard-Jones and Devonshire theory is developed into a self-consistent scheme for essentially complete thermodynamic information. The resulting methodology is compared with molecular simulation of the Lennard-Jones system in the face-centred-cubic solid state over an excessive range of state points. The thermal and caloric equations of state are in almost perfect agreement along the entire fluid-solid coexistence lines over more than six orders of magnitude in pressure. For homogeneous densities greater than twice the solid triple point density, the theory is essentially exact for derivatives of the Helmholtz energy. However, the fluid-solid phase equilibria are in disagreement with simulation. It is shown that the theory is in error by an additive constant to the Helmholtz energy A/(NkBT). Empirical inclusion of the error term makes all fluid-solid equilibria indistinguishable from exact results. Some arguments about the origin of the error are given.

Understanding the Evolution and Stability of the G-Matrix

PubMed Central

Arnold, Stevan J.; Bürger, Reinhard; Hohenlohe, Paul A.; Ajie, Beverley C.; Jones, Adam G.

2011-01-01

The G-matrix summarizes the inheritance of multiple, phenotypic traits. The stability and evolution of this matrix are important issues because they affect our ability to predict how the phenotypic traits evolve by selection and drift. Despite the centrality of these issues, comparative, experimental, and analytical approaches to understanding the stability and evolution of the G-matrix have met with limited success. Nevertheless, empirical studies often find that certain structural features of the matrix are remarkably constant, suggesting that persistent selection regimes or other factors promote stability. On the theoretical side, no one has been able to derive equations that would relate stability of the G-matrix to selection regimes, population size, migration, or to the details of genetic architecture. Recent simulation studies of evolving G-matrices offer solutions to some of these problems, as well as a deeper, synthetic understanding of both the G-matrix and adaptive radiations. PMID:18973631

The SZ-5 Spaceship Orbit Changes During The 2003 "Halloween Storm"

NASA Astrophysics Data System (ADS)

Huang, C.; Liu, D.; Guo, J.

2017-12-01

We analyse the daily major semi-axis variations of SZ-5 (ShenZhou V) spaceship during Oct. 20 to Dec. 30 in 2003, which includes the period of the 2003 "Halloween Storm". The significant orbital decay has been observed in late October due to the great solar flares and the severe geomagnetic storms. According to the equation of the air-drag-force on a spacecraft and the SZ-5 orbital decay information, we derive the thermospheric density relative changes during the 2003 "Halloween Storm" and compare the results with the Naval Research Laboratory Mass Spectrometer Incoherent Scatter Radar Extended Model (NRLMSISE-00). The analyses show that the thermosperic density (at the altitude of SZ-5, about 350 km) in storm time enchances to approximately three times as much as that in the quiet time but the empirical model may underestimate the thermospheric density changes during this severe storm.

The contribution of executive functions to emergent mathematic skills in preschool children.

PubMed

Espy, Kimberly Andrews; McDiarmid, Melanie M; Cwik, Mary F; Stalets, Melissa Meade; Hamby, Arlena; Senn, Theresa E

2004-01-01

Mathematical ability is related to both activation of the prefrontal cortex in neuroimaging studies of adults and to executive functions in school-age children. The purpose of this study was to determine whether executive functions were related to emergent mathematical proficiency in preschool children. Preschool children (N = 96) were administered an executive function battery that was reduced empirically to working memory (WM), inhibitory control (IC), and shifting abilities by calculating composite scores derived from principal component analysis. Both WM and IC predicted early arithmetic competency, with the observed relations robust after controlling statistically for child age, maternal education, and child vocabulary. Only IC accounted for unique variance in mathematical skills, after the contribution of other executive functions were controlled statistically as well. Specific executive functions are related to emergent mathematical proficiency in this age range. Longitudinal studies using structural equation modeling are necessary to better characterize these ontogenetic relations.

Constitutive Models for the Viscoelastic Behavior of Polyimide Membranes at Room and Deep Cryogenic Temperatures

DOE PAGES

Bhandarkar, Suhas; Betcher, Jacob; Smith, Ryan; ...

2016-06-30

Targets for ICF shots on NIF typically use ~500nm thin polyimide films with a coating of 25nm of aluminum as windows that seal the laser entrance hole or LEH. Their role is to contain the hohlraum gas and minimize the extraneous infra-red radiation getting in. This is necessary to precisely control the hohlraum thermal environment for layering inside the capsule with solid deuterium-tritium at 18K. Here, we use our empirical data on the bulging behavior of these foils under various different conditions to develop models to capture the complex viscoelastic behavior of these films at both ambient and cryogenic temperatures.more » The constitutive equations derived from these models give us the ability to quantitatively specify the film’s behavior during the fielding of these targets and set the best parameters for new target designs.« less

Fracture study of windshield glass panes

NASA Technical Reports Server (NTRS)

Yeh, H. Y.

1987-01-01

The major stresses which cause crack propagation in windshield glass panes are induced by bending moments which result from the pressure differentials across the panes. Hence the stress intensity factors for the finite plate with the semi-elliptical surface flaw and edge crack under the bending moments are examined. The results show that the crack growth will be upperbound if it is computed by using the stress intensity factor for the finite plate with the edge crack subjected to pure bending moments. Furthermore, if the ratio of crack depth to plate thickness, a/t, is within 0.3, the stress intensity factor can be conservatively assumed to be constant at the value of a/t equal to zero. A simplified equation to predict the structural life of glass panes is derived based on constant stress intensity factor. The accuracy of structural life is mainly dependent on how close the empirical parameter, m, can be estimated.

Preliminary study of soil permeability properties using principal component analysis

NASA Astrophysics Data System (ADS)

Yulianti, M.; Sudriani, Y.; Rustini, H. A.

2018-02-01

Soil permeability measurement is undoubtedly important in carrying out soil-water research such as rainfall-runoff modelling, irrigation water distribution systems, etc. It is also known that acquiring reliable soil permeability data is rather laborious, time-consuming, and costly. Therefore, it is desirable to develop the prediction model. Several studies of empirical equations for predicting permeability have been undertaken by many researchers. These studies derived the models from areas which soil characteristics are different from Indonesian soil, which suggest a possibility that these permeability models are site-specific. The purpose of this study is to identify which soil parameters correspond strongly to soil permeability and propose a preliminary model for permeability prediction. Principal component analysis (PCA) was applied to 16 parameters analysed from 37 sites consist of 91 samples obtained from Batanghari Watershed. Findings indicated five variables that have strong correlation with soil permeability, and we recommend a preliminary permeability model, which is potential for further development.

A phenomenological model for simulating the chemo-responsive shape memory effect in polymers undergoing a permeation transition

NASA Astrophysics Data System (ADS)

Lu, Haibao; Huang, Wei Min; Leng, Jinsong

2014-04-01

We present a phenomenological model for studying the constitutive relations and working mechanism of the chemo-responsive shape memory effect (SME) in shape memory polymers (SMPs). On the basis of the solubility parameter equation, diffusion model and permeation transition model, a phenomenological model is derived for quantitatively identifying the influential factors in the chemically induced SME in SMPs. After this, a permeability parallel model and series model are implemented in order to couple the constitutive relations of the permeability coefficient, stress and relaxation time as a function of stretch, separately. The inductive effect of the permeability transition on the transition temperature is confirmed as the driving force for the chemo-responsive SME. Furthermore, the analytical result from the phenomenological model is compared with the available experimental results and the simulation of a semi-empirical model reported in the literature for verification.

Computational Approaches to the Chemical Equilibrium Constant in Protein-ligand Binding.

PubMed

Montalvo-Acosta, Joel José; Cecchini, Marco

2016-12-01

The physiological role played by protein-ligand recognition has motivated the development of several computational approaches to the ligand binding affinity. Some of them, termed rigorous, have a strong theoretical foundation but involve too much computation to be generally useful. Some others alleviate the computational burden by introducing strong approximations and/or empirical calibrations, which also limit their general use. Most importantly, there is no straightforward correlation between the predictive power and the level of approximation introduced. Here, we present a general framework for the quantitative interpretation of protein-ligand binding based on statistical mechanics. Within this framework, we re-derive self-consistently the fundamental equations of some popular approaches to the binding constant and pinpoint the inherent approximations. Our analysis represents a first step towards the development of variants with optimum accuracy/efficiency ratio for each stage of the drug discovery pipeline. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Semi-empirical anzatz for Helmholtz free energy calculation: Thermal properties of silver along shock Hugoniot

NASA Astrophysics Data System (ADS)

Joshi, R. H.; Thakore, B. Y.; Bhatt, N. K.; Vyas, P. R.; Jani, A. R.

2018-02-01

A density functional theory along with electronic contribution is used to compute quasiharmonic total energy for silver, whereas explicit phonon anharmonic contribution is added through perturbative term in temperature. Within the Mie-Grüneisen approach, we propose a consistent computational scheme for calculating various thermophysical properties of a substance, in which the required Grüneisen parameter γth is calculated from the knowledge of binding energy. The present study demonstrates that no separate relation for volume dependence for γth is needed, and complete thermodynamics under simultaneous high-temperature and high-pressure condition can be derived in a consistent manner. We have calculated static and dynamic equation of states and some important thermodynamic properties along the shock Hugoniot. A careful examination of temperature dependence of Grüneisen parameter reveals the importance of temperature-effect on various thermal properties.

Storm time global thermosphere: A driven-dissipative thermodynamic system

NASA Astrophysics Data System (ADS)

Burke, W. J.; Lin, C. S.; Hagan, M. P.; Huang, C. Y.; Weimer, D. R.; Wise, J. O.; Gentile, L. C.; Marcos, F. A.

2009-06-01

Orbit-averaged mass densities $\\overline{\\rho and exospheric temperatures $\\overline{T ∞ inferred from measurements by accelerometers on the Gravity Recovery and Climate Experiment (GRACE) satellites are used to investigate global energy Eth and power Πth inputs to the thermosphere during two complex magnetic storms. Measurements show $\\overline{\\rho, $\\overline{T ∞, and Eth rising from and returning to prevailing baselines as the magnetospheric electric field $\\varepsilon$ VS and the Dst index wax and wane. Observed responses of Eth and $\\overline{T ∞ to $\\varepsilon$ VS driving suggest that the storm time thermosphere evolves as a driven-but-dissipative thermodynamic system, described by a first-order differential equation that is identical in form to that governing the behavior of Dst. Coupling and relaxation coefficients of the Eth, $\\overline{T ∞, and Dst equations are established empirically. Numerical solutions of the equations for $\\overline{T ∞ and Eth are shown to agree with GRACE data during large magnetic storms. Since $\\overline{T ∞ and Dst have the same $\\varepsilon$ VS driver, it is possible to combine their governing equations to obtain estimates of storm time thermospheric parameters, even when lacking information about interplanetary conditions. This approach has the potential for significantly improving the performance of operational models used to calculate trajectories of satellites and space debris and is also useful for developing forensic reconstructions of past magnetic storms. The essential correctness of the approach is supported by agreement between thermospheric power inputs calculated from both GRACE-based estimates of Eth and the Weimer Poynting flux model originally derived from electric and magnetic field measurements acquired by the Dynamics Explorer 2 satellite.

A gradual update method for simulating the steady-state solution of stiff differential equations in metabolic circuits.

PubMed

Shiraishi, Emi; Maeda, Kazuhiro; Kurata, Hiroyuki

2009-02-01

Numerical simulation of differential equation systems plays a major role in the understanding of how metabolic network models generate particular cellular functions. On the other hand, the classical and technical problems for stiff differential equations still remain to be solved, while many elegant algorithms have been presented. To relax the stiffness problem, we propose new practical methods: the gradual update of differential-algebraic equations based on gradual application of the steady-state approximation to stiff differential equations, and the gradual update of the initial values in differential-algebraic equations. These empirical methods show a high efficiency for simulating the steady-state solutions for the stiff differential equations that existing solvers alone cannot solve. They are effective in extending the applicability of dynamic simulation to biochemical network models.

Effective electronic-only Kohn–Sham equations for the muonic molecules

NASA Astrophysics Data System (ADS)

Rayka, Milad; Goli, Mohammad; Shahbazian, Shant

A set of effective electronic-only Kohn-Sham (EKS) equations are derived for the muonic molecules (containing a positively charged muon), which are completely equivalent to the coupled electronic-muonic Kohn-Sham equations derived previously within the framework of the Nuclear-Electronic Orbital density functional theory (NEO-DFT). The EKS equations contain effective non-coulombic external potentials depending on parameters describing muon vibration, which are optimized during the solution of the EKS equations making muon KS orbital reproducible. It is demonstrated that the EKS equations are derivable from a certain class of effective electronic Hamiltonians through applying the usual Hohenberg-Kohn theorems revealing a duality between the NEO-DFT and the effective electronic-only DFT methodologies. The EKS equations are computationally applied to a small set of muoniated organic radicals and it is demonstrated that a mean effective potential maybe derived for this class of muonic species while an electronic basis set is also designed for the muon. These computational ingredients are then applied to muoniated ferrocenyl radicals, which had been previously detected experimentally through adding muonium atom to ferrocene. In line with previous computational studies, from the six possible species the staggered conformer, where the muon is attached to the exo position of the cyclopentadienyl ring, is deduced to be the most stable ferrocenyl radical.

Effective electronic-only Kohn-Sham equations for the muonic molecules.

PubMed

Rayka, Milad; Goli, Mohammad; Shahbazian, Shant

2018-03-28

A set of effective electronic-only Kohn-Sham (EKS) equations are derived for the muonic molecules (containing a positively charged muon), which are completely equivalent to the coupled electronic-muonic Kohn-Sham equations derived previously within the framework of the nuclear-electronic orbital density functional theory (NEO-DFT). The EKS equations contain effective non-coulombic external potentials depending on parameters describing the muon's vibration, which are optimized during the solution of the EKS equations making the muon's KS orbital reproducible. It is demonstrated that the EKS equations are derivable from a certain class of effective electronic Hamiltonians through applying the usual Hohenberg-Kohn theorems revealing a "duality" between the NEO-DFT and the effective electronic-only DFT methodologies. The EKS equations are computationally applied to a small set of muoniated organic radicals and it is demonstrated that a mean effective potential may be derived for this class of muonic species while an electronic basis set is also designed for the muon. These computational ingredients are then applied to muoniated ferrocenyl radicals, which had been previously detected experimentally through adding a muonium atom to ferrocene. In line with previous computational studies, from the six possible species, the staggered conformer, where the muon is attached to the exo position of the cyclopentadienyl ring, is deduced to be the most stable ferrocenyl radical.

Estimating aspen crown fuels in northeastern Minnesota.

Treesearch

Robert M. Loomis; Peter J. Roussopoulos

1978-01-01

An application section presents tables for estimating foliage and branchwood (wood plus bark) of aspen tree crowns; the branchwood is subdivided by (1) living and dead material and by (2) living material alone into diameter size groups. A documentation section describes the derivation of equations and compares the equations derived with those derived by other...

Estimating Dynamical Systems: Derivative Estimation Hints From Sir Ronald A. Fisher.

PubMed

Deboeck, Pascal R

2010-08-06

The fitting of dynamical systems to psychological data offers the promise of addressing new and innovative questions about how people change over time. One method of fitting dynamical systems is to estimate the derivatives of a time series and then examine the relationships between derivatives using a differential equation model. One common approach for estimating derivatives, Local Linear Approximation (LLA), produces estimates with correlated errors. Depending on the specific differential equation model used, such correlated errors can lead to severely biased estimates of differential equation model parameters. This article shows that the fitting of dynamical systems can be improved by estimating derivatives in a manner similar to that used to fit orthogonal polynomials. Two applications using simulated data compare the proposed method and a generalized form of LLA when used to estimate derivatives and when used to estimate differential equation model parameters. A third application estimates the frequency of oscillation in observations of the monthly deaths from bronchitis, emphysema, and asthma in the United Kingdom. These data are publicly available in the statistical program R, and functions in R for the method presented are provided.

Empirically Derived Combinations of Tools and Clinical Cutoffs: An Illustrative Case with a Sample of Culturally/Linguistically Diverse Children

ERIC Educational Resources Information Center

Oetting, Janna B.; Cleveland, Lesli H.; Cope, Robert F., III

2008-01-01

Purpose: Using a sample of culturally/linguistically diverse children, we present data to illustrate the value of empirically derived combinations of tools and cutoffs for determining eligibility in child language impairment. Method: Data were from 95 4- and 6-year-olds (40 African American, 55 White; 18 with language impairment, 77 without) who…

Are Women Over-Represented in Dead-End Jobs? A Swedish Study Using Empirically Derived Measures of Dead-End Jobs

ERIC Educational Resources Information Center

Bihagen, Erik; Ohls, Marita

2007-01-01

It has been claimed that women experience fewer career opportunities than men do mainly because they are over-represented in "Dead-end Jobs" (DEJs). Using Swedish panel data covering 1.1 million employees with the same employer in 1999 and 2003, measures of DEJ are empirically derived from analyses of wage mobility. The results indicate…

Diagnostic Classification of Eating Disorders in Children and Adolescents: How Does DSM-IV-TR Compare to Empirically-Derived Categories?

ERIC Educational Resources Information Center

Eddy, Kamryn T.; Le Grange, Daniel; Crosby, Ross D.; Hoste, Renee Rienecke; Doyle, Angela Celio; Smyth, Angela; Herzog, David B.

2010-01-01

Objective: The purpose of this study was to empirically derive eating disorder phenotypes in a clinical sample of children and adolescents using latent profile analysis (LPA), and to compare these latent profile (LP) groups to the DSM-IV-TR eating disorder categories. Method: Eating disorder symptom data collected from 401 youth (aged 7 through 19…

Energy-state formulation of lumped volume dynamic equations with application to a simplified free piston Stirling engine

NASA Technical Reports Server (NTRS)

Daniele, C. J.; Lorenzo, C. F.

1979-01-01

Lumped volume dynamic equations are derived using an energy state formulation. This technique requires that kinetic and potential energy state functions be written for the physical system being investigated. To account for losses in the system, a Rayleigh dissipation function is formed. Using these functions, a Lagrangian is formed and using Lagrange's equation, the equations of motion for the system are derived. The results of the application of this technique to a lumped volume are used to derive a model for the free piston Stirling engine. The model was simplified and programmed on an analog computer. Results are given comparing the model response with experimental data.

Energy-state formulation of lumped volume dynamic equations with application to a simplified free piston Stirling engine

NASA Technical Reports Server (NTRS)

Daniele, C. J.; Lorenzo, C. F.

1979-01-01

Lumped volume dynamic equations are derived using an energy-state formulation. This technique requires that kinetic and potential energy state functions be written for the physical system being investigated. To account for losses in the system, a Rayleigh dissipation function is also formed. Using these functions, a Lagrangian is formed and using Lagrange's equation, the equations of motion for the system are derived. The results of the application of this technique to a lumped volume are used to derive a model for the free-piston Stirling engine. The model was simplified and programmed on an analog computer. Results are given comparing the model response with experimental data.

[Mobbing: a meta-analysis and integrative model of its antecedents and consequences].

PubMed

Topa Cantisano, Gabriela; Depolo, Marco; Morales Domínguez, J Francisco

2007-02-01

Although mobbing has been extensively studied, empirical research has not led to firm conclusions regarding its antecedents and consequences, both at personal and organizational levels. An extensive literature search yielded 86 empirical studies with 93 samples. The matrix correlation obtained through meta-analytic techniques was used to test a structural equation model. Results supported hypotheses regarding organizational environmental factors as main predictors of mobbing.

How to Quantify Deterministic and Random Influences on the Statistics of the Foreign Exchange Market

NASA Astrophysics Data System (ADS)

Friedrich, R.; Peinke, J.; Renner, Ch.

2000-05-01

It is shown that price changes of the U.S. dollar-German mark exchange rates upon different delay times can be regarded as a stochastic Marcovian process. Furthermore, we show how Kramers-Moyal coefficients can be estimated from the empirical data. Finally, we present an explicit Fokker-Planck equation which models very precisely the empirical probability distributions, in particular, their non-Gaussian heavy tails.

Quantitative model of the growth of floodplains by vertical accretion

USGS Publications Warehouse

Moody, J.A.; Troutman, B.M.

2000-01-01

A simple one-dimensional model is developed to quantitatively predict the change in elevation, over a period of decades, for vertically accreting floodplains. This unsteady model approximates the monotonic growth of a floodplain as an incremental but constant increase of net sediment deposition per flood for those floods of a partial duration series that exceed a threshold discharge corresponding to the elevation of the floodplain. Sediment deposition from each flood increases the elevation of the floodplain and consequently the magnitude of the threshold discharge resulting in a decrease in the number of floods and growth rate of the floodplain. Floodplain growth curves predicted by this model are compared to empirical growth curves based on dendrochronology and to direct field measurements at five floodplain sites. The model was used to predict the value of net sediment deposition per flood which best fits (in a least squares sense) the empirical and field measurements; these values fall within the range of independent estimates of the net sediment deposition per flood based on empirical equations. These empirical equations permit the application of the model to estimate of floodplain growth for other floodplains throughout the world which do not have detailed data of sediment deposition during individual floods. Copyright (C) 2000 John Wiley and Sons, Ltd.

Tap density equations of granular powders based on the rate process theory and the free volume concept.

PubMed

Hao, Tian

2015-02-28

The tap density of a granular powder is often linked to the flowability via the Carr index that measures how tight a powder can be packed, under an assumption that more easily packed powders usually flow poorly. Understanding how particles are packed is important for revealing why a powder flows better than others. There are two types of empirical equations that were proposed to fit the experimental data of packing fractions vs. numbers of taps in the literature: the inverse logarithmic and the stretched exponential. Using the rate process theory and the free volume concept under the assumption that particles will obey similar thermodynamic laws during the tapping process if the "granular temperature" is defined in a different way, we obtain the tap density equations, and they are reducible to the two empirical equations currently widely used in literature. Our equations could potentially fit experimental data better with an additional adjustable parameter. The tapping amplitude and frequency, the weight of the granular materials, and the environmental temperature are grouped into this parameter that weighs the pace of the packing process. The current results, in conjunction with our previous findings, may imply that both "dry" (granular) and "wet" (colloidal and polymeric) particle systems are governed by the same physical mechanisms in term of the role of the free volume and how particles behave (a rate controlled process).

Estimation of air-water gas exchange coefficient in a shallow lagoon based on 222Rn mass balance.

PubMed

Cockenpot, S; Claude, C; Radakovitch, O

2015-05-01

The radon-222 mass balance is now commonly used to quantify water fluxes due to Submarine Groundwater Discharge (SGD) in coastal areas. One of the main loss terms of this mass balance, the radon evasion to the atmosphere, is based on empirical equations. This term is generally estimated using one among the many empirical equations describing the gas transfer velocity as a function of wind speed that have been proposed in the literature. These equations were, however, mainly obtained from areas of deep water and may be less appropriate for shallow areas. Here, we calculate the radon mass balance for a windy shallow coastal lagoon (mean depth of 6m and surface area of 1.55*10(8) m(2)) and use these data to estimate the radon loss to the atmosphere and the corresponding gas transfer velocity. We present new equations, adapted to our shallow water body, to express the gas transfer velocity as a function of wind speed at 10 m height (wind range from 2 to 12.5 m/s). When compared with those from the literature, these equations fit particularly well with the one of Kremer et al. (2003). Finally, we emphasize that some gas transfer exchange may always occur, even for conditions without wind. Copyright © 2015 Elsevier Ltd. All rights reserved.

Semi-empirical airframe noise prediction model

NASA Technical Reports Server (NTRS)

Hersh, A. S.; Putnam, T. W.; Lasagna, P. L.; Burcham, F. W., Jr.

1976-01-01

A semi-empirical maximum overall sound pressure level (OASPL) airframe noise model was derived. The noise radiated from aircraft wings and flaps was modeled by using the trailing-edge diffracted quadrupole sound theory derived by Ffowcs Williams and Hall. The noise radiated from the landing gear was modeled by using the acoustic dipole sound theory derived by Curle. The model was successfully correlated with maximum OASPL flyover noise measurements obtained at the NASA Dryden Flight Research Center for three jet aircraft - the Lockheed JetStar, the Convair 990, and the Boeing 747 aircraft.

Comparisons of Multilevel Modeling and Structural Equation Modeling Approaches to Actor-Partner Interdependence Model.

PubMed

Hong, Sehee; Kim, Soyoung

2018-01-01

There are basically two modeling approaches applicable to analyzing an actor-partner interdependence model: the multilevel modeling (hierarchical linear model) and the structural equation modeling. This article explains how to use these two models in analyzing an actor-partner interdependence model and how these two approaches work differently. As an empirical example, marital conflict data were used to analyze an actor-partner interdependence model. The multilevel modeling and the structural equation modeling produced virtually identical estimates for a basic model. However, the structural equation modeling approach allowed more realistic assumptions on measurement errors and factor loadings, rendering better model fit indices.

Improvement of Method for Estimation of Site Amplification Factor Based on Average Shear-wave Velocity of Ground

NASA Astrophysics Data System (ADS)

Yamaguchi, Makoto; Midorikawa, Saburoh

The empirical equation for estimating the site amplification factor of ground motion by the average shear-wave velocity of ground (AVS) is examined. In the existing equations, the coefficient on dependence of the amplification factor on the AVS was treated as constant. The analysis showed that the coefficient varies with change of the AVS for short periods. A new estimation equation was proposed considering the dependence on the AVS. The new equation can represent soil characteristics that the softer soil has the longer predominant period, and can make better estimations for short periods than the existing method.

Diffusion equations and the time evolution of foreign exchange rates

NASA Astrophysics Data System (ADS)

Figueiredo, Annibal; de Castro, Marcio T.; da Fonseca, Regina C. B.; Gleria, Iram

2013-10-01

We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers-Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.

Nonlinear Equations of Motion for Cantilever Rotor Blades in Hover with Pitch Link Flexibility, Twist, Precone, Droop, Sweep, Torque Offset, and Blade Root Offset

NASA Technical Reports Server (NTRS)

Hodges, D. H.

1976-01-01

Nonlinear equations of motion for a cantilever rotor blade are derived for the hovering flight condition. The blade is assumed to have twist, precone, droop, sweep, torque offset and blade root offset, and the elastic axis and the axes of center of mass, tension, and aerodynamic center coincident at the quarter chord. The blade is cantilevered in bending, but has a torsional root spring to simulate pitch link flexibility. Aerodynamic forces acting on the blade are derived from strip theory based on quasi-steady two-dimensional airfoil theory. The equations are hybrid, consisting of one integro-differential equation for root torsion and three integro-partial differential equations for flatwise and chordwise bending and elastic torsion. The equations are specialized for a uniform blade and reduced to nonlinear ordinary differential equations by Galerkin's method. They are linearized for small perturbation motions about the equilibrium operating condition. Modal analysis leads to formulation of a standard eigenvalue problem where the elements of the stability matrix depend on the solution of the equilibrium equations. Two different forms of the root torsion equation are derived that yield virtually identical numerical results. This provides a reasonable check for the accuracy of the equations.

Friction in rail guns

NASA Technical Reports Server (NTRS)

Kay, P. K.

1984-01-01

The influence of friction is included in the present equations describing the performance of an inductively driven rail gun. These equations, which have their basis in an empirical formulation, are applied to results from two different experiments. Only an approximate physical description of the problem is attempted, in view of the complexity of details in the interaction among forces of this magnitude over time periods of the order of milisecs.

Steady-state solution of the semi-empirical diffusion equation for area sources. [air pollution studies

NASA Technical Reports Server (NTRS)

Lebedeff, S. A.; Hameed, S.

1975-01-01

The problem investigated can be solved exactly in a simple manner if the equations are written in terms of a similarity variable. The exact solution is used to explore two questions of interest in the modelling of urban air pollution, taking into account the distribution of surface concentration downwind of an area source and the distribution of concentration with height.

Empirical solution of Green-Ampt equation using soil conservation service - curve number values

NASA Astrophysics Data System (ADS)

Grimaldi, S.; Petroselli, A.; Romano, N.

2012-09-01

The Soil Conservation Service - Curve Number (SCS-CN) method is a popular widely used rainfall-runoff model for quantifying the total stream-flow volume generated by storm rainfall, but its application is not appropriate for sub-daily resolutions. In order to overcome this drawback, the Green-Ampt (GA) infiltration equation is considered and an empirical solution is proposed and evaluated. The procedure, named CN4GA (Curve Number for Green-Ampt), aims to calibrate the Green-Ampt model parameters distributing in time the global information provided by the SCS-CN method. The proposed procedure is evaluated by analysing observed rainfall-runoff events; results show that CN4GA seems to provide better agreement with the observed hydrographs respect to the classic SCS-CN method.

Prediction of unsteady transonic flow around missile configurations

NASA Technical Reports Server (NTRS)

Nixon, D.; Reisenthel, P. H.; Torres, T. O.; Klopfer, G. H.

1990-01-01

This paper describes the preliminary development of a method for predicting the unsteady transonic flow around missiles at transonic and supersonic speeds, with the final goal of developing a computer code for use in aeroelastic calculations or during maneuvers. The basic equations derived for this method are an extension of those derived by Klopfer and Nixon (1989) for steady flow and are a subset of the Euler equations. In this approach, the five Euler equations are reduced to an equation similar to the three-dimensional unsteady potential equation, and a two-dimensional Poisson equation. In addition, one of the equations in this method is almost identical to the potential equation for which there are well tested computer codes, allowing the development of a prediction method based in part on proved technology.

Use of digital land-cover data from the Landsat satellite in estimating streamflow characteristics in the Cumberland Plateau of Tennessee

USGS Publications Warehouse

Hollyday, E.F.; Hansen, G.R.

1983-01-01

Streamflow may be estimated with regression equations that relate streamflow characteristics to characteristics of the drainage basin. A statistical experiment was performed to compare the accuracy of equations using basin characteristics derived from maps and climatological records (control group equations) with the accuracy of equations using basin characteristics derived from Landsat data as well as maps and climatological records (experimental group equations). Results show that when the equations in both groups are arranged into six flow categories, there is no substantial difference in accuracy between control group equations and experimental group equations for this particular site where drainage area accounts for more than 90 percent of the variance in all streamflow characteristics (except low flows and most annual peak logarithms). (USGS)