Maximum entropy production principle for geostrophic turbulence

NASA Astrophysics Data System (ADS)

Sommeria, J.; Bouchet, F.; Chavanis, P. H.

2003-04-01

In 2D turbulence, complex stirring leads to the formation of steady organized states, once fine scale fluctuations have been filtered out. This self-organization can be explained in terms of statistical equilibrium for vorticity, as the most likely outcome of vorticity parcel rearrangements with the constraints of the conservation laws. A mixing entropy describing the vorticity rearrangements is introduced. Extension to the shallow water system has been proposed by Chavanis P.H. and Sommeria J. (2002), Phys. Rev. E. Generalization to multi-layer geostrophic flows is formally straightforward. Outside equilibrium, eddy fluxes should drive the system toward equilibrium, in the spirit of non equilibrium linear thermodynamics. This can been formalized in terms of a principle of maximum entropy production (MEP), as shown by Robert and Sommeria (1991), Phys. Rev. Lett. 69. Then a parameterization of eddy fluxes is obtained, involving an eddy diffusivity plus a drift term acting at larger scale. These two terms balance each other at equilibrium, resulting in a non trivial steady flow, which is the mean state of the statistical equilibrium. Applications of this eddy parametrization will be presented, in the context of oceanic circulation and Jupiter's Great Red Spot. Quantitative tests will be discussed, obtained by comparisons with direct numerical simulations. Kinetic models, inspired from plasma physics, provide a more precise description of the relaxation toward equilibrium, as shown by Chavanis P.H. 2000 ``Quasilinear theory of the 2D Euler equation'', Phys. Rev. Lett. 84. This approach provides relaxation equations with a form similar to the MEP, but not identical. In conclusion, the MEP provides the right trends of the system but its precise justification remains elusive.

Analysis of non-equilibrium phenomena in inductively coupled plasma generators

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

Zhang, W.; Panesi, M., E-mail: mpanesi@illinois.edu; Lani, A.

This work addresses the modeling of non-equilibrium phenomena in inductively coupled plasma discharges. In the proposed computational model, the electromagnetic induction equation is solved together with the set of Navier-Stokes equations in order to compute the electromagnetic and flow fields, accounting for their mutual interaction. Semi-classical statistical thermodynamics is used to determine the plasma thermodynamic properties, while transport properties are obtained from kinetic principles, with the method of Chapman and Enskog. Particle ambipolar diffusive fluxes are found by solving the Stefan-Maxwell equations with a simple iterative method. Two physico-mathematical formulations are used to model the chemical reaction processes: (1) Amore » Local Thermodynamics Equilibrium (LTE) formulation and (2) a thermo-chemical non-equilibrium (TCNEQ) formulation. In the TCNEQ model, thermal non-equilibrium between the translational energy mode of the gas and the vibrational energy mode of individual molecules is accounted for. The electronic states of the chemical species are assumed in equilibrium with the vibrational temperature, whereas the rotational energy mode is assumed to be equilibrated with translation. Three different physical models are used to account for the coupling of chemistry and energy transfer processes. Numerical simulations obtained with the LTE and TCNEQ formulations are used to characterize the extent of non-equilibrium of the flow inside the Plasmatron facility at the von Karman Institute. Each model was tested using different kinetic mechanisms to assess the sensitivity of the results to variations in the reaction parameters. A comparison of temperatures and composition profiles at the outlet of the torch demonstrates that the flow is in non-equilibrium for operating conditions characterized by pressures below 30 000 Pa, frequency 0.37 MHz, input power 80 kW, and mass flow 8 g/s.« less

Analysis of non-equilibrium phenomena in inductively coupled plasma generators

NASA Astrophysics Data System (ADS)

Zhang, W.; Lani, A.; Panesi, M.

2016-07-01

This work addresses the modeling of non-equilibrium phenomena in inductively coupled plasma discharges. In the proposed computational model, the electromagnetic induction equation is solved together with the set of Navier-Stokes equations in order to compute the electromagnetic and flow fields, accounting for their mutual interaction. Semi-classical statistical thermodynamics is used to determine the plasma thermodynamic properties, while transport properties are obtained from kinetic principles, with the method of Chapman and Enskog. Particle ambipolar diffusive fluxes are found by solving the Stefan-Maxwell equations with a simple iterative method. Two physico-mathematical formulations are used to model the chemical reaction processes: (1) A Local Thermodynamics Equilibrium (LTE) formulation and (2) a thermo-chemical non-equilibrium (TCNEQ) formulation. In the TCNEQ model, thermal non-equilibrium between the translational energy mode of the gas and the vibrational energy mode of individual molecules is accounted for. The electronic states of the chemical species are assumed in equilibrium with the vibrational temperature, whereas the rotational energy mode is assumed to be equilibrated with translation. Three different physical models are used to account for the coupling of chemistry and energy transfer processes. Numerical simulations obtained with the LTE and TCNEQ formulations are used to characterize the extent of non-equilibrium of the flow inside the Plasmatron facility at the von Karman Institute. Each model was tested using different kinetic mechanisms to assess the sensitivity of the results to variations in the reaction parameters. A comparison of temperatures and composition profiles at the outlet of the torch demonstrates that the flow is in non-equilibrium for operating conditions characterized by pressures below 30 000 Pa, frequency 0.37 MHz, input power 80 kW, and mass flow 8 g/s.

Equation of state of detonation products based on statistical mechanical theory

NASA Astrophysics Data System (ADS)

Zhao, Yanhong; Liu, Haifeng; Zhang, Gongmu; Song, Haifeng

2015-06-01

The equation of state (EOS) of gaseous detonation products is calculated using Ross's modification of hard-sphere variation theory and the improved one-fluid van der Waals mixture model. The condensed phase of carbon is a mixture of graphite, diamond, graphite-like liquid and diamond-like liquid. For a mixed system of detonation products, the free energy minimization principle is used to calculate the equilibrium compositions of detonation products by solving chemical equilibrium equations. Meanwhile, a chemical equilibrium code is developed base on the theory proposed in this article, and then it is used in the three typical calculations as follow: (i) Calculation for detonation parameters of explosive, the calculated values of detonation velocity, the detonation pressure and the detonation temperature are in good agreement with experimental ones. (ii) Calculation for isentropic unloading line of RDX explosive, whose starting points is the CJ point. Comparison with the results of JWL EOS it is found that the calculated value of gamma is monotonically decreasing using the presented theory in this paper, while double peaks phenomenon appears using JWL EOS.

Equation of state of detonation products based on statistical mechanical theory

NASA Astrophysics Data System (ADS)

Zhao, Yanhong; Liu, Haifeng; Zhang, Gongmu; Song, Haifeng; Iapcm Team

2013-06-01

The equation of state (EOS) of gaseous detonation products is calculated using Ross's modification of hard-sphere variation theory and the improved one-fluid van der Waals mixture model. The condensed phase of carbon is a mixture of graphite, diamond, graphite-like liquid and diamond-like liquid. For a mixed system of detonation products, the free energy minimization principle is used to calculate the equilibrium compositions of detonation products by solving chemical equilibrium equations. Meanwhile, a chemical equilibrium code is developed base on the theory proposed in this article, and then it is used in the three typical calculations as follow: (i) Calculation for detonation parameters of explosive, the calculated values of detonation velocity, the detonation pressure and the detonation temperature are in good agreement with experimental ones. (ii) Calculation for isentropic unloading line of RDX explosive, whose starting points is the CJ point. Comparison with the results of JWL EOS it is found that the calculated value of gamma is monotonically decreasing using the presented theory in this paper, while double peaks phenomenon appears using JWL EOS.

Non-equilibrium statistical mechanics theory for the large scales of geophysical flows

NASA Astrophysics Data System (ADS)

Eric, S.; Bouchet, F.

2010-12-01

The aim of any theory of turbulence is to understand the statistical properties of the velocity field. As a huge number of degrees of freedom is involved, statistical mechanics is a natural approach. The self-organization of two-dimensional and geophysical turbulent flows is addressed based on statistical mechanics methods. We discuss classical and recent works on this subject; from the statistical mechanics basis of the theory up to applications to Jupiter’s troposphere and ocean vortices and jets. The equilibrium microcanonical measure is built from the Liouville theorem. Important statistical mechanics concepts (large deviations, mean field approach) and thermodynamic concepts (ensemble inequivalence, negative heat capacity) are briefly explained and used to predict statistical equilibria for turbulent flows. This is applied to make quantitative models of two-dimensional turbulence, the Great Red Spot and other Jovian vortices, ocean jets like the Gulf-Stream, and ocean vortices. A detailed comparison between these statistical equilibria and real flow observations will be discussed. We also present recent results for non-equilibrium situations, for which forces and dissipation are in a statistical balance. As an example, the concept of phase transition allows us to describe drastic changes of the whole system when a few external parameters are changed. F. Bouchet and E. Simonnet, Random Changes of Flow Topology in Two-Dimensional and Geophysical Turbulence, Physical Review Letters 102 (2009), no. 9, 094504-+. F. Bouchet and J. Sommeria, Emergence of intense jets and Jupiter's Great Red Spot as maximum-entropy structures, Journal of Fluid Mechanics 464 (2002), 165-207. A. Venaille and F. Bouchet, Ocean rings and jets as statistical equilibrium states, submitted to JPO F. Bouchet and A. Venaille, Statistical mechanics of two-dimensional and geophysical flows, submitted to Physics Reports Non-equilibrium phase transitions for the 2D Navier-Stokes equations with stochastic forces (time series and probability density functions (PDFs) of the modulus of the largest scale Fourrier component, showing bistability between dipole and unidirectional flows). This bistability is predicted by statistical mechanics.

Analyzing the equilibrium states of a quasi-neutral spatially inhomogeneous system of charges above a liquid dielectric film based on the first principles of quantum statistics

NASA Astrophysics Data System (ADS)

Lytvynenko, D. M.; Slyusarenko, Yu V.

2017-08-01

A theory of quasi-neutral equilibrium states of charges above a liquid dielectric surface is developed. This theory is based on the first principles of quantum statistics for systems comprising many identical particles. The proposed approach involves applying the variational principle, modified for the considered systems, and the Thomas-Fermi model. In the terms of the developed theory self-consistency equations are obtained. These equations provide the relation between the main parameters describing the system: the potential of the static electric field, the distribution function of charges and the surface profile of the liquid dielectric. The equations are used to study the phase transition in the system to a spatially periodic state. The proposed method can be applied in analyzing the properties of the phase transition in the system in relation to the spatially periodic states of wave type. Using the analytical and numerical methods, we perform a detailed study of the dependence of the critical parameters of such a phase transition on the thickness of the liquid dielectric film. Some stability criteria for the new asymmetric phase of the studied system are discussed.

Ionization and excitation in cool giant stars. I - Hydrogen and helium

NASA Technical Reports Server (NTRS)

Luttermoser, Donald G.; Johnson, Hollis R.

1992-01-01

The influence that non-LTE radiative transfer has on the electron density, ionization equilibrium, and excitation equilibrium in model atmospheres representative of both oxygen-rich and carbon-rich red giant stars is demonstrated. The radiative transfer and statistical equilibrium equations are solved self-consistently for H, H(-), H2, He I, C I, C II, Na I, Mg I, Mg II, Ca I, and Ca II in a plane-parallel static medium. Calculations are made for both radiative-equilibrium model photospheres alone and model photospheres with attached chromospheric models as determined semiempirically with IUE spectra of g Her (M6 III) and TX Psc (C6, 2). The excitation and ionization results for hydrogen and helium are reported.

Nonequilibrium quantum field dynamics from the two-particle-irreducible effective action

NASA Astrophysics Data System (ADS)

Laurie, Nathan S.

The two-particle-irreducible effective action offers a powerful approach to the study of quantum field dynamics far from equilibrium. Recent and upcoming heavy ion collision experiments motivate the study of such nonequilibrium dynamics in an expanding space-time background. For the O(N) model I derive exact, causal evolution equations for the statistical and spectral functions in a longitudinally expanding system. It is followed by an investigation into how the expansion affects the prospect of the system reaching equilibrium. Results are obtained in 1+1 dimensions at next-to- leading order in loop- and 1/N-expansions of the 2PI effective action. I focus on the evolution of the statistical function from highly nonequilibrium initial conditions, presenting a detailed analysis of early, intermediate and late-time dynamics. It is found that dynamics at very early times is attracted by a nonthermal fixed point of the mean field equations, after which interactions attempt to drive the system to equilibrium. The competition between the interactions and the expansion is eventually won by the expansion, with so-called freeze-out emerging naturally in this description. In order to investigate the convergence of the 2PI-1/N expansion in the 0(N) model, I compare results obtained numerically in 1+1 dimensions at leading, next- to-leading and next-to-next-to-leading order in 1/N. Convergence with increasing N, and also with decreasing coupling are discussed. A comparison is also made in the classical statistical field theory limit, where exact numerical results are available. I focus on early-time dynamics and quasi-particle properties far from equilibrium and observe rapid effective convergence already for moderate values of 1/N or the coupling strength.

Some comments on thermodynamic consistency for equilibrium mixture equations of state

DOE PAGES

Grove, John W.

2018-03-28

We investigate sufficient conditions for thermodynamic consistency for equilibrium mixtures. Such models assume that the mass fraction average of the material component equations of state, when closed by a suitable equilibrium condition, provide a composite equation of state for the mixture. Here, we show that the two common equilibrium models of component pressure/temperature equilibrium and volume/temperature equilibrium (Dalton, 1808) define thermodynamically consistent mixture equations of state and that other equilibrium conditions can be thermodynamically consistent provided appropriate values are used for the mixture specific entropy and pressure.

Non-equilibrium Statistical Mechanics and the Sea Ice Thickness Distribution

NASA Astrophysics Data System (ADS)

Wettlaufer, John; Toppaladoddi, Srikanth

We use concepts from non-equilibrium statistical physics to transform the original evolution equation for the sea ice thickness distribution g (h) due to Thorndike et al., (1975) into a Fokker-Planck like conservation law. The steady solution is g (h) = calN (q) hqe - h / H , where q and H are expressible in terms of moments over the transition probabilities between thickness categories. The solution exhibits the functional form used in observational fits and shows that for h << 1 , g (h) is controlled by both thermodynamics and mechanics, whereas for h >> 1 only mechanics controls g (h) . Finally, we derive the underlying Langevin equation governing the dynamics of the ice thickness h, from which we predict the observed g (h) . This allows us to demonstrate that the ice thickness field is ergodic. The genericity of our approach provides a framework for studying the geophysical scale structure of the ice pack using methods of broad relevance in statistical mechanics. Swedish Research Council Grant No. 638-2013-9243, NASA Grant NNH13ZDA001N-CRYO and the National Science Foundation and the Office of Naval Research under OCE-1332750 for support.

Master equation theory applied to the redistribution of polarized radiation in the weak radiation field limit. III. Theory for the multilevel atom

NASA Astrophysics Data System (ADS)

Bommier, Véronique

2016-06-01

Context. We discuss the case of lines formed by scattering, which comprises both coherent and incoherent scattering. Both processes contribute to form the line profiles in the so-called second solar spectrum, which is the spectrum of the linear polarization of such lines observed close to the solar limb. However, most of the lines cannot be simply modeled with a two-level or two-term atom model, and we present a generalized formalism for this purpose. Aims: The aim is to obtain a formalism that is able to describe scattering in line centers (resonant scattering or incoherent scattering) and in far wings (Rayleigh/Raman scattering or coherent scattering) for a multilevel and multiline atom. Methods: The method is designed to overcome the Markov approximation, which is often performed in the atom-photon interaction description. The method was already presented in the two first papers of this series, but the final equations of those papers were for a two-level atom. Results: We present here the final equations generalized for the multilevel and multiline atom. We describe the main steps of the theoretical development, and, in particular, how we performed the series development to overcome the Markov approximation. Conclusions: The statistical equilibrium equations for the atomic density matrix and the radiative transfer equation coefficients are obtained with line profiles. The Doppler redistribution is also taken into account because we show that the statistical equilibrium equations must be solved for each atomic velocity class.

APPROACH TO EQUILIBRIUM OF A QUANTUM PLASMA

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

Balescu, R.

1961-01-01

The treatment of irreversible processes in a classical plasma (R. Balescu, Phys. Fluids 3, 62(1960)) was extended to a gas of charged particles obeying quantum statistics. The various contributions to the equation of evolution for the reduced one-particle Wigner function were written in a form analogous to the classical formalism. The summation was then performed in a straightforward manner. The resulting equation describes collisions between particles "dressed" by their polarization clouds, exactly as in the classical situation. (auth)

Gyrokinetic Statistical Absolute Equilibrium and Turbulence

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

Jian-Zhou Zhu and Gregory W. Hammett

2011-01-10

A paradigm based on the absolute equilibrium of Galerkin-truncated inviscid systems to aid in understanding turbulence [T.-D. Lee, "On some statistical properties of hydrodynamical and magnetohydrodynamical fields," Q. Appl. Math. 10, 69 (1952)] is taken to study gyrokinetic plasma turbulence: A finite set of Fourier modes of the collisionless gyrokinetic equations are kept and the statistical equilibria are calculated; possible implications for plasma turbulence in various situations are discussed. For the case of two spatial and one velocity dimension, in the calculation with discretization also of velocity v with N grid points (where N + 1 quantities are conserved, correspondingmore » to an energy invariant and N entropy-related invariants), the negative temperature states, corresponding to the condensation of the generalized energy into the lowest modes, are found. This indicates a generic feature of inverse energy cascade. Comparisons are made with some classical results, such as those of Charney-Hasegawa-Mima in the cold-ion limit. There is a universal shape for statistical equilibrium of gyrokinetics in three spatial and two velocity dimensions with just one conserved quantity. Possible physical relevance to turbulence, such as ITG zonal flows, and to a critical balance hypothesis are also discussed.« less

Quantum statistical mechanics of dense partially ionized hydrogen.

NASA Technical Reports Server (NTRS)

Dewitt, H. E.; Rogers, F. J.

1972-01-01

The theory of dense hydrogenic plasmas beginning with the two component quantum grand partition function is reviewed. It is shown that ionization equilibrium and molecular dissociation equilibrium can be treated in the same manner with proper consideration of all two-body states. A quantum perturbation expansion is used to give an accurate calculation of the equation of state of the gas for any degree of dissociation and ionization. In this theory, the effective interaction between any two charges is the dynamic screened potential obtained from the plasma dielectric function. We make the static approximation; and we carry out detailed numerical calculations with the bound and scattering states of the Debye potential, using the Beth-Uhlenbeck form of the quantum second virial coefficient. We compare our results with calculations from the Saha equation.

Graphical tests for Hardy-Weinberg equilibrium based on the ternary plot.

PubMed

Graffelman, Jan; Camarena, Jair Morales

2008-01-01

We design a graphical test for Hardy-Weinberg equilibrium. This can circumvent the calculation of p values and the statistical (non)significance of a large number of bi-allelic markers can be inferred from their position in a graph. By rewriting expressions for the chi(2) statistic (with and without continuity correction) in terms of the heterozygote frequency an acceptance region for Hardy-Weinberg equilibrium is obtained that can be depicted in a ternary plot. We obtain equations for curves in the ternary plot that separate markers that are out of Hardy-Weinberg equilibrium from those that are in equilibrium. The curves depend on the chosen significance level, the sample size and on a continuity correction parameter. Some examples of graphical tests using a set of 106 SNPs on the long arm of human chromosome 22 are described. Significant markers and poor markers with a lot of missing values are easily identified in the proposed plots. R software for making the diagrams is provided. The proposed graphs can be used as control charts for spotting problematic markers in large scale genotyping studies, and constitute an excellent tool for the graphical exploration of bi-allelic marker data. (c) 2007 S. Karger AG, Basel.

Gyrokinetic statistical absolute equilibrium and turbulence

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

Zhu Jianzhou; Hammett, Gregory W.

2010-12-15

A paradigm based on the absolute equilibrium of Galerkin-truncated inviscid systems to aid in understanding turbulence [T.-D. Lee, Q. Appl. Math. 10, 69 (1952)] is taken to study gyrokinetic plasma turbulence: a finite set of Fourier modes of the collisionless gyrokinetic equations are kept and the statistical equilibria are calculated; possible implications for plasma turbulence in various situations are discussed. For the case of two spatial and one velocity dimension, in the calculation with discretization also of velocity v with N grid points (where N+1 quantities are conserved, corresponding to an energy invariant and N entropy-related invariants), the negative temperaturemore » states, corresponding to the condensation of the generalized energy into the lowest modes, are found. This indicates a generic feature of inverse energy cascade. Comparisons are made with some classical results, such as those of Charney-Hasegawa-Mima in the cold-ion limit. There is a universal shape for statistical equilibrium of gyrokinetics in three spatial and two velocity dimensions with just one conserved quantity. Possible physical relevance to turbulence, such as ITG zonal flows, and to a critical balance hypothesis are also discussed.« less

On thermalization of electron-positron-photon plasma

NASA Astrophysics Data System (ADS)

Siutsou, I. A.; Aksenov, A. G.; Vereshchagin, G. V.

2015-12-01

Recently a progress has been made in understanding thermalization mechanism of relativistic plasma starting from a non-equilibrium state. Relativistic Boltzmann equations were solved numerically for homogeneous isotropic plasma with collision integrals for two- and three-particle interactions calculated from the first principles by means of QED matrix elements. All particles were assumed to fulfill Boltzmann statistics. In this work we follow plasma thermalization by accounting for Bose enhancement and Pauli blocking in particle interactions. Our results show that particle in equilibrium reach Bose-Einstein distribution for photons, and Fermi-Dirac one for electrons, respectively.

The photon gas formulation of thermal radiation

NASA Technical Reports Server (NTRS)

Ried, R. C., Jr.

1975-01-01

A statistical consideration of the energy, the linear momentum, and the angular momentum of the photons that make up a thermal radiation field was presented. A general nonequilibrium statistical thermodynamics approach toward a macroscopic description of thermal radiation transport was developed and then applied to the restricted equilibrium statistical thermostatics derivation of the energy, linear momentum, and intrinsic angular momentum equations for an isotropic photon gas. A brief treatment of a nonisotropic photon gas, as an example of the results produced by the nonequilibrium statistical thermodynamics approach, was given. The relativistic variation of temperature and the invariance of entropy were illustrated.

Atomic Data and Spectral Line Intensities for Ni XXI

NASA Technical Reports Server (NTRS)

Bhatia, A. K.; Landi, E.; Fisher, Richard R. (Technical Monitor)

2001-01-01

Electron impact collision strengths, energy levels, oscillator strengths and spontaneous radiative decay rates are calculated for Ni XXI. The configurations used are 2s(sup 2)2p(sup 4), 2s2p(sup 5), 2p(sup 6), 2s(sup 2)2p(sup 3)3s, and 2s(sup 2)3p(sup 3)3d giving rise to 58 fine-structure levels in intermediate coupling. Collision strengths are calculated at five incident energies, 85, 170, 255, 340, and 425 Ry. Excitation rate coefficients are calculated by assuming a Maxwellian electron velocity distribution at an electron temperature of log T(sub e)(K)=6.9, corresponding to maximum abundance of Ni XXI. Using the excitation rate coefficients and the radiative transition rates, statistical equilibrium equations for level populations are solved at electron densities 10(exp 8)-10(exp 14) per cubic centimeter. Relative spectral line intensities are calculated. Proton excitation rates between the lowest three levels have been included in the statistical equilibrium equations. The predicted intensity ratios are compared with available observations.

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

Grove, John W.

We investigate sufficient conditions for thermodynamic consistency for equilibrium mixtures. Such models assume that the mass fraction average of the material component equations of state, when closed by a suitable equilibrium condition, provide a composite equation of state for the mixture. Here, we show that the two common equilibrium models of component pressure/temperature equilibrium and volume/temperature equilibrium (Dalton, 1808) define thermodynamically consistent mixture equations of state and that other equilibrium conditions can be thermodynamically consistent provided appropriate values are used for the mixture specific entropy and pressure.

The non-equilibrium allele frequency spectrum in a Poisson random field framework.

PubMed

Kaj, Ingemar; Mugal, Carina F

2016-10-01

In population genetic studies, the allele frequency spectrum (AFS) efficiently summarizes genome-wide polymorphism data and shapes a variety of allele frequency-based summary statistics. While existing theory typically features equilibrium conditions, emerging methodology requires an analytical understanding of the build-up of the allele frequencies over time. In this work, we use the framework of Poisson random fields to derive new representations of the non-equilibrium AFS for the case of a Wright-Fisher population model with selection. In our approach, the AFS is a scaling-limit of the expectation of a Poisson stochastic integral and the representation of the non-equilibrium AFS arises in terms of a fixation time probability distribution. The known duality between the Wright-Fisher diffusion process and a birth and death process generalizing Kingman's coalescent yields an additional representation. The results carry over to the setting of a random sample drawn from the population and provide the non-equilibrium behavior of sample statistics. Our findings are consistent with and extend a previous approach where the non-equilibrium AFS solves a partial differential forward equation with a non-traditional boundary condition. Moreover, we provide a bridge to previous coalescent-based work, and hence tie several frameworks together. Since frequency-based summary statistics are widely used in population genetics, for example, to identify candidate loci of adaptive evolution, to infer the demographic history of a population, or to improve our understanding of the underlying mechanics of speciation events, the presented results are potentially useful for a broad range of topics. Copyright © 2016 Elsevier Inc. All rights reserved.

Solution of the comoving-frame equation of transfer in spherically symmetric flows. V - Multilevel atoms. [in early star atmospheres

NASA Technical Reports Server (NTRS)

Mihalas, D.; Kunasz, P. B.

1978-01-01

The coupled radiative transfer and statistical equilibrium equations for multilevel ionic structures in the atmospheres of early-type stars are solved. Both lines and continua are treated consistently; the treatment is applicable throughout a transonic wind, and allows for the presence of background continuum sources and sinks in the transfer. An equivalent-two-level-atoms approach provides the solution for the equations. Calculations for simplified He (+)-like model atoms in parameterized isothermal wind models indicate that subordinate line profiles are sensitive to the assumed mass-loss rate, and to the assumed structure of the velocity law in the atmospheres.

An accelerated lambda iteration method for multilevel radiative transfer. I - Non-overlapping lines with background continuum

NASA Technical Reports Server (NTRS)

Rybicki, G. B.; Hummer, D. G.

1991-01-01

A method is presented for solving multilevel transfer problems when nonoverlapping lines and background continuum are present and active continuum transfer is absent. An approximate lambda operator is employed to derive linear, 'preconditioned', statistical-equilibrium equations. A method is described for finding the diagonal elements of the 'true' numerical lambda operator, and therefore for obtaining the coefficients of the equations. Iterations of the preconditioned equations, in conjunction with the transfer equation's formal solution, are used to solve linear equations. Some multilevel problems are considered, including an eleven-level neutral helium atom. Diagonal and tridiagonal approximate lambda operators are utilized in the problems to examine the convergence properties of the method, and it is found to be effective for the line transfer problems.

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

Gevorkyan, A. S., E-mail: g-ashot@sci.am; Sahakyan, V. V.

We study the classical 1D Heisenberg spin glasses in the framework of nearest-neighboring model. Based on the Hamilton equations we obtained the system of recurrence equations which allows to perform node-by-node calculations of a spin-chain. It is shown that calculations from the first principles of classical mechanics lead to ℕℙ hard problem, that however in the limit of the statistical equilibrium can be calculated by ℙ algorithm. For the partition function of the ensemble a new representation is offered in the form of one-dimensional integral of spin-chains’ energy distribution.

Phase-space methods for the spin dynamics in condensed matter systems

PubMed Central

Hurst, Jérôme; Manfredi, Giovanni

2017-01-01

Using the phase-space formulation of quantum mechanics, we derive a four-component Wigner equation for a system composed of spin- fermions (typically, electrons) including the Zeeman effect and the spin–orbit coupling. This Wigner equation is coupled to the appropriate Maxwell equations to form a self-consistent mean-field model. A set of semiclassical Vlasov equations with spin effects is obtained by expanding the full quantum model to first order in the Planck constant. The corresponding hydrodynamic equations are derived by taking velocity moments of the phase-space distribution function. A simple closure relation is proposed to obtain a closed set of hydrodynamic equations. This article is part of the themed issue ‘Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces’. PMID:28320903

Rapid-Equilibrium Enzyme Kinetics

ERIC Educational Resources Information Center

Alberty, Robert A.

2008-01-01

Rapid-equilibrium rate equations for enzyme-catalyzed reactions are especially useful because if experimental data can be fit by these simpler rate equations, the Michaelis constants can be interpreted as equilibrium constants. However, for some reactions it is necessary to use the more complicated steady-state rate equations. Thermodynamics is…

How electronic dynamics with Pauli exclusion produces Fermi-Dirac statistics.

PubMed

Nguyen, Triet S; Nanguneri, Ravindra; Parkhill, John

2015-04-07

It is important that any dynamics method approaches the correct population distribution at long times. In this paper, we derive a one-body reduced density matrix dynamics for electrons in energetic contact with a bath. We obtain a remarkable equation of motion which shows that in order to reach equilibrium properly, rates of electron transitions depend on the density matrix. Even though the bath drives the electrons towards a Boltzmann distribution, hole blocking factors in our equation of motion cause the electronic populations to relax to a Fermi-Dirac distribution. These factors are an old concept, but we show how they can be derived with a combination of time-dependent perturbation theory and the extended normal ordering of Mukherjee and Kutzelnigg for a general electronic state. The resulting non-equilibrium kinetic equations generalize the usual Redfield theory to many-electron systems, while ensuring that the orbital occupations remain between zero and one. In numerical applications of our equations, we show that relaxation rates of molecules are not constant because of the blocking effect. Other applications to model atomic chains are also presented which highlight the importance of treating both dephasing and relaxation. Finally, we show how the bath localizes the electron density matrix.

A reaction-based paradigm to model reactive chemical transport in groundwater with general kinetic and equilibrium reactions.

PubMed

Zhang, Fan; Yeh, Gour-Tsyh; Parker, Jack C; Brooks, Scott C; Pace, Molly N; Kim, Young-Jin; Jardine, Philip M; Watson, David B

2007-06-16

This paper presents a reaction-based water quality transport model in subsurface flow systems. Transport of chemical species with a variety of chemical and physical processes is mathematically described by M partial differential equations (PDEs). Decomposition via Gauss-Jordan column reduction of the reaction network transforms M species reactive transport equations into two sets of equations: a set of thermodynamic equilibrium equations representing N(E) equilibrium reactions and a set of reactive transport equations of M-N(E) kinetic-variables involving no equilibrium reactions (a kinetic-variable is a linear combination of species). The elimination of equilibrium reactions from reactive transport equations allows robust and efficient numerical integration. The model solves the PDEs of kinetic-variables rather than individual chemical species, which reduces the number of reactive transport equations and simplifies the reaction terms in the equations. A variety of numerical methods are investigated for solving the coupled transport and reaction equations. Simulation comparisons with exact solutions were performed to verify numerical accuracy and assess the effectiveness of various numerical strategies to deal with different application circumstances. Two validation examples involving simulations of uranium transport in soil columns are presented to evaluate the ability of the model to simulate reactive transport with complex reaction networks involving both kinetic and equilibrium reactions.

Statistics of Point Vortex Turbulence in Non-neutral Flows and in Flows with Translational and Rotational Symmetries

NASA Astrophysics Data System (ADS)

Esler, J. G.

2017-12-01

A theory (Esler and Ashbee in J Fluid Mech 779:275-308, 2015) describing the statistics of N freely-evolving point vortices in a bounded two-dimensional domain is extended. First, the case of a non-neutral vortex gas is addressed, and it is shown that the density of states function can be identified with the probability density function of an infinite sum of independent non-central chi-squared random variables, the details of which depend only on the shape of the domain. Equations for the equilibrium energy spectrum and other statistical quantities follow, the validity of which are verified against direct numerical simulations of the equations of motion. Second, domains with additional conserved quantities associated with a symmetry (e.g., circle, periodic channel) are investigated, and it is shown that the treatment of the non-neutral case can be modified to account for the additional constraint.

Atomic Data and Spectral Line Intensities for Ne III

NASA Technical Reports Server (NTRS)

Bhatia, A. K.; Thomas, R. J.; Landi, E.; Fisher, Richard R. (Technical Monitor)

2001-01-01

Electron impact collision strengths, energy levels, oscillator strengths and spontaneous radiative decay rates are calculated for Ne III. The configurations used are 2s(sup 2) 2p(sup 4),2s2p(sup 5),2s(sup 2) 2p(sup 3)3s, and 2s(sup 2)3p(sup 3)3d giving rise to 57 fine-structure levels in intermediate coupling. Collision strengths are calculated at five incident energies, 5, 10, 15, 20, and 25 Ry. Excitation rate coefficients are calculated by assuming a Maxwellian electron velocity distribution at an electron temperature of logT,(K)=5.0, corresponding to maximum abundance of Ne III. Using the excitation rate coefficients and the radiative transition rates, statistical equilibrium equations for level populations are solved at electron densities covering the range of 10(exp 8)-10(exp 14) per cubic centimeter. Relative spectral line intensities are calculated. Proton excitation rates between the lowest three levels have been included in the statistical equilibrium equations. The predicted Ne III line intensities are compared with SERTS rocket measurements of a solar active region and of a laboratory EUV light source.

Distribution of nuclei in equilibrium stellar matter from the free-energy density in a Wigner-Seitz cell

NASA Astrophysics Data System (ADS)

Grams, G.; Giraud, S.; Fantina, A. F.; Gulminelli, F.

2018-03-01

The aim of the present study is to calculate the nuclear distribution associated at finite temperature to any given equation of state of stellar matter based on the Wigner-Seitz approximation, for direct applications in core-collapse simulations. The Gibbs free energy of the different configurations is explicitly calculated, with special care devoted to the calculation of rearrangement terms, ensuring thermodynamic consistency. The formalism is illustrated with two different applications. First, we work out the nuclear statistical equilibrium cluster distribution for the Lattimer and Swesty equation of state, widely employed in supernova simulations. Secondly, we explore the effect of including shell structure, and consider realistic nuclear mass tables from the Brussels-Montreal Hartree-Fock-Bogoliubov model (specifically, HFB-24). We show that the whole collapse trajectory is dominated by magic nuclei, with extremely spread and even bimodal distributions of the cluster probability around magic numbers, demonstrating the importance of cluster distributions with realistic mass models in core-collapse simulations. Simple analytical expressions are given, allowing further applications of the method to any relativistic or nonrelativistic subsaturation equation of state.

Statistical equilibrium calculations for silicon in early-type model stellar atmospheres

NASA Technical Reports Server (NTRS)

Kamp, L. W.

1976-01-01

Line profiles of 36 multiplets of silicon (Si) II, III, and IV were computed for a grid of model atmospheres covering the range from 15,000 to 35,000 K in effective temperature and 2.5 to 4.5 in log (gravity). The computations involved simultaneous solution of the steady-state statistical equilibrium equations for the populations and of the equation of radiative transfer in the lines. The variables were linearized, and successive corrections were computed until a minimal accuracy of 1/1000 in the line intensities was reached. The common assumption of local thermodynamic equilibrium (LTE) was dropped. The model atmospheres used also were computed by non-LTE methods. Some effects that were incorporated into the calculations were the depression of the continuum by free electrons, hydrogen and ionized helium line blocking, and auto-ionization and dielectronic recombination, which later were found to be insignificant. Use of radiation damping and detailed electron (quadratic Stark) damping constants had small but significant effects on the strong resonance lines of Si III and IV. For weak and intermediate-strength lines, large differences with respect to LTE computations, the results of which are also presented, were found in line shapes and strengths. For the strong lines the differences are generally small, except for the models at the hot, low-gravity extreme of our range. These computations should be useful in the interpretation of the spectra of stars in the spectral range B0-B5, luminosity classes III, IV, and V.

Statistics of Macroturbulence from Flow Equations

NASA Astrophysics Data System (ADS)

Marston, Brad; Iadecola, Thomas; Qi, Wanming

2012-02-01

Probability distribution functions of stochastically-driven and frictionally-damped fluids are governed by a linear framework that resembles quantum many-body theory. Besides the Fokker-Planck approach, there is a closely related Hopf functional methodfootnotetextOokie Ma and J. B. Marston, J. Stat. Phys. Th. Exp. P10007 (2005).; in both formalisms, zero modes of linear operators describe the stationary non-equilibrium statistics. To access the statistics, we generalize the flow equation approachfootnotetextF. Wegner, Ann. Phys. 3, 77 (1994). (also known as the method of continuous unitary transformationsfootnotetextS. D. Glazek and K. G. Wilson, Phys. Rev. D 48, 5863 (1993); Phys. Rev. D 49, 4214 (1994).) to find the zero mode. We test the approach using a prototypical model of geophysical and astrophysical flows on a rotating sphere that spontaneously organizes into a coherent jet. Good agreement is found with low-order equal-time statistics accumulated by direct numerical simulation, the traditional method. Different choices for the generators of the continuous transformations, and for closure approximations of the operator algebra, are discussed.

Turbulence Modeling Effects on the Prediction of Equilibrium States of Buoyant Shear Flows

NASA Technical Reports Server (NTRS)

Zhao, C. Y.; So, R. M. C.; Gatski, T. B.

2001-01-01

The effects of turbulence modeling on the prediction of equilibrium states of turbulent buoyant shear flows were investigated. The velocity field models used include a two-equation closure, a Reynolds-stress closure assuming two different pressure-strain models and three different dissipation rate tensor models. As for the thermal field closure models, two different pressure-scrambling models and nine different temperature variance dissipation rate, Epsilon(0) equations were considered. The emphasis of this paper is focused on the effects of the Epsilon(0)-equation, of the dissipation rate models, of the pressure-strain models and of the pressure-scrambling models on the prediction of the approach to equilibrium turbulence. Equilibrium turbulence is defined by the time rate (if change of the scaled Reynolds stress anisotropic tensor and heat flux vector becoming zero. These conditions lead to the equilibrium state parameters. Calculations show that the Epsilon(0)-equation has a significant effect on the prediction of the approach to equilibrium turbulence. For a particular Epsilon(0)-equation, all velocity closure models considered give an equilibrium state if anisotropic dissipation is accounted for in one form or another in the dissipation rate tensor or in the Epsilon(0)-equation. It is further found that the models considered for the pressure-strain tensor and the pressure-scrambling vector have little or no effect on the prediction of the approach to equilibrium turbulence.

An advanced kinetic theory for morphing continuum with inner structures

NASA Astrophysics Data System (ADS)

Chen, James

2017-12-01

Advanced kinetic theory with the Boltzmann-Curtiss equation provides a promising tool for polyatomic gas flows, especially for fluid flows containing inner structures, such as turbulence, polyatomic gas flows and others. Although a Hamiltonian-based distribution function was proposed for diatomic gas flow, a general distribution function for the generalized Boltzmann-Curtiss equations and polyatomic gas flow is still out of reach. With assistance from Boltzmann's entropy principle, a generalized Boltzmann-Curtiss distribution for polyatomic gas flow is introduced. The corresponding governing equations at equilibrium state are derived and compared with Eringen's morphing (micropolar) continuum theory derived under the framework of rational continuum thermomechanics. Although rational continuum thermomechanics has the advantages of mathematical rigor and simplicity, the presented statistical kinetic theory approach provides a clear physical picture for what the governing equations represent.

Data-driven parameterization of the generalized Langevin equation

DOE PAGES

Lei, Huan; Baker, Nathan A.; Li, Xiantao

2016-11-29

We present a data-driven approach to determine the memory kernel and random noise of the generalized Langevin equation. To facilitate practical implementations, we parameterize the kernel function in the Laplace domain by a rational function, with coefficients directly linked to the equilibrium statistics of the coarse-grain variables. Further, we show that such an approximation can be constructed to arbitrarily high order. Within these approximations, the generalized Langevin dynamics can be embedded in an extended stochastic model without memory. We demonstrate how to introduce the stochastic noise so that the fluctuation-dissipation theorem is exactly satisfied.

Polylogarithmic equilibrium treatment of molecular aggregation and critical concentrations.

PubMed

Michel, Denis; Ruelle, Philippe

2017-02-15

A full equilibrium treatment of molecular aggregation is presented for prototypes of 1D and 3D aggregates, with and without nucleation. By skipping complex kinetic parameters like aggregate size-dependent diffusion, the equilibrium treatment allows us to predict directly time-independent quantities such as critical concentrations. The relationships between the macroscopic equilibrium constants for different paths are first established by statistical corrections and so as to comply with the detailed balance constraints imposed by nucleation, and the composition of the mixture resulting from homogeneous aggregation is then analyzed using a polylogarithmic function. Several critical concentrations are distinguished: the residual monomer concentration at equilibrium (RMC) and the critical nucleation concentration (CNC), which is the threshold concentration of total subunits necessary for initiating aggregation. When increasing the concentration of total subunits, the RMC converges more strongly to its asymptotic value, the equilibrium constant of depolymerization, for 3D aggregates and in the case of nucleation. The CNC moderately depends on the number of subunits in the nucleus, but sharply increases with the difference between the equilibrium constants of polymerization and nucleation. As the RMC and CNC can be numerically but not analytically determined, ansatz equations connecting them to thermodynamic parameters are proposed.

Chemical Potential for the Interacting Classical Gas and the Ideal Quantum Gas Obeying a Generalized Exclusion Principle

ERIC Educational Resources Information Center

Sevilla, F. J.; Olivares-Quiroz, L.

2012-01-01

In this work, we address the concept of the chemical potential [mu] in classical and quantum gases towards the calculation of the equation of state [mu] = [mu](n, T) where n is the particle density and "T" the absolute temperature using the methods of equilibrium statistical mechanics. Two cases seldom discussed in elementary textbooks are…

Spontaneous collective synchronization in the Kuramoto model with additional non-local interactions

NASA Astrophysics Data System (ADS)

Gupta, Shamik

2017-10-01

In the context of the celebrated Kuramoto model of globally-coupled phase oscillators of distributed natural frequencies, which serves as a paradigm to investigate spontaneous collective synchronization in many-body interacting systems, we report on a very rich phase diagram in presence of thermal noise and an additional non-local interaction on a one-dimensional periodic lattice. Remarkably, the phase diagram involves both equilibrium and non-equilibrium phase transitions. In two contrasting limits of the dynamics, we obtain exact analytical results for the phase transitions. These two limits correspond to (i) the absence of thermal noise, when the dynamics reduces to that of a non-linear dynamical system, and (ii) the oscillators having the same natural frequency, when the dynamics becomes that of a statistical system in contact with a heat bath and relaxing to a statistical equilibrium state. In the former case, our exact analysis is based on the use of the so-called Ott-Antonsen ansatz to derive a reduced set of nonlinear partial differential equations for the macroscopic evolution of the system. Our results for the case of statistical equilibrium are on the other hand obtained by extending the well-known transfer matrix approach for nearest-neighbor Ising model to consider non-local interactions. The work offers a case study of exact analysis in many-body interacting systems. The results obtained underline the crucial role of additional non-local interactions in either destroying or enhancing the possibility of observing synchrony in mean-field systems exhibiting spontaneous synchronization.

Statistical Mechanics of the Human Placenta: A Stationary State of a Near-Equilibrium System in a Linear Regime.

PubMed

Lecarpentier, Yves; Claes, Victor; Hébert, Jean-Louis; Krokidis, Xénophon; Blanc, François-Xavier; Michel, Francine; Timbely, Oumar

2015-01-01

All near-equilibrium systems under linear regime evolve to stationary states in which there is constant entropy production rate. In an open chemical system that exchanges matter and energy with the exterior, we can identify both the energy and entropy flows associated with the exchange of matter and energy. This can be achieved by applying statistical mechanics (SM), which links the microscopic properties of a system to its bulk properties. In the case of contractile tissues such as human placenta, Huxley's equations offer a phenomenological formalism for applying SM. SM was investigated in human placental stem villi (PSV) (n = 40). PSV were stimulated by means of KCl exposure (n = 20) and tetanic electrical stimulation (n = 20). This made it possible to determine statistical entropy (S), internal energy (E), affinity (A), thermodynamic force (A / T) (T: temperature), thermodynamic flow (v) and entropy production rate (A / T x v). We found that PSV operated near equilibrium, i.e., A ≺≺ 2500 J/mol and in a stationary linear regime, i.e., (A / T) varied linearly with v. As v was dramatically low, entropy production rate which quantified irreversibility of chemical processes appeared to be the lowest ever observed in any contractile system.

Deviations from LTE in a stellar atmosphere

NASA Technical Reports Server (NTRS)

Kalkofen, W.; Klein, R. I.; Stein, R. F.

1979-01-01

Deviations for LTE are investigated in an atmosphere of hydrogen atoms with one bound level, satisfying the equations of radiative, hydrostatic, and statistical equilibrium. The departure coefficient and the kinetic temperature as functions of the frequency dependence of the radiative cross section are studied analytically and numerically. Near the outer boundary of the atmosphere, the departure coefficient is smaller than unity when the radiative cross section grows with frequency faster than with the square of frequency; it exceeds unity otherwise. Far from the boundary the departure coefficient tends to exceed unity for any frequency dependence of the radiative cross section. Overpopulation always implies that the kinetic temperature in the statistical-equilibrium atmosphere is higher than the temperature in the corresponding LTE atmosphere. Upper and lower bounds on the kinetic temperature are given for an atmosphere with deviations from LTE only in the optically shallow layers when the emergent intensity can be described by a radiation temperature.

Molecular finite-size effects in stochastic models of equilibrium chemical systems.

PubMed

Cianci, Claudia; Smith, Stephen; Grima, Ramon

2016-02-28

The reaction-diffusion master equation (RDME) is a standard modelling approach for understanding stochastic and spatial chemical kinetics. An inherent assumption is that molecules are point-like. Here, we introduce the excluded volume reaction-diffusion master equation (vRDME) which takes into account volume exclusion effects on stochastic kinetics due to a finite molecular radius. We obtain an exact closed form solution of the RDME and of the vRDME for a general chemical system in equilibrium conditions. The difference between the two solutions increases with the ratio of molecular diameter to the compartment length scale. We show that an increase in the fraction of excluded space can (i) lead to deviations from the classical inverse square root law for the noise-strength, (ii) flip the skewness of the probability distribution from right to left-skewed, (iii) shift the equilibrium of bimolecular reactions so that more product molecules are formed, and (iv) strongly modulate the Fano factors and coefficients of variation. These volume exclusion effects are found to be particularly pronounced for chemical species not involved in chemical conservation laws. Finally, we show that statistics obtained using the vRDME are in good agreement with those obtained from Brownian dynamics with excluded volume interactions.

Continuity equation for probability as a requirement of inference over paths

NASA Astrophysics Data System (ADS)

González, Diego; Díaz, Daniela; Davis, Sergio

2016-09-01

Local conservation of probability, expressed as the continuity equation, is a central feature of non-equilibrium Statistical Mechanics. In the existing literature, the continuity equation is always motivated by heuristic arguments with no derivation from first principles. In this work we show that the continuity equation is a logical consequence of the laws of probability and the application of the formalism of inference over paths for dynamical systems. That is, the simple postulate that a system moves continuously through time following paths implies the continuity equation. The translation between the language of dynamical paths to the usual representation in terms of probability densities of states is performed by means of an identity derived from Bayes' theorem. The formalism presented here is valid independently of the nature of the system studied: it is applicable to physical systems and also to more abstract dynamics such as financial indicators, population dynamics in ecology among others.

Detailed Balance of Thermalization Dynamics in Rydberg-Atom Quantum Simulators.

PubMed

Kim, Hyosub; Park, YeJe; Kim, Kyungtae; Sim, H-S; Ahn, Jaewook

2018-05-04

Dynamics of large complex systems, such as relaxation towards equilibrium in classical statistical mechanics, often obeys a master equation that captures essential information from the complexities. Here, we find that thermalization of an isolated many-body quantum state can be described by a master equation. We observe sudden quench dynamics of quantum Ising-like models implemented in our quantum simulator, defect-free single-atom tweezers in conjunction with Rydberg-atom interaction. Saturation of their local observables, a thermalization signature, obeys a master equation experimentally constructed by monitoring the occupation probabilities of prequench states and imposing the principle of the detailed balance. Our experiment agrees with theories and demonstrates the detailed balance in a thermalization dynamics that does not require coupling to baths or postulated randomness.

Detailed Balance of Thermalization Dynamics in Rydberg-Atom Quantum Simulators

NASA Astrophysics Data System (ADS)

Kim, Hyosub; Park, YeJe; Kim, Kyungtae; Sim, H.-S.; Ahn, Jaewook

2018-05-01

Dynamics of large complex systems, such as relaxation towards equilibrium in classical statistical mechanics, often obeys a master equation that captures essential information from the complexities. Here, we find that thermalization of an isolated many-body quantum state can be described by a master equation. We observe sudden quench dynamics of quantum Ising-like models implemented in our quantum simulator, defect-free single-atom tweezers in conjunction with Rydberg-atom interaction. Saturation of their local observables, a thermalization signature, obeys a master equation experimentally constructed by monitoring the occupation probabilities of prequench states and imposing the principle of the detailed balance. Our experiment agrees with theories and demonstrates the detailed balance in a thermalization dynamics that does not require coupling to baths or postulated randomness.

Equivalence of equations describing trace element distribution during equilibrium partial melting

NASA Technical Reports Server (NTRS)

Consolmagno, G. J.; Drake, M. J.

1976-01-01

It is shown that four equations used for calculating the evolution of trace-element abundances during equilibrium partial melting are mathematically equivalent. The equations include those of Hertogen and Gijbels (1976), Shaw (1970), Schilling (1971), and O'Nions and Clarke (1972). The general form to which all these equations reduce is presented, and an analysis is performed to demonstrate their mathematical equivalence. It is noted that the utility of the general equation flows from the nature of equilibrium (i.e., the final state is independent of the path by which that state is attained).

Stochastic optimal control as non-equilibrium statistical mechanics: calculus of variations over density and current

NASA Astrophysics Data System (ADS)

Chernyak, Vladimir Y.; Chertkov, Michael; Bierkens, Joris; Kappen, Hilbert J.

2014-01-01

In stochastic optimal control (SOC) one minimizes the average cost-to-go, that consists of the cost-of-control (amount of efforts), cost-of-space (where one wants the system to be) and the target cost (where one wants the system to arrive), for a system participating in forced and controlled Langevin dynamics. We extend the SOC problem by introducing an additional cost-of-dynamics, characterized by a vector potential. We propose derivation of the generalized gauge-invariant Hamilton-Jacobi-Bellman equation as a variation over density and current, suggest hydrodynamic interpretation and discuss examples, e.g., ergodic control of a particle-within-a-circle, illustrating non-equilibrium space-time complexity.

An Optimization Principle for Deriving Nonequilibrium Statistical Models of Hamiltonian Dynamics

NASA Astrophysics Data System (ADS)

Turkington, Bruce

2013-08-01

A general method for deriving closed reduced models of Hamiltonian dynamical systems is developed using techniques from optimization and statistical estimation. Given a vector of resolved variables, selected to describe the macroscopic state of the system, a family of quasi-equilibrium probability densities on phase space corresponding to the resolved variables is employed as a statistical model, and the evolution of the mean resolved vector is estimated by optimizing over paths of these densities. Specifically, a cost function is constructed to quantify the lack-of-fit to the microscopic dynamics of any feasible path of densities from the statistical model; it is an ensemble-averaged, weighted, squared-norm of the residual that results from submitting the path of densities to the Liouville equation. The path that minimizes the time integral of the cost function determines the best-fit evolution of the mean resolved vector. The closed reduced equations satisfied by the optimal path are derived by Hamilton-Jacobi theory. When expressed in terms of the macroscopic variables, these equations have the generic structure of governing equations for nonequilibrium thermodynamics. In particular, the value function for the optimization principle coincides with the dissipation potential that defines the relation between thermodynamic forces and fluxes. The adjustable closure parameters in the best-fit reduced equations depend explicitly on the arbitrary weights that enter into the lack-of-fit cost function. Two particular model reductions are outlined to illustrate the general method. In each example the set of weights in the optimization principle contracts into a single effective closure parameter.

Flow Equation Approach to the Statistics of Nonlinear Dynamical Systems

NASA Astrophysics Data System (ADS)

Marston, J. B.; Hastings, M. B.

2005-03-01

The probability distribution function of non-linear dynamical systems is governed by a linear framework that resembles quantum many-body theory, in which stochastic forcing and/or averaging over initial conditions play the role of non-zero . Besides the well-known Fokker-Planck approach, there is a related Hopf functional methodootnotetextUriel Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, 1995) chapter 9.5.; in both formalisms, zero modes of linear operators describe the stationary non-equilibrium statistics. To access the statistics, we investigate the method of continuous unitary transformationsootnotetextS. D. Glazek and K. G. Wilson, Phys. Rev. D 48, 5863 (1993); Phys. Rev. D 49, 4214 (1994). (also known as the flow equation approachootnotetextF. Wegner, Ann. Phys. 3, 77 (1994).), suitably generalized to the diagonalization of non-Hermitian matrices. Comparison to the more traditional cumulant expansion method is illustrated with low-dimensional attractors. The treatment of high-dimensional dynamical systems is also discussed.

Comment on "Proposal of a critical test of the Navier-Stokes-Fourier paradigm for compressible fluid continua".

PubMed

Felderhof, B U

2013-08-01

Recently, a critical test of the Navier-Stokes-Fourier equations for compressible fluid continua was proposed [H. Brenner, Phys. Rev. E 87, 013014 (2013)]. It was shown that the equations of bivelocity hydrodynamics imply that a compressible fluid in an isolated rotating circular cylinder attains a nonequilibrium steady state with a nonuniform temperature increasing radially with distance from the axis. We demonstrate that statistical mechanical arguments, involving Hamiltonian dynamics and ergodicity due to irregularity of the wall, lead instead to a thermal equilibrium state with uniform temperature. This is the situation to be expected in experiment.

Fermi liquid, clustering, and structure factor in dilute warm nuclear matter

NASA Astrophysics Data System (ADS)

Röpke, G.; Voskresensky, D. N.; Kryukov, I. A.; Blaschke, D.

2018-02-01

Properties of nuclear systems at subsaturation densities can be obtained from different approaches. We demonstrate the use of the density autocorrelation function which is related to the isothermal compressibility and, after integration, to the equation of state. This way we connect the Landau Fermi liquid theory well elaborated in nuclear physics with the approaches to dilute nuclear matter describing cluster formation. A quantum statistical approach is presented, based on the cluster decomposition of the polarization function. The fundamental quantity to be calculated is the dynamic structure factor. Comparing with the Landau Fermi liquid theory which is reproduced in lowest approximation, the account of bound state formation and continuum correlations gives the correct low-density result as described by the second virial coefficient and by the mass action law (nuclear statistical equilibrium). Going to higher densities, the inclusion of medium effects is more involved compared with other quantum statistical approaches, but the relation to the Landau Fermi liquid theory gives a promising approach to describe not only thermodynamic but also collective excitations and non-equilibrium properties of nuclear systems in a wide region of the phase diagram.

A finite difference scheme for the equilibrium equations of elastic bodies

NASA Technical Reports Server (NTRS)

Phillips, T. N.; Rose, M. E.

1984-01-01

A compact difference scheme is described for treating the first-order system of partial differential equations which describe the equilibrium equations of an elastic body. An algebraic simplification enables the solution to be obtained by standard direct or iterative techniques.

Application of a single model to study the adsorption equilibrium of prednisolone on six carbonaceous materials.

PubMed

Valenzuela-Calahorro, C; Cuerda-Correa, E; Navarrete-Guijosa, A; Gonzalez-Pradas, E

2002-06-01

The knowledge of sorption processes of nonelectrolytes in solution by solid adsorbents implies the study of kinetics, equilibrium, and thermodynamic functions. However, quite frequently the equilibrium isotherms are studied by comparing them with those corresponding to the Giles et al. classification (1); these isotherms are also analyzed by fitting them to equations based on thermodynamic or kinetic criteria, and even to empirical equations. Nevertheless, information obtained is more coherent and satisfactory if the adsorption isotherms are fitted by using an equation describing the equilibrium isotherms according to the kinetic laws. These mentioned laws would determine each one of the unitary processes (one or more) which condition the global process. In this paper, an adsorption process of prednisolone in solution by six carbonaceous materials is explained according to a previously proposed single model, which allows to establish a kinetic law which fits satisfactorily most of C vs t isotherms (2). According to the above-mentioned kinetic law, equations describing sorption equilibrium processes have been deducted, and experimental data points have been fitted to these equations; such a fitting yields to different values of adsorption capacity and kinetic equilibrium constants for the different processes at several temperatures. However, in spite of their practical interest, these constants have no thermodynamic signification. Thus, the thermodynamic equilibrium constant (K) has been calculated by using a modified expression of the Gaines et al. equation (3). Global average values of the thermodynamic functions have also been calculated from the K values. Information related to variations of DeltaH and DeltaS with the surface coverage fraction was obtained by using the corresponding Clausius-Clapeyron equations.

Advances in Statistical and Deterministic Modeling of Wind-Driven Seas

DTIC Science & Technology

2011-09-30

Zakharov. Scales of nonlinear relaxation and balance of wind- driven seas. Geophysical Research Abstracts Vol. 13, EGU2011-2042, 2011. EGU General ...Dyachenko A. “On canonical equation for water waves” at General Assembly 2011 of the European Geosciences Union in Vienna, Austria, 03 – 08 April...scattering and equilibrium ranges in wind- generated waves with application to spectrometry, J. Geoph. Res., 92, 49715029, 1987. [3] Hsiao S.V. and

University of California Conference on Statistical Mechanics (4th) Held March 26-28, 1990

DTIC Science & Technology

1990-03-28

and S. Lago, Chem. Phys., Z, 5750 (1983) Shear Viscosity Calculation via Equilibrium Molecular Dynamics: Einstenian vs. Green - Kubo Formalism by Adel A...through the application of the Green - Kubo approach. Although the theoretical equivalence between both formalisms was demonstrated by Helfand [3], their...like equations and of different expressions based on the Green - Kubo formalism. In contrast to Hoheisel and Vogelsang’s conclusions [2], we find that

Statistical mechanics of shell models for two-dimensional turbulence

NASA Astrophysics Data System (ADS)

Aurell, E.; Boffetta, G.; Crisanti, A.; Frick, P.; Paladin, G.; Vulpiani, A.

1994-12-01

We study shell models that conserve the analogs of energy and enstrophy and hence are designed to mimic fluid turbulence in two-dimensions (2D). The main result is that the observed state is well described as a formal statistical equilibrium, closely analogous to the approach to two-dimensional ideal hydrodynamics of Onsager [Nuovo Cimento Suppl. 6, 279 (1949)], Hopf [J. Rat. Mech. Anal. 1, 87 (1952)], and Lee [Q. Appl. Math. 10, 69 (1952)]. In the presence of forcing and dissipation we observe a forward flux of enstrophy and a backward flux of energy. These fluxes can be understood as mean diffusive drifts from a source to two sinks in a system which is close to local equilibrium with Lagrange multipliers (``shell temperatures'') changing slowly with scale. This is clear evidence that the simplest shell models are not adequate to reproduce the main features of two-dimensional turbulence. The dimensional predictions on the power spectra from a supposed forward cascade of enstrophy and from one branch of the formal statistical equilibrium coincide in these shell models in contrast to the corresponding predictions for the Navier-Stokes and Euler equations in 2D. This coincidence has previously led to the mistaken conclusion that shell models exhibit a forward cascade of enstrophy. We also study the dynamical properties of the models and the growth of perturbations.

GENERIC Integrators: Structure Preserving Time Integration for Thermodynamic Systems

NASA Astrophysics Data System (ADS)

Öttinger, Hans Christian

2018-04-01

Thermodynamically admissible evolution equations for non-equilibrium systems are known to possess a distinct mathematical structure. Within the GENERIC (general equation for the non-equilibrium reversible-irreversible coupling) framework of non-equilibrium thermodynamics, which is based on continuous time evolution, we investigate the possibility of preserving all the structural elements in time-discretized equations. Our approach, which follows Moser's [1] construction of symplectic integrators for Hamiltonian systems, is illustrated for the damped harmonic oscillator. Alternative approaches are sketched.

Maximum entropy and equations of state for random cellular structures

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

Rivier, N.

Random, space-filling cellular structures (biological tissues, metallurgical grain aggregates, foams, etc.) are investigated. Maximum entropy inference under a few constraints yields structural equations of state, relating the size of cells to their topological shape. These relations are known empirically as Lewis's law in Botany, or Desch's relation in Metallurgy. Here, the functional form of the constraints is now known as a priori, and one takes advantage of this arbitrariness to increase the entropy further. The resulting structural equations of state are independent of priors, they are measurable experimentally and constitute therefore a direct test for the applicability of MaxEnt inferencemore » (given that the structure is in statistical equilibrium, a fact which can be tested by another simple relation (Aboav's law)). 23 refs., 2 figs., 1 tab.« less

Information transport in classical statistical systems

NASA Astrophysics Data System (ADS)

Wetterich, C.

2018-02-01

For "static memory materials" the bulk properties depend on boundary conditions. Such materials can be realized by classical statistical systems which admit no unique equilibrium state. We describe the propagation of information from the boundary to the bulk by classical wave functions. The dependence of wave functions on the location of hypersurfaces in the bulk is governed by a linear evolution equation that can be viewed as a generalized Schrödinger equation. Classical wave functions obey the superposition principle, with local probabilities realized as bilinears of wave functions. For static memory materials the evolution within a subsector is unitary, as characteristic for the time evolution in quantum mechanics. The space-dependence in static memory materials can be used as an analogue representation of the time evolution in quantum mechanics - such materials are "quantum simulators". For example, an asymmetric Ising model on a Euclidean two-dimensional lattice represents the time evolution of free relativistic fermions in two-dimensional Minkowski space.

A probabilistic approach to radiative energy loss calculations for optically thick atmospheres - Hydrogen lines and continua

NASA Technical Reports Server (NTRS)

Canfield, R. C.; Ricchiazzi, P. J.

1980-01-01

An approximate probabilistic radiative transfer equation and the statistical equilibrium equations are simultaneously solved for a model hydrogen atom consisting of three bound levels and ionization continuum. The transfer equation for L-alpha, L-beta, H-alpha, and the Lyman continuum is explicitly solved assuming complete redistribution. The accuracy of this approach is tested by comparing source functions and radiative loss rates to values obtained with a method that solves the exact transfer equation. Two recent model solar-flare chromospheres are used for this test. It is shown that for the test atmospheres the probabilistic method gives values of the radiative loss rate that are characteristically good to a factor of 2. The advantage of this probabilistic approach is that it retains a description of the dominant physical processes of radiative transfer in the complete redistribution case, yet it achieves a major reduction in computational requirements.

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

Harstad, E. N.; Harlow, Francis Harvey,; Schreyer, H. L.

Our goal is to develop constitutive relations for the behavior of a solid polymer during high-strain-rate deformations. In contrast to the classic thermodynamic techniques for deriving stress-strain response in static (equilibrium) circumstances, we employ a statistical-mechanics approach, in which we evolve a probability distribution function (PDF) for the velocity fluctuations of the repeating units of the chain. We use a Langevin description for the dynamics of a single repeating unit and a Lioville equation to describe the variations of the PDF. Moments of the PDF give the conservation equations for a single polymer chain embedded in other similar chains. Tomore » extract single-chain analytical constitutive relations these equations have been solved for representative loading paths. By this process we discover that a measure of nonuniform chain link displacement serves this purpose very well. We then derive an evolution equation for the descriptor function, with the result being a history-dependent constitutive relation.« less

Linear and nonlinear stability criteria for compressible MHD flows in a gravitational field

NASA Astrophysics Data System (ADS)

Moawad, S. M.; Moawad

2013-10-01

The equilibrium and stability properties of ideal magnetohydrodynamics (MHD) of compressible flow in a gravitational field with a translational symmetry are investigated. Variational principles for the steady-state equations are formulated. The MHD equilibrium equations are obtained as critical points of a conserved Lyapunov functional. This functional consists of the sum of the total energy, the mass, the circulation along field lines (cross helicity), the momentum, and the magnetic helicity. In the unperturbed case, the equilibrium states satisfy a nonlinear second-order partial differential equation (PDE) associated with hydrodynamic Bernoulli law. The PDE can be an elliptic or a parabolic equation depending on increasing the poloidal flow speed. Linear and nonlinear Lyapunov stability conditions under translational symmetric perturbations are established for the equilibrium states.

Introduction

NASA Astrophysics Data System (ADS)

Cohen, E. G. D.

Lecture notes are organized around the key word dissipation, while focusing on a presentation of modern theoretical developments in the study of irreversible phenomena. A broad cross-disciplinary perspective towards non-equilibrium statistical mechanics is backed by the general theory of nonlinear and complex dynamical systems. The classical-quantum intertwine and semiclassical dissipative borderline issue (decoherence, "classical out of quantum") are here included . Special emphasis is put on links between the theory of classical and quantum dynamical systems (temporal disorder, dynamical chaos and transport processes) with central problems of non-equilibrium statistical mechanics like e.g. the connection between dynamics and thermodynamics, relaxation towards equilibrium states and mechanisms capable to drive and next maintain the physical system far from equilibrium, in a non-equilibrium steady (stationary) state. The notion of an equilibrium state - towards which a system naturally evolves if left undisturbed - is a fundamental concept of equilibrium statistical mechanics. Taken as a primitive point of reference that allows to give an unambiguous status to near equilibrium and far from equilibrium systems, together with the dynamical notion of a relaxation (decay) towards a prescribed asymptotic invariant measure or probability distribution (properties of ergodicity and mixing are implicit). A related issue is to keep under control the process of driving a physical system away from an initial state of equilibrium and either keeping it in another (non-equilibrium) steady state or allowing to restore the initial data (return back, relax). To this end various models of environment (heat bath, reservoir, thermostat, measuring instrument etc.), and the environment - system coupling are analyzed. The central theme of the book is the dynamics of dissipation and various mechanisms responsible for the irreversible behaviour (transport properties) of open systems on classical and quantum levels of description. A distinguishing feature of these lecture notes is that microscopic foundations of irreversibility are investigated basically in terms of "small" systems, when the "system" and/or "environment" may have a finite (and small) number of degrees of freedom and may be bounded. This is to be contrasted with the casual understanding of statistical mechanics which is regarded to refer to systems with a very large number of degrees of freedom. In fact, it is commonly accepted that the accumulation of effects due to many (range of the Avogadro number) particles is required for statistical mechanics reasoning. Albeit those large numbers are not at all sufficient for transport properties. A helpful hint towards this conceptual turnover comes from the observation that for chaotic dynamical systems the random time evolution proves to be compatible with the underlying purely deterministic laws of motion. Chaotic features of the classical dynamics already appear in systems with two degrees of freedom and such systems need to be described in statistical terms, if we wish to quantify the dynamics of relaxation towards an invariant ergodic measure. The relaxation towards equilibrium finds a statistical description through an analysis of statistical ensembles. This entails an extension of the range of validity of statistical mechanics to small classical systems. On the other hand, the dynamics of fluctuations in macroscopic dissipative systems (due to their molecular composition and thermal mobility) may render a characterization of such systems as being chaotic. That motivates attempts of understanding the role of microscopic chaos and various "chaotic hypotheses" - dynamical systems approach is being pushed down to the level of atoms, molecules and complex matter constituents, whose natural substitute are low-dimensional model subsystems (encompassing as well the mesoscopic "quantum chaos") - in non-equilibrium transport phenomena. On the way a number of questions is addressed like e.g.: is there, or what is the nature of a connection between chaos (modern theory of dynamical systems) and irreversible thermodynamics; can really quantum chaos explain some peculiar features of quantum transport? The answer in both cases is positive, modulo a careful discrimination between viewing the dynamical chaos as a necessary or sufficient basis for irreversibility. In those dynamical contexts, another key term dynamical semigroups refers to major technical tools appropriate for the "dissipative mathematics", modelling irreversible behaviour on the classical and quantum levels of description. Dynamical systems theory and "quantum chaos" research involve both a high level of mathematical sophistication and heavy computer "experimentation". One of the present volume specific flavors is a tutorial access to quite advanced mathematical tools. They gradually penetrate the classical and quantum dynamical semigroup description, while culminating in the noncommutative Brillouin zone construction as a prerequisite to understand transport in aperiodic solids. Lecture notes are structured into chapters to give a better insight into major conceptual streamlines. Chapter I is devoted to a discussion of non-equilibrium steady states and, through so-called chaotic hypothesis combined with suitable fluctuation theorems, elucidates the role of Sinai-Ruelle-Bowen distribution in both equilibrium and non-equilibrium statistical physics frameworks (E. G. D. Cohen). Links between dynamics and statistics (Boltzmann versus Tsallis) are also discussed. Fluctuation relations and a survey of deterministic thermostats are given in the context of non-equilibrium steady states of fluids (L. Rondoni). Response of systems driven far from equilibrium is analyzed on the basis of a central assertion about the existence of the statistical representation in terms of an ensemble of dynamical realizations of the driving process. Non-equilibrium work relation is deduced for irreversible processes (C. Jarzynski). The survey of non-equilibrium steady states in statistical mechanics of classical and quantum systems employs heat bath models and the random matrix theory input. The quantum heat bath analysis and derivation of fluctuation-dissipation theorems is performed by means of the influence functional technique adopted to solve quantum master equations (D. Kusnezov). Chapter II deals with an issue of relaxation and its dynamical theory in both classical and quantum contexts. Pollicott-Ruelle resonance background for the exponential decay scenario is discussed for irreversible processes of diffusion in the Lorentz gas and multibaker models (P. Gaspard). The Pollicott-Ruelle theory reappears as a major inspiration in the survey of the behaviour of ensembles of chaotic systems, with a focus on model systems for which no rigorous results concerning the exponential decay of correlations in time is available (S. Fishman). The observation, that non-equilibrium transport processes in simple classical chaotic systems can be described in terms of fractal structures developing in the system phase space, links their formation and properties with the entropy production in the course of diffusion processes displaying a low dimensional deterministic (chaotic) origin (J. R. Dorfman). Chapter III offers an introduction to the theory of dynamical semigroups. Asymptotic properties of Markov operators and Markov semigroups acting in the set of probability densities (statistical ensemble notion is implicit) are analyzed. Ergodicity, mixing, strong (complete) mixing and sweeping are discussed in the familiar setting of "noise, chaos and fractals" (R. Rudnicki). The next step comprises a passage to quantum dynamical semigroups and completely positive dynamical maps, with an ultimate goal to introduce a consistent framework for the analysis of irreversible phenomena in open quantum systems, where dissipation and decoherence are crucial concepts (R. Alicki). Friction and damping in classical and quantum mechanics of finite dissipative systems is analyzed by means of Markovian quantum semigroups with special emphasis on the issue of complete positivity (M. Fannes). Specific two-level model systems of elementary particle physics (kaons) and rudiments of neutron interferometry are employed to elucidate a distinction between positivity and complete positivity (F. Benatti). Quantization of dynamics of stochastic models related to equilibrium Gibbs states results in dynamical maps which form quantum stochastic dynamical semigroups (W. A. Majewski). Chapter IV addresses diverse but deeply interrelated features of driven chaotic (mesoscopic) classical and quantum systems, their dissipative properties, notions of quantum irreversibility, entanglement, dephasing and decoherence. A survey of non-perturbative quantum effects for open quantum systems is concluded by outlining the discrepancies between random matrix theory and non-perturbative semiclassical predictions (D. Cohen). As a useful supplement to the subject of bounded open systems, methods of quantum state control in a cavity (coherent versus incoherent dynamics and dissipation) are described for low dimensional quantum systems (A. Buchleitner). The dynamics of open quantum systems can be alternatively described by means of non-Markovian stochastic Schrödinger equation, jointly for an open system and its environment, which moves us beyond the Linblad evolution scenario of Markovian dynamical semigroups. The quantum Brownian motion is considered (W. Strunz) . Chapter V enforces a conceptual transition 'from "small" to "large" systems with emphasis on irreversible thermodynamics of quantum transport. Typical features of the statistical mechanics of infinitely extended systems and the dynamical (small) systems approach are described by means of representative examples of relaxation towards asymptotic steady states: quantum one-dimensional lattice conductor and an open multibaker map (S. Tasaki). Dissipative transport in aperiodic solids is reviewed by invoking methods on noncommutative geometry. The anomalous Drude formula is derived. The occurence of quantum chaos is discussed together with its main consequences (J. Bellissard). The chapter is concluded by a survey of scaling limits of the N-body Schrödinger quantum dynamics, where classical evolution equations of irreversible statistical mechanics (linear Boltzmann, Hartree, Vlasov) emerge "out of quantum". In particular, a scaling limit of one body quantum dynamics with impurities (static random potential) and that of quantum dynamics with weakly coupled phonons are shown to yield the linear Boltzmann equation (L. Erdös). Various interrelations between chapters and individual lectures, plus a detailed fine-tuned information about the subject matter coverage of the volume, can be recovered by examining an extensive index.

Integral Equation for the Equilibrium State of Colliding Electron Beams

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

Warnock, Robert L.

2002-11-11

We study a nonlinear integral equation for the equilibrium phase distribution of stored colliding electron beams. It is analogous to the Haissinski equation, being derived from Vlasov-Fokker-Planck theory, but is quite different in form. We prove existence of a unique solution, thus the existence of a unique equilibrium state, for sufficiently small current. This is done for the Chao-Ruth model of the beam-beam interaction in one degree of freedom. We expect no difficulty in generalizing the argument to more realistic models.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium

NASA Astrophysics Data System (ADS)

Horowitz, Jordan M.

2015-07-01

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium.

PubMed

Horowitz, Jordan M

2015-07-28

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

On the Convenience of Using the Complete Linearization Method in Modelling the BLR of AGN

NASA Astrophysics Data System (ADS)

Patriarchi, P.; Perinotto, M.

The Complete Linearization Method (Mihalas, 1978) consists in the determination of the radiation field (at a set of frequency points), atomic level populations, temperature, electron density etc., by resolving the system of radiative transfer, thermal equilibrium, statistical equilibrium equations simultaneously and self-consistently. Since the system is not linear, it must be solved by iteration after linearization, using a perturbative method, starting from an initial guess solution. Of course the Complete Linearization Method is more time consuming than the previous one. But how great can this disadvantage be in the age of supercomputers? It is possible to approximately evaluate the CPU time needed to run a model by computing the number of multiplications necessary to solve the system.

Small Systems and Limitations on the Use of Chemical Thermodynamics

NASA Astrophysics Data System (ADS)

Tovbin, Yu. K.

2018-01-01

Limitations on using chemical thermodynamics to describe small systems are formulated. These limitations follow from statistical mechanics for equilibrium and nonequilibrium processes and reflect (1) differences between characteristic relaxation times in momentum, energy, and mass transfer in different aggregate states of investigated systems; (2) achievements of statistical mechanics that allow us to determine criteria for the size of smallest region in which thermodynamics can be applied and the scale of the emergence of a new phase, along with criteria for the conditions of violating a local equilibrium. Based on this analysis, the main thermodynamic results are clarified: the phase rule for distorted interfaces, the sense and area of applicability of Gibbs's concept of passive forces, and the artificiality of Kelvin's equation as a result of limitations on the thermodynamic approach to considering small bodies. The wrongness of introducing molecular parameters into thermodynamic derivations, and the activity coefficient for an activated complex into the expression for a reaction rate constant, is demonstrated.

Nonlinear Viscoelastic Mechanics of Cross-linked Rubbers

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Leonov, Arkady I.; Gray, Hugh R. (Technical Monitor)

2002-01-01

The paper develops a general theory for finite rubber viscoelasticity, and specifies it in the form, convenient for solving problems important for rubber, tire and space industries. Based on the quasi-linear approach of non-equilibrium thermodynamics, a general nonlinear theory has been developed for arbitrary nonisothermal deformations of viscoelastic solids. In this theory, the constitutive equations are presented as the sum of known equilibrium (rubber elastic) and non-equilibrium (liquid polymer viscoelastic) terms. These equations are then simplified using several modeling arguments. Stability constraints for the proposed constitutive equations are also discussed. It is shown that only strong ellipticity criteria are applicable for assessing stability of the equations governing viscoelastic solids.

Evolution of probability densities in stochastic coupled map lattices

NASA Astrophysics Data System (ADS)

Losson, Jérôme; Mackey, Michael C.

1995-08-01

This paper describes the statistical properties of coupled map lattices subjected to the influence of stochastic perturbations. The stochastic analog of the Perron-Frobenius operator is derived for various types of noise. When the local dynamics satisfy rather mild conditions, this equation is shown to possess either stable, steady state solutions (i.e., a stable invariant density) or density limit cycles. Convergence of the phase space densities to these limit cycle solutions explains the nonstationary behavior of statistical quantifiers at equilibrium. Numerical experiments performed on various lattices of tent, logistic, and shift maps with diffusivelike interelement couplings are examined in light of these theoretical results.

The Approach to Equilibrium: Detailed Balance and the Master Equation

ERIC Educational Resources Information Center

Alexander, Millard H.; Hall, Gregory E.; Dagdigian, Paul J.

2011-01-01

The approach to the equilibrium (Boltzmann) distribution of populations of internal states of a molecule is governed by inelastic collisions in the gas phase and with surfaces. The set of differential equations governing the time evolution of the internal state populations is commonly called the master equation. An analytic solution to the master…

Efecto de la difusión y la velocidad en la ionización del átomo de Carbono

NASA Astrophysics Data System (ADS)

Rovira, M. G.; Fontenla, J. M.

The equations of statistical equilibrium for all ionization states of the atom are solved. The effects of diffusion and center of mass velocity are included. In order to estimate the modifications of the ionization curves, they were applied to the Carbon atom. To solve these equations, solar prominences' models obtained in a previous paper were adopted. They were extended to reach a temperature of 1.5 × 106 K and the complete model of the prominence was calculated. Ionization curves for different values of velocity, diffusion and medium models were obtained. The different models represent structures with different densities. Considerable modifications due to these effects are found.

On determining absolute entropy without quantum theory or the third law of thermodynamics

NASA Astrophysics Data System (ADS)

Steane, Andrew M.

2016-04-01

We employ classical thermodynamics to gain information about absolute entropy, without recourse to statistical methods, quantum mechanics or the third law of thermodynamics. The Gibbs-Duhem equation yields various simple methods to determine the absolute entropy of a fluid. We also study the entropy of an ideal gas and the ionization of a plasma in thermal equilibrium. A single measurement of the degree of ionization can be used to determine an unknown constant in the entropy equation, and thus determine the absolute entropy of a gas. It follows from all these examples that the value of entropy at absolute zero temperature does not need to be assigned by postulate, but can be deduced empirically.

Coagulation-Fragmentation Model for Animal Group-Size Statistics

NASA Astrophysics Data System (ADS)

Degond, Pierre; Liu, Jian-Guo; Pego, Robert L.

2017-04-01

We study coagulation-fragmentation equations inspired by a simple model proposed in fisheries science to explain data for the size distribution of schools of pelagic fish. Although the equations lack detailed balance and admit no H-theorem, we are able to develop a rather complete description of equilibrium profiles and large-time behavior, based on recent developments in complex function theory for Bernstein and Pick functions. In the large-population continuum limit, a scaling-invariant regime is reached in which all equilibria are determined by a single scaling profile. This universal profile exhibits power-law behavior crossing over from exponent -2/3 for small size to -3/2 for large size, with an exponential cutoff.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium

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

Horowitz, Jordan M., E-mail: jordan.horowitz@umb.edu

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochasticmore » thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.« less

Is “morphodynamic equilibrium” an oxymoron?

USGS Publications Warehouse

Zhou, Zeng; Coco, Giovanni; Townend, Ian; Olabarrieta, Maitane; van der Wegen, Mick; Gong, Zheng; D'Alpaos, Andrea; Gao, Shu; Jaffe, Bruce E.; Gelfenbaum, Guy R.; He, Qing; Wang, Yaping; Lanzoni, Stefano; Wang, Zhengbing; Winterwerp, Han; Zhang, Changkuan

2017-01-01

Morphodynamic equilibrium is a widely adopted yet elusive concept in the field of geomorphology of coasts, rivers and estuaries. Based on the Exner equation, an expression of mass conservation of sediment, we distinguish three types of equilibrium defined as static and dynamic, of which two different types exist. Other expressions such as statistical and quasi-equilibrium which do not strictly satisfy the Exner conditions are also acknowledged for their practical use. The choice of a temporal scale is imperative to analyse the type of equilibrium. We discuss the difference between morphodynamic equilibrium in the “real world” (nature) and the “virtual world” (model). Modelling studies rely on simplifications of the real world and lead to understanding of process interactions. A variety of factors affect the use of virtual-world predictions in the real world (e.g., variability in environmental drivers and variability in the setting) so that the concept of morphodynamic equilibrium should be mathematically unequivocal in the virtual world and interpreted over the appropriate spatial and temporal scale in the real world. We draw examples from estuarine settings which are subject to various governing factors which broadly include hydrodynamics, sedimentology and landscape setting. Following the traditional “tide-wave-river” ternary diagram, we summarize studies to date that explore the “virtual world”, discuss the type of equilibrium reached and how it relates to the real world.

Statics of wrinkling films

NASA Technical Reports Server (NTRS)

Zak, M.

1982-01-01

An analytical investigation of the equilibrium of wrinkling films is conducted. Zak (1979) has shown that wrinkling occurs in connection with the instability of a smooth film having no resistance to bending in the case of compression. The governing equation for the equilibrium of a film with possible regions of wrinkling is considered. The introduction of fictitious stress reduces the governing equation to a form which formally coincides with the governing equation for a string. Equilibrium conditions in the case of an absence of external forces are explored, taking into account the stretching of a semispherical film, the torsion of a convex film of revolution, and stress singularities. A study is conducted of the equilibrium under conditions in which external forces normal to the surface of a film are present. Attention is also given to the equilibrium in a potential field.

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

Wu, Wei; Wang, Jin, E-mail: jin.wang.1@stonybrook.edu; State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, 130022 Changchun, China and College of Physics, Jilin University, 130021 Changchun

We have established a general non-equilibrium thermodynamic formalism consistently applicable to both spatially homogeneous and, more importantly, spatially inhomogeneous systems, governed by the Langevin and Fokker-Planck stochastic dynamics with multiple state transition mechanisms, using the potential-flux landscape framework as a bridge connecting stochastic dynamics with non-equilibrium thermodynamics. A set of non-equilibrium thermodynamic equations, quantifying the relations of the non-equilibrium entropy, entropy flow, entropy production, and other thermodynamic quantities, together with their specific expressions, is constructed from a set of dynamical decomposition equations associated with the potential-flux landscape framework. The flux velocity plays a pivotal role on both the dynamic andmore » thermodynamic levels. On the dynamic level, it represents a dynamic force breaking detailed balance, entailing the dynamical decomposition equations. On the thermodynamic level, it represents a thermodynamic force generating entropy production, manifested in the non-equilibrium thermodynamic equations. The Ornstein-Uhlenbeck process and more specific examples, the spatial stochastic neuronal model, in particular, are studied to test and illustrate the general theory. This theoretical framework is particularly suitable to study the non-equilibrium (thermo)dynamics of spatially inhomogeneous systems abundant in nature. This paper is the second of a series.« less

Probability distributions for multimeric systems.

PubMed

Albert, Jaroslav; Rooman, Marianne

2016-01-01

We propose a fast and accurate method of obtaining the equilibrium mono-modal joint probability distributions for multimeric systems. The method necessitates only two assumptions: the copy number of all species of molecule may be treated as continuous; and, the probability density functions (pdf) are well-approximated by multivariate skew normal distributions (MSND). Starting from the master equation, we convert the problem into a set of equations for the statistical moments which are then expressed in terms of the parameters intrinsic to the MSND. Using an optimization package on Mathematica, we minimize a Euclidian distance function comprising of a sum of the squared difference between the left and the right hand sides of these equations. Comparison of results obtained via our method with those rendered by the Gillespie algorithm demonstrates our method to be highly accurate as well as efficient.

Helium emission from model flare layers. [of outer solar atmosphere

NASA Technical Reports Server (NTRS)

Kulander, J. I.

1976-01-01

The emission of visible and UV He I and He II line radiation from a plane-parallel model flare layer characterized by electron temperatures of 10,000 to 50,000 K and electron densities of 10 to the 10th power to 10 to the 15th power per cu cm is analyzed by solving the statistical-equilibrium equations for a 30-level He I-II-III system, using parametric representations of the line and continuum radiation fields. The atomic model was chosen to provide accurate solutions for the first two resonance lines of He I and He II as well as for the D3 and 10,830-A lines of He I. Reaction rates are discussed, and sample solutions to the steady-state population equations are given for a generally optically thin gas assumed to be irradiated over 2pi sr by a blackbody spectrum at 6000 K. Specific results are examined for ionization equilibrium, level populations, approximate optical depths of a 1000-km-thick flare layer, line intensities, and upper-level population rates.

A novel Kinetic Monte Carlo algorithm for Non-Equilibrium Simulations

NASA Astrophysics Data System (ADS)

Jha, Prateek; Kuzovkov, Vladimir; Grzybowski, Bartosz; Olvera de La Cruz, Monica

2012-02-01

We have developed an off-lattice kinetic Monte Carlo simulation scheme for reaction-diffusion problems in soft matter systems. The definition of transition probabilities in the Monte Carlo scheme are taken identical to the transition rates in a renormalized master equation of the diffusion process and match that of the Glauber dynamics of Ising model. Our scheme provides several advantages over the Brownian dynamics technique for non-equilibrium simulations. Since particle displacements are accepted/rejected in a Monte Carlo fashion as opposed to moving particles following a stochastic equation of motion, nonphysical movements (e.g., violation of a hard core assumption) are not possible (these moves have zero acceptance). Further, the absence of a stochastic ``noise'' term resolves the computational difficulties associated with generating statistically independent trajectories with definitive mean properties. Finally, since the timestep is independent of the magnitude of the interaction forces, much longer time-steps can be employed than Brownian dynamics. We discuss the applications of this scheme for dynamic self-assembly of photo-switchable nanoparticles and dynamical problems in polymeric systems.

An analysis of numerical convergence in discrete velocity gas dynamics for internal flows

NASA Astrophysics Data System (ADS)

Sekaran, Aarthi; Varghese, Philip; Goldstein, David

2018-07-01

The Discrete Velocity Method (DVM) for solving the Boltzmann equation has significant advantages in the modeling of non-equilibrium and near equilibrium flows as compared to other methods in terms of reduced statistical noise, faster solutions and the ability to handle transient flows. Yet the DVM performance for rarefied flow in complex, small-scale geometries, in microelectromechanical (MEMS) devices for instance, is yet to be studied in detail. The present study focuses on the performance of the DVM for locally large Knudsen number flows of argon around sharp corners and other sources for discontinuities in the distribution function. Our analysis details the nature of the solution for some benchmark cases and introduces the concept of solution convergence for the transport terms in the discrete velocity Boltzmann equation. The limiting effects of the velocity space discretization are also investigated and the constraints on obtaining a robust, consistent solution are derived. We propose techniques to maintain solution convergence and demonstrate the implementation of a specific strategy and its effect on the fidelity of the solution for some benchmark cases.

Wave propagation in a quasi-chemical equilibrium plasma

NASA Technical Reports Server (NTRS)

Fang, T.-M.; Baum, H. R.

1975-01-01

Wave propagation in a quasi-chemical equilibrium plasma is studied. The plasma is infinite and without external fields. The chemical reactions are assumed to result from the ionization and recombination processes. When the gas is near equilibrium, the dominant role describing the evolution of a reacting plasma is played by the global conservation equations. These equations are first derived and then used to study the small amplitude wave motion for a near-equilibrium situation. Nontrivial damping effects have been obtained by including the conduction current terms.

Multigrid method for the equilibrium equations of elasticity using a compact scheme

NASA Technical Reports Server (NTRS)

Taasan, S.

1986-01-01

A compact difference scheme is derived for treating the equilibrium equations of elasticity. The scheme is inconsistent and unstable. A multigrid method which takes into account these properties is described. The solution of the discrete equations, up to the level of discretization errors, is obtained by this method in just two multigrid cycles.

Gas-kinetic theory and Boltzmann equation of share price within an equilibrium market hypothesis and ad hoc strategy

NASA Astrophysics Data System (ADS)

Ausloos, M.

2000-09-01

Recent observations have indicated that the traditional equilibrium market hypothesis (EMH; also known as Efficient Market Hypothesis) is unrealistic. It is shown here that it is the analog of a Boltzmann equation in physics, thus having some bad properties of mean-field approximations like a Gaussian distribution of price fluctuations. A kinetic theory for prices can be simply derived, considering in a first approach that market actors have all identical relaxation times, and solved within a Chapman-Enskog like formalism. In closing the set of equations, (i) an equation of state with a pressure and (ii) the equilibrium (isothermal) equation for the price (taken as the order parameter) of a stock as a function of the volume of money available are obtained.

Physics-based statistical learning approach to mesoscopic model selection.

PubMed

Taverniers, Søren; Haut, Terry S; Barros, Kipton; Alexander, Francis J; Lookman, Turab

2015-11-01

In materials science and many other research areas, models are frequently inferred without considering their generalization to unseen data. We apply statistical learning using cross-validation to obtain an optimally predictive coarse-grained description of a two-dimensional kinetic nearest-neighbor Ising model with Glauber dynamics (GD) based on the stochastic Ginzburg-Landau equation (sGLE). The latter is learned from GD "training" data using a log-likelihood analysis, and its predictive ability for various complexities of the model is tested on GD "test" data independent of the data used to train the model on. Using two different error metrics, we perform a detailed analysis of the error between magnetization time trajectories simulated using the learned sGLE coarse-grained description and those obtained using the GD model. We show that both for equilibrium and out-of-equilibrium GD training trajectories, the standard phenomenological description using a quartic free energy does not always yield the most predictive coarse-grained model. Moreover, increasing the amount of training data can shift the optimal model complexity to higher values. Our results are promising in that they pave the way for the use of statistical learning as a general tool for materials modeling and discovery.

Zonal flows and turbulence in fluids and plasmas

NASA Astrophysics Data System (ADS)

Parker, Jeffrey Bok-Cheung

In geophysical and plasma contexts, zonal flows are well known to arise out of turbulence. We elucidate the transition from statistically homogeneous turbulence without zonal flows to statistically inhomogeneous turbulence with steady zonal flows. Starting from the Hasegawa--Mima equation, we employ both the quasilinear approximation and a statistical average, which retains a great deal of the qualitative behavior of the full system. Within the resulting framework known as CE2, we extend recent understanding of the symmetry-breaking 'zonostrophic instability'. Zonostrophic instability can be understood in a very general way as the instability of some turbulent background spectrum to a zonally symmetric coherent mode. As a special case, the background spectrum can consist of only a single mode. We find that in this case the dispersion relation of zonostrophic instability from the CE2 formalism reduces exactly to that of the 4-mode truncation of generalized modulational instability. We then show that zonal flows constitute pattern formation amid a turbulent bath. Zonostrophic instability is an example of a Type I s instability of pattern-forming systems. The broken symmetry is statistical homogeneity. Near the bifurcation point, the slow dynamics of CE2 are governed by a well-known amplitude equation, the real Ginzburg-Landau equation. The important features of this amplitude equation, and therefore of the CE2 system, are multiple. First, the zonal flow wavelength is not unique. In an idealized, infinite system, there is a continuous band of zonal flow wavelengths that allow a nonlinear equilibrium. Second, of these wavelengths, only those within a smaller subband are stable. Unstable wavelengths must evolve to reach a stable wavelength; this process manifests as merging jets. These behaviors are shown numerically to hold in the CE2 system, and we calculate a stability diagram. The stability diagram is in agreement with direct numerical simulations of the quasilinear system. The use of statistically-averaged equations and the pattern formation methodology provide a path forward for further systematic investigations of zonal flows and their interactions with turbulence.

Incorporation of a Chemical Equilibrium Equation of State into LOCI-Chem

NASA Technical Reports Server (NTRS)

Cox, Carey F.

2005-01-01

Renewed interest in development of advanced high-speed transport, reentry vehicles and propulsion systems has led to a resurgence of research into high speed aerodynamics. As this flow regime is typically dominated by hot reacting gaseous flow, efficient models for the characteristic chemical activity are necessary for accurate and cost effective analysis and design of aerodynamic vehicles that transit this regime. The LOCI-Chem code recently developed by Ed Luke at Mississippi State University for NASA/MSFC and used by NASA/MSFC and SSC represents an important step in providing an accurate, efficient computational tool for the simulation of reacting flows through the use of finite-rate kinetics [3]. Finite rate chemistry however, requires the solution of an additional N-1 species mass conservation equations with source terms involving reaction kinetics that are not fully understood. In the equilibrium limit, where the reaction rates approach infinity, these equations become very stiff. Through the use of the assumption of local chemical equilibrium the set of governing equations is reduced back to the usual gas dynamic equations, and thus requires less computation, while still allowing for the inclusion of reacting flow phenomenology. The incorporation of a chemical equilibrium equation of state module into the LOCI-Chem code was the primary objective of the current research. The major goals of the project were: (1) the development of a chemical equilibrium composition solver, and (2) the incorporation of chemical equilibrium solver into LOCI-Chem. Due to time and resource constraints, code optimization was not considered unless it was important to the proper functioning of the code.

The equilibrium-diffusion limit for radiation hydrodynamics

DOE PAGES

Ferguson, J. M.; Morel, J. E.; Lowrie, R.

2017-07-27

The equilibrium-diffusion approximation (EDA) is used to describe certain radiation-hydrodynamic (RH) environments. When this is done the RH equations reduce to a simplified set of equations. The EDA can be derived by asymptotically analyzing the full set of RH equations in the equilibrium-diffusion limit. Here, we derive the EDA this way and show that it and the associated set of simplified equations are both first-order accurate with transport corrections occurring at second order. Having established the EDA’s first-order accuracy we then analyze the grey nonequilibrium-diffusion approximation and the grey Eddington approximation and show that they both preserve this first-order accuracy.more » Further, these approximations preserve the EDA’s first-order accuracy when made in either the comoving-frame (CMF) or the lab-frame (LF). And while analyzing the Eddington approximation, we found that the CMF and LF radiation-source equations are equivalent when neglecting O(β 2) terms and compared in the LF. Of course, the radiation pressures are not equivalent. It is expected that simplified physical models and numerical discretizations of the RH equations that do not preserve this first-order accuracy will not retain the correct equilibrium-diffusion solutions. As a practical example, we show that nonequilibrium-diffusion radiative-shock solutions devolve to equilibrium-diffusion solutions when the asymptotic parameter is small.« less

A Simple Global View of Fuel Burnup

NASA Astrophysics Data System (ADS)

Sekimoto, Hiroshi

2017-01-01

Reactor physics and fuel burnup are discussed in order to obtain a simple global view of the effects of nuclear reactor characteristics to fuel cycle system performance. It may provide some idea of free thinking and overall vision, though it is still a small part of nuclear energy system. At the beginning of this lecture, governing equations for nuclear reactors are presented. Since the set of these equations is so big and complicated, it is simplified by imposing some extreme conditions and the nuclear equilibrium equation is derived. Some features of future nuclear equilibrium state are obtained by solving this equation. The contribution of a nucleus charged into reactor core to the system performance indexes such as criticality is worth for understanding the importance of each nuclide. It is called nuclide importance and can be evaluated by using the equations adjoint to the nuclear equilibrium equation. Examples of some importances and their application to criticalily search problem are presented.

Is the Reaction Equilibrium Composition in Non-ideal Mixtures Uniquely Determined by the Initial Composition?

NASA Astrophysics Data System (ADS)

Sefcik, Jan

1998-05-01

Reaction equilibrium can be mathematically described by the equilibrium equation and the reaction equilibrium composition can be calculated by solving this equation. It can be proved by non-elementary thermodynamic arguments that for a generic system with given initial composition, temperature and pressure there is a unique stable equilibrium state corresponding to the global minimum of the Gibbs free energy function. However, when the concept of equilibrium is introduced in undergraduate chemistry and chemical engineering courses, such arguments are generally not accessible. When there is a single reaction equilibrium among mixture components and the components form an ideal mixture, it has been demonstrated by a simple, elegant mathematical argument that there is a unique composition satisfying the equilibrium equation. It has been also suggested that this particular argument extends to non-ideal mixtures by simply incorporating activity coefficients. We show that the argument extension to non-ideal systems is not generally valid. Increasing non-ideality can result in non-monotonicity of the function crucial for the simple uniqueness argument, and only later it leads to non-uniqueness and hence phase separation. The main feature responsible for this is a composition dependence of activity coefficients in non-ideal mixtures.

Using Simple Quadratic Equations to Estimate Equilibrium Concentrations of an Acid

ERIC Educational Resources Information Center

Brilleslyper, Michael A.

2004-01-01

Application of quadratic equations to standard problem in chemistry like finding equilibrium concentrations of ions in an acid solution is explained. This clearly shows that pure mathematical analysis has meaningful applications in other areas as well.

Multiscale gyrokinetics for rotating tokamak plasmas: fluctuations, transport and energy flows.

PubMed

Abel, I G; Plunk, G G; Wang, E; Barnes, M; Cowley, S C; Dorland, W; Schekochihin, A A

2013-11-01

This paper presents a complete theoretical framework for studying turbulence and transport in rapidly rotating tokamak plasmas. The fundamental scale separations present in plasma turbulence are codified as an asymptotic expansion in the ratio ε = ρi/α of the gyroradius to the equilibrium scale length. Proceeding order by order in this expansion, a set of coupled multiscale equations is developed. They describe an instantaneous equilibrium, the fluctuations driven by gradients in the equilibrium quantities, and the transport-timescale evolution of mean profiles of these quantities driven by the interplay between the equilibrium and the fluctuations. The equilibrium distribution functions are local Maxwellians with each flux surface rotating toroidally as a rigid body. The magnetic equilibrium is obtained from the generalized Grad-Shafranov equation for a rotating plasma, determining the magnetic flux function from the mean pressure and velocity profiles of the plasma. The slow (resistive-timescale) evolution of the magnetic field is given by an evolution equation for the safety factor q. Large-scale deviations of the distribution function from a Maxwellian are given by neoclassical theory. The fluctuations are determined by the 'high-flow' gyrokinetic equation, from which we derive the governing principle for gyrokinetic turbulence in tokamaks: the conservation and local (in space) cascade of the free energy of the fluctuations (i.e. there is no turbulence spreading). Transport equations for the evolution of the mean density, temperature and flow velocity profiles are derived. These transport equations show how the neoclassical and fluctuating corrections to the equilibrium Maxwellian act back upon the mean profiles through fluxes and heating. The energy and entropy conservation laws for the mean profiles are derived from the transport equations. Total energy, thermal, kinetic and magnetic, is conserved and there is no net turbulent heating. Entropy is produced by the action of fluxes flattening gradients, Ohmic heating and the equilibration of interspecies temperature differences. This equilibration is found to include both turbulent and collisional contributions. Finally, this framework is condensed, in the low-Mach-number limit, to a more concise set of equations suitable for numerical implementation.

The Markov process admits a consistent steady-state thermodynamic formalism

NASA Astrophysics Data System (ADS)

Peng, Liangrong; Zhu, Yi; Hong, Liu

2018-01-01

The search for a unified formulation for describing various non-equilibrium processes is a central task of modern non-equilibrium thermodynamics. In this paper, a novel steady-state thermodynamic formalism was established for general Markov processes described by the Chapman-Kolmogorov equation. Furthermore, corresponding formalisms of steady-state thermodynamics for the master equation and Fokker-Planck equation could be rigorously derived in mathematics. To be concrete, we proved that (1) in the limit of continuous time, the steady-state thermodynamic formalism for the Chapman-Kolmogorov equation fully agrees with that for the master equation; (2) a similar one-to-one correspondence could be established rigorously between the master equation and Fokker-Planck equation in the limit of large system size; (3) when a Markov process is restrained to one-step jump, the steady-state thermodynamic formalism for the Fokker-Planck equation with discrete state variables also goes to that for master equations, as the discretization step gets smaller and smaller. Our analysis indicated that general Markov processes admit a unified and self-consistent non-equilibrium steady-state thermodynamic formalism, regardless of underlying detailed models.

The effect of restructuring student writing in the general chemistry laboratory on student understanding of chemistry and on students' approach to the laboratory course

NASA Astrophysics Data System (ADS)

Rudd, James Andrew, II

Many students encounter difficulties engaging with laboratory-based instruction, and reviews of research have indicated that the value of such instruction is not clearly evident. Traditional forms of writing associated with laboratory activities are commonly in a style used by professional scientists to communicate developed explanations. Students probably lack the interpretative skills of a professional, and writing in this style may not support students in learning how to develop scientific explanations. The Science Writing Heuristic (SWH) is an inquiry-based approach to laboratory instruction designed in part to promote student ability in developing such explanations. However, there is not a convincing body of evidence for the superiority of inquiry-based laboratory instruction in chemistry. In a series of studies, the performance of students using the SWH student template in place of the standard laboratory report format was compared to the performance of students using the standard format. The standard reports had Title, Purpose, Procedure, Data & Observations, Calculations & Graphs, and Discussion sections. The SWH reports had Beginning Questions & Ideas, Tests & Procedures, Observations, Claims, Evidence, and Reflection sections. The pilot study produced evidence that using the SWH improved the quality of laboratory reports, improved student performance on a laboratory exam, and improved student approach to laboratory work. A main study found that SWH students statistically exhibited a better understanding of physical equilibrium when written explanations and equations were analyzed on a lecture exam and performed descriptively better on a physical equilibrium practical exam task. In another main study, the activities covering the general equilibrium concept were restructured as an additional change, and it was found that SWH students exhibited a better understanding of chemical equilibrium as shown by statistically greater success in overcoming the common confusion of interpreting equilibrium as equal concentrations and by statistically better performance when explaining aspects of chemical equilibrium. Both main studies found that students and instructors spent less time on the SWH reports and that students preferred the SWH approach because it increased their level of mental engagement. The studies supported the conclusion that inquiry-based laboratory instruction benefits student learning and attitudes.

Entropy in self-similar shock profiles

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

Margolin, Len G.; Reisner, Jon Michael; Jordan, Pedro M.

In this paper, we study the structure of a gaseous shock, and in particular the distribution of entropy within, in both a thermodynamics and a statistical mechanics context. The problem of shock structure has a long and distinguished history that we review. We employ the Navier–Stokes equations to construct a self–similar version of Becker’s solution for a shock assuming a particular (physically plausible) Prandtl number; that solution reproduces the well–known result of Morduchow & Libby that features a maximum of the equilibrium entropy inside the shock profile. We then construct an entropy profile, based on gas kinetic theory, that ismore » smooth and monotonically increasing. The extension of equilibrium thermodynamics to irreversible processes is based in part on the assumption of local thermodynamic equilibrium. We show that this assumption is not valid except for the weakest shocks. Finally, we conclude by hypothesizing a thermodynamic nonequilibrium entropy and demonstrating that it closely estimates the gas kinetic nonequilibrium entropy within a shock.« less

Entropy in self-similar shock profiles

DOE PAGES

Margolin, Len G.; Reisner, Jon Michael; Jordan, Pedro M.

2017-07-16

In this paper, we study the structure of a gaseous shock, and in particular the distribution of entropy within, in both a thermodynamics and a statistical mechanics context. The problem of shock structure has a long and distinguished history that we review. We employ the Navier–Stokes equations to construct a self–similar version of Becker’s solution for a shock assuming a particular (physically plausible) Prandtl number; that solution reproduces the well–known result of Morduchow & Libby that features a maximum of the equilibrium entropy inside the shock profile. We then construct an entropy profile, based on gas kinetic theory, that ismore » smooth and monotonically increasing. The extension of equilibrium thermodynamics to irreversible processes is based in part on the assumption of local thermodynamic equilibrium. We show that this assumption is not valid except for the weakest shocks. Finally, we conclude by hypothesizing a thermodynamic nonequilibrium entropy and demonstrating that it closely estimates the gas kinetic nonequilibrium entropy within a shock.« less

Generalized hydrodynamics and non-equilibrium steady states in integrable many-body quantum systems

NASA Astrophysics Data System (ADS)

Vasseur, Romain; Bulchandani, Vir; Karrasch, Christoph; Moore, Joel

The long-time dynamics of thermalizing many-body quantum systems can typically be described in terms of a conventional hydrodynamics picture that results from the decay of all but a few slow modes associated with standard conservation laws (such as particle number, energy, or momentum). However, hydrodynamics is expected to fail for integrable systems that are characterized by an infinite number of conservation laws, leading to unconventional transport properties and to complex non-equilibrium states beyond the traditional dogma of statistical mechanics. In this talk, I will describe recent attempts to understand such stationary states far from equilibrium using a generalized hydrodynamics picture. I will discuss the consistency of ``Bethe-Boltzmann'' kinetic equations with linear response Drude weights and with density-matrix renormalization group calculations. This work was supported by the Department of Energy through the Quantum Materials program (R. V.), NSF DMR-1206515, AFOSR MURI and a Simons Investigatorship (J. E. M.), DFG through the Emmy Noether program KA 3360/2-1 (C. K.).

Remapping HELENA to incompressible plasma rotation parallel to the magnetic field

NASA Astrophysics Data System (ADS)

Poulipoulis, G.; Throumoulopoulos, G. N.; Konz, C.

2016-07-01

Plasma rotation in connection to both zonal and mean (equilibrium) flows can play a role in the transitions to the advanced confinement regimes in tokamaks, as the L-H transition and the formation of internal transport barriers (ITBs). For incompressible rotation, the equilibrium is governed by a generalised Grad-Shafranov (GGS) equation and a decoupled Bernoulli-type equation for the pressure. For parallel flow, the GGS equation can be transformed to one identical in form with the usual Grad-Shafranov equation. In the present study on the basis of the latter equation, we have extended HELENA, an equilibrium fixed boundary solver. The extended code solves the GGS equation for a variety of the two free-surface-function terms involved for arbitrary Alfvén Mach number and density functions. We have constructed diverted-boundary equilibria pertinent to ITER and examined their characteristics, in particular, as concerns the impact of rotation on certain equilibrium quantities. It turns out that the rotation and its shear affect noticeably the pressure and toroidal current density with the impact on the current density being stronger in the parallel direction than in the toroidal one.

Computer program determines chemical equilibria in complex systems

NASA Technical Reports Server (NTRS)

Gordon, S.; Zeleznik, F. J.

1966-01-01

Computer program numerically solves nonlinear algebraic equations for chemical equilibrium based on iteration equations independent of choice of components. This program calculates theoretical performance for frozen and equilibrium composition during expansion and Chapman-Jouguet flame properties, studies combustion, and designs hardware.

Probability distributions of molecular observables computed from Markov models. II. Uncertainties in observables and their time-evolution

NASA Astrophysics Data System (ADS)

Chodera, John D.; Noé, Frank

2010-09-01

Discrete-state Markov (or master equation) models provide a useful simplified representation for characterizing the long-time statistical evolution of biomolecules in a manner that allows direct comparison with experiments as well as the elucidation of mechanistic pathways for an inherently stochastic process. A vital part of meaningful comparison with experiment is the characterization of the statistical uncertainty in the predicted experimental measurement, which may take the form of an equilibrium measurement of some spectroscopic signal, the time-evolution of this signal following a perturbation, or the observation of some statistic (such as the correlation function) of the equilibrium dynamics of a single molecule. Without meaningful error bars (which arise from both approximation and statistical error), there is no way to determine whether the deviations between model and experiment are statistically meaningful. Previous work has demonstrated that a Bayesian method that enforces microscopic reversibility can be used to characterize the statistical component of correlated uncertainties in state-to-state transition probabilities (and functions thereof) for a model inferred from molecular simulation data. Here, we extend this approach to include the uncertainty in observables that are functions of molecular conformation (such as surrogate spectroscopic signals) characterizing each state, permitting the full statistical uncertainty in computed spectroscopic experiments to be assessed. We test the approach in a simple model system to demonstrate that the computed uncertainties provide a useful indicator of statistical variation, and then apply it to the computation of the fluorescence autocorrelation function measured for a dye-labeled peptide previously studied by both experiment and simulation.

Statistical effects related to low numbers of reacting molecules analyzed for a reversible association reaction A + B = C in ideally dispersed systems: An apparent violation of the law of mass action

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

Szymanski, R., E-mail: rszymans@cbmm.lodz.pl; Sosnowski, S.; Maślanka, Ł.

2016-03-28

Theoretical analysis and computer simulations (Monte Carlo and numerical integration of differential equations) show that the statistical effect of a small number of reacting molecules depends on a way the molecules are distributed among the small volume nano-reactors (droplets in this study). A simple reversible association A + B = C was chosen as a model reaction, enabling to observe both thermodynamic (apparent equilibrium constant) and kinetic effects of a small number of reactant molecules. When substrates are distributed uniformly among droplets, all containing the same equal number of substrate molecules, the apparent equilibrium constant of the association is highermore » than the chemical one (observed in a macroscopic—large volume system). The average rate of the association, being initially independent of the numbers of molecules, becomes (at higher conversions) higher than that in a macroscopic system: the lower the number of substrate molecules in a droplet, the higher is the rate. This results in the correspondingly higher apparent equilibrium constant. A quite opposite behavior is observed when reactant molecules are distributed randomly among droplets: the apparent association rate and equilibrium constants are lower than those observed in large volume systems, being the lower, the lower is the average number of reacting molecules in a droplet. The random distribution of reactant molecules corresponds to ideal (equal sizes of droplets) dispersing of a reaction mixture. Our simulations have shown that when the equilibrated large volume system is dispersed, the resulting droplet system is already at equilibrium and no changes of proportions of droplets differing in reactant compositions can be observed upon prolongation of the reaction time.« less

Controlling reactivity of nanoporous catalyst materials by tuning reaction product-pore interior interactions: Statistical mechanical modeling

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

Wang, Jing; Ackerman, David M.; Lin, Victor S.-Y.

2013-04-02

Statistical mechanical modeling is performed of a catalytic conversion reaction within a functionalized nanoporous material to assess the effect of varying the reaction product-pore interior interaction from attractive to repulsive. A strong enhancement in reactivity is observed not just due to the shift in reaction equilibrium towards completion but also due to enhanced transport within the pore resulting from reduced loading. The latter effect is strongest for highly restricted transport (single-file diffusion), and applies even for irreversible reactions. The analysis is performed utilizing a generalized hydrodynamic formulation of the reaction-diffusion equations which can reliably capture the complex interplay between reactionmore » and restricted transport.« less

CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY: Fatigue life of metal treated by magnetic field

NASA Astrophysics Data System (ADS)

Liu, Zhao-Long; Hu, Hai-Yun; Fan, Tian-You; Xing, Xiu-San

2009-03-01

This paper investigates theoretically the influence of magnetization on fatigue life by using non-equilibrium statistical theory of fatigue fracture for metals. The fatigue microcrack growth rate is obtained from the dynamic equation of microcrack growth, where the influence of magnetization is described by an additional term in the potential energy of microcrack. The statistical value of fatigue life of metal under magnetic field is derived, which is expressed in terms of magnetic field and macrophysical as well as microphysical quantities. The fatigue life of AISI 4140 steel in static magnetic field from this theory is basically consistent with the experimental data.

Surface thermodynamics, surface stress, equations at surfaces and triple lines for deformable bodies.

PubMed

Olives, Juan

2010-03-03

The thermodynamics and mechanics of the surface of a deformable body are studied here, following and refining the general approach of Gibbs. It is first shown that the 'local' thermodynamic variables of the state of the surface are only the temperature, the chemical potentials and the surface strain tensor (true thermodynamic variables, for a viscoelastic solid or a viscous fluid). A new definition of the surface stress is given and the corresponding surface thermodynamics equations are presented. The mechanical equilibrium equation at the surface is then obtained. It involves the surface stress and is similar to the Cauchy equation for the volume. Its normal component is a generalization of the Laplace equation. At a (body-fluid-fluid) triple contact line, two equations are obtained, which represent: (i) the equilibrium of the forces (surface stresses) for a triple line fixed on the body; (ii) the equilibrium relative to the motion of the line with respect to the body. This last equation leads to a strong modification of Young's classical capillary equation.

Low-frequency Carbon Radio Recombination Lines. I. Calculations of Departure Coefficients

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

Salgado, F.; Morabito, L. K.; Oonk, J. B. R.

In the first paper of this series, we study the level population problem of recombining carbon ions. We focus our study on high quantum numbers, anticipating observations of carbon radio recombination lines to be carried out by the Low Frequency Array. We solve the level population equation including angular momentum levels with updated collision rates up to high principal quantum numbers. We derive departure coefficients by solving the level population equation in the hydrogenic approximation and including low-temperature dielectronic capture effects. Our results in the hydrogenic approximation agree well with those of previous works. When comparing our results including dielectronicmore » capture, we find differences that we ascribe to updates in the atomic physics (e.g., collision rates) and to the approximate solution method of the statistical equilibrium equations adopted in previous studies. A comparison with observations is discussed in an accompanying article, as radiative transfer effects need to be considered.« less

An Updated Nuclear Equation of State for Neutron Stars and Supernova Simulations

NASA Astrophysics Data System (ADS)

Meixner, M. A.; Mathews, G. J.; Dalhed, H. E.; Lan, N. Q.

2011-10-01

We present an updated and improved Equation of State based upon the framework originally developed by Bowers & Wilson. The details of the EoS and improvements are described along with a description of how to access this EOS for numerical simulations. Among the improvements are an updated compressibility based upon recent measurements, the possibility of the formation of proton excess (Ye> 0.5) material and an improved treatment of the nuclear statistical equilibrium and the transition to pasta nuclei as the density approaches nuclear matter density. The possibility of a QCD chiral phase transition is also included at densities above nuclear matter density. We show comparisons of this EOS with the other two publicly available equations of state used in supernova collapse simulations. The advantages of the present EoS is that it is easily amenable to phenomenological parameterization to fit observed explosion properties and to accommodate new physical parameters.

The way from microscopic many-particle theory to macroscopic hydrodynamics.

PubMed

Haussmann, Rudolf

2016-03-23

Starting from the microscopic description of a normal fluid in terms of any kind of local interacting many-particle theory we present a well defined step by step procedure to derive the hydrodynamic equations for the macroscopic phenomena. We specify the densities of the conserved quantities as the relevant hydrodynamic variables and apply the methods of non-equilibrium statistical mechanics with projection operator techniques. As a result we obtain time-evolution equations for the hydrodynamic variables with three kinds of terms on the right-hand sides: reversible, dissipative and fluctuating terms. In their original form these equations are completely exact and contain nonlocal terms in space and time which describe nonlocal memory effects. Applying a few approximations the nonlocal properties and the memory effects are removed. As a result we find the well known hydrodynamic equations of a normal fluid with Gaussian fluctuating forces. In the following we investigate if and how the time-inversion invariance is broken and how the second law of thermodynamics comes about. Furthermore, we show that the hydrodynamic equations with fluctuating forces are equivalent to stochastic Langevin equations and the related Fokker-Planck equation. Finally, we investigate the fluctuation theorem and find a modification by an additional term.

Fluid dynamics of out of equilibrium boost invariant plasmas

NASA Astrophysics Data System (ADS)

Blaizot, Jean-Paul; Yan, Li

2018-05-01

By solving a simple kinetic equation, in the relaxation time approximation, and for a particular set of moments of the distribution function, we establish a set of equations which, on the one hand, capture exactly the dynamics of the kinetic equation, and, on the other hand, coincide with the hierarchy of equations of viscous hydrodynamics, to arbitrary order in the viscous corrections. This correspondence sheds light on the underlying mechanism responsible for the apparent success of hydrodynamics in regimes that are far from local equilibrium.

GROUNDWATER MASS TRANSPORT AND EQUILIBRIUM CHEMISTRY MODEL FOR MULTICOMPONENT SYSTEMS

EPA Science Inventory

A mass transport model, TRANQL, for a multicomponent solution system has been developed. The equilibrium interaction chemistry is posed independently of the mass transport equations which leads to a set of algebraic equations for the chemistry coupled to a set of differential equ...

Principle of Maximum Fisher Information from Hardy’s Axioms Applied to Statistical Systems

PubMed Central

Frieden, B. Roy; Gatenby, Robert A.

2014-01-01

Consider a finite-sized, multidimensional system in a parameter state a. The system is in either a state of equilibrium or general non-equilibrium, and may obey either classical or quantum physics. L. Hardy’s mathematical axioms provide a basis for the physics obeyed by any such system. One axiom is that the number N of distinguishable states a in the system obeys N = max. This assumes that N is known as deterministic prior knowledge. However, most observed systems suffer statistical fluctuations, for which N is therefore only known approximately. Then what happens if the scope of the axiom N = max is extended to include such observed systems? It is found that the state a of the system must obey a principle of maximum Fisher information, I = Imax. This is important because many physical laws have been derived, assuming as a working hypothesis that I = Imax. These derivations include uses of the principle of Extreme physical information (EPI). Examples of such derivations were of the De Broglie wave hypothesis, quantum wave equations, Maxwell’s equations, new laws of biology (e.g. of Coulomb force-directed cell development, and of in situ cancer growth), and new laws of economic fluctuation and investment. That the principle I = Imax itself derives, from suitably extended Hardy axioms, thereby eliminates its need to be assumed in these derivations. Thus, uses of I = Imax and EPI express physics at its most fundamental level – its axiomatic basis in math. PMID:24229152

Development and Assessment of a Computer-Based Equation of State for Equilibrium Air

DTIC Science & Technology

2013-09-01

for very low energies. However, the ideal gas EOS is appropriate for atmospheric flight at subsonic, transonic, and low supersonic flight speeds...Flow Properties About Blunt Bodies Moving at Supersonic Speeds in an Equilibrium Gas ,” NASA TR R-204, July 1964. 21. Tannehill, John C., and Mugge...changes are made. 15. Subject Terms Air, thermodynamic properties, equation of state, chemical equilibrium, real- gas 16. SECURITY CLASSIFICATION

Modelling of electronic excitation and radiation in the Direct Simulation Monte Carlo Macroscopic Chemistry Method

NASA Astrophysics Data System (ADS)

Goldsworthy, M. J.

2012-10-01

One of the most useful tools for modelling rarefied hypersonic flows is the Direct Simulation Monte Carlo (DSMC) method. Simulator particle movement and collision calculations are combined with statistical procedures to model thermal non-equilibrium flow-fields described by the Boltzmann equation. The Macroscopic Chemistry Method for DSMC simulations was developed to simplify the inclusion of complex thermal non-equilibrium chemistry. The macroscopic approach uses statistical information which is calculated during the DSMC solution process in the modelling procedures. Here it is shown how inclusion of macroscopic information in models of chemical kinetics, electronic excitation, ionization, and radiation can enhance the capabilities of DSMC to model flow-fields where a range of physical processes occur. The approach is applied to the modelling of a 6.4 km/s nitrogen shock wave and results are compared with those from existing shock-tube experiments and continuum calculations. Reasonable agreement between the methods is obtained. The quality of the comparison is highly dependent on the set of vibrational relaxation and chemical kinetic parameters employed.

Teaching at the edge of knowledge: Non-equilibrium statistical physics

NASA Astrophysics Data System (ADS)

Schmittmann, Beate

2007-03-01

As physicists become increasingly interested in biological problems, we frequently find ourselves confronted with complex open systems, involving many interacting constituents and characterized by non-vanishing fluxes of mass or energy. Faced with the task of predicting macroscopic behaviors from microscopic information for these non-equilibrium systems, the familiar Gibbs-Boltzmann framework fails. The development of a comprehensive theoretical characterization of non-equilibrium behavior is one of the key challenges of modern condensed matter physics. In its absence, several approaches have been developed, from master equations to thermostatted molecular dynamics, which provide key insights into the rich and often surprising phenomenology of systems far from equilibrium. In my talk, I will address some of these methods, selecting those that are most relevant for a broad range of interdisciplinary problems from biology to traffic, finance, and sociology. The ``portability'' of these methods makes them valuable for graduate students from a variety of disciplines. To illustrate how different methods can complement each other when probing a problem from, e.g., the life sciences, I will discuss some recent attempts at modeling translation, i.e., the process by which the genetic information encoded on an mRNA is translated into the corresponding protein.

Generation of zonal flows through symmetry breaking of statistical homogeneity

NASA Astrophysics Data System (ADS)

Parker, Jeffrey B.; Krommes, John A.

2014-03-01

In geophysical and plasma contexts, zonal flows (ZFs) are well known to arise out of turbulence. We elucidate the transition from homogeneous turbulence without ZFs to inhomogeneous turbulence with steady ZFs. Starting from the equation for barotropic flow on a β plane, we employ both the quasilinear approximation and a statistical average, which retains a great deal of the qualitative behavior of the full system. Within the resulting framework known as CE2, we extend recent understanding of the symmetry-breaking zonostrophic instability and show that it is an example of a Type {{\\text{I}}_{s}} instability within the pattern formation literature. The broken symmetry is statistical homogeneity. Near the bifurcation point, the slow dynamics of CE2 are governed by a well-known amplitude equation. The important features of this amplitude equation, and therefore of the CE2 system, are multiple. First, the ZF wavelength is not unique. In an idealized, infinite system, there is a continuous band of ZF wavelengths that allow a nonlinear equilibrium. Second, of these wavelengths, only those within a smaller subband are stable. Unstable wavelengths must evolve to reach a stable wavelength; this process manifests as merging jets. These behaviors are shown numerically to hold in the CE2 system. We also conclude that the stability of the equilibria near the bifurcation point, which is governed by the Eckhaus instability, is independent of the Rayleigh-Kuo criterion.

Exploring Chemical Equilibrium with Poker Chips: A General Chemistry Laboratory Exercise

ERIC Educational Resources Information Center

Bindel, Thomas H.

2012-01-01

A hands-on laboratory exercise at the general chemistry level introduces students to chemical equilibrium through a simulation that uses poker chips and rate equations. More specifically, the exercise allows students to explore reaction tables, dynamic chemical equilibrium, equilibrium constant expressions, and the equilibrium constant based on…

Chemical Equilibrium and Polynomial Equations: Beware of Roots.

ERIC Educational Resources Information Center

Smith, William R.; Missen, Ronald W.

1989-01-01

Describes two easily applied mathematical theorems, Budan's rule and Rolle's theorem, that in addition to Descartes's rule of signs and intermediate-value theorem, are useful in chemical equilibrium. Provides examples that illustrate the use of all four theorems. Discusses limitations of the polynomial equation representation of chemical…

Remarks on the chemical Fokker-Planck and Langevin equations: Nonphysical currents at equilibrium.

PubMed

Ceccato, Alessandro; Frezzato, Diego

2018-02-14

The chemical Langevin equation and the associated chemical Fokker-Planck equation are well-known continuous approximations of the discrete stochastic evolution of reaction networks. In this work, we show that these approximations suffer from a physical inconsistency, namely, the presence of nonphysical probability currents at the thermal equilibrium even for closed and fully detailed-balanced kinetic schemes. An illustration is given for a model case.

Nonequilibrium steady state of a weakly-driven Kardar–Parisi–Zhang equation

NASA Astrophysics Data System (ADS)

Meerson, Baruch; Sasorov, Pavel V.; Vilenkin, Arkady

2018-05-01

We consider an infinite interface of d  >  2 dimensions, governed by the Kardar–Parisi–Zhang (KPZ) equation with a weak Gaussian noise which is delta-correlated in time and has short-range spatial correlations. We study the probability distribution of the interface height H at a point of the substrate, when the interface is initially flat. We show that, in stark contrast with the KPZ equation in d  <  2, this distribution approaches a non-equilibrium steady state. The time of relaxation toward this state scales as the diffusion time over the correlation length of the noise. We study the steady-state distribution using the optimal-fluctuation method. The typical, small fluctuations of height are Gaussian. For these fluctuations the activation path of the system coincides with the time-reversed relaxation path, and the variance of can be found from a minimization of the (nonlocal) equilibrium free energy of the interface. In contrast, the tails of are nonequilibrium, non-Gaussian and strongly asymmetric. To determine them we calculate, analytically and numerically, the activation paths of the system, which are different from the time-reversed relaxation paths. We show that the slower-decaying tail of scales as , while the faster-decaying tail scales as . The slower-decaying tail has important implications for the statistics of directed polymers in random potential.

A Newton method for the magnetohydrodynamic equilibrium equations

NASA Astrophysics Data System (ADS)

Oliver, Hilary James

We have developed and implemented a (J, B) space Newton method to solve the full nonlinear three dimensional magnetohydrodynamic equilibrium equations in toroidal geometry. Various cases have been run successfully, demonstrating significant improvement over Picard iteration, including a 3D stellarator equilibrium at β = 2%. The algorithm first solves the equilibrium force balance equation for the current density J, given a guess for the magnetic field B. This step is taken from the Picard-iterative PIES 3D equilibrium code. Next, we apply Newton's method to Ampere's Law by expansion of the functional J(B), which is defined by the first step. An analytic calculation in magnetic coordinates, of how the Pfirsch-Schlüter currents vary in the plasma in response to a small change in the magnetic field, yields the Newton gradient term (analogous to ∇f . δx in Newton's method for f(x) = 0). The algorithm is computationally feasible because we do this analytically, and because the gradient term is flux surface local when expressed in terms of a vector potential in an Ar=0 gauge. The equations are discretized by a hybrid spectral/offset grid finite difference technique, and leading order radial dependence is factored from Fourier coefficients to improve finite- difference accuracy near the polar-like origin. After calculating the Newton gradient term we transfer the equation from the magnetic grid to a fixed background grid, which greatly improves the code's performance.

The ESS and replicator equation in matrix games under time constraints.

PubMed

Garay, József; Cressman, Ross; Móri, Tamás F; Varga, Tamás

2018-06-01

Recently, we introduced the class of matrix games under time constraints and characterized the concept of (monomorphic) evolutionarily stable strategy (ESS) in them. We are now interested in how the ESS is related to the existence and stability of equilibria for polymorphic populations. We point out that, although the ESS may no longer be a polymorphic equilibrium, there is a connection between them. Specifically, the polymorphic state at which the average strategy of the active individuals in the population is equal to the ESS is an equilibrium of the polymorphic model. Moreover, in the case when there are only two pure strategies, a polymorphic equilibrium is locally asymptotically stable under the replicator equation for the pure-strategy polymorphic model if and only if it corresponds to an ESS. Finally, we prove that a strict Nash equilibrium is a pure-strategy ESS that is a locally asymptotically stable equilibrium of the replicator equation in n-strategy time-constrained matrix games.

Universal laws of human society's income distribution

NASA Astrophysics Data System (ADS)

Tao, Yong

2015-10-01

General equilibrium equations in economics play the same role with many-body Newtonian equations in physics. Accordingly, each solution of the general equilibrium equations can be regarded as a possible microstate of the economic system. Since Arrow's Impossibility Theorem and Rawls' principle of social fairness will provide a powerful support for the hypothesis of equal probability, then the principle of maximum entropy is available in a just and equilibrium economy so that an income distribution will occur spontaneously (with the largest probability). Remarkably, some scholars have observed such an income distribution in some democratic countries, e.g. USA. This result implies that the hypothesis of equal probability may be only suitable for some "fair" systems (economic or physical systems). From this meaning, the non-equilibrium systems may be "unfair" so that the hypothesis of equal probability is unavailable.

Laser short-pulse heating of an aluminum thin film: Energy transfer in electron and lattice sub-systems

NASA Astrophysics Data System (ADS)

Bin Mansoor, Saad; Sami Yilbas, Bekir

2015-08-01

Laser short-pulse heating of an aluminum thin film is considered and energy transfer in the film is formulated using the Boltzmann equation. Since the heating duration is short and the film thickness is considerably small, thermal separation of electron and lattice sub-systems is incorporated in the analysis. The electron-phonon coupling is used to formulate thermal communication of both sub-systems during the heating period. Equivalent equilibrium temperature is introduced to account for the average energy of all phonons around a local point when they redistribute adiabatically to an equilibrium state. Temperature predictions of the Boltzmann equation are compared with those obtained from the two-equation model. It is found that temperature predictions from the Boltzmann equation differ slightly from the two-equation model results. Temporal variation of equivalent equilibrium temperature does not follow the laser pulse intensity in the electron sub-system. The time occurrence of the peak equivalent equilibrium temperature differs for electron and lattice sub-systems, which is attributed to phonon scattering in the irradiated field in the lattice sub-system. In this case, time shift is observed for occurrence of the peak temperature in the lattice sub-system.

On the statistical mechanics of the 2D stochastic Euler equation

NASA Astrophysics Data System (ADS)

Bouchet, Freddy; Laurie, Jason; Zaboronski, Oleg

2011-12-01

The dynamics of vortices and large scale structures is qualitatively very different in two dimensional flows compared to its three dimensional counterparts, due to the presence of multiple integrals of motion. These are believed to be responsible for a variety of phenomena observed in Euler flow such as the formation of large scale coherent structures, the existence of meta-stable states and random abrupt changes in the topology of the flow. In this paper we study stochastic dynamics of the finite dimensional approximation of the 2D Euler flow based on Lie algebra su(N) which preserves all integrals of motion. In particular, we exploit rich algebraic structure responsible for the existence of Euler's conservation laws to calculate the invariant measures and explore their properties and also study the approach to equilibrium. Unexpectedly, we find deep connections between equilibrium measures of finite dimensional su(N) truncations of the stochastic Euler equations and random matrix models. Our work can be regarded as a preparation for addressing the questions of large scale structures, meta-stability and the dynamics of random transitions between different flow topologies in stochastic 2D Euler flows.

Economic consequences of aviation system disruptions: A reduced-form computable general equilibrium analysis

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

Chen, Zhenhua; Rose, Adam Z.; Prager, Fynnwin

The state of the art approach to economic consequence analysis (ECA) is computable general equilibrium (CGE) modeling. However, such models contain thousands of equations and cannot readily be incorporated into computerized systems used by policy analysts to yield estimates of economic impacts of various types of transportation system failures due to natural hazards, human related attacks or technological accidents. This paper presents a reduced-form approach to simplify the analytical content of CGE models to make them more transparent and enhance their utilization potential. The reduced-form CGE analysis is conducted by first running simulations one hundred times, varying key parameters, suchmore » as magnitude of the initial shock, duration, location, remediation, and resilience, according to a Latin Hypercube sampling procedure. Statistical analysis is then applied to the “synthetic data” results in the form of both ordinary least squares and quantile regression. The analysis yields linear equations that are incorporated into a computerized system and utilized along with Monte Carlo simulation methods for propagating uncertainties in economic consequences. Although our demonstration and discussion focuses on aviation system disruptions caused by terrorist attacks, the approach can be applied to a broad range of threat scenarios.« less

Non-equilibrium magnetic colloidal dispersions at liquid-air interfaces: dynamic patterns, magnetic order and self-assembled swimmers.

PubMed

Snezhko, Alexey

2011-04-20

Colloidal dispersions of interacting particles subjected to an external periodic forcing often develop nontrivial self-assembled patterns and complex collective behavior. A fundamental issue is how collective ordering in such non-equilibrium systems arises from the dynamics of discrete interacting components. In addition, from a practical viewpoint, by working in regimes far from equilibrium new self-organized structures which are generally not available through equilibrium thermodynamics can be created. In this review spontaneous self-assembly phenomena in magnetic colloidal dispersions suspended at liquid-air interfaces and driven out of equilibrium by an alternating magnetic field are presented. Experiments reveal a new type of nontrivially ordered self-assembled structures emerging in such systems in a certain range of excitation parameters. These dynamic structures emerge as a result of the competition between magnetic and hydrodynamic forces and have complex unconventional magnetic ordering. Nontrivial self-induced hydrodynamic fields accompany each out-of-equilibrium pattern. Spontaneous symmetry breaking of the self-induced surface flows leading to a formation of self-propelled microstructures has been discovered. Some features of the self-localized structures can be understood in the framework of the amplitude equation (Ginzburg-Landau type equation) for parametric waves coupled to the conservation law equation describing the evolution of the magnetic particle density and the Navier-Stokes equation for hydrodynamic flows. To understand the fundamental microscopic mechanisms governing self-assembly processes in magnetic colloidal dispersions at liquid-air interfaces a first-principle model for a non-equilibrium self-assembly is presented. The latter model allows us to capture in detail the entire process of out-of-equilibrium self-assembly in the system and reproduces most of the observed phenomenology.

Geometric approach to nuclear pasta phases

NASA Astrophysics Data System (ADS)

Kubis, Sebastian; Wójcik, Włodzimierz

2016-12-01

By use of the variational methods and differential geometry in the framework of the liquid drop model we formulate appropriate equilibrium equations for pasta phases with imposed periodicity. The extension of the Young-Laplace equation in the case of charged fluid is obtained. The β equilibrium and virial theorem are also generalized. All equations are shown in gauge invariant form. For the first time, the pasta shape stability analysis is carried out. The proper stability condition in the form of the generalized Jacobi equation is derived. The presented formalism is tested on some particular cases.

A Tale of Two Limpets (Patella vulgata and Patella stellaeformis): Evaluating a New Proxy for Late Holocene Climate Change in Coastal Areas

NASA Astrophysics Data System (ADS)

Fenger, T. L.; Surge, D. M.; Schoene, B. R.; Carter, J. G.; Milner, N.

2006-12-01

Shells of the European limpet, Patella vulgata, from Late Holocene archaeological deposits potentially contain critical information about climate change in coastal areas. Before deciphering climate information preserved in these zooarchaeological records, we studied the controls on oxygen isotope ratios (δ18O) in modern specimens. We tested the hypothesis that P. vulgata precipitates its shell in isotopic equilibrium with ambient water by comparing δ18OSHELL with expected values. Expected δ18OSHELL was constructed using the calcite-water fractionation equation, observed sea surface temperature (SST), and assuming δ18OWATER is +0.10‰ (VSMOW). Comparison between expected and measured δ18OSHELL revealed a +1.51±0.21‰ (VPDB) offset from expected values. Consequently, estimated SST calculated from δ18OSHELL was 6.50±2.45°C lower than observed SST. However, because the offset was relatively uniform, an adjustment can be made to account for this predictable vital effect and past SST can be reliably reconstructed. To further investigate the source of offset in this genus, we analyzed a fully marine tropical species (Patella stellaeformis) to minimize seasonal variation in environmental factors that influence δ18OSHELL. P. stellaeformis was evaluated to determine whether it has a similar offset from equilibrium as P. vulgata. We tested the hypotheses that: (1) δ18OSHELL in tropical species also displays vital effects; and (2) the offset from equilibrium (if any) would be constant and predictable. Our results indicated: (1) aragonite comprises most of P. stellaeformis' shell; and (2) δ18OSHELL is statistically indistinguishable from expected values calculated using the aragonite-water fractionation equation (Kolmogorov-Smirnov test statistic=0.61, D0.05[56, 57]=1.36) in contrast with our observations in P. vulgata. Differences in mineralogy or growth rates at different latitudes may play a role in mechanisms that influence vital effects.

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

Lei, Huan; Baker, Nathan A.; Li, Xiantao

We present a data-driven approach to determine the memory kernel and random noise of the generalized Langevin equation. To facilitate practical implementations, we parameterize the kernel function in the Laplace domain by a rational function, with coefficients directly linked to the equilibrium statistics of the coarse-grain variables. Further, we show that such an approximation can be constructed to arbitrarily high order. Within these approximations, the generalized Langevin dynamics can be embedded in an extended stochastic model without memory. We demonstrate how to introduce the stochastic noise so that the fluctuation-dissipation theorem is exactly satisfied.

A statistical formulation of one-dimensional electron fluid turbulence

NASA Technical Reports Server (NTRS)

Fyfe, D.; Montgomery, D.

1977-01-01

A one-dimensional electron fluid model is investigated using the mathematical methods of modern fluid turbulence theory. Non-dissipative equilibrium canonical distributions are determined in a phase space whose co-ordinates are the real and imaginary parts of the Fourier coefficients for the field variables. Spectral densities are calculated, yielding a wavenumber electric field energy spectrum proportional to k to the negative second power for large wavenumbers. The equations of motion are numerically integrated and the resulting spectra are found to compare well with the theoretical predictions.

Stochastic approach to equilibrium and nonequilibrium thermodynamics.

PubMed

Tomé, Tânia; de Oliveira, Mário J

2015-04-01

We develop the stochastic approach to thermodynamics based on stochastic dynamics, which can be discrete (master equation) and continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of entropy itself and the second the definition of entropy production rate, which is non-negative and vanishes in thermodynamic equilibrium. Based on these assumptions, we study interacting systems with many degrees of freedom in equilibrium or out of thermodynamic equilibrium and how the macroscopic laws are derived from the stochastic dynamics. These studies include the quasiequilibrium processes; the convexity of the equilibrium surface; the monotonic time behavior of thermodynamic potentials, including entropy; the bilinear form of the entropy production rate; the Onsager coefficients and reciprocal relations; and the nonequilibrium steady states of chemical reactions.

Stability of equations with a distributed delay, monotone production and nonlinear mortality

NASA Astrophysics Data System (ADS)

Berezansky, Leonid; Braverman, Elena

2013-10-01

We consider population dynamics models dN/dt = f(N(tτ)) - d(N(t)) with an increasing fecundity function f and any mortality function d which can be quadratic, as in the logistic equation, or have a different form provided that the equation has at most one positive equilibrium. Here the delay in the production term can be distributed and unbounded. It is demonstrated that the positive equilibrium is globally attractive if it exists, otherwise all positive solutions tend to zero. Moreover, we demonstrate that solutions of the equation are intrinsically non-oscillatory: once the initial function is less/greater than the equilibrium K > 0, so is the solution for any positive time value. The assumptions on f, d and the delay are rather nonrestrictive, and several examples demonstrate that none of them can be omitted.

Self-organization and feedback effects in the shock compressed media

NASA Astrophysics Data System (ADS)

Khantuleva, Tatyana

2005-07-01

New theoretical approach to the transport in condensed matter far from equilibrium combines methods of statistical mechanics and cybernetic physics in order to construct closed mathematical model of a system with self-organization and self-regulation. Mesoscopic effects are considered as a result of the structure formation and the feedback effects in an open system under dynamic loading. Nonequilibrium state equations had been involved to incorporate the velocity dispersion. Integrodifferential balance equations describe both wave and dissipative transport properties. Boundary conditions determine the internal scale spectra. The model is completed by the feedback that introduces the structure evolution basing the methods of cybernetic physics. The obtained results open a wide prospective for the control methods in applications to new technologies, intellectual systems and prediction of catastrophic phenomena.

A comparative study of the adsorption equilibrium of progesterone by a carbon black and a commercial activated carbon

NASA Astrophysics Data System (ADS)

Valenzuela-Calahorro, Cristóbal; Navarrete-Guijosa, Antonio; Stitou, Mostafa; Cuerda-Correa, Eduardo M.

2007-04-01

In this paper the adsorption process of a natural steroid hormone (progesterone) by a carbon black and a commercial activated carbon has been studied. The corresponding equilibrium isotherms have been analyzed according to a previously proposed model which establishes a kinetic law satisfactorily fitting the C versus t isotherms. The analysis of the experimental data points out the existence of two well-defined sections in the equilibrium isotherms. A general equation including these two processes has been proposed, the global adsorption process being fitted to such equation. From the values of the kinetic equilibrium constant so obtained, values of standard average adsorption enthalpy ( ΔH°) and entropy ( ΔS°) have been calculated. Finally, information related to variations of differential adsorption enthalpy ( ΔH) and entropy ( ΔS) with the surface coverage fraction ( θ) was obtained by using the corresponding Clausius-Clapeyron equations.

Plasma Equilibrium in a Magnetic Field with Stochastic Field-Line Trajectories

NASA Astrophysics Data System (ADS)

Krommes, J. A.; Reiman, A. H.

2008-11-01

The nature of plasma equilibrium in a magnetic field with stochastic field lines is examined, expanding upon the ideas first described by Reiman et al. The magnetic partial differential equation (PDE) that determines the equilibrium Pfirsch-Schlüter currents is treated as a passive stochastic PDE for μj/B. Renormalization leads to a stochastic Langevin equation for μ in which the resonances at the rational surfaces are broadened by the stochastic diffusion of the field lines; even weak radial diffusion can significantly affect the equilibrium, which need not be flattened in the stochastic region. Particular attention is paid to satisfying the periodicity constraints in toroidal configurations with sheared magnetic fields. A numerical scheme that couples the renormalized Langevin equation to Ampere's law is described. A. Reiman et al, Nucl. Fusion 47, 572--8 (2007). J. A. Krommes, Phys. Reports 360, 1--351.

Statistical mechanics of the Huxley-Simmons model

NASA Astrophysics Data System (ADS)

Caruel, M.; Truskinovsky, L.

2016-06-01

The chemomechanical model of Huxley and Simmons (HS) [A. F. Huxley and R. M. Simmons, Nature 233, 533 (1971), 10.1038/233533a0] provides a paradigmatic description of mechanically induced collective conformational changes relevant in a variety of biological contexts, from muscles power stroke and hair cell gating to integrin binding and hairpin unzipping. We develop a statistical mechanical perspective on the HS model by exploiting a formal analogy with a paramagnetic Ising model. We first study the equilibrium HS model with a finite number of elements and compute explicitly its mechanical and thermal properties. To model kinetics, we derive a master equation and solve it for several loading protocols. The developed formalism is applicable to a broad range of allosteric systems with mean-field interactions.

Transfer Kinetics at the Aqueous/Non-Aqueous Phase Liquid Interface. A Statistical Mechanic Approach

NASA Astrophysics Data System (ADS)

Doss, S. K.; Ezzedine, S.; Ezzedine, S.; Ziagos, J. P.; Hoffman, F.; Gelinas, R. J.

2001-05-01

Many modeling efforts in the literature use a first-order, linear-driving-force model to represent the chemical dissolution process at the non-aqueous/aqueous phase liquid (NAPL/APL) interface. In other words, NAPL to APL phase flux is assumed to be equal to the difference between the solubility limit and the "bulk aqueous solution" concentrations times a mass transfer coefficient. Under such assumptions, a few questions are raised: where, in relation to a region of pure NAPL, does the "bulk aqueous solution" regime begin and how does it behave? The answers are assumed to be associated with an arbitrary, predetermined boundary layer, which separates the NAPL from the surrounding solution. The mass transfer rate is considered to be, primarily, limited by diffusion of the component through the boundary layer. In fact, compositional models of interphase mass transfer usually assume that a local equilibrium is reached between phases. Representing mass flux as a rate-limiting process is equivalent to assuming diffusion through a stationary boundary layer with an instantaneous local equilibrium and linear concentration profile. Some environmental researchers have enjoyed success explaining their data using chemical engineering-based correlations. Correlations are strongly dependent on the experimental conditions employed. A universally applicable theory for NAPL dissolution in natural systems does not exist. These correlations are usually expressed in terms of the modified Sherwood number as a function of Reynolds, Peclet, and Schmidt numbers. The Sherwood number may be interpreted as the ratio between the grain size and the thickness of the Nernst stagnant film. In the present study, we show that transfer kinetics at the NAPL/APL interface under equilibrium conditions disagree with approaches based on the Nernst stagnant film concept. It is unclear whether local equilibrium assumptions used in current models are suitable for all situations.A statistical mechanic framework has been chosen to study the transfer kinetic processes at the microscale level. The rationale for our approach is based on both the activation energy of transfer of an ion and its velocity across the NAPL/APL interface. There are four major energies controlling the interfacial NAPL dissolution kinetics: (de)solvation energy, interfacial tension energy, electrostatic energy, and thermal fluctuation energy. Transfer of an ion across the NAPL/APL interface is accelerated by the viscous forces which can be described using the averaged Langevin master equation. The resulting energies and viscous forces were combined using the Boltzmann probability distribution. Asymptotic time limits of the resulting kinetics lead to instantaneous local equilibrium conditions that contradict the Nernst equilibrium equation. The NAPL/APL interface is not an ideal one: it does not conserve energy and heat. In our case the interface is treated as a thin film or slush zone that alters the thermodynamic variables. Such added zone, between the two phases, is itself a phase, and, therefore, the equilibrium does not occur between two phases but rather three. All these findings led us to develop a new non-linearly coupled flow and transport system of equations which is able to account for specific chemical dissolution processes and precludes the need for empirical mass-transfer parameters. Work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract W-7405-Eng-48.

Nonlinear Equations of Equilibrium for Elastic Helicopter or Wind Turbine Blades Undergoing Moderate Deformation

NASA Technical Reports Server (NTRS)

Rosen, A.; Friedmann, P. P.

1978-01-01

A set of nonlinear equations of equilibrium for an elastic wind turbine or helicopter blades are presented. These equations are derived for the case of small strains and moderate rotations (slopes). The derivation includes several assumptions which are carefully stated. For the convenience of potential users the equations are developed with respect to two different systems of coordinates, the undeformed and the deformed coordinates of the blade. Furthermore, the loads acting on the blade are given in a general form so as to make them suitable for a variety of applications. The equations obtained in the study are compared with those obtained in previous studies.

Non-Equilibrium Turbulence and Two-Equation Modeling

NASA Technical Reports Server (NTRS)

Rubinstein, Robert

2011-01-01

Two-equation turbulence models are analyzed from the perspective of spectral closure theories. Kolmogorov theory provides useful information for models, but it is limited to equilibrium conditions in which the energy spectrum has relaxed to a steady state consistent with the forcing at large scales; it does not describe transient evolution between such states. Transient evolution is necessarily through nonequilibrium states, which can only be found from a theory of turbulence evolution, such as one provided by a spectral closure. When the departure from equilibrium is small, perturbation theory can be used to approximate the evolution by a two-equation model. The perturbation theory also gives explicit conditions under which this model can be valid, and when it will fail. Implications of the non-equilibrium corrections for the classic Tennekes-Lumley balance in the dissipation rate equation are drawn: it is possible to establish both the cancellation of the leading order Re1/2 divergent contributions to vortex stretching and enstrophy destruction, and the existence of a nonzero difference which is finite in the limit of infinite Reynolds number.

Nonlinear dynamics of electromagnetic turbulence in a nonuniform magnetized plasma

NASA Astrophysics Data System (ADS)

Shukla, P. K.; Mirza, Arshad M.; Faria, R. T.

1998-03-01

By using the hydrodynamic electron response with fixed (kinetic) ions along with Poisson's equation as well as Ampère's law, a system of nonlinear equations for low-frequency (in comparison with the electron gyrofrequency) long-(short-) wavelength electromagnetic waves in a nonuniform resistive magnetoplasma has been derived. The plasma contains equilibrium density gradient and sheared equilibrium plasma flows. In the linear limit, local dispersion relations are obtained and analyzed. It is found that sheared equilibrium flows can cause instability of Alfvén-like electromagnetic waves even in the absence of a density gradient. Furthermore, it is shown that possible stationary solutions of the nonlinear equations without dissipation can be represented in the form of various types of vortices. On the other hand, the temporal behavior of our nonlinear dissipative systems without the equilibrium density inhomogeneity can be described by the generalized Lorenz equations which admit chaotic trajectories. The density inhomogeneity may lead to even qualitative changes in the chaotic dynamics. The results of our investigation should be useful in understanding the linear and nonlinear properties of nonthermal electromagnetic waves in space and laboratory plasmas.

Zonal Flows and Turbulence in Fluids and Plasmas

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

Parker, Jeffrey

2014-09-01

In geophysical and plasma contexts, zonal flows are well known to arise out of turbulence. We elucidate the transition from statistically homogeneous turbulence without zonal flows to statistically inhomogeneous turbulence with steady zonal flows. Starting from the Hasegawa--Mima equation, we employ both the quasilinear approximation and a statistical average, which retains a great deal of the qualitative behavior of the full system. Within the resulting framework known as CE2, we extend recent understanding of the symmetry-breaking `zonostrophic instability'. Zonostrophic instability can be understood in a very general way as the instability of some turbulent background spectrum to a zonally symmetricmore » coherent mode. As a special case, the background spectrum can consist of only a single mode. We find that in this case the dispersion relation of zonostrophic instability from the CE2 formalism reduces exactly to that of the 4-mode truncation of generalized modulational instability. We then show that zonal flows constitute pattern formation amid a turbulent bath. Zonostrophic instability is an example of a Type Is instability of pattern-forming systems. The broken symmetry is statistical homogeneity. Near the bifurcation point, the slow dynamics of CE2 are governed by a well-known amplitude equation, the real Ginzburg-Landau equation. The important features of this amplitude equation, and therefore of the CE2 system, are multiple. First, the zonal flow wavelength is not unique. In an idealized, infinite system, there is a continuous band of zonal flow wavelengths that allow a nonlinear equilibrium. Second, of these wavelengths, only those within a smaller subband are stable. Unstable wavelengths must evolve to reach a stable wavelength; this process manifests as merging jets. These behaviors are shown numerically to hold in the CE2 system, and we calculate a stability diagram. The stability diagram is in agreement with direct numerical simulations of the quasilinear system. The use of statistically-averaged equations and the pattern formation methodology provide a path forward for further systematic investigations of zonal flows and their interactions with turbulence.« less

H theorem for generalized entropic forms within a master-equation framework

NASA Astrophysics Data System (ADS)

Casas, Gabriela A.; Nobre, Fernando D.; Curado, Evaldo M. F.

2016-03-01

The H theorem is proven for generalized entropic forms, in the case of a discrete set of states. The associated probability distributions evolve in time according to a master equation, for which the corresponding transition rates depend on these entropic forms. An important equation describing the time evolution of the transition rates and probabilities in such a way as to drive the system towards an equilibrium state is found. In the particular case of Boltzmann-Gibbs entropy, it is shown that this equation is satisfied in the microcanonical ensemble only for symmetric probability transition rates, characterizing a single path to the equilibrium state. This equation fulfils the proof of the H theorem for generalized entropic forms, associated with systems characterized by complex dynamics, e.g., presenting nonsymmetric probability transition rates and more than one path towards the same equilibrium state. Some examples considering generalized entropies of the literature are discussed, showing that they should be applicable to a wide range of natural phenomena, mainly those within the realm of complex systems.

Plasma Equilibria With Stochastic Magnetic Fields

NASA Astrophysics Data System (ADS)

Krommes, J. A.; Reiman, A. H.

2009-05-01

Plasma equilibria that include regions of stochastic magnetic fields are of interest in a variety of applications, including tokamaks with ergodic limiters and high-pressure stellarators. Such equilibria are examined theoretically, and a numerical algorithm for their construction is described.^2,3 % The balance between stochastic diffusion of magnetic lines and small effects^2 omitted from the simplest MHD description can support pressure and current profiles that need not be flattened in stochastic regions. The diffusion can be described analytically by renormalizing stochastic Langevin equations for pressure and parallel current j, with particular attention being paid to the satisfaction of the periodicity constraints in toroidal configurations with sheared magnetic fields. The equilibrium field configuration can then be constructed by coupling the prediction for j to Amp'ere's law, which is solved numerically. A. Reiman et al., Pressure-induced breaking of equilibrium flux surfaces in the W7AS stellarator, Nucl. Fusion 47, 572--8 (2007). J. A. Krommes and A. H. Reiman, Plasma equilibrium in a magnetic field with stochastic regions, submitted to Phys. Plasmas. J. A. Krommes, Fundamental statistical theories of plasma turbulence in magnetic fields, Phys. Reports 360, 1--351.

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

Rasouli, C.; Abbasi Davani, F.; Rokrok, B.

Plasma confinement using external magnetic field is one of the successful ways leading to the controlled nuclear fusion. Development and validation of the solution process for plasma equilibrium in the experimental toroidal fusion devices is the main subject of this work. Solution of the nonlinear 2D stationary problem as posed by the Grad-Shafranov equation gives quantitative information about plasma equilibrium inside the vacuum chamber of hot fusion devices. This study suggests solving plasma equilibrium equation which is essential in toroidal nuclear fusion devices, using a mesh-free method in a condition that the plasma boundary is unknown. The Grad-Shafranov equation hasmore » been solved numerically by the point interpolation collocation mesh-free method. Important features of this approach include truly mesh free, simple mathematical relationships between points and acceptable precision in comparison with the parametric results. The calculation process has been done by using the regular and irregular nodal distribution and support domains with different points. The relative error between numerical and analytical solution is discussed for several test examples such as small size Damavand tokamak, ITER-like equilibrium, NSTX-like equilibrium, and typical Spheromak.« less

Electron-Impact Excitation Cross Sections for Modeling Non-Equilibrium Gas

NASA Technical Reports Server (NTRS)

Huo, Winifred M.; Liu, Yen; Panesi, Marco; Munafo, Alessandro; Wray, Alan; Carbon, Duane F.

2015-01-01

In order to provide a database for modeling hypersonic entry in a partially ionized gas under non-equilibrium, the electron-impact excitation cross sections of atoms have been calculated using perturbation theory. The energy levels covered in the calculation are retrieved from the level list in the HyperRad code. The downstream flow-field is determined by solving a set of continuity equations for each component. The individual structure of each energy level is included. These equations are then complemented by the Euler system of equations. Finally, the radiation field is modeled by solving the radiative transfer equation.

A geometrically nonlinear theory of elastic plates

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Atilgan, Ali R.; Danielson, D. A.

1992-01-01

A set of kinematic and intrinsic equilibrium equations is derived for plates undergoing large deflection and rotation but with small strain. The large rotation is treated by the general finite rotation of a frame in which the material points that are originally along a normal line in the undeformed plate undergo only small displacements. Exact intrinsic virtual strain-displacement relations are derived; using a reduced 2-D strain energy function from which the warping has been systematically eliminated, a set of intrinsic equilibrium equations follows. It is demonstrated that only five equilibrium equations can be derived in this way, because the component of virtual rotation about the normal is not independent. These equations include terms which cannot be obtained without the use of a finite rotation vector which contains three nonzero components. These extra terms correspond to the difference of in-plane shear stress resultants in other theories.

Understanding the Nernst Equation and Other Electrochemical Concepts: An Easy Experimental Approach for Students

ERIC Educational Resources Information Center

Vidal-Iglesias, Francisco J.; Solla-Gullon, Jose; Rodes, Antonio; Herrero, Enrique; Aldaz, Antonio

2012-01-01

The goal of the present laboratory experiment is to deepen the understanding of the Nernst equation and some other concepts that are essential in electrochemistry. In this practical laboratory session, students first learn that the equilibrium potential of an electrode is related to the difference between two equilibrium inner electric potentials…

Non-equilibrium reaction rates in chemical kinetic equations

NASA Astrophysics Data System (ADS)

Gorbachev, Yuriy

2018-05-01

Within the recently proposed asymptotic method for solving the Boltzmann equation for chemically reacting gas mixture, the chemical kinetic equations has been derived. Corresponding one-temperature non-equilibrium reaction rates are expressed in terms of specific heat capacities of the species participate in the chemical reactions, bracket integrals connected with the internal energy transfer in inelastic non-reactive collisions and energy transfer coefficients. Reactions of dissociation/recombination of homonuclear and heteronuclear diatomic molecules are considered. It is shown that all reaction rates are the complex functions of the species densities, similarly to the unimolecular reaction rates. For determining the rate coefficients it is recommended to tabulate corresponding bracket integrals, additionally to the equilibrium rate constants. Correlation of the obtained results with the irreversible thermodynamics is established.

The chromospheres of late-type stars. I - Eridani as a test case of multiline modelling

NASA Technical Reports Server (NTRS)

Thatcher, John D.; Robinson, Richard D.; Rees, David E.

1991-01-01

A new model of the lower chromosphere of the dwarf K2 star Epsilon Eridani is derived by matching flux profiles of the Ca IR triplet lines 8498 and 8542 A H-alpha and H-beta lines and the Na D lines (all observed simultaneously at the AAT), and the Ca II K line. The coupled non-LTE equations of statistical equilibrium and radiative transfer are solved under the constraint of hydrostatic equilibrium using the Carlsson (1986) code. Within the framework of the model, the Na D lines are an important photospheric diagnostic, and the Ca IR triplet lines can be used to locate the temperature minimum. The computed H-alpha and H-beta depths are highly sensitive constraints on the transition zone gradients and base pressures allowing us to derive a pressure at the base of the transition zone of 0.9 dyn/cm.

The number statistics and optimal history of non-equilibrium steady states of mortal diffusing particles

NASA Astrophysics Data System (ADS)

Meerson, Baruch

2015-05-01

Suppose that a point-like steady source at x = 0 injects particles into a half-infinite line. The particles diffuse and die. At long times a non-equilibrium steady state sets in, and we assume that it involves many particles. If the particles are non-interacting, their total number N in the steady state is Poisson-distributed with mean \\bar{N} predicted from a deterministic reaction-diffusion equation. Here we determine the most likely density history of this driven system conditional on observing a given N. We also consider two prototypical examples of interacting diffusing particles: (i) a family of mortal diffusive lattice gases with constant diffusivity (as illustrated by the simple symmetric exclusion process with mortal particles), and (ii) random walkers that can annihilate in pairs. In both examples we calculate the variances of the (non-Poissonian) stationary distributions of N.

Dusty Pair Plasma—Wave Propagation and Diffusive Transition of Oscillations

NASA Astrophysics Data System (ADS)

Atamaniuk, Barbara; Turski, Andrzej J.

2011-11-01

The crucial point of the paper is the relation between equilibrium distributions of plasma species and the type of propagation or diffusive transition of plasma response to a disturbance. The paper contains a unified treatment of disturbance propagation (transport) in the linearized Vlasov electron-positron and fullerene pair plasmas containing charged dust impurities, based on the space-time convolution integral equations. Electron-positron-dust/ion (e-p-d/i) plasmas are rather widespread in nature. Space-time responses of multi-component linearized Vlasov plasmas on the basis of multiple integral equations are invoked. An initial-value problem for Vlasov-Poisson/Ampère equations is reduced to the one multiple integral equation and the solution is expressed in terms of forcing function and its space-time convolution with the resolvent kernel. The forcing function is responsible for the initial disturbance and the resolvent is responsible for the equilibrium velocity distributions of plasma species. By use of resolvent equations, time-reversibility, space-reflexivity and the other symmetries are revealed. The symmetries carry on physical properties of Vlasov pair plasmas, e.g., conservation laws. Properly choosing equilibrium distributions for dusty pair plasmas, we can reduce the resolvent equation to: (i) the undamped dispersive wave equations, (ii) and diffusive transport equations of oscillations.

Memetic computing through bio-inspired heuristics integration with sequential quadratic programming for nonlinear systems arising in different physical models.

PubMed

Raja, Muhammad Asif Zahoor; Kiani, Adiqa Kausar; Shehzad, Azam; Zameer, Aneela

2016-01-01

In this study, bio-inspired computing is exploited for solving system of nonlinear equations using variants of genetic algorithms (GAs) as a tool for global search method hybrid with sequential quadratic programming (SQP) for efficient local search. The fitness function is constructed by defining the error function for systems of nonlinear equations in mean square sense. The design parameters of mathematical models are trained by exploiting the competency of GAs and refinement are carried out by viable SQP algorithm. Twelve versions of the memetic approach GA-SQP are designed by taking a different set of reproduction routines in the optimization process. Performance of proposed variants is evaluated on six numerical problems comprising of system of nonlinear equations arising in the interval arithmetic benchmark model, kinematics, neurophysiology, combustion and chemical equilibrium. Comparative studies of the proposed results in terms of accuracy, convergence and complexity are performed with the help of statistical performance indices to establish the worth of the schemes. Accuracy and convergence of the memetic computing GA-SQP is found better in each case of the simulation study and effectiveness of the scheme is further established through results of statistics based on different performance indices for accuracy and complexity.

MHD Equilibrium with Reversed Current Density and Magnetic Islands Revisited: the Vacuum Vector Potential Calculus

NASA Astrophysics Data System (ADS)

L. Braga, F.

2013-10-01

The solution of Grad-Shafranov equation determines the stationary behavior of fusion plasma inside a tokamak. To solve the equation it is necessary to know the toroidal current density profile. Recent works show that it is possible to determine a magnetohydrodynamic (MHD) equilibrium with reversed current density (RCD) profiles that presents magnetic islands. In this work we show analytical MHD equilibrium with a RCD profile and analyze the structure of the vacuum vector potential associated with these equilibria using the virtual casing principle.

A rapid method for the computation of equilibrium chemical composition of air to 15000 K

NASA Technical Reports Server (NTRS)

Prabhu, Ramadas K.; Erickson, Wayne D.

1988-01-01

A rapid computational method has been developed to determine the chemical composition of equilibrium air to 15000 K. Eleven chemically reacting species, i.e., O2, N2, O, NO, N, NO+, e-, N+, O+, Ar, and Ar+ are included. The method involves combining algebraically seven nonlinear equilibrium equations and four linear elemental mass balance and charge neutrality equations. Computational speeds for determining the equilibrium chemical composition are significantly faster than the often used free energy minimization procedure. Data are also included from which the thermodynamic properties of air can be computed. A listing of the computer program together with a set of sample results are included.

The Schrödinger–Langevin equation with and without thermal fluctuations

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

Katz, R., E-mail: roland.katz@subatech.in2p3.fr; Gossiaux, P.B., E-mail: Pol-Bernard.Gossiaux@subatech.in2p3.fr

2016-05-15

The Schrödinger–Langevin equation (SLE) is considered as an effective open quantum system formalism suitable for phenomenological applications involving a quantum subsystem interacting with a thermal bath. We focus on two open issues relative to its solutions: the stationarity of the excited states of the non-interacting subsystem when one considers the dissipation only and the thermal relaxation toward asymptotic distributions with the additional stochastic term. We first show that a proper application of the Madelung/polar transformation of the wave function leads to a non zero damping of the excited states of the quantum subsystem. We then study analytically and numerically themore » SLE ability to bring a quantum subsystem to the thermal equilibrium of statistical mechanics. To do so, concepts about statistical mixed states and quantum noises are discussed and a detailed analysis is carried with two kinds of noise and potential. We show that within our assumptions the use of the SLE as an effective open quantum system formalism is possible and discuss some of its limitations.« less

Treatment of wastewater containing toxic chromium using new activated carbon developed from date palm seed.

PubMed

El Nemr, Ahmed; Khaled, Azza; Abdelwahab, Ola; El-Sikaily, Amany

2008-03-21

The use of a new activated carbon developed from date palm seed wastes, generated in the jam industry, for removing toxic chromium from aqueous solution has been investigated. The activated carbon has been achieved from date palm seed by dehydrating methods using concentrated sulfuric acid. The batch experiments were conducted to determine the adsorption capacity of the biomass. The effect of initial metal concentration (25-125mgl(-1)), pH, contact time, and concentration of date palm seed carbon have been studied at room temperature. A strong dependence of the adsorption capacity on pH was observed, the capacity increase as pH value decrease and the optimum pH value is pH 1.0. Kinetics and adsorption equilibrium were studied at different sorbent doses. The adsorption process was fast and the equilibrium was reached within 180min. The maximum removal was 100% for 75mgl(-1) of Cr(+ concentration on 4gl(-1) carbon concentration and the maximum adsorption capacity was 120.48mgg(-1). The kinetic data were analyzed using various kinetic models - pseudo-first order equation, pseudo-second order equation, Elovich equation and intraparticle diffusion equation - and the equilibrium data were tested using several isotherm models, Langmuir, Freundlich, Koble-Corrigan, Redlich-Peterson, Tempkin, Dubinin-Radushkevich and Generalized isotherm equations. The Elovich equation and pseudo-second order equation provide the greatest accuracy for the kinetic data and Koble-Corrigan and Langmuir models the closest fit for the equilibrium data. Activation energy of sorption has also been evaluated as 0.115 and 0.229kJmol(-1).

Photocatalytic TMO-NMs adsorbent: Temperature-Time dependent Safranine degradation, sorption study validated under optimized effective equilibrium models parameter with standardized statistical analysis

PubMed Central

Wahab, Rizwan; Khan, Farheen; Kaushik, Nagendra Kumar; Musarrat, Javed; Al-Khedhairy, Abdulaziz A.

2017-01-01

In this paper, chemically synthesized copper oxide nanoparticles (CuO-NPs), were employed for two processes: one is photocatalytic degradation and second one adsorption for the sorption of safranine (SA) dye in an aqueous medium at pH = 12.01. The optimized analytes amount (nano-adsorbent = 0.10 g, conc. range of SA dye 56.13 ppm to 154.37 ppm, pH = 12.01, temperature 303 K) reached to equilibrium point in 80 min, which acquired for chemical adsorption-degradation reactions. The degredated SA dye data’s recorded by UV-visible spectroscopy for the occurrence of TMO-NMs of CuO-NPs at anticipated period of interval. The feasible performance of CuO-NPs was admirable, shows good adsorption capacity qm = 53.676 mg g−1 and most convenient to best fitted results establish by linear regression equation, corresponded for selected kinetic model (pseudo second order (R2 = 0.9981), equilibrium isotherm models (Freundlich, Langmuir, Dubnin-Radushkevich (D-R), Temkin, H-J and Halsey), and thermodynamic parameters (∆H° = 75461.909 J mol−1, ∆S° = 253.761 J mol−1, ∆G° = −1427.93 J mol−1, Ea = 185.142 J mol−1) with error analysis. The statistical study revealed that CuO-NPs was an effective adsorbent certified photocatalytic efficiency (η = 84.88%) for degradation of SA dye, exhibited more feasibility and good affinity toward adsorbate, the sorption capacity increases with increased temperature at equilibrium point. PMID:28195174

Beating the curse of dimension with accurate statistics for the Fokker-Planck equation in complex turbulent systems.

PubMed

Chen, Nan; Majda, Andrew J

2017-12-05

Solving the Fokker-Planck equation for high-dimensional complex dynamical systems is an important issue. Recently, the authors developed efficient statistically accurate algorithms for solving the Fokker-Planck equations associated with high-dimensional nonlinear turbulent dynamical systems with conditional Gaussian structures, which contain many strong non-Gaussian features such as intermittency and fat-tailed probability density functions (PDFs). The algorithms involve a hybrid strategy with a small number of samples [Formula: see text], where a conditional Gaussian mixture in a high-dimensional subspace via an extremely efficient parametric method is combined with a judicious Gaussian kernel density estimation in the remaining low-dimensional subspace. In this article, two effective strategies are developed and incorporated into these algorithms. The first strategy involves a judicious block decomposition of the conditional covariance matrix such that the evolutions of different blocks have no interactions, which allows an extremely efficient parallel computation due to the small size of each individual block. The second strategy exploits statistical symmetry for a further reduction of [Formula: see text] The resulting algorithms can efficiently solve the Fokker-Planck equation with strongly non-Gaussian PDFs in much higher dimensions even with orders in the millions and thus beat the curse of dimension. The algorithms are applied to a [Formula: see text]-dimensional stochastic coupled FitzHugh-Nagumo model for excitable media. An accurate recovery of both the transient and equilibrium non-Gaussian PDFs requires only [Formula: see text] samples! In addition, the block decomposition facilitates the algorithms to efficiently capture the distinct non-Gaussian features at different locations in a [Formula: see text]-dimensional two-layer inhomogeneous Lorenz 96 model, using only [Formula: see text] samples. Copyright © 2017 the Author(s). Published by PNAS.

Static Analysis of Large-Scale Multibody System Using Joint Coordinates and Spatial Algebra Operator

PubMed Central

Omar, Mohamed A.

2014-01-01

Initial transient oscillations inhibited in the dynamic simulations responses of multibody systems can lead to inaccurate results, unrealistic load prediction, or simulation failure. These transients could result from incompatible initial conditions, initial constraints violation, and inadequate kinematic assembly. Performing static equilibrium analysis before the dynamic simulation can eliminate these transients and lead to stable simulation. Most exiting multibody formulations determine the static equilibrium position by minimizing the system potential energy. This paper presents a new general purpose approach for solving the static equilibrium in large-scale articulated multibody. The proposed approach introduces an energy drainage mechanism based on Baumgarte constraint stabilization approach to determine the static equilibrium position. The spatial algebra operator is used to express the kinematic and dynamic equations of the closed-loop multibody system. The proposed multibody system formulation utilizes the joint coordinates and modal elastic coordinates as the system generalized coordinates. The recursive nonlinear equations of motion are formulated using the Cartesian coordinates and the joint coordinates to form an augmented set of differential algebraic equations. Then system connectivity matrix is derived from the system topological relations and used to project the Cartesian quantities into the joint subspace leading to minimum set of differential equations. PMID:25045732

A novel multiphysic model for simulation of swelling equilibrium of ionized thermal-stimulus responsive hydrogels

NASA Astrophysics Data System (ADS)

Li, Hua; Wang, Xiaogui; Yan, Guoping; Lam, K. Y.; Cheng, Sixue; Zou, Tao; Zhuo, Renxi

2005-03-01

In this paper, a novel multiphysic mathematical model is developed for simulation of swelling equilibrium of ionized temperature sensitive hydrogels with the volume phase transition, and it is termed the multi-effect-coupling thermal-stimulus (MECtherm) model. This model consists of the steady-state Nernst-Planck equation, Poisson equation and swelling equilibrium governing equation based on the Flory's mean field theory, in which two types of polymer-solvent interaction parameters, as the functions of temperature and polymer-network volume fraction, are specified with or without consideration of the hydrogen bond interaction. In order to examine the MECtherm model consisting of nonlinear partial differential equations, a meshless Hermite-Cloud method is used for numerical solution of one-dimensional swelling equilibrium of thermal-stimulus responsive hydrogels immersed in a bathing solution. The computed results are in very good agreements with experimental data for the variation of volume swelling ratio with temperature. The influences of the salt concentration and initial fixed-charge density are discussed in detail on the variations of volume swelling ratio of hydrogels, mobile ion concentrations and electric potential of both interior hydrogels and exterior bathing solution.

Static analysis of large-scale multibody system using joint coordinates and spatial algebra operator.

PubMed

Omar, Mohamed A

2014-01-01

Initial transient oscillations inhibited in the dynamic simulations responses of multibody systems can lead to inaccurate results, unrealistic load prediction, or simulation failure. These transients could result from incompatible initial conditions, initial constraints violation, and inadequate kinematic assembly. Performing static equilibrium analysis before the dynamic simulation can eliminate these transients and lead to stable simulation. Most exiting multibody formulations determine the static equilibrium position by minimizing the system potential energy. This paper presents a new general purpose approach for solving the static equilibrium in large-scale articulated multibody. The proposed approach introduces an energy drainage mechanism based on Baumgarte constraint stabilization approach to determine the static equilibrium position. The spatial algebra operator is used to express the kinematic and dynamic equations of the closed-loop multibody system. The proposed multibody system formulation utilizes the joint coordinates and modal elastic coordinates as the system generalized coordinates. The recursive nonlinear equations of motion are formulated using the Cartesian coordinates and the joint coordinates to form an augmented set of differential algebraic equations. Then system connectivity matrix is derived from the system topological relations and used to project the Cartesian quantities into the joint subspace leading to minimum set of differential equations.

Theory and modeling of atmospheric turbulence, part 2

NASA Technical Reports Server (NTRS)

Chen, C. M.

1984-01-01

Two dimensional geostrophic turbulence driven by a random force is investigated. Based on the Liouville equation, which simulates the primitive hydrodynamical equations, a group-kinetic theory of turbulence is developed and the kinetic equation of the scaled singlet distribution is derived. The kinetic equation is transformed into an equation of spectral balance in the equilibrium and non-equilibrium states. Comparison is made between the propagators and the Green's functions in the case of the non-asymptotic quasi-linear equation to prove the equivalence of both kinds of approximations used to describe perturbed trajectories of plasma turbulence. The microdynamical state of fluid turbulence is described by a hydrodynamical system and transformed into a master equation analogous to the Vlasov equation for plasma turbulence. The spectral balance for the velocity fluctuations of individual components shows that the scaled pressure strain correlation and the cascade transfer are two transport functions that play the most important roles.

Modeling stock return distributions with a quantum harmonic oscillator

NASA Astrophysics Data System (ADS)

Ahn, K.; Choi, M. Y.; Dai, B.; Sohn, S.; Yang, B.

2017-11-01

We propose a quantum harmonic oscillator as a model for the market force which draws a stock return from short-run fluctuations to the long-run equilibrium. The stochastic equation governing our model is transformed into a Schrödinger equation, the solution of which features “quantized” eigenfunctions. Consequently, stock returns follow a mixed χ distribution, which describes Gaussian and non-Gaussian features. Analyzing the Financial Times Stock Exchange (FTSE) All Share Index, we demonstrate that our model outperforms traditional stochastic process models, e.g., the geometric Brownian motion and the Heston model, with smaller fitting errors and better goodness-of-fit statistics. In addition, making use of analogy, we provide an economic rationale of the physics concepts such as the eigenstate, eigenenergy, and angular frequency, which sheds light on the relationship between finance and econophysics literature.

Entropy-based artificial viscosity stabilization for non-equilibrium Grey Radiation-Hydrodynamics

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

Delchini, Marc O., E-mail: delchinm@email.tamu.edu; Ragusa, Jean C., E-mail: jean.ragusa@tamu.edu; Morel, Jim, E-mail: jim.morel@tamu.edu

2015-09-01

The entropy viscosity method is extended to the non-equilibrium Grey Radiation-Hydrodynamic equations. The method employs a viscous regularization to stabilize the numerical solution. The artificial viscosity coefficient is modulated by the entropy production and peaks at shock locations. The added dissipative terms are consistent with the entropy minimum principle. A new functional form of the entropy residual, suitable for the Radiation-Hydrodynamic equations, is derived. We demonstrate that the viscous regularization preserves the equilibrium diffusion limit. The equations are discretized with a standard Continuous Galerkin Finite Element Method and a fully implicit temporal integrator within the MOOSE multiphysics framework. The methodmore » of manufactured solutions is employed to demonstrate second-order accuracy in both the equilibrium diffusion and streaming limits. Several typical 1-D radiation-hydrodynamic test cases with shocks (from Mach 1.05 to Mach 50) are presented to establish the ability of the technique to capture and resolve shocks.« less

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

USGS Publications Warehouse

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

1996-01-01

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

Calculating phase equilibrium properties of plasma pseudopotential model using hybrid Gibbs statistical ensemble Monte-Carlo technique

NASA Astrophysics Data System (ADS)

Butlitsky, M. A.; Zelener, B. B.; Zelener, B. V.

2015-11-01

Earlier a two-component pseudopotential plasma model, which we called a “shelf Coulomb” model has been developed. A Monte-Carlo study of canonical NVT ensemble with periodic boundary conditions has been undertaken to calculate equations of state, pair distribution functions, internal energies and other thermodynamics properties of the model. In present work, an attempt is made to apply so-called hybrid Gibbs statistical ensemble Monte-Carlo technique to this model. First simulation results data show qualitatively similar results for critical point region for both methods. Gibbs ensemble technique let us to estimate the melting curve position and a triple point of the model (in reduced temperature and specific volume coordinates): T* ≈ 0.0476, v* ≈ 6 × 10-4.

Acoustic equations of state for simple lattice Boltzmann velocity sets.

PubMed

Viggen, Erlend Magnus

2014-07-01

The lattice Boltzmann (LB) method typically uses an isothermal equation of state. This is not sufficient to simulate a number of acoustic phenomena where the equation of state cannot be approximated as linear and constant. However, it is possible to implement variable equations of state by altering the LB equilibrium distribution. For simple velocity sets with velocity components ξ(iα)∈(-1,0,1) for all i, these equilibria necessarily cause error terms in the momentum equation. These error terms are shown to be either correctable or negligible at the cost of further weakening the compressibility. For the D1Q3 velocity set, such an equilibrium distribution is found and shown to be unique. Its sound propagation properties are found for both forced and free waves, with some generality beyond D1Q3. Finally, this equilibrium distribution is applied to a nonlinear acoustics simulation where both mechanisms of nonlinearity are simulated with good results. This represents an improvement on previous such simulations and proves that the compressibility of the method is still sufficiently strong even for nonlinear acoustics.

Potential and flux field landscape theory. I. Global stability and dynamics of spatially dependent non-equilibrium systems.

PubMed

Wu, Wei; Wang, Jin

2013-09-28

We established a potential and flux field landscape theory to quantify the global stability and dynamics of general spatially dependent non-equilibrium deterministic and stochastic systems. We extended our potential and flux landscape theory for spatially independent non-equilibrium stochastic systems described by Fokker-Planck equations to spatially dependent stochastic systems governed by general functional Fokker-Planck equations as well as functional Kramers-Moyal equations derived from master equations. Our general theory is applied to reaction-diffusion systems. For equilibrium spatially dependent systems with detailed balance, the potential field landscape alone, defined in terms of the steady state probability distribution functional, determines the global stability and dynamics of the system. The global stability of the system is closely related to the topography of the potential field landscape in terms of the basins of attraction and barrier heights in the field configuration state space. The effective driving force of the system is generated by the functional gradient of the potential field alone. For non-equilibrium spatially dependent systems, the curl probability flux field is indispensable in breaking detailed balance and creating non-equilibrium condition for the system. A complete characterization of the non-equilibrium dynamics of the spatially dependent system requires both the potential field and the curl probability flux field. While the non-equilibrium potential field landscape attracts the system down along the functional gradient similar to an electron moving in an electric field, the non-equilibrium flux field drives the system in a curly way similar to an electron moving in a magnetic field. In the small fluctuation limit, the intrinsic potential field as the small fluctuation limit of the potential field for spatially dependent non-equilibrium systems, which is closely related to the steady state probability distribution functional, is found to be a Lyapunov functional of the deterministic spatially dependent system. Therefore, the intrinsic potential landscape can characterize the global stability of the deterministic system. The relative entropy functional of the stochastic spatially dependent non-equilibrium system is found to be the Lyapunov functional of the stochastic dynamics of the system. Therefore, the relative entropy functional quantifies the global stability of the stochastic system with finite fluctuations. Our theory offers an alternative general approach to other field-theoretic techniques, to study the global stability and dynamics of spatially dependent non-equilibrium field systems. It can be applied to many physical, chemical, and biological spatially dependent non-equilibrium systems.

A well-balanced finite volume scheme for the Euler equations with gravitation. The exact preservation of hydrostatic equilibrium with arbitrary entropy stratification

NASA Astrophysics Data System (ADS)

Käppeli, R.; Mishra, S.

2016-03-01

Context. Many problems in astrophysics feature flows which are close to hydrostatic equilibrium. However, standard numerical schemes for compressible hydrodynamics may be deficient in approximating this stationary state, where the pressure gradient is nearly balanced by gravitational forces. Aims: We aim to develop a second-order well-balanced scheme for the Euler equations. The scheme is designed to mimic a discrete version of the hydrostatic balance. It therefore can resolve a discrete hydrostatic equilibrium exactly (up to machine precision) and propagate perturbations, on top of this equilibrium, very accurately. Methods: A local second-order hydrostatic equilibrium preserving pressure reconstruction is developed. Combined with a standard central gravitational source term discretization and numerical fluxes that resolve stationary contact discontinuities exactly, the well-balanced property is achieved. Results: The resulting well-balanced scheme is robust and simple enough to be very easily implemented within any existing computer code that solves time explicitly or implicitly the compressible hydrodynamics equations. We demonstrate the performance of the well-balanced scheme for several astrophysically relevant applications: wave propagation in stellar atmospheres, a toy model for core-collapse supernovae, convection in carbon shell burning, and a realistic proto-neutron star.

BINARY CORRELATIONS IN IONIZED GASES

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

Balescu, R.; Taylor, H.S.

1961-01-01

An equation of evolution for the binary distribution function in a classical homogeneous, nonequilibrium plasma was derived. It is shown that the asymptotic (long-time) solution of this equation is the Debye distribution, thus providing a rigorous dynamical derivation of the equilibrium distribution. This proof is free from the fundamental conceptual difficulties of conventional equilibrium derivations. Out of equilibrium, a closed formula was obtained for the long living correlations, in terms of the momentum distribution function. These results should form an appropriate starting point for a rigorous theory of transport phenomena in plasmas, including the effect of molecular correlations. (auth)

On magnetoelectric coupling at equilibrium in continua with microstructure

NASA Astrophysics Data System (ADS)

Romeo, Maurizio

2017-10-01

A theory of micromorphic continua, applied to electromagnetic solids, is exploited to study magnetoelectric effects at equilibrium. Microcurrents are modeled by the microgyration tensor of stationary micromotions, compatibly with the balance equations for null microdeformation. The equilibrium of the continuum subject to electric and magnetic fields is reformulated accounting for electric multipoles which are related to microdeformation by evolution equations. Polarization and magnetization are derived for uniform fields under the micropolar reduction in terms of microstrain and octupole structural parameters. Nonlinear dependance on the electromagnetic fields is evidenced, compatibly with known theoretical and experimental results on magnetoelectric coupling.

Dynamical System Analysis of Reynolds Stress Closure Equations

NASA Technical Reports Server (NTRS)

Girimaji, Sharath S.

1997-01-01

In this paper, we establish the causality between the model coefficients in the standard pressure-strain correlation model and the predicted equilibrium states for homogeneous turbulence. We accomplish this by performing a comprehensive fixed point analysis of the modeled Reynolds stress and dissipation rate equations. The results from this analysis will be very useful for developing improved pressure-strain correlation models to yield observed equilibrium behavior.

Rapid computation of chemical equilibrium composition - An application to hydrocarbon combustion

NASA Technical Reports Server (NTRS)

Erickson, W. D.; Prabhu, R. K.

1986-01-01

A scheme for rapidly computing the chemical equilibrium composition of hydrocarbon combustion products is derived. A set of ten governing equations is reduced to a single equation that is solved by the Newton iteration method. Computation speeds are approximately 80 times faster than the often used free-energy minimization method. The general approach also has application to many other chemical systems.

Flux Jacobian Matrices For Equilibrium Real Gases

NASA Technical Reports Server (NTRS)

Vinokur, Marcel

1990-01-01

Improved formulation includes generalized Roe average and extension to three dimensions. Flux Jacobian matrices derived for use in numerical solutions of conservation-law differential equations of inviscid flows of ideal gases extended to real gases. Real-gas formulation of these matrices retains simplifying assumptions of thermodynamic and chemical equilibrium, but adds effects of vibrational excitation, dissociation, and ionization of gas molecules via general equation of state.

A gravitational potential finding for rotating cosmological body in the context of proto-planetary dynamics problem solving

NASA Astrophysics Data System (ADS)

Krot, Alexander M.

2008-09-01

The statistical theory for a cosmological body forming (so-called the spheroidal body model) has been proposed in [1]-[9]. Within the framework of this theory, bodies have fuzzy outlines and are represented by means of spheroidal forms [1],[2]. In the work [3], it has been investigated a slowly evolving in time process of a gravitational compression of a spheroidal body close to an unstable equilibrium state. In the papers [4],[5], the equation of motion of particles inside the weakly gravitating spheroidal body modeled by means of an ideal liquid has been obtained. Using Schwarzschild's and Kerr's metrics a consistency of the proposed statistical model with the general relativity has been shown in [6]. The proposed theory follows from the conception for forming a spheroidal body from protoplanetary nebula [7],[8]; it permits to derive the form of distribution functions for an immovable [1]-[5] and rotating spheroidal body [6]-[8] as well as their density masses and also the distribution function of specific angular momentum of the rotating uniformly spheroidal body [7],[8]. It is well-known there is not a statistical equilibrium in a gas-dust proto-planetary cloud because of long relaxation time for proto-planets formation in own gravitational field. This proto-planetary system behavior can be described by Jeans' equation in partial derivations relative to a distribution function [9]. The problem for finding a general solution of Jeans' equation is connected directly with an analytical expression for potential of gravitational field. Thus, the determination of gravitational potential is the main problem of statistical dynamics for proto-planetary system [9]. This work shows this task of proto-planetary dynamics can be solved on the basis of spheroidal bodies theory. The proposed theory permits to derive the form of gravitational potential for a rotating spheroidal body at a long distance from its center. Using the obtained analytical expression for potential of gravitational field, the gravitational strength (as well as angular momentum space function) in a remote zone of a slowly gravitational compressed rotating spheroidal body is obtained. As a result, a distribution function describing mechanical state of proto-planetary system can be found from the Jeans' equation. References: [1] Krot AM. The statistical model of gravitational interaction of particles. Uspekhi Sovremennoï Radioelektroniki (special issue "Cosmic Radiophysics", Moscow) 1996; 8: 66-81 (in Russian). [2] Krot AM. Use of the statistical model of gravity for analysis of nonhomogeneity in earth surface. Proc. SPIE's 13th Annual Intern. Symposium "AeroSense", Orlando, Florida, USA, April 5-9, 1999; 3710: 1248-1259. [3] Krot AM. Statistical description of gravitational field: a new approach. Proc. SPIE's 14th Annual Intern.Symposium "AeroSense", Orlando, Florida, USA, April 24-28, 2000; 4038: 1318-1329. [4] Krot AM. Gravidynamical equations for a weakly gravitating spheroidal body. Proc. SPIE's 15th Annual Intern. Symposium "AeroSense", Orlando, Florida, USA, April 16-20, 2001; 4394: 1271-1282. [5] Krot AM. Development of gravidynamical equations for a weakly gravitating body in the vicinity of absolute zero temperature. Proc. 53rd Intern. Astronautical Congress (IAC) - The 2nd World Space Congress-2002, Houston, Texas, USA, October 10-19, 2002; Preprint IAC-02-J.P.01: 1-11. [6] Krot AM. The statistical model of rotating and gravitating spheroidal body with the point of view of general relativity. Proc. 35th COSPAR Scientific Assembly, Paris, France, July 18-25, 2004; Abstract-Nr. COSPAR 04-A- 00162. [7] Krot A. The statistical approach to exploring formation of Solar system. Proc. European Geoscinces Union (EGU) General Assembly, Vienna, Austria, April 02-07, 2006; Geophysical Research Abstracts, vol. 8: EGU06-A- 00216, SRef-ID: 1607-7962/gra/. [8] Krot AM. The statistical model of original and evolution planets of Solar system and planetary satellities. Proc. European Planetary Science Congress, Berlin, Germany, September 18-22, 2006; Planetary Research Abstracts, ESPC2006-A-00014. [9] Krot A. On the principal difficulties and ways to their solution in the theory of gravitational condensation of infinitely distributed dust substance. Proc. XXIV IUGG General Assembly, Perugia, Italy, July 2-13, 2007; GS002 Symposium "Gravity Field", Abstract GS002-3598: 143-144.

Topographies and dynamics on multidimensional potential energy surfaces

NASA Astrophysics Data System (ADS)

Ball, Keith Douglas

The stochastic master equation is a valuable tool for elucidating potential energy surface (PES) details that govern structural relaxation in clusters, bulk systems, and protein folding. This work develops a comprehensive framework for studying non-equilibrium relaxation dynamics using the master equation. Since our master equations depend upon accurate partition function models for use in Rice-Ramsperger-Kassel-Marcus (RRK(M) transition state theory, this work introduces several such models employing various harmonic and anharmonic approximations and compares their predicted equilibrium population distributions with those determined from molecular dynamics. This comparison is performed for the fully-delineated surfaces (KCl)5 and Ar9 to evaluate model performance for potential surfaces with long- and short-range interactions, respectively. For each system, several models perform better than a simple harmonic approximation. While no model gives acceptable results for all minima, and optimal modeling strategies differ for (KCl)5 and Ar9, a particular one-parameter model gives the best agreement with simulation for both systems. We then construct master equations from these models and compare their isothermal relaxation predictions for (KCl)5 and Ar9 with molecular dynamics simulations. This is the first comprehensive test of the kinetic performance of partition function models of its kind. Our results show that accurate modeling of transition-state partition functions is more important for (KCl)5 than for Ar9 in reproducing simulation results, due to a marked stiffening anharmonicity in the transition-state normal modes of (KCl)5. For both systems, several models yield qualitative agreement with simulation over a large temperature range. To examine the robustness of the master equation when applied to larger systems, for which full topographical descriptions would be either impossible or infeasible, we compute relaxation predictions for Ar11 using a master equation constructed from data representing the full PES, and compare these predictions to those of reduced master equations based on statistical samples of the full PES. We introduce a sampling method which generates random, Boltzmann-weighted, energetically 'downhill' sequences. The study reveals that, at moderate temperatures, the slowest relaxation timescale converges as the number of sequences in a sample grows to ~1000. Furthermore, the asymptotic timescale is comparable to the full-PES value.

Quantum Kinetics and the Zeno Ansatz: Sterile Neutrino Dark Matter in the Early Universe

NASA Astrophysics Data System (ADS)

Dvornikov, Olexiy V.

We solved the quantum kinetic equations for the evolution of neutrino states in the early universe. Starting at high temperatures, we evolve neutrino states to observe the resonant conversion of active-to-sterile neutrinos in a lepton asymmetric (more neutrinos than anti-neutrinos) universe. We find that at high temperatures, the high neutrino scattering and oscillation rates enforce a local equilibrium that balances the growth of coherence at the oscillation rate and the damping of coherence through scattering. This equilibrium, which we call a "quantum kinetic equilibrium," appears to approximately hold throughout the neutrino evolution, from the initial conditions through resonances that may be non adiabatic. Using this quantum kinetic equilibrium informs a proper choice of the initial conditions of the neutrino state and the relaxation process that occurs to this equilibrium when the initial conditions (as are typically chosen in the literature) are not coincident with the equilibrium values. We also discuss how to use this equilibrium to reduce the computational expense of solving the full quantum kinetic equations for neutrino states evolving in the early universe.

Prediction of gas/particle partitioning of polybrominated diphenyl ethers (PBDEs) in global air: A theoretical study

NASA Astrophysics Data System (ADS)

Li, Y.-F.; Ma, W.-L.; Yang, M.

2015-02-01

Gas/particle (G/P) partitioning of semi-volatile organic compounds (SVOCs) is an important process that primarily governs their atmospheric fate, long-range atmospheric transport, and their routes of entering the human body. All previous studies on this issue are hypothetically based on equilibrium conditions, the results of which do not predict results from monitoring studies well in most cases. In this study, a steady-state model instead of an equilibrium-state model for the investigation of the G/P partitioning behavior of polybrominated diphenyl ethers (PBDEs) was established, and an equation for calculating the partition coefficients under steady state (KPS) of PBDEs (log KPS = log KPE + logα) was developed in which an equilibrium term (log KPE = log KOA + logfOM -11.91 where fOM is organic matter content of the particles) and a non-equilibrium term (log α, caused by dry and wet depositions of particles), both being functions of log KOA (octanol-air partition coefficient), are included. It was found that the equilibrium is a special case of steady state when the non-equilibrium term equals zero. A criterion to classify the equilibrium and non-equilibrium status of PBDEs was also established using two threshold values of log KOA, log KOA1, and log KOA2, which divide the range of log KOA into three domains: equilibrium, non-equilibrium, and maximum partition domain. Accordingly, two threshold values of temperature t, tTH1 when log KOA = log KOA1 and tTH2 when log KOA = log KOA2, were identified, which divide the range of temperature also into the same three domains for each PBDE congener. We predicted the existence of the maximum partition domain (the values of log KPS reach a maximum constant of -1.53) that every PBDE congener can reach when log KOA ≥ log KOA2, or t ≤ tTH2. The novel equation developed in this study was applied to predict the G/P partition coefficients of PBDEs for our Chinese persistent organic pollutants (POPs) Soil and Air Monitoring Program, Phase 2 (China-SAMP-II) program and other monitoring programs worldwide, including in Asia, Europe, North America, and the Arctic, and the results matched well with all the monitoring data, except those obtained at e-waste sites due to the unpredictable PBDE emissions at these sites. This study provided evidence that the newly developed steady-state-based equation is superior to the equilibrium-state-based equation that has been used in describing the G/P partitioning behavior over decades. We suggest that the investigation on G/P partitioning behavior for PBDEs should be based onsteady-state, not equilibrium state, and equilibrium is just a special case of steady-state when non-equilibrium factors can be ignored. We also believe that our new equation provides a useful tool for environmental scientists in both monitoring and modeling research on G/P partitioning of PBDEs and can be extended to predict G/P partitioning behavior for other SVOCs as well.

On axisymmetric resistive MHD equilibria with flow free of Pfirsch-Schlüter diffusion

NASA Astrophysics Data System (ADS)

Throumoulopoulos, George N.; Tasso, Henri

2002-11-01

The equilibrium of an axisymmetric magnetically confined plasma with anisotropic electrical conductivity and flows parallel to the magnetic field is investigated within the framework of the MHD theory by keeping the convective flow term in the momentum equation. It turns out that the stationary states are determined by a second-order partial differential equation for the poloidal magnetic flux function along with a Bernoulli equation for the density identical in form with the respective ideal MHD equations; equilibrium consistent expressions for the conductivities σ_allel and σ_⊥ parallel and perpendicular to the magnetic field are also derived from Ohm's and Faraday's laws. Unlike in the case of stationary states with isotropic conductivity and parallel flows (see [1]) the equilibrium is compatible with non-vanishing poloidal currents. For incompressible flows exact solutions of the above mentioned set of equations can be constructed with σ_allel and σ_⊥ profiles compatible with collisional conductivity profiles, i.e. profiles peaked close to the magnetic axis, vanishing on the boundary and such that σ_allel> σ_⊥. In particular, an exact equilibrium describing a toroidal plasma of arbitrary aspect ratio being contained within a perfectly conducting boundary of rectangular cross-section and peaked toroidal current density profile vanishing on the boundary is further considered. For this equilibrium in the case of vanishing flows the difference σ_allel-σ_⊥ for the reversed field pinch scaling Bp Bt (where Bp and Bt are the poloidal and toroidal magnetic field components) is nearly two times larger than that for the tokamak scaling B_p 0.1 B_t. [1] G. N. Throumoulopoulos, H. Tasso, J. Plasma Physics 64, 601 (2000).

Modelling non-equilibrium thermodynamic systems from the speed-gradient principle.

PubMed

Khantuleva, Tatiana A; Shalymov, Dmitry S

2017-03-06

The application of the speed-gradient (SG) principle to the non-equilibrium distribution systems far away from thermodynamic equilibrium is investigated. The options for applying the SG principle to describe the non-equilibrium transport processes in real-world environments are discussed. Investigation of a non-equilibrium system's evolution at different scale levels via the SG principle allows for a fresh look at the thermodynamics problems associated with the behaviour of the system entropy. Generalized dynamic equations for finite and infinite number of constraints are proposed. It is shown that the stationary solution to the equations, resulting from the SG principle, entirely coincides with the locally equilibrium distribution function obtained by Zubarev. A new approach to describe time evolution of systems far from equilibrium is proposed based on application of the SG principle at the intermediate scale level of the system's internal structure. The problem of the high-rate shear flow of viscous fluid near the rigid plane plate is discussed. It is shown that the SG principle allows closed mathematical models of non-equilibrium processes to be constructed.This article is part of the themed issue 'Horizons of cybernetical physics'. © 2017 The Author(s).

Modelling non-equilibrium thermodynamic systems from the speed-gradient principle

NASA Astrophysics Data System (ADS)

Khantuleva, Tatiana A.; Shalymov, Dmitry S.

2017-03-01

The application of the speed-gradient (SG) principle to the non-equilibrium distribution systems far away from thermodynamic equilibrium is investigated. The options for applying the SG principle to describe the non-equilibrium transport processes in real-world environments are discussed. Investigation of a non-equilibrium system's evolution at different scale levels via the SG principle allows for a fresh look at the thermodynamics problems associated with the behaviour of the system entropy. Generalized dynamic equations for finite and infinite number of constraints are proposed. It is shown that the stationary solution to the equations, resulting from the SG principle, entirely coincides with the locally equilibrium distribution function obtained by Zubarev. A new approach to describe time evolution of systems far from equilibrium is proposed based on application of the SG principle at the intermediate scale level of the system's internal structure. The problem of the high-rate shear flow of viscous fluid near the rigid plane plate is discussed. It is shown that the SG principle allows closed mathematical models of non-equilibrium processes to be constructed. This article is part of the themed issue 'Horizons of cybernetical physics'.

Modelling non-equilibrium thermodynamic systems from the speed-gradient principle

PubMed Central

Khantuleva, Tatiana A.

2017-01-01

The application of the speed-gradient (SG) principle to the non-equilibrium distribution systems far away from thermodynamic equilibrium is investigated. The options for applying the SG principle to describe the non-equilibrium transport processes in real-world environments are discussed. Investigation of a non-equilibrium system's evolution at different scale levels via the SG principle allows for a fresh look at the thermodynamics problems associated with the behaviour of the system entropy. Generalized dynamic equations for finite and infinite number of constraints are proposed. It is shown that the stationary solution to the equations, resulting from the SG principle, entirely coincides with the locally equilibrium distribution function obtained by Zubarev. A new approach to describe time evolution of systems far from equilibrium is proposed based on application of the SG principle at the intermediate scale level of the system's internal structure. The problem of the high-rate shear flow of viscous fluid near the rigid plane plate is discussed. It is shown that the SG principle allows closed mathematical models of non-equilibrium processes to be constructed. This article is part of the themed issue ‘Horizons of cybernetical physics’. PMID:28115617

The Equilibrium State of Colliding Electron Beams

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

Warnock, R

2003-12-12

We study a nonlinear integral equation that is a necessary condition on the equilibrium phase space distribution function of stored, colliding electron beams. It is analogous to the Haissinski equation, being derived from Vlasov-Fokker-Planck theory, but is quite different in form. The equation is analyzed for the case of the Chao-Ruth model of the beam-beam interaction in one degree of freedom, a so-called strong-strong model with nonlinear beam-beam force. We prove existence of a unique solution, for sufficiently small beam current, by an application of the implicit function theorem. We have not yet proved that this solution is positive, asmore » would be required to establish existence of an equilibrium. There is, however, numerical evidence of a positive solution. We expect that our analysis can be extended to more realistic models.« less

Solving nonlinear equilibrium equations of deformable systems by method of embedded polygons

NASA Astrophysics Data System (ADS)

Razdolsky, A. G.

2017-09-01

Solving of nonlinear algebraic equations is an obligatory stage of studying the equilibrium paths of nonlinear deformable systems. The iterative method for solving a system of nonlinear algebraic equations stated in an explicit or implicit form is developed in the present work. The method consists of constructing a sequence of polygons in Euclidean space that converge into a single point that displays the solution of the system. Polygon vertices are determined on the assumption that individual equations of the system are independent from each other and each of them is a function of only one variable. Initial positions of vertices for each subsequent polygon are specified at the midpoints of certain straight segments determined at the previous iteration. The present algorithm is applied for analytical investigation of the behavior of biaxially compressed nonlinear-elastic beam-column with an open thin-walled cross-section. Numerical examples are made for the I-beam-column on the assumption that its material follows a bilinear stress-strain diagram. A computer program based on the shooting method is developed for solving the problem. The method is reduced to numerical integration of a system of differential equations and to the solution of a system of nonlinear algebraic equations between the boundary values of displacements at the ends of the beam-column. A stress distribution at the beam-column cross-sections is determined by subdividing the cross-section area into many small cells. The equilibrium path for the twisting angle and the lateral displacements tend to the stationary point when the load is increased. Configuration of the path curves reveals that the ultimate load is reached shortly once the maximal normal stresses at the beam-column fall outside the limit of the elastic region. The beam-column has a unique equilibrium state for each value of the load, that is, there are no equilibrium states once the maximum load is reached.

Effect of helicity on the correlation time of large scales in turbulent flows

NASA Astrophysics Data System (ADS)

Cameron, Alexandre; Alexakis, Alexandros; Brachet, Marc-Étienne

2017-11-01

Solutions of the forced Navier-Stokes equation have been conjectured to thermalize at scales larger than the forcing scale, similar to an absolute equilibrium obtained for the spectrally truncated Euler equation. Using direct numeric simulations of Taylor-Green flows and general-periodic helical flows, we present results on the probability density function, energy spectrum, autocorrelation function, and correlation time that compare the two systems. In the case of highly helical flows, we derive an analytic expression describing the correlation time for the absolute equilibrium of helical flows that is different from the E-1 /2k-1 scaling law of weakly helical flows. This model predicts a new helicity-based scaling law for the correlation time as τ (k ) ˜H-1 /2k-1 /2 . This scaling law is verified in simulations of the truncated Euler equation. In simulations of the Navier-Stokes equations the large-scale modes of forced Taylor-Green symmetric flows (with zero total helicity and large separation of scales) follow the same properties as absolute equilibrium including a τ (k ) ˜E-1 /2k-1 scaling for the correlation time. General-periodic helical flows also show similarities between the two systems; however, the largest scales of the forced flows deviate from the absolute equilibrium solutions.

Thermostatted kinetic equations as models for complex systems in physics and life sciences.

PubMed

Bianca, Carlo

2012-12-01

Statistical mechanics is a powerful method for understanding equilibrium thermodynamics. An equivalent theoretical framework for nonequilibrium systems has remained elusive. The thermodynamic forces driving the system away from equilibrium introduce energy that must be dissipated if nonequilibrium steady states are to be obtained. Historically, further terms were introduced, collectively called a thermostat, whose original application was to generate constant-temperature equilibrium ensembles. This review surveys kinetic models coupled with time-reversible deterministic thermostats for the modeling of large systems composed both by inert matter particles and living entities. The introduction of deterministic thermostats allows to model the onset of nonequilibrium stationary states that are typical of most real-world complex systems. The first part of the paper is focused on a general presentation of the main physical and mathematical definitions and tools: nonequilibrium phenomena, Gauss least constraint principle and Gaussian thermostats. The second part provides a review of a variety of thermostatted mathematical models in physics and life sciences, including Kac, Boltzmann, Jager-Segel and the thermostatted (continuous and discrete) kinetic for active particles models. Applications refer to semiconductor devices, nanosciences, biological phenomena, vehicular traffic, social and economics systems, crowds and swarms dynamics. Copyright © 2012 Elsevier B.V. All rights reserved.

Latitudinal oscillations of plasma within the Io torus

NASA Technical Reports Server (NTRS)

Cummings, W. D.; Dessler, A. J.; Hill, T. W.

1980-01-01

The equilibrium latitude and the period of oscillations about this equilibrium latitude are calculated for a plasma in a centrifugally dominated tilted dipole magnetic field representing Jupiter's inner magnetosphere. It is found that for a hot plasma the equilibrium latitude in the magnetic equator, for a cold plasma it is the centrifugal equator, and for a warm plasma it is somewhere in between. An illustrative model is adopted in which atoms are sputtered from the Jupiter-facing hemisphere of Io and escape Io's gravity to be subsequently ionized some distance from Io. Finally, it is shown that ionization generally does not occur at the equilibrium altitude, and that the resulting latitudinal oscillations provide an explanation for the irregularities in electron concentration within the torus, as reported by the radioastronomy experiment aboard Voyager I.

Contour-time approach to the Bose-Hubbard model in the strong coupling regime: Studying two-point spatio-temporal correlations at the Hartree-Fock-Bogoliubov level

NASA Astrophysics Data System (ADS)

Fitzpatrick, Matthew R. C.; Kennett, Malcolm P.

2018-05-01

We develop a formalism that allows the study of correlations in space and time in both the superfluid and Mott insulating phases of the Bose-Hubbard Model. Specifically, we obtain a two particle irreducible effective action within the contour-time formalism that allows for both equilibrium and out of equilibrium phenomena. We derive equations of motion for both the superfluid order parameter and two-point correlation functions. To assess the accuracy of this formalism, we study the equilibrium solution of the equations of motion and compare our results to existing strong coupling methods as well as exact methods where possible. We discuss applications of this formalism to out of equilibrium situations.

Spectral-Lagrangian methods for collisional models of non-equilibrium statistical states

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

Gamba, Irene M.; Tharkabhushanam, Sri Harsha

We propose a new spectral Lagrangian based deterministic solver for the non-linear Boltzmann transport equation (BTE) in d-dimensions for variable hard sphere (VHS) collision kernels with conservative or non-conservative binary interactions. The method is based on symmetries of the Fourier transform of the collision integral, where the complexity in its computation is reduced to a separate integral over the unit sphere S{sup d-1}. The conservation of moments is enforced by Lagrangian constraints. The resulting scheme, implemented in free space, is very versatile and adjusts in a very simple manner to several cases that involve energy dissipation due to local micro-reversibilitymore » (inelastic interactions) or elastic models of slowing down process. Our simulations are benchmarked with available exact self-similar solutions, exact moment equations and analytical estimates for the homogeneous Boltzmann equation, both for elastic and inelastic VHS interactions. Benchmarking of the simulations involves the selection of a time self-similar rescaling of the numerical distribution function which is performed using the continuous spectrum of the equation for Maxwell molecules as studied first in Bobylev et al. [A.V. Bobylev, C. Cercignani, G. Toscani, Proof of an asymptotic property of self-similar solutions of the Boltzmann equation for granular materials, Journal of Statistical Physics 111 (2003) 403-417] and generalized to a wide range of related models in Bobylev et al. [A.V. Bobylev, C. Cercignani, I.M. Gamba, On the self-similar asymptotics for generalized non-linear kinetic Maxwell models, Communication in Mathematical Physics, in press. URL: ()]. The method also produces accurate results in the case of inelastic diffusive Boltzmann equations for hard spheres (inelastic collisions under thermal bath), where overpopulated non-Gaussian exponential tails have been conjectured in computations by stochastic methods [T.V. Noije, M. Ernst, Velocity distributions in homogeneously cooling and heated granular fluids, Granular Matter 1(57) (1998); M.H. Ernst, R. Brito, Scaling solutions of inelastic Boltzmann equations with over-populated high energy tails, Journal of Statistical Physics 109 (2002) 407-432; S.J. Moon, M.D. Shattuck, J. Swift, Velocity distributions and correlations in homogeneously heated granular media, Physical Review E 64 (2001) 031303; I.M. Gamba, S. Rjasanow, W. Wagner, Direct simulation of the uniformly heated granular Boltzmann equation, Mathematical and Computer Modelling 42 (2005) 683-700] and rigorously proven in Gamba et al. [I.M. Gamba, V. Panferov, C. Villani, On the Boltzmann equation for diffusively excited granular media, Communications in Mathematical Physics 246 (2004) 503-541(39)] and [A.V. Bobylev, I.M. Gamba, V. Panferov, Moment inequalities and high-energy tails for Boltzmann equations with inelastic interactions, Journal of Statistical Physics 116 (2004) 1651-1682].« less

Global Dynamics of Certain Homogeneous Second-Order Quadratic Fractional Difference Equation

PubMed Central

Garić-Demirović, M.; Kulenović, M. R. S.; Nurkanović, M.

2013-01-01

We investigate the basins of attraction of equilibrium points and minimal period-two solutions of the difference equation of the form x n+1 = x n−1 2/(ax n 2 + bx n x n−1 + cx n−1 2), n = 0,1, 2,…, where the parameters a,  b, and  c are positive numbers and the initial conditions x −1 and x 0 are arbitrary nonnegative numbers. The unique feature of this equation is the coexistence of an equilibrium solution and the minimal period-two solution both of which are locally asymptotically stable. PMID:24369451

Mesoscale Modeling of LX-17 Under Isentropic Compression

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

Springer, H K; Willey, T M; Friedman, G

Mesoscale simulations of LX-17 incorporating different equilibrium mixture models were used to investigate the unreacted equation-of-state (UEOS) of TATB. Candidate TATB UEOS were calculated using the equilibrium mixture models and benchmarked with mesoscale simulations of isentropic compression experiments (ICE). X-ray computed tomography (XRCT) data provided the basis for initializing the simulations with realistic microstructural details. Three equilibrium mixture models were used in this study. The single constituent with conservation equations (SCCE) model was based on a mass-fraction weighted specific volume and the conservation of mass, momentum, and energy. The single constituent equation-of-state (SCEOS) model was based on a mass-fraction weightedmore » specific volume and the equation-of-state of the constituents. The kinetic energy averaging (KEA) model was based on a mass-fraction weighted particle velocity mixture rule and the conservation equations. The SCEOS model yielded the stiffest TATB EOS (0.121{micro} + 0.4958{micro}{sup 2} + 2.0473{micro}{sup 3}) and, when incorporated in mesoscale simulations of the ICE, demonstrated the best agreement with VISAR velocity data for both specimen thicknesses. The SCCE model yielded a relatively more compliant EOS (0.1999{micro}-0.6967{micro}{sup 2} + 4.9546{micro}{sup 3}) and the KEA model yielded the most compliant EOS (0.1999{micro}-0.6967{micro}{sup 2}+4.9546{micro}{sup 3}) of all the equilibrium mixture models. Mesoscale simulations with the lower density TATB adiabatic EOS data demonstrated the least agreement with VISAR velocity data.« less

On the Boltzmann-Grad Limit for Smooth Hard-Sphere Systems

NASA Astrophysics Data System (ADS)

Tessarotto, Massimo; Cremaschini, Claudio; Mond, Michael; Asci, Claudio; Soranzo, Alessandro; Tironi, Gino

2018-03-01

The problem is posed of the prescription of the so-called Boltzmann-Grad limit operator (L_{BG}) for the N-body system of smooth hard-spheres which undergo unary, binary as well as multiple elastic instantaneous collisions. It is proved, that, despite the non-commutative property of the operator L_{BG}, the Boltzmann equation can nevertheless be uniquely determined. In particular, consistent with the claim of Uffink and Valente (Found Phys 45:404, 2015) that there is "no time-asymmetric ingredient" in its derivation, the Boltzmann equation is shown to be time-reversal symmetric. The proof is couched on the "ab initio" axiomatic approach to the classical statistical mechanics recently developed (Tessarotto et al. in Eur Phys J Plus 128:32, 2013). Implications relevant for the physical interpretation of the Boltzmann H-theorem and the phenomenon of decay to kinetic equilibrium are pointed out.

The solution of radiative transfer problems in molecular bands without the LTE assumption by accelerated lambda iteration methods

NASA Technical Reports Server (NTRS)

Kutepov, A. A.; Kunze, D.; Hummer, D. G.; Rybicki, G. B.

1991-01-01

An iterative method based on the use of approximate transfer operators, which was designed initially to solve multilevel NLTE line formation problems in stellar atmospheres, is adapted and applied to the solution of the NLTE molecular band radiative transfer in planetary atmospheres. The matrices to be constructed and inverted are much smaller than those used in the traditional Curtis matrix technique, which makes possible the treatment of more realistic problems using relatively small computers. This technique converges much more rapidly than straightforward iteration between the transfer equation and the equations of statistical equilibrium. A test application of this new technique to the solution of NLTE radiative transfer problems for optically thick and thin bands (the 4.3 micron CO2 band in the Venusian atmosphere and the 4.7 and 2.3 micron CO bands in the earth's atmosphere) is described.

Parametrically coupled fermionic oscillators: Correlation functions and phase-space description

NASA Astrophysics Data System (ADS)

Ghosh, Arnab

2015-01-01

A fermionic analog of a parametric amplifier is used to describe the joint quantum state of the two interacting fermionic modes. Based on a two-mode generalization of the time-dependent density operator, time evolution of the fermionic density operator is determined in terms of its two-mode Wigner and P function. It is shown that the equation of motion of the Wigner function corresponds to a fermionic analog of Liouville's equation. The equilibrium density operator for fermionic fields developed by Cahill and Glauber is thus extended to a dynamical context to show that the mathematical structures of both the correlation functions and the weight factors closely resemble their bosonic counterpart. It has been shown that the fermionic correlation functions are marked by a characteristic upper bound due to Fermi statistics, which can be verified in the matter wave counterpart of photon down-conversion experiments.

Comparison of linear and non-linear method in estimating the sorption isotherm parameters for safranin onto activated carbon.

PubMed

Kumar, K Vasanth; Sivanesan, S

2005-08-31

Comparison analysis of linear least square method and non-linear method for estimating the isotherm parameters was made using the experimental equilibrium data of safranin onto activated carbon at two different solution temperatures 305 and 313 K. Equilibrium data were fitted to Freundlich, Langmuir and Redlich-Peterson isotherm equations. All the three isotherm equations showed a better fit to the experimental equilibrium data. The results showed that non-linear method could be a better way to obtain the isotherm parameters. Redlich-Peterson isotherm is a special case of Langmuir isotherm when the Redlich-Peterson isotherm constant g was unity.

A Thermodynamic Theory of Solid Viscoelasticity. Part II:; Nonlinear Thermo-viscoelasticity

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Leonov, Arkady I.; Gray, Hugh R. (Technical Monitor)

2002-01-01

This paper, second in the series of three papers, develops a general, nonlinear, non-isothermal, compressible theory for finite rubber viscoelasticity and specifies it in a form convenient for solving problems important to the rubber, tire, automobile, and air-space industries, among others. Based on the quasi-linear approach of non-equilibrium thermodynamics, a general nonlinear theory of differential type has been developed for arbitrary non-isothermal deformations of viscoelastic solids. In this theory, the constitutive equations were presented as the sum of a rubber elastic (equilibrium) and a liquid type viscoelastic (non-equilibrium) terms. These equations have then been simplified using several modeling and simplicity arguments.

Decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio.

PubMed

Hu, Kainan; Zhang, Hongwu; Geng, Shaojuan

2016-10-01

A decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio is proposed. The local equilibrium distribution function including the rotational velocity of particle is decoupled into two parts, i.e., the local equilibrium distribution function of the translational velocity of particle and that of the rotational velocity of particle. From these two local equilibrium functions, two lattice Boltzmann models are derived via the Hermite expansion, namely one is in relation to the translational velocity and the other is connected with the rotational velocity. Accordingly, the distribution function is also decoupled. After this, the evolution equation is decoupled into the evolution equation of the translational velocity and that of the rotational velocity. The two evolution equations evolve separately. The lattice Boltzmann models used in the scheme proposed by this work are constructed via the Hermite expansion, so it is easy to construct new schemes of higher-order accuracy. To validate the proposed scheme, a one-dimensional shock tube simulation is performed. The numerical results agree with the analytical solutions very well.

Nonlinear theory for laminated and thick plates and shells including the effects of transverse shearing

NASA Technical Reports Server (NTRS)

Stein, M.

1985-01-01

Nonlinear strain displacement relations for three-dimensional elasticity are determined in orthogonal curvilinear coordinates. To develop a two-dimensional theory, the displacements are expressed by trigonometric series representation through-the-thickness. The nonlinear strain-displacement relations are expanded into series which contain all first and second degree terms. In the series for the displacements only the first few terms are retained. Insertion of the expansions into the three-dimensional virtual work expression leads to nonlinear equations of equilibrium for laminated and thick plates and shells that include the effects of transverse shearing. Equations of equilibrium and buckling equations are derived for flat plates and cylindrical shells. The shell equations reduce to conventional transverse shearing shell equations when the effects of the trigonometric terms are omitted and to classical shell equations when the trigonometric terms are omitted and the shell is assumed to be thin.

Equilibrium gas-oil ratio measurements using a microfluidic technique.

PubMed

Fisher, Robert; Shah, Mohammad Khalid; Eskin, Dmitry; Schmidt, Kurt; Singh, Anil; Molla, Shahnawaz; Mostowfi, Farshid

2013-07-07

A method for measuring the equilibrium GOR (gas-oil ratio) of reservoir fluids using microfluidic technology is developed. Live crude oils (crude oil with dissolved gas) are injected into a long serpentine microchannel at reservoir pressure. The fluid forms a segmented flow as it travels through the channel. Gas and liquid phases are produced from the exit port of the channel that is maintained at atmospheric conditions. The process is analogous to the production of crude oil from a formation. By using compositional analysis and thermodynamic principles of hydrocarbon fluids, we show excellent equilibrium between the produced gas and liquid phases is achieved. The GOR of a reservoir fluid is a key parameter in determining the equation of state of a crude oil. Equations of state that are commonly used in petroleum engineering and reservoir simulations describe the phase behaviour of a fluid at equilibrium state. Therefore, to accurately determine the coefficients of an equation of state, the produced gas and liquid phases have to be as close to the thermodynamic equilibrium as possible. In the examples presented here, the GORs measured with the microfluidic technique agreed with GOR values obtained from conventional methods. Furthermore, when compared to conventional methods, the microfluidic technique was simpler to perform, required less equipment, and yielded better repeatability.

Statistical Mechanics of Coherent Ising Machine — The Case of Ferromagnetic and Finite-Loading Hopfield Models —

NASA Astrophysics Data System (ADS)

Aonishi, Toru; Mimura, Kazushi; Utsunomiya, Shoko; Okada, Masato; Yamamoto, Yoshihisa

2017-10-01

The coherent Ising machine (CIM) has attracted attention as one of the most effective Ising computing architectures for solving large scale optimization problems because of its scalability and high-speed computational ability. However, it is difficult to implement the Ising computation in the CIM because the theories and techniques of classical thermodynamic equilibrium Ising spin systems cannot be directly applied to the CIM. This means we have to adapt these theories and techniques to the CIM. Here we focus on a ferromagnetic model and a finite loading Hopfield model, which are canonical models sharing a common mathematical structure with almost all other Ising models. We derive macroscopic equations to capture nonequilibrium phase transitions in these models. The statistical mechanical methods developed here constitute a basis for constructing evaluation methods for other Ising computation models.

A parallel domain decomposition-based implicit method for the Cahn–Hilliard–Cook phase-field equation in 3D

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

Zheng, Xiang; Yang, Chao; State Key Laboratory of Computer Science, Chinese Academy of Sciences, Beijing 100190

2015-03-15

We present a numerical algorithm for simulating the spinodal decomposition described by the three dimensional Cahn–Hilliard–Cook (CHC) equation, which is a fourth-order stochastic partial differential equation with a noise term. The equation is discretized in space and time based on a fully implicit, cell-centered finite difference scheme, with an adaptive time-stepping strategy designed to accelerate the progress to equilibrium. At each time step, a parallel Newton–Krylov–Schwarz algorithm is used to solve the nonlinear system. We discuss various numerical and computational challenges associated with the method. The numerical scheme is validated by a comparison with an explicit scheme of high accuracymore » (and unreasonably high cost). We present steady state solutions of the CHC equation in two and three dimensions. The effect of the thermal fluctuation on the spinodal decomposition process is studied. We show that the existence of the thermal fluctuation accelerates the spinodal decomposition process and that the final steady morphology is sensitive to the stochastic noise. We also show the evolution of the energies and statistical moments. In terms of the parallel performance, it is found that the implicit domain decomposition approach scales well on supercomputers with a large number of processors.« less

A New Approach to Modeling Densities and Equilibria of Ice and Gas Hydrate Phases

NASA Astrophysics Data System (ADS)

Zyvoloski, G.; Lucia, A.; Lewis, K. C.

2011-12-01

The Gibbs-Helmholtz Constrained (GHC) equation is a new cubic equation of state that was recently derived by Lucia (2010) and Lucia et al. (2011) by constraining the energy parameter in the Soave form of the Redlich-Kwong equation to satisfy the Gibbs-Helmholtz equation. The key attributes of the GHC equation are: 1) It is a multi-scale equation because it uses the internal energy of departure, UD, as a natural bridge between the molecular and bulk phase length scales. 2) It does not require acentric factors, volume translation, regression of parameters to experimental data, binary (kij) interaction parameters, or other forms of empirical correlations. 3) It is a predictive equation of state because it uses a database of values of UD determined from NTP Monte Carlo simulations. 4) It can readily account for differences in molecular size and shape. 5) It has been successfully applied to non-electrolyte mixtures as well as weak and strong aqueous electrolyte mixtures over wide ranges of temperature, pressure and composition to predict liquid density and phase equilibrium with up to four phases. 6) It has been extensively validated with experimental data. 7) The AAD% error between predicted and experimental liquid density is 1% while the AAD% error in phase equilibrium predictions is 2.5%. 8) It has been used successfully within the subsurface flow simulation program FEHM. In this work we describe recent extensions of the multi-scale predictive GHC equation to modeling the phase densities and equilibrium behavior of hexagonal ice and gas hydrates. In particular, we show that radial distribution functions, which can be determined by NTP Monte Carlo simulations, can be used to establish correct standard state fugacities of 1h ice and gas hydrates. From this, it is straightforward to determine both the phase density of ice or gas hydrates as well as any equilibrium involving ice and/or hydrate phases. A number of numerical results for mixtures of N2, O2, CH4, CO2, water, and NaCl in permafrost conditions are presented to illustrate the predictive capabilities of the multi-scale GHC equation. In particular, we show that the GHC equation correctly predicts 1) The density of 1h ice and methane hydrate to within 1%. 2) The melting curve for hexagonal ice. 3) The hydrate-gas phase co-existence curve. 4) Various phase equilibrium involving ice and hydrate phases. We also show that the GHC equation approach can be readily incorporated into subsurface flow simulation programs like FEHM to predict the behavior of permafrost and other reservoirs where ice and/or hydrates are present. Many geometric illustrations are used to elucidate key concepts. References A. Lucia, A Multi-Scale Gibbs Helmholtz Constrained Cubic Equation of State. J. Thermodynamics: Special Issue on Advances in Gas Hydrate Thermodynamics and Transport Properties. Available on-line [doi:10.1155/2010/238365]. A. Lucia, B.M. Bonk, A. Roy and R.R. Waterman, A Multi-Scale Framework for Multi-Phase Equilibrium Flash. Comput. Chem. Engng. In press.

Statistical Physics on the Eve of the 21st Century: in Honour of J B McGuire on the Occasion of His 65th Birthday

NASA Astrophysics Data System (ADS)

Batchelor, Murray T.; Wille, Luc T.

The Table of Contents for the book is as follows: * Preface * Modelling the Immune System - An Example of the Simulation of Complex Biological Systems * Brief Overview of Quantum Computation * Quantal Information in Statistical Physics * Modeling Economic Randomness: Statistical Mechanics of Market Phenomena * Essentially Singular Solutions of Feigenbaum- Type Functional Equations * Spatiotemporal Chaotic Dynamics in Coupled Map Lattices * Approach to Equilibrium of Chaotic Systems * From Level to Level in Brain and Behavior * Linear and Entropic Transformations of the Hydrophobic Free Energy Sequence Help Characterize a Novel Brain Polyprotein: CART's Protein * Dynamical Systems Response to Pulsed High-Frequency Fields * Bose-Einstein Condensates in the Light of Nonlinear Physics * Markov Superposition Expansion for the Entropy and Correlation Functions in Two and Three Dimensions * Calculation of Wave Center Deflection and Multifractal Analysis of Directed Waves Through the Study of su(1,1)Ferromagnets * Spectral Properties and Phases in Hierarchical Master Equations * Universality of the Distribution Functions of Random Matrix Theory * The Universal Chiral Partition Function for Exclusion Statistics * Continuous Space-Time Symmetries in a Lattice Field Theory * Quelques Cas Limites du Problème à N Corps Unidimensionnel * Integrable Models of Correlated Electrons * On the Riemann Surface of the Three-State Chiral Potts Model * Two Exactly Soluble Lattice Models in Three Dimensions * Competition of Ferromagnetic and Antiferromagnetic Order in the Spin-l/2 XXZ Chain at Finite Temperature * Extended Vertex Operator Algebras and Monomial Bases * Parity and Charge Conjugation Symmetries and S Matrix of the XXZ Chain * An Exactly Solvable Constrained XXZ Chain * Integrable Mixed Vertex Models Ftom the Braid-Monoid Algebra * From Yang-Baxter Equations to Dynamical Zeta Functions for Birational Tlansformations * Hexagonal Lattice Directed Site Animals * Direction in the Star-Triangle Relations * A Self-Avoiding Walk Through Exactly Solved Lattice Models in Statistical Mechanics

Entropy Production and Non-Equilibrium Steady States

NASA Astrophysics Data System (ADS)

Suzuki, Masuo

2013-01-01

The long-term issue of entropy production in transport phenomena is solved by separating the symmetry of the non-equilibrium density matrix ρ(t) in the von Neumann equation, as ρ(t) = ρs(t) + ρa(t) with the symmetric part ρs(t) and antisymmetric part ρa(t). The irreversible entropy production (dS/dt)irr is given in M. Suzuki, Physica A 390(2011)1904 by (dS/dt)irr = Tr( {H}(dρ s{(t)/dt))}/T for the Hamiltonian {H} of the relevant system. The general formulation of the extended von Neumann equation with energy supply and heat extraction is reviewed from the author's paper (M. S.,Physica A391(2012)1074). irreversibility; entropy production; transport phenomena; electric conduction; thermal conduction; linear response; Kubo formula; steady state; non-equilibrium density matrix; energy supply; symmetry-separated von Neumann equation; unboundedness.

Thermodynamic Study of Solid-Liquid Equilibrium in NaCl-NaBr-H2O System at 288.15 K

NASA Astrophysics Data System (ADS)

Li, Dan; Meng, Ling-zong; Deng, Tian-long; Guo, Ya-fei; Fu, Qing-Tao

2018-06-01

The solubility data, composition of the solid solution and refractive indices of the NaCl-NaBr-H2O system at 288.15 K were studied with the isothermal equilibrium dissolution method. The solubility diagram and refractive index diagram of this system were plotted at 288.15 K. The solubility diagram consists of two crystallization zones for solid solution Na(Cl,Br) · 2H2O and Na(Cl,Br), one invariant points cosaturated with two solid solution and two univariant solubility isothermal curves. On the basis of Pitzer and Harvie-Weare (HW) chemical models, the composition equations and solubility equilibrium constant equations of the solid solutions at 288.15 K were acquired using the solubility data, the composition of solid solutions, and binary Pitzer parameters. The solubilities calculated using the new method combining the equations are in good agreement with the experimental data.

Rapid determination of molar mass in modified Archibald experiments using direct fitting of the Lamm equation.

PubMed

Schuck, P; Millar, D B

1998-05-15

A new method is described that allows measurement of the molar mass of the solute within 15 to 30 min after start of a conventional long-column sedimentation equilibrium experiment. A series of scans of the concentration distribution in close vicinity of the meniscus, taken in rapid succession after the start of the centrifuge run, is analyzed by direct fitting using the Lamm equation and the Svedberg equation. In case of a single solute, this analysis of the initial depletion at the meniscus reveals its buoyant molar mass and sedimentation coefficient with an accuracy of approximately 10% and provides gross information about sample heterogeneity. This method can be used to study macromolecules that do not possess the prolonged stability needed in conventional sedimentation equilibrium experiments and it can increase the efficiency of sedimentation equilibrium experiments of previously uncharacterized samples.

Statistical equilibrium in cometary C2. II - Swan/Phillips band ratios

NASA Technical Reports Server (NTRS)

Swamy, K. S. K.; Odell, C. R.

1979-01-01

Statistical equilibrium calculations have been made for both the triplet and ground state singlets for C2 in comets, using the exchange rate as a free parameter. The predictions of the results are consistent with optical observations and may be tested definitively by accurate observations of the Phillips and Swan band ratios. Comparison with the one reported observation indicates compatibility with a low exchange rate and resonance fluorescence statistical equilibrium.

I -Love- Q relations for white dwarf stars

NASA Astrophysics Data System (ADS)

Boshkayev, K.; Quevedo, H.; Zhami, B.

2017-02-01

We investigate the equilibrium configurations of uniformly rotating white dwarfs, using Chandrasekhar and Salpeter equations of state in the framework of Newtonian physics. The Hartle formalism is applied to integrate the field equation together with the hydrostatic equilibrium condition. We consider the equations of structure up to the second order in the angular velocity, and compute all basic parameters of rotating white dwarfs to test the so-called moment of inertia, rotational Love number, and quadrupole moment (I-Love-Q) relations. We found that the I-Love-Q relations are also valid for white dwarfs regardless of the equation of state and nuclear composition. In addition, we show that the moment of inertia, quadrupole moment, and eccentricity (I-Q-e) relations are valid as well.

Statistical Physics of Electron Temperature of Low-Pressure Discharge Nitrogen Plasma with Non-Maxwellian EEDF

NASA Astrophysics Data System (ADS)

Akatsuka, Hiroshi; Tanaka, Yoshinori

2016-09-01

We reconsider electron temperature of non-equilibrium plasmas on the basis of thermodynamics and statistical physics. Following our previous study on the oxygen plasma in GEC 2015, we discuss the common issue for the nitrogen plasma. First, we solve the Boltzmann equation to obtain the electron energy distribution function (EEDF) F(ɛ) of the nitrogen plasma as a function of the reduced electric field E / N . We also simultaneously solve the chemical kinetic equations of some essential excite species of nitrogen molecules and atoms, including vibrational distribution function (VDF). Next, we calculate the electron mean energy as U = < ɛ > =∫0∞ɛF(ɛ) dɛ and entropy S = - k∫0∞F(ɛ) ln [ F(ɛ) ] dɛ for each value of E / N . Then, we can obtain the electron temperature as Testat =[ ∂S / ∂U ] - 1 . After that, we discuss the difference between Testat and the kinetic temperature Tekin ≡(2 / 3) < ɛ > , as well as the temperature given as a slope of the calculated EEDF for each value of E / N . We found Testat is close to the slope at ɛ 4 eV in the EEPF.

Einstein's Approach to Statistical Mechanics: The 1902-04 Papers

NASA Astrophysics Data System (ADS)

Peliti, Luca; Rechtman, Raúl

2017-05-01

We summarize the papers published by Einstein in the Annalen der Physik in the years 1902-1904 on the derivation of the properties of thermal equilibrium on the basis of the mechanical equations of motion and of the calculus of probabilities. We point out the line of thought that led Einstein to an especially economical foundation of the discipline, and to focus on fluctuations of the energy as a possible tool for establishing the validity of this foundation. We also sketch a comparison of Einstein's approach with that of Gibbs, suggesting that although they obtained similar results, they had different motivations and interpreted them in very different ways.

Departures from LTE Populations Versus Anomalous Abundances: the Effects of Heating

NASA Technical Reports Server (NTRS)

Underhill, A. B.

1985-01-01

The deposit of nonradiative heat and momentum in the mantle of a hot star affects the interpretation of the stellar spectrum in two ways. First, a superheated and moving plasma should be considered when doing the analysis, and second, a model atom which is appropriate for the physical state of the line forming regions. Some examples are presented for H and He showing how the changes in the electron temperature affect the solution of the equations of statistical equilibrium. The observed spectra of the Wolf-Raynet stars HD 191765, HD 192103, and HD 192163 are compatible with a normal H/He abundance ratio.

On the origins of approximations for stochastic chemical kinetics.

PubMed

Haseltine, Eric L; Rawlings, James B

2005-10-22

This paper considers the derivation of approximations for stochastic chemical kinetics governed by the discrete master equation. Here, the concepts of (1) partitioning on the basis of fast and slow reactions as opposed to fast and slow species and (2) conditional probability densities are used to derive approximate, partitioned master equations, which are Markovian in nature, from the original master equation. Under different conditions dictated by relaxation time arguments, such approximations give rise to both the equilibrium and hybrid (deterministic or Langevin equations coupled with discrete stochastic simulation) approximations previously reported. In addition, the derivation points out several weaknesses in previous justifications of both the hybrid and equilibrium systems and demonstrates the connection between the original and approximate master equations. Two simple examples illustrate situations in which these two approximate methods are applicable and demonstrate the two methods' efficiencies.

Sedimentation of a two-dimensional colloidal mixture exhibiting liquid-liquid and gas-liquid phase separation: a dynamical density functional theory study.

PubMed

Malijevský, Alexandr; Archer, Andrew J

2013-10-14

We present dynamical density functional theory results for the time evolution of the density distribution of a sedimenting model two-dimensional binary mixture of colloids. The interplay between the bulk phase behaviour of the mixture, its interfacial properties at the confining walls, and the gravitational field gives rise to a rich variety of equilibrium and non-equilibrium morphologies. In the fluid state, the system exhibits both liquid-liquid and gas-liquid phase separation. As the system sediments, the phase separation significantly affects the dynamics and we explore situations where the final state is a coexistence of up to three different phases. Solving the dynamical equations in two-dimensions, we find that in certain situations the final density profiles of the two species have a symmetry that is different from that of the external potentials, which is perhaps surprising, given the statistical mechanics origin of the theory. The paper concludes with a discussion on this.

Non-LTE CO, revisited

NASA Technical Reports Server (NTRS)

Ayres, Thomas R.; Wiedemann, Gunter R.

1989-01-01

A more extensive and detailed non-LTE simulation of the Delta v = 1 bands of CO than attempted previously is reported. The equations of statistical equilibrium are formulated for a model molecule containing 10 bound vibrational levels, each split into 121 rotational substates and connected by more than 1000 radiative transitions. Solutions are obtained for self-consistent populations and radiation fields by iterative application of the 'Lambda-operator' to an initial LTE distribution. The formalism is used to illustrate models of the sun and Arcturus. For the sun, negligible departures from LTE are found in either a theoretical radiative-equilibrium photosphere with outwardly falling temperatures in its highest layers or in a semiempirical hot chromosphere that reproduces the spatially averaged emission cores of Ca II H and K. The simulations demonstrate that the puzzling 'cool cores' of the CO Delta V = 1 bands observed in limb spectra of the sun and in flux spectra of Arcturus cannot be explained simply by non-LTE scattering effects.

Dynamics of Large-Scale Fluctuations in Native Proteins.

NASA Astrophysics Data System (ADS)

Erman, Burak; Erkip, Albert

2003-03-01

The fluctuations of residues of proteins about their equilibrium configurations are analyzed by Langevin dynamics. Residue pairs that are within a given cutoff distance of each other are assumed to be connected by linear springs. The action of the solvent and intramolecular interactions on each residue are treated as random noise. The correlations of fluctuations resulting from the solution of the Langevin equation are observed to be identical to those obtained by the Gaussian Network Model based on equilibrium statistical mechanics. The time delayed correlations of fluctuations, and the response of the protein to a given frequency and to a window of frequencies are determined. The fluctuations of the residues resulting from a given fixed externally applied frequency are evaluated for different modes of the system. Synchronous and asynchronous components of correlations for different modes are formulated. The results of the present study are applied to study the fluctuation dynamics of the 241 residue protein S. marcescens endonuclease (1QL0).

Thermal Conductivity of Gas Mixtures in Chemical Equilibrium

NASA Technical Reports Server (NTRS)

Brokaw, Richard S.

1960-01-01

The expression for the thermal conductivity of gas mixtures in chemical equilibrium is presented in a simpler and less restrictive form. This new form is shown to be equivalent to the previous equations.

Mathematical and computational studies of equilibrium capillary free surfaces

NASA Technical Reports Server (NTRS)

Albright, N.; Chen, N. F.; Concus, P.; Finn, R.

1977-01-01

The results of several independent studies are presented. The general question is considered of whether a wetting liquid always rises higher in a small capillary tube than in a larger one, when both are dipped vertically into an infinite reservoir. An analytical investigation is initiated to determine the qualitative behavior of the family of solutions of the equilibrium capillary free-surface equation that correspond to rotationally symmetric pendent liquid drops and the relationship of these solutions to the singular solution, which corresponds to an infinite spike of liquid extending downward to infinity. The block successive overrelaxation-Newton method and the generalized conjugate gradient method are investigated for solving the capillary equation on a uniform square mesh in a square domain, including the case for which the solution is unbounded at the corners. Capillary surfaces are calculated on the ellipse, on a circle with reentrant notches, and on other irregularly shaped domains using JASON, a general purpose program for solving nonlinear elliptic equations on a nonuniform quadrilaterial mesh. Analytical estimates for the nonexistence of solutions of the equilibrium capillary free-surface equation on the ellipse in zero gravity are evaluated.

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.

Infinite-mode squeezed coherent states and non-equilibrium statistical mechanics (phase-space-picture approach)

NASA Technical Reports Server (NTRS)

Yeh, Leehwa

1993-01-01

The phase-space-picture approach to quantum non-equilibrium statistical mechanics via the characteristic function of infinite-mode squeezed coherent states is introduced. We use quantum Brownian motion as an example to show how this approach provides an interesting geometrical interpretation of quantum non-equilibrium phenomena.

On the statistical mechanics of species abundance distributions.

PubMed

Bowler, Michael G; Kelly, Colleen K

2012-09-01

A central issue in ecology is that of the factors determining the relative abundance of species within a natural community. The proper application of the principles of statistical physics to species abundance distributions (SADs) shows that simple ecological properties could account for the near universal features observed. These properties are (i) a limit on the number of individuals in an ecological guild and (ii) per capita birth and death rates. They underpin the neutral theory of Hubbell (2001), the master equation approach of Volkov et al. (2003, 2005) and the idiosyncratic (extreme niche) theory of Pueyo et al. (2007); they result in an underlying log series SAD, regardless of neutral or niche dynamics. The success of statistical mechanics in this application implies that communities are in dynamic equilibrium and hence that niches must be flexible and that temporal fluctuations on all sorts of scales are likely to be important in community structure. Copyright © 2012 Elsevier Inc. All rights reserved.

Statistical theory and applications of lock-in carrierographic image pixel brightness dependence on multi-crystalline Si solar cell efficiency and photovoltage

NASA Astrophysics Data System (ADS)

Mandelis, Andreas; Zhang, Yu; Melnikov, Alexander

2012-09-01

A solar cell lock-in carrierographic image generation theory based on the concept of non-equilibrium radiation chemical potential was developed. An optoelectronic diode expression was derived linking the emitted radiative recombination photon flux (current density), the solar conversion efficiency, and the external load resistance via the closed- and/or open-circuit photovoltage. The expression was shown to be of a structure similar to the conventional electrical photovoltaic I-V equation, thereby allowing the carrierographic image to be used in a quantitative statistical pixel brightness distribution analysis with outcome being the non-contacting measurement of mean values of these important parameters averaged over the entire illuminated solar cell surface. This is the optoelectronic equivalent of the electrical (contacting) measurement method using an external resistor circuit and the outputs of the solar cell electrode grid, the latter acting as an averaging distribution network over the surface. The statistical theory was confirmed using multi-crystalline Si solar cells.

Modeling of non-thermal plasma in flammable gas mixtures

NASA Astrophysics Data System (ADS)

Napartovich, A. P.; Kochetov, I. V.; Leonov, S. B.

2008-07-01

An idea of using plasma-assisted methods of fuel ignition is based on non-equilibrium generation of chemically active species that speed up the combustion process. It is believed that gain in energy consumed for combustion acceleration by plasmas is due to the non-equilibrium nature of discharge plasma, which allows radicals to be produced in an above-equilibrium amount. Evidently, the size of the effect is strongly dependent on the initial temperature, pressure, and composition of the mixture. Of particular interest is comparison between thermal ignition of a fuel-air mixture and non-thermal plasma initiation of the combustion. Mechanisms of thermal ignition in various fuel-air mixtures have been studied for years, and a number of different mechanisms are known providing an agreement with experiments at various conditions. The problem is -- how to conform thermal chemistry approach to essentially non-equilibrium plasma description. The electric discharge produces much above-equilibrium amounts of chemically active species: atoms, radicals and ions. The point is that despite excess concentrations of a number of species, total concentration of these species is far below concentrations of the initial gas mixture. Therefore, rate coefficients for reactions of these discharge produced species with other gas mixture components are well known quantities controlled by the translational temperature, which can be calculated from the energy balance equation taking into account numerous processes initiated by plasma. A numerical model was developed combining traditional approach of thermal combustion chemistry with advanced description of the plasma kinetics based on solution of electron Boltzmann equation. This approach allows us to describe self-consistently strongly non-equilibrium electric discharge in chemically unstable (ignited) gas. Equations of pseudo-one-dimensional gas dynamics were solved in parallel with a system of thermal chemistry equations, kinetic equations for charged particles (electrons, positive and negative ions), and with the electric circuit equation. The electric circuit comprises power supply, ballast resistor connected in series with the discharge and capacity. Rate coefficients for electron-assisted reactions were calculated from solving the two-term spherical harmonic expansion of the Boltzmann equation. Such an approach allows us to describe influence of thermal chemistry reactions (burning) on the discharge characteristics. Results of comparison between the discharge and thermal ignition effects for mixtures of hydrogen or ethylene with dry air will be reported. Effects of acceleration of ignition by discharge plasma will be analyzed. In particular, the role of singlet oxygen produced effectively in the discharge in ignition speeding up will be discussed.

Tripolar vortex formation in dense quantum plasma with ion-temperature-gradients

NASA Astrophysics Data System (ADS)

Qamar, Anisa; Ata-ur-Rahman, Mirza, Arshad M.

2012-05-01

We have derived system of nonlinear equations governing the dynamics of low-frequency electrostatic toroidal ion-temperature-gradient mode for dense quantum magnetoplasma. For some specific profiles of the equilibrium density, temperature, and ion velocity gradients, the nonlinear equations admit a stationary solution in the form of a tripolar vortex. These results are relevant to understand nonlinear structure formation in dense quantum plasmas in the presence of equilibrium ion-temperature and density gradients.

Integrable structure in discrete shell membrane theory

PubMed Central

Schief, W. K.

2014-01-01

We present natural discrete analogues of two integrable classes of shell membranes. By construction, these discrete shell membranes are in equilibrium with respect to suitably chosen internal stresses and external forces. The integrability of the underlying equilibrium equations is proved by relating the geometry of the discrete shell membranes to discrete O surface theory. We establish connections with generalized barycentric coordinates and nine-point centres and identify a discrete version of the classical Gauss equation of surface theory. PMID:24808755

Integrable structure in discrete shell membrane theory.

PubMed

Schief, W K

2014-05-08

We present natural discrete analogues of two integrable classes of shell membranes. By construction, these discrete shell membranes are in equilibrium with respect to suitably chosen internal stresses and external forces. The integrability of the underlying equilibrium equations is proved by relating the geometry of the discrete shell membranes to discrete O surface theory. We establish connections with generalized barycentric coordinates and nine-point centres and identify a discrete version of the classical Gauss equation of surface theory.

Three dimensional PNS solutions of hypersonic internal flows with equilibrium chemistry

NASA Technical Reports Server (NTRS)

Liou, May-Fun

1989-01-01

An implicit procedure for solving parabolized Navier-Stokes equations under the assumption of a general equation of state for a gas in chemical equilibrium is given. A general and consistent approach for the evaluation of Jacobian matrices in the implicit operator avoids the use of unnecessary auxiliary quantities and approximations, and leads to a simple expression. Applications to two- and three-dimensional flow problems show efficiency in computer time and economy in storage.

Atmospheric Chemistry for Astrophysicists: A Self-consistent Formalism and Analytical Solutions for Arbitrary C/O

NASA Astrophysics Data System (ADS)

Heng, Kevin; Lyons, James R.; Tsai, Shang-Min

2016-01-01

We present a self-consistent formalism for computing and understanding the atmospheric chemistry of exoplanets from the viewpoint of an astrophysicist. Starting from the first law of thermodynamics, we demonstrate that the van’t Hoff equation (which describes the equilibrium constant), Arrhenius equation (which describes the rate coefficients), and procedures associated with the Gibbs free energy (minimization, rescaling) have a common physical and mathematical origin. We address an ambiguity associated with the equilibrium constant, which is used to relate the forward and reverse rate coefficients, and restate its two definitions. By necessity, one of the equilibrium constants must be dimensionless and equate to an exponential function involving the Gibbs free energy, while the other is a ratio of rate coefficients and must therefore possess physical units. We demonstrate that the Arrhenius equation takes on a functional form that is more general than previously stated without recourse to tagging on ad hoc functional forms. Finally, we derive analytical models of chemical systems, in equilibrium, with carbon, hydrogen, and oxygen. We include acetylene and are able to reproduce several key trends, versus temperature and carbon-to-oxygen ratio, published in the literature. The rich variety of behavior that mixing ratios exhibit as a function of the carbon-to-oxygen ratio is merely the outcome of stoichiometric book-keeping and not the direct consequence of temperature or pressure variations.

A thermodynamic equation of jamming

NASA Astrophysics Data System (ADS)

Lu, Kevin; Pirouz Kavehpour, H.

2008-03-01

Materials ranging from sand to fire-retardant to toothpaste are considered fragile, able to exhibit both solid and fluid-like properties across the jamming transition. Guided by granular flow experiments, our equation of jammed states is path-dependent, definable at different athermal equilibrium states. The non-equilibrium thermodynamics based on a structural temperature incorporate physical ageing to address the non-exponential, non-Arrhenious relaxation of granular flows. In short, jamming is simply viewed as a thermodynamic transition that occurs to preserve a positive configurational entropy above absolute zero. Without any free parameters, the proposed equation-of-state governs the mechanism of shear-banding and the associated features of shear-softening and thickness-invariance.

General multi-group macroscopic modeling for thermo-chemical non-equilibrium gas mixtures.

PubMed

Liu, Yen; Panesi, Marco; Sahai, Amal; Vinokur, Marcel

2015-04-07

This paper opens a new door to macroscopic modeling for thermal and chemical non-equilibrium. In a game-changing approach, we discard conventional theories and practices stemming from the separation of internal energy modes and the Landau-Teller relaxation equation. Instead, we solve the fundamental microscopic equations in their moment forms but seek only optimum representations for the microscopic state distribution function that provides converged and time accurate solutions for certain macroscopic quantities at all times. The modeling makes no ad hoc assumptions or simplifications at the microscopic level and includes all possible collisional and radiative processes; it therefore retains all non-equilibrium fluid physics. We formulate the thermal and chemical non-equilibrium macroscopic equations and rate coefficients in a coupled and unified fashion for gases undergoing completely general transitions. All collisional partners can have internal structures and can change their internal energy states after transitions. The model is based on the reconstruction of the state distribution function. The internal energy space is subdivided into multiple groups in order to better describe non-equilibrium state distributions. The logarithm of the distribution function in each group is expressed as a power series in internal energy based on the maximum entropy principle. The method of weighted residuals is applied to the microscopic equations to obtain macroscopic moment equations and rate coefficients succinctly to any order. The model's accuracy depends only on the assumed expression of the state distribution function and the number of groups used and can be self-checked for accuracy and convergence. We show that the macroscopic internal energy transfer, similar to mass and momentum transfers, occurs through nonlinear collisional processes and is not a simple relaxation process described by, e.g., the Landau-Teller equation. Unlike the classical vibrational energy relaxation model, which can only be applied to molecules, the new model is applicable to atoms, molecules, ions, and their mixtures. Numerical examples and model validations are carried out with two gas mixtures using the maximum entropy linear model: one mixture consists of nitrogen molecules undergoing internal excitation and dissociation and the other consists of nitrogen atoms undergoing internal excitation and ionization. Results show that the original hundreds to thousands of microscopic equations can be reduced to two macroscopic equations with almost perfect agreement for the total number density and total internal energy using only one or two groups. We also obtain good prediction of the microscopic state populations using 5-10 groups in the macroscopic equations.

The Onset of Double Diffusive Convection in a Viscoelastic Fluid-Saturated Porous Layer with Non-Equilibrium Model

PubMed Central

Yang, Zhixin; Wang, Shaowei; Zhao, Moli; Li, Shucai; Zhang, Qiangyong

2013-01-01

The onset of double diffusive convection in a viscoelastic fluid-saturated porous layer is studied when the fluid and solid phase are not in local thermal equilibrium. The modified Darcy model is used for the momentum equation and a two-field model is used for energy equation each representing the fluid and solid phases separately. The effect of thermal non-equilibrium on the onset of double diffusive convection is discussed. The critical Rayleigh number and the corresponding wave number for the exchange of stability and over-stability are obtained, and the onset criterion for stationary and oscillatory convection is derived analytically and discussed numerically. PMID:24312193

The onset of double diffusive convection in a viscoelastic fluid-saturated porous layer with non-equilibrium model.

PubMed

Yang, Zhixin; Wang, Shaowei; Zhao, Moli; Li, Shucai; Zhang, Qiangyong

2013-01-01

The onset of double diffusive convection in a viscoelastic fluid-saturated porous layer is studied when the fluid and solid phase are not in local thermal equilibrium. The modified Darcy model is used for the momentum equation and a two-field model is used for energy equation each representing the fluid and solid phases separately. The effect of thermal non-equilibrium on the onset of double diffusive convection is discussed. The critical Rayleigh number and the corresponding wave number for the exchange of stability and over-stability are obtained, and the onset criterion for stationary and oscillatory convection is derived analytically and discussed numerically.

Modeling Inflation Using a Non-Equilibrium Equation of Exchange

NASA Technical Reports Server (NTRS)

Chamberlain, Robert G.

2013-01-01

Inflation is a change in the prices of goods that takes place without changes in the actual values of those goods. The Equation of Exchange, formulated clearly in a seminal paper by Irving Fisher in 1911, establishes an equilibrium relationship between the price index P (also known as "inflation"), the economy's aggregate output Q (also known as "the real gross domestic product"), the amount of money available for spending M (also known as "the money supply"), and the rate at which money is reused V (also known as "the velocity of circulation of money"). This paper offers first a qualitative discussion of what can cause these factors to change and how those causes might be controlled, then develops a quantitative model of inflation based on a non-equilibrium version of the Equation of Exchange. Causal relationships are different from equations in that the effects of changes in the causal variables take time to play out-often significant amounts of time. In the model described here, wages track prices, but only after a distributed lag. Prices change whenever the money supply, aggregate output, or the velocity of circulation of money change, but only after a distributed lag. Similarly, the money supply depends on the supplies of domestic and foreign money, which depend on the monetary base and a variety of foreign transactions, respectively. The spreading of delays mitigates the shocks of sudden changes to important inputs, but the most important aspect of this model is that delays, which often have dramatic consequences in dynamic systems, are explicitly incorporated.macroeconomics, inflation, equation of exchange, non-equilibrium, Athena Project

Heterogeneous nucleation in multi-component vapor on a partially wettable charged conducting particle. II. The generalized Laplace, Gibbs-Kelvin, and Young equations and application to nucleation.

PubMed

Noppel, M; Vehkamäki, H; Winkler, P M; Kulmala, M; Wagner, P E

2013-10-07

Based on the results of a previous paper [M. Noppel, H. Vehkamäki, P. M. Winkler, M. Kulmala, and P. E. Wagner, J. Chem. Phys. 139, 134107 (2013)], we derive a thermodynamically consistent expression for reversible or minimal work needed to form a dielectric liquid nucleus of a new phase on a charged insoluble conducting sphere within a uniform macroscopic one- or multicomponent mother phase. The currently available model for ion-induced nucleation assumes complete spherical symmetry of the system, implying that the seed ion is immediately surrounded by the condensing liquid from all sides. We take a step further and treat more realistic geometries, where a cap-shaped liquid cluster forms on the surface of the seed particle. We derive the equilibrium conditions for such a cluster. The equalities of chemical potentials of each species between the nucleus and the vapor represent the conditions of chemical equilibrium. The generalized Young equation that relates contact angle with surface tensions, surface excess polarizations, and line tension, also containing the electrical contribution from triple line excess polarization, expresses the condition of thermodynamic equilibrium at three-phase contact line. The generalized Laplace equation gives the condition of mechanical equilibrium at vapor-liquid dividing surface: it relates generalized pressures in neighboring bulk phases at an interface with surface tension, excess surface polarization, and dielectric displacements in neighboring phases with two principal radii of surface curvature and curvatures of equipotential surfaces in neighboring phases at that point. We also re-express the generalized Laplace equation as a partial differential equation, which, along with electrostatic Laplace equations for bulk phases, determines the shape of a nucleus. We derive expressions that are suitable for calculations of the size and composition of a critical nucleus (generalized version of the classical Kelvin-Thomson equation).

Non-equilibrium dog-flea model

NASA Astrophysics Data System (ADS)

Ackerson, Bruce J.

2017-11-01

We develop the open dog-flea model to serve as a check of proposed non-equilibrium theories of statistical mechanics. The model is developed in detail. Then it is applied to four recent models for non-equilibrium statistical mechanics. Comparison of the dog-flea solution with these different models allows checking claims and giving a concrete example of the theoretical models.

Dynamics of tethered satellites in the vicinity of the Lagrangian point L2 of the Earth-Moon system

NASA Astrophysics Data System (ADS)

Baião, M. F.; Stuchi, T. J.

2017-08-01

This paper analyzes the dynamical evolution of satellites formed by two masses connected by a cable— tethered satellites. We derive the Lagrangian equations of motion in the neighborhood of the collinear equilibrium points, especially for the L2 , of the restricted problem of three bodies. The rigid body configuration is expanded in Legendre polynomials up to fourth degree. We present some numerical simulations of the influence of the parameters such as cable length, mass ratio and initial conditions in the behavior of the tethered satellites. The equation for the collinear equilibrium point is derived and numerically solved. The evolution of the equilibria with the variation of the cable length as a parameter is studied. We also present a discussion of the linear stability around these equilibria. Based on this analysis calculate some unstable Lyapunov orbits associated to these equilibrium points. We found periodic orbits in which the tether travels parallel to itself without involving the angular motion. The numerical applications are focused on the Earth-Moon system. However, the general character of the equations allows applications to the L1 equilibrium and obviously to systems other than the Earth-Moon.

Modeling of a complex, polar system with a modified Soave-Redlich-Kwong equation

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

Sturnfield, E.A.; Matherne, J.L.

1988-01-01

It is computationally feasible to use a simple equation of state (like a Redlich-Kwong) to calculate liquid fugacity but the simpler equations work well only for moderately non-ideal systems. More complex equations (like Ghemling-Lui-Prausnitz) predict system behavior more accurately but are much more complicated to use and can require fitting many parameters to data. This paper illustrates success in using a modified Redlich-Kwong to model a complex system including water, hydrogen, sub and supercritical ammonia, and amines. The binary interaction parameter ({Kappa}/sub ij/) of the Soave-Redlich-Kwong equation has been modified to be both asymmetric and temperature dependent. Further, the aimore » constant was determined by fitting vapor pressure data. Predicted model results are compared to literature (example 1) or plant data (examples 2-4) for four systems: 1. The ammonia-water binary over a wide range of pressure and temperature including ammonia above its critical. 2. A multicomponent Vapor-Liquid equilibrium flash tank and condenser containg hydrogen, amonia, water, and other heavier compounds. 3. A multicomponent vapor-liquid equilibrium flash tank containing water, heavier mines, and the amine salts. 4. A Liquid-Liquid-Vapor equilibrium decanter system containing water, ammonia, and an organic chloride.« less

Self-Consistency of the Theory of Elementary Stage Rates of Reversible Processes and the Equilibrium Distribution of Reaction Mixture Components

NASA Astrophysics Data System (ADS)

Tovbin, Yu. K.

2018-06-01

An analysis is presented of one of the key concepts of physical chemistry of condensed phases: the theory self-consistency in describing the rates of elementary stages of reversible processes and the equilibrium distribution of components in a reaction mixture. It posits that by equating the rates of forward and backward reactions, we must obtain the same equation for the equilibrium distribution of reaction mixture components, which follows directly from deducing the equation in equilibrium theory. Ideal reaction systems always have this property, since the theory is of a one-particle character. Problems arise in considering interparticle interactions responsible for the nonideal behavior of real systems. The Eyring and Temkin approaches to describing nonideal reaction systems are compared. Conditions for the self-consistency of the theory for mono- and bimolecular processes in different types of interparticle potentials, the degree of deviation from the equilibrium state, allowing for the internal motions of molecules in condensed phases, and the electronic polarization of the reagent environment are considered within the lattice gas model. The inapplicability of the concept of an activated complex coefficient for reaching self-consistency is demonstrated. It is also shown that one-particle approximations for considering intermolecular interactions do not provide a theory of self-consistency for condensed phases. We must at a minimum consider short-range order correlations.

Steady-State Electrodiffusion from the Nernst-Planck Equation Coupled to Local Equilibrium Monte Carlo Simulations.

PubMed

Boda, Dezső; Gillespie, Dirk

2012-03-13

We propose a procedure to compute the steady-state transport of charged particles based on the Nernst-Planck (NP) equation of electrodiffusion. To close the NP equation and to establish a relation between the concentration and electrochemical potential profiles, we introduce the Local Equilibrium Monte Carlo (LEMC) method. In this method, Grand Canonical Monte Carlo simulations are performed using the electrochemical potential specified for the distinct volume elements. An iteration procedure that self-consistently solves the NP and flux continuity equations with LEMC is shown to converge quickly. This NP+LEMC technique can be used in systems with diffusion of charged or uncharged particles in complex three-dimensional geometries, including systems with low concentrations and small applied voltages that are difficult for other particle simulation techniques.

Xcas as a Programming Environment for Stability Conditions for a Class of Differential Equation Models in Economics

NASA Astrophysics Data System (ADS)

Halkos, George E.; Tsilika, Kyriaki D.

2011-09-01

In this paper we examine the property of asymptotic stability in several dynamic economic systems, modeled in ordinary differential equation formulations of time parameter t. Asymptotic stability ensures intertemporal equilibrium for the economic quantity the solution stands for, regardless of what the initial conditions happen to be. Existence of economic equilibrium in continuous time models is checked via a Symbolic language, the Xcas program editor. Using stability theorems of differential equations as background a brief overview of symbolic capabilities of free software Xcas is given. We present computational experience with a programming style for stability results of ordinary linear and nonlinear differential equations. Numerical experiments on traditional applications of economic dynamics exhibit the simplicity clarity and brevity of input and output of our computer codes.

Evaporation in Capillary Porous Media at the Perfect Piston-Like Invasion Limit: Evidence of Nonlocal Equilibrium Effects

NASA Astrophysics Data System (ADS)

Attari Moghaddam, Alireza; Prat, Marc; Tsotsas, Evangelos; Kharaghani, Abdolreza

2017-12-01

The classical continuum modeling of evaporation in capillary porous media is revisited from pore network simulations of the evaporation process. The computed moisture diffusivity is characterized by a minimum corresponding to the transition between liquid and vapor transport mechanisms confirming previous interpretations. Also the study suggests an explanation for the scattering generally observed in the moisture diffusivity obtained from experimental data. The pore network simulations indicate a noticeable nonlocal equilibrium effect leading to a new interpretation of the vapor pressure-saturation relationship classically introduced to obtain the one-equation continuum model of evaporation. The latter should not be understood as a desorption isotherm as classically considered but rather as a signature of a nonlocal equilibrium effect. The main outcome of this study is therefore that nonlocal equilibrium two-equation model must be considered for improving the continuum modeling of evaporation.

Solute transport with multiple equilibrium-controlled or kinetically controlled chemical reactions

USGS Publications Warehouse

Friedly, John C.; Rubin, Jacob

1992-01-01

A new approach is applied to the problem of modeling solute transport accompanied by many chemical reactions. The approach, based on concepts of the concentration space and its stoichiometric subspaces, uses elements of the subspaces as primary dependent variables. It is shown that the resulting model equations are compact in form, isolate the chemical reaction expressions from flow expressions, and can be used for either equilibrium or kinetically controlled reactions. The implications of the results on numerical algorithms for solving the equations are discussed. The application of the theory is illustrated throughout with examples involving a simple but broadly representative set of reactions previously considered in the literature. Numerical results are presented for four interconnected reactions: a homogeneous complexation reaction, two sorption reactions, and a dissolution/precipitation reaction. Three cases are considered: (1) four kinetically controlled reactions, (2) four equilibrium-controlled reactions, and (3) a system with two kinetically controlled reactions and two equilibrium-controlled reactions.

Efficient steady-state solver for hierarchical quantum master equations

NASA Astrophysics Data System (ADS)

Zhang, Hou-Dao; Qiao, Qin; Xu, Rui-Xue; Zheng, Xiao; Yan, YiJing

2017-07-01

Steady states play pivotal roles in many equilibrium and non-equilibrium open system studies. Their accurate evaluations call for exact theories with rigorous treatment of system-bath interactions. Therein, the hierarchical equations-of-motion (HEOM) formalism is a nonperturbative and non-Markovian quantum dissipation theory, which can faithfully describe the dissipative dynamics and nonlinear response of open systems. Nevertheless, solving the steady states of open quantum systems via HEOM is often a challenging task, due to the vast number of dynamical quantities involved. In this work, we propose a self-consistent iteration approach that quickly solves the HEOM steady states. We demonstrate its high efficiency with accurate and fast evaluations of low-temperature thermal equilibrium of a model Fenna-Matthews-Olson pigment-protein complex. Numerically exact evaluation of thermal equilibrium Rényi entropies and stationary emission line shapes is presented with detailed discussion.

A statistical mechanics approach to computing rare transitions in multi-stable turbulent geophysical flows

NASA Astrophysics Data System (ADS)

Laurie, J.; Bouchet, F.

2012-04-01

Many turbulent flows undergo sporadic random transitions, after long periods of apparent statistical stationarity. For instance, paths of the Kuroshio [1], the Earth's magnetic field reversal, atmospheric flows [2], MHD experiments [3], 2D turbulence experiments [4,5], 3D flows [6] show this kind of behavior. The understanding of this phenomena is extremely difficult due to the complexity, the large number of degrees of freedom, and the non-equilibrium nature of these turbulent flows. It is however a key issue for many geophysical problems. A straightforward study of these transitions, through a direct numerical simulation of the governing equations, is nearly always impracticable. This is mainly a complexity problem, due to the large number of degrees of freedom involved for genuine turbulent flows, and the extremely long time between two transitions. In this talk, we consider two-dimensional and geostrophic turbulent models, with stochastic forces. We consider regimes where two or more attractors coexist. As an alternative to direct numerical simulation, we propose a non-equilibrium statistical mechanics approach to the computation of this phenomenon. Our strategy is based on large deviation theory [7], derived from a path integral representation of the stochastic process. Among the trajectories connecting two non-equilibrium attractors, we determine the most probable one. Moreover, we also determine the transition rates, and in which cases this most probable trajectory is a typical one. Interestingly, we prove that in the class of models we consider, a mechanism exists for diffusion over sets of connected attractors. For the type of stochastic forces that allows this diffusion, the transition between attractors is not a rare event. It is then very difficult to characterize the flow as bistable. However for another class of stochastic forces, this diffusion mechanism is prevented, and genuine bistability or multi-stability is observed. We discuss how these results are probably connected to the long debated existence of multi-stability in the atmosphere and oceans.

Kinetics of low-temperature transitions and a reaction rate theory from non-equilibrium distributions

PubMed Central

Aquilanti, Vincenzo; Coutinho, Nayara Dantas

2017-01-01

This article surveys the empirical information which originated both by laboratory experiments and by computational simulations, and expands previous understanding of the rates of chemical processes in the low-temperature range, where deviations from linearity of Arrhenius plots were revealed. The phenomenological two-parameter Arrhenius equation requires improvement for applications where interpolation or extrapolations are demanded in various areas of modern science. Based on Tolman's theorem, the dependence of the reciprocal of the apparent activation energy as a function of reciprocal absolute temperature permits the introduction of a deviation parameter d covering uniformly a variety of rate processes, from those where quantum mechanical tunnelling is significant and d < 0, to those where d > 0, corresponding to the Pareto–Tsallis statistical weights: these generalize the Boltzmann–Gibbs weight, which is recovered for d = 0. It is shown here how the weights arise, relaxing the thermodynamic equilibrium limit, either for a binomial distribution if d > 0 or for a negative binomial distribution if d < 0, formally corresponding to Fermion-like or Boson-like statistics, respectively. The current status of the phenomenology is illustrated emphasizing case studies; specifically (i) the super-Arrhenius kinetics, where transport phenomena accelerate processes as the temperature increases; (ii) the sub-Arrhenius kinetics, where quantum mechanical tunnelling propitiates low-temperature reactivity; (iii) the anti-Arrhenius kinetics, where processes with no energetic obstacles are rate-limited by molecular reorientation requirements. Particular attention is given for case (i) to the treatment of diffusion and viscosity, for case (ii) to formulation of a transition rate theory for chemical kinetics including quantum mechanical tunnelling, and for case (iii) to the stereodirectional specificity of the dynamics of reactions strongly hindered by the increase of temperature. This article is part of the themed issue ‘Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces’. PMID:28320904

Kinetics of low-temperature transitions and a reaction rate theory from non-equilibrium distributions.

PubMed

Aquilanti, Vincenzo; Coutinho, Nayara Dantas; Carvalho-Silva, Valter Henrique

2017-04-28

This article surveys the empirical information which originated both by laboratory experiments and by computational simulations, and expands previous understanding of the rates of chemical processes in the low-temperature range, where deviations from linearity of Arrhenius plots were revealed. The phenomenological two-parameter Arrhenius equation requires improvement for applications where interpolation or extrapolations are demanded in various areas of modern science. Based on Tolman's theorem, the dependence of the reciprocal of the apparent activation energy as a function of reciprocal absolute temperature permits the introduction of a deviation parameter d covering uniformly a variety of rate processes, from those where quantum mechanical tunnelling is significant and d  < 0, to those where d  > 0, corresponding to the Pareto-Tsallis statistical weights: these generalize the Boltzmann-Gibbs weight, which is recovered for d  = 0. It is shown here how the weights arise, relaxing the thermodynamic equilibrium limit, either for a binomial distribution if d  > 0 or for a negative binomial distribution if d  < 0, formally corresponding to Fermion-like or Boson-like statistics, respectively. The current status of the phenomenology is illustrated emphasizing case studies; specifically (i) the super -Arrhenius kinetics, where transport phenomena accelerate processes as the temperature increases; (ii) the sub -Arrhenius kinetics, where quantum mechanical tunnelling propitiates low-temperature reactivity; (iii) the anti -Arrhenius kinetics, where processes with no energetic obstacles are rate-limited by molecular reorientation requirements. Particular attention is given for case (i) to the treatment of diffusion and viscosity, for case (ii) to formulation of a transition rate theory for chemical kinetics including quantum mechanical tunnelling, and for case (iii) to the stereodirectional specificity of the dynamics of reactions strongly hindered by the increase of temperature.This article is part of the themed issue 'Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces'. © 2017 The Author(s).

Computer model of one-dimensional equilibrium controlled sorption processes

USGS Publications Warehouse

Grove, D.B.; Stollenwerk, K.G.

1984-01-01

A numerical solution to the one-dimensional solute-transport equation with equilibrium-controlled sorption and a first-order irreversible-rate reaction is presented. The computer code is written in FORTRAN language, with a variety of options for input and output for user ease. Sorption reactions include Langmuir, Freundlich, and ion-exchange, with or without equal valance. General equations describing transport and reaction processes are solved by finite-difference methods, with nonlinearities accounted for by iteration. Complete documentation of the code, with examples, is included. (USGS)

Einstein-Langevin and Einstein-Fokker-Planck equations for Oppenheimer-Snyder gravitational collapse in a spacetime with conformal vacuum fluctuations

NASA Astrophysics Data System (ADS)

Miller, Steven David

1999-10-01

A consistent extension of the Oppenheimer-Snyder gravitational collapse formalism is presented which incorporates stochastic, conformal, vacuum fluctuations of the metric tensor. This results in a tractable approach to studying the possible effects of vacuum fluctuations on collapse and singularity formation. The motivation here, is that it is known that coupling stochastic noise to a classical field theory can lead to workable methodologies that accommodate or reproduce many aspects of quantum theory, turbulence or structure formation. The effect of statistically averaging over the metric fluctuations gives the appearance of a deterministic Riemannian structure, with an induced non-vanishing cosmological constant arising from the nonlinearity. The Oppenheimer-Snyder collapse of a perfect fluid or dust star in the fluctuating or `turbulent' spacetime, is reformulated in terms of nonlinear Einstein-Langevin field equations, with an additional noise source in the energy-momentum tensor. The smooth deterministic worldlines of collapsing matter within the classical Oppenheimer-Snyder model, now become nonlinear Brownian motions due to the backreaction induced by vacuum fluctuations. As the star collapses, the matter worldlines become increasingly randomized since the backreaction coupling to the vacuum fluctuations is nonlinear; the input assumptions of the Hawking-Penrose singularity theorems should then be violated. Solving the nonlinear Einstein-Langevin field equation for collapse - via the Ito interpretation - gives a singularity-free solution, which is equivalent to the original Oppenheimer solution but with higher-order stochastic corrections; the original singular solution is recovered in the limit of zero vacuum fluctuations. The `geometro-hydrodynamics' of noisy gravitational collapse, were also translated into an equivalent mathematical formulation in terms of nonlinear Einstein-Fokker-Planck (EFP) continuity equations with respect to comoving coordinates: these describe the collapse as a conserved flow of probability. A solution was found in the dilute limit of weak fluctuations where the EFP equation is linearized. There is zero probability that the star collapses to a singular state in the presence of background vacuum fluctuations, but the singularity returns with unit probability when the fluctuations are reduced to zero. Finally, an EFP equation was considered with respect to standard exterior coordinates. Using the thermal Brownian motion paradigm, an exact stationary or equilibrium solution was found in the infinite standard time relaxation limit. The solution gives the conditions required for the final collapsed object (a black hole) to be in thermal equilibrium with the background vacuum fluctuations. From this solution, one recovers the Hawking temperature without using field theory. The stationary solution then seems to correspond to a black hole in thermal equilibrium with a fluctuating conformal scalar field; or the Hawking-Hartle state.

Kinetic Equation for an Unstable Plasma

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

Balescu, R.

1963-01-01

A kinetic equation is derived for the description of the evolution in time of the distribution of velocities in a spatially homogeneous ionized gas that, at the initial time, is able to sustain exponentially growing oscillations. This equation is expressed in terms of a functional of the distribution finction that obeys the same integral equation as in the stable case. Although the method of solution used in the stable case breaks down, the equation can still be solved in closed form under unstable conditions, and hence an explicit form of the kinetic equation is obtained. The latter contains the normalmore » collision term and a new additional term describing the stabilization of the plasma. The latter acts through friction and diffusion and brings the plasma into a state of neutral stability. From there on the system evolves toward thermal equilibrium under the action of the normal collision term as well as of an additional Fokker-Planck- like term with timedependent coefficients, which however becomes less and less efficient as the plasma approaches equilibrium.« less

Local equilibrium and the second law of thermodynamics for irreversible systems with thermodynamic inertia.

PubMed

Glavatskiy, K S

2015-10-28

Validity of local equilibrium has been questioned for non-equilibrium systems which are characterized by delayed response. In particular, for systems with non-zero thermodynamic inertia, the assumption of local equilibrium leads to negative values of the entropy production, which is in contradiction with the second law of thermodynamics. In this paper, we address this question by suggesting a variational formulation of irreversible evolution of a system with non-zero thermodynamic inertia. We introduce the Lagrangian, which depends on the properties of the normal and the so-called "mirror-image" systems. We show that the standard evolution equations, in particular, the Maxwell-Cattaneo-Vernotte equation, can be derived from the variational procedure without going beyond the assumption of local equilibrium. We also argue that the second law of thermodynamics in non-equilibrium should be understood as a consequence of the variational procedure and the property of local equilibrium. For systems with instantaneous response this leads to the standard requirement of the local instantaneous entropy production being always positive. However, if a system is characterized by delayed response, the formulation of the second law of thermodynamics should be altered. In particular, the quantity, which is always positive, is not the instantaneous entropy production, but the entropy production averaged over a proper time interval.

On an Acoustic Wave Equation Arising in Non-Equilibrium Gasdynamics. Classroom Notes

ERIC Educational Resources Information Center

Chandran, Pallath

2004-01-01

The sixth-order wave equation governing the propagation of one-dimensional acoustic waves in a viscous, heat conducting gaseous medium subject to relaxation effects has been considered. It has been reduced to a system of lower order equations corresponding to the finite speeds occurring in the equation, following a method due to Whitham. The lower…

Macroscopic Fluctuation Theory for Stationary Non-Equilibrium States

NASA Astrophysics Data System (ADS)

Bertini, L.; de Sole, A.; Gabrielli, D.; Jona-Lasinio, G.; Landim, C.

2002-05-01

We formulate a dynamical fluctuation theory for stationary non-equilibrium states (SNS) which is tested explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Within this theory we derive the following results: the modification of the Onsager-Machlup theory in the SNS; a general Hamilton-Jacobi equation for the macroscopic entropy; a non-equilibrium, nonlinear fluctuation dissipation relation valid for a wide class of systems; an H theorem for the entropy. We discuss in detail two models of stochastic boundary driven lattice gases: the zero range and the simple exclusion processes. In the first model the invariant measure is explicitly known and we verify the predictions of the general theory. For the one dimensional simple exclusion process, as recently shown by Derrida, Lebowitz, and Speer, it is possible to express the macroscopic entropy in terms of the solution of a nonlinear ordinary differential equation; by using the Hamilton-Jacobi equation, we obtain a logically independent derivation of this result.

The effect of capturing the correct turbulence dissipation rate in BHR

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

Schwarzkopf, John Dennis; Ristorcelli, Raymond

In this manuscript, we discuss the shortcoming of a quasi-equilibrium assumption made in the BHR closure model. Turbulence closure models generally assume fully developed turbulence, which is not applicable to 1) non-equilibrium turbulence (e.g. change in mean pressure gradient) or 2) laminar-turbulence transition flows. Based on DNS data, we show that the current BHR dissipation equation [modeled based on the fully developed turbulence phenomenology] does not capture important features of nonequilibrium flows. To demonstrate our thesis, we use the BHR equations to predict a non-equilibrium flow both with the BHR dissipation and the dissipation from DNS. We find that themore » prediction can be substantially improved, both qualitatively and quantitatively, with the correct dissipation rate. We conclude that a new set of nonequilibrium phenomenological assumptions must be used to develop a new model equation for the dissipation to accurately predict the turbulence time scale used by other models.« less

Gyrokinetic Magnetohydrodynamics and the Associated Equilibrium

NASA Astrophysics Data System (ADS)

Lee, W. W.; Hudson, S. R.; Ma, C. H.

2017-10-01

A proposed scheme for the calculations of gyrokinetic MHD and its associated equilibrium is discussed related a recent paper on the subject. The scheme is based on the time-dependent gyrokinetic vorticity equation and parallel Ohm's law, as well as the associated gyrokinetic Ampere's law. This set of equations, in terms of the electrostatic potential, ϕ, and the vector potential, ϕ , supports both spatially varying perpendicular and parallel pressure gradients and their associated currents. The MHD equilibrium can be reached when ϕ -> 0 and A becomes constant in time, which, in turn, gives ∇ . (J|| +J⊥) = 0 and the associated magnetic islands. Examples in simple cylindrical geometry will be given. The present work is partially supported by US DoE Grant DE-AC02-09CH11466.

Perturbative Out of Equilibrium Quantum Field Theory beyond the Gradient Approximation and Generalized Boltzmann Equation

NASA Astrophysics Data System (ADS)

Ozaki, H.

2004-01-01

Using the closed-time-path formalism, we construct perturbative frameworks, in terms of quasiparticle picture, for studying quasiuniform relativistic quantum field systems near equilibrium and non-equilibrium quasistationary systems. We employ the derivative expansion and take in up to the second-order term, i.e., one-order higher than the gradient approximation. After constructing self-energy resummed propagator, we formulated two kinds of mutually equivalent perturbative frameworks: The first one is formulated on the basis of the ``bare'' number density function, and the second one is formulated on the basis of ``physical'' number density function. In the course of construction of the second framework, the generalized Boltzmann equations directly come out, which describe the evolution of the system.

Computing diffusivities from particle models out of equilibrium

NASA Astrophysics Data System (ADS)

Embacher, Peter; Dirr, Nicolas; Zimmer, Johannes; Reina, Celia

2018-04-01

A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have Gaussian fluctuations but it is otherwise allowed to undergo arbitrary out-of-equilibrium evolutions. This could be potentially relevant for particle data obtained from experimental applications. The key idea underlying the method is that finite, yet large, particle systems formally obey stochastic partial differential equations of gradient flow type satisfying a fluctuation-dissipation relation. The strategy is here applied to three classic particle models, namely independent random walkers, a zero-range process and a symmetric simple exclusion process in one space dimension, to allow the comparison with analytic solutions.

A Simplified Method of Elastic-Stability Analysis for Thin Cylindrical Shells

NASA Technical Reports Server (NTRS)

Batdorf, S B

1947-01-01

This paper develops a new method for determining the buckling stresses of cylindrical shells under various loading conditions. In part I, the equation for the equilibrium of cylindrical shells introduced by Donnell in NACA report no. 479 to find the critical stresses of cylinders in torsion is applied to find critical stresses for cylinders with simply supported edges under other loading conditions. In part II, a modified form of Donnell's equation for the equilibrium of thin cylindrical shells is derived which is equivalent to Donnell's equation but has certain advantages in physical interpretation and in ease of solution, particularly in the case of shells having clamped edges. The question of implicit boundary conditions is also considered.

Some Theoretical Aspects of Nonzero Sum Differential Games and Applications to Combat Problems

DTIC Science & Technology

1971-06-01

the Equilibrium Solution . 7 Hamilton-Jacobi-Bellman Partial Differential Equations ............. .............. 9 Influence Function Differential...Linearly .......... ............ 18 Problem Statement .......... ............ 18 Formulation of LJB Equations, Influence Function Equations and the TPBVP...19 Control Lawe . . .. ...... ........... 21 Conditions for Influence Function Continuity along Singular Surfaces

Multiscale Multiphysics and Multidomain Models I: Basic Theory

PubMed Central

Wei, Guo-Wei

2013-01-01

This work extends our earlier two-domain formulation of a differential geometry based multiscale paradigm into a multidomain theory, which endows us the ability to simultaneously accommodate multiphysical descriptions of aqueous chemical, physical and biological systems, such as fuel cells, solar cells, nanofluidics, ion channels, viruses, RNA polymerases, molecular motors and large macromolecular complexes. The essential idea is to make use of the differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain of solvent from the microscopic domain of solute, and dynamically couple continuum and discrete descriptions. Our main strategy is to construct energy functionals to put on an equal footing of multiphysics, including polar (i.e., electrostatic) solvation, nonpolar solvation, chemical potential, quantum mechanics, fluid mechanics, molecular mechanics, coarse grained dynamics and elastic dynamics. The variational principle is applied to the energy functionals to derive desirable governing equations, such as multidomain Laplace-Beltrami (LB) equations for macromolecular morphologies, multidomain Poisson-Boltzmann (PB) equation or Poisson equation for electrostatic potential, generalized Nernst-Planck (NP) equations for the dynamics of charged solvent species, generalized Navier-Stokes (NS) equation for fluid dynamics, generalized Newton's equations for molecular dynamics (MD) or coarse-grained dynamics and equation of motion for elastic dynamics. Unlike the classical PB equation, our PB equation is an integral-differential equation due to solvent-solute interactions. To illustrate the proposed formalism, we have explicitly constructed three models, a multidomain solvation model, a multidomain charge transport model and a multidomain chemo-electro-fluid-MD-elastic model. Each solute domain is equipped with distinct surface tension, pressure, dielectric function, and charge density distribution. In addition to long-range Coulombic interactions, various non-electrostatic solvent-solute interactions are considered in the present modeling. We demonstrate the consistency between the non-equilibrium charge transport model and the equilibrium solvation model by showing the systematical reduction of the former to the latter at equilibrium. This paper also offers a brief review of the field. PMID:25382892

Multiscale Multiphysics and Multidomain Models I: Basic Theory.

PubMed

Wei, Guo-Wei

2013-12-01

This work extends our earlier two-domain formulation of a differential geometry based multiscale paradigm into a multidomain theory, which endows us the ability to simultaneously accommodate multiphysical descriptions of aqueous chemical, physical and biological systems, such as fuel cells, solar cells, nanofluidics, ion channels, viruses, RNA polymerases, molecular motors and large macromolecular complexes. The essential idea is to make use of the differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain of solvent from the microscopic domain of solute, and dynamically couple continuum and discrete descriptions. Our main strategy is to construct energy functionals to put on an equal footing of multiphysics, including polar (i.e., electrostatic) solvation, nonpolar solvation, chemical potential, quantum mechanics, fluid mechanics, molecular mechanics, coarse grained dynamics and elastic dynamics. The variational principle is applied to the energy functionals to derive desirable governing equations, such as multidomain Laplace-Beltrami (LB) equations for macromolecular morphologies, multidomain Poisson-Boltzmann (PB) equation or Poisson equation for electrostatic potential, generalized Nernst-Planck (NP) equations for the dynamics of charged solvent species, generalized Navier-Stokes (NS) equation for fluid dynamics, generalized Newton's equations for molecular dynamics (MD) or coarse-grained dynamics and equation of motion for elastic dynamics. Unlike the classical PB equation, our PB equation is an integral-differential equation due to solvent-solute interactions. To illustrate the proposed formalism, we have explicitly constructed three models, a multidomain solvation model, a multidomain charge transport model and a multidomain chemo-electro-fluid-MD-elastic model. Each solute domain is equipped with distinct surface tension, pressure, dielectric function, and charge density distribution. In addition to long-range Coulombic interactions, various non-electrostatic solvent-solute interactions are considered in the present modeling. We demonstrate the consistency between the non-equilibrium charge transport model and the equilibrium solvation model by showing the systematical reduction of the former to the latter at equilibrium. This paper also offers a brief review of the field.

Available Energy via Nonequilibrium Thermodynamics.

ERIC Educational Resources Information Center

Woollett, E. L.

1979-01-01

Presents basic relations involving the concept of available energy that are derived from the local equations of nonequilibrium thermodynamics. The equations and applications of the local thermodynamic equilibrium LTD model are also presented. (HM)

Comparison of Themodynamic and Transport Property Models for Computing Equilibrium High Enthalpy Flows

NASA Astrophysics Data System (ADS)

Ramasahayam, Veda Krishna Vyas; Diwakar, Anant; Bodi, Kowsik

2017-11-01

To study the flow of high temperature air in vibrational and chemical equilibrium, accurate models for thermodynamic state and transport phenomena are required. In the present work, the performance of a state equation model and two mixing rules for determining equilibrium air thermodynamic and transport properties are compared with that of curve fits. The thermodynamic state model considers 11 species which computes flow chemistry by an iterative process and the mixing rules considered for viscosity are Wilke and Armaly-Sutton. The curve fits of Srinivasan, which are based on Grabau type transition functions, are chosen for comparison. A two-dimensional Navier-Stokes solver is developed to simulate high enthalpy flows with numerical fluxes computed by AUSM+-up. The accuracy of state equation model and curve fits for thermodynamic properties is determined using hypersonic inviscid flow over a circular cylinder. The performance of mixing rules and curve fits for viscosity are compared using hypersonic laminar boundary layer prediction on a flat plate. It is observed that steady state solutions from state equation model and curve fits match with each other. Though curve fits are significantly faster the state equation model is more general and can be adapted to any flow composition.

Predicting mixture phase equilibria and critical behavior using the SAFT-VRX approach.

PubMed

Sun, Lixin; Zhao, Honggang; Kiselev, Sergei B; McCabe, Clare

2005-05-12

The SAFT-VRX equation of state combines the SAFT-VR equation with a crossover function that smoothly transforms the classical equation into a nonanalytical form close to the critical point. By a combinination of the accuracy of the SAFT-VR approach away from the critical region with the asymptotic scaling behavior seen at the critical point of real fluids, the SAFT-VRX equation can accurately describe the global fluid phase diagram. In previous work, we demonstrated that the SAFT-VRX equation very accurately describes the pvT and phase behavior of both nonassociating and associating pure fluids, with a minimum of fitting to experimental data. Here, we present a generalized SAFT-VRX equation of state for binary mixtures that is found to accurately predict the vapor-liquid equilibrium and pvT behavior of the systems studied. In particular, we examine binary mixtures of n-alkanes and carbon dioxide + n-alkanes. The SAFT-VRX equation accurately describes not only the gas-liquid critical locus for these systems but also the vapor-liquid equilibrium phase diagrams and thermal properties in single-phase regions.

Non-equilibrium Quasi-Chemical Nucleation Model

NASA Astrophysics Data System (ADS)

Gorbachev, Yuriy E.

2018-04-01

Quasi-chemical model, which is widely used for nucleation description, is revised on the basis of recent results in studying of non-equilibrium effects in reacting gas mixtures (Kolesnichenko and Gorbachev in Appl Math Model 34:3778-3790, 2010; Shock Waves 23:635-648, 2013; Shock Waves 27:333-374, 2017). Non-equilibrium effects in chemical reactions are caused by the chemical reactions themselves and therefore these contributions should be taken into account in the corresponding expressions for reaction rates. Corrections to quasi-equilibrium reaction rates are of two types: (a) spatially homogeneous (caused by physical-chemical processes) and (b) spatially inhomogeneous (caused by gas expansion/compression processes and proportional to the velocity divergency). Both of these processes play an important role during the nucleation and are included into the proposed model. The method developed for solving the generalized Boltzmann equation for chemically reactive gases is applied for solving the set of equations of the revised quasi-chemical model. It is shown that non-equilibrium processes lead to essential deviation of the quasi-stationary distribution and therefore the nucleation rate from its traditional form.

[Aluminum mobilization models of forest yellow earth in South China].

PubMed

Xin, Yan; Zhao, Yu; Duan, Lei

2009-07-15

For the application of acidification models in predicting effects of acid deposition and formulating control strategy in China, it is important selecting regionally applicable models of soil aluminum mobilization and determining their parameters. Based on the long-term monitoring results of soil water chemistry from four forested watersheds in South China, the applicability of a range of equilibriums describing aluminum mobilization was evaluated. The tested equilibriums included those for gibbsite, jurbanite, kaolinite, imogolite, and SOM-Al: Results show that the gibbsite equilibrium commonly used in several acidification models is not suitable for the typical forest soil in South China, while the modified empirical gibbsite equation is applicable with pK = - 2.40, a = 1.65 (for upper layer) and pK = - 2.82, a = 1.66 (for lower layers) at only pH > or = 4. Comparing with the empirical gibbsite equation, the other equilibriums do not perform better. It can also be seen that pAl varies slightly with pH decreases at pH < 4, which is unexplainable by any of these suggested equilibriums.

A new PIC noise reduction technique

NASA Astrophysics Data System (ADS)

Barnes, D. C.

2014-10-01

Numerical solution of the Vlasov equation is considered in a general situation in which there is an underlying static solution (equilibrium). There are no further assumptions about dimensionality, smallenss of orbits, or disparate time scales. The semi-characteristic (SC) method for Vlasov solution is described. The usual characteristics of the equation, which are the single particle orbits, are modified in such a way that the equilibrium phase-space flow is removed. In this way, the shot noise introduced by the usual discrete particle representation of the equilibrium is static in time and can be removed completely by subtraction. An almost exact algorithm for this is based on the observation that a (infinitesimal or) discrete time step of any equilibrium MC realization is again a realization of the equilibrium, building up strings of associated simulation particles. In this way, the only added discretization error arises from the need to extrapolate backward in time the chain end points one dt using a canonical transformation. Previously developed energy-conserving time-implicit methods are applied without modification. 1D ES examples of Landau damping and velocity-space instability are given to illustrate the method.

Spread of Ebola disease with susceptible exposed infected isolated recovered (SEIIhR) model

NASA Astrophysics Data System (ADS)

Azizah, Afina; Widyaningsih, Purnami; Retno Sari Saputro, Dewi

2017-06-01

Ebola is a deadly infectious disease and has caused an epidemic on several countries in West Africa. Mathematical modeling to study the spread of Ebola disease has been developed, including through models susceptible infected removed (SIR) and susceptible exposed infected removed (SEIR). Furthermore, susceptible exposed infected isolated recovered (SEIIhR) model has been derived. The aims of this research are to derive SEIIhR model for Ebola disease, to determine the patterns of its spread, to determine the equilibrium point and stability of the equilibrium point using phase plane analysis, and also to apply the SEIIhR model on Ebola epidemic in Sierra Leone in 2014. The SEIIhR model is a differential equation system. Pattern of ebola disease spread with SEIIhR model is solution of the differential equation system. The equilibrium point of SEIIhR model is unique and it is a disease-free equilibrium point that stable. Application of the model is based on the data Ebola epidemic in Sierra Leone. The free-disease equilibrium point (Se; Ee; Ie; Ihe; Re )=(5743865, 0, 0, 0, 0) is stable.

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).

A review on the solution of Grad-Shafranov equation in the cylindrical coordinates based on the Chebyshev collocation technique

NASA Astrophysics Data System (ADS)

Amerian, Z.; Salem, M. K.; Salar Elahi, A.; Ghoranneviss, M.

2017-03-01

Equilibrium reconstruction consists of identifying, from experimental measurements, a distribution of the plasma current density that satisfies the pressure balance constraint. Numerous methods exist to solve the Grad-Shafranov equation, describing the equilibrium of plasma confined by an axisymmetric magnetic field. In this paper, we have proposed a new numerical solution to the Grad-Shafranov equation (an axisymmetric, magnetic field transformed in cylindrical coordinates solved with the Chebyshev collocation method) when the source term (current density function) on the right-hand side is linear. The Chebyshev collocation method is a method for computing highly accurate numerical solutions of differential equations. We describe a circular cross-section of the tokamak and present numerical result of magnetic surfaces on the IR-T1 tokamak and then compare the results with an analytical solution.

Kardar-Parisi-Zhang universality in the phase distributions of one-dimensional exciton-polaritons

NASA Astrophysics Data System (ADS)

Squizzato, Davide; Canet, Léonie; Minguzzi, Anna

2018-05-01

Exciton-polaritons under driven-dissipative conditions exhibit a condensation transition that belongs to a different universality class from that of equilibrium Bose-Einstein condensates. By numerically solving the generalized Gross-Pitaevskii equation with realistic experimental parameters, we show that one-dimensional exciton-polaritons display fine features of Kardar-Parisi-Zhang (KPZ) dynamics. Beyond the scaling exponents, we show that their phase distribution follows the Tracy-Widom form predicted for KPZ growing interfaces. We moreover evidence a crossover to the stationary Baik-Rains statistics. We finally show that these features are unaffected on a certain timescale by the presence of a smooth disorder often present in experimental setups.

Nonequilibrium Precondensation of Classical Waves in Two Dimensions Propagating through Atomic Vapors

NASA Astrophysics Data System (ADS)

Šantić, Neven; Fusaro, Adrien; Salem, Sabeur; Garnier, Josselin; Picozzi, Antonio; Kaiser, Robin

2018-02-01

The nonlinear Schrödinger equation, used to describe the dynamics of quantum fluids, is known to be valid not only for massive particles but also for the propagation of light in a nonlinear medium, predicting condensation of classical waves. Here we report on the initial evolution of random waves with Gaussian statistics using atomic vapors as an efficient two dimensional nonlinear medium. Experimental and theoretical analysis of near field images reveal a phenomenon of nonequilibrium precondensation, characterized by a fast relaxation towards a precondensate fraction of up to 75%. Such precondensation is in contrast to complete thermalization to the Rayleigh-Jeans equilibrium distribution, requiring prohibitive long interaction lengths.

Detecting temperature fluctuations at equilibrium.

PubMed

Dixit, Purushottam D

2015-05-21

The Gibbs and the Boltzmann definition of temperature agree only in the macroscopic limit. The ambiguity in identifying the equilibrium temperature of a finite-sized 'small' system exchanging energy with a bath is usually understood as a limitation of conventional statistical mechanics. We interpret this ambiguity as resulting from a stochastically fluctuating temperature coupled with the phase space variables giving rise to a broad temperature distribution. With this ansatz, we develop the equilibrium statistics and dynamics of small systems. Numerical evidence using an analytically tractable model shows that the effects of temperature fluctuations can be detected in the equilibrium and dynamical properties of the phase space of the small system. Our theory generalizes statistical mechanics to small systems relevant in biophysics and nanotechnology.

Prediction of gas/particle partitioning of polybrominated diphenyl ethers (PBDEs) in global air: a theoretical study

NASA Astrophysics Data System (ADS)

Li, Y.-F.; Ma, W.-L.; Yang, M.

2014-09-01

Gas/particle (G / P) partitioning for most semivolatile organic compounds (SVOCs) is an important process that primarily governs their atmospheric fate, long-range atmospheric transport potential, and their routs to enter human body. All previous studies on this issue have been hypothetically derived from equilibrium conditions, the results of which do not predict results from monitoring studies well in most cases. In this study, a steady-state model instead of an equilibrium-state model for the investigation of the G / P partitioning behavior for polybrominated diphenyl ethers (PBDEs) was established, and an equation for calculating the partition coefficients under steady state (KPS) for PBDE congeners (log KPS = log KPE + logα) was developed, in which an equilibrium term (log KPE = log KOA + logfOM -11.91, where fOM is organic matter content of the particles) and a nonequilibrium term (logα, mainly caused by dry and wet depositions of particles), both being functions of log KOA (octanol-air partition coefficient), are included, and the equilibrium is a special case of steady state when the nonequilibrium term equals to zero. A criterion to classify the equilibrium and nonequilibrium status for PBDEs was also established using two threshold values of log KOA, log KOA1 and log KOA2, which divide the range of log KOA into 3 domains: equilibrium, nonequilibrium, and maximum partition domains; and accordingly, two threshold values of temperature t, tTH1 when log KOA = log KOA1 and tTH2 when log KOA = log KOA2, were identified, which divide the range of temperature also into the same 3 domains for each BDE congener. We predicted the existence of the maximum partition domain (the values of log KPS reach a maximum constant of -1.53) that every PBDE congener can reach when log KOA ≥ log KOA2, or t ≤ tTH2. The novel equation developed in this study was applied to predict the G / P partition coefficients of PBDEs for the published monitoring data worldwide, including Asia, Europe, North America, and the Arctic, and the results matched well with all the monitoring data, except those obtained at e-waste sites due to the unpredictable PBDE emissions at these sites. This study provided evidence that, the new developed steady-state-based equation is superior to the equilibrium-state-based equation that has been used in describing the G / P partitioning behavior in decades. We suggest that, the investigation on G / P partitioning behavior for PBDEs should be based on steady state, not equilibrium state, and equilibrium is just a special case of steady state when nonequilibrium factors can be ignored. We also believe that our new equation provides a useful tool for environmental scientists in both monitoring and modeling research on G / P partitioning for PBDEs and can be extended to predict G / P partitioning behavior for other SVOCs as well.

Thermodynamic and transport properties of gaseous tetrafluoromethane in chemical equilibrium

NASA Technical Reports Server (NTRS)

Hunt, J. L.; Boney, L. R.

1973-01-01

Equations and in computer code are presented for the thermodynamic and transport properties of gaseous, undissociated tetrafluoromethane (CF4) in chemical equilibrium. The computer code calculates the thermodynamic and transport properties of CF4 when given any two of five thermodynamic variables (entropy, temperature, volume, pressure, and enthalpy). Equilibrium thermodynamic and transport property data are tabulated and pressure-enthalpy diagrams are presented.

Stability of the thermodynamic equilibrium - A test of the validity of dynamic models as applied to gyroviscous perpendicular magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Faghihi, Mustafa; Scheffel, Jan; Spies, Guenther O.

1988-05-01

Stability of the thermodynamic equilibrium is put forward as a simple test of the validity of dynamic equations, and is applied to perpendicular gyroviscous magnetohydrodynamics (i.e., perpendicular magnetohydrodynamics with gyroviscosity added). This model turns out to be invalid because it predicts exponentially growing Alfven waves in a spatially homogeneous static equilibrium with scalar pressure.

Entropy is in Flux V3.4

NASA Astrophysics Data System (ADS)

Kadanoff, Leo P.

2017-05-01

The science of thermodynamics was put together in the Nineteenth Century to describe large systems in equilibrium. One part of thermodynamics defines entropy for equilibrium systems and demands an ever-increasing entropy for non-equilibrium ones. Since thermodynamics does not define entropy out of equilibrium, pure thermodynamics cannot follow the details of how this increase occurs. However, starting with the work of Ludwig Boltzmann in 1872, and continuing to the present day, various models of non-equilibrium behavior have been put together with the specific aim of generalizing the concept of entropy to non-equilibrium situations. This kind of entropy has been termed kinetic entropy to distinguish it from the thermodynamic variety. Knowledge of kinetic entropy started from Boltzmann's insight about his equation for the time dependence of gaseous systems. In this paper, his result is stated as a definition of kinetic entropy in terms of a local equation for the entropy density. This definition is then applied to Landau's theory of the Fermi liquid thereby giving the kinetic entropy within that theory. The dynamics of many condensed matter systems including Fermi liquids, low temperature superfluids, and ordinary metals lend themselves to the definition of kinetic entropy. In fact, entropy has been defined and used for a wide variety of situations in which a condensed matter system has been allowed to relax for a sufficient period so that the very most rapid fluctuations have been ironed out. One of the broadest applications of non-equilibrium analysis considers quantum degenerate systems using Martin-Schwinger Green's functions (Phys Rev 115:1342-1373, 1959) as generalized Wigner functions, g^<({p},ω ,{R},T) and g^>({p},ω ,{R},T). This paper describes once again how the quantum kinetic equations for these functions give locally defined conservation laws for mass momentum and energy. In local thermodynamic equilibrium, this kinetic theory enables a reasonable definition of the density of kinetic entropy. However, when the system is outside of local equilibrium, this definition fails. It is speculated that quantum entanglement is the source of this failure.

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.

One parameter family of master equations for logistic growth and BCM theory

NASA Astrophysics Data System (ADS)

De Oliveira, L. R.; Castellani, C.; Turchetti, G.

2015-02-01

We propose a one parameter family of master equations, for the evolution of a population, having the logistic equation as mean field limit. The parameter α determines the relative weight of linear versus nonlinear terms in the population number n ⩽ N entering the loss term. By varying α from 0 to 1 the equilibrium distribution changes from maximum growth to almost extinction. The former is a Gaussian centered at n = N, the latter is a power law peaked at n = 1. A bimodal distribution is observed in the transition region. When N grows and tends to ∞, keeping the value of α fixed, the distribution tends to a Gaussian centered at n = N whose limit is a delta function corresponding to the stable equilibrium of the mean field equation. The choice of the master equation in this family depends on the equilibrium distribution for finite values of N. The presence of an absorbing state for n = 0 does not change this picture since the extinction mean time grows exponentially fast with N. As a consequence for α close to zero extinction is not observed, whereas when α approaches 1 the relaxation to a power law is observed before extinction occurs. We extend this approach to a well known model of synaptic plasticity, the so called BCM theory in the case of a single neuron with one or two synapses.

Thermal Non-Equilibrium Flows in Three Space Dimensions

NASA Astrophysics Data System (ADS)

Zeng, Yanni

2016-01-01

We study the equations describing the motion of a thermal non-equilibrium gas in three space dimensions. It is a hyperbolic system of six equations with a relaxation term. The dissipation mechanism induced by the relaxation is weak in the sense that the Shizuta-Kawashima criterion is violated. This implies that a perturbation of a constant equilibrium state consists of two parts: one decays in time while the other stays. In fact, the entropy wave grows weakly along the particle path as the process is irreversible. We study thermal properties related to the well-posedness of the nonlinear system. We also obtain a detailed pointwise estimate on the Green's function for the Cauchy problem when the system is linearized around an equilibrium constant state. The Green's function provides a complete picture of the wave pattern, with an exact and explicit leading term. Comparing with existing results for one dimensional flows, our results reveal a new feature of three dimensional flows: not only does the entropy wave not decay, but the velocity also contains a non-decaying part, strongly coupled with its decaying one. The new feature is supported by the second order approximation via the Chapman-Enskog expansions, which are the Navier-Stokes equations with vanished shear viscosity and heat conductivity.

Linearized theory of inhomogeneous multiple 'water-bag' plasmas

NASA Technical Reports Server (NTRS)

Bloomberg, H. W.; Berk, H. L.

1973-01-01

Equations are derived for describing the inhomogeneous equilibrium and small deviations from the equilibrium, giving particular attention to systems with trapped particles. An investigation is conducted of periodic systems with a single trapped-particle water bag, taking into account the behavior of the perturbation equations at the turning points. An outline is provided concerning a procedure for obtaining the eigenvalues. The results of stability calculations connected with the sideband effects are considered along with questions regarding the general applicability of the multiple water-bag approach in stability calculations.

Exact solutions for the selection-mutation equilibrium in the Crow-Kimura evolutionary model.

PubMed

Semenov, Yuri S; Novozhilov, Artem S

2015-08-01

We reformulate the eigenvalue problem for the selection-mutation equilibrium distribution in the case of a haploid asexually reproduced population in the form of an equation for an unknown probability generating function of this distribution. The special form of this equation in the infinite sequence limit allows us to obtain analytically the steady state distributions for a number of particular cases of the fitness landscape. The general approach is illustrated by examples; theoretical findings are compared with numerical calculations. Copyright © 2015. Published by Elsevier Inc.

Estimation of Regional Evapotranspiration Using Remotely Sensed Land Surface Temperature. Part 2: Application of Equilibrium Evaporation Model to Estimate Evapotranspiration by Remote Sensing Technique. [Japan

NASA Technical Reports Server (NTRS)

Kotoda, K.; Nakagawa, S.; Kai, K.; Yoshino, M. M.; Takeda, K.; Seki, K.

1985-01-01

In a humid region like Japan, it seems that the radiation term in the energy balance equation plays a more important role for evapotranspiration then does the vapor pressure difference between the surface and lower atmospheric boundary layer. A Priestley-Taylor type equation (equilibrium evaporation model) is used to estimate evapotranspiration. Net radiation, soil heat flux, and surface temperature data are obtained. Only temperature data obtained by remotely sensed techniques are used.

Equations of state for explosive detonation products: The PANDA model

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

Kerley, G.I.

1994-05-01

This paper discusses a thermochemical model for calculating equations of state (EOS) for the detonation products of explosives. This model, which was first presented at the Eighth Detonation Symposium, is available in the PANDA code and is referred to here as ``the Panda model``. The basic features of the PANDA model are as follows. (1) Statistical-mechanical theories are used to construct EOS tables for each of the chemical species that are to be allowed in the detonation products. (2) The ideal mixing model is used to compute the thermodynamic functions for a mixture of these species, and the composition ofmore » the system is determined from assumption of chemical equilibrium. (3) For hydrocode calculations, the detonation product EOS are used in tabular form, together with a reactive burn model that allows description of shock-induced initiation and growth or failure as well as ideal detonation wave propagation. This model has been implemented in the three-dimensional Eulerian code, CTH.« less

Einstein's osmotic equilibrium of colloidal suspensions in conservative force fields

NASA Astrophysics Data System (ADS)

Fu, Jinxin; Ou-Yang, H. Daniel

2014-09-01

Predicted by Einstein in his 1905 paper on Brownian motion, colloidal particles in suspension reach osmotic equilibrium under gravity. The idea was demonstrated by J.B. Perrin to win Nobel Prize in Physics in 1926. We show Einstein's equation for osmotic equilibrium can be applied to colloids in a conservative force field generated by optical gradient forces. We measure the osmotic equation of state of 100nm Polystyrene latex particles in the presence of KCl salt and PEG polymer. We also obtain the osmotic compressibility, which is important for determining colloidal stability and the internal chemical potential, which is useful for predicting the phase transition of colloidal systems. This generalization allows for the use of any conservative force fields for systems ranging from colloidal systems to macromolecular solutions.

Local equilibrium and the second law of thermodynamics for irreversible systems with thermodynamic inertia

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

Glavatskiy, K. S.

Validity of local equilibrium has been questioned for non-equilibrium systems which are characterized by delayed response. In particular, for systems with non-zero thermodynamic inertia, the assumption of local equilibrium leads to negative values of the entropy production, which is in contradiction with the second law of thermodynamics. In this paper, we address this question by suggesting a variational formulation of irreversible evolution of a system with non-zero thermodynamic inertia. We introduce the Lagrangian, which depends on the properties of the normal and the so-called “mirror-image” systems. We show that the standard evolution equations, in particular, the Maxwell-Cattaneo-Vernotte equation, can bemore » derived from the variational procedure without going beyond the assumption of local equilibrium. We also argue that the second law of thermodynamics in non-equilibrium should be understood as a consequence of the variational procedure and the property of local equilibrium. For systems with instantaneous response this leads to the standard requirement of the local instantaneous entropy production being always positive. However, if a system is characterized by delayed response, the formulation of the second law of thermodynamics should be altered. In particular, the quantity, which is always positive, is not the instantaneous entropy production, but the entropy production averaged over a proper time interval.« less

Principle of maximum Fisher information from Hardy's axioms applied to statistical systems.

PubMed

Frieden, B Roy; Gatenby, Robert A

2013-10-01

Consider a finite-sized, multidimensional system in parameter state a. The system is either at statistical equilibrium or general nonequilibrium, and may obey either classical or quantum physics. L. Hardy's mathematical axioms provide a basis for the physics obeyed by any such system. One axiom is that the number N of distinguishable states a in the system obeys N=max. This assumes that N is known as deterministic prior knowledge. However, most observed systems suffer statistical fluctuations, for which N is therefore only known approximately. Then what happens if the scope of the axiom N=max is extended to include such observed systems? It is found that the state a of the system must obey a principle of maximum Fisher information, I=I(max). This is important because many physical laws have been derived, assuming as a working hypothesis that I=I(max). These derivations include uses of the principle of extreme physical information (EPI). Examples of such derivations were of the De Broglie wave hypothesis, quantum wave equations, Maxwell's equations, new laws of biology (e.g., of Coulomb force-directed cell development and of in situ cancer growth), and new laws of economic fluctuation and investment. That the principle I=I(max) itself derives from suitably extended Hardy axioms thereby eliminates its need to be assumed in these derivations. Thus, uses of I=I(max) and EPI express physics at its most fundamental level, its axiomatic basis in math.

Regarding `Information Preservation and Weather Forecasting for Black Holes' by S. W. Hawking

NASA Astrophysics Data System (ADS)

Winterberg, Friedwardt

2014-06-01

It is proposed that the `apparent horizons' assumed by Hawking to resolve the black hole information paradox, are in reality the regions where in Lorentzian relativity the absolute velocity against a preferred reference system at rest with the zero point vacuum energy reaches the velocity of light, and where an elliptical differential equation holding matter in a stable equilibrium goes over a transluminal Euler-Tricomi equation into a hyperbolic differential equation where such an equilibrium is not more possible, with matter in approaching this region disintegrating into radiation. Hawking's proposal depends on the anti-de Sitter/conformal field theory (AdS/CFT) conjecture which in turn depends on string/M theory which in the absence of super-symmetry will not work.

Reduced-order model based feedback control of the modified Hasegawa-Wakatani model

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

Goumiri, I. R.; Rowley, C. W.; Ma, Z.

2013-04-15

In this work, the development of model-based feedback control that stabilizes an unstable equilibrium is obtained for the Modified Hasegawa-Wakatani (MHW) equations, a classic model in plasma turbulence. First, a balanced truncation (a model reduction technique that has proven successful in flow control design problems) is applied to obtain a low dimensional model of the linearized MHW equation. Then, a model-based feedback controller is designed for the reduced order model using linear quadratic regulators. Finally, a linear quadratic Gaussian controller which is more resistant to disturbances is deduced. The controller is applied on the non-reduced, nonlinear MHW equations to stabilizemore » the equilibrium and suppress the transition to drift-wave induced turbulence.« less

Reduced-Order Model Based Feedback Control For Modified Hasegawa-Wakatani Model

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

Goumiri, I. R.; Rowley, C. W.; Ma, Z.

2013-01-28

In this work, the development of model-based feedback control that stabilizes an unstable equilibrium is obtained for the Modi ed Hasegawa-Wakatani (MHW) equations, a classic model in plasma turbulence. First, a balanced truncation (a model reduction technique that has proven successful in ow control design problems) is applied to obtain a low dimensional model of the linearized MHW equation. Then a modelbased feedback controller is designed for the reduced order model using linear quadratic regulators (LQR). Finally, a linear quadratic gaussian (LQG) controller, which is more resistant to disturbances is deduced. The controller is applied on the non-reduced, nonlinear MHWmore » equations to stabilize the equilibrium and suppress the transition to drift-wave induced turbulence.« less

Standard electrode potential, Tafel equation, and the solvation thermodynamics.

PubMed

Matyushov, Dmitry V

2009-06-21

Equilibrium in the electronic subsystem across the solution-metal interface is considered to connect the standard electrode potential to the statistics of localized electronic states in solution. We argue that a correct derivation of the Nernst equation for the electrode potential requires a careful separation of the relevant time scales. An equation for the standard metal potential is derived linking it to the thermodynamics of solvation. The Anderson-Newns model for electronic delocalization between the solution and the electrode is combined with a bilinear model of solute-solvent coupling introducing nonlinear solvation into the theory of heterogeneous electron transfer. We therefore are capable of addressing the question of how nonlinear solvation affects electrochemical observables. The transfer coefficient of electrode kinetics is shown to be equal to the derivative of the free energy, or generalized force, required to shift the unoccupied electronic level in the bulk. The transfer coefficient thus directly quantifies the extent of nonlinear solvation of the redox couple. The current model allows the transfer coefficient to deviate from the value of 0.5 of the linear solvation models at zero electrode overpotential. The electrode current curves become asymmetric in respect to the change in the sign of the electrode overpotential.

Optimal control of a coupled partial and ordinary differential equations system for the assimilation of polarimetry Stokes vector measurements in tokamak free-boundary equilibrium reconstruction with application to ITER

NASA Astrophysics Data System (ADS)

Faugeras, Blaise; Blum, Jacques; Heumann, Holger; Boulbe, Cédric

2017-08-01

The modelization of polarimetry Faraday rotation measurements commonly used in tokamak plasma equilibrium reconstruction codes is an approximation to the Stokes model. This approximation is not valid for the foreseen ITER scenarios where high current and electron density plasma regimes are expected. In this work a method enabling the consistent resolution of the inverse equilibrium reconstruction problem in the framework of non-linear free-boundary equilibrium coupled to the Stokes model equation for polarimetry is provided. Using optimal control theory we derive the optimality system for this inverse problem. A sequential quadratic programming (SQP) method is proposed for its numerical resolution. Numerical experiments with noisy synthetic measurements in the ITER tokamak configuration for two test cases, the second of which is an H-mode plasma, show that the method is efficient and that the accuracy of the identification of the unknown profile functions is improved compared to the use of classical Faraday measurements.

SkyNet: A Modular Nuclear Reaction Network Library

NASA Astrophysics Data System (ADS)

Lippuner, Jonas; Roberts, Luke F.

2017-12-01

Almost all of the elements heavier than hydrogen that are present in our solar system were produced by nuclear burning processes either in the early universe or at some point in the life cycle of stars. In all of these environments, there are dozens to thousands of nuclear species that interact with each other to produce successively heavier elements. In this paper, we present SkyNet, a new general-purpose nuclear reaction network that evolves the abundances of nuclear species under the influence of nuclear reactions. SkyNet can be used to compute the nucleosynthesis evolution in all astrophysical scenarios where nucleosynthesis occurs. SkyNet is free and open source, and aims to be easy to use and flexible. Any list of isotopes can be evolved, and SkyNet supports different types of nuclear reactions. SkyNet is modular so that new or existing physics, like nuclear reactions or equations of state, can easily be added or modified. Here, we present in detail the physics implemented in SkyNet with a focus on a self-consistent transition to and from nuclear statistical equilibrium to non-equilibrium nuclear burning, our implementation of electron screening, and coupling of the network to an equation of state. We also present comprehensive code tests and comparisons with existing nuclear reaction networks. We find that SkyNet agrees with published results and other codes to an accuracy of a few percent. Discrepancies, where they exist, can be traced to differences in the physics implementations.

An Analytic Approach to Modeling Land-Atmosphere Interaction: 1. Construct and Equilibrium Behavior

NASA Astrophysics Data System (ADS)

Brubaker, Kaye L.; Entekhabi, Dara

1995-03-01

A four-variable land-atmosphere model is developed to investigate the coupled exchanges of water and energy between the land surface and atmosphere and the role of these exchanges in the statistical behavior of continental climates. The land-atmosphere system is substantially simplified and formulated as a set of ordinary differential equations that, with the addition of random noise, are suitable for analysis in the form of the multivariate Îto equation. The model treats the soil layer and the near-surface atmosphere as reservoirs with storage capacities for heat and water. The transfers between these reservoirs are regulated by four states: soil saturation, soil temperature, air specific humidity, and air potential temperature. The atmospheric reservoir is treated as a turbulently mixed boundary layer of fixed depth. Heat and moisture advection, precipitation, and layer-top air entrainment are parameterized. The system is forced externally by solar radiation and the lateral advection of air and water mass. The remaining energy and water mass exchanges are expressed in terms of the state variables. The model development and equilibrium solutions are presented. Although comparisons between observed data and steady state model results re inexact, the model appears to do a reasonable job of partitioning net radiation into sensible and latent heat flux in appropriate proportions for bare-soil midlatitude summer conditions. Subsequent work will introduce randomness into the forcing terms to investigate the effect of water-energy coupling and land-atmosphere interaction on variability and persistence in the climatic system.

Applications of the Peng-Robinson Equation of State Using Mathematica

ERIC Educational Resources Information Center

Binous, Housam

2008-01-01

A single equation of state (EOS) such as the Peng-Robinson EOS can accurately describe both the liquid and vapor phase. We present several applications of this equation of state including adiabatic flash calculation, determination of the solubility of methanol in natural gas, and the calculation of high-pressure chemical equilibrium. The problems…

Dynamics of a gravity-gradient stabilized flexible spacecraft

NASA Technical Reports Server (NTRS)

Meirovitch, L.; Juang, J. N.

1974-01-01

The dynamics of gravity-gradient stabilized flexible satellite in the neighborhood of a deformed equilibrium configuration are discussed. First the equilibrium configuration was determined by solving a set of nonlinear differential equations. Then stability of motion about the deformed equilibrium was tested by means of the Liapunov direct method. The natural frequencies of oscillation of the complete structure were calculated. The analysis is applicable to the RAE/B satellite.

A Dealer Model of Foreign Exchange Market with Finite Assets

NASA Astrophysics Data System (ADS)

Hamano, Tomoya; Kanazawa, Kiyoshi; Takayasu, Hideki; Takayasu, Misako

An agent-based model is introduced to study the finite-asset effect in foreign exchange markets. We find that the transacted price asymptotically approaches an equilibrium price, which is determined by the monetary balance between the pair of currencies. We phenomenologically derive a formula to estimate the equilibrium price, and we model its relaxation dynamics around the equilibrium price on the basis of a Langevin-like equation.

Edge equilibrium code for tokamaks

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

Li, Xujing; Zakharov, Leonid E.; Drozdov, Vladimir V.

2014-01-15

The edge equilibrium code (EEC) described in this paper is developed for simulations of the near edge plasma using the finite element method. It solves the Grad-Shafranov equation in toroidal coordinate and uses adaptive grids aligned with magnetic field lines. Hermite finite elements are chosen for the numerical scheme. A fast Newton scheme which is the same as implemented in the equilibrium and stability code (ESC) is applied here to adjust the grids.

A moving mesh finite difference method for equilibrium radiation diffusion equations

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

Yang, Xiaobo, E-mail: xwindyb@126.com; Huang, Weizhang, E-mail: whuang@ku.edu; Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn

2015-10-01

An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativitymore » of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.« less

A Viscoelastic Hybrid Shell Finite Element

NASA Technical Reports Server (NTRS)

Johnson, Arthur

1999-01-01

An elastic large displacement thick-shell hybrid finite element is modified to allow for the calculation of viscoelastic stresses. Internal strain variables are introduced at he element's stress nodes and are employed to construct a viscous material model. First order ordinary differential equations relate the internal strain variables to the corresponding elastic strains at the stress nodes. The viscous stresses are computed from the internal strain variables using viscous moduli which are a fraction of the elastic moduli. The energy dissipated by the action of the viscous stresses in included in the mixed variational functional. Nonlinear quasi-static viscous equilibrium equations are then obtained. Previously developed Taylor expansions of the equilibrium equations are modified to include the viscous terms. A predictor-corrector time marching solution algorithm is employed to solve the algebraic-differential equations. The viscous shell element is employed to numerically simulate a stair-step loading and unloading of an aircraft tire in contact with a frictionless surface.

Measurement of the Surface Dilatational Viscosity of an Insoluble Surfactant Monolayer at the Air/Water Interface Using a Pendant Drop Apparatus

NASA Technical Reports Server (NTRS)

Lorenzo, Jose; Couzis, Alex; Maldarelli, Charles; Singh, Bhim S. (Technical Monitor)

2000-01-01

When a fluid interface with surfactants is at rest, the interfacial stress is isotropic (as given by the equilibrium interfacial tension), and is described by the equation of state which relates the surface tension to the surfactant surface concentration. When surfactants are subjected to shear and dilatational flows, flow induced interaction of the surfactants; can create interfacial stresses apart from the equilibrium surface tension. The simplest relationship between surface strain rate and surface stress is the Boussinesq-Scriven constitutive equation completely characterized by three coefficients: equilibrium interfacial tension, surface shear viscosity, and surface dilatational viscosity Equilibrium interfacial tension and surface shear viscosity measurements are very well established. On the other hand, surface dilatational viscosity measurements are difficult because a flow which change the surface area also changes the surfactant surface concentration creating changes in the equilibrium interfacial tension that must be also taken into account. Surface dilatational viscosity measurements of existing techniques differ by five orders of magnitude and use spatially damped surface waves and rapidly expanding bubbles. In this presentation we introduce a new technique for measuring the surface dilatational viscosity by contracting an aqueous pendant drop attached to a needle tip and having and insoluble surfactant monolayer at the air-water interface. The isotropic total tension on the surface consists of the equilibrium surface tension and the tension due to the dilation. Compression rates are undertaken slow enough so that bulk hydrodynamic stresses are small compared to the surface tension force. Under these conditions we show that the total tension is uniform along the surface and that the Young-Laplace equation governs the drop shape with the equilibrium surface tension replaced by the constant surface isotropic stress. We illustrate this technique using DPPC as the insoluble surfacant monolayer and measured for it a surface dilatational viscosity in the LE phase that is 20 surface poise.

Deterministic time-reversible thermostats: chaos, ergodicity, and the zeroth law of thermodynamics

NASA Astrophysics Data System (ADS)

Patra, Puneet Kumar; Sprott, Julien Clinton; Hoover, William Graham; Griswold Hoover, Carol

2015-09-01

The relative stability and ergodicity of deterministic time-reversible thermostats, both singly and in coupled pairs, are assessed through their Lyapunov spectra. Five types of thermostat are coupled to one another through a single Hooke's-law harmonic spring. The resulting dynamics shows that three specific thermostat types, Hoover-Holian, Ju-Bulgac, and Martyna-Klein-Tuckerman, have very similar Lyapunov spectra in their equilibrium four-dimensional phase spaces and when coupled in equilibrium or nonequilibrium pairs. All three of these oscillator-based thermostats are shown to be ergodic, with smooth analytic Gaussian distributions in their extended phase spaces (coordinate, momentum, and two control variables). Evidently these three ergodic and time-reversible thermostat types are particularly useful as statistical-mechanical thermometers and thermostats. Each of them generates Gibbs' universal canonical distribution internally as well as for systems to which they are coupled. Thus they obey the zeroth law of thermodynamics, as a good heat bath should. They also provide dissipative heat flow with relatively small nonlinearity when two or more such temperature baths interact and provide useful deterministic replacements for the stochastic Langevin equation.

Adapting HYDRUS-1D to Simulate Overland Flow and Reactive Transport During Sheet Flow Deviations

NASA Astrophysics Data System (ADS)

Liang, J.; Bradford, S. A.; Simunek, J.; Hartmann, A.

2017-12-01

The HYDRUS-1D code is a popular numerical model for solving the Richards equation for variably-saturated water flow and solute transport in porous media. This code was adapted to solve rather than the Richards equation for subsurface flow the diffusion wave equation for overland flow at the soil surface. The numerical results obtained by the new model produced an excellent agreement with the analytical solution of the kinematic wave equation. Model tests demonstrated its applicability to simulate the transport and fate of many different solutes, such as non-adsorbing tracers, nutrients, pesticides, and microbes. However, the diffusion wave or kinematic wave equations describe surface runoff as sheet flow with a uniform depth and velocity across the slope. In reality, overland water flow and transport processes are rarely uniform. Local soil topography, vegetation, and spatial soil heterogeneity control directions and magnitudes of water fluxes, and strongly influence runoff characteristics. There is increasing evidence that variations in soil surface characteristics influence the distribution of overland flow and transport of pollutants. These spatially varying surface characteristics are likely to generate non-equilibrium flow and transport processes. HYDRUS-1D includes a hierarchical series of models of increasing complexity to account for both physical equilibrium and non-equilibrium, e.g., dual-porosity and dual-permeability models, up to a dual-permeability model with immobile water. The same conceptualization as used for the subsurface was implemented to simulate non-equilibrium overland flow and transport at the soil surface. The developed model improves our ability to describe non-equilibrium overland flow and transport processes and to improves our understanding of factors that cause this behavior. The HYDRUS-1D overland flow and transport model was additionally also extended to simulate soil erosion. The HYDRUS-1D Soil Erosion Model has been verified by comparing with other soil erosion models. The model performed well when the average soil particle size is relatively large. The performance of the soil erosion model has been further validated by comparing with selected experimental datasets from the literature.

Chemical potentials and thermodynamic characteristics of ideal Bose- and Fermi-gases in the region of quantum degeneracy

NASA Astrophysics Data System (ADS)

Sotnikov, A. G.; Sereda, K. V.; Slyusarenko, Yu. V.

2017-01-01

Calculations of chemical potentials for ideal monatomic gases with Bose-Einstein and Fermi-Dirac statistics as functions of temperature, across the temperature region that is typical for the collective quantum degeneracy effect, are presented. Numerical calculations are performed without any additional approximations, and explicit dependences of the chemical potentials on temperature are constructed at a fixed density of gas particles. Approximate polynomial dependences of chemical potentials on temperature are obtained that allow for the results to be used in further studies without re-applying the involved numerical methods. The ease of using the obtained representations is demonstrated on examples of deformation of distribution for a population of energy states at low temperatures, and on the impact of quantum statistics (exchange interaction) on the equations of state for ideal gases and some of the thermodynamic properties thereof. The results of this study essentially unify two opposite limiting cases in an intermediate region that are used to describe the equilibrium states of ideal gases, which are well known from university courses on statistical physics, thus adding value from an educational point of view.

Design of off-statistics axial-flow fans by means of vortex law optimization

NASA Astrophysics Data System (ADS)

Lazari, Andrea; Cattanei, Andrea

2014-12-01

Off-statistics input data sets are common in axial-flow fans design and may easily result in some violation of the requirements of a good aerodynamic blade design. In order to circumvent this problem, in the present paper, a solution to the radial equilibrium equation is found which minimizes the outlet kinetic energy and fulfills the aerodynamic constraints, thus ensuring that the resulting blade has acceptable aerodynamic performance. The presented method is based on the optimization of a three-parameters vortex law and of the meridional channel size. The aerodynamic quantities to be employed as constraints are individuated and their suitable ranges of variation are proposed. The method is validated by means of a design with critical input data values and CFD analysis. Then, by means of systematic computations with different input data sets, some correlations and charts are obtained which are analogous to classic correlations based on statistical investigations on existing machines. Such new correlations help size a fan of given characteristics as well as study the feasibility of a given design.

Gas-kinetic unified algorithm for hypersonic flows covering various flow regimes solving Boltzmann model equation in nonequilibrium effect

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

Li, Zhihui; Ma, Qiang; Wu, Junlin

2014-12-09

Based on the Gas-Kinetic Unified Algorithm (GKUA) directly solving the Boltzmann model equation, the effect of rotational non-equilibrium is investigated recurring to the kinetic Rykov model with relaxation property of rotational degrees of freedom. The spin movement of diatomic molecule is described by moment of inertia, and the conservation of total angle momentum is taken as a new Boltzmann collision invariant. The molecular velocity distribution function is integrated by the weight factor on the internal energy, and the closed system of two kinetic controlling equations is obtained with inelastic and elastic collisions. The optimization selection technique of discrete velocity ordinatemore » points and numerical quadrature rules for macroscopic flow variables with dynamic updating evolvement are developed to simulate hypersonic flows, and the gas-kinetic numerical scheme is constructed to capture the time evolution of the discretized velocity distribution functions. The gas-kinetic boundary conditions in thermodynamic non-equilibrium and numerical procedures are studied and implemented by directly acting on the velocity distribution function, and then the unified algorithm of Boltzmann model equation involving non-equilibrium effect is presented for the whole range of flow regimes. The hypersonic flows involving non-equilibrium effect are numerically simulated including the inner flows of shock wave structures in nitrogen with different Mach numbers of 1.5-Ma-25, the planar ramp flow with the whole range of Knudsen numbers of 0.0009-Kn-10 and the three-dimensional re-entering flows around tine double-cone body.« less

A New Chaotic Flow with Hidden Attractor: The First Hyperjerk System with No Equilibrium

NASA Astrophysics Data System (ADS)

Ren, Shuili; Panahi, Shirin; Rajagopal, Karthikeyan; Akgul, Akif; Pham, Viet-Thanh; Jafari, Sajad

2018-02-01

Discovering unknown aspects of non-equilibrium systems with hidden strange attractors is an attractive research topic. A novel quadratic hyperjerk system is introduced in this paper. It is noteworthy that this non-equilibrium system can generate hidden chaotic attractors. The essential properties of such systems are investigated by means of equilibrium points, phase portrait, bifurcation diagram, and Lyapunov exponents. In addition, a fractional-order differential equation of this new system is presented. Moreover, an electronic circuit is also designed and implemented to verify the feasibility of the theoretical model.

Modeling of high pressure arc-discharge with a fully-implicit Navier-Stokes stabilized finite element flow solver

NASA Astrophysics Data System (ADS)

Sahai, A.; Mansour, N. N.; Lopez, B.; Panesi, M.

2017-05-01

This work addresses the modeling of high pressure electric discharge in an arc-heated wind tunnel. The combined numerical solution of Poisson’s equation, radiative transfer equations, and the set of Favre-averaged thermochemical nonequilibrium Navier-Stokes equations allows for the determination of the electric, radiation, and flow fields, accounting for their mutual interaction. Semi-classical statistical thermodynamics is used to determine the plasma thermodynamic properties, while transport properties are obtained from kinetic principles with the Chapman-Enskog method. A multi-temperature formulation is used to account for thermal non-equilibrium. Finally, the turbulence closure of the flow equations is obtained by means of the Spalart-Allmaras model, which requires the solution of an additional scalar transport equation. A Streamline upwind Petrov-Galerkin stabilized finite element formulation is employed to solve the Navier-Stokes equation. The electric field equation is solved using the standard Galerkin formulation. A stable formulation for the radiative transfer equations is obtained using the least-squares finite element method. The developed simulation framework has been applied to investigate turbulent plasma flows in the 20 MW Aerodynamic Heating Facility at NASA Ames Research Center. The current model is able to predict the process of energy addition and re-distribution due to Joule heating and thermal radiation, resulting in a hot central core surrounded by colder flow. The use of an unsteady three-dimensional treatment also allows the asymmetry due to a dynamic electric arc attachment point in the cathode chamber to be captured accurately. The current work paves the way for detailed estimation of operating characteristics for arc-heated wind tunnels which are critical in testing thermal protection systems.

Stability of nonuniform rotor blades in hover using a mixed formulation

NASA Technical Reports Server (NTRS)

Stephens, W. B.; Hodges, D. H.; Avila, J. H.; Kung, R. M.

1980-01-01

A mixed formulation for calculating static equilibrium and stability eigenvalues of nonuniform rotor blades in hover is presented. The static equilibrium equations are nonlinear and are solved by an accurate and efficient collocation method. The linearized perturbation equations are solved by a one step, second order integration scheme. The numerical results correlate very well with published results from a nearly identical stability analysis based on a displacement formulation. Slight differences in the results are traced to terms in the equations that relate moments to derivatives of rotations. With the present ordering scheme, in which terms of the order of squares of rotations are neglected with respect to unity, it is not possible to achieve completely equivalent models based on mixed and displacement formulations. The one step methods reveal that a second order Taylor expansion is necessary to achieve good convergence for nonuniform rotating blades. Numerical results for a hypothetical nonuniform blade, including the nonlinear static equilibrium solution, were obtained with no more effort or computer time than that required for a uniform blade.

Comments on the article entitled “Incompatibility of the Shuttleworth equation with Hermann’s mathematical structure of thermodynamics” by D.J. Bottomley, Lasse Makkonen and Kari Kolari [Surf. Sci. 603 (2009) 97

NASA Astrophysics Data System (ADS)

Hecquet, Pascal

2010-02-01

In the Shuttleworth's equation gij=γδij+dγ/dɛij, γ is the surface energy and gij is the surface stress with respect to the corresponding bulk quantity. At equilibrium and T=0 K, the bulk energy is the cohesive energy and the bulk stress is zero ( p=0). For i=j ( ɛii is hydrostatic) and for a flat surface, we show that the equilibrium surface stress gii corresponds to a surface pressure located mainly at the first monolayer and that the presence of the surface energy γ in the Shuttleworth's equation results from the matter conservation rule. Indeed, γ is an energy calculated per constant unit area while the atomic surface varies with the deformation as ( 1+ɛii). The equilibrium surface stress gii present at the surface is parallel to the surface. When gii is positive, this signifies that the surface atoms tend to contract together in the direction i even if the bulk pressure p is zero.

The influence of pressure relaxation on the structure of an axial vortex

NASA Astrophysics Data System (ADS)

Ash, Robert L.; Zardadkhan, Irfan; Zuckerwar, Allan J.

2011-07-01

Governing equations including the effects of pressure relaxation have been utilized to study an incompressible, steady-state viscous axial vortex with specified far-field circulation. When sound generation is attributed to a velocity gradient tensor-pressure gradient product, the modified conservation of momentum equations that result yield an exact solution for a steady, incompressible axial vortex. The vortex velocity profile has been shown to closely approximate experimental vortex measurements in air and water over a wide range of circulation-based Reynolds numbers. The influence of temperature and humidity on the pressure relaxation coefficient in air has been examined using theoretical and empirical approaches, and published axial vortex experiments have been employed to estimate the pressure relaxation coefficient in water. Non-equilibrium pressure gradient forces have been shown to balance the viscous stresses in the vortex core region, and the predicted pressure deficits that result from this non-equilibrium balance can be substantially larger than the pressure deficits predicted using a Bernoulli equation approach. Previously reported pressure deficit distributions for dust devils and tornados have been employed to validate the non-equilibrium pressure deficit predictions.

Mechanical approach to chemical transport

PubMed Central

Kocherginsky, Nikolai; Gruebele, Martin

2016-01-01

Nonequilibrium thermodynamics describes the rates of transport phenomena with the aid of various thermodynamic forces, but often the phenomenological transport coefficients are not known, and the description is not easily connected with equilibrium relations. We present a simple and intuitive model to address these issues. Our model is based on Lagrangian dynamics for chemical systems with dissipation, so one may think of the model as physicochemical mechanics. Using one main equation, the model allows a systematic derivation of all transport and equilibrium equations, subject to the limitation that heat generated or absorbed in the system must be small for the model to be valid. A table with all major examples of transport and equilibrium processes described using physicochemical mechanics is given. In equilibrium, physicochemical mechanics reduces to standard thermodynamics and the Gibbs–Duhem relation, and we show that the First and Second Laws of thermodynamics are satisfied for our system plus bath model. Out of equilibrium, our model provides relationships between transport coefficients and describes system evolution in the presence of several simultaneous external fields. The model also leads to an extension of the Onsager–Casimir reciprocal relations for properties simultaneously transported by many components. PMID:27647899

Equilibrium problems for Raney densities

NASA Astrophysics Data System (ADS)

Forrester, Peter J.; Liu, Dang-Zheng; Zinn-Justin, Paul

2015-07-01

The Raney numbers are a class of combinatorial numbers generalising the Fuss-Catalan numbers. They are indexed by a pair of positive real numbers (p, r) with p > 1 and 0 < r ⩽ p, and form the moments of a probability density function. For certain (p, r) the latter has the interpretation as the density of squared singular values for certain random matrix ensembles, and in this context equilibrium problems characterising the Raney densities for (p, r) = (θ + 1, 1) and (θ/2 + 1, 1/2) have recently been proposed. Using two different techniques—one based on the Wiener-Hopf method for the solution of integral equations and the other on an analysis of the algebraic equation satisfied by the Green's function—we establish the validity of the equilibrium problems for general θ > 0 and similarly use both methods to identify the equilibrium problem for (p, r) = (θ/q + 1, 1/q), θ > 0 and q \\in Z+ . The Wiener-Hopf method is used to extend the latter to parameters (p, r) = (θ/q + 1, m + 1/q) for m a non-negative integer, and also to identify the equilibrium problem for a family of densities with moments given by certain binomial coefficients.

The role of non-equilibrium fluxes in the relaxation processes of the linear chemical master equation

NASA Astrophysics Data System (ADS)

de Oliveira, Luciana Renata; Bazzani, Armando; Giampieri, Enrico; Castellani, Gastone C.

2014-08-01

We propose a non-equilibrium thermodynamical description in terms of the Chemical Master Equation (CME) to characterize the dynamics of a chemical cycle chain reaction among m different species. These systems can be closed or open for energy and molecules exchange with the environment, which determines how they relax to the stationary state. Closed systems reach an equilibrium state (characterized by the detailed balance condition (D.B.)), while open systems will reach a non-equilibrium steady state (NESS). The principal difference between D.B. and NESS is due to the presence of chemical fluxes. In the D.B. condition the fluxes are absent while for the NESS case, the chemical fluxes are necessary for the state maintaining. All the biological systems are characterized by their "far from equilibrium behavior," hence the NESS is a good candidate for a realistic description of the dynamical and thermodynamical properties of living organisms. In this work we consider a CME written in terms of a discrete Kolmogorov forward equation, which lead us to write explicitly the non-equilibrium chemical fluxes. For systems in NESS, we show that there is a non-conservative "external vector field" whose is linearly proportional to the chemical fluxes. We also demonstrate that the modulation of these external fields does not change their stationary distributions, which ensure us to study the same system and outline the differences in the system's behavior when it switches from the D.B. regime to NESS. We were interested to see how the non-equilibrium fluxes influence the relaxation process during the reaching of the stationary distribution. By performing analytical and numerical analysis, our central result is that the presence of the non-equilibrium chemical fluxes reduces the characteristic relaxation time with respect to the D.B. condition. Within a biochemical and biological perspective, this result can be related to the "plasticity property" of biological systems and to their capabilities to switch from one state to another as is observed during synaptic plasticity, cell fate determination, and differentiation.

The role of non-equilibrium fluxes in the relaxation processes of the linear chemical master equation.

PubMed

de Oliveira, Luciana Renata; Bazzani, Armando; Giampieri, Enrico; Castellani, Gastone C

2014-08-14

We propose a non-equilibrium thermodynamical description in terms of the Chemical Master Equation (CME) to characterize the dynamics of a chemical cycle chain reaction among m different species. These systems can be closed or open for energy and molecules exchange with the environment, which determines how they relax to the stationary state. Closed systems reach an equilibrium state (characterized by the detailed balance condition (D.B.)), while open systems will reach a non-equilibrium steady state (NESS). The principal difference between D.B. and NESS is due to the presence of chemical fluxes. In the D.B. condition the fluxes are absent while for the NESS case, the chemical fluxes are necessary for the state maintaining. All the biological systems are characterized by their "far from equilibrium behavior," hence the NESS is a good candidate for a realistic description of the dynamical and thermodynamical properties of living organisms. In this work we consider a CME written in terms of a discrete Kolmogorov forward equation, which lead us to write explicitly the non-equilibrium chemical fluxes. For systems in NESS, we show that there is a non-conservative "external vector field" whose is linearly proportional to the chemical fluxes. We also demonstrate that the modulation of these external fields does not change their stationary distributions, which ensure us to study the same system and outline the differences in the system's behavior when it switches from the D.B. regime to NESS. We were interested to see how the non-equilibrium fluxes influence the relaxation process during the reaching of the stationary distribution. By performing analytical and numerical analysis, our central result is that the presence of the non-equilibrium chemical fluxes reduces the characteristic relaxation time with respect to the D.B. condition. Within a biochemical and biological perspective, this result can be related to the "plasticity property" of biological systems and to their capabilities to switch from one state to another as is observed during synaptic plasticity, cell fate determination, and differentiation.

Analytic, High-beta Solutions of the Helical Grad-Shafranov Equation

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

D.R. Smith; A.H. Reiman

We present analytic, high-beta ({beta} {approx} O(1)), helical equilibrium solutions for a class of helical axis configurations having large helical aspect ratio, with the helix assumed to be tightly wound. The solutions develop a narrow boundary layer of strongly compressed flux, similar to that previously found in high beta tokamak equilibrium solutions. The boundary layer is associated with a strong localized current which prevents the equilibrium from having zero net current.

Edge Equilibrium Code (EEC) For Tokamaks

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

Li, Xujling

2014-02-24

The edge equilibrium code (EEC) described in this paper is developed for simulations of the near edge plasma using the finite element method. It solves the Grad-Shafranov equation in toroidal coordinate and uses adaptive grids aligned with magnetic field lines. Hermite finite elements are chosen for the numerical scheme. A fast Newton scheme which is the same as implemented in the equilibrium and stability code (ESC) is applied here to adjust the grids

Comparison of the Marcus and Pekar partitions in the context of non-equilibrium, polarizable-continuum solvation models

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

You, Zhi-Qiang; Herbert, John M., E-mail: herbert@chemistry.ohio-state.edu; Mewes, Jan-Michael

2015-11-28

The Marcus and Pekar partitions are common, alternative models to describe the non-equilibrium dielectric polarization response that accompanies instantaneous perturbation of a solute embedded in a dielectric continuum. Examples of such a perturbation include vertical electronic excitation and vertical ionization of a solution-phase molecule. Here, we provide a general derivation of the accompanying polarization response, for a quantum-mechanical solute described within the framework of a polarizable continuum model (PCM) of electrostatic solvation. Although the non-equilibrium free energy is formally equivalent within the two partitions, albeit partitioned differently into “fast” versus “slow” polarization contributions, discretization of the PCM integral equations failsmore » to preserve certain symmetries contained in these equations (except in the case of the conductor-like models or when the solute cavity is spherical), leading to alternative, non-equivalent matrix equations. Unlike the total equilibrium solvation energy, however, which can differ dramatically between different formulations, we demonstrate that the equivalence of the Marcus and Pekar partitions for the non-equilibrium solvation correction is preserved to high accuracy. Differences in vertical excitation and ionization energies are <0.2 eV (and often <0.01 eV), even for systems specifically selected to afford a large polarization response. Numerical results therefore support the interchangeability of the Marcus and Pekar partitions, but also caution against relying too much on the fast PCM charges for interpretive value, as these charges differ greatly between the two partitions, especially in polar solvents.« less

A Bayesian perspective on Markovian dynamics and the fluctuation theorem

NASA Astrophysics Data System (ADS)

Virgo, Nathaniel

2013-08-01

One of E. T. Jaynes' most important achievements was to derive statistical mechanics from the maximum entropy (MaxEnt) method. I re-examine a relatively new result in statistical mechanics, the Evans-Searles fluctuation theorem, from a MaxEnt perspective. This is done in the belief that interpreting such results in Bayesian terms will lead to new advances in statistical physics. The version of the fluctuation theorem that I will discuss applies to discrete, stochastic systems that begin in a non-equilibrium state and relax toward equilibrium. I will show that for such systems the fluctuation theorem can be seen as a consequence of the fact that the equilibrium distribution must obey the property of detailed balance. Although the principle of detailed balance applies only to equilibrium ensembles, it puts constraints on the form of non-equilibrium trajectories. This will be made clear by taking a novel kind of Bayesian perspective, in which the equilibrium distribution is seen as a prior over the system's set of possible trajectories. Non-equilibrium ensembles are calculated from this prior using Bayes' theorem, with the initial conditions playing the role of the data. I will also comment on the implications of this perspective for the question of how to derive the second law.

Applications of the Peng-Robinson Equation of State Using MATLAB[R

ERIC Educational Resources Information Center

Nasri, Zakia; Binous, Housam

2009-01-01

A single equation of state (EOS) such as the Peng-Robinson (PR) EOS can accurately describe both the liquid and vapor phase. We present several applications of this equation of state, including estimation of pure component properties and computation of the vapor-liquid equilibrium (VLE) diagram for binary mixtures. We perform high-pressure…

Nakedly singular non-vacuum gravitating equilibrium states

NASA Astrophysics Data System (ADS)

Woszczyna, Andrzej; Kutschera, Marek; Kubis, Sebastian; Czaja, Wojciech; Plaszczyk, Piotr; Golda, Zdzisław A.

2016-01-01

Non-vacuum static spherically symmetric spacetimes with central point-like repulsive gravity sources are investigated. Both the symmetries of spacetime and the degree of irregularity of curvature invariants, are the same as for the Schwarzschild case. The equilibrium configurations are modelled using the neutron star polytrope equation of state.

Photon emission from quark-gluon plasma out of equilibrium

NASA Astrophysics Data System (ADS)

Hauksson, Sigtryggur; Jeon, Sangyong; Gale, Charles

2018-01-01

The photon emission from a nonequilibrium quark-gluon plasma is analyzed. We derive an integral equation that describes photon production through quark-antiquark annihilation and quark bremsstrahlung. It includes coherence between different scattering sites, also known as the Landau-Pomeranchuk-Migdal effect. These leading-order processes are studied for the first time together in an out-of-equilibrium field theoretical treatment that enables the inclusion of viscous corrections to the calculation of electromagnetic emission rates. In the special case of an isotropic, viscous, plasma the integral equation only depends on three constants, which capture the nonequilibrium nature of the medium.

Combustion of hydrogen-air jets in local chemical equilibrium: A guide to the CHARNAL computer program

NASA Technical Reports Server (NTRS)

Spalding, D. B.; Launder, B. E.; Morse, A. P.; Maples, G.

1974-01-01

A guide to a computer program, written in FORTRAN 4, for predicting the flow properties of turbulent mixing with combustion of a circular jet of hydrogen into a co-flowing stream of air is presented. The program, which is based upon the Imperial College group's PASSA series, solves differential equations for diffusion and dissipation of turbulent kinetic energy and also of the R.M.S. fluctuation of hydrogen concentration. The effective turbulent viscosity for use in the shear stress equation is computed. Chemical equilibrium is assumed throughout the flow.

Transverse kinetics of a charged drop in an external electric field

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

Bondarenko, S.; Komoshvili, K.

2016-01-22

We investigate a non-equilibrium behavior of a small, dense and charged drop in the transverse plane. A collective motion of the drop’s particles with constant entropy is described. Namely, we solve Vlasov’s equation with non-isotropic initial conditions. Thereby a non-equilibrium distribution function of the process of the droplet evolution in the transverse plane is calculated. An external electric field is included in the initial conditions of the equation that affects on the form of the obtained solution. Applicability of the results to the description of initial states of quark-gluon plasma is also discussed.

Scale matters

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

Margolin, L. G.

The applicability of Navier–Stokes equations is limited to near-equilibrium flows in which the gradients of density, velocity and energy are small. Here I propose an extension of the Chapman–Enskog approximation in which the velocity probability distribution function (PDF) is averaged in the coordinate phase space as well as the velocity phase space. I derive a PDF that depends on the gradients and represents a first-order generalization of local thermodynamic equilibrium. I then integrate this PDF to derive a hydrodynamic model. Finally, I discuss the properties of that model and its relation to the discrete equations of computational fluid dynamics.

Scale matters

DOE PAGES

Margolin, L. G.

2018-03-19

The applicability of Navier–Stokes equations is limited to near-equilibrium flows in which the gradients of density, velocity and energy are small. Here I propose an extension of the Chapman–Enskog approximation in which the velocity probability distribution function (PDF) is averaged in the coordinate phase space as well as the velocity phase space. I derive a PDF that depends on the gradients and represents a first-order generalization of local thermodynamic equilibrium. I then integrate this PDF to derive a hydrodynamic model. Finally, I discuss the properties of that model and its relation to the discrete equations of computational fluid dynamics.

ON THE DYNAMICAL DERIVATION OF EQUILIBRIUM STATISTICAL MECHANICS

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

Prigogine, I.; Balescu, R.; Henin, F.

1960-12-01

Work on nonequilibrium statistical mechanics, which allows an extension of the kinetic proof to all results of equilibrium statistical mechanics involving a finite number of degrees of freedom, is summarized. As an introduction to the general N-body problem, the scattering theory in classical mechanics is considered. The general N-body problem is considered for the case of classical mechanics, quantum mechanics with Boltzmann statistics, and quantum mechanics including quantum statistics. Six basic diagrams, which describe the elementary processes of the dynamics of correlations, were obtained. (M.C.G.)

Nonlinear dynamics that appears in the dynamical model of drying process of a polymer solution coated on a flat substrate

NASA Astrophysics Data System (ADS)

Kagami, Hiroyuki

2007-01-01

We have proposed and modified the dynamical model of drying process of polymer solution coated on a flat substrate for flat polymer film fabrication and have presented the fruits through some meetings and so on. Though basic equations of the dynamical model have characteristic nonlinearity, character of the nonlinearity has not been studied enough yet. In this paper, at first, we derive nonlinear equations from the dynamical model of drying process of polymer solution. Then we introduce results of numerical simulations of the nonlinear equations and consider roles of various parameters. Some of them are indirectly concerned in strength of non-equilibriumity. Through this study, we approach essential qualities of nonlinearity in non-equilibrium process of drying process.

Optimal Protocols and Optimal Transport in Stochastic Thermodynamics

NASA Astrophysics Data System (ADS)

Aurell, Erik; Mejía-Monasterio, Carlos; Muratore-Ginanneschi, Paolo

2011-06-01

Thermodynamics of small systems has become an important field of statistical physics. Such systems are driven out of equilibrium by a control, and the question is naturally posed how such a control can be optimized. We show that optimization problems in small system thermodynamics are solved by (deterministic) optimal transport, for which very efficient numerical methods have been developed, and of which there are applications in cosmology, fluid mechanics, logistics, and many other fields. We show, in particular, that minimizing expected heat released or work done during a nonequilibrium transition in finite time is solved by the Burgers equation and mass transport by the Burgers velocity field. Our contribution hence considerably extends the range of solvable optimization problems in small system thermodynamics.

Optimal protocols and optimal transport in stochastic thermodynamics.

PubMed

Aurell, Erik; Mejía-Monasterio, Carlos; Muratore-Ginanneschi, Paolo

2011-06-24

Thermodynamics of small systems has become an important field of statistical physics. Such systems are driven out of equilibrium by a control, and the question is naturally posed how such a control can be optimized. We show that optimization problems in small system thermodynamics are solved by (deterministic) optimal transport, for which very efficient numerical methods have been developed, and of which there are applications in cosmology, fluid mechanics, logistics, and many other fields. We show, in particular, that minimizing expected heat released or work done during a nonequilibrium transition in finite time is solved by the Burgers equation and mass transport by the Burgers velocity field. Our contribution hence considerably extends the range of solvable optimization problems in small system thermodynamics.

PROM7: 1D modeler of solar filaments or prominences

NASA Astrophysics Data System (ADS)

Gouttebroze, P.

2018-05-01

PROM7 is an update of PROM4 (ascl:1306.004) and computes simple models of solar prominences and filaments using Partial Radiative Distribution (PRD). The models consist of plane-parallel slabs standing vertically above the solar surface. Each model is defined by 5 parameters: temperature, density, geometrical thickness, microturbulent velocity and height above the solar surface. It solves the equations of radiative transfer, statistical equilibrium, ionization and pressure equilibria, and computes electron and hydrogen level population and hydrogen line profiles. Moreover, the code treats calcium atom which is reduced to 3 ionization states (Ca I, Ca II, CA III). Ca II ion has 5 levels which are useful for computing 2 resonance lines (H and K) and infrared triplet (to 8500 A).

A non-LTE study of silicon line formation in early-type main-sequence atmospheres.

NASA Technical Reports Server (NTRS)

Kamp, L. W.

1973-01-01

We have computed populations of 16 levels of Si III-V and radiation fields in all connecting transitions; in particular the first six Si III triplet levels, including the 4553 line, and the first six Si IV levels including 4089. The computations were done for four non-LTE H-He model atmospheres, provided by Auer and Mihalas. Estimates of corresponding MK types are B1.5 V, B0.5 V, O9 V, and O6. Solutions were obtained by iterating the linearized equations of radiative transfer and statistical equilibrium, except that for less important lines an approximate equivalent two-level atom treatment was used. Continuous opacities of C, N, O, and Ne were included. All abundances were solar values.

Radiative interactions in molecular gases under local and nonlocal thermodynamic equilibrium conditions

NASA Technical Reports Server (NTRS)

Tiwari, S. N.; Jha, M. K.

1993-01-01

Basic formulations, analyses, and numerical procedures are presented to investigate radiative heat interactions in diatomic and polyatomic gases under local and nonlocal thermodynamic equilibrium conditions. Essential governing equations are presented for both gray and nongray gases. Information is provided on absorption models, relaxation times, and transfer equations. Radiative flux equations are developed which are applicable under local and nonlocal thermodynamic equilibrium conditions. The problem is solved for fully developed laminar incompressible flows between two parallel plates under the boundary condition of a uniform surface heat flux. For specific applications, three diatomic and three polyatomic gases are considered. The results are obtained numerically by employing the method of variation of parameters. The results are compared under local and nonlocal thermodynamic equilibrium conditions at different temperature and pressure conditions. Both gray and nongray studies are conducted extensively for all molecular gases considered. The particular gases selected for this investigation are CO, NO, OH, CO2, H2O, and CH4. The temperature and pressure range considered are 300-2000 K and 0.1-10 atmosphere, respectively. In general, results demonstrate that the gray gas approximation overestimates the effect of radiative interaction for all conditions. The conditions of NLTE, however, result in underestimation of radiative interactions. The method developed for this study can be extended to solve complex problems of radiative heat transfer involving nonequilibrium phenomena.

ATMOSPHERIC CHEMISTRY FOR ASTROPHYSICISTS: A SELF-CONSISTENT FORMALISM AND ANALYTICAL SOLUTIONS FOR ARBITRARY C/O

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

Heng, Kevin; Tsai, Shang-Min; Lyons, James R., E-mail: kevin.heng@csh.unibe.ch

2016-01-10

We present a self-consistent formalism for computing and understanding the atmospheric chemistry of exoplanets from the viewpoint of an astrophysicist. Starting from the first law of thermodynamics, we demonstrate that the van’t Hoff equation (which describes the equilibrium constant), Arrhenius equation (which describes the rate coefficients), and procedures associated with the Gibbs free energy (minimization, rescaling) have a common physical and mathematical origin. We address an ambiguity associated with the equilibrium constant, which is used to relate the forward and reverse rate coefficients, and restate its two definitions. By necessity, one of the equilibrium constants must be dimensionless and equatemore » to an exponential function involving the Gibbs free energy, while the other is a ratio of rate coefficients and must therefore possess physical units. We demonstrate that the Arrhenius equation takes on a functional form that is more general than previously stated without recourse to tagging on ad hoc functional forms. Finally, we derive analytical models of chemical systems, in equilibrium, with carbon, hydrogen, and oxygen. We include acetylene and are able to reproduce several key trends, versus temperature and carbon-to-oxygen ratio, published in the literature. The rich variety of behavior that mixing ratios exhibit as a function of the carbon-to-oxygen ratio is merely the outcome of stoichiometric book-keeping and not the direct consequence of temperature or pressure variations.« less

Emergence and equilibration of jets in planetary turbulence

NASA Astrophysics Data System (ADS)

Constantinou, Navid; Ioannou, Petros; Farrell, Brian

2013-04-01

Spatially and temporally coherent large scale jets that are not forced directly at the jet scale are prominent feature of rotating turbulence. A familiar example is the midlatitude jet in the Earth's atmosphere and the banded winds of the giants planets. These jets arise and are supported by the systematic organisation of the turbulent Reynolds stresses. Understanding the mechanism producing the required eddy momentum flux convergence, and how the jets and associated eddy field mutually adjust to maintain a steady jet structure at finite amplitude, constitute fundamental theoretical problems. Stochastic Structural Stability Theory (SSST) gives an explanation for jet formation that is fundamentally based on the interaction between jets and their associated field of turbulent eddies. SSST combines the full dynamics of the zonal mean flow with the second order statistics of the turbulent field obtained from a stochastic turbulence model (STM). The quasi-linear (QL) approximation to the full nonlinear dynamics (NL) results when the perturbation-perturbation interactions are parameterized in the perturbation equations, while interaction between the perturbations and the zonal mean flow is retained in the zonal mean equation. SSST consists of an infinite ensemble of perturbations evolving under QL. Therefore, SSST provides a set of dynamical equations for the mean flow and the second order statistics of the second cummulant of the perturbation vorticity field, which are autonomous and fluctuation free and can facilitate analytic study of turbulent equilibria and their stability as a function of parameters. Thus, jet formation in homogeneous beta-turbulence can be identified with an SSST structural instability of a homogeneous (mean flow free) SSTT equilibrium. We investigate the emergence and equilibration of jets from homogeneous barotropic beta-plane turbulence in the absence of coherent external forcing. SSST predicts that infinitesimal perturbations with zonal jet form organise homogeneous turbulence to produce systematic upgradient fluxes, giving rise to exponential jet growth and eventually to the establishment of finite amplitude equilibrium jets. We compare these predictions with simulations of the NL equations and their QL approximation in order to examine further the mechanism of emergence and equilibration of jets from turbulence. We concentrate on the effects of perturbation-perturbation nonlinearity on jet bifurcation and equilibration, and on the influence of perturbations in exciting the manifold of SSST modes with jet structure. We find that the bifurcation structure predicted by SSST for the emergence of zonal jets from a homogeneous turbulent state is confirmed by both QL and NL simulations. Moreover, we show that the finite amplitude equilibrium jets found in NL and QL simulations are as predicted by the fixed point solutions of SSST. Obtaining this agreement between NL and both SSST and QL simulations required in some cases that the modification of the turbulent spectrum caused by the perturbation-perturbation nonlinearity in NL be accounted for in the specification of the stochastic forcing in QL and SSST. These results confirm that jet emergence in barotropic beta-plane turbulence can be traced to the cooperative mean flow/perturbation instability that is captured by SSST.

Analysis of a Multi-Fidelity Surrogate for Handling Real Gas Equations of State

NASA Astrophysics Data System (ADS)

Ouellet, Frederick; Park, Chanyoung; Rollin, Bertrand; Balachandar, S.

2017-06-01

The explosive dispersal of particles is a complex multiphase and multi-species fluid flow problem. In these flows, the detonation products of the explosive must be treated as real gas while the ideal gas equation of state is used for the surrounding air. As the products expand outward from the detonation point, they mix with ambient air and create a mixing region where both state equations must be satisfied. One of the most accurate, yet computationally expensive, methods to handle this problem is an algorithm that iterates between both equations of state until pressure and thermal equilibrium are achieved inside of each computational cell. This work aims to use a multi-fidelity surrogate model to replace this process. A Kriging model is used to produce a curve fit which interpolates selected data from the iterative algorithm using Bayesian statistics. We study the model performance with respect to the iterative method in simulations using a finite volume code. The model's (i) computational speed, (ii) memory requirements and (iii) computational accuracy are analyzed to show the benefits of this novel approach. Also, optimizing the combination of model accuracy and computational speed through the choice of sampling points is explained. This work was supported by the U.S. Department of Energy, National Nuclear Security Administration, Advanced Simulation and Computing Program as a Cooperative Agreement under the Predictive Science Academic Alliance Program under Contract No. DE-NA0002378.

Near-equilibrium dumb-bell-shaped figures for cohesionless small bodies

NASA Astrophysics Data System (ADS)

Descamps, Pascal

2016-02-01

In a previous paper (Descamps, P. [2015]. Icarus 245, 64-79), we developed a specific method aimed to retrieve the main physical characteristics (shape, density, surface scattering properties) of highly elongated bodies from their rotational lightcurves through the use of dumb-bell-shaped equilibrium figures. The present work is a test of this method. For that purpose we introduce near-equilibrium dumb-bell-shaped figures which are base dumb-bell equilibrium shapes modulated by lognormal statistics. Such synthetic irregular models are used to generate lightcurves from which our method is successfully applied. Shape statistical parameters of such near-equilibrium dumb-bell-shaped objects are in good agreement with those calculated for example for the Asteroid (216) Kleopatra from its dog-bone radar model. It may suggest that such bilobed and elongated asteroids can be approached by equilibrium figures perturbed be the interplay with a substantial internal friction modeled by a Gaussian random sphere.

Solitons of the Kadomtsev-Petviashvili equation based on lattice Boltzmann model

NASA Astrophysics Data System (ADS)

Wang, Huimin

2017-01-01

In this paper, a lattice Boltzmann model for the Kadomtsev-Petviashvili equation is proposed. By using the Chapman-Enskog expansion and the multi-scale time expansion, a series of partial differential equations in different time scales are obtained. Due to the asymmetry in x direction and y direction of the equation, the moments of the equilibrium distribution function are selected are asymmetric. The numerical results demonstrate the lattice Boltzmann method is an effective method to simulate the solitons of the Kadomtsev-Petviashvili equation.

Numerical Problem Solving Using Mathcad in Undergraduate Reaction Engineering

ERIC Educational Resources Information Center

Parulekar, Satish J.

2006-01-01

Experience in using a user-friendly software, Mathcad, in the undergraduate chemical reaction engineering course is discussed. Example problems considered for illustration deal with simultaneous solution of linear algebraic equations (kinetic parameter estimation), nonlinear algebraic equations (equilibrium calculations for multiple reactions and…

A Nonlinear, Multiinput, Multioutput Process Control Laboratory Experiment

ERIC Educational Resources Information Center

Young, Brent R.; van der Lee, James H.; Svrcek, William Y.

2006-01-01

Experience in using a user-friendly software, Mathcad, in the undergraduate chemical reaction engineering course is discussed. Example problems considered for illustration deal with simultaneous solution of linear algebraic equations (kinetic parameter estimation), nonlinear algebraic equations (equilibrium calculations for multiple reactions and…

Feynman-Kac equation for anomalous processes with space- and time-dependent forces

NASA Astrophysics Data System (ADS)

Cairoli, Andrea; Baule, Adrian

2017-04-01

Functionals of a stochastic process Y(t) model many physical time-extensive observables, for instance particle positions, local and occupation times or accumulated mechanical work. When Y(t) is a normal diffusive process, their statistics are obtained as the solution of the celebrated Feynman-Kac equation. This equation provides the crucial link between the expected values of diffusion processes and the solutions of deterministic second-order partial differential equations. When Y(t) is non-Brownian, e.g. an anomalous diffusive process, generalizations of the Feynman-Kac equation that incorporate power-law or more general waiting time distributions of the underlying random walk have recently been derived. A general representation of such waiting times is provided in terms of a Lévy process whose Laplace exponent is directly related to the memory kernel appearing in the generalized Feynman-Kac equation. The corresponding anomalous processes have been shown to capture nonlinear mean square displacements exhibiting crossovers between different scaling regimes, which have been observed in numerous experiments on biological systems like migrating cells or diffusing macromolecules in intracellular environments. However, the case where both space- and time-dependent forces drive the dynamics of the generalized anomalous process has not been solved yet. Here, we present the missing derivation of the Feynman-Kac equation in such general case by using the subordination technique. Furthermore, we discuss its extension to functionals explicitly depending on time, which are of particular relevance for the stochastic thermodynamics of anomalous diffusive systems. Exact results on the work fluctuations of a simple non-equilibrium model are obtained. An additional aim of this paper is to provide a pedagogical introduction to Lévy processes, semimartingales and their associated stochastic calculus, which underlie the mathematical formulation of anomalous diffusion as a subordinated process.

Determination and theoretical aspects of the equilibrium between dissolved organic matter and hydrophobic organic micropollutants in water (Kdoc).

PubMed

Krop, H B; van Noort, P C; Govers, H A

2001-01-01

Literature on the equilibrium constant for distribution between dissolved organic carbon (DOC) (Kdoc) data of strongly hydrophobic organic contaminants were collected and critically analyzed. About 900 Kdoc entries for experimental values were retrieved and tabulated, including those factors that can influence them. In addition, quantitative structure-activity relationship (QSAR) prediction equations were retrieved and tabulated. Whether a partition or association process between the contaminant and DOC takes place could not be fully established, but indications toward an association process are strong in several cases. Equilibrium between a contaminant and DOC in solution was shown to be achieved within a minute. When the equilibrium shifts in time, this was caused by either a physical or chemical change of the DOC, affecting the lighter fractions most. Adsorption isotherms turned out to be linear in the contaminant concentration for the relevant DOC concentration up to 100 mg of C/L. Eighteen experimental methods have been developed for the determination of the pertinent distribution constant. Experimental Kdoc values revealed the expected high correlation with partition coefficients over n-octanol and water (Kow) for all experimental methods, except for the HPLC and apparent solubility (AS) method. Only fluorescence quenching (FQ) and solid-phase microextraction (SPME) methods could quantify fast equilibration. Only 21% of the experimental values had a 95% confidence interval, which was statistically significantly different from zero. Variation in Kdoc values was shown to be high, caused mainly by the large variation of DOC in water samples. Even DOC from one sample gave different equilibrium constants for different DOC fractions. Measured Kdoc values should, therefore, be regarded as average values. Kdoc was shown to increase on increasing molecular mass, indicating that the molecular mass distribution is a proper normalization function for the average Kdoc at the current state of knowledge. The weakly bound fraction could easily be desorbed when other adsorbing media, such as a SepPak column or living organism, are present. The amount that moves from the DOC to the other medium will depend, among other reasons, on the size of the labile DOC fraction and the equilibrium constant of the other medium. Variation of Kdoc with temperature turned out to be small, probably caused by a small enthalpy of transfer from water to DOC. Ionic strength turned out to be more important, leading to changes of a factor of 2-5. The direction of this effect depends on the type of ion. With respect to QSAR relationships between Kdoc and macroscopic or molecular descriptors, it was concluded that only a small number of equations are available in the literature, for apolar compounds only, and with poor statistics and predictive power. Therefore, a first requirement is the improvement of the availability and quality of experimental data. Along with this, theoretical (mechanistic) models for the relationship between DOC plus contaminant descriptors on the one side and Kdoc on the other should be further developed. Correlations between Kdoc and Kow and those between the soil-water partition constant (Koc) and Kow were significantly different only in the case of natural aquatic DOC, pointing at substantial differences between these two types of organic material and at a high correspondence for other types of commercial and natural DOC.

Non-equilibrium hydrogen ionization in 2D simulations of the solar atmosphere

NASA Astrophysics Data System (ADS)

Leenaarts, J.; Carlsson, M.; Hansteen, V.; Rutten, R. J.

2007-10-01

Context: The ionization of hydrogen in the solar chromosphere and transition region does not obey LTE or instantaneous statistical equilibrium because the timescale is long compared with important hydrodynamical timescales, especially of magneto-acoustic shocks. Since the pressure, temperature, and electron density depend sensitively on hydrogen ionization, numerical simulation of the solar atmosphere requires non-equilibrium treatment of all pertinent hydrogen transitions. The same holds for any diagnostic application employing hydrogen lines. Aims: To demonstrate the importance and to quantify the effects of non-equilibrium hydrogen ionization, both on the dynamical structure of the solar atmosphere and on hydrogen line formation, in particular Hα. Methods: We implement an algorithm to compute non-equilibrium hydrogen ionization and its coupling into the MHD equations within an existing radiation MHD code, and perform a two-dimensional simulation of the solar atmosphere from the convection zone to the corona. Results: Analysis of the simulation results and comparison to a companion simulation assuming LTE shows that: a) non-equilibrium computation delivers much smaller variations of the chromospheric hydrogen ionization than for LTE. The ionization is smaller within shocks but subsequently remains high in the cool intershock phases. As a result, the chromospheric temperature variations are much larger than for LTE because in non-equilibrium, hydrogen ionization is a less effective internal energy buffer. The actual shock temperatures are therefore higher and the intershock temperatures lower. b) The chromospheric populations of the hydrogen n = 2 level, which governs the opacity of Hα, are coupled to the ion populations. They are set by the high temperature in shocks and subsequently remain high in the cool intershock phases. c) The temperature structure and the hydrogen level populations differ much between the chromosphere above photospheric magnetic elements and above quiet internetwork. d) The hydrogen n = 2 population and column density are persistently high in dynamic fibrils, suggesting that these obtain their visibility from being optically thick in Hα also at low temperature. Movie and Appendix A are only available in electronic form at http://www.aanda.org

Biosorption of Cu(II) from aqueous solutions by mimosa tannin gel.

PubMed

Sengil, I Ayhan; Ozacar, Mahmut

2008-09-15

The biosorption of Cu(II) from aqueous solutions by mimosa tannin resin (MTR) was investigated as a function of particle size, initial pH, contact time and initial metal ion concentration. The aim of this study was to understand the mechanisms that govern copper removal and find a suitable equilibrium isotherm and kinetic model for the copper removal in a batch reactor. The experimental isotherm data were analysed using the Langmuir, Freundlich and Temkin equations. The equilibrium data fit well in the Langmiur isotherm. The experimental data were analysed using four sorption kinetic models -- the pseudo-first- and second-order equations, and the Elovich and the intraparticle diffusion equation -- to determine the best fit equation for the biosorption of copper ions onto mimosa tannin resin. Results show that the pseudo-second-order equation provides the best correlation for the biosorption process, whereas the Elovich equation also fits the experimental data well. Thermodynamic parameters such as the entropy change, enthalpy change and Gibb's free energy change were found out to be 153.0 J mol(-1)K(-1), 42.09 kJ mol(-1) and -2.47 kJ mol(-1), respectively.

Microscopic Simulation and Macroscopic Modeling for Thermal and Chemical Non-Equilibrium

NASA Technical Reports Server (NTRS)

Liu, Yen; Panesi, Marco; Vinokur, Marcel; Clarke, Peter

2013-01-01

This paper deals with the accurate microscopic simulation and macroscopic modeling of extreme non-equilibrium phenomena, such as encountered during hypersonic entry into a planetary atmosphere. The state-to-state microscopic equations involving internal excitation, de-excitation, dissociation, and recombination of nitrogen molecules due to collisions with nitrogen atoms are solved time-accurately. Strategies to increase the numerical efficiency are discussed. The problem is then modeled using a few macroscopic variables. The model is based on reconstructions of the state distribution function using the maximum entropy principle. The internal energy space is subdivided into multiple groups in order to better describe the non-equilibrium gases. The method of weighted residuals is applied to the microscopic equations to obtain macroscopic moment equations and rate coefficients. The modeling is completely physics-based, and its accuracy depends only on the assumed expression of the state distribution function and the number of groups used. The model makes no assumption at the microscopic level, and all possible collisional and radiative processes are allowed. The model is applicable to both atoms and molecules and their ions. Several limiting cases are presented to show that the model recovers the classical twotemperature models if all states are in one group and the model reduces to the microscopic equations if each group contains only one state. Numerical examples and model validations are carried out for both the uniform and linear distributions. Results show that the original over nine thousand microscopic equations can be reduced to 2 macroscopic equations using 1 to 5 groups with excellent agreement. The computer time is decreased from 18 hours to less than 1 second.

Inventory Control: A Small Electronic Device for Studying Chemical Kinetics.

ERIC Educational Resources Information Center

Perez-Rodriguez, A. L.; Calvo-Aguilar, J. L.

1984-01-01

Shows how the rate of reaction can be studied using a simple electronic device that overcomes the difficulty students encounter in solving the differential equations describing chemical equilibrium. The device, used in conjunction with an oscilloscope, supplies the voltages that represent the chemical variables that take part in the equilibrium.…

Hammett analyses of halocarbene-halocarbanion equilibria.

PubMed

Wang, Lei; Moss, Robert A; Krogh-Jespersen, Karsten

2013-04-19

Substituted arylchlorocarbenes (X = H, p-Cl, p-CF3, p-F, m-Cl) reacted reversibly with Cl(-) in dichloroethane to form the corresponding aryldichloromethide carbanions. Equilibrium constants and rate constants for the forward and reverse reactions were correlated by the Hammett equation. DFT methods were used to compute equilibrium constants and electronic absorption spectra.

Steady bipartite coherence induced by non-equilibrium environment

NASA Astrophysics Data System (ADS)

Huangfu, Yong; Jing, Jun

2018-01-01

We study the steady state of two coupled two-level atoms interacting with a non-equilibrium environment that consists of two heat baths at different temperatures. Specifically, we analyze four cases with respect to the configuration about the interactions between atoms and heat baths. Using secular approximation, the conventional master equation usually neglects steady-state coherence, even when the system is coupled with a non-equilibrium environment. When employing the master equation with no secular approximation, we find that the system coherence in our model, denoted by the off-diagonal terms in the reduced density matrix spanned by the eigenvectors of the system Hamiltonian, would survive after a long-time decoherence evolution. The absolute value of residual coherence in the system relies on different configurations of interaction channels between the system and the heat baths. We find that a large steady quantum coherence term can be achieved when the two atoms are resonant. The absolute value of quantum coherence decreases in the presence of additional atom-bath interaction channels. Our work sheds new light on the mechanism of steady-state coherence in microscopic quantum systems in non-equilibrium environments.

Population annealing simulations of a binary hard-sphere mixture

NASA Astrophysics Data System (ADS)

Callaham, Jared; Machta, Jonathan

2017-06-01

Population annealing is a sequential Monte Carlo scheme well suited to simulating equilibrium states of systems with rough free energy landscapes. Here we use population annealing to study a binary mixture of hard spheres. Population annealing is a parallel version of simulated annealing with an extra resampling step that ensures that a population of replicas of the system represents the equilibrium ensemble at every packing fraction in an annealing schedule. The algorithm and its equilibration properties are described, and results are presented for a glass-forming fluid composed of a 50/50 mixture of hard spheres with diameter ratio of 1.4:1. For this system, we obtain precise results for the equation of state in the glassy regime up to packing fractions φ ≈0.60 and study deviations from the Boublik-Mansoori-Carnahan-Starling-Leland equation of state. For higher packing fractions, the algorithm falls out of equilibrium and a free volume fit predicts jamming at packing fraction φ ≈0.667 . We conclude that population annealing is an effective tool for studying equilibrium glassy fluids and the jamming transition.

Two-phase vesicles: a study on evolutionary and stationary models.

PubMed

Sahebifard, MohammadMahdi; Shahidi, Alireza; Ziaei-Rad, Saeed

2017-05-01

In the current article, the dynamic evolution of two-phase vesicles is presented as an extension to a previous stationary model and based on an equilibrium of local forces. In the simplified model, ignoring the effects of membrane inertia, a dynamic equilibrium between the membrane bending potential and local fluid friction is considered in each phase. The equilibrium equations at the domain borders are completed by extended introduction of membrane section reactions. We show that in some cases, the results of stationary and evolutionary models are in agreement with each other and also with experimental observations, while in others the two models differ markedly. The value of our approach is that we can account for unresponsive points of uncertainty using our equations with the local velocity of the lipid membranes and calculating the intermediate states (shapes) in the consequent evolutionary, or response, path.

Nonequilibrium Entropy in a Shock

DOE PAGES

Margolin, Len G.

2017-07-19

In a classic paper, Morduchow and Libby use an analytic solution for the profile of a Navier–Stokes shock to show that the equilibrium thermodynamic entropy has a maximum inside the shock. There is no general nonequilibrium thermodynamic formulation of entropy; the extension of equilibrium theory to nonequililbrium processes is usually made through the assumption of local thermodynamic equilibrium (LTE). However, gas kinetic theory provides a perfectly general formulation of a nonequilibrium entropy in terms of the probability distribution function (PDF) solutions of the Boltzmann equation. In this paper I will evaluate the Boltzmann entropy for the PDF that underlies themore » Navier–Stokes equations and also for the PDF of the Mott–Smith shock solution. I will show that both monotonically increase in the shock. As a result, I will propose a new nonequilibrium thermodynamic entropy and show that it is also monotone and closely approximates the Boltzmann entropy.« less

Transport processes and sound velocity in vibrationally non-equilibrium gas of anharmonic oscillators

NASA Astrophysics Data System (ADS)

Rydalevskaya, Maria A.; Voroshilova, Yulia N.

2018-05-01

Vibrationally non-equilibrium flows of chemically homogeneous diatomic gases are considered under the conditions that the distribution of the molecules over vibrational levels differs significantly from the Boltzmann distribution. In such flows, molecular collisions can be divided into two groups: the first group corresponds to "rapid" microscopic processes whereas the second one corresponds to "slow" microscopic processes (their rate is comparable to or larger than that of gasdynamic parameters variation). The collisions of the first group form quasi-stationary vibrationally non-equilibrium distribution functions. The model kinetic equations are used to study the transport processes under these conditions. In these equations, the BGK-type approximation is used to model only the collision operators of the first group. It allows us to simplify derivation of the transport fluxes and calculation of the kinetic coefficients. Special attention is given to the connection between the formulae for the bulk viscosity coefficient and the sound velocity square.

Non-canonical distribution and non-equilibrium transport beyond weak system-bath coupling regime: A polaron transformation approach

NASA Astrophysics Data System (ADS)

Xu, Dazhi; Cao, Jianshu

2016-08-01

The concept of polaron, emerged from condense matter physics, describes the dynamical interaction of moving particle with its surrounding bosonic modes. This concept has been developed into a useful method to treat open quantum systems with a complete range of system-bath coupling strength. Especially, the polaron transformation approach shows its validity in the intermediate coupling regime, in which the Redfield equation or Fermi's golden rule will fail. In the polaron frame, the equilibrium distribution carried out by perturbative expansion presents a deviation from the canonical distribution, which is beyond the usual weak coupling assumption in thermodynamics. A polaron transformed Redfield equation (PTRE) not only reproduces the dissipative quantum dynamics but also provides an accurate and efficient way to calculate the non-equilibrium steady states. Applications of the PTRE approach to problems such as exciton diffusion, heat transport and light-harvesting energy transfer are presented.

Chemical reactions simulated by ground-water-quality models

USGS Publications Warehouse

Grove, David B.; Stollenwerk, Kenneth G.

1987-01-01

Recent literature concerning the modeling of chemical reactions during transport in ground water is examined with emphasis on sorption reactions. The theory of transport and reactions in porous media has been well documented. Numerous equations have been developed from this theory, to provide both continuous and sequential or multistep models, with the water phase considered for both mobile and immobile phases. Chemical reactions can be either equilibrium or non-equilibrium, and can be quantified in linear or non-linear mathematical forms. Non-equilibrium reactions can be separated into kinetic and diffusional rate-limiting mechanisms. Solutions to the equations are available by either analytical expressions or numerical techniques. Saturated and unsaturated batch, column, and field studies are discussed with one-dimensional, laboratory-column experiments predominating. A summary table is presented that references the various kinds of models studied and their applications in predicting chemical concentrations in ground waters.

Nonequilibrium Entropy in a Shock

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

Margolin, Len G.

In a classic paper, Morduchow and Libby use an analytic solution for the profile of a Navier–Stokes shock to show that the equilibrium thermodynamic entropy has a maximum inside the shock. There is no general nonequilibrium thermodynamic formulation of entropy; the extension of equilibrium theory to nonequililbrium processes is usually made through the assumption of local thermodynamic equilibrium (LTE). However, gas kinetic theory provides a perfectly general formulation of a nonequilibrium entropy in terms of the probability distribution function (PDF) solutions of the Boltzmann equation. In this paper I will evaluate the Boltzmann entropy for the PDF that underlies themore » Navier–Stokes equations and also for the PDF of the Mott–Smith shock solution. I will show that both monotonically increase in the shock. As a result, I will propose a new nonequilibrium thermodynamic entropy and show that it is also monotone and closely approximates the Boltzmann entropy.« less

Lagrangian formulation of irreversible thermodynamics and the second law of thermodynamics.

PubMed

Glavatskiy, K S

2015-05-28

We show that the equations which describe irreversible evolution of a system can be derived from a variational principle. We suggest a Lagrangian, which depends on the properties of the normal and the so-called "mirror-image" system. The Lagrangian is symmetric in time and therefore compatible with microscopic reversibility. The evolution equations in the normal and mirror-imaged systems are decoupled and describe therefore independent irreversible evolution of each of the systems. The second law of thermodynamics follows from a symmetry of the Lagrangian. Entropy increase in the normal system is balanced by the entropy decrease in the mirror-image system, such that there exists an "integral of evolution" which is a constant. The derivation relies on the property of local equilibrium, which states that the local relations between the thermodynamic quantities in non-equilibrium are the same as in equilibrium.

On the equilibrium structures of self-gravitating masses of gas containing axisymmetric magnetic fields

NASA Technical Reports Server (NTRS)

Lerche, I.; Low, B. C.

1980-01-01

The general equations describing the equilibrium shapes of self-gravitating gas clouds containing axisymmetric magnetic fields are presented. The general equations admit of a large class of solutions. It is shown that if one additional (ad hoc) asumption is made that the mass be spherically symmetrically distributed, then the gas pressure and the boundary conditions are sufficiently constraining that the general topological structure of the solution is effectively determined. The further assumption of isothermal conditions for this case demands that all solutions possess force-free axisymmetric magnetic fields. It is also shown how the construction of aspherical (but axisymmetric) configurations can be achieved in some special cases, and it is demonstrated that the detailed form of the possible equilibrium shapes depends upon the arbitrary choice of the functional form of the variation of the gas pressure along the field lines.

Lagrangian formulation of irreversible thermodynamics and the second law of thermodynamics

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

Glavatskiy, K. S.

We show that the equations which describe irreversible evolution of a system can be derived from a variational principle. We suggest a Lagrangian, which depends on the properties of the normal and the so-called “mirror-image” system. The Lagrangian is symmetric in time and therefore compatible with microscopic reversibility. The evolution equations in the normal and mirror-imaged systems are decoupled and describe therefore independent irreversible evolution of each of the systems. The second law of thermodynamics follows from a symmetry of the Lagrangian. Entropy increase in the normal system is balanced by the entropy decrease in the mirror-image system, such thatmore » there exists an “integral of evolution” which is a constant. The derivation relies on the property of local equilibrium, which states that the local relations between the thermodynamic quantities in non-equilibrium are the same as in equilibrium.« less

Thermodynamic model effects on the design and optimization of natural gas plants

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

Diaz, S.; Zabaloy, M.; Brignole, E.A.

1999-07-01

The design and optimization of natural gas plants is carried out on the basis of process simulators. The physical property package is generally based on cubic equations of state. By rigorous thermodynamics phase equilibrium conditions, thermodynamic functions, equilibrium phase separations, work and heat are computed. The aim of this work is to analyze the NGL turboexpansion process and identify possible process computations that are more sensitive to model predictions accuracy. Three equations of state, PR, SRK and Peneloux modification, are used to study the effect of property predictions on process calculations and plant optimization. It is shown that turboexpander plantsmore » have moderate sensitivity with respect to phase equilibrium computations, but higher accuracy is required for the prediction of enthalpy and turboexpansion work. The effect of modeling CO{sub 2} solubility is also critical in mixtures with high CO{sub 2} content in the feed.« less

A mixture-energy-consistent six-equation two-phase numerical model for fluids with interfaces, cavitation and evaporation waves

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

Pelanti, Marica, E-mail: marica.pelanti@ensta-paristech.fr; Shyue, Keh-Ming, E-mail: shyue@ntu.edu.tw

2014-02-15

We model liquid–gas flows with cavitation by a variant of the six-equation single-velocity two-phase model with stiff mechanical relaxation of Saurel–Petitpas–Berry (Saurel et al., 2009) [9]. In our approach we employ phasic total energy equations instead of the phasic internal energy equations of the classical six-equation system. This alternative formulation allows us to easily design a simple numerical method that ensures consistency with mixture total energy conservation at the discrete level and agreement of the relaxed pressure at equilibrium with the correct mixture equation of state. Temperature and Gibbs free energy exchange terms are included in the equations as relaxationmore » terms to model heat and mass transfer and hence liquid–vapor transition. The algorithm uses a high-resolution wave propagation method for the numerical approximation of the homogeneous hyperbolic portion of the model. In two dimensions a fully-discretized scheme based on a hybrid HLLC/Roe Riemann solver is employed. Thermo-chemical terms are handled numerically via a stiff relaxation solver that forces thermodynamic equilibrium at liquid–vapor interfaces under metastable conditions. We present numerical results of sample tests in one and two space dimensions that show the ability of the proposed model to describe cavitation mechanisms and evaporation wave dynamics.« less

Modified TOV in gravity’s rainbow: properties of neutron stars and dynamical stability conditions

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

Hendi, S.H.; Research Institute for Astronomy and Astrophysics of Maragha; Bordbar, G.H.

In this paper, we consider a spherical symmetric metric to extract the hydrostatic equilibrium equation of stars in (3+1)-dimensional gravity’s rainbow in the presence of cosmological constant. Then, we generalize the hydrostatic equilibrium equation to d-dimensions and obtain the hydrostatic equilibrium equation for this gravity. Also, we obtain the maximum mass of neutron star using the modern equations of state of neutron star matter derived from the microscopic calculations. It is notable that, in this paper, we consider the effects of rainbow functions on the diagrams related to the mass-central mass density (M-ρ{sub c}) relation and also the mass-radius (M-R)more » relation of neutron star. We also study the effects of rainbow functions on the other properties of neutron star such as the Schwarzschild radius, average density, strength of gravity and gravitational redshift. Then, we apply the cosmological constant to this theory to obtain the diagrams of M-ρ{sub c} (or M-R) and other properties of these stars. Next, we investigate the dynamical stability condition for these stars in gravity’s rainbow and show that these stars have dynamical stability. We also obtain a relation between mass of neutron stars and Planck mass. In addition, we compare obtained results of this theory with the observational data.« less

Global dynamics of a delay differential equation with spatial non-locality in an unbounded domain

NASA Astrophysics Data System (ADS)

Yi, Taishan; Zou, Xingfu

In this paper, we study the global dynamics of a class of differential equations with temporal delay and spatial non-locality in an unbounded domain. Adopting the compact open topology, we describe the delicate asymptotic properties of the nonlocal delayed effect and establish some a priori estimate for nontrivial solutions which enables us to show the permanence of the equation. Combining these results with a dynamical systems approach, we determine the global dynamics of the equation under appropriate conditions. Applying the main results to the model with Ricker's birth function and Mackey-Glass's hematopoiesis function, we obtain threshold results for the global dynamics of these two models. We explain why our results on the global attractivity of the positive equilibrium in C∖{0} under the compact open topology becomes invalid in C∖{0} with respect to the usual supremum norm, and we identify a subset of C∖{0} in which the positive equilibrium remains attractive with respect to the supremum norm.

Stellar structure model in hydrostatic equilibrium in the context of f({\\mathscr{R}})-gravity

NASA Astrophysics Data System (ADS)

André, Raíla; Kremer, Gilberto M.

2017-12-01

In this work we present a stellar structure model from the f({\\mathscr{R}})-gravity point of view capable of describing some classes of stars (white dwarfs, brown dwarfs, neutron stars, red giants and the Sun). This model is based on f({\\mathscr{R}})-gravity field equations for f({\\mathscr{R}})={\\mathscr{R}}+{f}2{{\\mathscr{R}}}2, hydrostatic equilibrium equation and a polytropic equation of state. We compare the results obtained with those found by Newtonian theory. It has been observed that in these systems, where high curvature regimes emerge, stellar structure equations undergo modifications. Despite the simplicity of this model, the results are satisfactory. The estimated values of pressure, density and temperature of the stars are within those determined by observations. This f({\\mathscr{R}})-gravity model has proved to be necessary to describe stars with strong fields such as white dwarfs, neutron stars and brown dwarfs, while stars with weaker fields, such as red giants and the Sun, are best described by Newtonian theory.

Quasi-Static Viscoelastic Finite Element Model of an Aircraft Tire

NASA Technical Reports Server (NTRS)

Johnson, Arthur R.; Tanner, John A.; Mason, Angela J.

1999-01-01

An elastic large displacement thick-shell mixed finite element is modified to allow for the calculation of viscoelastic stresses. Internal strain variables are introduced at the element's stress nodes and are employed to construct a viscous material model. First order ordinary differential equations relate the internal strain variables to the corresponding elastic strains at the stress nodes. The viscous stresses are computed from the internal strain variables using viscous moduli which are a fraction of the elastic moduli. The energy dissipated by the action of the viscous stresses is included in the mixed variational functional. The nonlinear quasi-static viscous equilibrium equations are then obtained. Previously developed Taylor expansions of the nonlinear elastic equilibrium equations are modified to include the viscous terms. A predictor-corrector time marching solution algorithm is employed to solve the algebraic-differential equations. The viscous shell element is employed to computationally simulate a stair-step loading and unloading of an aircraft tire in contact with a frictionless surface.

Self-consistent electro-opto-thermal model of quantum cascade lasers with coupled electron and phonon interactions far from equilibrium

NASA Astrophysics Data System (ADS)

Yousefvand, Hossein Reza

2017-12-01

A self-consistent model of quantum cascade lasers (QCLs) is presented here for the study of the QCL's behavior in the far from equilibrium conditions. The approach is developed by employing a number of physics-based models such as the carrier and photon rate equations, the energy balance equation, the heat transfer equation and a simplified rate equation for the creation and annihilation of nonequilibrium optical phonons. The temperature dependency of the relevant physical effects such as stimulated gain cross section, longitudinal optical (LO) phonons and hot-phonon generation rates are included in the model. Using the presented model, the static and transient device characteristics are calculated and analyzed for a wide range of heat sink temperatures. Besides the output characteristics, this model also provides a way to study the hot-phonon dynamics in the device, and to explore the electron temperature and thermal roll-over in the QCLs.

On Determination of the Equation of State of Colloidal Suspensions

NASA Astrophysics Data System (ADS)

Sirorattanakul, Krittanon; Huang, Hao; Uhl, Christopher; Ou-Yang, Daniel

Colloidal suspensions are the main ingredients for a variety of materials in our daily life, e.g., milk, salad dressing, skin lotions and paint for wall coatings. Material properties of these systems require an understanding of the equation of state of these materials. Our project aims to experimentally determine the equation of state of colloidal suspensions by microfluidics, dielectrophoresis (DEP) and optical imaging. We use fluorescent polystyrene latexes as a model system for this study. Placing semi-permeable membranes between microfluidics channels, which made from PDMS, we control the particle concentration and ionic strengths of the suspension. We use osmotic equilibrium equation to analyze the particle concentration distribution in a potential force field created by DEP. We use confocal optical imaging to measure the spatial distribution of the particle concentration. We compare the results of our experimental study with data obtained by computer simulation of osmotic equilibrium of interacting colloids. NSF DMR-0923299, Emulsion Polymer Institute, Department of Physics, Bioengineering Program of Lehigh University.

RAS one-equation turbulence model with non-singular eddy-viscosity coefficient

NASA Astrophysics Data System (ADS)

Rahman, M. M.; Agarwal, R. K.; Siikonen, T.

2016-02-01

A simplified consistency formulation for Pk/ε (production to dissipation ratio) is devised to obtain a non-singular Cμ (coefficient of eddy-viscosity) in the explicit algebraic Reynolds stress model of Gatski and Speziale. The coefficient Cμ depends non-linearly on both rotational/irrotational strains and is used in the framework of an improved RAS (Rahman-Agarwal-Siikonen) one-equation turbulence model to calculate a few well-documented turbulent flows, yielding predictions in good agreement with the direct numerical simulation and experimental data. The strain-dependent Cμ assists the RAS model in constructing the coefficients and functions such as to benefit complex flows with non-equilibrium turbulence. Comparisons with the Spalart-Allmaras one-equation model and the shear stress transport k-ω model demonstrate that Cμ improves the response of RAS model to non-equilibrium effects.

An examination of the rheology of flocculated clay suspensions

NASA Astrophysics Data System (ADS)

Spearman, Jeremy

2017-04-01

A dense cohesive sediment suspension, sometimes referred to as fluid mud, is a thixotropic fluid with a true yield stress. Current rheological formulations struggle to reconcile the structural dynamics of cohesive sediment suspensions with the equilibrium behaviour of these suspensions across the range of concentrations and shear. This paper is concerned with establishing a rheological framework for the range of sediment concentrations from the yield point to Newtonian flow. The shear stress equation is based on floc fractal theory, put forward by Mills and Snabre (1988). This results in a Casson-like rheology equation. Additional structural dynamics is then added, using a theory on the self-similarity of clay suspensions proposed by Coussot (1995), giving an equation which has the ability to match the equilibrium and time-dependent viscous rheology of a wide range of suspensions of different concentration and mineralogy.

Recommendations for numerical solution of reinforced-panel and fuselage-ring problems

NASA Technical Reports Server (NTRS)

Hoff, N J; Libby, Paul A

1949-01-01

Procedures are recommended for solving the equations of equilibrium of reinforced panels and isolated fuselage rings as represented by the external loads and the operations table established according to Southwell's method. From the solution of these equations the stress distribution can be easily determined. The method of systematic relaxations, the matrix-calculus method, and several other methods applicable in special cases are discussed. Definite recommendations are made for obtaining the solution of reinforced-panel problems which are generally designated as shear lag problems. The procedures recommended are demonstrated in the analysis of a number of panels. In the case of fuselage rings it is not possible to make definite recommendations for the solution of the equilibrium equations for all rings and loadings. However, suggestions based on the latest experience are made and demonstrated on several rings.

Stellar Equilibrium in Semiclassical Gravity.

PubMed

Carballo-Rubio, Raúl

2018-02-09

The phenomenon of quantum vacuum polarization in the presence of a gravitational field is well understood and is expected to have a physical reality, but studies of its backreaction on the dynamics of spacetime are practically nonexistent outside of the specific context of homogeneous cosmologies. Building on previous results of quantum field theory in curved spacetimes, in this Letter we first derive the semiclassical equations of stellar equilibrium in the s-wave Polyakov approximation. It is highlighted that incorporating the polarization of the quantum vacuum leads to a generalization of the classical Tolman-Oppenheimer-Volkoff equation. Despite the complexity of the resulting field equations, it is possible to find exact solutions. Aside from being the first known exact solutions that describe relativistic stars including the nonperturbative backreaction of semiclassical effects, these are identified as a nontrivial combination of the black star and gravastar proposals.

Atwood and Poggendorff: an insightful analogy

NASA Astrophysics Data System (ADS)

Coelho, R. L.; Borges, P. F.; Karam, R.

2016-11-01

Atwood’s treatise, in which the Atwood machine appears, was published in 1784. About 70 years later, Poggendorff showed experimentally that the weight of an Atwood machine is reduced when it is brought to motion. In the present paper, a twofold connection between this experiment and the Atwood machine is established. Firstly, if the Poggendorff apparatus is taken as an ideal one, the equations of motion of the apparatus coincide with the equations of motion of the compound Atwood machine. Secondly, if the Poggendorff apparatus, which works as a lever, is rebalanced, the equations of this equilibrium provide us with the solution for a compound Atwood machine with the same bodies. This analogy is pedagogically useful because it illustrates a common strategy to transform a dynamic in a static situation improving students’ comprehension of Newton’s laws and equilibrium.

Large eddy simulation of cavitating flows

NASA Astrophysics Data System (ADS)

Gnanaskandan, Aswin; Mahesh, Krishnan

2014-11-01

Large eddy simulation on unstructured grids is used to study hydrodynamic cavitation. The multiphase medium is represented using a homogeneous equilibrium model that assumes thermal equilibrium between the liquid and the vapor phase. Surface tension effects are ignored and the governing equations are the compressible Navier Stokes equations for the liquid/vapor mixture along with a transport equation for the vapor mass fraction. A characteristic-based filtering scheme is developed to handle shocks and material discontinuities in non-ideal gases and mixtures. A TVD filter is applied as a corrector step in a predictor-corrector approach with the predictor scheme being non-dissipative and symmetric. The method is validated for canonical one dimensional flows and leading edge cavitation over a hydrofoil, and applied to study sheet to cloud cavitation over a wedge. This work is supported by the Office of Naval Research.

Modeling non-equilibrium mass transport in biologically reactive porous media

NASA Astrophysics Data System (ADS)

Davit, Yohan; Debenest, Gérald; Wood, Brian D.; Quintard, Michel

2010-09-01

We develop a one-equation non-equilibrium model to describe the Darcy-scale transport of a solute undergoing biodegradation in porous media. Most of the mathematical models that describe the macroscale transport in such systems have been developed intuitively on the basis of simple conceptual schemes. There are two problems with such a heuristic analysis. First, it is unclear how much information these models are able to capture; that is, it is not clear what the model's domain of validity is. Second, there is no obvious connection between the macroscale effective parameters and the microscopic processes and parameters. As an alternative, a number of upscaling techniques have been developed to derive the appropriate macroscale equations that are used to describe mass transport and reactions in multiphase media. These approaches have been adapted to the problem of biodegradation in porous media with biofilms, but most of the work has focused on systems that are restricted to small concentration gradients at the microscale. This assumption, referred to as the local mass equilibrium approximation, generally has constraints that are overly restrictive. In this article, we devise a model that does not require the assumption of local mass equilibrium to be valid. In this approach, one instead requires only that, at sufficiently long times, anomalous behaviors of the third and higher spatial moments can be neglected; this, in turn, implies that the macroscopic model is well represented by a convection-dispersion-reaction type equation. This strategy is very much in the spirit of the developments for Taylor dispersion presented by Aris (1956). On the basis of our numerical results, we carefully describe the domain of validity of the model and show that the time-asymptotic constraint may be adhered to even for systems that are not at local mass equilibrium.

MHD waves and instabilities for gravitating, magnetized configurations in motion

NASA Astrophysics Data System (ADS)

Keppens, Rony; Goedbloed, Hans J. P.

Seismic probing of equilibrium configurations is of course well-known from geophysics, but has also been succesfully used to determine the internal structure of the Sun to an amazing accuracy. The results of helioseismology are quite impressive, although they only exploit an equilibrium structure where inward gravity is balanced by a pressure gradient in a 1D radial fashion. In principle, one can do the same for stationary, gravitating, magnetized plasma equilibria, as needed to perform MHD seismology in astrophysical jets or accretion disks. The introduction of (sheared) differential rotation does require the important switch from diagnosing static to stationary equilibrium configurations. The theory to describe all linear waves and instabilities in ideal MHD, given an exact stationary, gravitating, magnetized plasma equilibrium, in any dimensionality (1D, 2D, 3D) has been known since 1960, and is governed by the Frieman-Rotenberg equation. The full (mathematical) power of spectral theory governing physical eigenmode determination comes into play when using the Frieman-Rotenberg equation for moving equilibria, as applicable to astrophysical jets, accretion disks, but also solar flux ropes with stationary flow patterns. I will review exemplary seismic studies of flowing equilibrium configurations, covering solar to astrophysical configurations in motion. In that case, even essentially 1D configurations require quantification of the spectral web of eigenmodes, organizing the complex eigenfrequency plane.

Modeling multicomponent ion exchange equilibrium utilizing hydrous crystalline silicotitanates by a multiple interactive ion exchange site model

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

Zheng, Z.; Anthony, R.G.; Miller, J.E.

1997-06-01

An equilibrium multicomponent ion exchange model is presented for the ion exchange of group I metals by TAM-5, a hydrous crystalline silicotitanate. On the basis of the data from ion exchange and structure studies, the solid phase is represented as Na{sub 3}X instead of the usual form of NaX. By using this solid phase representation, the solid can be considered as an ideal phase. A set of model ion exchange reactions is proposed for ion exchange between H{sup +}, Na{sup +}, K{sup +}, Rb{sup +}, and Cs{sup +}. The equilibrium constants for these reactions were estimated from experiments with simplemore » ion exchange systems. Bromley`s model for activity coefficients of electrolytic solutions was used to account for liquid phase nonideality. Bromley`s model parameters for CsOH at high ionic strength and for NO{sub 2}{sup {minus}} and Al(OH){sub 4}{sup {minus}} were estimated in order to apply the model for complex waste simulants. The equilibrium compositions and distribution coefficients of counterions were calculated for complex simulants typical of DOE wastes by solving the equilibrium equations for the model reactions and material balance equations. The predictions match the experimental results within 10% for all of these solutions.« less

Functional thermo-dynamics: a generalization of dynamic density functional theory to non-isothermal situations.

PubMed

Anero, Jesús G; Español, Pep; Tarazona, Pedro

2013-07-21

We present a generalization of Density Functional Theory (DFT) to non-equilibrium non-isothermal situations. By using the original approach set forth by Gibbs in his consideration of Macroscopic Thermodynamics (MT), we consider a Functional Thermo-Dynamics (FTD) description based on the density field and the energy density field. A crucial ingredient of the theory is an entropy functional, which is a concave functional. Therefore, there is a one to one connection between the density and energy fields with the conjugate thermodynamic fields. The connection between the three levels of description (MT, DFT, FTD) is clarified through a bridge theorem that relates the entropy of different levels of description and that constitutes a generalization of Mermin's theorem to arbitrary levels of description whose relevant variables are connected linearly. Although the FTD level of description does not provide any new information about averages and correlations at equilibrium, it is a crucial ingredient for the dynamics in non-equilibrium states. We obtain with the technique of projection operators the set of dynamic equations that describe the evolution of the density and energy density fields from an initial non-equilibrium state towards equilibrium. These equations generalize time dependent density functional theory to non-isothermal situations. We also present an explicit model for the entropy functional for hard spheres.

One-dimensional thermohydraulic code THESEUS and its application to chilldown process simulation in two-phase hydrogen flows

NASA Astrophysics Data System (ADS)

Papadimitriou, P.; Skorek, T.

THESUS is a thermohydraulic code for the calculation of steady state and transient processes of two-phase cryogenic flows. The physical model is based on four conservation equations with separate liquid and gas phase mass conservation equations. The thermohydraulic non-equilibrium is calculated by means of evaporation and condensation models. The mechanical non-equilibrium is modeled by a full-range drift-flux model. Also heat conduction in solid structures and heat exchange for the full spectrum of heat transfer regimes can be simulated. Test analyses of two-channel chilldown experiments and comparisons with the measured data have been performed.

Nonequilibrium itinerant-electron magnetism: A time-dependent mean-field theory

NASA Astrophysics Data System (ADS)

Secchi, A.; Lichtenstein, A. I.; Katsnelson, M. I.

2016-08-01

We study the dynamical magnetic susceptibility of a strongly correlated electronic system in the presence of a time-dependent hopping field, deriving a generalized Bethe-Salpeter equation that is valid also out of equilibrium. Focusing on the single-orbital Hubbard model within the time-dependent Hartree-Fock approximation, we solve the equation in the nonequilibrium adiabatic regime, obtaining a closed expression for the transverse magnetic susceptibility. From this, we provide a rigorous definition of nonequilibrium (time-dependent) magnon frequencies and exchange parameters, expressed in terms of nonequilibrium single-electron Green's functions and self-energies. In the particular case of equilibrium, we recover previously known results.

Applications of the Soave-Redlich-Kwong Equations of State Using Mathematic

NASA Astrophysics Data System (ADS)

Sun, Lanyi; Zhai, Cheng; Zhang, Hui

The application of the Peng-Robinson equations of state (PR EOS) using Matlab and Mathematic has already been demonstrated. In this paper, using Mathematic to solve Soave-Redlich-Kwong (SRK) EOS, as well as the estimation of pure component properties, plotting of vapor-liquid equilibrium (VLE) diagram and calculation of chemical equilibrium, is presented. First the SRK EOS is used to predict several pure-component properties, such as liquid and gas molar volumes for isobutane. The vapor-liquid isobaric diagram is then plotted for a binary mixture composed of n-pentane and n-hexane under the pressures of 2*10^5 and 8*10^5 Pa respectively.

Scale matters

NASA Astrophysics Data System (ADS)

Margolin, L. G.

2018-04-01

The applicability of Navier-Stokes equations is limited to near-equilibrium flows in which the gradients of density, velocity and energy are small. Here I propose an extension of the Chapman-Enskog approximation in which the velocity probability distribution function (PDF) is averaged in the coordinate phase space as well as the velocity phase space. I derive a PDF that depends on the gradients and represents a first-order generalization of local thermodynamic equilibrium. I then integrate this PDF to derive a hydrodynamic model. I discuss the properties of that model and its relation to the discrete equations of computational fluid dynamics. This article is part of the theme issue `Hilbert's sixth problem'.

Characterization of Weak Convergence of Probability-Valued Solutions of General One-Dimensional Kinetic Equations

NASA Astrophysics Data System (ADS)

Perversi, Eleonora; Regazzini, Eugenio

2015-05-01

For a general inelastic Kac-like equation recently proposed, this paper studies the long-time behaviour of its probability-valued solution. In particular, the paper provides necessary and sufficient conditions for the initial datum in order that the corresponding solution converges to equilibrium. The proofs rest on the general CLT for independent summands applied to a suitable Skorokhod representation of the original solution evaluated at an increasing and divergent sequence of times. It turns out that, roughly speaking, the initial datum must belong to the standard domain of attraction of a stable law, while the equilibrium is presentable as a mixture of stable laws.

Lie-algebraic Approach to Dynamics of Closed Quantum Systems and Quantum-to-Classical Correspondence

NASA Astrophysics Data System (ADS)

Galitski, Victor

2012-02-01

I will briefly review our recent work on a Lie-algebraic approach to various non-equilibrium quantum-mechanical problems, which has been motivated by continuous experimental advances in the field of cold atoms. First, I will discuss non-equilibrium driven dynamics of a generic closed quantum system. It will be emphasized that mathematically a non-equilibrium Hamiltonian represents a trajectory in a Lie algebra, while the evolution operator is a trajectory in a Lie group generated by the underlying algebra via exponentiation. This turns out to be a constructive statement that establishes, in particular, the fact that classical and quantum unitary evolutions are two sides of the same coin determined uniquely by the same dynamic generators in the group. An equation for these generators - dubbed dual Schr"odinger-Bloch equation - will be derived and analyzed for a few of specific examples. This non-linear equation allows one to construct new exact non-linear solutions to quantum-dynamical systems. An experimentally-relevant example of a family of exact solutions to the many-body Landau-Zener problem will be presented. One practical application of the latter result includes dynamical means to optimize molecular production rate following a quench across the Feshbach resonance.

Non-equilibrium voltage noise generated by ion transport through pores.

PubMed

Frehland, E; Solleder, P

1985-01-01

In this paper, we describe a systematic approach to the theoretical analysis of non-equilibrium voltage noise that arises from ions moving through pores in membranes. We assume that an ion must cross one or two barriers in the pore in order to move from one side of the membrane to the other. In our analysis, we consider the following factors: a) surface charge as a variable in the kinetic equations, b) linearization of the kinetic equations, c) master equation approach to fluctuations. To analyze the voltage noise arising from ion movement through a two barrier (i.e., one binding site) pore, we included the effects of ions in the channel's interior on the voltage noise. The current clamp is considered as a white noise generating additional noise in the system. In contrast to what is found for current noise, at low frequencies the voltage noise intensity is reduced by increasing voltage across the membrane. With this approach, we demonstrate explicitly for the examples treated that, apart from additional noise generated by the current clamp, the non-equilibrium voltage fluctuations can be related to the current fluctuations by the complex admittance.

Steady-state heat transport: Ballistic-to-diffusive with Fourier's law

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

Maassen, Jesse, E-mail: jmaassen@purdue.edu; Lundstrom, Mark

2015-01-21

It is generally understood that Fourier's law does not describe ballistic phonon transport, which is important when the length of a material is similar to the phonon mean-free-path. Using an approach adapted from electron transport, we demonstrate that Fourier's law and the heat equation do capture ballistic effects, including temperature jumps at ideal contacts, and are thus applicable on all length scales. Local thermal equilibrium is not assumed, because allowing the phonon distribution to be out-of-equilibrium is important for ballistic and quasi-ballistic transport. The key to including the non-equilibrium nature of the phonon population is to apply the proper boundarymore » conditions to the heat equation. Simple analytical solutions are derived, showing that (i) the magnitude of the temperature jumps is simply related to the material properties and (ii) the observation of reduced apparent thermal conductivity physically stems from a reduction in the temperature gradient and not from a reduction in actual thermal conductivity. We demonstrate how our approach, equivalent to Fourier's law, easily reproduces results of the Boltzmann transport equation, in all transport regimes, even when using a full phonon dispersion and mean-free-path distribution.« less

Perfect fluidity of a dissipative system: Analytical solution for the Boltzmann equation in AdS 2 Ⓧ S 2

DOE PAGES

Noronha, Jorge; Denicol, Gabriel S.

2015-12-30

In this paper we obtain an analytical solution of the relativistic Boltzmann equation under the relaxation time approximation that describes the out-of-equilibrium dynamics of a radially expanding massless gas. This solution is found by mapping this expanding system in flat spacetime to a static flow in the curved spacetime AdS 2 Ⓧ S 2. We further derive explicit analytic expressions for the momentum dependence of the single-particle distribution function as well as for the spatial dependence of its moments. We find that this dissipative system has the ability to flow as a perfect fluid even though its entropy density doesmore » not match the equilibrium form. The nonequilibrium contribution to the entropy density is shown to be due to higher-order scalar moments (which possess no hydrodynamical interpretation) of the Boltzmann equation that can remain out of equilibrium but do not couple to the energy-momentum tensor of the system. Furthermore, in this system the slowly moving hydrodynamic degrees of freedom can exhibit true perfect fluidity while being totally decoupled from the fast moving, nonhydrodynamical microscopic degrees of freedom that lead to entropy production.« less

Dielectric permeability tensor and linear waves in spin-1/2 quantum kinetics with non-trivial equilibrium spin-distribution functions

NASA Astrophysics Data System (ADS)

Andreev, Pavel A.; Kuz'menkov, L. S.

2017-11-01

A consideration of waves propagating parallel to the external magnetic field is presented. The dielectric permeability tensor is derived from the quantum kinetic equations with non-trivial equilibrium spin-distribution functions in the linear approximation on the amplitude of wave perturbations. It is possible to consider the equilibrium spin-distribution functions with nonzero z-projection proportional to the difference of the Fermi steps of electrons with the chosen spin direction, while x- and y-projections are equal to zero. It is called the trivial equilibrium spin-distribution functions. In the general case, x- and y-projections of the spin-distribution functions are nonzero which is called the non-trivial regime. A corresponding equilibrium solution is found in Andreev [Phys. Plasmas 23, 062103 (2016)]. The contribution of the nontrivial part of the spin-distribution function appears in the dielectric permeability tensor in the additive form. It is explicitly found here. A corresponding modification in the dispersion equation for the transverse waves is derived. The contribution of the nontrivial part of the spin-distribution function in the spectrum of transverse waves is calculated numerically. It is found that the term caused by the nontrivial part of the spin-distribution function can be comparable with the classic terms for the relatively small wave vectors and frequencies above the cyclotron frequency. In a majority of regimes, the extra spin caused term dominates over the spin term found earlier, except the small frequency regime, where their contributions in the whistler spectrum are comparable. A decrease of the left-hand circularly polarized wave frequency, an increase of the high-frequency right-hand circularly polarized wave frequency, and a decrease of frequency changing by an increase of frequency at the growth of the wave vector for the whistler are found. A considerable decrease of the spin wave frequency is found either. It results in an increase of module of the negative group velocity of the spin wave. The found dispersion equations are used for obtaining of an effective quantum hydrodynamics reproducing these results. This generalization requires the introduction of the corresponding equation of state for the thermal part of the spin current in the spin evolution equation.

A computer program to generate equations of motion matrices, L217 (EOM). Volume 1: Engineering and usage

NASA Technical Reports Server (NTRS)

Kroll, R. I.; Clemmons, R. E.

1979-01-01

The equations of motion program L217 formulates the matrix coefficients for a set of second order linear differential equations that describe the motion of an airplane relative to its level equilibrium flight condition. Aerodynamic data from FLEXSTAB or Doublet Lattice (L216) programs can be used to derive the equations for quasi-steady or full unsteady aerodynamics. The data manipulation and the matrix coefficient formulation are described.

Mathematical modeling of impact of two metal plates using two-fluid approach

NASA Astrophysics Data System (ADS)

Utkin, P. S.; Fortova, S. V.

2018-01-01

The paper is devoted to the development of the two-fluid mathematical model and the computational algorithm for the modeling of two metal plates impact. In one-dimensional case the governing system of equations comprises seven equations: three conservation laws for each fluid and transfer equation for the volume fraction of one of the fluids. Both fluids are considered to be compressible and equilibrium on velocities. Pressures equilibrium is used as fluids interface condition. The system has hyperbolic type but could not be written in the conservative form because of nozzling terms in the right-hand side of the equations. The algorithm is based on the Harten-Lax-van Leer numerical flux function. The robust computation in the presence of the interface boundary is carried out due to the special pressure relaxation procedure. The problem is solved using stiffened gas equations of state for each fluid. The parameters in the equations of state are calibrated using the results of computations using wide-range equations of state for the metals. In simulations of metal plates impact we get two shocks after the initial impact that propagate to the free surfaces of the samples. The characteristics of shock waves are close (maximum relative error in characteristics of shocks is not greater than 7%) to the data from the wide-range equations of states computations.

Free energy surfaces from nonequilibrium processes without work measurement

NASA Astrophysics Data System (ADS)

Adib, Artur B.

2006-04-01

Recent developments in statistical mechanics have allowed the estimation of equilibrium free energies from the statistics of work measurements during processes that drive the system out of equilibrium. Here a different class of processes is considered, wherein the system is prepared and released from a nonequilibrium state, and no external work is involved during its observation. For such "clamp-and-release" processes, a simple strategy for the estimation of equilibrium free energies is offered. The method is illustrated with numerical simulations and analyzed in the context of tethered single-molecule experiments.

Ghanaian Teacher Trainees' Conceptual Understanding of Stoichiometry

ERIC Educational Resources Information Center

Hanson, Ruby

2015-01-01

Chemical stoichiometry is a conceptual framework that encompasses other concepts such as the mole, writing of chemical equations in word and representative form, balancing of equations and the equilibrium concept. The underlying concepts enable students to understand relationships among entities of matter and required amounts for use when…

Ghanaian Teacher Trainees' Conceptual Understanding of Stoichiometry

ERIC Educational Resources Information Center

Hanson, Ruby

2016-01-01

Chemical stoichiometry is a conceptual framework that encompasses other concepts such as the mole, writing of chemical equations in word and representative form, balancing of equations and the equilibrium concept. The underlying concepts enable students to understand relationships among entities of matter and required amounts for use when…

Stochastic population dynamics in spatially extended predator-prey systems

NASA Astrophysics Data System (ADS)

Dobramysl, Ulrich; Mobilia, Mauro; Pleimling, Michel; Täuber, Uwe C.

2018-02-01

Spatially extended population dynamics models that incorporate demographic noise serve as case studies for the crucial role of fluctuations and correlations in biological systems. Numerical and analytic tools from non-equilibrium statistical physics capture the stochastic kinetics of these complex interacting many-particle systems beyond rate equation approximations. Including spatial structure and stochastic noise in models for predator-prey competition invalidates the neutral Lotka-Volterra population cycles. Stochastic models yield long-lived erratic oscillations stemming from a resonant amplification mechanism. Spatially extended predator-prey systems display noise-stabilized activity fronts that generate persistent correlations. Fluctuation-induced renormalizations of the oscillation parameters can be analyzed perturbatively via a Doi-Peliti field theory mapping of the master equation; related tools allow detailed characterization of extinction pathways. The critical steady-state and non-equilibrium relaxation dynamics at the predator extinction threshold are governed by the directed percolation universality class. Spatial predation rate variability results in more localized clusters, enhancing both competing species’ population densities. Affixing variable interaction rates to individual particles and allowing for trait inheritance subject to mutations induces fast evolutionary dynamics for the rate distributions. Stochastic spatial variants of three-species competition with ‘rock-paper-scissors’ interactions metaphorically describe cyclic dominance. These models illustrate intimate connections between population dynamics and evolutionary game theory, underscore the role of fluctuations to drive populations toward extinction, and demonstrate how space can support species diversity. Two-dimensional cyclic three-species May-Leonard models are characterized by the emergence of spiraling patterns whose properties are elucidated by a mapping onto a complex Ginzburg-Landau equation. Multiple-species extensions to general ‘food networks’ can be classified on the mean-field level, providing both fundamental understanding of ensuing cooperativity and profound insight into the rich spatio-temporal features and coarsening kinetics in the corresponding spatially extended systems. Novel space-time patterns emerge as a result of the formation of competing alliances; e.g. coarsening domains that each incorporate rock-paper-scissors competition games.

General framework for fluctuating dynamic density functional theory

NASA Astrophysics Data System (ADS)

Durán-Olivencia, Miguel A.; Yatsyshin, Peter; Goddard, Benjamin D.; Kalliadasis, Serafim

2017-12-01

We introduce a versatile bottom-up derivation of a formal theoretical framework to describe (passive) soft-matter systems out of equilibrium subject to fluctuations. We provide a unique connection between the constituent-particle dynamics of real systems and the time evolution equation of their measurable (coarse-grained) quantities, such as local density and velocity. The starting point is the full Hamiltonian description of a system of colloidal particles immersed in a fluid of identical bath particles. Then, we average out the bath via Zwanzig’s projection-operator techniques and obtain the stochastic Langevin equations governing the colloidal-particle dynamics. Introducing the appropriate definition of the local number and momentum density fields yields a generalisation of the Dean-Kawasaki (DK) model, which resembles the stochastic Navier-Stokes description of a fluid. Nevertheless, the DK equation still contains all the microscopic information and, for that reason, does not represent the dynamical law of observable quantities. We address this controversial feature of the DK description by carrying out a nonequilibrium ensemble average. Adopting a natural decomposition into local-equilibrium and nonequilibrium contribution, where the former is related to a generalised version of the canonical distribution, we finally obtain the fluctuating-hydrodynamic equation governing the time-evolution of the mesoscopic density and momentum fields. Along the way, we outline the connection between the ad hoc energy functional introduced in previous DK derivations and the free-energy functional from classical density-functional theory. The resultant equation has the structure of a dynamical density-functional theory (DDFT) with an additional fluctuating force coming from the random interactions with the bath. We show that our fluctuating DDFT formalism corresponds to a particular version of the fluctuating Navier-Stokes equations, originally derived by Landau and Lifshitz. Our framework thus provides the formal apparatus for ab initio derivations of fluctuating DDFT equations capable of describing the dynamics of soft-matter systems in and out of equilibrium.

Roughness topographical effects on mean momentum and stress budgets in developed turbulent channel flows

NASA Astrophysics Data System (ADS)

Aghaei Jouybari, Mostafa; Yuan, Junlin

2017-11-01

Direct numerical simulations of turbulent channel flows are carried out over two surfaces: a synthesized sand-grain surface and a realistic turbine roughness that is characterized by more prominent large-scale surface features. To separate the effects of wall-normal variation of the roughness area fraction from the (true) variation of flow statistics, the governing equations are area-averaged using intrinsic averaging, contrary to the usually practice based on the total area (i.e., superficial averaging). Additional terms appear in the mean-momentum equation resulted from the wall-normal variation of the solid fraction and play a role in the near-wall balance. Results from surfaces with a step solidity function (e.g., cubes) will also be discussed. Compared to the sand grains, the turbine surface generates stronger form-induced fluctuations, despite weaker dispersive shear stress. This is associated with more significant form-induced productions (comparable to shear production) in Reynolds stress budgets, weaker pressure work, and, consequently, more anisotropic redistribution of turbulent kinetic energy in the roughness sublayer, which potentially leads to different turbulent responses between the two surfaces in non-equilibrium flows.

Transport processes in magnetically confined plasmas in the nonlinear regime.

PubMed

Sonnino, Giorgio

2006-06-01

A field theory approach to transport phenomena in magnetically confined plasmas is presented. The thermodynamic field theory (TFT), previously developed for treating the generic thermodynamic system out of equilibrium, is applied to plasmas physics. Transport phenomena are treated here as the effect of the field linking the thermodynamic forces with their conjugate flows combined with statistical mechanics. In particular, the Classical and the Pfirsch-Schluter regimes are analyzed by solving the thermodynamic field equations of the TFT in the weak-field approximation. We found that, the TFT does not correct the expressions of the ionic heat fluxes evaluated by the neoclassical theory in these two regimes. On the other hand, the fluxes of matter and electronic energy (heat flow) is further enhanced in the nonlinear Classical and Pfirsch-Schluter regimes. These results seem to be in line with the experimental observations. The complete set of the electronic and ionic transport equations in the nonlinear Banana regime, is also reported. A paper showing the comparison between our theoretic results and the experimental observations in the JET machine is currently in preparation.

A new baryonic equation of state at sub-nuclear densities for core-collapse simulations

NASA Astrophysics Data System (ADS)

Furusawa, Shun; Yamada, Shoichi; Sumiyoshi, Kohsuke; Suzuki, Hideyuki

2012-11-01

We construct a new equation of state for baryons at sub-nuclear densities for the use in core-collapse simulations of massive stars. The formulation is based on the nuclear statistical equilibrium description and the liquid drop approximation of nuclei. The model free energy to minimize is calculated by using relativistic mean field theory for nucleons and the mass formula for nuclei with atomic number up to ~ 1000. We have also taken into account the pasta phase. We find that the free energy and other thermodynamical quantities are not very different from those given in the standard EOSs that adopt the single nucleus approximation. On the other hand, the average mass is systematically different, which may have an important effect to the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores. It is also interesting that the root mean square of the mass number is not very different from the average mass number, since the former is important for the evaluation of coherent scattering rates on nuclei but has been unavailable so far.

STUDYING THE EFFECTS OF CALCIUM AND MAGNESIUM ON SIZE-DISTRIBUTED NITRATE AND AMMONIUM WITH EQUISOLV II. (R823186)

EPA Science Inventory

Abstract

A chemical equilibrium code was improved and used to show that calcium and magnesium have a large yet different effect on the aerosol size distribution in different regions of Los Angeles. In the code, a new technique of solving individual equilibrium equation...

Exploring the Clapeyron Equation and the Phase Rule Using a Mechanical Drawing Toy

ERIC Educational Resources Information Center

Darvesh, Katherine V.

2013-01-01

The equilibrium between phases is a key concept from the introductory physical chemistry curriculum. Phase diagrams display which phase is the most stable at a given temperature and pressure. If more than one phase has the lowest Gibbs energy, then those phases are in equilibrium under those conditions. An activity designed to demonstrate the…

A time-accurate implicit method for chemical non-equilibrium flows at all speeds

NASA Technical Reports Server (NTRS)

Shuen, Jian-Shun

1992-01-01

A new time accurate coupled solution procedure for solving the chemical non-equilibrium Navier-Stokes equations over a wide range of Mach numbers is described. The scheme is shown to be very efficient and robust for flows with velocities ranging from M less than or equal to 10(exp -10) to supersonic speeds.

A Simple Method to Calculate the Temperature Dependence of the Gibbs Energy and Chemical Equilibrium Constants

ERIC Educational Resources Information Center

Vargas, Francisco M.

2014-01-01

The temperature dependence of the Gibbs energy and important quantities such as Henry's law constants, activity coefficients, and chemical equilibrium constants is usually calculated by using the Gibbs-Helmholtz equation. Although, this is a well-known approach and traditionally covered as part of any physical chemistry course, the required…

Nonlinear inhomogeneous Fokker-Planck equations: Entropy and free-energy time evolution.

PubMed

Sicuro, Gabriele; Rapčan, Peter; Tsallis, Constantino

2016-12-01

We extend a recently introduced free-energy formalism for homogeneous Fokker-Planck equations to a wide, and physically appealing, class of inhomogeneous nonlinear Fokker-Planck equations. In our approach, the free-energy functional is expressed in terms of an entropic functional and an auxiliary potential, both derived from the coefficients of the equation. With reference to the introduced entropic functional, we discuss the entropy production in a relaxation process towards equilibrium. The properties of the stationary solutions of the considered Fokker-Planck equations are also discussed.

Numerical method based on the lattice Boltzmann model for the Fisher equation.

PubMed

Yan, Guangwu; Zhang, Jianying; Dong, Yinfeng

2008-06-01

In this paper, a lattice Boltzmann model for the Fisher equation is proposed. First, the Chapman-Enskog expansion and the multiscale time expansion are used to describe higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. Second, the modified partial differential equation of the Fisher equation with the higher-order truncation error is obtained. Third, comparison between numerical results of the lattice Boltzmann models and exact solution is given. The numerical results agree well with the classical ones.

A new vapor-liquid equilibrium apparatus for hydrogen fluoride containing systems

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

Jongcheon Lee; Hwayong Kim; Jong Sung Lim

1996-12-31

A new circulating type apparatus has been constructed to obtain reliable equilibrium PTxy data for hydrogen fluoride (HF) containing system. Equilibrium cell with Pyrex windows protected by Teflon PFA sheets to prevent the corrosion was used. Isothermal vapor-liquid equilibrium data for the 1,1-difluoroethane (HFC-152a) + HF system at 288.23 and 298.35 K were obtained, and compared with PTx measurement results. Experimental data were correlated using Lencka and Anderko equation of state for HF with the Wong-Sandler mixing rule as well as the van der Waals one fluid mixing rule. The Wong-Sandler mixing rule gives better results. 5 refs., 3 figs.

IONIZATION EQUILIBRIUM TIMESCALES IN COLLISIONAL PLASMAS

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

Smith, Randall K.; Hughes, John P., E-mail: rsmith@cfa.harvard.ed, E-mail: jph@physics.rutgers.ed

2010-07-20

Astrophysical shocks or bursts from a photoionizing source can disturb the typical collisional plasma found in galactic interstellar media or the intergalactic medium. The spectrum emitted by this plasma contains diagnostics that have been used to determine the time since the disturbing event, although this determination becomes uncertain as the elements in the plasma return to ionization equilibrium. A general solution for the equilibrium timescale for each element arises from the elegant eigenvector method of solution to the problem of a non-equilibrium plasma described by Masai and Hughes and Helfand. In general, the ionization evolution of an element Z inmore » a constant electron temperature plasma is given by a coupled set of Z + 1 first-order differential equations. However, they can be recast as Z uncoupled first-order differential equations using an eigenvector basis for the system. The solution is then Z separate exponential functions, with the time constants given by the eigenvalues of the rate matrix. The smallest of these eigenvalues gives the scale of the slowest return to equilibrium independent of the initial conditions, while conversely the largest eigenvalue is the scale of the fastest change in the ion population. These results hold for an ionizing plasma, a recombining plasma, or even a plasma with random initial conditions, and will allow users of these diagnostics to determine directly if their best-fit result significantly limits the timescale since a disturbance or is so close to equilibrium as to include an arbitrarily long time.« less

Event-driven Monte Carlo: Exact dynamics at all time scales for discrete-variable models

NASA Astrophysics Data System (ADS)

Mendoza-Coto, Alejandro; Díaz-Méndez, Rogelio; Pupillo, Guido

2016-06-01

We present an algorithm for the simulation of the exact real-time dynamics of classical many-body systems with discrete energy levels. In the same spirit of kinetic Monte Carlo methods, a stochastic solution of the master equation is found, with no need to define any other phase-space construction. However, unlike existing methods, the present algorithm does not assume any particular statistical distribution to perform moves or to advance the time, and thus is a unique tool for the numerical exploration of fast and ultra-fast dynamical regimes. By decomposing the problem in a set of two-level subsystems, we find a natural variable step size, that is well defined from the normalization condition of the transition probabilities between the levels. We successfully test the algorithm with known exact solutions for non-equilibrium dynamics and equilibrium thermodynamical properties of Ising-spin models in one and two dimensions, and compare to standard implementations of kinetic Monte Carlo methods. The present algorithm is directly applicable to the study of the real-time dynamics of a large class of classical Markovian chains, and particularly to short-time situations where the exact evolution is relevant.

Correlated Fluctuations in Strongly Coupled Binary Networks Beyond Equilibrium

NASA Astrophysics Data System (ADS)

Dahmen, David; Bos, Hannah; Helias, Moritz

2016-07-01

Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering glassy magnetism and frustration, combinatorial optimization, protein folding, stock market dynamics, and social dynamics. The phase diagram of these systems is obtained in the thermodynamic limit by averaging over the quenched randomness of the couplings. However, many applications require the statistics of activity for a single realization of the possibly asymmetric couplings in finite-sized networks. Examples include reconstruction of couplings from the observed dynamics, representation of probability distributions for sampling-based inference, and learning in the central nervous system based on the dynamic and correlation-dependent modification of synaptic connections. The systematic cumulant expansion for kinetic binary (Ising) threshold units with strong, random, and asymmetric couplings presented here goes beyond mean-field theory and is applicable outside thermodynamic equilibrium; a system of approximate nonlinear equations predicts average activities and pairwise covariances in quantitative agreement with full simulations down to hundreds of units. The linearized theory yields an expansion of the correlation and response functions in collective eigenmodes, leads to an efficient algorithm solving the inverse problem, and shows that correlations are invariant under scaling of the interaction strengths.

Effect of accelerated aging on the cross-link density of medical grade silicones.

PubMed

Mahomed, Aziza; Pormehr, Negin Bagheri

2016-11-25

Four specimens of Nagor silicone of different hardness (soft, medium and hard) were swollen, until they reached equilibrium (i.e. constant mass) in five liquids at 25°C, before and after accelerated aging. For the specimens swollen before accelerated aging, the greatest swelling was obtained in methyl cyclohexane, while for the specimens swollen after accelerated aging, the greatest swelling was obtained in cyclohexane. The cross-link density, υ, was also calculated from the swelling measurements for all the specimens, before and after accelerated aging, using the Flory-Rehner equation. The softer silicones, which swelled the most, had lower υ values than harder silicones. The amount of swelling (measured in terms of ϕ) and υ varied significantly (p<0.05) in some cases, between the different silicone hardness and between different liquids. Furthermore, the cross-link density, υ, significantly (p<0.05) increased after accelerated aging in most liquids.Note: ϕ is defined as the volume fraction of polymer in its equilibrium swollen state. A probability value of statistical significance of 0.05 or 5% was selected, hence if a p value of less than 0.05 was obtained, the null hypothesis was rejected (i.e. significant if p<0.05).

Nonlinear waves in viscoelastic magnetized complex astroplasmas with polarized dust-charge variations

NASA Astrophysics Data System (ADS)

Das, Papari; Karmakar, Pralay Kumar

2018-01-01

A nonextensive nonthermal magnetized viscoelastic astrofluid, compositionally containing nonthermal electrons and ions together with massive polarized dust micro-spherical grains of variable electric charge, is allowed to endure weakly nonlinear perturbation around its equilibrium. The nonextensivity originating from the large-scale non-local effects is included via the Tsallis thermo-statistical distribution laws describing the lighter species. Assuming the equilibrium as a homogeneous hydrostatic one, the dust polarization effects are incorporated via the conventional homogeneous polarization force law. The perturbed fluid model evolves as a unique conjugate pair of coupled extended Korteweg-de Vries (e-KdV) equations. A constructed numerical tapestry shows the collective excitations of a new pair of distinct classes of nonlinear mode structures in new parametric space. The first family indicates periodic electrostatic compressive eigenmodes in the form of soliton-chains. Likewise, the second one reveals gravitational rarefactive solitary patterns. Their microphysical multi-parametric dependencies of the eigen-patterns are illustratively analyzed and bolstered. The paper ends up with some promising implications and applications in the astro-cosmo-plasmic context of wave-induced accretive triggering processes responsible for gravitationally bounded (gravito-condensed) astro-structure formation, such as stellesimals, planetsimals, etc.

The Heat Is on: An Inquiry-Based Investigation for Specific Heat

ERIC Educational Resources Information Center

Herrington, Deborah G.

2011-01-01

A substantial number of upper-level science students and practicing physical science teachers demonstrate confusion about thermal equilibrium, heat transfer, heat capacity, and specific heat capacity. The traditional method of instruction, which involves learning the related definitions and equations, using equations to solve heat transfer…

Invariants for the generalized Lotka-Volterra equations

NASA Astrophysics Data System (ADS)

Cairó, Laurent; Feix, Marc R.; Goedert, Joao

A generalisation of Lotka-Volterra System is given when self limiting terms are introduced in the model. We use a modification of the Carleman embedding method to find invariants for this system of equations. The position and stability of the equilibrium point and the regression of system under invariant conditions are studied.

NUMERICAL TECHNIQUES TO SOLVE CONDENSATIONAL AND DISSOLUTIONAL GROWTH EQUATIONS WHEN GROWTH IS COUPLED TO REVERSIBLE REACTIONS (R823186)

EPA Science Inventory

Noniterative, unconditionally stable numerical techniques for solving condensational and
dissolutional growth equations are given. Growth solutions are compared to Gear-code solutions for
three cases when growth is coupled to reversible equilibrium chemistry. In all cases, ...

Titration Calculations with Computer Algebra Software

ERIC Educational Resources Information Center

Lachance, Russ; Biaglow, Andrew

2012-01-01

This article examines the symbolic algebraic solution of the titration equations for a diprotic acid, as obtained using "Mathematica," "Maple," and "Mathcad." The equilibrium and conservation equations are solved symbolically by the programs to eliminate the approximations that normally would be performed by the student. Of the three programs,…

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.

Inhomogeneous kinetic effects related to intermittent magnetic discontinuities

NASA Astrophysics Data System (ADS)

Greco, A.; Valentini, F.; Servidio, S.; Matthaeus, W. H.

2012-12-01

A connection between kinetic processes and two-dimensional intermittent plasma turbulence is observed using direct numerical simulations of a hybrid Vlasov-Maxwell model, in which the Vlasov equation is solved for protons, while the electrons are described as a massless fluid. During the development of turbulence, the proton distribution functions depart from the typical configuration of local thermodynamic equilibrium, displaying statistically significant non-Maxwellian features. In particular, temperature anisotropy and distortions are concentrated near coherent structures, generated as the result of the turbulent cascade, such as current sheets, which are nonuniformly distributed in space. Here, the partial variance of increments (PVI) method has been employed to identify high magnetic stress regions within a two-dimensional turbulent pattern. A quantitative association between non-Maxwellian features and coherent structures is established.

The Statistical Basis of Chemical Equilibria.

ERIC Educational Resources Information Center

Hauptmann, Siegfried; Menger, Eva

1978-01-01

Describes a machine which demonstrates the statistical bases of chemical equilibrium, and in doing so conveys insight into the connections among statistical mechanics, quantum mechanics, Maxwell Boltzmann statistics, statistical thermodynamics, and transition state theory. (GA)

Efficient statistically accurate algorithms for the Fokker-Planck equation in large dimensions

NASA Astrophysics Data System (ADS)

Chen, Nan; Majda, Andrew J.

2018-02-01

Solving the Fokker-Planck equation for high-dimensional complex turbulent dynamical systems is an important and practical issue. However, most traditional methods suffer from the curse of dimensionality and have difficulties in capturing the fat tailed highly intermittent probability density functions (PDFs) of complex systems in turbulence, neuroscience and excitable media. In this article, efficient statistically accurate algorithms are developed for solving both the transient and the equilibrium solutions of Fokker-Planck equations associated with high-dimensional nonlinear turbulent dynamical systems with conditional Gaussian structures. The algorithms involve a hybrid strategy that requires only a small number of ensembles. Here, a conditional Gaussian mixture in a high-dimensional subspace via an extremely efficient parametric method is combined with a judicious non-parametric Gaussian kernel density estimation in the remaining low-dimensional subspace. Particularly, the parametric method provides closed analytical formulae for determining the conditional Gaussian distributions in the high-dimensional subspace and is therefore computationally efficient and accurate. The full non-Gaussian PDF of the system is then given by a Gaussian mixture. Different from traditional particle methods, each conditional Gaussian distribution here covers a significant portion of the high-dimensional PDF. Therefore a small number of ensembles is sufficient to recover the full PDF, which overcomes the curse of dimensionality. Notably, the mixture distribution has significant skill in capturing the transient behavior with fat tails of the high-dimensional non-Gaussian PDFs, and this facilitates the algorithms in accurately describing the intermittency and extreme events in complex turbulent systems. It is shown in a stringent set of test problems that the method only requires an order of O (100) ensembles to successfully recover the highly non-Gaussian transient PDFs in up to 6 dimensions with only small errors.

Enhanced configurational sampling with hybrid non-equilibrium molecular dynamics-Monte Carlo propagator

NASA Astrophysics Data System (ADS)

Suh, Donghyuk; Radak, Brian K.; Chipot, Christophe; Roux, Benoît

2018-01-01

Molecular dynamics (MD) trajectories based on classical equations of motion can be used to sample the configurational space of complex molecular systems. However, brute-force MD often converges slowly due to the ruggedness of the underlying potential energy surface. Several schemes have been proposed to address this problem by effectively smoothing the potential energy surface. However, in order to recover the proper Boltzmann equilibrium probability distribution, these approaches must then rely on statistical reweighting techniques or generate the simulations within a Hamiltonian tempering replica-exchange scheme. The present work puts forth a novel hybrid sampling propagator combining Metropolis-Hastings Monte Carlo (MC) with proposed moves generated by non-equilibrium MD (neMD). This hybrid neMD-MC propagator comprises three elementary elements: (i) an atomic system is dynamically propagated for some period of time using standard equilibrium MD on the correct potential energy surface; (ii) the system is then propagated for a brief period of time during what is referred to as a "boosting phase," via a time-dependent Hamiltonian that is evolved toward the perturbed potential energy surface and then back to the correct potential energy surface; (iii) the resulting configuration at the end of the neMD trajectory is then accepted or rejected according to a Metropolis criterion before returning to step 1. A symmetric two-end momentum reversal prescription is used at the end of the neMD trajectories to guarantee that the hybrid neMD-MC sampling propagator obeys microscopic detailed balance and rigorously yields the equilibrium Boltzmann distribution. The hybrid neMD-MC sampling propagator is designed and implemented to enhance the sampling by relying on the accelerated MD and solute tempering schemes. It is also combined with the adaptive biased force sampling algorithm to examine. Illustrative tests with specific biomolecular systems indicate that the method can yield a significant speedup.

Enhanced configurational sampling with hybrid non-equilibrium molecular dynamics-Monte Carlo propagator.

PubMed

Suh, Donghyuk; Radak, Brian K; Chipot, Christophe; Roux, Benoît

2018-01-07

Molecular dynamics (MD) trajectories based on classical equations of motion can be used to sample the configurational space of complex molecular systems. However, brute-force MD often converges slowly due to the ruggedness of the underlying potential energy surface. Several schemes have been proposed to address this problem by effectively smoothing the potential energy surface. However, in order to recover the proper Boltzmann equilibrium probability distribution, these approaches must then rely on statistical reweighting techniques or generate the simulations within a Hamiltonian tempering replica-exchange scheme. The present work puts forth a novel hybrid sampling propagator combining Metropolis-Hastings Monte Carlo (MC) with proposed moves generated by non-equilibrium MD (neMD). This hybrid neMD-MC propagator comprises three elementary elements: (i) an atomic system is dynamically propagated for some period of time using standard equilibrium MD on the correct potential energy surface; (ii) the system is then propagated for a brief period of time during what is referred to as a "boosting phase," via a time-dependent Hamiltonian that is evolved toward the perturbed potential energy surface and then back to the correct potential energy surface; (iii) the resulting configuration at the end of the neMD trajectory is then accepted or rejected according to a Metropolis criterion before returning to step 1. A symmetric two-end momentum reversal prescription is used at the end of the neMD trajectories to guarantee that the hybrid neMD-MC sampling propagator obeys microscopic detailed balance and rigorously yields the equilibrium Boltzmann distribution. The hybrid neMD-MC sampling propagator is designed and implemented to enhance the sampling by relying on the accelerated MD and solute tempering schemes. It is also combined with the adaptive biased force sampling algorithm to examine. Illustrative tests with specific biomolecular systems indicate that the method can yield a significant speedup.

Local thermodynamic equilibrium for globally disequilibrium open systems under stress

NASA Astrophysics Data System (ADS)

Podladchikov, Yury

2016-04-01

Predictive modeling of far and near equilibrium processes is essential for understanding of patterns formation and for quantifying of natural processes that are never in global equilibrium. Methods of both equilibrium and non-equilibrium thermodynamics are needed and have to be combined. For example, predicting temperature evolution due to heat conduction requires simultaneous use of equilibrium relationship between internal energy and temperature via heat capacity (the caloric equation of state) and disequilibrium relationship between heat flux and temperature gradient. Similarly, modeling of rocks deforming under stress, reactions in system open for the porous fluid flow, or kinetic overstepping of the equilibrium reaction boundary necessarily needs both equilibrium and disequilibrium material properties measured under fundamentally different laboratory conditions. Classical irreversible thermodynamics (CIT) is the well-developed discipline providing the working recipes for the combined application of mutually exclusive experimental data such as density and chemical potential at rest under constant pressure and temperature and viscosity of the flow under stress. Several examples will be presented.

Influence of neural adaptation on dynamics and equilibrium state of neural activities in a ring neural network

NASA Astrophysics Data System (ADS)

Takiyama, Ken

2017-12-01

How neural adaptation affects neural information processing (i.e. the dynamics and equilibrium state of neural activities) is a central question in computational neuroscience. In my previous works, I analytically clarified the dynamics and equilibrium state of neural activities in a ring-type neural network model that is widely used to model the visual cortex, motor cortex, and several other brain regions. The neural dynamics and the equilibrium state in the neural network model corresponded to a Bayesian computation and statistically optimal multiple information integration, respectively, under a biologically inspired condition. These results were revealed in an analytically tractable manner; however, adaptation effects were not considered. Here, I analytically reveal how the dynamics and equilibrium state of neural activities in a ring neural network are influenced by spike-frequency adaptation (SFA). SFA is an adaptation that causes gradual inhibition of neural activity when a sustained stimulus is applied, and the strength of this inhibition depends on neural activities. I reveal that SFA plays three roles: (1) SFA amplifies the influence of external input in neural dynamics; (2) SFA allows the history of the external input to affect neural dynamics; and (3) the equilibrium state corresponds to the statistically optimal multiple information integration independent of the existence of SFA. In addition, the equilibrium state in a ring neural network model corresponds to the statistically optimal integration of multiple information sources under biologically inspired conditions, independent of the existence of SFA.

Viscous dissipation effects on MHD slip flow and heat transfer in porous micro duct with LTNE assumptions using modified lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Rabhi, R.; Amami, B.; Dhahri, H.; Mhimid, A.

2017-11-01

This paper deals with heat transfer and fluid flow in a porous micro duct under local thermal non equilibrium conditions subjected to an external oriented magnetic field. The considered sample is a micro duct filled with porous media assumed to be homogenous, isotropic and saturated. The slip velocity and the temperature jump were uniformly imposed to the wall. In modeling the flow, the Brinkmann-Forchheimer extended Darcy model was incorporated into the momentum equations. In the energy equation, the local thermal non equilibrium between the two phases was adopted. A modified axisymmetric lattice Boltzmann method was used to solve the obtained governing equation system. Attention was focused on the influence of the emerging parameters such as Knudsen number, Kn, Hartmann number, Ha, Eckert number, Ec, Biot number, Bi and the magnetic field inclination γ on flow and heat transfer throughout this paper.

An extension of stochastic hierarchy equations of motion for the equilibrium correlation functions

NASA Astrophysics Data System (ADS)

Ke, Yaling; Zhao, Yi

2017-06-01

A traditional stochastic hierarchy equations of motion method is extended into the correlated real-time and imaginary-time propagations, in this paper, for its applications in calculating the equilibrium correlation functions. The central idea is based on a combined employment of stochastic unravelling and hierarchical techniques for the temperature-dependent and temperature-free parts of the influence functional, respectively, in the path integral formalism of the open quantum systems coupled to a harmonic bath. The feasibility and validity of the proposed method are justified in the emission spectra of homodimer compared to those obtained through the deterministic hierarchy equations of motion. Besides, it is interesting to find that the complex noises generated from a small portion of real-time and imaginary-time cross terms can be safely dropped to produce the stable and accurate position and flux correlation functions in a broad parameter regime.

Recursive thoughts on the simulation of the flexible multibody dynamics of slender offshore structures

NASA Astrophysics Data System (ADS)

Schilder, J.; Ellenbroek, M.; de Boer, A.

2017-12-01

In this work, the floating frame of reference formulation is used to create a flexible multibody model of slender offshore structures such as pipelines and risers. It is shown that due to the chain-like topology of the considered structures, the equation of motion can be expressed in terms of absolute interface coordinates. In the presented form, kinematic constraint equations are satisfied explicitly and the Lagrange multipliers are eliminated from the equations. Hence, the structures can be conveniently coupled to finite element or multibody models of for example seabed and vessel. The chain-like topology enables the efficient use of recursive solution procedures for both transient dynamic analysis and equilibrium analysis. For this, the transfer matrix method is used. In order to improve the convergence of the equilibrium analysis, the analytical solution of an ideal catenary is used as an initial configuration, reducing the number of required iterations.

Three-dimensional finite elements for the analysis of soil contamination using a multiple-porosity approach

NASA Astrophysics Data System (ADS)

El-Zein, Abbas; Carter, John P.; Airey, David W.

2006-06-01

A three-dimensional finite-element model of contaminant migration in fissured clays or contaminated sand which includes multiple sources of non-equilibrium processes is proposed. The conceptual framework can accommodate a regular network of fissures in 1D, 2D or 3D and immobile solutions in the macro-pores of aggregated topsoils, as well as non-equilibrium sorption. A Galerkin weighted-residual statement for the three-dimensional form of the equations in the Laplace domain is formulated. Equations are discretized using linear and quadratic prism elements. The system of algebraic equations is solved in the Laplace domain and solution is inverted to the time domain numerically. The model is validated and its scope is illustrated through the analysis of three problems: a waste repository deeply buried in fissured clay, a storage tank leaking into sand and a sanitary landfill leaching into fissured clay over a sand aquifer.

Equilibrium, kinetics and process design of acid yellow 132 adsorption onto red pine sawdust.

PubMed

Can, Mustafa

2015-01-01

Linear and non-linear regression procedures have been applied to the Langmuir, Freundlich, Tempkin, Dubinin-Radushkevich, and Redlich-Peterson isotherms for adsorption of acid yellow 132 (AY132) dye onto red pine (Pinus resinosa) sawdust. The effects of parameters such as particle size, stirring rate, contact time, dye concentration, adsorption dose, pH, and temperature were investigated, and interaction was characterized by Fourier transform infrared spectroscopy and field emission scanning electron microscope. The non-linear method of the Langmuir isotherm equation was found to be the best fitting model to the equilibrium data. The maximum monolayer adsorption capacity was found as 79.5 mg/g. The calculated thermodynamic results suggested that AY132 adsorption onto red pine sawdust was an exothermic, physisorption, and spontaneous process. Kinetics was analyzed by four different kinetic equations using non-linear regression analysis. The pseudo-second-order equation provides the best fit with experimental data.

Homogeneous quantum electrodynamic turbulence

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1992-01-01

The electromagnetic field equations and Dirac equations for oppositely charged wave functions are numerically time-integrated using a spatial Fourier method. The numerical approach used, a spectral transform technique, is based on a continuum representation of physical space. The coupled classical field equations contain a dimensionless parameter which sets the strength of the nonlinear interaction (as the parameter increases, interaction volume decreases). For a parameter value of unity, highly nonlinear behavior in the time-evolution of an individual wave function, analogous to ideal fluid turbulence, is observed. In the truncated Fourier representation which is numerically implemented here, the quantum turbulence is homogeneous but anisotropic and manifests itself in the nonlinear evolution of equilibrium modal spatial spectra for the probability density of each particle and also for the electromagnetic energy density. The results show that nonlinearly interacting fermionic wave functions quickly approach a multi-mode, dynamic equilibrium state, and that this state can be determined by numerical means.

Crystal structure optimisation using an auxiliary equation of state

NASA Astrophysics Data System (ADS)

Jackson, Adam J.; Skelton, Jonathan M.; Hendon, Christopher H.; Butler, Keith T.; Walsh, Aron

2015-11-01

Standard procedures for local crystal-structure optimisation involve numerous energy and force calculations. It is common to calculate an energy-volume curve, fitting an equation of state around the equilibrium cell volume. This is a computationally intensive process, in particular, for low-symmetry crystal structures where each isochoric optimisation involves energy minimisation over many degrees of freedom. Such procedures can be prohibitive for non-local exchange-correlation functionals or other "beyond" density functional theory electronic structure techniques, particularly where analytical gradients are not available. We present a simple approach for efficient optimisation of crystal structures based on a known equation of state. The equilibrium volume can be predicted from one single-point calculation and refined with successive calculations if required. The approach is validated for PbS, PbTe, ZnS, and ZnTe using nine density functionals and applied to the quaternary semiconductor Cu2ZnSnS4 and the magnetic metal-organic framework HKUST-1.

The equilibrium and stability of the gaseous component of the galaxy, 2

NASA Technical Reports Server (NTRS)

Kellman, S. A.

1971-01-01

A time-independent, linear, plane and axially-symmetric stability analysis was performed on a self-gravitating, plane-parallel, isothermal layer of nonmagnetic, nonrotating gas. The gas layer was immersed in a plane-stratified field isothermal layer of stars which supply a self-consistent gravitational field. Only the gaseous component was perturbed. Expressions were derived for the perturbed gas potential and perturbed gas density that satisfied both the Poisson and hydrostatic equilibrium equations. The equation governing the size of the perturbations in the mid-plane was found to be analogous to the one-dimensional time-independent Schrodinger equation for a particle bound by a potential well, and with similar boundary conditions. The radius of the neutral state was computed numerically and compared with the Jeans' and Ledoux radius. The inclusion of a rigid stellar component increased the Ledoux radius, though only slightly. Isodensity contours of the neutrual or marginally unstable state were constructed.

Well-balanced schemes for the Euler equations with gravitation: Conservative formulation using global fluxes

NASA Astrophysics Data System (ADS)

Chertock, Alina; Cui, Shumo; Kurganov, Alexander; Özcan, Şeyma Nur; Tadmor, Eitan

2018-04-01

We develop a second-order well-balanced central-upwind scheme for the compressible Euler equations with gravitational source term. Here, we advocate a new paradigm based on a purely conservative reformulation of the equations using global fluxes. The proposed scheme is capable of exactly preserving steady-state solutions expressed in terms of a nonlocal equilibrium variable. A crucial step in the construction of the second-order scheme is a well-balanced piecewise linear reconstruction of equilibrium variables combined with a well-balanced central-upwind evolution in time, which is adapted to reduce the amount of numerical viscosity when the flow is at (near) steady-state regime. We show the performance of our newly developed central-upwind scheme and demonstrate importance of perfect balance between the fluxes and gravitational forces in a series of one- and two-dimensional examples.

A Bayesian test for Hardy–Weinberg equilibrium of biallelic X-chromosomal markers

PubMed Central

Puig, X; Ginebra, J; Graffelman, J

2017-01-01

The X chromosome is a relatively large chromosome, harboring a lot of genetic information. Much of the statistical analysis of X-chromosomal information is complicated by the fact that males only have one copy. Recently, frequentist statistical tests for Hardy–Weinberg equilibrium have been proposed specifically for dealing with markers on the X chromosome. Bayesian test procedures for Hardy–Weinberg equilibrium for the autosomes have been described, but Bayesian work on the X chromosome in this context is lacking. This paper gives the first Bayesian approach for testing Hardy–Weinberg equilibrium with biallelic markers at the X chromosome. Marginal and joint posterior distributions for the inbreeding coefficient in females and the male to female allele frequency ratio are computed, and used for statistical inference. The paper gives a detailed account of the proposed Bayesian test, and illustrates it with data from the 1000 Genomes project. In that implementation, a novel approach to tackle multiple testing from a Bayesian perspective through posterior predictive checks is used. PMID:28900292

Nondimensional parameters and equations for buckling of symmetrically laminated thin elastic shallow shells

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

1991-01-01

A method of deriving nondimensional equations and identifying the fundamental parameters associated with bifurcation buckling of anisotropic shells subjected to combined loads is presented. The procedure and rationale used to obtain useful nondimensional forms of the transverse equilibrium and compatibility equations for buckling are presented. Fundamental parameters are identified that represent the importance of both membrane and bending orthotropy and anisotropy on the results.

Research and Development of Methods for Estimating Physicochemical Properties of Organic Compounds of Environmental Concern

DTIC Science & Technology

1979-02-01

coefficient (at equilibrium) when hysteresis is apparent. 6. Coefficient n in Freundlich equation for 1/n soil or sediment adsorption isotherms ýX - KC . 7...Biodegradation Chemical structures cal clasaes (e.g., Diffusion Correlations phenols). General Diffusion coefficients Equations terms for organic...OF THE FATE AND TRANSPORT OF ORGANIC CHEMICALS Adsorption coefficients: K, n* from Freundlich equation + Desorption coefficients: K’*, n’* from

A Dynamic Model for Modern Military Conflict.

DTIC Science & Technology

1982-10-01

within the generalized form of the Lotka - Volterra equations, that can account for the important interactions of modern military conflicts described in...Mx + These equations are seen to be of the generalized Lotka - Volterra form; however, only 20 of the 32 parameters that might possibly be included...determine one equilibrium as the solution of a system of linear equations. The method is derived for the general nth order Lotka - Volterra model in

Algebraic Riccati equations in zero-sum differential games

NASA Technical Reports Server (NTRS)

Johnson, T. L.; Chao, A.

1974-01-01

The procedure for finding the closed-loop Nash equilibrium solution of two-player zero-sum linear time-invariant differential games with quadratic performance criteria and classical information pattern may be reduced in most cases to the solution of an algebraic Riccati equation. Based on the results obtained by Willems, necessary and sufficient conditions for existence of solutions to these equations are derived, and explicit conditions for a scalar example are given.

Computing molecular fluctuations in biochemical reaction systems based on a mechanistic, statistical theory of irreversible processes.

PubMed

Kulasiri, Don

2011-01-01

We discuss the quantification of molecular fluctuations in the biochemical reaction systems within the context of intracellular processes associated with gene expression. We take the molecular reactions pertaining to circadian rhythms to develop models of molecular fluctuations in this chapter. There are a significant number of studies on stochastic fluctuations in intracellular genetic regulatory networks based on single cell-level experiments. In order to understand the fluctuations associated with the gene expression in circadian rhythm networks, it is important to model the interactions of transcriptional factors with the E-boxes in the promoter regions of some of the genes. The pertinent aspects of a near-equilibrium theory that would integrate the thermodynamical and particle dynamic characteristics of intracellular molecular fluctuations would be discussed, and the theory is extended by using the theory of stochastic differential equations. We then model the fluctuations associated with the promoter regions using general mathematical settings. We implemented ubiquitous Gillespie's algorithms, which are used to simulate stochasticity in biochemical networks, for each of the motifs. Both the theory and the Gillespie's algorithms gave the same results in terms of the time evolution of means and variances of molecular numbers. As biochemical reactions occur far away from equilibrium-hence the use of the Gillespie algorithm-these results suggest that the near-equilibrium theory should be a good approximation for some of the biochemical reactions. © 2011 Elsevier Inc. All rights reserved.

The non-equilibrium and energetic cost of sensory adaptation

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

Lan, G.; Sartori, Pablo; Tu, Y.

2011-03-24

Biological sensory systems respond to external signals in short time and adapt to permanent environmental changes over a longer timescale to maintain high sensitivity in widely varying environments. In this work we have shown how all adaptation dynamics are intrinsically non-equilibrium and free energy is dissipated. We show that the dissipated energy is utilized to maintain adaptation accuracy. A universal relation between the energy dissipation and the optimum adaptation accuracy is established by both a general continuum model and a discrete model i n the specific case of the well-known E. coli chemo-sensory adaptation. Our study suggests that cellular levelmore » adaptations are fueled by hydrolysis of high energy biomolecules, such as ATP. The relevance of this work lies on linking the functionality of a biological system (sensory adaptation) with a concept rooted in statistical physics (energy dissipation), by a mathematical law. This has been made possible by identifying a general sensory system with a non-equilibrium steady state (a stationary state in which the probability current is not zero, but its divergence is, see figure), and then numerically and analytically solving the Fokker-Planck and Master Equations which describe the sensory adaptive system. The application of our general results to the case of E. Coli has shed light on why this system uses the high energy SAM molecule to perform adaptation, since using the more common ATP would not suffice to obtain the required adaptation accuracy.« less

Far-from-Equilibrium Route to Superthermal Light in Bimodal Nanolasers

NASA Astrophysics Data System (ADS)

Marconi, Mathias; Javaloyes, Julien; Hamel, Philippe; Raineri, Fabrice; Levenson, Ariel; Yacomotti, Alejandro M.

2018-02-01

Microscale and nanoscale lasers inherently exhibit rich photon statistics due to complex light-matter interaction in a strong spontaneous emission noise background. It is well known that they may display superthermal fluctuations—photon superbunching—in specific situations due to either gain competition, leading to mode-switching instabilities, or carrier-carrier coupling in superradiant microcavities. Here we show a generic route to superbunching in bimodal nanolasers by preparing the system far from equilibrium through a parameter quench. We demonstrate, both theoretically and experimentally, that transient dynamics after a short-pump-pulse-induced quench leads to heavy-tailed superthermal statistics when projected onto the weak mode. We implement a simple experimental technique to access the probability density functions that further enables quantifying the distance from thermal equilibrium via the thermodynamic entropy. The universality of this mechanism relies on the far-from-equilibrium dynamical scenario, which can be mapped to a fast cooling process of a suspension of Brownian particles in a liquid. Our results open up new avenues to mold photon statistics in multimode optical systems and may constitute a test bed to investigate out-of-equilibrium thermodynamics using micro or nanocavity arrays.

Temperature in and out of equilibrium: A review of concepts, tools and attempts

NASA Astrophysics Data System (ADS)

Puglisi, A.; Sarracino, A.; Vulpiani, A.

2017-11-01

We review the general aspects of the concept of temperature in equilibrium and non-equilibrium statistical mechanics. Although temperature is an old and well-established notion, it still presents controversial facets. After a short historical survey of the key role of temperature in thermodynamics and statistical mechanics, we tackle a series of issues which have been recently reconsidered. In particular, we discuss different definitions and their relevance for energy fluctuations. The interest in such a topic has been triggered by the recent observation of negative temperatures in condensed matter experiments. Moreover, the ability to manipulate systems at the micro and nano-scale urges to understand and clarify some aspects related to the statistical properties of small systems (as the issue of temperature's ;fluctuations;). We also discuss the notion of temperature in a dynamical context, within the theory of linear response for Hamiltonian systems at equilibrium and stochastic models with detailed balance, and the generalized fluctuation-response relations, which provide a hint for an extension of the definition of temperature in far-from-equilibrium systems. To conclude we consider non-Hamiltonian systems, such as granular materials, turbulence and active matter, where a general theoretical framework is still lacking.

Transonic flow of steam with non-equilibrium and homogenous condensation

NASA Astrophysics Data System (ADS)

Virk, Akashdeep Singh; Rusak, Zvi

2017-11-01

A small-disturbance model for studying the physical behavior of a steady transonic flow of steam with non-equilibrium and homogeneous condensation around a thin airfoil is derived. The steam thermodynamic behavior is described by van der Waals equation of state. The water condensation rate is calculated according to classical nucleation and droplet growth models. The current study is based on an asymptotic analysis of the fluid flow and condensation equations and boundary conditions in terms of the small thickness of the airfoil, small angle of attack, closeness of upstream flow Mach number to unity and small amount of condensate. The asymptotic analysis gives the similarity parameters that govern the problem. The flow field may be described by a non-homogeneous transonic small-disturbance equation coupled with a set of four ordinary differential equations for the calculation of the condensate mass fraction. An iterative numerical scheme which combines Murman & Cole's (1971) method with Simpson's integration rule is applied to solve the coupled system of equations. The model is used to study the effects of energy release from condensation on the aerodynamic performance of airfoils operating at high pressures and temperatures and near the vapor-liquid saturation conditions.

Validity of the Electrodiffusion Model for Calculating Conductance of Simple Ion Channels.

PubMed

Pohorille, Andrew; Wilson, Michael A; Wei, Chenyu

2017-04-20

We examine the validity and utility of the electrodiffusion (ED) equation, i.e., the generalized Nernst-Planck equation, to characterize, in combination with molecular dynamics, the electrophysiological behavior of simple ion channels. As models, we consider three systems-two naturally occurring channels formed by α-helical bundles of peptaibols, trichotoxin, and alamethicin, and a synthetic, hexameric channel, formed by a peptide that contains only leucine and serine. All these channels mediate transport of potassium and chloride ions. Starting with equilibrium properties, such as the potential of mean force experienced by an ion traversing the channel and diffusivity, obtained from molecular dynamics simulations, the ED equation can be used to determine the full current-voltage dependence with modest or no additional effort. The potential of mean force can be obtained not only from equilibrium simulations, but also, with comparable accuracy, from nonequilibrium simulations at a single voltage. The main assumptions underlying the ED equation appear to hold well for the channels and voltages studied here. To expand the utility of the ED equation, we examine what are the necessary and sufficient conditions for Ohmic and nonrectifying behavior and relate deviations from this behavior to the shape of the ionic potential of mean force.

On the non-stationary generalized Langevin equation

NASA Astrophysics Data System (ADS)

Meyer, Hugues; Voigtmann, Thomas; Schilling, Tanja

2017-12-01

In molecular dynamics simulations and single molecule experiments, observables are usually measured along dynamic trajectories and then averaged over an ensemble ("bundle") of trajectories. Under stationary conditions, the time-evolution of such averages is described by the generalized Langevin equation. By contrast, if the dynamics is not stationary, it is not a priori clear which form the equation of motion for an averaged observable has. We employ the formalism of time-dependent projection operator techniques to derive the equation of motion for a non-equilibrium trajectory-averaged observable as well as for its non-stationary auto-correlation function. The equation is similar in structure to the generalized Langevin equation but exhibits a time-dependent memory kernel as well as a fluctuating force that implicitly depends on the initial conditions of the process. We also derive a relation between this memory kernel and the autocorrelation function of the fluctuating force that has a structure similar to a fluctuation-dissipation relation. In addition, we show how the choice of the projection operator allows us to relate the Taylor expansion of the memory kernel to data that are accessible in MD simulations and experiments, thus allowing us to construct the equation of motion. As a numerical example, the procedure is applied to Brownian motion initialized in non-equilibrium conditions and is shown to be consistent with direct measurements from simulations.

Stellar equilibrium configurations of compact stars in f ( R , T ) theory of gravity

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

Moraes, P.H.R.S.; Arbañil, José D.V.; Malheiro, M., E-mail: moraes.phrs@gmail.com, E-mail: arbanil@ita.br, E-mail: malheiro@ita.br

In this article we study the hydrostatic equilibrium configuration of neutron stars and strange stars, whose fluid pressure is computed from the equations of state p =ωρ{sup 5/3} and p =0.28(ρ−4B), respectively, with ω and B being constants and ρ the energy density of the fluid. We start by deriving the hydrostatic equilibrium equation for the f ( R , T ) theory of gravity, with R and T standing for the Ricci scalar and trace of the energy-momentum tensor, respectively. Such an equation is a generalization of the one obtained from general relativity, and the latter can be retrievedmore » for a certain limit of the theory. For the f ( R , T )= R +2λ T functional form, with λ being a constant, we find that some physical properties of the stars, such as pressure, energy density, mass and radius, are affected when λ is changed. We show that for a fixed central star energy density, the mass of neutron and strange stars can increase with λ. Concerning the star radius, it increases for neutron stars and it decreases for strange stars with the increment of λ. Thus, in f ( R , T ) theory of gravity we can push the maximum mass above the observational limits. This implies that the equation of state cannot be eliminated if the maximum mass within General Relativity lies below the limit given by observed pulsars.« less

Stellar equilibrium configurations of compact stars in f(R,T) theory of gravity

NASA Astrophysics Data System (ADS)

Moraes, P. H. R. S.; Arbañil, José D. V.; Malheiro, M.

2016-06-01

In this article we study the hydrostatic equilibrium configuration of neutron stars and strange stars, whose fluid pressure is computed from the equations of state p=ωρ5/3 and p=0.28(ρ-4Script B), respectively, with ω and Script B being constants and ρ the energy density of the fluid. We start by deriving the hydrostatic equilibrium equation for the f(R,T) theory of gravity, with R and T standing for the Ricci scalar and trace of the energy-momentum tensor, respectively. Such an equation is a generalization of the one obtained from general relativity, and the latter can be retrieved for a certain limit of the theory. For the f(R,T)=R+2λ T functional form, with λ being a constant, we find that some physical properties of the stars, such as pressure, energy density, mass and radius, are affected when λ is changed. We show that for a fixed central star energy density, the mass of neutron and strange stars can increase with λ. Concerning the star radius, it increases for neutron stars and it decreases for strange stars with the increment of λ. Thus, in f(R,T) theory of gravity we can push the maximum mass above the observational limits. This implies that the equation of state cannot be eliminated if the maximum mass within General Relativity lies below the limit given by observed pulsars.

Understand rotating isothermal collapses yet

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

Tohline, J.E.

1985-01-01

A scalar virial equation is used to describe the dynamic properties of equilibrium gas clouds, taking into account the relative effects of surface pressure, rotation, self gravity and internal isothermal pressure. Details concerning the internal structure of the clouds are ignored in order to obtain a globalized analytical expression. The obtained solution to the equation is found to agree with the surface-pressure-dominated model of Stahler (1983), and the rotation-dominated model of Hayashi, Narita, and Miyama (1982). On the basis of the analytical expression of virial equilibrium in the clouds, some of the limiting properties of isothermal clouds are described, andmore » a realistic starting model for cloud collapse is proposed. 18 references.« less

Force Model for Control of Tendon Driven Hands

NASA Technical Reports Server (NTRS)

Pena, Edward; Thompson, David E.

1997-01-01

Knowing the tendon forces generated for a given task such as grasping via a model, an artificial hand can be controlled. A two-dimensional force model for the index finger was developed. This system is assumed to be in static equilibrium, therefore, the equations of equilibrium were applied at each joint. Constraint equations describing the tendon branch connectivity were used. Gaussian elimination was used to solve for the unknowns of the Linear system. Results from initial work on estimating tendon forces in post-operative hands during active motion therapy were discussed. The results are important for understanding the effects of hand position on tendon tension, elastic effects on tendon tension, and overall functional anatomy of the hand.

Matrix-valued Boltzmann equation for the nonintegrable Hubbard chain.

PubMed

Fürst, Martin L R; Mendl, Christian B; Spohn, Herbert

2013-07-01

The standard Fermi-Hubbard chain becomes nonintegrable by adding to the nearest neighbor hopping additional longer range hopping amplitudes. We assume that the quartic interaction is weak and investigate numerically the dynamics of the chain on the level of the Boltzmann type kinetic equation. Only the spatially homogeneous case is considered. We observe that the huge degeneracy of stationary states in the case of nearest neighbor hopping is lost and the convergence to the thermal Fermi-Dirac distribution is restored. The convergence to equilibrium is exponentially fast. However for small next-nearest neighbor hopping amplitudes one has a rapid relaxation towards the manifold of quasistationary states and slow relaxation to the final equilibrium state.

A time-accurate algorithm for chemical non-equilibrium viscous flows at all speeds

NASA Technical Reports Server (NTRS)

Shuen, J.-S.; Chen, K.-H.; Choi, Y.

1992-01-01

A time-accurate, coupled solution procedure is described for the chemical nonequilibrium Navier-Stokes equations over a wide range of Mach numbers. This method employs the strong conservation form of the governing equations, but uses primitive variables as unknowns. Real gas properties and equilibrium chemistry are considered. Numerical tests include steady convergent-divergent nozzle flows with air dissociation/recombination chemistry, dump combustor flows with n-pentane-air chemistry, nonreacting flow in a model double annular combustor, and nonreacting unsteady driven cavity flows. Numerical results for both the steady and unsteady flows demonstrate the efficiency and robustness of the present algorithm for Mach numbers ranging from the incompressible limit to supersonic speeds.

Physical aspects of biophotons.

PubMed

Popp, F A; Li, K H; Mei, W P; Galle, M; Neurohr, R

1988-07-15

By comparing the theoretically expected results of photon emission from a chaotic (thermal) field and those of an ordered (fully coherent) field with the actual experimental data, one finds ample indications for the hypothesis that 'biophotons' originate from a coherent field occurring within living tissues. A direct proof may be seen in the hyperbolic relaxation dynamics of spectral delayed luminescence under ergodic conditions. A possible mechanism has to be founded on Einstein's balance equation and, under stationary conditions, on energy conservation including a photochemical potential. It is shown that the considered equations deliver, besides the thermal equilibrium, a conditionally stable region far away from equilibrium, which can help to describe both 'biophoton emission' and biological regulation.

Non-equilibrium steady-state distributions of colloids in a tilted periodic potential

NASA Astrophysics Data System (ADS)

Ma, Xiaoguang; Lai, Pik-Yin; Ackerson, Bruce; Tong, Penger

A two-layer colloidal system is constructed to study the effects of the external force F on the non-equilibrium steady-state (NESS) dynamics of the diffusing particles over a tilted periodic potential, in which detailed balance is broken due to the presence of a steady particle flux. The periodic potential is provided by the bottom layer colloidal spheres forming a fixed crystalline pattern on a glass substrate. The corrugated surface of the bottom colloidal crystal provides a gravitational potential field for the top layer diffusing particles. By tilting the sample with respect to gravity, a tangential component F is applied to the diffusing particles. The measured NESS probability density function Pss (x , y) of the particles is found to deviate from the equilibrium distribution depending on the driving or distance from equilibrium. The experimental results are compared with the exact solution of the 1D Smoluchowski equation and the numerical results of the 2D Smoluchowski equation. Moreover, from the obtained exact 1D solution, we develop an analytical method to accurately extract the 1D potential U0 (x) from the measured Pss (x) . Work supported in part by the Research Grants Council of Hong Kong SAR.

High-order regularization in lattice-Boltzmann equations

NASA Astrophysics Data System (ADS)

Mattila, Keijo K.; Philippi, Paulo C.; Hegele, Luiz A.

2017-04-01

A lattice-Boltzmann equation (LBE) is the discrete counterpart of a continuous kinetic model. It can be derived using a Hermite polynomial expansion for the velocity distribution function. Since LBEs are characterized by discrete, finite representations of the microscopic velocity space, the expansion must be truncated and the appropriate order of truncation depends on the hydrodynamic problem under investigation. Here we consider a particular truncation where the non-equilibrium distribution is expanded on a par with the equilibrium distribution, except that the diffusive parts of high-order non-equilibrium moments are filtered, i.e., only the corresponding advective parts are retained after a given rank. The decomposition of moments into diffusive and advective parts is based directly on analytical relations between Hermite polynomial tensors. The resulting, refined regularization procedure leads to recurrence relations where high-order non-equilibrium moments are expressed in terms of low-order ones. The procedure is appealing in the sense that stability can be enhanced without local variation of transport parameters, like viscosity, or without tuning the simulation parameters based on embedded optimization steps. The improved stability properties are here demonstrated using the perturbed double periodic shear layer flow and the Sod shock tube problem as benchmark cases.

Zeroth Law, Entropy, Equilibrium, and All That

NASA Astrophysics Data System (ADS)

Canagaratna, Sebastian G.

2008-05-01

The place of the zeroth law in the teaching of thermodynamics is examined in the context of the recent discussion by Gislason and Craig of some problems involving the establishment of thermal equilibrium. The concept of thermal equilibrium is introduced through the zeroth law. The relation between the zeroth law and the second law in the traditional approach to thermodynamics is discussed. It is shown that the traditional approach does not need to appeal to the second law to solve with rigor the type of problems discussed by Gislason and Craig: in problems not involving chemical reaction, the zeroth law and the condition for mechanical equilibrium, complemented by the first law and any necessary equations of state, are sufficient to determine the final state. We have to invoke the second law only if we wish to calculate the change of entropy. Since most students are exposed to a traditional approach to thermodynamics, the examples of Gislason and Craig are re-examined in terms of the traditional formulation. The maximization of the entropy in the final state can be verified in the traditional approach quite directly by the use of the fundamental equations of thermodynamics. This approach uses relatively simple mathematics in as general a setting as possible.

Physics of Magnetospheric Variability

NASA Astrophysics Data System (ADS)

Vasyliūnas, Vytenis M.

2011-01-01

Many widely used methods for describing and understanding the magnetosphere are based on balance conditions for quasi-static equilibrium (this is particularly true of the classical theory of magnetosphere/ionosphere coupling, which in addition presupposes the equilibrium to be stable); they may therefore be of limited applicability for dealing with time-variable phenomena as well as for determining cause-effect relations. The large-scale variability of the magnetosphere can be produced both by changing external (solar-wind) conditions and by non-equilibrium internal dynamics. Its developments are governed by the basic equations of physics, especially Maxwell's equations combined with the unique constraints of large-scale plasma; the requirement of charge quasi-neutrality constrains the electric field to be determined by plasma dynamics (generalized Ohm's law) and the electric current to match the existing curl of the magnetic field. The structure and dynamics of the ionosphere/magnetosphere/solar-wind system can then be described in terms of three interrelated processes: (1) stress equilibrium and disequilibrium, (2) magnetic flux transport, (3) energy conversion and dissipation. This provides a framework for a unified formulation of settled as well as of controversial issues concerning, e.g., magnetospheric substorms and magnetic storms.

Integrated Force Method Solution to Indeterminate Structural Mechanics Problems

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Hopkins, Dale A.; Halford, Gary R.

2004-01-01

Strength of materials problems have been classified into determinate and indeterminate problems. Determinate analysis primarily based on the equilibrium concept is well understood. Solutions of indeterminate problems required additional compatibility conditions, and its comprehension was not exclusive. A solution to indeterminate problem is generated by manipulating the equilibrium concept, either by rewriting in the displacement variables or through the cutting and closing gap technique of the redundant force method. Compatibility improvisation has made analysis cumbersome. The authors have researched and understood the compatibility theory. Solutions can be generated with equal emphasis on the equilibrium and compatibility concepts. This technique is called the Integrated Force Method (IFM). Forces are the primary unknowns of IFM. Displacements are back-calculated from forces. IFM equations are manipulated to obtain the Dual Integrated Force Method (IFMD). Displacement is the primary variable of IFMD and force is back-calculated. The subject is introduced through response variables: force, deformation, displacement; and underlying concepts: equilibrium equation, force deformation relation, deformation displacement relation, and compatibility condition. Mechanical load, temperature variation, and support settling are equally emphasized. The basic theory is discussed. A set of examples illustrate the new concepts. IFM and IFMD based finite element methods are introduced for simple problems.

A rumor transmission model with incubation in social networks

NASA Astrophysics Data System (ADS)

Jia, Jianwen; Wu, Wenjiang

2018-02-01

In this paper, we propose a rumor transmission model with incubation period and constant recruitment in social networks. By carrying out an analysis of the model, we study the stability of rumor-free equilibrium and come to the local stable condition of the rumor equilibrium. We use the geometric approach for ordinary differential equations for showing the global stability of the rumor equilibrium. And when ℜ0 = 1, the new model occurs a transcritical bifurcation. Furthermore, numerical simulations are used to support the analysis. At last, some conclusions are presented.

Variational multiscale models for charge transport.

PubMed

Wei, Guo-Wei; Zheng, Qiong; Chen, Zhan; Xia, Kelin

2012-01-01

This work presents a few variational multiscale models for charge transport in complex physical, chemical and biological systems and engineering devices, such as fuel cells, solar cells, battery cells, nanofluidics, transistors and ion channels. An essential ingredient of the present models, introduced in an earlier paper (Bulletin of Mathematical Biology, 72, 1562-1622, 2010), is the use of differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain from the microscopic domain, meanwhile, dynamically couple discrete and continuum descriptions. Our main strategy is to construct the total energy functional of a charge transport system to encompass the polar and nonpolar free energies of solvation, and chemical potential related energy. By using the Euler-Lagrange variation, coupled Laplace-Beltrami and Poisson-Nernst-Planck (LB-PNP) equations are derived. The solution of the LB-PNP equations leads to the minimization of the total free energy, and explicit profiles of electrostatic potential and densities of charge species. To further reduce the computational complexity, the Boltzmann distribution obtained from the Poisson-Boltzmann (PB) equation is utilized to represent the densities of certain charge species so as to avoid the computationally expensive solution of some Nernst-Planck (NP) equations. Consequently, the coupled Laplace-Beltrami and Poisson-Boltzmann-Nernst-Planck (LB-PBNP) equations are proposed for charge transport in heterogeneous systems. A major emphasis of the present formulation is the consistency between equilibrium LB-PB theory and non-equilibrium LB-PNP theory at equilibrium. Another major emphasis is the capability of the reduced LB-PBNP model to fully recover the prediction of the LB-PNP model at non-equilibrium settings. To account for the fluid impact on the charge transport, we derive coupled Laplace-Beltrami, Poisson-Nernst-Planck and Navier-Stokes equations from the variational principle for chemo-electro-fluid systems. A number of computational algorithms is developed to implement the proposed new variational multiscale models in an efficient manner. A set of ten protein molecules and a realistic ion channel, Gramicidin A, are employed to confirm the consistency and verify the capability. Extensive numerical experiment is designed to validate the proposed variational multiscale models. A good quantitative agreement between our model prediction and the experimental measurement of current-voltage curves is observed for the Gramicidin A channel transport. This paper also provides a brief review of the field.

Variational multiscale models for charge transport

PubMed Central

Wei, Guo-Wei; Zheng, Qiong; Chen, Zhan; Xia, Kelin

2012-01-01

This work presents a few variational multiscale models for charge transport in complex physical, chemical and biological systems and engineering devices, such as fuel cells, solar cells, battery cells, nanofluidics, transistors and ion channels. An essential ingredient of the present models, introduced in an earlier paper (Bulletin of Mathematical Biology, 72, 1562-1622, 2010), is the use of differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain from the microscopic domain, meanwhile, dynamically couple discrete and continuum descriptions. Our main strategy is to construct the total energy functional of a charge transport system to encompass the polar and nonpolar free energies of solvation, and chemical potential related energy. By using the Euler-Lagrange variation, coupled Laplace-Beltrami and Poisson-Nernst-Planck (LB-PNP) equations are derived. The solution of the LB-PNP equations leads to the minimization of the total free energy, and explicit profiles of electrostatic potential and densities of charge species. To further reduce the computational complexity, the Boltzmann distribution obtained from the Poisson-Boltzmann (PB) equation is utilized to represent the densities of certain charge species so as to avoid the computationally expensive solution of some Nernst-Planck (NP) equations. Consequently, the coupled Laplace-Beltrami and Poisson-Boltzmann-Nernst-Planck (LB-PBNP) equations are proposed for charge transport in heterogeneous systems. A major emphasis of the present formulation is the consistency between equilibrium LB-PB theory and non-equilibrium LB-PNP theory at equilibrium. Another major emphasis is the capability of the reduced LB-PBNP model to fully recover the prediction of the LB-PNP model at non-equilibrium settings. To account for the fluid impact on the charge transport, we derive coupled Laplace-Beltrami, Poisson-Nernst-Planck and Navier-Stokes equations from the variational principle for chemo-electro-fluid systems. A number of computational algorithms is developed to implement the proposed new variational multiscale models in an efficient manner. A set of ten protein molecules and a realistic ion channel, Gramicidin A, are employed to confirm the consistency and verify the capability. Extensive numerical experiment is designed to validate the proposed variational multiscale models. A good quantitative agreement between our model prediction and the experimental measurement of current-voltage curves is observed for the Gramicidin A channel transport. This paper also provides a brief review of the field. PMID:23172978

Emergent equilibrium in many-body optical bistability

NASA Astrophysics Data System (ADS)

Foss-Feig, Michael; Niroula, Pradeep; Young, Jeremy; Hafezi, Mohammad; Gorshkov, Alexey; Wilson, Ryan; Maghrebi, Mohammad

2017-04-01

Many-body systems constructed of quantum-optical building blocks can now be realized in experimental platforms ranging from exciton-polariton fluids to Rydberg gases, establishing a fascinating interface between traditional many-body physics and the non-equilibrium setting of cavity-QED. At this interface the standard intuitions of both fields are called into question, obscuring issues as fundamental as the role of fluctuations, dimensionality, and symmetry on the nature of collective behavior and phase transitions. We study the driven-dissipative Bose-Hubbard model, a minimal description of atomic, optical, and solid-state systems in which particle loss is countered by coherent driving. Despite being a lattice version of optical bistability-a foundational and patently non-equilibrium model of cavity-QED-the steady state possesses an emergent equilibrium description in terms of an Ising model. We establish this picture by identifying a limit in which the quantum dynamics is asymptotically equivalent to non-equilibrium Langevin equations, which support a phase transition described by model A of the Hohenberg-Halperin classification. Simulations of the Langevin equations corroborate this picture, producing results consistent with the behavior of a finite-temperature Ising model. M.F.M., J.T.Y., and A.V.G. acknowledge support by ARL CDQI, ARO MURI, NSF QIS, ARO, NSF PFC at JQI, and AFOSR. R.M.W. acknowledges partial support from the NSF under Grant No. PHYS-1516421. M.H. acknowledges support by AFOSR-MURI, ONR and Sloan Foundation.

Group Contribution Methods for Phase Equilibrium Calculations.

PubMed

Gmehling, Jürgen; Constantinescu, Dana; Schmid, Bastian

2015-01-01

The development and design of chemical processes are carried out by solving the balance equations of a mathematical model for sections of or the whole chemical plant with the help of process simulators. For process simulation, besides kinetic data for the chemical reaction, various pure component and mixture properties are required. Because of the great importance of separation processes for a chemical plant in particular, a reliable knowledge of the phase equilibrium behavior is required. The phase equilibrium behavior can be calculated with the help of modern equations of state or g(E)-models using only binary parameters. But unfortunately, only a very small part of the experimental data for fitting the required binary model parameters is available, so very often these models cannot be applied directly. To solve this problem, powerful predictive thermodynamic models have been developed. Group contribution methods allow the prediction of the required phase equilibrium data using only a limited number of group interaction parameters. A prerequisite for fitting the required group interaction parameters is a comprehensive database. That is why for the development of powerful group contribution methods almost all published pure component properties, phase equilibrium data, excess properties, etc., were stored in computerized form in the Dortmund Data Bank. In this review, the present status, weaknesses, advantages and disadvantages, possible applications, and typical results of the different group contribution methods for the calculation of phase equilibria are presented.

Stability and bifurcation analysis on a ratio-dependent predator-prey model with time delay

NASA Astrophysics Data System (ADS)

Xu, Rui; Gan, Qintao; Ma, Zhien

2009-08-01

A ratio-dependent predator-prey model with time delay due to the gestation of the predator is investigated. By analyzing the corresponding characteristic equations, the local stability of a positive equilibrium and a semi-trivial boundary equilibrium is discussed, respectively. Further, it is proved that the system undergoes a Hopf bifurcation at the positive equilibrium. Using the normal form theory and the center manifold reduction, explicit formulae are derived to determine the direction of bifurcations and the stability and other properties of bifurcating periodic solutions. By means of an iteration technique, sufficient conditions are obtained for the global attractiveness of the positive equilibrium. By comparison arguments, the global stability of the semi-trivial equilibrium is also addressed. Numerical simulations are carried out to illustrate the main results.

Nonlinear response from transport theory and quantum field theory at finite temperature

NASA Astrophysics Data System (ADS)

Carrington, M. E.; Defu, Hou; Kobes, R.

2001-07-01

We study the nonlinear response in weakly coupled hot φ4 theory. We obtain an expression for a quadratic shear viscous response coefficient using two different formalisms: transport theory and response theory. The transport theory calculation is done by assuming a local equilibrium form for the distribution function and expanding in the gradient of the local four dimensional velocity field. By performing a Chapman-Enskog expansion on the Boltzmann equation we obtain a hierarchy of equations for the coefficients of the expanded distribution function. To do the response theory calculation we use Zubarev's techniques in nonequilibrium statistical mechanics to derive a generalized Kubo formula. Using this formula allows us to obtain the quadratic shear viscous response from the three-point retarded Green function of the viscous shear stress tensor. We use the closed time path formalism of real time finite temperature field theory to show that this three-point function can be calculated by writing it as an integral equation involving a four-point vertex. This four-point vertex can in turn be obtained from an integral equation which represents the resummation of an infinite series of ladder and extended-ladder diagrams. The connection between transport theory and response theory is made when we show that the integral equation for this four-point vertex has exactly the same form as the equation obtained from the Boltzmann equation for the coefficient of the quadratic term of the gradient expansion of the distribution function. We conclude that calculating the quadratic shear viscous response using transport theory and keeping terms that are quadratic in the gradient of the velocity field in the Chapman-Enskog expansion of the Boltzmann equation is equivalent to calculating the quadratic shear viscous response from response theory using the next-to-linear response Kubo formula, with a vertex given by an infinite resummation of ladder and extended-ladder diagrams.

Advanced classical thermodynamics

NASA Astrophysics Data System (ADS)

Emanuel, George

The theoretical and mathematical foundations of thermodynamics are presented in an advanced text intended for graduate engineering students. Chapters are devoted to definitions and postulates, the fundamental equation, equilibrium, the application of Jacobian theory to thermodynamics, the Maxwell equations, stability, the theory of real gases, critical-point theory, and chemical thermodynamics. Diagrams, graphs, tables, and sample problems are provided.

New Wine in Old Flasks: A New Solution of the Clapeyron Equation

ERIC Educational Resources Information Center

Shilo, Doron; Ghez, Richard

2008-01-01

The coexisting equilibrium states between single-component gas and condensed phases (liquid or solid) are often calculated by assuming that the condensed phase's molar volume is negligible in comparison with the gas's. Here, we present an analytic solution of Clapeyron's equation when this assumption is relaxed. It differs substantially from…

The H-theorem and equation of state for kinetic model of imperfect gas

NASA Astrophysics Data System (ADS)

Bishaev, A. M.; Rikov, V. A.; Abgaryan, M. V.

2018-03-01

In the offered article, having used earlier constructed kinetic model for imperfect gas, the equation of state for such gas which takes place which is able in a thermodynamic equilibrium is received and also expression for critical temperature as functions is received from an interaction potential between molecules.

Numerical simulation of advective-dispersive multisolute transport with sorption, ion exchange and equilibrium chemistry

USGS Publications Warehouse

Lewis, F.M.; Voss, C.I.; Rubin, Jacob

1986-01-01

A model was developed that can simulate the effect of certain chemical and sorption reactions simultaneously among solutes involved in advective-dispersive transport through porous media. The model is based on a methodology that utilizes physical-chemical relationships in the development of the basic solute mass-balance equations; however, the form of these equations allows their solution to be obtained by methods that do not depend on the chemical processes. The chemical environment is governed by the condition of local chemical equilibrium, and may be defined either by the linear sorption of a single species and two soluble complexation reactions which also involve that species, or binary ion exchange and one complexation reaction involving a common ion. Partial differential equations that describe solute mass balance entirely in the liquid phase are developed for each tenad (a chemical entity whose total mass is independent of the reaction process) in terms of their total dissolved concentration. These equations are solved numerically in two dimensions through the modification of an existing groundwater flow/transport computer code. (Author 's abstract)

Molecular description of steady supersonic free jets

NASA Astrophysics Data System (ADS)

Montero, S.

2017-09-01

A detailed analysis of the non-local thermal equilibrium (n-LTE) problem in the paraxial zone of silence of supersonic free jets is reported. The study is based on a hybrid approach that combines Navier-Stokes equations with a kinetic equation derived from the generalized Boltzmann (Waldmann-Snider) equation. The resulting system is solved for those flow quantities not easily amenable to experimental measure (translational temperature, flow velocity, and entropy) in terms of the quantities that can be measured accurately (distance, number density, population of rotational states, and their gradients). The reported solutions are essentially exact and are formulated in terms of macroscopic quantities, as well as in terms of elementary collision processes. Emphasis is made on the influence of dissipative effects onto the flow (viscous and diabatic) and of the breakdown of thermal equilibrium onto the evolution of entropy and translational temperature. The influence of inelastic collisions onto these effects is analysed in depth. The reported equations are aimed at optimizing the experimental knowledge of the n-LTE problem and its quantitative interpretation in terms of state-to-state rates for inelastic collisions.

Nonlinear Interaction of Detuned Instability Waves in Boundary-Layer Transition: Amplitude Equations

NASA Technical Reports Server (NTRS)

Lee, Sang Soo

1998-01-01

The non-equilibrium critical-layer analysis of a system of frequency-detuned resonant-triads is presented. In this part of the analysis, the system of partial differential critical-layer equations derived in Part I is solved analytically to yield the amplitude equations which are analyzed using a combination of asymptotic and numerical methods. Numerical solutions of the inviscid non-equilibrium oblique-mode amplitude equations show that the frequency-detuned self-interaction enhances the growth of the lower-frequency oblique modes more than the higher-frequency ones. All amplitudes become singular at the same finite downstream position. The frequency detuning delays the occurrence of the singularity. The spanwise-periodic mean-flow distortion and low-frequency nonlinear modes are generated by the critical-layer interaction between frequency-detuned oblique modes. The nonlinear mean flow and higher harmonics as well as the primary instabilities become as large as the base mean flow in the inviscid wall layer in the downstream region where the distance from the singularity is of the order of the wavelength scale.

On a viable first-order formulation of relativistic viscous fluids and its applications to cosmology

NASA Astrophysics Data System (ADS)

Disconzi, Marcelo M.; Kephart, Thomas W.; Scherrer, Robert J.

We consider a first-order formulation of relativistic fluids with bulk viscosity based on a stress-energy tensor introduced by Lichnerowicz. Choosing a barotropic equation-of-state, we show that this theory satisfies basic physical requirements and, under the further assumption of vanishing vorticity, that the equations of motion are causal, both in the case of a fixed background and when the equations are coupled to Einstein's equations. Furthermore, Lichnerowicz's proposal does not fit into the general framework of first-order theories studied by Hiscock and Lindblom, and hence their instability results do not apply. These conclusions apply to the full-fledged nonlinear theory, without any equilibrium or near equilibrium assumptions. Similarities and differences between the approach explored here and other theories of relativistic viscosity, including the Mueller-Israel-Stewart formulation, are addressed. Cosmological models based on the Lichnerowicz stress-energy tensor are studied. As the topic of (relativistic) viscous fluids is also of interest outside the general relativity and cosmology communities, such as, for instance, in applications involving heavy-ion collisions, we make our presentation largely self-contained.

On equilibrium positions and stabilization of electrodynamic tether system in the orbital frame

NASA Astrophysics Data System (ADS)

Tikhonov, A. A.; Shcherbakova, L. F.

2018-05-01

An electrodynamic tether system (EDTS) in a near-Earth circular orbit is considered. EDTS contains conductive tether with lumped masses attached to it at the ends. Possible equilibrium positions of the stretched tether under the influence of gravity gradient, Ampere and Lorentz forces in orbital frame are investigated. It is shown that in addition to the vertical equilibrium position, the "inclined" equilibrium positions of the tensioned tether are also possible. Conditions are obtained for the EDTS parameters, under which there is only one vertical position of the tether equilibrium. On the basis of nonlinear differential equations of motion, using the Lyapunov functions method, sufficient conditions for the stability of the vertical position of the tether equi-librium are obtained. It is shown that stabilization of the tether in this position is possible in the presence of damping in the EDTS system. The results of numerical simulation are presented.

Phase equilibrium measurements on nine binary mixtures

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

Wilding, W.V.; Giles, N.F.; Wilson, L.C.

1996-11-01

Phase equilibrium measurements have been performed on nine binary mixtures. The PTx method was used to obtain vapor-liquid equilibrium data for the following systems at two temperatures each: (aminoethyl)piperazine + diethylenetriamine; 2-butoxyethyl acetate + 2-butoxyethanol; 2-methyl-2-propanol + 2-methylbutane; 2-methyl-2-propanol + 2-methyl-2-butene; methacrylonitrile + methanol; 1-chloro-1,1-difluoroethane + hydrogen chloride; 2-(hexyloxy)ethanol + ethylene glycol; butane + ammonia; propionaldehyde + butane. Equilibrium vapor and liquid phase compositions were derived form the PTx data using the Soave equation of state to represent the vapor phase and the Wilson or the NRTL activity coefficient model to represent the liquid phase. A large immiscibility region existsmore » in the butane + ammonia system at 0 C. Therefore, separate vapor-liquid-liquid equilibrium measurements were performed on this system to more precisely determine the miscibility limits and the composition of the vapor phase in equilibrium with the two liquid phases.« less

Equation of State for Supercooled Water at Pressures up to 400 MPa

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

Holten, Vincent; Sengers, Jan V.; Anisimov, Mikhail A., E-mail: anisimov@umd.edu

2014-12-01

An equation of state is presented for the thermodynamic properties of cold and supercooled water. It is valid for temperatures from the homogeneous ice nucleation temperature up to 300 K and for pressures up to 400 MPa, and can be extrapolated up to 1000 MPa. The equation of state is compared with experimental data for the density, expansion coefficient, isothermal compressibility, speed of sound, and heat capacity. Estimates for the accuracy of the equation are given. The melting curve of ice I is calculated from the phase-equilibrium condition between the proposed equation and an existing equation of state for icemore » I.« less

Generalized Boltzmann-Type Equations for Aggregation in Gases

NASA Astrophysics Data System (ADS)

Adzhiev, S. Z.; Vedenyapin, V. V.; Volkov, Yu. A.; Melikhov, I. V.

2017-12-01

The coalescence and fragmentation of particles in a dispersion system are investigated by applying kinetic theory methods, namely, by generalizing the Boltzmann kinetic equation to coalescence and fragmentation processes. Dynamic equations for the particle concentrations in the system are derived using the kinetic equations of motion. For particle coalescence and fragmentation, equations for the particle momentum, coordinate, and mass distribution functions are obtained and the coalescence and fragmentation coefficients are calculated. The equilibrium mass and velocity distribution functions of the particles in the dispersion system are found in the approximation of an active terminal group (Becker-Döring-type equation). The transition to a continuum description is performed.

Water Sorption Isotherm of Pea Starch Edible Films and Prediction Models.

PubMed

Saberi, Bahareh; Vuong, Quan V; Chockchaisawasdee, Suwimol; Golding, John B; Scarlett, Christopher J; Stathopoulos, Costas E

2015-12-24

The moisture sorption isotherm of pea starch films prepared with various glycerol contents as plasticizer was investigated at different storage relative humidities (11%-96% RH) and at 5 ± 1, 15 ± 1, 25 ± 1 and 40 ± 1 °C by using gravimetric method. The results showed that the equilibrium moisture content of all films increased substantially above a w = 0.6. Films plasticized with glycerol, under all temperatures and RH conditions (11%-96%), adsorbed more moisture resulting in higher equilibrium moisture contents. Reduction of the temperature enhanced the equilibrium moisture content and monolayer water of the films. The obtained experimental data were fitted to different models including two-parameter equations (Oswin, Henderson, Brunauer-Emmitt-Teller (BET), Flory-Huggins, and Iglesias-Chirife), three-parameter equations Guggenhiem-Anderson-deBoer (GAB), Ferro-Fontan, and Lewicki) and a four-parameter equation (Peleg). The three-parameter Lewicki model was found to be the best-fitted model for representing the experimental data within the studied temperatures and whole range of relative humidities (11%-98%). Addition of glycerol increased the net isosteric heat of moisture sorption of pea starch film. The results provide important information with estimating of stability and functional characteristics of the films in various environments.

Water Sorption Isotherm of Pea Starch Edible Films and Prediction Models

PubMed Central

Saberi, Bahareh; Vuong, Quan V.; Chockchaisawasdee, Suwimol; Golding, John B.; Scarlett, Christopher J.; Stathopoulos, Costas E.

2015-01-01

The moisture sorption isotherm of pea starch films prepared with various glycerol contents as plasticizer was investigated at different storage relative humidities (11%–96% RH) and at 5 ± 1, 15 ± 1, 25 ± 1 and 40 ± 1 °C by using gravimetric method. The results showed that the equilibrium moisture content of all films increased substantially above aw = 0.6. Films plasticized with glycerol, under all temperatures and RH conditions (11%–96%), adsorbed more moisture resulting in higher equilibrium moisture contents. Reduction of the temperature enhanced the equilibrium moisture content and monolayer water of the films. The obtained experimental data were fitted to different models including two-parameter equations (Oswin, Henderson, Brunauer–Emmitt–Teller (BET), Flory–Huggins, and Iglesias–Chirife), three-parameter equations Guggenhiem–Anderson–deBoer (GAB), Ferro–Fontan, and Lewicki) and a four-parameter equation (Peleg). The three-parameter Lewicki model was found to be the best-fitted model for representing the experimental data within the studied temperatures and whole range of relative humidities (11%–98%). Addition of glycerol increased the net isosteric heat of moisture sorption of pea starch film. The results provide important information with estimating of stability and functional characteristics of the films in various environments. PMID:28231096

Hot super-dense compact object with particular EoS

NASA Astrophysics Data System (ADS)

Tito, E. P.; Pavlov, V. I.

2018-03-01

We show the possibility of existence of a self-gravitating spherically-symmetric equilibrium configuration for a neutral matter with neutron-like density, small mass M ≪ M_{⊙}, and small radius R ≪ R_{⊙}. We incorporate the effects of both the special and general theories of relativity. Such object may be formed in a cosmic cataclysm, perhaps an exotic one. Since the base equations of hydrostatic equilibrium are completed by the equation of state (EoS) for the matter of the object, we offer a novel, interpolating experimental data from high-energy physics, EoS which permits the existence of such compact system of finite radius. This EoS model possesses a critical state characterized by density ρc and temperature Tc. For such an object, we derive a radial distribution for the super-dense matter in "liquid" phase using Tolman-Oppenheimer-Volkoff equations for hydrostatic equilibrium. We demonstrate that a stable configuration is indeed possible (only) for temperatures smaller than the critical one. We derive the mass-radius relation (adjusted for relativistic corrections) for such small (M ≪ M_{⊙}) super-dense compact objects. The results are within the constraints established by both heavy-ion collision experiments and theoretical studies of neutron-rich matter.

Supersonic flow of chemically reacting gas-particle mixtures. Volume 1: A theoretical analysis and development of the numerical solution

NASA Technical Reports Server (NTRS)

Penny, M. M.; Smith, S. D.; Anderson, P. G.; Sulyma, P. R.; Pearson, M. L.

1976-01-01

A numerical solution for chemically reacting supersonic gas-particle flows in rocket nozzles and exhaust plumes was described. The gas-particle flow solution is fully coupled in that the effects of particle drag and heat transfer between the gas and particle phases are treated. Gas and particles exchange momentum via the drag exerted on the gas by the particles. Energy is exchanged between the phases via heat transfer (convection and/or radiation). Thermochemistry calculations (chemical equilibrium, frozen or chemical kinetics) were shown to be uncoupled from the flow solution and, as such, can be solved separately. The solution to the set of governing equations is obtained by utilizing the method of characteristics. The equations cast in characteristic form are shown to be formally the same for ideal, frozen, chemical equilibrium and chemical non-equilibrium reacting gas mixtures. The particle distribution is represented in the numerical solution by a finite distribution of particle sizes.

Universality of electronic friction. II. Equivalence of the quantum-classical Liouville equation approach with von Oppen's nonequilibrium Green's function methods out of equilibrium

NASA Astrophysics Data System (ADS)

Dou, Wenjie; Subotnik, Joseph E.

2018-02-01

In a recent publication [W. Dou et al., Phys. Rev. Lett. 119, 046001 (2017), 10.1103/PhysRevLett.119.046001], using the quantum-classical Liouville equation (QCLE), we derived a very general form for the electronic friction felt by a molecule moving near one or many metal surfaces. Moreover, we have already proved the equivalence of the QCLE electronic friction with the Head-Gordon-Tully model as well as a generalized version of von Oppen's nonequilibrium Green's function (NEGF) method at equilibrium [W. Dou and J. E. Subotnik, Phys. Rev. B 96, 104305 (2017), 10.1103/PhysRevB.96.104305]. In the present paper, we now further prove the equivalence between the QCLE friction and the NEGF friction for the case of multiple metal surfaces and an out-of-equilibrium electronic current without electron-electron interactions. The present results reinforce our recent claim that there is only one universal electronic friction tensor arising from the Born-Oppenheimer approximation.

Solutions for Reacting and Nonreacting Viscous Shock Layers with Multicomponent Diffusion and Mass Injection. Ph.D. Thesis - Virginia Polytechnic Inst. and State Univ.

NASA Technical Reports Server (NTRS)

Moss, J. N.

1971-01-01

Numerical solutions are presented for the viscous shocklayer equations where the chemistry is treated as being either frozen, equilibrium, or nonequilibrium. Also the effects of the diffusion model, surface catalyticity, and mass injection on surface transport and flow parameters are considered. The equilibrium calculations for air species using multicomponent: diffusion provide solutions previously unavailable. The viscous shock-layer equations are solved by using an implicit finite-difference scheme. The flow is treated as a mixture of inert and thermally perfect species. Also the flow is assumed to be in vibrational equilibrium. All calculations are for a 45 deg hyperboloid. The flight conditions are those for various altitudes and velocities in the earth's atmosphere. Data are presented showing the effects of the chemical models; diffusion models; surface catalyticity; and mass injection of air, water, and ablation products on heat transfer; skin friction; shock stand-off distance; wall pressure distribution; and tangential velocity, temperature, and species profiles.

Modelling Equilibrium and Fractional Crystallization in the System MgO-FeO-CaO-Al2O3-SiO2

NASA Technical Reports Server (NTRS)

Herbert, F.

1985-01-01

A mathematical modelling technique for use in petrogenesis calculations in the system MgO-FeO-CaO-Al2O3-SiO2 is reported. Semiempirical phase boundary and elemental distribution information was combined with mass balance to compute approximate equilibrium crystallization paths for arbitrary system compositions. The calculation is applicable to a range of system compositions and fractionation calculations are possible. The goal of the calculation is the computation of the composition and quantity of each phase present as a function of the degree of solidification. The degree of solidification is parameterized by the heat released by the solidifying phases. The mathematical requirement for the solution of this problem is: (1) An equation constraining the composition of the magma for each solid phase in equilibrium with the liquidus phase, and (2) an equation for each solid phase and each component giving the distribution of that element between that phase and the magma.

Driven Langevin systems: fluctuation theorems and faithful dynamics

NASA Astrophysics Data System (ADS)

Sivak, David; Chodera, John; Crooks, Gavin

2014-03-01

Stochastic differential equations of motion (e.g., Langevin dynamics) provide a popular framework for simulating molecular systems. Any computational algorithm must discretize these equations, yet the resulting finite time step integration schemes suffer from several practical shortcomings. We show how any finite time step Langevin integrator can be thought of as a driven, nonequilibrium physical process. Amended by an appropriate work-like quantity (the shadow work), nonequilibrium fluctuation theorems can characterize or correct for the errors introduced by the use of finite time steps. We also quantify, for the first time, the magnitude of deviations between the sampled stationary distribution and the desired equilibrium distribution for equilibrium Langevin simulations of solvated systems of varying size. We further show that the incorporation of a novel time step rescaling in the deterministic updates of position and velocity can correct a number of dynamical defects in these integrators. Finally, we identify a particular splitting that has essentially universally appropriate properties for the simulation of Langevin dynamics for molecular systems in equilibrium, nonequilibrium, and path sampling contexts.

Revisiting kinetic boundary conditions at the surface of fuel droplet hydrocarbons: An atomistic computational fluid dynamics simulation

PubMed Central

Nasiri, Rasoul

2016-01-01

The role of boundary conditions at the interface for both Boltzmann equation and the set of Navier-Stokes equations have been suggested to be important for studying of multiphase flows such as evaporation/condensation process which doesn’t always obey the equilibrium conditions. Here we present aspects of transition-state theory (TST) alongside with kinetic gas theory (KGT) relevant to the study of quasi-equilibrium interfacial phenomena and the equilibrium gas phase processes, respectively. A two-state mathematical model for long-chain hydrocarbons which have multi-structural specifications is introduced to clarify how kinetics and thermodynamics affect evaporation/condensation process at the surface of fuel droplet, liquid and gas phases and then show how experimental observations for a number of n-alkane may be reproduced using a hybrid framework TST and KGT with physically reasonable parameters controlling the interface, gas and liquid phases. The importance of internal activation dynamics at the surface of n-alkane droplets is established during the evaporation/condensation process. PMID:27215897

Magnetospheric equilibrium configurations and slow adiabatic convection

NASA Technical Reports Server (NTRS)

Voigt, Gerd-Hannes

1986-01-01

This review paper demonstrates how the magnetohydrostatic equilibrium (MHE) theory can be used to describe the large-scale magnetic field configuration of the magnetosphere and its time evolution under the influence of magnetospheric convection. The equilibrium problem is reviewed, and levels of B-field modelling are examined for vacuum models, quasi-static equilibrium models, and MHD models. Results from two-dimensional MHE theory as they apply to the Grad-Shafranov equation, linear equilibria, the asymptotic theory, magnetospheric convection and the substorm mechanism, and plasma anisotropies are addressed. Results from three-dimensional MHE theory are considered as they apply to an intermediate analytical magnetospheric model, magnetotail configurations, and magnetopause boundary conditions and the influence of the IMF.