The Approach to Equilibrium: Detailed Balance and the Master Equation

Science.gov (United States)

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…

From statistic mechanic outside equilibrium to transport equations

International Nuclear Information System (INIS)

Balian, R.

1995-01-01

This lecture notes give a synthetic view on the foundations of non-equilibrium statistical mechanics. The purpose is to establish the transport equations satisfied by the relevant variables, starting from the microscopic dynamics. The Liouville representation is introduced, and a projection associates with any density operator , for given choice of relevant observables, a reduced density operator. An exact integral-differential equation for the relevant variables is thereby derived. A short-memory approximation then yields the transport equations. A relevant entropy which characterizes the coarseness of the description is associated with each level of description. As an illustration, the classical gas, with its three levels of description and with the Chapman-Enskog method, is discussed. (author). 3 figs., 5 refs

Calculation of NARM's Equilibrium with Peng-Robinson Equation of State

Institute of Scientific and Technical Information of China (English)

LI Tingxun; GUO Kaihua; WANG Ruzhu; FAN Shuanshi

2001-01-01

The liquid molar volumes of nonazeotropic refrigerant mixtures (NARM), calculated with Peng Robinson (PR)equation, were compared with vapor -liquid equilibrium experimental data in this paper. Provided with coreaction coefficient kij, the discrepancies of liquid molar volume data for R22+Rl14 and R22+R142b using PR equation are 7.7% and 8.1% , respectively. When HBT (Hankinson-Brobst-Thomson) equation was joined with PR equation, the deviations are reduced to less than 1.5% for both R22+Rl14 and R22+R142b.

Simulations of NMR pulse sequences during equilibrium and non-equilibrium chemical exchange

International Nuclear Information System (INIS)

Helgstrand, Magnus; Haerd, Torleif; Allard, Peter

2000-01-01

The McConnell equations combine the differential equations for a simple two-state chemical exchange process with the Bloch differential equations for a classical description of the behavior of nuclear spins in a magnetic field. This equation system provides a useful starting point for the analysis of slow, intermediate and fast chemical exchange studied using a variety of NMR experiments. The McConnell equations are in the mathematical form of an inhomogeneous system of first-order differential equations. Here we rewrite the McConnell equations in a homogeneous form in order to facilitate fast and simple numerical calculation of the solution to the equation system. The McConnell equations can only treat equilibrium chemical exchange. We therefore also present a homogeneous equation system that can handle both equilibrium and non-equilibrium chemical processes correctly, as long as the kinetics is of first-order. Finally, the same method of rewriting the inhomogeneous form of the McConnell equations into a homogeneous form is applied to a quantum mechanical treatment of a spin system in chemical exchange. In order to illustrate the homogeneous McConnell equations, we have simulated pulse sequences useful for measuring exchange rates in slow, intermediate and fast chemical exchange processes. A stopped-flow NMR experiment was simulated using the equations for non-equilibrium chemical exchange. The quantum mechanical treatment was tested by the simulation of a sensitivity enhanced 15 N-HSQC with pulsed field gradients during slow chemical exchange and by the simulation of the transfer efficiency of a two-dimensional heteronuclear cross-polarization based experiment as a function of both chemical shift difference and exchange rate constants

On equilibrium real exchange rates in euro area: Special focus on behavioral equilibrium exchange rates in Ireland and Greece

Directory of Open Access Journals (Sweden)

Klára Plecitá

2012-01-01

Full Text Available This paper focuses on the intra-euro-area imbalances. Therefore the first aim of this paper is to identify euro-area countries exhibiting macroeconomic imbalances. The subsequent aim is to estimate equilibrium real exchange rates for these countries and to compute their degrees of real exchange rate misalignment. The intra-area balance is assessed using the Cluster Analysis and the Principle Component Analysis; on this basis Greece and Ireland are selected as the two euro-area countries with largest imbalances in 2010. Further the medium-run equilibrium exchange rates for Greece and Ireland are estimated applying the Behavioral Equilibrium Exchange Rate (BEER approach popularised by Clark and MacDonald (1998. In addition, the long-run equilibrium exchange rates are estimated using the Permanent Equilibrium Exchange Rate (PEER model. Employing the BEER and PEER approaches on quarterly time series of real effective exchange rates (REER from 1997: Q1 to 2010: Q4 we identify an undervaluation of the Greek and Irish REER around their entrance to the euro area. For the rest of the period analysed their REER is broadly in line with estimated BEER and PEER levels.

Extended rate equations

International Nuclear Information System (INIS)

Shore, B.W.

1981-01-01

The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence

Memory loss process and non-Gibbsian equilibrium solutions of master equations

International Nuclear Information System (INIS)

Cataldo, H.M.; Hernandez, E.S.

1988-01-01

The phonon dynamics of a harmonic oscillator coupled to a steady reservoir is studied. In the Markovian limit, the equilibrium is reached through a progressive loss of memory process which involves the moments of the initial distribution. The relationship to the non-Markovian equations of motion and its resolvent poles is settled. As a particular model of the coupling mechanism is adopted, the possibility of non-Gibbsian equilibrium distribution arises, which is analyzed focusing upon the dependence of various parameters of the system on an effective equilibrium temperature

Heat and fluid flow during rapid solidification of non-equilibrium materials

International Nuclear Information System (INIS)

Negli, S.C.; Eddingfield, D.L.; Brower, W.E. Jr.

1990-01-01

Rapid solidification technology (RST) is an advanced solidification process which is being utilized to produce non-equilibrium structures with properties not previously available with conventionally cast materials. An iron based alloy rapidly quenched to form a metallic glass is being installed on a large scale in electric power transformers where it cuts heat losses dramatically. The formation of a non-equilibrium structure usually requires a cooling rate of at least a million degrees per second. Achieving this high a cooling rate depends not only on the heat transfer conditions during the quenching process, but also on the fluid flow conditions in the molten metal before and during solidification. This paper presents a model of both heat and fluid flow during RST by the hammer and anvil method. The symmetry of two sided cooling permits analysis which is still applicable to the one sided cooling that occurs during melt spinning, the prevalent method of RST. The heat flow is modeled as one dimensional, normal to the quench surface. Previous models have shown the heat flow in the plane of the quench surface not to be significant. The fluid flow portion of the model utilizes the squeeze film solution for flow between two parallel flat plates. The model predicts the effects of superheat of the melt and of the quench hammer speed upon cooling rate during the formation of nonequilibrium phases. An unexpected result is that increased superheat results in much higher cooling rates, due to fluid flow before a potential transformation would take place; this enhanced liquid metal flow results in a thinner section casting which in turn has a dominant effect on the cooling rate. The model also predicts an expanded regime of Newtonian (interface controlled) cooling by about a factor of ten as compared to previous model of RST

Partial chemical equilibrium in fluid dynamics

International Nuclear Information System (INIS)

Ramshaw, J.D.

1980-01-01

An analysis is given for the flow of a multicomponent fluid in which an arbitrary number of chemical reactions may occur, some of which are in equilibrium while the others proceed kinetically. The primitive equations describing this situation are inconvenient to use because the progress rates omega-dot/sub s/ for the equilibrium reactions are determined implicitly by the associated equilibrium constraint conditions. Two alternative equivalent equation systems that are more pleasant to deal with are derived. In the first system, the omega-dot/sub s/ are eliminated by replacing the transport equations for the chemical species involved in the equilibrium reactions with transport equations for the basic components of which these species are composed. The second system retains the usual species transport equations, but eliminates the nonlinear algebraic equilibrium constraint conditions by deriving an explicit expression for the omega-dot/sub s/. Both systems are specialized to the case of an ideal gas mixture. Considerations involved in solving these equation systems numerically are discussed briefly

On Regularly Varying and History-Dependent Convergence Rates of Solutions of a Volterra Equation with Infinite Memory

OpenAIRE

John A. D. Appleby

2010-01-01

We consider the rate of convergence to equilibrium of Volterra integrodifferential equations with infinite memory. We show that if the kernel of Volterra operator is regularly varying at infinity, and the initial history is regularly varying at minus infinity, then the rate of convergence to the equilibrium is regularly varying at infinity, and the exact pointwise rate of convergence can be determined in terms of the rate of decay of the kernel and the rate of growth of the initial history. ...

Evolution of a Network of Vortex Loops in He-II: Exact Solution of the Rate Equation

International Nuclear Information System (INIS)

Nemirovskii, Sergey K.

2006-01-01

The evolution of a network of vortex loops in He-II due to the fusion and breakdown of vortex loops is studied. We perform investigation on the base of the ''rate equation'' for the distribution function n(l) of number of loops of length l. By use of the special ansatz we have found the exact powerlike solution of the rate equation in a stationary case. That solution is the famous equilibrium distribution n(l)∝l -5/2 obtained earlier from thermodynamic arguments. Our result, however, is not equilibrium; it describes the state with two mutual fluxes of the length (or energy) in l space. Analyzing this solution we drew several results on the structure and dynamics of the vortex tangle in the superfluid turbulent helium. In particular, we obtained that the mean radius of the curvature is of the order of interline space and that the decay of the vortex tangle obeys the Vinen equation. We also evaluated the full rate of reconnection

Evolution of a network of vortex loops in He-II: exact solution of the rate equation.

Science.gov (United States)

Nemirovskii, Sergey K

2006-01-13

The evolution of a network of vortex loops in He-II due to the fusion and breakdown of vortex loops is studied. We perform investigation on the base of the "rate equation" for the distribution function n(l) of number of loops of length l. By use of the special ansatz we have found the exact power-like solution of the rate equation in a stationary case. That solution is the famous equilibrium distribution n(l) proportional l(-5/2) obtained earlier from thermodynamic arguments. Our result, however, is not equilibrium; it describes the state with two mutual fluxes of the length (or energy) in l space. Analyzing this solution we drew several results on the structure and dynamics of the vortex tangle in the superfluid turbulent helium. In particular, we obtained that the mean radius of the curvature is of the order of interline space and that the decay of the vortex tangle obeys the Vinen equation. We also evaluated the full rate of reconnection.

Energy equation for the analysis of magnetization relaxation to equilibrium

Energy Technology Data Exchange (ETDEWEB)

Bertotti, G. [IEN Galileo Ferraris, Materials Department, Strada delle Cacce, 91, I-10135 Torino (Italy)]. E-mail: bertotti@ien.it; Bonin, R. [Dipartimento di Fisica, Politecnico di Torino, I-10129 Torino (Italy); Magni, A. [IEN Galileo Ferraris, Materials Department, Strada delle Cacce, 91, I-10135 Torino (Italy); Mayergoyz, I.D. [Department of Electrical and Computer Engineering, University of Maryland, College Park, Maryland, 20742 (United States); Serpico, C. [Dipartimento di Ingegneria Elettrica, Universita di Napoli ' Federico II' , I-80125 Naples (Italy)

2005-02-01

Magnetization relaxation starting from a generic non-equilibrium state is analytically described. An equation for the energy decay is obtained. On this basis, an approximate expression for the magnetization motion during the ringing process is obtained in terms of Jacobi elliptic functions with time-dependent parameters.

Energy equation for the analysis of magnetization relaxation to equilibrium

International Nuclear Information System (INIS)

Bertotti, G.; Bonin, R.; Magni, A.; Mayergoyz, I.D.; Serpico, C.

2005-01-01

Magnetization relaxation starting from a generic non-equilibrium state is analytically described. An equation for the energy decay is obtained. On this basis, an approximate expression for the magnetization motion during the ringing process is obtained in terms of Jacobi elliptic functions with time-dependent parameters

Using Simple Quadratic Equations to Estimate Equilibrium Concentrations of an Acid

Science.gov (United States)

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.

The Donnan equilibrium: I. On the thermodynamic foundation of the Donnan equation of state

NARCIS (Netherlands)

Philipse, A.P.; Vrij, A.

2011-01-01

The thermodynamic equilibrium between charged colloids and an electrolyte reservoir is named after Frederic Donnan who first published on it one century ago (Donnan 1911 Z. Electrochem. 17 572). One of the intriguing features of the Donnan equilibrium is the ensuing osmotic equation of state which

On a class of quantum Langevin equations and the question of approach to equilibrium

International Nuclear Information System (INIS)

Maassen, J.D.M.

1982-01-01

This thesis is concerned with a very simple 'open' quantum system, i.e. being in contact with the outer world. It is asked whether the motion of this system shows frictional behaviour in that it tends to thermal equilibrium. A partial positive answer is given to this question, more precisely, to the question if the solution of the quantum mechanical Langevin equation that describes the Lamb-model (a harmonic oscillator damped by coupling with a string), approaches an equilibrium state. In two sections, the classical and quantum Langevin equations are treated analogously. (Auth.)

Non-equilibrium Economics

Directory of Open Access Journals (Sweden)

Katalin Martinás

2007-02-01

Full Text Available A microeconomic, agent based framework to dynamic economics is formulated in a materialist approach. An axiomatic foundation of a non-equilibrium microeconomics is outlined. Economic activity is modelled as transformation and transport of commodities (materials owned by the agents. Rate of transformations (production intensity, and the rate of transport (trade are defined by the agents. Economic decision rules are derived from the observed economic behaviour. The non-linear equations are solved numerically for a model economy. Numerical solutions for simple model economies suggest that the some of the results of general equilibrium economics are consequences only of the equilibrium hypothesis. We show that perfect competition of selfish agents does not guarantee the stability of economic equilibrium, but cooperativity is needed, too.

A general nonlinear evolution equation for irreversible conservative approach to stable equilibrium

International Nuclear Information System (INIS)

Beretta, G.P.

1986-01-01

This paper addresses a mathematical problem relevant to the question of nonequilibrium and irreversibility, namely, that of ''designing'' a general evolution equation capable of describing irreversible but conservative relaxtion towards equilibrium. The objective is to present an interesting mathematical solution to this design problem, namely, a new nonlinear evolution equation that satisfies a set of very stringent relevant requirements. Three different frameworks are defined from which the new equation could be adopted, with entirely different interpretations. Some useful well-known mathematics involving Gram determinants are presented and a nonlinear evolution equation is given which meets the stringent design specifications

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

Science.gov (United States)

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.

Finding equilibrium in the spatiotemporal chaos of the complex Ginzburg-Landau equation

Science.gov (United States)

Ballard, Christopher C.; Esty, C. Clark; Egolf, David A.

2016-11-01

Equilibrium statistical mechanics allows the prediction of collective behaviors of large numbers of interacting objects from just a few system-wide properties; however, a similar theory does not exist for far-from-equilibrium systems exhibiting complex spatial and temporal behavior. We propose a method for predicting behaviors in a broad class of such systems and apply these ideas to an archetypal example, the spatiotemporal chaotic 1D complex Ginzburg-Landau equation in the defect chaos regime. Building on the ideas of Ruelle and of Cross and Hohenberg that a spatiotemporal chaotic system can be considered a collection of weakly interacting dynamical units of a characteristic size, the chaotic length scale, we identify underlying, mesoscale, chaotic units and effective interaction potentials between them. We find that the resulting equilibrium Takahashi model accurately predicts distributions of particle numbers. These results suggest the intriguing possibility that a class of far-from-equilibrium systems may be well described at coarse-grained scales by the well-established theory of equilibrium statistical mechanics.

Dynamical equations for time-ordered Green’s functions: from the Keldysh time-loop contour to equilibrium at finite and zero temperature

International Nuclear Information System (INIS)

Ness, H; Dash, L K

2012-01-01

We study the dynamical equation of the time-ordered Green’s function at finite temperature. We show that the time-ordered Green’s function obeys a conventional Dyson equation only at equilibrium and in the limit of zero temperature. In all other cases, i.e. finite temperature at equilibrium or non-equilibrium, the time-ordered Green’s function obeys instead a modified Dyson equation. The derivation of this result is obtained from the general formalism of the non-equilibrium Green’s functions on the Keldysh time-loop contour. At equilibrium, our result is fully consistent with the Matsubara temperature Green’s function formalism and also justifies rigorously the correction terms introduced in an ad hoc way with Hedin and Lundqvist. Our results show that one should use the appropriate dynamical equation for the time-ordered Green’s function when working beyond the equilibrium zero-temperature limit.

Stochastic approach to equilibrium and nonequilibrium thermodynamics.

Science.gov (United States)

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.

The Donnan equilibrium: I. On the thermodynamic foundation of the Donnan equation of state

International Nuclear Information System (INIS)

Philipse, A; Vrij, A

2011-01-01

The thermodynamic equilibrium between charged colloids and an electrolyte reservoir is named after Frederic Donnan who first published on it one century ago (Donnan 1911 Z. Electrochem. 17 572). One of the intriguing features of the Donnan equilibrium is the ensuing osmotic equation of state which is a nonlinear one, even when both colloids and ions obey Van 't Hoff's ideal osmotic pressure law. The Donnan equation of state, nevertheless, is internally consistent; we demonstrate it to be a rigorous consequence of the phenomenological thermodynamics of a neutral bulk suspension equilibrating with an infinite salt reservoir. Our proof is based on an exact thermodynamic relation between osmotic pressure and salt adsorption which, when applied to ideal ions, does indeed entail the Donnan equation of state. Our derivation also shows that, contrary to what is often assumed, the Donnan equilibrium does not require ideality of the colloids: the Donnan model merely evaluates the osmotic pressure of homogeneously distributed ions, in excess of the pressure exerted by an arbitrary reference fluid of uncharged colloids. We also conclude that results from the phenomenological Donnan model coincide with predictions from statistical thermodynamics in the limit of weakly charged, point-like colloids.

The Estimation of the Equilibrium Real Exchange Rate for Romania

OpenAIRE

Bogdan Andrei Dumitrescu; Vasile Dedu

2009-01-01

This paper aims to estimate the equilibrium real exchange rate for Romania, respectively the real exchange rate consistent with the macroeconomic balance, which is achieved when the economy is operating at full employment and low inflation (internal balance) and has a current account that is sustainable (external balance). This equilibrium real exchange rate is very important for an economy because deviations of the real exchange rate from its equilibrium value can affect the competitiveness ...

Arsenic Adsorption Equilibrium Concentration and Adsorption Rate of Activated Carbon Coated with Ferric-Aluminum Hydroxides

Science.gov (United States)

Zhang, M.; Sugita, H.; Oguma, T.; Hara, J.; Takahashi, S.

2015-12-01

In some areas of developing countries, ground or well water contaminated with arsenic has been reluctantly used as drinking water. It is highly desirable that effective and inexpensive arsenic removal agents should be developed and provided to reduce the potential health risk. Previous studies demonstrated that activated carbon coated with ferric-aluminum hydroxides (Fe-Al-C) has high adsorptive potential for removal of arsenic. In this study, a series of experiments using Fe-Al-C were carried to discuss adsorption equilibrium time, adsorption equilibrium concentration and adsorption rate of arsenic for Fe-Al-C. Fe-Al-C used in this study was provided by Astec Co., Ltd. Powder reagent of disodium hydrogen arsenate heptahydrate was dissolved into ion-exchanged water. The solution was then further diluted with ion-exchanged water to be 1 and 10 mg/L as arsenic concentration. The pH of the solution was adjusted to be around 7 by adding HCl and/or NaOH. The solution was used as artificial arsenic contaminated water in two types of experiments (arsenic adsorption equilibrium and arsenic adsorption rate tests). The results of the arsenic equilibrium tests were showed that a time period of about 3 days to reach apparent adsorption equilibrium for arsenic. The apparent adsorption equilibrium concentration and adsorbed amount of arsenic on Fe-Al-C adsorbent could be estimated by application of various adsorption isotherms, but the distribution coefficient of arsenic between solid and liquid varies with experimental conditions such as initial concentration of arsenic and addition concentration of adsorbent. An adsorption rate equation that takes into account the reduction in the number of effective adsorption sites on the adsorbent caused by the arsenic adsorption reaction was derived based on the data obtained from the arsenic adsorption rate tests.

A new perspective on the electron transfer: recovering the Butler-Volmer equation in non-equilibrium thermodynamics.

Science.gov (United States)

Dreyer, Wolfgang; Guhlke, Clemens; Müller, Rüdiger

2016-09-28

Electron transfer reactions are commonly described by the phenomenological Butler-Volmer equation which has its origin in kinetic theories. The Butler-Volmer equation relates interfacial reaction rates to bulk quantities like the electrostatic potential and electrolyte concentrations. Although the general structure of the equation is well accepted, for modern electrochemical systems like batteries and fuel cells there is still intensive discussion about the specific dependencies of the coefficients. A general guideline for the derivation of Butler-Volmer type equations is missing in the literature. We derive very general relations of Butler-Volmer structure which are based on a rigorous non-equilibrium thermodynamic model and allow for adaption to a wide variety of electrochemical systems. We discuss the application of the new thermodynamic approach to different scenarios like the classical electron transfer reactions at metal electrodes and the intercalation process in lithium-iron-phosphate electrodes. Furthermore we show that under appropriate conditions also adsorption processes can lead to Butler-Volmer equations. We illustrate the application of our theory by a strongly simplified example of electroplating.

On the use temperature parameterized rate coefficients in the estimation of non-equilibrium reaction rates

Science.gov (United States)

Shizgal, Bernie D.; Chikhaoui, Aziz

2006-06-01

The present paper considers a detailed analysis of the nonequilibrium effects for a model reactive system with the Chapman-Eskog (CE) solution of the Boltzmann equation as well as an explicit time dependent solution. The elastic cross sections employed are a hard sphere cross section and the Maxwell molecule cross section. Reactive cross sections which model reactions with and without activation energy are used. A detailed comparison is carried out with these solutions of the Boltzmann equation and the approximation introduced by Cukrowski and coworkers [J. Chem. Phys. 97 (1992) 9086; Chem. Phys. 89 (1992) 159; Physica A 188 (1992) 344; Chem. Phys. Lett. A 297 (1998) 402; Physica A 275 (2000) 134; Chem. Phys. Lett. 341 (2001) 585; Acta Phys. Polonica B 334 (2003) 3607.] based on the temperature of the reactive particles. We show that the Cukrowski approximation has limited applicability for the large class of reactive systems studied in this paper. The explicit time dependent solutions of the Boltzmann equation demonstrate that the CE approach is valid only for very slow reactions for which the corrections to the equilibrium rate coefficient are very small.

Travelling wave solutions for the Richards equation incorporating non-equilibrium effects in the capillarity pressure

NARCIS (Netherlands)

van Duijn, C. J.; Mitra, K.; Pop, I. S.

2018-01-01

The Richards equation is a mathematical model for unsaturated flow through porous media. This paper considers an extension of the Richards equation, where non-equilibrium effects like hysteresis and dynamic capillarity are incorporated in the relationship that relates the water pressure and the

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

Science.gov (United States)

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.

Vapour-liquid equilibrium properties for two- and three-dimensional Lennard-Jones fluids from equations of state

International Nuclear Information System (INIS)

Mulero, A.; Cuadros, F; Faundez, C.A.

1999-01-01

Vapour-liquid equilibrium properties for both three- and two-dimensional Lennard-Jones fluids were obtained using simple cubic-in-density equations of state proposed by the authors. Results were compared with those obtained by other workers from computer simulations and also with results given by other more complex semi-theoretical or semi-empirical equations of state. In the three-dimensional case good agreement is found for all properties and all temperatures. In the two-dimensional case only the coexistence densities were compared, producing good agreement for low temperatures only. The present work is the first to give numerical data for the vapour-liquid equilibrium properties of Lennard-Jones fluids calculated from equations of state. Copyright (1999) CSIRO Australia

Comments on equilibrium, transient equilibrium, and secular equilibrium in serial radioactive decay

International Nuclear Information System (INIS)

Prince, J.R.

1979-01-01

Equations describing serial radioactive decay are reviewed along with published descriptions or transient and secular equilibrium. It is shown that terms describing equilibrium are not used in the same way by various authors. Specific definitions are proposed; they suggest that secular equilibrium is a subset of transient equilibrium

Vapor-liquid equilibrium prediction with pseudo-cubic equation of state for binary mixtures containing hydrogen, helium, or neon

Energy Technology Data Exchange (ETDEWEB)

Kato, M.; Tanaka, H. (Nihon Univ.,Fukushima, (Japan). Faculty of Enineering)

1990-03-01

As an equation of state of vapor-liquid equilibrium, an original pseudo-cubic equation of state was previously proposed by the authors of this report and its study is continued. In the present study, new effective critical values of hydrogen, helium and neon were determined empirically from vapor-liquid equilibrium data of literature values against their critical temperatures, critical pressures and critical volumes. The vapor-liquid equilibrium relations of binary system quantum gas mixtures were predicted combining the conventinal pseudo-cubic equation of state and the new effective critical values, and without using binary heteromolecular interaction parameter. The predicted values of hydrogen-ethylene, helium-propane and neon-oxygen systems were compared with literature values. As a result, it was indicated that the vapor-liquid relations of binary system mixtures containing hydrogen, helium and neon can be predicted with favorable accuracy combining the effective critical values and the three parameter pseudo-cubic equation of state. 37 refs., 3 figs., 4 tabs.

Chemical reaction rates and non-equilibrium pressure of reacting gas mixtures in the state-to-state approach

International Nuclear Information System (INIS)

Kustova, Elena V.; Kremer, Gilberto M.

2014-01-01

Highlights: • State-to-state approach for coupled vibrational relaxation and chemical reactions. • Self-consistent model for rates of non-equilibrium reactions and energy transitions. • In viscous flows mass action law is violated. • Cross coupling between reaction rates and non-equilibrium pressure in viscous flow. • Results allow implementing the state-to-state approach for viscous flow simulations. - Abstract: Viscous gas flows with vibrational relaxation and chemical reactions in the state-to-state approach are analyzed. A modified Chapman–Enskog method is used for the determination of chemical reaction and vibrational transition rates and non-equilibrium pressure. Constitutive equations depend on the thermodynamic forces: velocity divergence and chemical reaction/transition affinity. As an application, N 2 flow with vibrational relaxation across a shock wave is investigated. Two distinct processes occur behind the shock: for small values of the distance the affinity is large and vibrational relaxation is in its initial stage; for large distances the affinity is small and the chemical reaction is in its final stage. The affinity contributes more to the transition rate than the velocity divergence and the effect of these two contributions are more important for small distances from the shock front. For the non-equilibrium pressure, the term associated with the bulk viscosity increases by a small amount the hydrostatic pressure

Chemical reaction rates and non-equilibrium pressure of reacting gas mixtures in the state-to-state approach

Energy Technology Data Exchange (ETDEWEB)

Kustova, Elena V., E-mail: e.kustova@spbu.ru [Department of Mathematics and Mechanics, Saint Petersburg State University, 198504 Universitetskiy pr. 28, Saint Petersburg (Russian Federation); Kremer, Gilberto M., E-mail: kremer@fisica.ufpr.br [Departamento de Física, Universidade Federal do Paraná, Caixa Postal 19044, 81531-980 Curitiba (Brazil)

2014-12-05

Highlights: • State-to-state approach for coupled vibrational relaxation and chemical reactions. • Self-consistent model for rates of non-equilibrium reactions and energy transitions. • In viscous flows mass action law is violated. • Cross coupling between reaction rates and non-equilibrium pressure in viscous flow. • Results allow implementing the state-to-state approach for viscous flow simulations. - Abstract: Viscous gas flows with vibrational relaxation and chemical reactions in the state-to-state approach are analyzed. A modified Chapman–Enskog method is used for the determination of chemical reaction and vibrational transition rates and non-equilibrium pressure. Constitutive equations depend on the thermodynamic forces: velocity divergence and chemical reaction/transition affinity. As an application, N{sub 2} flow with vibrational relaxation across a shock wave is investigated. Two distinct processes occur behind the shock: for small values of the distance the affinity is large and vibrational relaxation is in its initial stage; for large distances the affinity is small and the chemical reaction is in its final stage. The affinity contributes more to the transition rate than the velocity divergence and the effect of these two contributions are more important for small distances from the shock front. For the non-equilibrium pressure, the term associated with the bulk viscosity increases by a small amount the hydrostatic pressure.

Stochastic substitute for coupled rate equations in the modeling of highly ionized transient plasmas

International Nuclear Information System (INIS)

Eliezer, S.; Falquina, R.; Minguez, E.

1994-01-01

Plasmas produced by intense laser pulses incident on solid targets often do not satisfy the conditions for local thermodynamic equilibrium, and so cannot be modeled by transport equations relying on equations of state. A proper description involves an excessively large number of coupled rate equations connecting many quantum states of numerous species having different degrees of ionization. Here we pursue a recent suggestion to model the plasma by a few dominant states perturbed by a stochastic driving force. The driving force is taken to be a Poisson impulse process, giving a Langevin equation which is equivalent to a Fokker-Planck equation for the probability density governing the distribution of electron density. An approximate solution to the Langevin equation permits calculation of the characteristic relaxation rate. An exact stationary solution to the Fokker-Planck equation is given as a function of the strength of the stochastic driving force. This stationary solution is used, along with a Laplace transform, to convert the Fokker-Planck equation to one of Schroedinger type. We consider using the classical Hamiltonian formalism and the WKB method to obtain the time-dependent solution

On the fundamental equation of nonequilibrium statistical physics—Nonequilibrium entropy evolution equation and the formula for entropy production rate

Institute of Scientific and Technical Information of China (English)

无

2010-01-01

another entropy increase rate, obtained a theoretical expression for unifying thermodynamic degradation and self-organizing evolution, and revealed that the entropy diffusion mechanism caused the system to approach to equilibrium. As application, we used these entropy formulas in calculating and discussing some actual physical topics in the nonequilibrium and stationary states. All these derivations and results are unified and rigorous from the new fundamental equation without adding any extra new assumption.

Estimating the equilibrium real exchange rate in Venezuela

OpenAIRE

Hilde Bjørnland

2004-01-01

To determine whether the real exchange rate is misaligned with respect to its long-run equilibrium is an important issue for policy makers. This paper clarifies and calculates the concept of the equilibrium real exchange rate, using a structural vector autoregression (VAR) model. By imposing long-run restrictions on a VAR model for Venezuela, four structural shocks are identified: Nominal demand, real demand, supply and oil price shocks. The identified shocks and their impulse responses are c...

MHD equilibrium with toroidal rotation

International Nuclear Information System (INIS)

Li, J.

1987-03-01

The present work attempts to formulate the equilibrium of axisymmetric plasma with purely toroidal flow within ideal MHD theory. In general, the inertial term Rho(v.Del)v caused by plasma flow is so complicated that the equilibrium equation is completely different from the Grad-Shafranov equation. However, in the case of purely toroidal flow the equilibrium equation can be simplified so that it resembles the Grad-Shafranov equation. Generally one arbitrary two-variable functions and two arbitrary single variable functions, instead of only four single-variable functions, are allowed in the new equilibrium equations. Also, the boundary conditions of the rotating (with purely toroidal fluid flow, static - without any fluid flow) equilibrium are the same as those of the static equilibrium. So numerically one can calculate the rotating equilibrium as a static equilibrium. (author)

Non-equilibrium Quasi-Chemical Nucleation Model

Science.gov (United States)

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.

A control volume based finite difference method for solving the equilibrium equations in terms of displacements

DEFF Research Database (Denmark)

Hattel, Jesper; Hansen, Preben

1995-01-01

This paper presents a novel control volume based FD method for solving the equilibrium equations in terms of displacements, i.e. the generalized Navier equations. The method is based on the widely used cv-FDM solution of heat conduction and fluid flow problems involving a staggered grid formulati....... The resulting linear algebraic equations are solved by line-Gauss-Seidel....

A moving mesh finite difference method for equilibrium radiation diffusion equations

Energy Technology Data Exchange (ETDEWEB)

Yang, Xiaobo, E-mail: xwindyb@126.com [Department of Mathematics, College of Science, China University of Mining and Technology, Xuzhou, Jiangsu 221116 (China); Huang, Weizhang, E-mail: whuang@ku.edu [Department of Mathematics, University of Kansas, Lawrence, KS 66045 (United States); Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn [School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing, Xiamen University, Xiamen, Fujian 361005 (China)

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 nonnegativity 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.

A moving mesh finite difference method for equilibrium radiation diffusion equations

International Nuclear Information System (INIS)

Yang, Xiaobo; Huang, Weizhang; Qiu, Jianxian

2015-01-01

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 nonnegativity 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

BREIT code: Analytical solution of the balance rate equations for charge-state evolutions of heavy-ion beams in matter

Energy Technology Data Exchange (ETDEWEB)

Winckler, N., E-mail: n.winckler@gsi.de [GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt (Germany); Rybalchenko, A. [GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt (Germany); Shevelko, V.P. [P.N. Lebedev Physical Institute, 119991 Moscow (Russian Federation); Al-Turany, M. [GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt (Germany); CERN, European Organization for Nuclear Research, 1211 Geneve 23 (Switzerland); Kollegger, T. [GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt (Germany); Stöhlker, Th. [GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt (Germany); Helmholtz-Institute Jena, D-07743 Jena (Germany); Institut für Optik und Quantenelektronik, Friedrich-Schiller-Universität, D-07743 Jena (Germany)

2017-02-01

A detailed description of a recently developed BREIT computer code (Balance Rate Equations of Ion Transportation) for calculating charge-state fractions of ion beams passing through matter is presented. The code is based on the analytical solutions of the differential balance equations for the charge-state fractions as a function of the target thickness and can be used for calculating the ion evolutions in gaseous, solid and plasma targets. The BREIT code is available on-line and requires the charge-changing cross sections and initial conditions in the input file. The eigenvalue decomposition method, applied to obtain the analytical solutions of the rate equations, is described in the paper. Calculations of non-equilibrium and equilibrium charge-state fractions, performed by the BREIT code, are compared with experimental data and results of other codes for ion beams in gaseous and solid targets. Ability and limitations of the BREIT code are discussed in detail.

Equilibrium and non-equilibrium charge-state distributions of 2.0 MeV/u carbon ions passing through carbon foils

International Nuclear Information System (INIS)

Imai, M.; Sataka, M.; Matsuda, M.; Okayasu, S.; Kawatsura, K.; Takahiro, K.; Komaki, K.; Shibata, H.; Nishio, K.

2015-01-01

Both equilibrium and non-equilibrium charge-state distributions were studied experimentally for 2.0 MeV/u carbon ions after passing through carbon foils. Measured charge-state distribution established the equilibrium at a target thickness of 10 μg/cm 2 and this remained unchanged until a maximum target thickness of 98 μg/cm 2 . The equilibrium charge-state distribution, the equilibrium mean charge-state, and the width and skewness of the equilibrium distribution were compared with predictions using existing semi-empirical formulae as well as simulation results, including the ETACHA code. It was found that charge-state distributions, mean charge states, and distribution widths for C 2+ , C 3+ , and C 4+ incident ions merged into quasi-equilibrium values at a target thickness of 5.7 μg/cm 2 in the pre-equilibrium region and evolved simultaneously to the ‘real equilibrium’ values for all of the initial charge states, including C 5+ and C 6+ ions, as previously demonstrated for sulfur projectile ions at the same velocity (Imai et al., 2009). Two kinds of simulation, ETACHA and solution of rate equations taking only single electron transfers into account, were used, and both of them reproduced the measured charge evolution qualitatively. The quasi-equilibrium behavior could be reproduced with the ETACHA code, but not with solution of elementary rate equations

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

Science.gov (United States)

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…

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

Science.gov (United States)

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.

Description of the approach to equilibrium in the Boltzmann equation

Energy Technology Data Exchange (ETDEWEB)

Barrachina, R.O.; Fujii, D.H.; Garibotti, C.R.

1985-06-01

An integral transform of the Boltzmann equation with a clear physical interpretation is introduced. It is applied to different interaction models and initial conditions, relevant information about the way the equilibrium is reached. This method leads quite naturally to the introduction of an N-pole approximant of the distribution function which seems to be a rather useful technique not only in view of its simplicity but also because of its capability to keep track of the temporal evolution features of the chosen interaction model. 6 references.

submitter BREIT code: Analytical solution of the balance rate equations for charge-state evolutions of heavy-ion beams in matter

CERN Document Server

Winckler, N; Shevelko, V P; Al-Turany, M; Kollegger, T; Stöhlker, Th

2017-01-01

A detailed description of a recently developed BREIT computer code (Balance Rate Equations of Ion Transportation) for calculating charge-state fractions of ion beams passing through matter is presented. The code is based on the analytical solutions of the differential balance equations for the charge-state fractions as a function of the target thickness and can be used for calculating the ion evolutions in gaseous, solid and plasma targets. The BREIT code is available on-line and requires the charge-changing cross sections and initial conditions in the input file. The eigenvalue decomposition method, applied to obtain the analytical solutions of the rate equations, is described in the paper. Calculations of non-equilibrium and equilibrium charge-state fractions, performed by the BREIT code, are compared with experimental data and results of other codes for ion beams in gaseous and solid targets. Ability and limitations of the BREIT code are discussed in detail.

Maintenance of equilibrium point control during an unexpectedly loaded rapid limb movement.

Science.gov (United States)

Simmons, R W; Richardson, C

1984-06-08

Two experiments investigated whether the equilibrium point hypothesis or the mass-spring model of motor control subserves positioning accuracy during spring loaded, rapid, bi-articulated movement. For intact preparations, the equilibrium point hypothesis predicts response accuracy to be determined by a mixture of afferent and efferent information, whereas the mass-spring model predicts positioning to be under a direct control system. Subjects completed a series of load-resisted training trials to a spatial target. The magnitude of a sustained spring load was unexpectedly increased on selected trials. Results indicated positioning accuracy and applied force varied with increases in load, which suggests that the original efferent commands are modified by afferent information during the movement as predicted by the equilibrium point hypothesis.

Non-Equilibrium Liouville and Wigner Equations: Moment Methods and Long-Time Approximations

Directory of Open Access Journals (Sweden)

Ramon F. Álvarez-Estrada

2014-03-01

Full Text Available We treat the non-equilibrium evolution of an open one-particle statistical system, subject to a potential and to an external “heat bath” (hb with negligible dissipation. For the classical equilibrium Boltzmann distribution, Wc,eq, a non-equilibrium three-term hierarchy for moments fulfills Hermiticity, which allows one to justify an approximate long-time thermalization. That gives partial dynamical support to Boltzmann’s Wc,eq, out of the set of classical stationary distributions, Wc;st, also investigated here, for which neither Hermiticity nor that thermalization hold, in general. For closed classical many-particle systems without hb (by using Wc,eq, the long-time approximate thermalization for three-term hierarchies is justified and yields an approximate Lyapunov function and an arrow of time. The largest part of the work treats an open quantum one-particle system through the non-equilibrium Wigner function, W. Weq for a repulsive finite square well is reported. W’s (< 0 in various cases are assumed to be quasi-definite functionals regarding their dependences on momentum (q. That yields orthogonal polynomials, HQ,n(q, for Weq (and for stationary Wst, non-equilibrium moments, Wn, of W and hierarchies. For the first excited state of the harmonic oscillator, its stationary Wst is a quasi-definite functional, and the orthogonal polynomials and three-term hierarchy are studied. In general, the non-equilibrium quantum hierarchies (associated with Weq for the Wn’s are not three-term ones. As an illustration, we outline a non-equilibrium four-term hierarchy and its solution in terms of generalized operator continued fractions. Such structures also allow one to formulate long-time approximations, but make it more difficult to justify thermalization. For large thermal and de Broglie wavelengths, the dominant Weq and a non-equilibrium equation for W are reported: the non-equilibrium hierarchy could plausibly be a three-term one and possibly not

A new equation of state Based on Nuclear Statistical Equilibrium for Core-Collapse Simulations

Science.gov (United States)

Furusawa, Shun; Yamada, Shoichi; Sumiyoshi, Kohsuke; Suzuki, Hideyuki

2012-09-01

We calculate a new equation of state for baryons at sub-nuclear densities for the use in core-collapse simulations of massive stars. The formulation is the nuclear statistical equilibrium description and the liquid drop approximation of nuclei. The model free energy to minimize is calculated by 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 on the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores.

The Rate-Controlled Constrained-Equilibrium Approach to Far-From-Local-Equilibrium Thermodynamics

Directory of Open Access Journals (Sweden)

Hameed Metghalchi

2012-01-01

Full Text Available The Rate-Controlled Constrained-Equilibrium (RCCE method for the description of the time-dependent behavior of dynamical systems in non-equilibrium states is a general, effective, physically based method for model order reduction that was originally developed in the framework of thermodynamics and chemical kinetics. A generalized mathematical formulation is presented here that allows including nonlinear constraints in non-local equilibrium systems characterized by the existence of a non-increasing Lyapunov functional under the system’s internal dynamics. The generalized formulation of RCCE enables to clarify the essentials of the method and the built-in general feature of thermodynamic consistency in the chemical kinetics context. In this paper, we work out the details of the method in a generalized mathematical-physics framework, but for definiteness we detail its well-known implementation in the traditional chemical kinetics framework. We detail proofs and spell out explicit functional dependences so as to bring out and clarify each underlying assumption of the method. In the standard context of chemical kinetics of ideal gas mixtures, we discuss the relations between the validity of the detailed balance condition off-equilibrium and the thermodynamic consistency of the method. We also discuss two examples of RCCE gas-phase combustion calculations to emphasize the constraint-dependent performance of the RCCE method.

Development of the PARVMEC Code for Rapid Analysis of 3D MHD Equilibrium

Science.gov (United States)

Seal, Sudip; Hirshman, Steven; Cianciosa, Mark; Wingen, Andreas; Unterberg, Ezekiel; Wilcox, Robert; ORNL Collaboration

2015-11-01

The VMEC three-dimensional (3D) MHD equilibrium has been used extensively for designing stellarator experiments and analyzing experimental data in such strongly 3D systems. Recent applications of VMEC include 2D systems such as tokamaks (in particular, the D3D experiment), where application of very small (delB/B ~ 10-3) 3D resonant magnetic field perturbations render the underlying assumption of axisymmetry invalid. In order to facilitate the rapid analysis of such equilibria (for example, for reconstruction purposes), we have undertaken the task of parallelizing the VMEC code (PARVMEC) to produce a scalable and temporally rapidly convergent equilibrium code for use on parallel distributed memory platforms. The parallelization task naturally splits into three distinct parts 1) radial surfaces in the fixed-boundary part of the calculation; 2) two 2D angular meshes needed to compute the Green's function integrals over the plasma boundary for the free-boundary part of the code; and 3) block tridiagonal matrix needed to compute the full (3D) pre-conditioner near the final equilibrium state. Preliminary results show that scalability is achieved for tasks 1 and 3, with task 2 still nearing completion. The impact of this work on the rapid reconstruction of D3D plasmas using PARVMEC in the V3FIT code will be discussed. Work supported by U.S. DOE under Contract DE-AC05-00OR22725 with UT-Battelle, LLC.

Two-temperature chemically non-equilibrium modelling of an air supersonic ICP

Energy Technology Data Exchange (ETDEWEB)

El Morsli, Mbark; Proulx, Pierre [Laboratoire de Modelisation de Procedes Chimiques par Ordinateur Oppus, Departement de Genie Chimique, Universite de Sherbrooke (Ciheam) J1K 2R1 (Canada)

2007-08-21

In this work, a non-equilibrium mathematical model for an air inductively coupled plasma torch with a supersonic nozzle is developed without making thermal and chemical equilibrium assumptions. Reaction rate equations are written, and two coupled energy equations are used, one for the calculation of the translational-rotational temperature T{sub hr} and one for the calculation of the electro-vibrational temperature T{sub ev}. The viscous dissipation is taken into account in the translational-rotational energy equation. The electro-vibrational energy equation also includes the pressure work of the electrons, the Ohmic heating power and the exchange due to elastic collision. Higher order approximations of the Chapman-Enskog method are used to obtain better accuracy for transport properties, taking advantage of the most recent sets of collisions integrals available in the literature. The results obtained are compared with those obtained using a chemical equilibrium model and a one-temperature chemical non-equilibrium model. The influence of the power and the pressure chamber on the chemical and thermal non-equilibrium is investigated.

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

Science.gov (United States)

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

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

International Nuclear Information System (INIS)

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

2014-01-01

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

Equilibrium reconstruction in the TCA/Br tokamak

International Nuclear Information System (INIS)

Sa, Wanderley Pires de

1996-01-01

The accurate and rapid determination of the Magnetohydrodynamic (MHD) equilibrium configuration in tokamaks is a subject for the magnetic confinement of the plasma. With the knowledge of characteristic plasma MHD equilibrium parameters it is possible to control the plasma position during its formation using feed-back techniques. It is also necessary an on-line analysis between successive discharges to program external parameters for the subsequent discharges. In this work it is investigated the MHD equilibrium configuration reconstruction of the TCA/BR tokamak from external magnetic measurements, using a method that is able to fast determine the main parameters of discharge. The thesis has two parts. Firstly it is presented the development of an equilibrium code that solves de Grad-Shafranov equation for the TCA/BR tokamak geometry. Secondly it is presented the MHD equilibrium reconstruction process from external magnetic field and flux measurements using the Function Parametrization FP method. this method. This method is based on the statistical analysis of a database of simulated equilibrium configurations, with the goal of obtaining a simple relationship between the parameters that characterize the equilibrium and the measurements. The results from FP are compared with conventional methods. (author)

Adiabatic out-of-equilibrium solutions to the Boltzmann equation in warm inflation

Science.gov (United States)

Bastero-Gil, Mar; Berera, Arjun; Ramos, Rudnei O.; Rosa, João G.

2018-02-01

We show that, in warm inflation, the nearly constant Hubble rate and temperature lead to an adiabatic evolution of the number density of particles interacting with the thermal bath, even if thermal equilibrium cannot be maintained. In this case, the number density is suppressed compared to the equilibrium value but the associated phase-space distribution retains approximately an equilibrium form, with a smaller amplitude and a slightly smaller effective temperature. As an application, we explicitly construct a baryogenesis mechanism during warm inflation based on the out-of-equilibrium decay of particles in such an adiabatically evolving state. We show that this generically leads to small baryon isocurvature perturbations, within the bounds set by the Planck satellite. These are correlated with the main adiabatic curvature perturbations but exhibit a distinct spectral index, which may constitute a smoking gun for baryogenesis during warm inflation. Finally, we discuss the prospects for other applications of adiabatically evolving out-of-equilibrium states.

On equilibrium real exchange rates in euro area: Special focus on behavioral equilibrium exchange rates in Ireland and Greece

OpenAIRE

Klára Plecitá; Luboš Střelec

2012-01-01

This paper focuses on the intra-euro-area imbalances. Therefore the first aim of this paper is to identify euro-area countries exhibiting macroeconomic imbalances. The subsequent aim is to estimate equilibrium real exchange rates for these countries and to compute their degrees of real exchange rate misalignment. The intra-area balance is assessed using the Cluster Analysis and the Principle Component Analysis; on this basis Greece and Ireland are selected as the two euro-area countries with ...

Equilibrium exchange rate assessment in Serbia using the IMF external sustainability approach

Directory of Open Access Journals (Sweden)

Pažun Brankica

2014-01-01

Full Text Available The exchange rate has always been a topical issue, particularly in the last two decades, at the time of strong world economy globalisation, as well as liberalization of international flows of goods, services and factors of production, which has resulted in stronger trade and financial integration. There has been a rise in the share of trade in world GDP. Growing developing countries contribute significantly to this growth, which is evident from the data that show increase of their share in world trade , as well as their importance in international capital flows. One of the most important concepts in open macroeconomics is the equilibrium real exchange rate - ERER. Deviations of the real exchange rate are considered to be the cause of the loss of competitiveness and economic slowdown, as well as possible currency crisis (overvaluation and undervaluation. Disadvantages of traditional concepts in exchange rate assessment which are very often reflected in unsuccessful empirical results, motivate experts to seek alternative models to assist in equilibrium exchange rate analysis. This paper aims to present one of three complementary methodologies used by the International Monetary Fund, for the equilibrium real exchange rate assessment in Serbia, as well as the deviation of the real exchange rate from its (estimated equilibrium, that is external sustainability approach.

Derivation of the chemical-equilibrium rate coefficient using scattering theory

Science.gov (United States)

Mickens, R. E.

1977-01-01

Scattering theory is applied to derive the equilibrium rate coefficient for a general homogeneous chemical reaction involving ideal gases. The reaction rate is expressed in terms of the product of a number of normalized momentum distribution functions, the product of the number of molecules with a given internal energy state, and the spin-averaged T-matrix elements. An expression for momentum distribution at equilibrium for an arbitrary molecule is presented, and the number of molecules with a given internal-energy state is represented by an expression which includes the partition function.

Equilibrium and non-equilibrium dynamics simultaneously operate in the Galápagos islands.

Science.gov (United States)

Valente, Luis M; Phillimore, Albert B; Etienne, Rampal S

2015-08-01

Island biotas emerge from the interplay between colonisation, speciation and extinction and are often the scene of spectacular adaptive radiations. A common assumption is that insular diversity is at a dynamic equilibrium, but for remote islands, such as Hawaii or Galápagos, this idea remains untested. Here, we reconstruct the temporal accumulation of terrestrial bird species of the Galápagos using a novel phylogenetic method that estimates rates of biota assembly for an entire community. We show that species richness on the archipelago is in an ascending phase and does not tend towards equilibrium. The majority of the avifauna diversifies at a slow rate, without detectable ecological limits. However, Darwin's finches form an exception: they rapidly reach a carrying capacity and subsequently follow a coalescent-like diversification process. Together, these results suggest that avian diversity of remote islands is rising, and challenge the mutual exclusivity of the non-equilibrium and equilibrium ecological paradigms. © 2015 The Authors Ecology Letters published by John Wiley & Sons Ltd and CNRS.

A reduction method for phase equilibrium calculations with cubic equations of state

Directory of Open Access Journals (Sweden)

D. V. Nichita

2006-09-01

Full Text Available In this work we propose a new reduction method for phase equilibrium calculations using a general form of cubic equations of state (CEOS. The energy term in the CEOS is a quadratic form, which is diagonalized by applying a linear transformation. The number of the reduction parameters is related to the rank of the matrix C with elements (1-Cij, where Cij denotes the binary interaction parameters (BIPs. The dimensionality of the problem depends only on the number of reduction parameters, and is independent of the number of components in the mixture.

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

Science.gov (United States)

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.

Non-Equilibrium Properties from Equilibrium Free Energy Calculations

Science.gov (United States)

Pohorille, Andrew; Wilson, Michael A.

2012-01-01

Calculating free energy in computer simulations is of central importance in statistical mechanics of condensed media and its applications to chemistry and biology not only because it is the most comprehensive and informative quantity that characterizes the eqUilibrium state, but also because it often provides an efficient route to access dynamic and kinetic properties of a system. Most of applications of equilibrium free energy calculations to non-equilibrium processes rely on a description in which a molecule or an ion diffuses in the potential of mean force. In general case this description is a simplification, but it might be satisfactorily accurate in many instances of practical interest. This hypothesis has been tested in the example of the electrodiffusion equation . Conductance of model ion channels has been calculated directly through counting the number of ion crossing events observed during long molecular dynamics simulations and has been compared with the conductance obtained from solving the generalized Nernst-Plank equation. It has been shown that under relatively modest conditions the agreement between these two approaches is excellent, thus demonstrating the assumptions underlying the diffusion equation are fulfilled. Under these conditions the electrodiffusion equation provides an efficient approach to calculating the full voltage-current dependence routinely measured in electrophysiological experiments.

Population decay time and distribution of exciton states analyzed by rate equations based on theoretical phononic and electron-collisional rate coefficients

Science.gov (United States)

Oki, Kensuke; Ma, Bei; Ishitani, Yoshihiro

2017-11-01

Population distributions and transition fluxes of the A exciton in bulk GaN are theoretically analyzed using rate equations of states of the principal quantum number n up to 5 and the continuum. These rate equations consist of the terms of radiative, electron-collisional, and phononic processes. The dependence of the rate coefficients on temperature is revealed on the basis of the collisional-radiative model of hydrogen plasma for the electron-collisional processes and theoretical formulation using Fermi's "golden rule" for the phononic processes. The respective effects of the variations in electron, exciton, and lattice temperatures are exhibited. This analysis is a base of the discussion on nonthermal equilibrium states of carrier-exciton-phonon dynamics. It is found that the exciton dissociation is enhanced even below 150 K mainly by the increase in the lattice temperature. When the thermal-equilibrium temperature increases, the population fluxes between the states of n >1 and the continuum become more dominant. Below 20 K, the severe deviation from the Saha-Boltzmann distribution occurs owing to the interband excitation flux being higher than the excitation flux from the 1 S state. The population decay time of the 1 S state at 300 K is more than ten times longer than the recombination lifetime of excitons with kinetic energy but without the upper levels (n >1 and the continuum). This phenomenon is caused by a shift of population distribution to the upper levels. This phonon-exciton-radiation model gives insights into the limitations of conventional analyses such as the ABC model, the Arrhenius plot, the two-level model (n =1 and the continuum), and the neglect of the upper levels.

Para-equilibrium phase diagrams

International Nuclear Information System (INIS)

Pelton, Arthur D.; Koukkari, Pertti; Pajarre, Risto; Eriksson, Gunnar

2014-01-01

Highlights: • A rapidly cooled system may attain a state of para-equilibrium. • In this state rapidly diffusing elements reach equilibrium but others are immobile. • Application of the Phase Rule to para-equilibrium phase diagrams is discussed. • A general algorithm to calculate para-equilibrium phase diagrams is described. - Abstract: If an initially homogeneous system at high temperature is rapidly cooled, a temporary para-equilibrium state may result in which rapidly diffusing elements have reached equilibrium but more slowly diffusing elements have remained essentially immobile. The best known example occurs when homogeneous austenite is quenched. A para-equilibrium phase assemblage may be calculated thermodynamically by Gibbs free energy minimization under the constraint that the ratios of the slowly diffusing elements are the same in all phases. Several examples of calculated para-equilibrium phase diagram sections are presented and the application of the Phase Rule is discussed. Although the rules governing the geometry of these diagrams may appear at first to be somewhat different from those for full equilibrium phase diagrams, it is shown that in fact they obey exactly the same rules with the following provision. Since the molar ratios of non-diffusing elements are the same in all phases at para-equilibrium, these ratios act, as far as the geometry of the diagram is concerned, like “potential” variables (such as T, pressure or chemical potentials) rather than like “normal” composition variables which need not be the same in all phases. A general algorithm to calculate para-equilibrium phase diagrams is presented. In the limit, if a para-equilibrium calculation is performed under the constraint that no elements diffuse, then the resultant phase diagram shows the single phase with the minimum Gibbs free energy at any point on the diagram; such calculations are of interest in physical vapor deposition when deposition is so rapid that phase

Usefulness of an equal-probability assumption for out-of-equilibrium states: A master equation approach

KAUST Repository

Nogawa, Tomoaki

2012-10-18

We examine the effectiveness of assuming an equal probability for states far from equilibrium. For this aim, we propose a method to construct a master equation for extensive variables describing nonstationary nonequilibrium dynamics. The key point of the method is the assumption that transient states are equivalent to the equilibrium state that has the same extensive variables, i.e., an equal probability holds for microscopic states in nonequilibrium. We demonstrate an application of this method to the critical relaxation of the two-dimensional Potts model by Monte Carlo simulations. While the one-variable description, which is adequate for equilibrium, yields relaxation dynamics that are very fast, the redundant two-variable description well reproduces the true dynamics quantitatively. These results suggest that some class of the nonequilibrium state can be described with a small extension of degrees of freedom, which may lead to an alternative way to understand nonequilibrium phenomena. © 2012 American Physical Society.

Usefulness of an equal-probability assumption for out-of-equilibrium states: A master equation approach

KAUST Repository

Nogawa, Tomoaki; Ito, Nobuyasu; Watanabe, Hiroshi

2012-01-01

We examine the effectiveness of assuming an equal probability for states far from equilibrium. For this aim, we propose a method to construct a master equation for extensive variables describing nonstationary nonequilibrium dynamics. The key point of the method is the assumption that transient states are equivalent to the equilibrium state that has the same extensive variables, i.e., an equal probability holds for microscopic states in nonequilibrium. We demonstrate an application of this method to the critical relaxation of the two-dimensional Potts model by Monte Carlo simulations. While the one-variable description, which is adequate for equilibrium, yields relaxation dynamics that are very fast, the redundant two-variable description well reproduces the true dynamics quantitatively. These results suggest that some class of the nonequilibrium state can be described with a small extension of degrees of freedom, which may lead to an alternative way to understand nonequilibrium phenomena. © 2012 American Physical Society.

Equilibrium states for a plane incompressible perfect fluid

Energy Technology Data Exchange (ETDEWEB)

Boldrighini, C; Frigio, S [Camerino Univ. (Italy). Istituto di Matematica

1980-01-01

We associate to the plane incompressible Euler equation with periodic conditions the corresponding Hopf equation, as an equation for measures on the space of solenoidal distributions. We define equilibrium states as the solutions of the stationary Hopf equation. We find a class of equilibrium states which corresponds to a class of infinitely divisible distributions, and investigate the properties of gaussian and poissonian states. Equilibrium dynamics for a class of poissonian states is constructed by means of the Onsager vortex equations.

Representing Rate Equations for Enzyme-Catalyzed Reactions

Science.gov (United States)

Ault, Addison

2011-01-01

Rate equations for enzyme-catalyzed reactions are derived and presented in a way that makes it easier for the nonspecialist to see how the rate of an enzyme-catalyzed reaction depends upon kinetic constants and concentrations. This is done with distribution equations that show how the rate of the reaction depends upon the relative quantities of…

Plasma equilibrium and stability in stellarators

International Nuclear Information System (INIS)

Pustovitov, V.D.; Shafranov, V.D.

1987-01-01

A review of theoretical methods of investigating plasma equilibrium and stability in stellarators is given. Principles forming the basis of toroidal plasma equilibrium and its stabilization, and the main results of analytical theory and numerical calculations are presented. Configurations with spiral symmetry and usual stellarators with plane axis and spiral fields are considered in detail. Derivation of scalar two-dimensional equations, describing equilibrium in these systems is given. These equations were used to obtain one-dimensional equations for displacement and ellipticity of magnetic surfaces. The model of weak-elliptic displaced surfaces was used to consider the evolution of plasma equilibrium in stellarators after elevation of its pressure: change of profile of rotational transformation after change of plasma pressure, current generation during its fast heating and its successive damping due to finite plasma conductivity were described. The derivation of equations of small oscillations in the form, suitable for local disturbance investigation is presented. These equations were used to obtain Mercier criteria and ballon model equations. General sufficient conditions of plasma stability in systems with magnetic confinement were derived

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

Science.gov (United States)

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).

Out-of-equilibrium dynamical mean-field equations for the perceptron model

Science.gov (United States)

Agoritsas, Elisabeth; Biroli, Giulio; Urbani, Pierfrancesco; Zamponi, Francesco

2018-02-01

Perceptrons are the building blocks of many theoretical approaches to a wide range of complex systems, ranging from neural networks and deep learning machines, to constraint satisfaction problems, glasses and ecosystems. Despite their applicability and importance, a detailed study of their Langevin dynamics has never been performed yet. Here we derive the mean-field dynamical equations that describe the continuous random perceptron in the thermodynamic limit, in a very general setting with arbitrary noise and friction kernels, not necessarily related by equilibrium relations. We derive the equations in two ways: via a dynamical cavity method, and via a path-integral approach in its supersymmetric formulation. The end point of both approaches is the reduction of the dynamics of the system to an effective stochastic process for a representative dynamical variable. Because the perceptron is formally very close to a system of interacting particles in a high dimensional space, the methods we develop here can be transferred to the study of liquid and glasses in high dimensions. Potentially interesting applications are thus the study of the glass transition in active matter, the study of the dynamics around the jamming transition, and the calculation of rheological properties in driven systems.

Utility rate equations of group population dynamics in biological and social systems.

Directory of Open Access Journals (Sweden)

Vyacheslav I Yukalov

Full Text Available We present a novel system of equations to describe the evolution of self-organized structured societies (biological or human composed of several trait groups. The suggested approach is based on the combination of ideas employed in the theory of biological populations, system theory, and utility theory. The evolution equations are defined as utility rate equations, whose parameters are characterized by the utility of each group with respect to the society as a whole and by the mutual utilities of groups with respect to each other. We analyze in detail the cases of two groups (cooperators and defectors and of three groups (cooperators, defectors, and regulators and find that, in a self-organized society, neither defectors nor regulators can overpass the maximal fractions of about [Formula: see text] each. This is in agreement with the data for bee and ant colonies. The classification of societies by their distance from equilibrium is proposed. We apply the formalism to rank the countries according to the introduced metric quantifying their relative stability, which depends on the cost of defectors and regulators as well as their respective population fractions. We find a remarkable concordance with more standard economic ranking based, for instance, on GDP per capita.

Utility Rate Equations of Group Population Dynamics in Biological and Social Systems

Science.gov (United States)

Yukalov, Vyacheslav I.; Yukalova, Elizaveta P.; Sornette, Didier

2013-01-01

We present a novel system of equations to describe the evolution of self-organized structured societies (biological or human) composed of several trait groups. The suggested approach is based on the combination of ideas employed in the theory of biological populations, system theory, and utility theory. The evolution equations are defined as utility rate equations, whose parameters are characterized by the utility of each group with respect to the society as a whole and by the mutual utilities of groups with respect to each other. We analyze in detail the cases of two groups (cooperators and defectors) and of three groups (cooperators, defectors, and regulators) and find that, in a self-organized society, neither defectors nor regulators can overpass the maximal fractions of about each. This is in agreement with the data for bee and ant colonies. The classification of societies by their distance from equilibrium is proposed. We apply the formalism to rank the countries according to the introduced metric quantifying their relative stability, which depends on the cost of defectors and regulators as well as their respective population fractions. We find a remarkable concordance with more standard economic ranking based, for instance, on GDP per capita. PMID:24386163

Biosorption of zinc (II) by Rhizopus arrhizus: equilibrium and kinetic ...

African Journals Online (AJOL)

... in light of the Lagergren equation and the process followed a second order rate kinetics. The equilibrium data were analyzed using the Langmuir, Freundlich, ... All the isotherms provided the best correlation for zinc (II) onto the R. arrhizus.

Reaction-rate formula in out of equilibrium quantum field theory

OpenAIRE

Niegawa, A.; Okano, K.; Ozaki, H.

1999-01-01

A complete derivation, from first principles, of the reaction-rate formula for a generic reaction taking place in an out of equilibrium quantum-field system is given. It is shown that the formula involves no finite-volume correction. Each term of the reaction-rate formula represents a set of physical processes that contribute to the reaction under consideration.

Quick and Easy Rate Equations for Multistep Reactions

Science.gov (United States)

Savage, Phillip E.

2008-01-01

Students rarely see closed-form analytical rate equations derived from underlying chemical mechanisms that contain more than a few steps unless restrictive simplifying assumptions (e.g., existence of a rate-determining step) are made. Yet, work published decades ago allows closed-form analytical rate equations to be written quickly and easily for…

Studies on Microwave Heated Drying-rate Equations of Foods

OpenAIRE

呂, 聯通; 久保田, 清; 鈴木, 寛一; 岡崎, 尚; 山下, 洋右

1990-01-01

In order to design various microwave heated drying apparatuses, we must take drying-rate equations which are based on simple drying-rate models. In a previous paper (KUBOTA, et al., 1990), we have studied a convenient microwave heated drying instrument, and studied the simple drying-rate equations of potato and so on by using the simple empirical rate equations that have been reported in previous papers (KUBOTA, 1979-1, 1979-2). In this paper, we studied the microwave drying rate of the const...

A Study of Interactions between Mixing and Chemical Reaction Using the Rate-Controlled Constrained-Equilibrium Method

Science.gov (United States)

Hadi, Fatemeh; Janbozorgi, Mohammad; Sheikhi, M. Reza H.; Metghalchi, Hameed

2016-10-01

The rate-controlled constrained-equilibrium (RCCE) method is employed to study the interactions between mixing and chemical reaction. Considering that mixing can influence the RCCE state, the key objective is to assess the accuracy and numerical performance of the method in simulations involving both reaction and mixing. The RCCE formulation includes rate equations for constraint potentials, density and temperature, which allows taking account of mixing alongside chemical reaction without splitting. The RCCE is a dimension reduction method for chemical kinetics based on thermodynamics laws. It describes the time evolution of reacting systems using a series of constrained-equilibrium states determined by RCCE constraints. The full chemical composition at each state is obtained by maximizing the entropy subject to the instantaneous values of the constraints. The RCCE is applied to a spatially homogeneous constant pressure partially stirred reactor (PaSR) involving methane combustion in oxygen. Simulations are carried out over a wide range of initial temperatures and equivalence ratios. The chemical kinetics, comprised of 29 species and 133 reaction steps, is represented by 12 RCCE constraints. The RCCE predictions are compared with those obtained by direct integration of the same kinetics, termed detailed kinetics model (DKM). The RCCE shows accurate prediction of combustion in PaSR with different mixing intensities. The method also demonstrates reduced numerical stiffness and overall computational cost compared to DKM.

Helical axis stellarator equilibrium model

International Nuclear Information System (INIS)

Koniges, A.E.; Johnson, J.L.

1985-02-01

An asymptotic model is developed to study MHD equilibria in toroidal systems with a helical magnetic axis. Using a characteristic coordinate system based on the vacuum field lines, the equilibrium problem is reduced to a two-dimensional generalized partial differential equation of the Grad-Shafranov type. A stellarator-expansion free-boundary equilibrium code is modified to solve the helical-axis equations. The expansion model is used to predict the equilibrium properties of Asperators NP-3 and NP-4. Numerically determined flux surfaces, magnetic well, transform, and shear are presented. The equilibria show a toroidal Shafranov shift

Lanthanum-modified drinking water treatment residue for initial rapid and long-term equilibrium phosphorus immobilization to control eutrophication.

Science.gov (United States)

Wang, Changhui; Wu, Yu; Wang, Youquan; Bai, Leilei; Jiang, Helong; Yu, Juhua

2018-06-15

This study presents an approach for developing inactivating materials to achieve an initial rapid and a long-term equilibrium P immobilization to control eutrophication based on drinking water treatment residue (DWTR), which is a byproduct of potable water production. By taking advantage of the long-term equilibrium P adsorption by DWTR, the La chemical properties, and the previous success of using La-modified bentonite clay (Phoslock ® ), we used DWTR as a La carrier with different ratios to develop the specific materials. The La loading mechanisms, the potentially toxic effect of La-modified DWTR on snail Bellamya aeruginosa (within 120 d), and the short- and long-term (within 80 d) P immobilization characteristics of the modified DWTR were investigated to understand the performance of the developed materials. The results showed that La loading into DWTR was based on ligand exchanges and the formation of new particles; DWTR loaded with <5% La had no toxicity against the snail. Most importantly, the loading of 5% La to DWTR substantially enhanced the rapid immobilization capacity of DWTR, achieving an initial rapid and a long-term equilibrium P adsorption in aqueous solutions. This study promotes the beneficial recycling of DWTR and results in a win-win situation for lake restoration. Copyright © 2018 Elsevier Ltd. All rights reserved.

Equilibrium: two-dimensional configurations

International Nuclear Information System (INIS)

Anon.

1987-01-01

In Chapter 6, the problem of toroidal force balance is addressed in the simplest, nontrivial two-dimensional geometry, that of an axisymmetric torus. A derivation is presented of the Grad-Shafranov equation, the basic equation describing axisymmetric toroidal equilibrium. The solutions to equations provide a complete description of ideal MHD equilibria: radial pressure balance, toroidal force balance, equilibrium Beta limits, rotational transform, shear, magnetic wall, etc. A wide number of configurations are accurately modeled by the Grad-Shafranov equation. Among them are all types of tokamaks, the spheromak, the reversed field pinch, and toroidal multipoles. An important aspect of the analysis is the use of asymptotic expansions, with an inverse aspect ratio serving as the expansion parameter. In addition, an equation similar to the Grad-Shafranov equation, but for helically symmetric equilibria, is presented. This equation represents the leading-order description low-Beta and high-Beta stellarators, heliacs, and the Elmo bumpy torus. The solutions all correspond to infinitely long straight helices. Bending such a configuration into a torus requires a full three-dimensional calculation and is discussed in Chapter 7

Three-scale expansion of the solution of MHD and Reynolds equations for tokamak

International Nuclear Information System (INIS)

Maslov, V.P.; Omel'yanov, G.A.

1994-01-01

An asymptotic solution of the magnetohydrodynamic equations is constructed. The three scales asymptotic solution describes the non-linear evolution of small, rapidly varying perturbations of equilibrium. It is shown, that an anisotropic coherent structure appears in the linear nonstability situation, and the structures evolution directs to energy interaction between high-frequency and low-frequency waves. The closed system of MHD Reynolds equations for anisotropic structure is derived

Equilibrium calculations for helical axis stellarators

International Nuclear Information System (INIS)

Hender, T.C.; Carreras, B.A.

1984-04-01

An average method based on a vacuum flux coordinate system is presented. This average method permits the study of helical axis stellarators with toroidally dominated shifts. An ordering is introduced, and to lowest order the toroidally averaged equilibrium equations are reduced to a Grad-Shafranov equation. Also, to lowest order, a Poisson-type equation is obtained for the toroidally varying corrections to the equilibium. By including these corrections, systems that are toroidally dominated, but with significant helical distortion to the equilibrium, may be studied. Numerical solutions of the average method equations are shown to agree well with three-dimensional calculations

Computation of Phase Equilibrium and Phase Envelopes

DEFF Research Database (Denmark)

Ritschel, Tobias Kasper Skovborg; Jørgensen, John Bagterp

formulate the involved equations in terms of the fugacity coefficients. We present expressions for the first-order derivatives. Such derivatives are necessary in computationally efficient gradient-based methods for solving the vapor-liquid equilibrium equations and for computing phase envelopes. Finally, we......In this technical report, we describe the computation of phase equilibrium and phase envelopes based on expressions for the fugacity coefficients. We derive those expressions from the residual Gibbs energy. We consider 1) ideal gases and liquids modeled with correlations from the DIPPR database...... and 2) nonideal gases and liquids modeled with cubic equations of state. Next, we derive the equilibrium conditions for an isothermal-isobaric (constant temperature, constant pressure) vapor-liquid equilibrium process (PT flash), and we present a method for the computation of phase envelopes. We...

Multi-diffusive nonlinear Fokker–Planck equation

International Nuclear Information System (INIS)

Ribeiro, Mauricio S; Casas, Gabriela A; Nobre, Fernando D

2017-01-01

Nonlinear Fokker–Planck equations, characterized by more than one diffusion term, have appeared recently in literature. Here, it is shown that these equations may be derived either from approximations in a master equation, or from a Langevin-type approach. An H-theorem is proven, relating these Fokker–Planck equations to an entropy composed by a sum of contributions, each of them associated with a given diffusion term. Moreover, the stationary state of the Fokker–Planck equation is shown to coincide with the equilibrium state, obtained by extremization of the entropy, in the sense that both procedures yield precisely the same equation. Due to the nonlinear character of this equation, the equilibrium probability may be obtained, in most cases, only by means of numerical approaches. Some examples are worked out, where the equilibrium probability distribution is computed for nonlinear Fokker–Planck equations presenting two diffusion terms, corresponding to an entropy characterized by a sum of two contributions. It is shown that the resulting equilibrium distribution, in general, presents a form that differs from a sum of the equilibrium distributions that maximizes each entropic contribution separately, although in some cases one may construct such a linear combination as a good approximation for the equilibrium distribution. (paper)

Charge equilibrium processes of energetic incident ions and their range

International Nuclear Information System (INIS)

Kawagoshi, Hiroshi; Karashima, Shosuke; Watanabe, Tsutomu.

1984-01-01

The charge state of energetic ions passing through a certain matter is varied by charge-exchange processes. A rate equation for charge fraction is given by using electron loss and capture cross sections in collision with a target atom under idealized condition. We solved the rate equation of the charge-exchange process of a single electron in a form of linear coupled differential equation. Our calcuiation for the range of ion were carried out for He, Ne and Ar ions passing through an atomic hydrogen gas target. We discuss the charge states of the projectile in relation to a local charge balance consituting a state of charge equilibrium in the target. (author)

Use of the SSF equations in the Kojima-Moon-Ochi thermodynamic consistency test of isothermal vapour-liquid equilibrium data

Directory of Open Access Journals (Sweden)

SLOBODAN P. SERBANOVIC

2000-12-01

Full Text Available The Kojima-Moon-Ochi (KMO thermodynamic consistency test of vapour–liquid equilibrium (VLE measurements for 32 isothermal data sets of binary systems of various complexity was applied using two fitting equations: the Redlich-Kister equation and the Sum of Symmetrical Functions. It was shown that the enhanced reliability of the fitting of the experimental data can change the conclusions drawn on their thermodynamic consistency in those cases of VLE data sets that are estimated to be near the border of consistency.

Equilibrium sorption of cobalt, cesium, and strontium on Bandelier Tuff: analysis of alternative mathematical modeling

International Nuclear Information System (INIS)

Polzer, W.L.; Fuentes, H.R.; Essington, E.H.; Roensch, F.R.

1985-01-01

Sorption isotherms are derived from batch equilibrium data for cobalt, cesium and strontium on Bandelier Tuff. Experiments were conducted at an average temperature of 23 0 C and equilibrium was defined at 48 hours. The solute concentrations ranged from 0 to 500 mg/L. The radioactive isotopes 60 Co, 137 Cs, and 85 Sr were used to trace the sorption of the stable solutes. The Linear, Langmuir, Freundlich and a Modified Freundlich isotherm equations are evaluated. The Modified Freundlich isotherm equation is validated as a preferred general mathematical tool for representing the sorption of the three solutes. The empirical constants derived from the Modified Freundlich isotherm equation indicate that under dynamic flow conditions strontium will move most rapidly and cobalt least rapidly. On the other hand, chemical dispersion will be greatest for cesium and least for strontium. Hill Plots of the sorption data suggest that in the region of low saturation sorption of all three solutes is impeded by interactions among sorption sites; cobalt exhibits the greatest effect of interactions and strontium shows only a minimal effect. In the saturation region of 50% or more, sorption of cobalt is enhanced slightly by interactions among sorption sites whereas sorption of cesium and strontium appears to be independent of site interactions. 9 references, 4 figures, 2 tables

Possibility of rapidly reporting 226Ra activity in 226Ra-222Rn samples with unknown equilibrium factor by γ spectrometer

Institute of Scientific and Technical Information of China (English)

SU Qiong; ZHENG Rui; CHEN Yong; CHENG Jian-Ping

2004-01-01

This paper reports the observed changes for equilibrium factors between 226Ra and 222Rn with sealing time of the samples. The samples include soil, raw coal, mineral water, cement, rock, etc. Especially the conceptions of "pre-equilibrium time" and "pre-equilibrium factor" have been put forward and methods of measuring and processing data have been given which can be used for rapidly reporting activity of 226Ra in samples with unknown equilibrium factor. It is definitely concluded that, using methods given in the paper, a test report will be completed in 3～7days, instead of one month, after receiving the sample whose activity is not lower than LLD of the spectrometer.

Dynamical System Analysis of Reynolds Stress Closure Equations

Science.gov (United States)

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.

BINARY NEUTRON STARS IN QUASI-EQUILIBRIUM

International Nuclear Information System (INIS)

Taniguchi, Keisuke; Shibata, Masaru

2010-01-01

Quasi-equilibrium sequences of binary neutron stars are constructed for a variety of equations of state in general relativity. Einstein's constraint equations in the Isenberg-Wilson-Mathews approximation are solved together with the relativistic equations of hydrostationary equilibrium under the assumption of irrotational flow. We focus on unequal-mass sequences as well as equal-mass sequences, and compare those results. We investigate the behavior of the binding energy and total angular momentum along a quasi-equilibrium sequence, the endpoint of sequences, and the orbital angular velocity as a function of time, changing the mass ratio, the total mass of the binary system, and the equation of state of a neutron star. It is found that the orbital angular velocity at the mass-shedding limit can be determined by an empirical formula derived from an analytic estimation. We also provide tables for 160 sequences, which will be useful as a guideline of numerical simulations for the inspiral and merger performed in the near future.

Entanglement Equilibrium and the Einstein Equation.

Science.gov (United States)

Jacobson, Ted

2016-05-20

A link between the semiclassical Einstein equation and a maximal vacuum entanglement hypothesis is established. The hypothesis asserts that entanglement entropy in small geodesic balls is maximized at fixed volume in a locally maximally symmetric vacuum state of geometry and quantum fields. A qualitative argument suggests that the Einstein equation implies the validity of the hypothesis. A more precise argument shows that, for first-order variations of the local vacuum state of conformal quantum fields, the vacuum entanglement is stationary if and only if the Einstein equation holds. For nonconformal fields, the same conclusion follows modulo a conjecture about the variation of entanglement entropy.

Hypocoercivity for linear kinetic equations conserving mass

KAUST Repository

Dolbeault, Jean; Mouhot, Clé ment; Schmeiser, Christian

2015-01-01

We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $ L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. - See more at: http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06012-7/#sthash.ChjyK6rc.dpuf

Hypocoercivity for linear kinetic equations conserving mass

KAUST Repository

Dolbeault, Jean

2015-02-03

We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $ L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. - See more at: http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06012-7/#sthash.ChjyK6rc.dpuf

Dependence of equilibrium properties of channeled particles on transverse quasi temperature

International Nuclear Information System (INIS)

Kashlev, Yu.A.

2006-01-01

Quasi-equilibrium and kinetic characteristics of channeled particles are investigated by methods of nonequilibrium statistical thermodynamics. The equilibrium equation of the transverse energy of fast particles and the equilibrium equation of the transverse momentum of particles are derived. It is shown that equilibrium equations solution permits to obtain the expression for the transverse quasi-temperature of the channeled particle subsystem. The quasi-equilibrium angular distribution of particles after transmission through a thin monocrystal and the angular distribution at backscattering are studied. The evaluated data of the transverse quasi-temperature are presented for the case of iodine ion channeling through silver crystals [ru

Linear rate-equilibrium relations arising from ion channel-bilayer energetic coupling

DEFF Research Database (Denmark)

Greisen, Per Junior; Lum, Kevin; Ashrafuzzaman, Md

2011-01-01

Linear rate-equilibrium (RE) relations, also known as linear free energy relations, are widely observed in chemical reactions, including protein folding, enzymatic catalysis, and channel gating. Despite the widespread occurrence of linear RE relations, the principles underlying the linear relatio...

Kinematic equations for resolved-rate control of an industrial robot arm

Science.gov (United States)

Barker, L. K.

1983-01-01

An operator can use kinematic, resolved-rate equations to dynamically control a robot arm by watching its response to commanded inputs. Known resolved-rate equations for the control of a particular six-degree-of-freedom industrial robot arm and proceeds to simplify the equations for faster computations are derived. Methods for controlling the robot arm in regions which normally cause mathematical singularities in the resolved-rate equations are discussed.

Equilibrium and out-of-equilibrium thermodynamics in supercooled liquids and glasses

International Nuclear Information System (INIS)

Mossa, S; Nave, E La; Tartaglia, P; Sciortino, F

2003-01-01

We review the inherent structure thermodynamical formalism and the formulation of an equation of state (EOS) for liquids in equilibrium based on the (volume) derivatives of the statistical properties of the potential energy surface. We also show that, under the hypothesis that during ageing the system explores states associated with equilibrium configurations, it is possible to generalize the proposed EOS to out-of-equilibrium (OOE) conditions. The proposed formulation is based on the introduction of one additional parameter which, in the chosen thermodynamic formalism, can be chosen as the local minimum where the slowly relaxing OOE liquid is trapped

A Unified Kinetics and Equilibrium Experiment: Rate Law, Activation Energy, and Equilibrium Constant for the Dissociation of Ferroin

Science.gov (United States)

Sattar, Simeen

2011-01-01

Tris(1,10-phenanthroline)iron(II) is the basis of a suite of four experiments spanning 5 weeks. Students determine the rate law, activation energy, and equilibrium constant for the dissociation of the complex ion in acid solution and base dissociation constant for phenanthroline. The focus on one chemical system simplifies a daunting set of…

Relaxation with high-speed plasma flows and singularity analysis in MHD equilibrium

International Nuclear Information System (INIS)

Shiraishi, Junya; Ohsaki, Shuichi; Yoshida, Zensho

2004-01-01

Relaxation model that leads to plasma confinement with rigid-rotation is presented. This model applies to Jupiter's magnetosphere. It is shown that the invariance of canonical angular momentum of electron fluid, which is realized by axisymmetry through self-organization process, yields plasma confinement. including poloidal flows in equilibrium equation makes the problem rather complicated. Singularity due to the poloidal flow is focused on. It is shown that the singular equation for equilibrium has the same structure as the equation for linear Alfven wave. Since the singular solution for equilibrium equation is physically inadequate, the singularity may be removed by another physical effect. The Hall-effect is taken into account as a singular perturbation that removes the singularity of equilibrium equation for ideal magnetohydrodynamics. (author)

Restraining approach for the spurious kinematic modes in hybrid equilibrium element

Science.gov (United States)

Parrinello, F.

2013-10-01

The present paper proposes a rigorous approach for the elimination of spurious kinematic modes in hybrid equilibrium elements, for three well known mesh patches. The approach is based on the identification of the dependent equations in the set of inter-element and boundary equilibrium equations of the sides involved in the spurious kinematic mode. Then the kinematic variables related to the dependent equations are reciprocally constrained and, by application of master slave elimination method, the set of inter-element equilibrium equations is reduced to full rank. The elastic solutions produced by means of the proposed approach verify the homogeneous, the inter-element and the boundary equilibrium equations. Hybrid stress formulation is developed in a rigorous mathematical setting. The results of linear elastic analysis obtained by the proposed approach and by classical displacement based method are compared for some structural examples.

Connecting Related Rates and Differential Equations

Science.gov (United States)

Brandt, Keith

2012-01-01

This article points out a simple connection between related rates and differential equations. The connection can be used for in-class examples or homework exercises, and it is accessible to students who are familiar with separation of variables.

Wave propagation in a quasi-chemical equilibrium plasma

Science.gov (United States)

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.

Rates and equilibrium constants of the ligand-induced conformational transition of an HCN ion channel protein domain determined by DEER spectroscopy.

Science.gov (United States)

Collauto, Alberto; DeBerg, Hannah A; Kaufmann, Royi; Zagotta, William N; Stoll, Stefan; Goldfarb, Daniella

2017-06-14

Ligand binding can induce significant conformational changes in proteins. The mechanism of this process couples equilibria associated with the ligand binding event and the conformational change. Here we show that by combining the application of W-band double electron-electron resonance (DEER) spectroscopy with microfluidic rapid freeze quench (μRFQ) it is possible to resolve these processes and obtain both equilibrium constants and reaction rates. We studied the conformational transition of the nitroxide labeled, isolated carboxy-terminal cyclic-nucleotide binding domain (CNBD) of the HCN2 ion channel upon binding of the ligand 3',5'-cyclic adenosine monophosphate (cAMP). Using model-based global analysis, the time-resolved data of the μRFQ DEER experiments directly provide fractional populations of the open and closed conformations as a function of time. We modeled the ligand-induced conformational change in the protein using a four-state model: apo/open (AO), apo/closed (AC), bound/open (BO), bound/closed (BC). These species interconvert according to AC + L ⇌ AO + L ⇌ BO ⇌ BC. By analyzing the concentration dependence of the relative contributions of the closed and open conformations at equilibrium, we estimated the equilibrium constants for the two conformational equilibria and the open-state ligand dissociation constant. Analysis of the time-resolved μRFQ DEER data gave estimates for the intrinsic rates of ligand binding and unbinding as well as the rates of the conformational change. This demonstrates that DEER can quantitatively resolve both the thermodynamics and the kinetics of ligand binding and the associated conformational change.

A Comparison of the Computation Times of Thermal Equilibrium and Non-equilibrium Models of Droplet Field in a Two-Fluid Three-Field Model

Energy Technology Data Exchange (ETDEWEB)

Park, Ik Kyu; Cho, Heong Kyu; Kim, Jong Tae; Yoon, Han Young; Jeong, Jae Jun

2007-12-15

A computational model for transient, 3 dimensional 2 phase flows was developed by using 'unstructured-FVM-based, non-staggered, semi-implicit numerical scheme' considering the thermally non-equilibrium droplets. The assumption of the thermally equilibrium between liquid and droplets of previous studies was not used any more, and three energy conservation equations for vapor, liquid, liquid droplets were set up. Thus, 9 conservation equations for mass, momentum, and energy were established to simulate 2 phase flows. In this report, the governing equations and a semi-implicit numerical sheme for a transient 1 dimensional 2 phase flows was described considering the thermally non-equilibrium between liquid and liquid droplets. The comparison with the previous model considering the thermally non-equilibrium between liquid and liquid droplets was also reported.

A cosmic equation of state for the inhomogeneous universe: can a global far-from-equilibrium state explain dark energy?

International Nuclear Information System (INIS)

Buchert, Thomas

2005-01-01

A system of effective Einstein equations for spatially averaged scalar variables of inhomogeneous cosmological models can be solved by providing a 'cosmic equation of state'. Recent efforts to explain dark energy focus on 'backreaction effects' of inhomogeneities on the effective evolution of cosmological parameters in our Hubble volume, avoiding a cosmological constant in the equation of state. In this letter, it is argued that if kinematical backreaction effects are indeed of the order of the averaged density (or larger as needed for an accelerating domain of the universe), then the state of our regional Hubble volume would have to be in the vicinity of a far-from-equilibrium state that balances kinematical backreaction and average density. This property, if interpreted globally, is shared by a stationary cosmos with effective equation of state p eff = -1/3 ρ eff . It is concluded that a confirmed explanation of dark energy by kinematical backreaction may imply a paradigmatic change of cosmology. (letter to the editor)

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

Energy Technology Data Exchange (ETDEWEB)

Liu, Yen, E-mail: yen.liu@nasa.gov; Vinokur, Marcel [NASA Ames Research Center, Moffett Field, California 94035 (United States); Panesi, Marco; Sahai, Amal [University of Illinois, Urbana-Champaign, Illinois 61801 (United States)

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

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

Science.gov (United States)

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

2015-04-01

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

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

Science.gov (United States)

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

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

International Nuclear Information System (INIS)

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

2015-01-01

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

Calculation code NIRVANA for free boundary MHD equilibrium

International Nuclear Information System (INIS)

Ninomiya, Hiromasa; Suzuki, Yasuo; Kameari, Akihisa

1975-03-01

The calculation method and code of solving the free boundary problem for MHD equilibrium has been developed. Usage of the code ''NIRVANA'' is described. The toroidal plasma current density determined as a function of the flux function PSI is substituted by a group of the ring currents, whereby the equation of MHD equilibrium is transformed into an integral equation. Either of the two iterative methods is chosen to solve the integral equation, depending on the assumptions made of the plasma surface points. Calculation of the magnetic field configurations is possible when the plasma surface coincides self-consistently with the magnetic flux including the separatrix points. The code is usable in calculation of the circular or non-circular shell-less Tokamak equilibrium. (auth.)

Analysis of the trend to equilibrium of a chemically reacting system

International Nuclear Information System (INIS)

Kremer, Gilberto M; Bianchi, Miriam Pandolfi; Soares, Ana Jacinta

2007-01-01

In this present paper, a quaternary gaseous reactive mixture, for which the chemical reaction is close to its final stage and the elastic and reactive frequencies are comparable, is modelled within the Boltzmann equation extended to reacting gases. The main objective is a detailed analysis of the non-equilibrium effects arising in the reactive system A 1 + A 2 ↔ A 3 + A 4 , in a flow regime which is considered not far away from thermal, mechanical and chemical equilibrium. A first-order perturbation solution technique is applied to the macroscopic field equations for the spatially homogeneous gas system, and the trend to equilibrium is studied in detail. Adopting elastic hard-spheres and reactive line-of-centres cross sections and an appropriate choice of the input distribution functions-which allows us to distinguish the two cases where the constituents are either at same or different temperatures-explicit computations of the linearized production terms for mass, momentum and total energy are performed for each gas species. The departures from the equilibrium states of densities, temperatures and diffusion fluxes are characterized by small perturbations of their corresponding equilibrium values. For the hydrogen-chlorine system, the perturbations are plotted as functions of time for both cases where the species are either at the same or different temperatures. Moreover, the trend to equilibrium of the reaction rates is represented for the forward and backward reaction H 2 + Cl ↔ HCl + H

Application of a mechanism-based rate equation to black liquor gasification rate data

Energy Technology Data Exchange (ETDEWEB)

Overacker, N.L.; Waag, K.J.; Frederick, W.J. [Oregon State University, OR (United States). Dept. of Chemical Engineering; Whitty, K.J.

1995-09-01

There is growing interest worldwide to develop alternate chemical recovery processes for paper mills which are cheaper, safer, more efficient and more environmentally sound than traditional technology. Pressurized gasification of black liquor is the basis for many proposed schemes and offers the possibility to double the amount of electricity generated per unit of dry black liquor solids. Such technology also has capital, safety and environmental advantages. One of the most important considerations regarding this emerging technology is the kinetics of the gasification reaction. This has been studied empirically at Aabo Akademi University for the pressurized gasification with carbon dioxide and steam. For the purposes of reactor modeling and scale-up, however, a thorough understanding of the mechanism behind the reaction is desirable. This report discusses the applicability of a mechanism-based rate equation to gasification of black liquor. The mechanism considered was developed for alkali-catalyzed gasification of carbon and is tested using black liquor gasification data obtained during simultaneous reaction with H{sub 2}O and CO. Equilibrium considerations and the influence of the water-gas shift reaction are also discussed. The work presented here is a cooperative effort between Aabo Akademi University and Oregon State University. The experimental work and some of the data analysis was performed at Aabo Akademi University. Development of the models and consideration of their applicability was performed primarily at Oregon State University

Theory of nanolaser devices: Rate equation analysis versus microscopic theory

DEFF Research Database (Denmark)

Lorke, Michael; Skovgård, Troels Suhr; Gregersen, Niels

2013-01-01

A rate equation theory for quantum-dot-based nanolaser devices is developed. We show that these rate equations are capable of reproducing results of a microscopic semiconductor theory, making them an appropriate starting point for complex device simulations of nanolasers. The input...

Equilibrium statistical mechanics

CERN Document Server

Mayer, J E

1968-01-01

The International Encyclopedia of Physical Chemistry and Chemical Physics, Volume 1: Equilibrium Statistical Mechanics covers the fundamental principles and the development of theoretical aspects of equilibrium statistical mechanics. Statistical mechanical is the study of the connection between the macroscopic behavior of bulk matter and the microscopic properties of its constituent atoms and molecules. This book contains eight chapters, and begins with a presentation of the master equation used for the calculation of the fundamental thermodynamic functions. The succeeding chapters highlight t

The Equilibrium Real Exchange Rate of the Malagasy Franc; Estimation and Assessment

OpenAIRE

John Cady

2003-01-01

Employing cointegration techniques, the long-run determinants of Madagascar's real exchange rate are examined from a stock-flow perspective. The long-run behavior of the real effective exchange rate is explained by the net foreign asset position and factors affecting trade flows. An index of the long-run equilibrium real exchange rate is developed to assess the degree of misalignment. The general conclusions are that the Malagasy franc has experienced significant misalignment in the past, but...

Fokker-Planck equation in mirror research

International Nuclear Information System (INIS)

Post, R.F.

1983-01-01

Open confinement systems based on the magnetic mirror principle depend on the maintenance of particle distributions that may deviate substantially from Maxwellian distributions. Mirror research has therefore from the beginning relied on theoretical predictions of non-equilibrium rate processes obtained from solutions to the Fokker-Planck equation. The F-P equation plays three roles: Design of experiments, creation of classical standards against which to compare experiment, and predictions concerning mirror based fusion power systems. Analytical and computational approaches to solving the F-P equation for mirror systems will be reviewed, together with results and examples that apply to specific mirror systems, such as the tandem mirror

New fundamental equations of thermodynamics for systems in chemical equilibrium at a specified partial pressure of a reactant and the standard transformed formation properties of reactants

International Nuclear Information System (INIS)

Alberty, R.A.; Oppenheim, I.

1993-01-01

When temperature, pressure, and the partial pressure of a reactant are fixed, the criterion of chemical equilibrium can be expressed in terms of the transformed Gibbs energy G' that is obtained by using a Legendre transform involving the chemical potential of the reactant that is fixed. For reactions of ideal gases, the most natural variables to use in the fundamental equation are T, P', and P B , where P' is the partial pressure of the reactants other than the one that is fixed and P B is the partial pressure of the reactant that is fixed. The fundamental equation for G' yields the expression for the transformed entropy S', and a transformed enthalpy can be defined by the additional Legendre transform H'=G'+TS'. This leads to an additional form of the fundamental equation. The calculation of transformed thermodynamic properties and equilibrium compositions is discussed for a simple system and for a general multireaction system. The change, in a reaction, of the binding of the reactant that is at a specified pressure can be calculated using one of the six Maxwell equations of the fundamental equation in G'

Matrix-valued Boltzmann equation for the nonintegrable Hubbard chain.

Science.gov (United States)

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.

Evaporation rate of nucleating clusters.

Science.gov (United States)

Zapadinsky, Evgeni

2011-11-21

The Becker-Döring kinetic scheme is the most frequently used approach to vapor liquid nucleation. In the present study it has been extended so that master equations for all cluster configurations are included into consideration. In the Becker-Döring kinetic scheme the nucleation rate is calculated through comparison of the balanced steady state and unbalanced steady state solutions of the set of kinetic equations. It is usually assumed that the balanced steady state produces equilibrium cluster distribution, and the evaporation rates are identical in the balanced and unbalanced steady state cases. In the present study we have shown that the evaporation rates are not identical in the equilibrium and unbalanced steady state cases. The evaporation rate depends on the number of clusters at the limit of the cluster definition. We have shown that the ratio of the number of n-clusters at the limit of the cluster definition to the total number of n-clusters is different in equilibrium and unbalanced steady state cases. This causes difference in evaporation rates for these cases and results in a correction factor to the nucleation rate. According to rough estimation it is 10(-1) by the order of magnitude and can be lower if carrier gas effectively equilibrates the clusters. The developed approach allows one to refine the correction factor with Monte Carlo and molecular dynamic simulations.

Averaged description of 3D MHD equilibrium

International Nuclear Information System (INIS)

Medvedev, S.Yu.; Drozdov, V.V.; Ivanov, A.A.; Martynov, A.A.; Pashekhonov, Yu.Yu.; Mikhailov, M.I.

2001-01-01

A general approach by S.A.Galkin et al. in 1991 to 2D description of MHD equilibrium and stability in 3D systems was proposed. The method requires a background 3D equilibrium with nested flux surfaces to generate the metric of a Riemannian space in which the background equilibrium is described by the 2D equation of Grad-Shafranov type. The equation can be solved then varying plasma profiles and shape to get approximate 3D equilibria. In the framework of the method both planar axis conventional stellarators and configurations with spatial magnetic axis can be studied. In the present report the formulation and numerical realization of the equilibrium problem for stellarators with planar axis is reviewed. The input background equilibria with nested flux surfaces are taken from vacuum magnetic field approximately described by analytic scalar potential

Dye removal from wastewater using activated carbon developed from sawdust: adsorption equilibrium and kinetics.

Science.gov (United States)

Malik, P K

2004-09-10

Mahogany sawdust was used to develop an effective carbon adsorbent. This adsorbent was employed for the removal of direct dyes from spent textile dyeing wastewater. The experimental data were analysed by the Langmuir and Freundlich models of adsorption. Equilibrium data fitted well with the Langmuir model. The rates of adsorption were found to conform to the pseudo-second-order kinetics with good correlation. The equilibrium adsorption capacity of the sawdust carbon was determined with the Langmuir equation as well as the pseudo-second-order rate equation and found to be >300 mg dye per gram of the adsorbent. The most ideal pH for adsorption of direct dyes onto sawdust carbon was found to be 3 and below. The results indicate that the Mahogany sawdust carbon could be employed as a low cost alternative to commercial activated carbon in the removal of dyes from wastewater.

Approach to transverse equilibrium in axial channeling

International Nuclear Information System (INIS)

Fearick, R.W.

2000-01-01

Analytical treatments of channeling rely on the assumption of equilibrium on the transverse energy shell. The approach to equilibrium, and the nature of the equilibrium achieved, is examined using solutions of the equations of motion in the continuum multi-string model. The results show that the motion is chaotic in the absence of dissipative processes, and a complicated structure develops in phase space which prevent the development of the simple equilibrium usually assumed. The role of multiple scattering in smoothing out the equilibrium distribution is investigated

Local effect of equilibrium current on tearing mode stability

International Nuclear Information System (INIS)

Cozzani, F.

1985-12-01

The local effect of the equilibrium current on the linear stability of low poloidal number tearing modes in tokamaks is investigated analytically. The plasma response inside the tearing layer is derived from fluid theory and the local equilibrium current is shown to couple to the mode dynamics through its gradient, which is proportional to the local electron temperature gradient under the approximations used in the analysis. The relevant eigenmode equations, expressing Ampere's law and the plasma quasineutrality condition, respectively, are suitably combined in a single integral equation, from which a variational principle is formulated to derive the mode dispersion relations for several cases of interest. The local equilibrium current is treated as a small perturbation of the known results for the m greater than or equal to 2 and the m = 1 tearing modes in the collisional regime, and the m greater than or equal to 2 tearing mode in the semicollisional regime; its effect is found to enhance stabilization for the m greater than or equal to 2 drift-tearing mode in the collisional regime, whereas the m = 1 growth rate is very slightly increased and the stabilizing effect of the parallel thermal conduction on the m greater than or equal to 2 mode in the semicollisional regime is slightly reduced

Equilibrium reconstruction in the TCA/Br tokamak; Reconstrucao do equilibrio no tokamak TCA/BR

Energy Technology Data Exchange (ETDEWEB)

Sa, Wanderley Pires de

1996-12-31

The accurate and rapid determination of the Magnetohydrodynamic (MHD) equilibrium configuration in tokamaks is a subject for the magnetic confinement of the plasma. With the knowledge of characteristic plasma MHD equilibrium parameters it is possible to control the plasma position during its formation using feed-back techniques. It is also necessary an on-line analysis between successive discharges to program external parameters for the subsequent discharges. In this work it is investigated the MHD equilibrium configuration reconstruction of the TCA/BR tokamak from external magnetic measurements, using a method that is able to fast determine the main parameters of discharge. The thesis has two parts. Firstly it is presented the development of an equilibrium code that solves de Grad-Shafranov equation for the TCA/BR tokamak geometry. Secondly it is presented the MHD equilibrium reconstruction process from external magnetic field and flux measurements using the Function Parametrization FP method. this method. This method is based on the statistical analysis of a database of simulated equilibrium configurations, with the goal of obtaining a simple relationship between the parameters that characterize the equilibrium and the measurements. The results from FP are compared with conventional methods. (author) 68 refs., 31 figs., 16 tabs.

Nonlinear fluctuations-induced rate equations for linear birth-death processes

Science.gov (United States)

Honkonen, J.

2008-05-01

The Fock-space approach to the solution of master equations for one-step Markov processes is reconsidered. It is shown that in birth-death processes with an absorbing state at the bottom of the occupation-number spectrum and occupation-number independent annihilation probability of occupation-number fluctuations give rise to rate equations drastically different from the polynomial form typical of birth-death processes. The fluctuation-induced rate equations with the characteristic exponential terms are derived for Mikhailov’s ecological model and Lanchester’s model of modern warfare.

Nonlinear fluctuation-induced rate equations for linear birth-death processes

International Nuclear Information System (INIS)

Honkonen, J.

2008-01-01

The Fock-space approach to the solution of master equations for the one-step Markov processes is reconsidered. It is shown that in birth-death processes with an absorbing state at the bottom of the occupation-number spectrum and occupation-number independent annihilation probability occupation-number fluctuations give rise to rate equations drastically different from the polynomial form typical of birth-death processes. The fluctuation-induced rate equations with the characteristic exponential terms are derived for Mikhailov's ecological model and Lanchester's model of modern warfare

Physics of future equilibrium state of nuclear energy utilization

International Nuclear Information System (INIS)

Sekimoto, H.

1994-01-01

The governing equations for future equilibrium nuclear state are presented and their characteristics are discussed. These equations are solved for several typical cases. In the present study on the equilibrium state, two coincidences are found. The first is the coincidence on the neutron balance performed by the nuclides satisfying the equilibrium condition. The finite neutron multiplication factor is near unity. The second is the coincidence on the toxicity. The produced long-life fission product toxicity is near the incinerated natural fuel toxicity. (author). 2 refs., 2 tabs., 4 figs

Analytical Model of Inlet Growth and Equilibrium Cross-Sectional Area

Science.gov (United States)

2016-04-01

classic Escoffier (1940) inlet stability analysis to produce a new quadratic formula derived from simplified momentum and conservation equations ...neglecting time dependence and taking the maximum current gives the following quadratic equation : 2 0 0 d b d ghagAhU U c LA c Lω + − = (5) with the...or quadratic approach as the equilibrium area can be determined through Equation 9. As an alternative, cross- sectional equilibrium is expressed in

Physical entropy, information entropy and their evolution equations

Institute of Scientific and Technical Information of China (English)

无

2001-01-01

Inspired by the evolution equation of nonequilibrium statistical physics entropy and the concise statistical formula of the entropy production rate, we develop a theory of the dynamic information entropy and build a nonlinear evolution equation of the information entropy density changing in time and state variable space. Its mathematical form and physical meaning are similar to the evolution equation of the physical entropy: The time rate of change of information entropy density originates together from drift, diffusion and production. The concise statistical formula of information entropy production rate is similar to that of physical entropy also. Furthermore, we study the similarity and difference between physical entropy and information entropy and the possible unification of the two statistical entropies, and discuss the relationship among the principle of entropy increase, the principle of equilibrium maximum entropy and the principle of maximum information entropy as well as the connection between them and the entropy evolution equation.

Deviations from mass transfer equilibrium and mathematical modeling of mixer-settler contactors

International Nuclear Information System (INIS)

Beyerlein, A.L.; Geldard, J.F.; Chung, H.F.; Bennett, J.E.

1980-01-01

This paper presents the mathematical basis for the computer model PUBG of mixer-settler contactors which accounts for deviations from mass transfer equilibrium. This is accomplished by formulating the mass balance equations for the mixers such that the mass transfer rate of nuclear materials between the aqueous and organic phases is accounted for. 19 refs

Analysis of equilibrium in a tokamak by the finite-difference method

International Nuclear Information System (INIS)

Kim, K.E.; Jeun, G.D.

1983-01-01

Ideal magnetohydrodynamic equilibrium in a Tokamak having a small radius with an elongated rectangular cross section is studied by applying the finite-difference method to the Grad-Shafranov equation to determine possible limitations for *b=8*pPsup(2)/Bsup(2). The coupled first-order differential equations resulting from the finite-difference Grad-Shafranov equation is solved by the numarical method:1)We concluded that equilibrium consideration alone gives no limitation even for *b approx.1. 2)We have obtained the equilibrium magnetic field configuration charcterized by a set of three parameters;the aspect ratio, *b,and the safety factor. (Author)

Analytic and numerical studies of Scyllac equilibrium

International Nuclear Information System (INIS)

Barnes, D.C.; Brackbill, J.U.; Dagazian, R.Y.; Freidberg, J.P.; Schneider, W.; Betancourt, O.; Garabedian, P.

1976-01-01

The results of both numerical and analytic studies of the Scyllac equilibria are presented. Analytic expansions are used to derive equilibrium equations appropriate to noncircular cross sections, and compute the stellarator fields which produce toroidal force balance. Numerical algorithms are used to solve both the equilibrium equations and the full system of dynamical equations in three dimensions. Numerical equilibria are found for both l = 1,0 and l= 1,2 systems. It is found that the stellarator fields which produce equilibria in the l = 1.0 system are larger for diffuse than for sharp boundary plasma profiles, and that the stability of the equilibria depends strongly on the harmonic content of the stellarator fields

Isotope effects in the equilibrium and non-equilibrium vaporization of tritiated water and ice

International Nuclear Information System (INIS)

Baumgaertner, F.; Kim, M.-A.

1990-01-01

The vaporization isotope effect of the HTO/H 2 O system has been measured at various temperatures and pressures under equilibrium as well as non-equilibrium conditions. The isotope effect values measured in equilibrium sublimation or distillation are in good agreement with the theoretical values based on the harmonic oscillator model. In non-equilibrium vaporization at low temperatures ( 0 C), the isotope effect decreases rapidly with decreasing system pressure and becomes negligible when the system pressure is lowered more than one tenth of the equilibrium vapor pressure. At higher temperatures, the isotope effect decreases very slowly with decreasing system pressure. Discussion is extended for the application of the present results to the study of biological enrichment of tritium. (author)

Approaching a problem of the long-run real equilibrium exchange rate of Polish zloty while entering the ERM-2 and Euro zone

OpenAIRE

Przystupa, Jan

2009-01-01

Taking into account a large number of types of nominal and real exchange rates, while estimating the real equilibrium exchange rate, one should always remember that there is no a single, universal equilibrium exchange rate. A point value or a path of that exchange rate depends on the adopted definitions and assumptions as well as on the method and purpose of the analysis. However, a value added of each estimation of the equilibrium exchange rate is an answer, whether the economic policy cause...

Validity of Saha's equation of thermal ionization for negatively charged spherical particles in complex plasmas in thermal equilibrium

International Nuclear Information System (INIS)

Sodha, M. S.; Mishra, S. K.

2011-01-01

The authors have discussed the validity of Saha's equation for the charging of negatively charged spherical particles in a complex plasma in thermal equilibrium, even when the tunneling of the electrons, through the potential energy barrier surrounding the particle is considered. It is seen that the validity requires the probability of tunneling of an electron through the potential energy barrier surrounding the particle to be independent of the direction (inside to outside and vice versa) or in other words the Born's approximation should be valid.

Cooling equilibrium and beam loss with internal targets in high energy storage rings

International Nuclear Information System (INIS)

Boine-Frankenheim, O.; Hasse, R.; Hinterberger, F.; Lehrach, A.; Zenkevich, P.

2006-01-01

The beam cooling equilibrium with internal target interaction is analyzed for parameters relevant to the proposed High Energy Storage Ring (HESR). For the proposed experiments with anti-protons high luminosities together with low momentum spreads are required. Rate equations are used to predict the rms equilibrium beam parameters. The cooling and IBS rate coefficients are obtained from simplified models. Energy loss straggling in the target and the associated beam loss are analyzed analytically assuming a thin target. A longitudinal kinetic simulation code is used to study the evolution of the momentum distribution in coasting and bunched beams. Analytic expressions for the target induced momentum tail are found in good agreement with the simulation results

The instantaneous local transition of a stable equilibrium to a chaotic attractor in piecewise-smooth systems of differential equations

Energy Technology Data Exchange (ETDEWEB)

Simpson, D.J.W., E-mail: d.j.w.simpson@massey.ac.nz

2016-09-07

An attractor of a piecewise-smooth continuous system of differential equations can bifurcate from a stable equilibrium to a more complicated invariant set when it collides with a switching manifold under parameter variation. Here numerical evidence is provided to show that this invariant set can be chaotic. The transition occurs locally (in a neighbourhood of a point) and instantaneously (for a single critical parameter value). This phenomenon is illustrated for the normal form of a boundary equilibrium bifurcation in three dimensions using parameter values adapted from of a piecewise-linear model of a chaotic electrical circuit. The variation of a secondary parameter reveals a period-doubling cascade to chaos with windows of periodicity. The dynamics is well approximated by a one-dimensional unimodal map which explains the bifurcation structure. The robustness of the attractor is also investigated by studying the influence of nonlinear terms. - Highlights: • A boundary equilibrium bifurcation involving stable and saddle foci is considered. • A two-dimensional return map is constructed and approximated by a one-dimensional map. • A trapping region and Smale horseshoe are identified for a Rössler-like attractor. • Bifurcation diagrams reveal period-doubling cascades and windows of periodicity.

Dynamical TAP equations for non-equilibrium Ising spin glasses

DEFF Research Database (Denmark)

Roudi, Yasser; Hertz, John

2011-01-01

We derive and study dynamical TAP equations for Ising spin glasses obeying both synchronous and asynchronous dynamics using a generating functional approach. The system can have an asymmetric coupling matrix, and the external fields can be time-dependent. In the synchronously updated model, the TAP...... equations take the form of self consistent equations for magnetizations at time t+1, given the magnetizations at time t. In the asynchronously updated model, the TAP equations determine the time derivatives of the magnetizations at each time, again via self consistent equations, given the current values...... of the magnetizations. Numerical simulations suggest that the TAP equations become exact for large systems....

Equilibrium composition for the reaction of plutonium hydride with air

International Nuclear Information System (INIS)

Zou Lexi; Sun Ying; Xue Weidong; Zhu Zhenghe; Wang Rong; Luo Deli

2002-01-01

There are six independent constituents with 4 chemical elements, i.e. PuH 2.7 (s), PuN(s), Pu 2 O 3 (s), N 2 , O 2 and H 2 , therefore, the system described involves of 2 independent reactions, both ΔG 0 <<0. The calculated equilibrium compositions are in agreement with those of the experimental, which indicates that the chemical equilibrium is nearly completely approached. Therefore, it is believed that the reaction rate of plutonium hydride with air is extremely rapid. The author has briefly discussed the simultaneous reactions and its thermodynamic coupling effect

Quantum hydrodynamics and nonlinear differential equations for degenerate Fermi gas

International Nuclear Information System (INIS)

Bettelheim, Eldad; Abanov, Alexander G; Wiegmann, Paul B

2008-01-01

We present new nonlinear differential equations for spacetime correlation functions of Fermi gas in one spatial dimension. The correlation functions we consider describe non-stationary processes out of equilibrium. The equations we obtain are integrable equations. They generalize known nonlinear differential equations for correlation functions at equilibrium [1-4] and provide vital tools for studying non-equilibrium dynamics of electronic systems. The method we developed is based only on Wick's theorem and the hydrodynamic description of the Fermi gas. Differential equations appear directly in bilinear form. (fast track communication)

Thermodynamic equilibrium-air correlations for flowfield applications

Science.gov (United States)

Zoby, E. V.; Moss, J. N.

1981-01-01

Equilibrium-air thermodynamic correlations have been developed for flowfield calculation procedures. A comparison between the postshock results computed by the correlation equations and detailed chemistry calculations is very good. The thermodynamic correlations are incorporated in an approximate inviscid flowfield code with a convective heating capability for the purpose of defining the thermodynamic environment through the shock layer. Comparisons of heating rates computed by the approximate code and a viscous-shock-layer method are good. In addition to presenting the thermodynamic correlations, the impact of several viscosity models on the convective heat transfer is demonstrated.

Problems with the concept of plasma equilibrium in tokamaks

International Nuclear Information System (INIS)

Carreras, B.A.

1992-01-01

The equilibrium condition for a magnetically confined plasma in normally formulated in terms of macroscopic equations. In these equations, the plasma pressure is assumed to be a function of the magnetic flux with continuous derivatives. However, in three- dimensional systems this is not necessarily the case. Here, we look at the case of an intrinsically three-dimensional realistic tokamak, and we discuss the possible interconnection between the equilibrium and anomalous transport

Numerical Simulation of Non-Equilibrium Two-Phase Wet Steam Flow through an Asymmetric Nozzle

Directory of Open Access Journals (Sweden)

Miah Md Ashraful Alam

2017-11-01

Full Text Available The present study reported of the numerical investigation of a high-speed wet steam flow through an asymmetric nozzle. The spontaneous non-equilibrium homogeneous condensation of wet steam was numerically modeled based on the classical nucleation theory and droplet growth rate equation combined with the field conservations within the computational fluid dynamics (CFD code of ANSYS Fluent 13.0. The equations describing droplet formations and interphase change were solved sequentially after solving the main flow conservation equations. The calculations were carried out assuming the flow two-dimensional, compressible, turbulent, and viscous. The SST k-ω model was used for modeling the turbulence within an unstructured mesh solver. The validation of numerical model was accomplished, and the results showed a good agreement between the numerical simulation and experimental data. The effect of spontaneous non-equilibrium condensation on the jet and shock structures was revealed, and the condensation shown a great influence on the jet structure.

An Empirical Analysis of China's Equilibrium Exchange Rate and Misalignment of the RMB

OpenAIRE

Zhu, Lin

2012-01-01

As economic globalization develops in depth, the exchange rate as an important means of macroeconomic control and economic leverage has played a critical role in the economic development in China. Moreover, the real exchange rate can affect the competitiveness of a country’s economy. In fact, a large number of scholars claim that a country should maintain the real exchange rate at its “equilibrium level” in order to keep a steady growth of the economy. Thus, many studies have emphasized on e...

Parameter Estimation for a Computable General Equilibrium Model

DEFF Research Database (Denmark)

Arndt, Channing; Robinson, Sherman; Tarp, Finn

We introduce a maximum entropy approach to parameter estimation for computable general equilibrium (CGE) models. The approach applies information theory to estimating a system of nonlinear simultaneous equations. It has a number of advantages. First, it imposes all general equilibrium constraints...

Determination of equilibrium electron temperature and times using an electron swarm model with BOLSIG+ calculated collision frequencies and rate coefficients

International Nuclear Information System (INIS)

Pusateri, Elise N.; Morris, Heidi E.; Nelson, Eric M.; Ji, Wei

2015-01-01

Electromagnetic pulse (EMP) events produce low-energy conduction electrons from Compton electron or photoelectron ionizations with air. It is important to understand how conduction electrons interact with air in order to accurately predict EMP evolution and propagation. An electron swarm model can be used to monitor the time evolution of conduction electrons in an environment characterized by electric field and pressure. Here a swarm model is developed that is based on the coupled ordinary differential equations (ODEs) described by Higgins et al. (1973), hereinafter HLO. The ODEs characterize the swarm electric field, electron temperature, electron number density, and drift velocity. Important swarm parameters, the momentum transfer collision frequency, energy transfer collision frequency, and ionization rate, are calculated and compared to the previously reported fitted functions given in HLO. These swarm parameters are found using BOLSIG+, a two term Boltzmann solver developed by Hagelaar and Pitchford (2005), which utilizes updated cross sections from the LXcat website created by Pancheshnyi et al. (2012). We validate the swarm model by comparing to experimental effective ionization coefficient data in Dutton (1975) and drift velocity data in Ruiz-Vargas et al. (2010). In addition, we report on electron equilibrium temperatures and times for a uniform electric field of 1 StatV/cm for atmospheric heights from 0 to 40 km. We show that the equilibrium temperature and time are sensitive to the modifications in the collision frequencies and ionization rate based on the updated electron interaction cross sections

Comparing models of rapidly rotating relativistic stars constructed by two numerical methods

Science.gov (United States)

Stergioulas, Nikolaos; Friedman, John L.

1995-05-01

We present the first direct comparison of codes based on two different numerical methods for constructing rapidly rotating relativistic stars. A code based on the Komatsu-Eriguchi-Hachisu (KEH) method (Komatsu et al. 1989), written by Stergioulas, is compared to the Butterworth-Ipser code (BI), as modified by Friedman, Ipser, & Parker. We compare models obtained by each method and evaluate the accuracy and efficiency of the two codes. The agreement is surprisingly good, and error bars in the published numbers for maximum frequencies based on BI are dominated not by the code inaccuracy but by the number of models used to approximate a continuous sequence of stars. The BI code is faster per iteration, and it converges more rapidly at low density, while KEH converges more rapidly at high density; KEH also converges in regions where BI does not, allowing one to compute some models unstable against collapse that are inaccessible to the BI code. A relatively large discrepancy recently reported (Eriguchi et al. 1994) for models based on Friedman-Pandharipande equation of state is found to arise from the use of two different versions of the equation of state. For two representative equations of state, the two-dimensional space of equilibrium configurations is displayed as a surface in a three-dimensional space of angular momentum, mass, and central density. We find, for a given equation of state, that equilibrium models with maximum values of mass, baryon mass, and angular momentum are (generically) either all unstable to collapse or are all stable. In the first case, the stable model with maximum angular velocity is also the model with maximum mass, baryon mass, and angular momentum. In the second case, the stable models with maximum values of these quantities are all distinct. Our implementation of the KEH method will be available as a public domain program for interested users.

Perturbation theory for continuous stochastic equations

International Nuclear Information System (INIS)

Chechetkin, V.R.; Lutovinov, V.S.

1987-01-01

The various general perturbational schemes for continuous stochastic equations are considered. These schemes have many analogous features with the iterational solution of Schwinger equation for S-matrix. The following problems are discussed: continuous stochastic evolution equations for probability distribution functionals, evolution equations for equal time correlators, perturbation theory for Gaussian and Poissonian additive noise, perturbation theory for birth and death processes, stochastic properties of systems with multiplicative noise. The general results are illustrated by diffusion-controlled reactions, fluctuations in closed systems with chemical processes, propagation of waves in random media in parabolic equation approximation, and non-equilibrium phase transitions in systems with Poissonian breeding centers. The rate of irreversible reaction X + X → A (Smoluchowski process) is calculated with the use of general theory based on continuous stochastic equations for birth and death processes. The threshold criterion and range of fluctuational region for synergetic phase transition in system with Poissonian breeding centers are also considered. (author)

Post-CHF heat transfer: a non-equilibrium, relaxation model

International Nuclear Information System (INIS)

Jones, O.C. Jr.; Zuber, N.

1977-01-01

Existing phenomenological models of heat transfer in the non-equilibrium, liquid-deficient, dispersed flow regime can sometimes predict the thermal behavior fairly well but are quite complex, requiring coupled simultaneous differential equations to describe the axial gradients of mass and energy along with those of droplet acceleration and size. In addition, empirical relations are required to express the droplet breakup and increased effective heat transfer due to holdup. This report describes the development of a different approach to the problem. It is shown that the non-equilibrium component of the total energy can be expressed as a first order, inhomogeneous relaxation equation in terms of one variable coefficient termed the Superheat Relaxation number. A demonstration is provided to show that this relaxation number can be correlated using local variables in such a manner to allow the single non-equilibrium equation to accurately calculate the effects of mass velocity and heat flux along with tube length, diameter, and critical quality for equilibrium qualities from 0.13 to over 3.0

Isomorph invariance of Couette shear flows simulated by the SLLOD equations of motion

DEFF Research Database (Denmark)

Separdar, Leila; Bailey, Nicholas; Schrøder, Thomas

2013-01-01

fluctuations of virial and potential energy. Such systems have good isomorphs (curves in the thermodynamic phase diagram along which structural, dynamical, and some thermodynamic quantities are invariant when expressed in reduced units). The SLLOD equations of motion were used to simulate Couette shear flows......Non-equilibrium molecular dynamics simulations were performed to study the thermodynamic, structural, and dynamical properties of the single-component Lennard-Jones and the Kob-Andersen binary Lennard-Jones liquids. Both systems are known to have strong correlations between equilibrium thermal...... of the two systems. We show analytically that these equations are isomorph invariant provided the reduced strain rate is fixed along the isomorph. Since isomorph invariance is generally only approximate, a range of strain rates were simulated to test for the predicted invariance, covering both the linear...

A new equilibrium torus solution and GRMHD initial conditions

Science.gov (United States)

Penna, Robert F.; Kulkarni, Akshay; Narayan, Ramesh

2013-11-01

Context. General relativistic magnetohydrodynamic (GRMHD) simulations are providing influential models for black hole spin measurements, gamma ray bursts, and supermassive black hole feedback. Many of these simulations use the same initial condition: a rotating torus of fluid in hydrostatic equilibrium. A persistent concern is that simulation results sometimes depend on arbitrary features of the initial torus. For example, the Bernoulli parameter (which is related to outflows), appears to be controlled by the Bernoulli parameter of the initial torus. Aims: In this paper, we give a new equilibrium torus solution and describe two applications for the future. First, it can be used as a more physical initial condition for GRMHD simulations than earlier torus solutions. Second, it can be used in conjunction with earlier torus solutions to isolate the simulation results that depend on initial conditions. Methods: We assume axisymmetry, an ideal gas equation of state, constant entropy, and ignore self-gravity. We fix an angular momentum distribution and solve the relativistic Euler equations in the Kerr metric. Results: The Bernoulli parameter, rotation rate, and geometrical thickness of the torus can be adjusted independently. Our torus tends to be more bound and have a larger radial extent than earlier torus solutions. Conclusions: While this paper was in preparation, several GRMHD simulations appeared based on our equilibrium torus. We believe it will continue to provide a more realistic starting point for future simulations.

Diffusion equations and the time evolution of foreign exchange rates

Energy Technology Data Exchange (ETDEWEB)

Figueiredo, Annibal; Castro, Marcio T. de [Institute of Physics, Universidade de Brasília, Brasília DF 70910-900 (Brazil); Fonseca, Regina C.B. da [Department of Mathematics, Instituto Federal de Goiás, Goiânia GO 74055-110 (Brazil); Gleria, Iram, E-mail: iram@fis.ufal.br [Institute of Physics, Federal University of Alagoas, Brazil, Maceió AL 57072-900 (Brazil)

2013-10-01

We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers–Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.

Diffusion equations and the time evolution of foreign exchange rates

Science.gov (United States)

Figueiredo, Annibal; de Castro, Marcio T.; da Fonseca, Regina C. B.; Gleria, Iram

2013-10-01

We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers-Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.

Diffusion equations and the time evolution of foreign exchange rates

International Nuclear Information System (INIS)

Figueiredo, Annibal; Castro, Marcio T. de; Fonseca, Regina C.B. da; Gleria, Iram

2013-01-01

We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers–Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.

Three-dimensional plasma equilibrium model based on the poloidal representation of the magnetic field

International Nuclear Information System (INIS)

Gruber, R.; Degtyarev, L.M.; Kuper, A.; Martynov, A.A.; Medvedev, S.Yu.; Shafranov, V.D.

1996-01-01

Equations for the three-dimensional equilibrium of a plasma are formulated in the poloidal representation. The magnetic field is expressed in terms of the poloidal magnetic flux Ψ and the poloidal electric current F. As a result, three-dimensional equilibrium configurations are analyzed with the help of a set of equations including the elliptical equation for the poloidal flux, the magnetic differential equation for the parallel current, and the equations for the basis vector field b. To overcome the difficulties associated with peculiarities that can arise in solving the magnetic differential equation at rational toroidal magnetic surfaces, small regulating corrections are introduced into the proposed set of equations. In this case, second-order differential terms with a small parameter appear in the magnetic differential equations. As a result, these equations take the form of elliptical equations. Three versions of regulating corrections are proposed. The equations obtained can be used to develop numerical codes for calculating three-dimensional equilibrium plasma configurations with an island structure

Validation of predictive equations for glomerular filtration rate in the Saudi population

Directory of Open Access Journals (Sweden)

Al Wakeel Jamal

2009-01-01

Full Text Available Predictive equations provide a rapid method of assessing glomerular filtration rate (GFR. To compare the various predictive equations for the measurement of this parameter in the Saudi population, we measured GFR by the Modification of Diet in Renal Disease (MDRD and Cockcroft-Gault formulas, cystatin C, reciprocal of cystatin C, creatinine clearance, reciprocal of creatinine, and inulin clearance in 32 Saudi subjects with different stages of renal disease. We com-pared GFR measured by inulin clearance and the estimated GFR by the equations. The study included 19 males (59.4% and 13 (40.6% females with a mean age of 42.3 ± 15.2 years and weight of 68.6 ± 17.7 kg. The mean serum creatinine was 199 ± 161 μmol/L. The GFR measured by inulin clearance was 50.9 ± 33.5 mL/min, and the estimated by Cockcroft-Gault and by MDRD equations was 56.3 ± 33.3 and 52.8 ± 32.0 mL/min, respectively. The GFR estimated by MDRD revealed the strongest correlation with the measured inulin clearance (r= 0.976, P= 0.0000 followed by the GFR estimated by Cockcroft-Gault, serum cystatin C, and serum creatinine (r= 0.953, P= 0.0000 (r= 0.787, P= 0.0001 (r= -0.678, P= 0.001, respectively. The reciprocal of cystatin C and serum creatinine revealed a correlation coefficient of 0.826 and 0.93, respectively. Cockroft-Gault for-mula overestimated the GFR by 5.40 ± 10.3 mL/min in comparison to the MDRD formula, which exhibited the best correlation with inulin clearance in different genders, age groups, body mass index, renal transplant recipients, chronic kidney disease stages when compared to other GFR predictive equations.

Parameter Estimation for a Computable General Equilibrium Model

DEFF Research Database (Denmark)

Arndt, Channing; Robinson, Sherman; Tarp, Finn

2002-01-01

We introduce a maximum entropy approach to parameter estimation for computable general equilibrium (CGE) models. The approach applies information theory to estimating a system of non-linear simultaneous equations. It has a number of advantages. First, it imposes all general equilibrium constraints...

Approximate variational solutions of the Grad-Shafranov equation

International Nuclear Information System (INIS)

Ludwig, G.O.

2001-01-01

Approximate solutions of the Grad-Schlueter-Shafranov equation based on variational methods are developed. The power series solutions of the Euler-Lagrange equations for equilibrium are compared with direct variational results for a low aspect ratio tokamak equilibrium. (author)

Empirical rate equation model and rate calculations of hydrogen generation for Hanford tank waste

International Nuclear Information System (INIS)

HU, T.A.

1999-01-01

Empirical rate equations are derived to estimate hydrogen generation based on chemical reactions, radiolysis of water and organic compounds, and corrosion processes. A comparison of the generation rates observed in the field with the rates calculated for twenty eight tanks shows agreement within a factor of two to three

Equilibrium Bird Species Diversity in Atlantic Islands.

Science.gov (United States)

Valente, Luis; Illera, Juan Carlos; Havenstein, Katja; Pallien, Tamara; Etienne, Rampal S; Tiedemann, Ralph

2017-06-05

Half a century ago, MacArthur and Wilson proposed that the number of species on islands tends toward a dynamic equilibrium diversity around which species richness fluctuates [1]. The current prevailing view in island biogeography accepts the fundamentals of MacArthur and Wilson's theory [2] but questions whether their prediction of equilibrium can be fulfilled over evolutionary timescales, given the unpredictable and ever-changing nature of island geological and biotic features [3-7]. Here we conduct a complete molecular phylogenetic survey of the terrestrial bird species from four oceanic archipelagos that make up the diverse Macaronesian bioregion-the Azores, the Canary Islands, Cape Verde, and Madeira [8, 9]. We estimate the times at which birds colonized and speciated in the four archipelagos, including many previously unsampled endemic and non-endemic taxa and their closest continental relatives. We develop and fit a new multi-archipelago dynamic stochastic model to these data, explicitly incorporating information from 91 taxa, both extant and extinct. Remarkably, we find that all four archipelagos have independently achieved and maintained a dynamic equilibrium over millions of years. Biogeographical rates are homogeneous across archipelagos, except for the Canary Islands, which exhibit higher speciation and colonization. Our finding that the avian communities of the four Macaronesian archipelagos display an equilibrium diversity pattern indicates that a diversity plateau may be rapidly achieved on islands where rates of in situ radiation are low and extinction is high. This study reveals that equilibrium processes may be more prevalent than recently proposed, supporting MacArthur and Wilson's 50-year-old theory. Copyright © 2017 Elsevier Ltd. All rights reserved.

Extinction rates in tumour public goods games.

Science.gov (United States)

Gerlee, Philip; Altrock, Philipp M

2017-09-01

Cancer evolution and progression are shaped by cellular interactions and Darwinian selection. Evolutionary game theory incorporates both of these principles, and has been proposed as a framework to understand tumour cell population dynamics. A cornerstone of evolutionary dynamics is the replicator equation, which describes changes in the relative abundance of different cell types, and is able to predict evolutionary equilibria. Typically, the replicator equation focuses on differences in relative fitness. We here show that this framework might not be sufficient under all circumstances, as it neglects important aspects of population growth. Standard replicator dynamics might miss critical differences in the time it takes to reach an equilibrium, as this time also depends on cellular turnover in growing but bounded populations. As the system reaches a stable manifold, the time to reach equilibrium depends on cellular death and birth rates. These rates shape the time scales, in particular, in coevolutionary dynamics of growth factor producers and free-riders. Replicator dynamics might be an appropriate framework only when birth and death rates are of similar magnitude. Otherwise, population growth effects cannot be neglected when predicting the time to reach an equilibrium, and cell-type-specific rates have to be accounted for explicitly. © 2017 The Authors.

Ionic diffusion through confined geometries: from Langevin equations to partial differential equations

International Nuclear Information System (INIS)

Nadler, Boaz; Schuss, Zeev; Singer, Amit; Eisenberg, R S

2004-01-01

Ionic diffusion through and near small domains is of considerable importance in molecular biophysics in applications such as permeation through protein channels and diffusion near the charged active sites of macromolecules. The motion of the ions in these settings depends on the specific nanoscale geometry and charge distribution in and near the domain, so standard continuum type approaches have obvious limitations. The standard machinery of equilibrium statistical mechanics includes microscopic details, but is also not applicable, because these systems are usually not in equilibrium due to concentration gradients and to the presence of an external applied potential, which drive a non-vanishing stationary current through the system. We present a stochastic molecular model for the diffusive motion of interacting particles in an external field of force and a derivation of effective partial differential equations and their boundary conditions that describe the stationary non-equilibrium system. The interactions can include electrostatic, Lennard-Jones and other pairwise forces. The analysis yields a new type of Poisson-Nernst-Planck equations, that involves conditional and unconditional charge densities and potentials. The conditional charge densities are the non-equilibrium analogues of the well studied pair correlation functions of equilibrium statistical physics. Our proposed theory is an extension of equilibrium statistical mechanics of simple fluids to stationary non-equilibrium problems. The proposed system of equations differs from the standard Poisson-Nernst-Planck system in two important aspects. First, the force term depends on conditional densities and thus on the finite size of ions, and second, it contains the dielectric boundary force on a discrete ion near dielectric interfaces. Recently, various authors have shown that both of these terms are important for diffusion through confined geometries in the context of ion channels

Diffusion kinetics and spinodal decay of quasi-equilibrium solid solutions

International Nuclear Information System (INIS)

Zakharov, M.A.

2000-01-01

Phenomenological theory for rearrangement of solid solutions with the hierarchy of the component atomic mobilities is elaborated in the approximation of the local equilibrium. The hydrodynamic stage of the evolution of these solutions is studied as a sequence of quasi-equilibrium states characterized by implementation of some conditions of the total equilibrium. On the basis of separation of fast and slow constituents of diffusion and on the basis of the method of reduced description one derived equation for evolution of separations of fast components in quasi-equilibrium solid solutions at the arbitrary stages of rearrangement in terms of the generalized lattice model taking account of the proper volumes of the components. The conditions of the stability of quasi-equilibrium solutions to the spinodal decomposition are determined and the equations of metastability boundaries of such systems are derived [ru

Zero-rating food in South Africa: A computable general equilibrium analysis

Directory of Open Access Journals (Sweden)

M Kearney

2004-04-01

Full Text Available Zero-rating food is considered to alleviate poverty of poor households who spend the largest proportion of their income on food.  However, this will result in a loss of revenue for government.  A Computable General Equilibrium (CGE model is used to analyze the combined effects on zero-rating food and using alternative revenue sources to compensate for the loss in revenue.  To prohibit excessively high increases in the statutory VAT rates of business and financial services, increasing direct taxes or increasing VAT to 16 per cent, is investigated.  Increasing direct taxes is the most successful option when creating a more progressive tax structure, and still generating a positive impact on GDP.  The results indicate that zero-rating food combined with a proportional percentage increase in direct taxes can improve the welfare of poor households.

Equilibrium state of colliding electron beams

Directory of Open Access Journals (Sweden)

R. L. Warnock

2003-10-01

Full Text Available 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 Haïssinski 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 1 degree of freedom, a so-called strong-strong model with nonlinear beam-beam force. We prove the 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, as 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.

ECONOMETRIC APPROACH TO DIFFERENCE EQUATIONS MODELING OF EXCHANGE RATES CHANGES

Directory of Open Access Journals (Sweden)

Josip Arnerić

2010-12-01

Full Text Available Time series models that are commonly used in econometric modeling are autoregressive stochastic linear models (AR and models of moving averages (MA. Mentioned models by their structure are actually stochastic difference equations. Therefore, the objective of this paper is to estimate difference equations containing stochastic (random component. Estimated models of time series will be used to forecast observed data in the future. Namely, solutions of difference equations are closely related to conditions of stationary time series models. Based on the fact that volatility is time varying in high frequency data and that periods of high volatility tend to cluster, the most successful and popular models in modeling time varying volatility are GARCH type models and their variants. However, GARCH models will not be analyzed because the purpose of this research is to predict the value of the exchange rate in the levels within conditional mean equation and to determine whether the observed variable has a stable or explosive time path. Based on the estimated difference equation it will be examined whether Croatia is implementing a stable policy of exchange rates.

Modeling of the equilibrium of a tokamak plasma

International Nuclear Information System (INIS)

Grandgirard, V.

1999-12-01

The simulation and the control of a plasma discharge in a tokamak require an efficient and accurate solving of the equilibrium because this equilibrium needs to be calculated again every microsecond to simulate discharges that can last up to 1000 seconds. The purpose of this thesis is to propose numerical methods in order to calculate these equilibrium with acceptable computer time and memory size. Chapter 1 deals with hydrodynamics equation and sets up the problem. Chapter 2 gives a method to take into account the boundary conditions. Chapter 3 is dedicated to the optimization of the inversion of the system matrix. This matrix being quasi-symmetric, the Woodbury method combined with Cholesky method has been used. This direct method has been compared with 2 iterative methods: GMRES (generalized minimal residual) and BCG (bi-conjugate gradient). The 2 last chapters study the control of the plasma equilibrium, this work is presented in the formalism of the optimized control of distributed systems and leads to non-linear equations of state and quadratic functionals that are solved numerically by a quadratic sequential method. This method is based on the replacement of the initial problem with a series of control problems involving linear equations of state. (A.C.)

Equilibrium and stability of off-axis periodically focused particle beams

International Nuclear Information System (INIS)

Moraes, J.S.; Pakter, R.; Rizzato, F.B.

2004-01-01

A general equation for the centroid motion of free, continuous, intense beams propagating off axis in solenoidal periodic focusing fields is derived. The centroid equation is found to be independent of the specific beam distribution and may exhibit unstable solutions. A new Vlasov equilibrium for off-axis beam propagation is also obtained. The properties of the equilibrium and the relevance of centroid motion to beam confinement are discussed

Multiple spatial scaling and the weak-coupling approximation. I. General formulation and equilibrium theory

Energy Technology Data Exchange (ETDEWEB)

Kleinsmith, P E [Carnegie-Mellon Univ., Pittsburgh, Pa. (USA)

1976-04-01

Multiple spatial scaling is incorporated in a modified form of the Bogoliubov plasma cluster expansion; then this proposed reformulation of the plasma weak-coupling approximation is used to derive, from the BBGKY Hierarchy, a decoupled set of equations for the one-and two-particle distribution functions in the limit as the plasma parameter goes to zero. Because the reformulated cluster expansion permits retention of essential two-particle collisional information in the limiting equations, while simultaneously retaining the well-established Debye-scale relative ordering of the correlation functions, decoupling of the Hierarchy is accomplished without introduction of the divergence problems encountered in the Bogoliubov theory, as is indicated by an exact solution of the limiting equations for the equilibrium case. To establish additional links with existing plasma equilibrium theories, the two-particle equilibrium correlation function is used to calculate the interaction energy and the equation of state. The limiting equation for the equilibrium three-particle correlation function is then developed, and a formal solution is obtained.

Equilibrium and stability properties of relativistic electron rings and E-layers

International Nuclear Information System (INIS)

Uhm, H.

1976-01-01

Equilibrium and stability properties of magnetically confined partially-neutralized thin electron ring and E-layer are investigated using the Vlasov-Maxwell equations. The analysis is carried out within the context of the assumption that the minor dimensions (a,b) of the system are much less than the collisionless skin depth (c/antiω/sub p/). The equilibrium configuration of the E-layer is assumed to be an infinitely long, azimuthally symmetric hollow electron beam which is aligned parallel to a uniform axial magnetic field. On the other hand, the electron ring is located at the midplane of an externally imposed mirror field which acts to confine the ring both axially and radially. The equilibrium properties of the E-layer and electron ring are obtained self-consistently for several choices of equilibrium electron distribution function. The negative-mass instability analysis is carried out for the relativistic E-layer equilibrium in which all of the electrons have the same transverse energy and a spread in canonical angular momentum, assuming a fixed ion background. The ion resonance instability properties are investigated for a relativistic nonneutral E-layer aligned parallel to a uniform magnetic field and located between two ground coaxial cylindrical conductors. The stability properties of a nonrelativistic electron ring is investigated within the framework of the linearized Vlasov-Poisson equations. The dispersion relation is obtained for the self-consistent electron distribution function in which all electrons have the same value of energy an the same value of canonical angular momentum. The positive ions in the electron ring are assumed to form an immobile partially neutralizing background. The stability criteria as well as the instability growth rates are derived and discussed including the effect of geometrical configuration of the system. Equilibrium space-charge effects play a significant role in stability behavior

Computational methods for reversed-field equilibrium

International Nuclear Information System (INIS)

Boyd, J.K.; Auerbach, S.P.; Willmann, P.A.; Berk, H.L.; McNamara, B.

1980-01-01

Investigating the temporal evolution of reversed-field equilibrium caused by transport processes requires the solution of the Grad-Shafranov equation and computation of field-line-averaged quantities. The technique for field-line averaging and the computation of the Grad-Shafranov equation are presented. Application of Green's function to specify the Grad-Shafranov equation boundary condition is discussed. Hill's vortex formulas used to verify certain computations are detailed. Use of computer software to implement computational methods is described

3D equilibrium codes for mirror machines

International Nuclear Information System (INIS)

Kaiser, T.B.

1983-01-01

The codes developed for cumputing three-dimensional guiding center equilibria for quadrupole tandem mirrors are discussed. TEBASCO (Tandem equilibrium and ballooning stability code) is a code developed at LLNL that uses a further expansion of the paraxial equilibrium equation in powers of β (plasma pressure/magnetic pressure). It has been used to guide the design of the TMX-U and MFTF-B experiments at Livermore. Its principal weakness is its perturbative nature, which renders its validity for high-β calculation open to question. In order to compute high-β equilibria, the reduced MHD technique that has been proven useful for determining toroidal equilibria was adapted to the tandem mirror geometry. In this approach, the paraxial expansion of the MHD equations yields a set of coupled nonlinear equations of motion valid for arbitrary β, that are solved as an initial-value problem. Two particular formulations have been implemented in computer codes developed at NYU/Kyoto U and LLNL. They differ primarily in the type of grid, the location of the lateral boundary and the damping techniques employed, and in the method of calculating pressure-balance equilibrium. Discussions on these codes are presented in this paper. (Kato, T.)

Warm-fluid description of intense beam equilibrium and electrostatic stability properties

International Nuclear Information System (INIS)

Lund, S.M.; Davidson, R.C.

1998-01-01

A nonrelativistic warm-fluid model is employed in the electrostatic approximation to investigate the equilibrium and stability properties of an unbunched, continuously focused intense ion beam. A closed macroscopic model is obtained by truncating the hierarchy of moment equations by the assumption of negligible heat flow. Equations describing self-consistent fluid equilibria are derived and elucidated with examples corresponding to thermal equilibrium, the Kapchinskij endash Vladimirskij (KV) equilibrium, and the waterbag equilibrium. Linearized fluid equations are derived that describe the evolution of small-amplitude perturbations about an arbitrary equilibrium. Electrostatic stability properties are analyzed in detail for a cold beam with step-function density profile, and then for axisymmetric flute perturbations with ∂/∂θ=0 and ∂/∂z=0 about a warm-fluid KV beam equilibrium. The radial eigenfunction describing axisymmetric flute perturbations about the KV equilibrium is found to be identical to the eigenfunction derived in a full kinetic treatment. However, in contrast to the kinetic treatment, the warm-fluid model predicts stable oscillations. None of the instabilities that are present in a kinetic description are obtained in the fluid model. A careful comparison of the mode oscillation frequencies associated with the fluid and kinetic models is made in order to delineate which stability features of a KV beam are model-dependent and which may have general applicability. copyright 1998 American Institute of Physics

Internal equilibrium layer growth over forest

DEFF Research Database (Denmark)

Dellwik, E.; Jensen, N.O.

2000-01-01

the magnitude of the scatter. Different theoretical friction velocity profiles for the Internal Boundary Layer (IBL) are tested against the forest data. The results yield information on the Internal Equilibrium Layer (IEL) growth and an equation for the IEL height fur neutral conditions is derived. For stable...... conditions the results indicate that very long fetches are required in order to measure parameters in equilibrium with the actual surface....

Time-dependent free boundary equilibrium and resistive diffusion in a tokamak plasma

International Nuclear Information System (INIS)

Selig, G.

2012-12-01

In a Tokamak, in order to create the necessary conditions for nuclear fusion to occur, a plasma is maintained by applying magnetic fields. Under the hypothesis of an axial symmetry of the tokamak, the study of the magnetic configuration at equilibrium is done in two dimensions, and is deduced from the poloidal flux function. This function is solution of a non linear partial differential equation system, known as equilibrium problem. This thesis presents the time dependent free boundary equilibrium problem, where the circuit equations in the tokamak coils and passive conductors are solved together with the Grad-Shafranov equation to produce a dynamic simulation of the plasma. In this framework, the Finite Element equilibrium code CEDRES has been improved in order to solve the aforementioned dynamic problem. Consistency tests and comparisons with the DINA-CH code on an ITER vertical instability case have validated the results. Then, the resistive diffusion of the plasma current density has been simulated using a coupling between CEDRES and the averaged one-dimensional diffusion equation, and it has been successfully compared with the integrated modeling code CRONOS. (author)

Gyrokinetic Magnetohydrodynamics and the Associated Equilibrium

Science.gov (United States)

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.

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

International Nuclear Information System (INIS)

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

2007-01-01

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 NE equilibrium reactions and a set of reactive transport equations of M-NE 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

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

Science.gov (United States)

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.

Rate equation modelling of the optically pumped spin-exchange source

International Nuclear Information System (INIS)

Stenger, J.; Rith, K.

1995-01-01

Sources for spin polarized hydrogen or deuterium, polarized via spin-exchange of a laser optically pumped alkali metal, can be modelled by rate equations. The rate equations for this type of source, operated either with hydrogen or deuterium, are given explicitly with the intention of providing a useful tool for further source optimization and understanding. Laser optical pumping of alkali metal, spin-exchange collisions of hydrogen or deuterium atoms with each other and with alkali metal atoms are included, as well as depolarization due to flow and wall collisions. (orig.)

Rate equation analysis and non-Hermiticity in coupled semiconductor laser arrays

Science.gov (United States)

Gao, Zihe; Johnson, Matthew T.; Choquette, Kent D.

2018-05-01

Optically coupled semiconductor laser arrays are described by coupled rate equations. The coupled mode equations and carrier densities are included in the analysis, which inherently incorporate the carrier-induced nonlinearities including gain saturation and amplitude-phase coupling. We solve the steady-state coupled rate equations and consider the cavity frequency detuning and the individual laser pump rates as the experimentally controlled variables. We show that the carrier-induced nonlinearities play a critical role in the mode control, and we identify gain contrast induced by cavity frequency detuning as a unique mechanism for mode control. Photon-mediated energy transfer between cavities is also discussed. Parity-time symmetry and exceptional points in this system are studied. Unbroken parity-time symmetry can be achieved by judiciously combining cavity detuning and unequal pump rates, while broken symmetry lies on the boundary of the optical locking region. Exceptional points are identified at the intersection between broken symmetry and unbroken parity-time symmetry.

Creatinine Clearance Is Not Equal to Glomerular Filtration Rate and Cockcroft-Gault Equation Is Not Equal to CKD-EPI Collaboration Equation.

Science.gov (United States)

Fernandez-Prado, Raul; Castillo-Rodriguez, Esmeralda; Velez-Arribas, Fernando Javier; Gracia-Iguacel, Carolina; Ortiz, Alberto

2016-12-01

Direct oral anticoagulants (DOACs) may require dose reduction or avoidance when glomerular filtration rate is low. However, glomerular filtration rate is not usually measured in routine clinical practice. Rather, equations that incorporate different variables use serum creatinine to estimate either creatinine clearance in mL/min or glomerular filtration rate in mL/min/1.73 m 2 . The Cockcroft-Gault equation estimates creatinine clearance and incorporates weight into the equation. By contrast, the Modification of Diet in Renal Disease and Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equations estimate glomerular filtration rate and incorporate ethnicity but not weight. As a result, an individual patient may have very different renal function estimates, depending on the equation used. We now highlight these differences and discuss the impact on routine clinical care for anticoagulation to prevent embolization in atrial fibrillation. Pivotal DOAC clinical trials used creatinine clearance as a criterion for patient enrollment, and dose adjustment and Federal Drug Administration recommendations are based on creatinine clearance. However, clinical biochemistry laboratories provide CKD-EPI glomerular filtration rate estimations, resulting in discrepancies between clinical trial and routine use of the drugs. Copyright © 2016 Elsevier Inc. All rights reserved.

Generalized reduced magnetohydrodynamic equations

International Nuclear Information System (INIS)

Kruger, S.E.

1999-01-01

A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-Alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson. The equations have been programmed into a spectral initial value code and run with shear flow that is consistent with the equilibrium input into the code. Linear results of tearing modes with shear flow are presented which differentiate the effects of shear flow gradients in the layer with the effects of the shear flow decoupling multiple harmonics

The Influence of Non-Equilibrium Excitation on the Electron Density in One-Dimensional MFD Channel Flow

Energy Technology Data Exchange (ETDEWEB)

Eichert, K.; Kaeppeler, H. J. [Institut fuer Plasmaforschung der Technischen Hochschule Stuttgart, Federal Republic of Germany (Germany)

1966-10-15

In previous publications, a system of equations was derived from the gas-kinetic description of a multi-component reacting plasma and employed for the calculation of one-dimensional subsonic flows. This system is now extended to include non-equilibrium excitation. No thermal or chemical equilibrium between the various components of the plasma is assumed. The components of the plasma considered are a non-reacting working fluid, an alkali metal vapour as a seeding material, ions of this seeding substance, and electrons. Three levels for the excited states are introduced. The reactions considered are excitation and ionization by electron collisions, and photo-ionization, as well as the corresponding reverse processes. For the reaction velocities, analytical equations are introduced permitting insertion of any excitation or ionization cross-sections of either experimental or theoretical origin. The method employed had been previously suggested by one of the authors. As examples, the degrees of excitation and ionization in the flow of a helium working fluid with 1% caesium seeding through a channel against transverse magnetic fields of 15 and 40 kg at Mach numbers of 0.7 and 0.8, respectively, were calculated. The results of the calculations show that for relatively small magnetic fields there is no rapid rise of the ionization to Saha-equilibrium as a function of electron temperature. A comparison with the results of a calculation neglecting excitation shows that especially for relatively large magnetic fields non-equilibrium excitation has an essential influence on the electron density and its approach to equilibrium. Neglecting excitation, there results a nearly frozen behaviour of the degree of ionization within channel lengths of technical interest for small magnetic fields. (author)

Thermomechanic equations for magnetic fluids of equilibrium magnetization

International Nuclear Information System (INIS)

Bashtovoy, V.G.; Berkovsky, B.M.; Vislovich, A.N.

1988-01-01

The main physical prerequisite for the existence of equilibrium magnetization is the assumption that nothing, except thermal motion, hinders the orientation of elementary magnetic moments along the field and that the mean value of magnetization is achieved instantaneously, i.e., within the times much shorter than the characteristic times of macroscopic processes (hydrodynamic, thermal, electromagnetic, etc.). This assumption makes it possible to consider the fluid magnetization vector M-vector at a given instant to be parallel to the vector of magnetic field intensity H-vector, which in the general form may be related as M-vector = (M/H)H-vector. Magnetization M is determined by the fluid temperature and density and by field intensity: M = M(T,rho,H). It is natural that it decreases with rising temperature and increases with the field intensity. The condition for the vectors M-vector and H-vector to be parallel is realized in a MF only for certain colloid characteristics. Nevertheless, for a wide range of problems this condition may be regarded as fulfilled and enables one to study those effects in a MF which are caused to occur by the volume magnetic force due to the interaction between equilibrium magnetization and the magnetic field

Computational studies in tokamak equilibrium and transport

International Nuclear Information System (INIS)

Braams, B.J.

1986-01-01

This thesis is concerned with some problems arising in the magnetic confinement approach to controlled thermonuclear fusion. The work address the numerical modelling of equilibrium and transport properties of a confined plasma and the interpretation of experimental data. The thesis is divided in two parts. Part 1 is devoted to some aspects of the MHD equilibrium problem, both in the 'direct' formulation (given an equation for the plasma current, the corresponding equilibrium is to be determined) and in the 'inverse' formulation (the interpretation of measurements at the plasma edge). Part 2 is devoted to numerical studies of the edge plasma. The appropriate Navier-Stokes system of fluid equations is solved in a two-dimensional geometry. The main interest of this work is to develop an understanding of particle and energy transport in the scrape-off layer and onto material boundaries, and also to contribute to the conceptual design of the NET/INTOR tokamak reactor experiment. (Auth.)

Coupled force-balance and particle-occupation rate equations for high-field electron transport

International Nuclear Information System (INIS)

Lei, X. L.

2008-01-01

It is pointed out that in the framework of balance-equation approach, the coupled force-balance and particle-occupation rate equations can be used as a complete set of equations to determine the high-field transport of semiconductors in both strong and weak electron-electron interaction limits. We call to attention that the occupation rate equation conserves the total particle number and maintains the energy balance of the relative electron system, and there is no need to introduce any other term in it. The addition of an energy-drift term in the particle-occupation rate equation [Phys. Rev. B 71, 195205 (2005)] is physically inadequate for the violation of the total particle-number conservation and the energy balance. It may lead to a substantial unphysical increase of the total particle number by the application of a dc electric field

Ionization equilibrium and equation of state in the solar interior

International Nuclear Information System (INIS)

Rogers, F.J.

1984-01-01

Many-body formulations of the equations of state are restated as a set of Saha-like equations. It is shown that the resulting equations are unique and convergent. These equations are similar to the usual Saha equations to the order of the Debye-Huckel theory. Higher order corrections, however, require a more general formulation. It is demonstrated that the positive free energy resulting from the interaction of unscreened particles in high orbits depletes the occupation of these states, without the introduction of shifted energy levels

Elements of non-equilibrium (ℎ, k)-dynamics at zero and finite temperatures

International Nuclear Information System (INIS)

Golubeva, O.N.; Sukhanov, A.D.

2011-01-01

We suggest a method which allows developing some elements of non-equilibrium (ℎ, k)-dynamics without use of Schroedinger equation. It is based on the generalization pf Fokker-Planck and Hamilton-Jacobi equations. Sequential considering of stochastic influence of vacuum is realized in the quantum heat bath model. We show that at the presence of quantum-thermal diffusion non-equilibrium wave functions describe the process of nearing to generalized state of thermal equilibrium at zero and finite temperatures. They can be used as a ground for universal description of transport phenomena

equilibrium approach in thederivation of differential equations

African Journals Online (AJOL)

user

DEPT OF CIVIL ENGINEERING, ENUGU STATE UNIVERSITY OF SCIENCE & TECHNOLOGY ... In this paper, the differential equations of Mindlin plates are derived from basic principles by ..... Journal of Applied Mechanics, pages 31-38.

Equilibrium and stability of a rotating plasma

International Nuclear Information System (INIS)

Janssen, P.A.E.M.

1979-01-01

The author considers the equilibrium and stability of a rotating plasma. The kinetic equations for ions and electrons supplemented with the Maxwell equations and the appropriate boundary conditions are used. Two different models for the rotating plasma are considered: the equilibrium of a 'fast' rotating plasma (Magneto Hydrodynamic ordering) and the stability of a slowly rotating, 'weakly' unstable plasma (Finite Larmor Radius ordering). A striking difference between these orderings is the fact that, regarding the stability of the plasma, for a F.L.R. plasma viscosity effects due to the finite Larmor radius are important, whereas in a M.H.D. plasma they are negligible (at least to the required order). (Auth.)

Modeling Electric Discharges with Entropy Production Rate Principles

Directory of Open Access Journals (Sweden)

Thomas Christen

2009-12-01

Full Text Available Under which circumstances are variational principles based on entropy production rate useful tools for modeling steady states of electric (gas discharge systems far from equilibrium? It is first shown how various different approaches, as Steenbeck’s minimum voltage and Prigogine’s minimum entropy production rate principles are related to the maximum entropy production rate principle (MEPP. Secondly, three typical examples are discussed, which provide a certain insight in the structure of the models that are candidates for MEPP application. It is then thirdly argued that MEPP, although not being an exact physical law, may provide reasonable model parameter estimates, provided the constraints contain the relevant (nonlinear physical effects and the parameters to be determined are related to disregarded weak constraints that affect mainly global entropy production. Finally, it is additionally conjectured that a further reason for the success of MEPP in certain far from equilibrium systems might be based on a hidden linearity of the underlying kinetic equation(s.

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

Science.gov (United States)

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.

Forces and energy dissipation in inhomogeneous non-equilibrium superconductors

International Nuclear Information System (INIS)

Poluehktov, Yu.M.; Slezov, V.V.

1987-01-01

The phenomenological theory of volume forces and dissipation processes in inhomogeneous non-equilibrium superconductors near temperature transition from the normal to superconducting state is constructed. The approach is based on application of dynamic equations of superconductivity formulated on the basis of the Lagrangian formalism. These equations are generalized the Ginzburg-Landau theory in the nonstationary non-equilibrium case for ''foul'' superconductors. The value estimations of volume forces arising in inhomogeneities during relaxation of an order parameter and when the electrical field is penetrated into the superconductor, are given

Fractional Bhatnagar-Gross-Krook kinetic equation

Science.gov (United States)

Goychuk, Igor

2017-11-01

The linear Boltzmann equation (LBE) approach is generalized to describe fractional superdiffusive transport of the Lévy walk type in external force fields. The time distribution between scattering events is assumed to have a finite mean value and infinite variance. It is completely characterized by the two scattering rates, one fractional and a normal one, which defines also the mean scattering rate. We formulate a general fractional LBE approach and exemplify it with a particularly simple case of the Bohm and Gross scattering integral leading to a fractional generalization of the Bhatnagar, Gross and Krook (BGK) kinetic equation. Here, at each scattering event the particle velocity is completely randomized and takes a value from equilibrium Maxwell distribution at a given fixed temperature. We show that the retardation effects are indispensable even in the limit of infinite mean scattering rate and argue that this novel fractional kinetic equation provides a viable alternative to the fractional Kramers-Fokker-Planck (KFP) equation by Barkai and Silbey and its generalization by Friedrich et al. based on the picture of divergent mean time between scattering events. The case of divergent mean time is also discussed at length and compared with the earlier results obtained within the fractional KFP. Also a phenomenological fractional BGK equation without retardation effects is proposed in the limit of infinite scattering rates. It cannot be, however, rigorously derived from a scattering model, being rather clever postulated. It this respect, this retardationless equation is similar to the fractional KFP by Barkai and Silbey. However, it corresponds to the opposite, much more physical limit and, therefore, also presents a viable alternative.

Equilibrium gas-oil ratio measurements using a microfluidic technique.

Science.gov (United States)

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.

Relevance of equilibrium in multifragmentation

International Nuclear Information System (INIS)

Furuta, Takuya; Ono, Akira

2009-01-01

The relevance of equilibrium in a multifragmentation reaction of very central 40 Ca + 40 Ca collisions at 35 MeV/nucleon is investigated by using simulations of antisymmetrized molecular dynamics (AMD). Two types of ensembles are compared. One is the reaction ensemble of the states at each reaction time t in collision events simulated by AMD, and the other is the equilibrium ensemble prepared by solving the AMD equation of motion for a many-nucleon system confined in a container for a long time. The comparison of the ensembles is performed for the fragment charge distribution and the excitation energies. Our calculations show that there exists an equilibrium ensemble that well reproduces the reaction ensemble at each reaction time t for the investigated period 80≤t≤300 fm/c. However, there are some other observables that show discrepancies between the reaction and equilibrium ensembles. These may be interpreted as dynamical effects in the reaction. The usual static equilibrium at each instant is not realized since any equilibrium ensemble with the same volume as that of the reaction system cannot reproduce the fragment observables

A non-local-thermodynamic equilibrium formulation of the transport equation for polarized light in the presence of weak magnetic fields. Doctoral thesis

International Nuclear Information System (INIS)

McNamara, D.J.

1977-01-01

The present work is motivated by the desire to better understand solar magnetism. Just as stellar astrophysics and radiative transfer have been coupled in the history of research in physics, so too has the study of radiative transfer of polarized light in magnetic fields and solar magnetism been a history of mutual growth. The Stokes parameters characterize the state of polarization of a beam of radiation. The author considers the changes in polarization, and therefore in the Stokes parameters, due to the transport of a beam through an optically thick medium in a weak magnetic field. The transport equation is derived from a general density matrix equation of motion. This allows the possibility of interference effects arising from the mixing of atomic sublevels in a weak magnetic field to be taken into account. The statistical equilibrium equations are similarly derived. Finally, the coupled system of equations is presented, and the order of magnitude of the interference effects, shown. Collisional effects are not considered. The magnitude of the interference effects in magnetic field measurements of the sun may be evaluated

Non-Equilibrium Thermodynamics of Self-Replicating Protocells

DEFF Research Database (Denmark)

Fellermann, Harold; Corominas-Murtra, Bernat; Hansen, Per Lyngs

2018-01-01

We provide a non-equilibrium thermodynamic description of the life-cycle of a droplet based, chemically feasible, system of protocells. By coupling the protocells metabolic kinetics with its thermodynamics, we demonstrate how the system can be driven out of equilibrium to ensure protocell growth...... and replication. This coupling allows us to derive the equations of evolution and to rigorously demonstrate how growth and replication life-cycle can be understood as a non-equilibrium thermodynamic cycle. The process does not appeal to genetic information or inheritance, and is based only on non......-equilibrium physics considerations. Our non-equilibrium thermodynamic description of simple, yet realistic, processes of protocell growth and replication, represents an advance in our physical understanding of a central biological phenomenon both in connection to the origin of life and for modern biology....

The lagRST Model: A Turbulence Model for Non-Equilibrium Flows

Science.gov (United States)

Lillard, Randolph P.; Oliver, A. Brandon; Olsen, Michael E.; Blaisdell, Gregory A.; Lyrintzis, Anastasios S.

2011-01-01

This study presents a new class of turbulence model designed for wall bounded, high Reynolds number flows with separation. The model addresses deficiencies seen in the modeling of nonequilibrium turbulent flows. These flows generally have variable adverse pressure gradients which cause the turbulent quantities to react at a finite rate to changes in the mean flow quantities. This "lag" in the response of the turbulent quantities can t be modeled by most standard turbulence models, which are designed to model equilibrium turbulent boundary layers. The model presented uses a standard 2-equation model as the baseline for turbulent equilibrium calculations, but adds transport equations to account directly for non-equilibrium effects in the Reynolds Stress Tensor (RST) that are seen in large pressure gradients involving shock waves and separation. Comparisons are made to several standard turbulence modeling validation cases, including an incompressible boundary layer (both neutral and adverse pressure gradients), an incompressible mixing layer and a transonic bump flow. In addition, a hypersonic Shock Wave Turbulent Boundary Layer Interaction with separation is assessed along with a transonic capsule flow. Results show a substantial improvement over the baseline models for transonic separated flows. The results are mixed for the SWTBLI flows assessed. Separation predictions are not as good as the baseline models, but the over prediction of the peak heat flux downstream of the reattachment shock that plagues many models is reduced.

Fractional Diffusion Limit for Collisional Kinetic Equations

KAUST Repository

Mellet, Antoine

2010-08-20

This paper is devoted to diffusion limits of linear Boltzmann equations. When the equilibrium distribution function is a Maxwellian distribution, it is well known that for an appropriate time scale, the small mean free path limit gives rise to a diffusion equation. In this paper, we consider situations in which the equilibrium distribution function is a heavy-tailed distribution with infinite variance. We then show that for an appropriate time scale, the small mean free path limit gives rise to a fractional diffusion equation. © 2010 Springer-Verlag.

Kelvin Equation for a Non-Ideal Multicomponent Mixture

DEFF Research Database (Denmark)

Shapiro, Alexander; Stenby, Erling Halfdan

1997-01-01

The Kelvin equation is generalized by application to a case of a multicomponent non-ideal mixture. Such a generalization is necessary in order to describe the two-phase equilibrium in a capillary medium with respect to both normal and retrograde condensation. The equation obtained is applied...... to the equilibrium state of a hydrocarbon mixture ina gas-condensate reservoir....

On solutions to equilibrium problems for systems of stiffened gases

OpenAIRE

Flåtten, Tore; Morin, Alexandre; Munkejord, Svend Tollak

2011-01-01

We consider an isolated system of N immiscible fluids, each following a stiffened-gas equation of state. We consider the problem of calculating equilibrium states from the conserved fluid-mechanical properties, i.e., the partial densities and internal energies. We consider two cases; in each case mechanical equilibrium is assumed, but the fluids may or may not be in thermal equilibrium. For both cases, we address the issues of existence, uniqueness, and physical validity of equilibrium soluti...

Thermodynamically based constraints for rate coefficients of large biochemical networks.

Science.gov (United States)

Vlad, Marcel O; Ross, John

2009-01-01

Wegscheider cyclicity conditions are relationships among the rate coefficients of a complex reaction network, which ensure the compatibility of kinetic equations with the conditions for thermodynamic equilibrium. The detailed balance at equilibrium, that is the equilibration of forward and backward rates for each elementary reaction, leads to compatibility between the conditions of kinetic and thermodynamic equilibrium. Therefore, Wegscheider cyclicity conditions can be derived by eliminating the equilibrium concentrations from the conditions of detailed balance. We develop matrix algebra tools needed to carry out this elimination, reexamine an old derivation of the general form of Wegscheider cyclicity condition, and develop new derivations which lead to more compact and easier-to-use formulas. We derive scaling laws for the nonequilibrium rates of a complex reaction network, which include Wegscheider conditions as a particular case. The scaling laws for the rates are used for clarifying the kinetic and thermodynamic meaning of Wegscheider cyclicity conditions. Finally, we discuss different ways of using Wegscheider cyclicity conditions for kinetic computations in systems biology.

Solution of the stellar structure equations in Eulerian coordinates

International Nuclear Information System (INIS)

Deupree, R.G.

1976-01-01

The equations of hydrostatic and thermal equilibrium, assuming only radiative energy transport and spherical symmetry, are solved in Eulerian coordinates by a suitable modification of the Henyey method. An Eulerian approach may possibly be more suitably extended to more spatial dimensions than the usual Lagrangian procedure. The principle advantage of this method is that the equations of hydrostatic and thermal equilibrium and Poisson's equation may be solved simultaneously

Effects of centrifugal modification of magnetohydrodynamic equilibrium on resistive wall mode stability

International Nuclear Information System (INIS)

Shiraishi, J.; Aiba, N.; Miyato, N.; Yagi, M.

2014-01-01

Toroidal rotation effects are self-consistently taken into account not only in the linear magnetohydrodynamic (MHD) stability analysis but also in the equilibrium calculation. The MHD equilibrium computation is affected by centrifugal force due to the toroidal rotation. To study the toroidal rotation effects on resistive wall modes (RWMs), a new code has been developed. The RWMaC modules, which solve the electromagnetic dynamics in vacuum and the resistive wall, have been implemented in the MINERVA code, which solves the Frieman–Rotenberg equation that describes the linear ideal MHD dynamics in a rotating plasma. It is shown that modification of MHD equilibrium by the centrifugal force significantly reduces growth rates of RWMs with fast rotation in the order of M 2  = 0.1 where M is the Mach number. Moreover, it can open a stable window which does not exist under the assumption that the rotation affects only the linear dynamics. The rotation modifies the equilibrium pressure gradient and current density profiles, which results in the change of potential energy including rotational effects. (paper)

Homogeneous non-equilibrium two-phase critical flow model

International Nuclear Information System (INIS)

Schroeder, J.J.; Vuxuan, N.

1987-01-01

An important aspect of nuclear and chemical reactor safety is the ability to predict the maximum or critical mass flow rate from a break or leak in a pipe system. At the beginning of such a blowdown, if the stagnation condition of the fluid is subcooled or slightly saturated thermodynamic non-equilibrium exists in the downstream, e.g. the fluid becomes superheated to a degree determined by the liquid pressure. A simplified non-equilibrium model, explained in this report, is valid for rapidly decreasing pressure along the flow path. It presumes that fluid has to be superheated by an amount governed by physical principles before it starts to flash into steam. The flow is assumed to be homogeneous, i.e. the steam and liquid velocities are equal. An adiabatic flow calculation mode (Fanno lines) is employed to evaluate the critical flow rate for long pipes. The model is found to satisfactorily describe critical flow tests. Good agreement is obtained with the large scale Marviken tests as well as with small scale experiments. (orig.)

Numerical method for partial equilibrium flow

International Nuclear Information System (INIS)

Ramshaw, J.D.; Cloutman, L.D.; Los Alamos, New Mexico 87545)

1981-01-01

A numerical method is presented for chemically reactive fluid flow in which equilibrium and nonequilibrium reactions occur simultaneously. The equilibrium constraints on the species concentrations are established by a quadratic iterative procedure. If the equilibrium reactions are uncoupled and of second or lower order, the procedure converges in a single step. In general, convergence is most rapid when the reactions are weakly coupled. This can frequently be achieved by a judicious choice of the independent reactions. In typical transient calculations, satisfactory accuracy has been achieved with about five iterations per time step

Estimating the market premium in short term interest rates

OpenAIRE

Hansen, Hans Fredrik

2006-01-01

Looking at the term structure in the interest rate market one can’t help notice the evident market premium above the central banks target rate. What factors might decide this premium? By using different variations of simple regression models we see that the model is constantly lagging the real time series. Acknowledging the fact that market clearings often are subject to several equations; we’re better able to develop a sensible model using a simultaneous equilibrium model. The multiple equat...

Mathematical modeling of the radiation-chemical behavior of neptunium in HNO3. Equilibrium states

International Nuclear Information System (INIS)

Vladimirova, M.V.

1995-01-01

A mathematical model of the radiation-chemical behavior of neptunium is presented for a wide range of α-and γ-irradiation doses. Equations determining the equilibrium concentrations of NP(IV), Np(V), and Np(VI) are derived for various concentrations of HNO 3 and dose rates of the ionizing irradiation. The rate constants of the reactions NP(IV) + OH, Np(IV) + NO 3 , Np(V) + NO 2 , Np(V) + H, Np(IV), and Np(V) + Np(V) are obtained by the mathematical modeling

Exact and approximate solutions for the decades-old Michaelis-Menten equation: Progress-curve analysis through integrated rate equations.

Science.gov (United States)

Goličnik, Marko

2011-01-01

The Michaelis-Menten rate equation can be found in most general biochemistry textbooks, where the time derivative of the substrate is a hyperbolic function of two kinetic parameters (the limiting rate V, and the Michaelis constant K(M) ) and the amount of substrate. However, fundamental concepts of enzyme kinetics can be difficult to understand fully, or can even be misunderstood, by students when based only on the differential form of the Michaelis-Menten equation, and the variety of methods available to calculate the kinetic constants from rate versus substrate concentration "textbook data." Consequently, enzyme kinetics can be confusing if an analytical solution of the Michaelis-Menten equation is not available. Therefore, the still rarely known exact solution to the Michaelis-Menten equation is presented here through the explicit closed-form equation in terms of the Lambert W(x) function. Unfortunately, as the W(x) is not available in standard curve-fitting computer programs, the practical use of this direct solution is limited for most life-science students. Thus, the purpose of this article is to provide analytical approximations to the equation for modeling Michaelis-Menten kinetics. The elementary and explicit nature of these approximations can provide students with direct and simple estimations of kinetic parameters from raw experimental time-course data. The Michaelis-Menten kinetics studied in the latter context can provide an ideal alternative to the 100-year-old problems of data transformation, graphical visualization, and data analysis of enzyme-catalyzed reactions. Hence, the content of the course presented here could gradually become an important component of the modern biochemistry curriculum in the 21st century. Copyright © 2011 Wiley Periodicals, Inc.

Generalized reduced MHD equations

International Nuclear Information System (INIS)

Kruger, S.E.; Hegna, C.C.; Callen, J.D.

1998-07-01

A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general toroidal configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson

Equilibrium distribution function in collisionless systems

International Nuclear Information System (INIS)

Pergamenshchik, V.M.

1988-01-01

Collisionless systems of a large number of N particles interacting by Coulomb forces are widely spread in cosmic and laboratory plasma. A statistical theory of equilibrium state of collisionless Coulomb systems which evolution obeys Vlasov equation is proposed. The developed formalism permits a sequential consideration of such distributed in one-particle six-dimensional phase space of a system and to obtain a simple result: equilibrium distribution function has the form of Fermi-Dirac distribution and doesn't depend on initial state factors

Gluon transport equation in the small angle approximation and the onset of Bose–Einstein condensation

Energy Technology Data Exchange (ETDEWEB)

Blaizot, Jean-Paul [Institut de Physique Théorique, CNRS/URA 2306, CEA Saclay, F-91191 Gif-sur-Yvette (France); Liao, Jinfeng [Physics Dept. and CEEM, Indiana University, 2401 N Milo B. Sampson Lane, Bloomington, IN 47408 (United States); RIKEN BNL Research Center, Bldg. 510A, Brookhaven National Laboratory, Upton, NY 11973 (United States); McLerran, Larry [Physics Dept., Bldg. 510A, Brookhaven National Laboratory, Upton, NY 11973 (United States); RIKEN BNL Research Center, Bldg. 510A, Brookhaven National Laboratory, Upton, NY 11973 (United States); Physics Department, China Central Normal University, Wuhan (China)

2014-11-15

To understand the evolution of a dense system of gluons, such as those produced in the early stages of ultra-relativistic heavy ion collisions, is an important and challenging problem. We describe the approach to thermal equilibrium using the small angle approximation for gluon scattering in a Boltzmann equation that includes the effects of Bose statistics. The role of Bose statistical factors in amplifying the rapid growth of the population of the soft modes is essential. With these factors properly taken into account, one finds that elastic scattering alone provides an efficient mechanism for populating soft modes, and in fact leads to rapid infrared local thermalization. Furthermore, recent developments suggest that high initial overpopulation plays a key role and may lead to dynamical Bose–Einstein condensation. The kinetics of condensation is an interesting problem in itself. By solving the transport equation for initial conditions with a large enough initial phase-space density the equilibrium state contains a Bose condensate, and we present numerical evidence that such over-occupied systems reach the onset of Bose–Einstein condensation in a finite time. It is also found that the approach to condensation is characterized by a scaling behavior. Finally we discuss a number of extensions of the present study.

Gluon transport equation in the small angle approximation and the onset of Bose–Einstein condensation

International Nuclear Information System (INIS)

Blaizot, Jean-Paul; Liao, Jinfeng; McLerran, Larry

2014-01-01

To understand the evolution of a dense system of gluons, such as those produced in the early stages of ultra-relativistic heavy ion collisions, is an important and challenging problem. We describe the approach to thermal equilibrium using the small angle approximation for gluon scattering in a Boltzmann equation that includes the effects of Bose statistics. The role of Bose statistical factors in amplifying the rapid growth of the population of the soft modes is essential. With these factors properly taken into account, one finds that elastic scattering alone provides an efficient mechanism for populating soft modes, and in fact leads to rapid infrared local thermalization. Furthermore, recent developments suggest that high initial overpopulation plays a key role and may lead to dynamical Bose–Einstein condensation. The kinetics of condensation is an interesting problem in itself. By solving the transport equation for initial conditions with a large enough initial phase-space density the equilibrium state contains a Bose condensate, and we present numerical evidence that such over-occupied systems reach the onset of Bose–Einstein condensation in a finite time. It is also found that the approach to condensation is characterized by a scaling behavior. Finally we discuss a number of extensions of the present study

Systematic Constraint Selection Strategy for Rate-Controlled Constrained-Equilibrium Modeling of Complex Nonequilibrium Chemical Kinetics

Science.gov (United States)

Beretta, Gian Paolo; Rivadossi, Luca; Janbozorgi, Mohammad

2018-04-01

Rate-Controlled Constrained-Equilibrium (RCCE) modeling of complex chemical kinetics provides acceptable accuracies with much fewer differential equations than for the fully Detailed Kinetic Model (DKM). Since its introduction by James C. Keck, a drawback of the RCCE scheme has been the absence of an automatable, systematic procedure to identify the constraints that most effectively warrant a desired level of approximation for a given range of initial, boundary, and thermodynamic conditions. An optimal constraint identification has been recently proposed. Given a DKM with S species, E elements, and R reactions, the procedure starts by running a probe DKM simulation to compute an S-vector that we call overall degree of disequilibrium (ODoD) because its scalar product with the S-vector formed by the stoichiometric coefficients of any reaction yields its degree of disequilibrium (DoD). The ODoD vector evolves in the same (S-E)-dimensional stoichiometric subspace spanned by the R stoichiometric S-vectors. Next we construct the rank-(S-E) matrix of ODoD traces obtained from the probe DKM numerical simulation and compute its singular value decomposition (SVD). By retaining only the first C largest singular values of the SVD and setting to zero all the others we obtain the best rank-C approximation of the matrix of ODoD traces whereby its columns span a C-dimensional subspace of the stoichiometric subspace. This in turn yields the best approximation of the evolution of the ODoD vector in terms of only C parameters that we call the constraint potentials. The resulting order-C RCCE approximate model reduces the number of independent differential equations related to species, mass, and energy balances from S+2 to C+E+2, with substantial computational savings when C ≪ S-E.

Potential and flux field landscape theory. II. Non-equilibrium thermodynamics of spatially inhomogeneous stochastic dynamical systems

International Nuclear Information System (INIS)

Wu, Wei; Wang, Jin

2014-01-01

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 and 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

Validation of vibration-dissociation coupling models in hypersonic non-equilibrium separated flows

Science.gov (United States)

Shoev, G.; Oblapenko, G.; Kunova, O.; Mekhonoshina, M.; Kustova, E.

2018-03-01

The validation of recently developed models of vibration-dissociation coupling is discussed in application to numerical solutions of the Navier-Stokes equations in a two-temperature approximation for a binary N2/N flow. Vibrational-translational relaxation rates are computed using the Landau-Teller formula generalized for strongly non-equilibrium flows obtained in the framework of the Chapman-Enskog method. Dissociation rates are calculated using the modified Treanor-Marrone model taking into account the dependence of the model parameter on the vibrational state. The solutions are compared to those obtained using traditional Landau-Teller and Treanor-Marrone models, and it is shown that for high-enthalpy flows, the traditional and recently developed models can give significantly different results. The computed heat flux and pressure on the surface of a double cone are in a good agreement with experimental data available in the literature on low-enthalpy flow with strong thermal non-equilibrium. The computed heat flux on a double wedge qualitatively agrees with available data for high-enthalpy non-equilibrium flows. Different contributions to the heat flux calculated using rigorous kinetic theory methods are evaluated. Quantitative discrepancy of numerical and experimental data is discussed.

The principal equations of state for classical particles, photons, and neutrinos

DEFF Research Database (Denmark)

Essex, Christopher; Andresen, Bjarne Bøgeskov

2013-01-01

Functions, not dynamical equations, are the definitive mathematical objects in equilibrium thermodynamics. However, more than one function is often described as “the” equation of state for any one physical system. Usually these so named equations only capture incomplete physical content in the re......Functions, not dynamical equations, are the definitive mathematical objects in equilibrium thermodynamics. However, more than one function is often described as “the” equation of state for any one physical system. Usually these so named equations only capture incomplete physical content...

Equilibrium-torus bifurcation in nonsmooth systems

DEFF Research Database (Denmark)

Zhusubahyev, Z.T.; Mosekilde, Erik

2008-01-01

Considering a set of two coupled nonautonomous differential equations with discontinuous right-hand sides describing the behavior of a DC/DC power converter, we discuss a border-collision bifurcation that can lead to the birth of a two-dimensional invariant torus from a stable node equilibrium...... point. We obtain the chart of dynamic modes and show that there is a region of parameter space in which the system has a single stable node equilibrium point. Under variation of the parameters, this equilibrium may disappear as it collides with a discontinuity boundary between two smooth regions...... in the phase space. The disappearance of the equilibrium point is accompanied by the soft appearance of an unstable focus period-1 orbit surrounded by a resonant or ergodic torus. Detailed numerical calculations are supported by a theoretical investigation of the normal form map that represents the piecewise...

Are the Concepts of Dynamic Equilibrium and the Thermodynamic Criteria for Spontaneity, Nonspontaneity, and Equilibrium Compatible?

Science.gov (United States)

Silverberg, Lee J.; Raff, Lionel M.

2015-01-01

Thermodynamic spontaneity-equilibrium criteria require that in a single-reaction system, reactions in either the forward or reverse direction at equilibrium be nonspontaneous. Conversely, the concept of dynamic equilibrium holds that forward and reverse reactions both occur at equal rates at equilibrium to the extent allowed by kinetic…

DC electrophoresis and viscosity of realistic salt-free concentrated suspensions: non-equilibrium dissociation-association processes.

Science.gov (United States)

Ruiz-Reina, Emilio; Carrique, Félix; Lechuga, Luis

2014-03-01

Most of the suspensions usually found in industrial applications are concentrated, aqueous and in contact with the atmospheric CO2. The case of suspensions with a high concentration of added salt is relatively well understood and has been considered in many studies. In this work we are concerned with the case of concentrated suspensions that have no ions different than: (1) those stemming from the charged colloidal particles (the added counterions, that counterbalance their surface charge); (2) the H(+) and OH(-) ions from water dissociation, and (3) the ions generated by the atmospheric CO2 contamination. We call this kind of systems "realistic salt-free suspensions". We show some theoretical results about the electrophoretic mobility of a colloidal particle and the electroviscous effect of realistic salt-free concentrated suspensions. The theoretical framework is based on a cell model that accounts for particle-particle interactions in concentrated suspensions, which has been successfully applied to many different phenomena in concentrated suspensions. On the other hand, the water dissociation and CO2 contamination can be described following two different levels of approximation: (a) by local equilibrium mass-action equations, because it is supposed that the reactions are so fast that chemical equilibrium is attained everywhere in the suspension, or (b) by non-equilibrium dissociation-association kinetic equations, because it is considered that some reactions are not rapid enough to ensure local chemical equilibrium. Both approaches give rise to different results in the range from dilute to semidilute suspensions, causing possible discrepancies when comparing standard theories and experiments concerning transport properties of realistic salt-free suspensions. Copyright © 2013 Elsevier Inc. All rights reserved.

Status of rates and rate equations for thermal leptogenesis

Science.gov (United States)

Biondini, S.; Bödeker, D.; Brambilla, N.; Garny, M.; Ghiglieri, J.; Hohenegger, A.; Laine, M.; Mendizabal, S.; Millington, P.; Salvio, A.; Vairo, A.

2018-02-01

In many realizations of leptogenesis, heavy right-handed neutrinos play the main role in the generation of an imbalance between matter and antimatter in the early Universe. Hence, it is relevant to address quantitatively their dynamics in a hot and dense environment by taking into account the various thermal aspects of the problem at hand. The strong washout regime offers an interesting framework to carry out calculations systematically and reduce theoretical uncertainties. Indeed, any matter-antimatter asymmetry generated when the temperature of the hot plasma T exceeds the right-handed neutrino mass scale M is efficiently erased, and one can focus on the temperature window T ≪ M. We review recent progress in the thermal field theoretic derivation of the key ingredients for the leptogenesis mechanism: the right-handed neutrino production rate, the CP asymmetry in the heavy-neutrino decays and the washout rates. The derivation of evolution equations for the heavy-neutrino and lepton-asymmetry number densities, their rigorous formulation and applicability are also discussed.

Laser Rate Equation Based Filtering for Carrier Recovery in Characterization and Communication

DEFF Research Database (Denmark)

Piels, Molly; Iglesias Olmedo, Miguel; Xue, Weiqi

2015-01-01

We formulate a semiconductor laser rate equationbased approach to carrier recovery in a Bayesian filtering framework. Filter stability and the effect of model inaccuracies (unknown or un-useable rate equation coefficients) are discussed. Two potential application areas are explored: laser...... characterization and carrier recovery in coherent communication. Two rate equation based Bayesian filters, the particle filter and extended Kalman filter, are used in conjunction with a coherent receiver to measure frequency noise spectrum of a photonic crystal cavity laser with less than 20 nW of fiber...

Multiple Reserve Requirements, Exchange Rates, Sudden Stops and Equilibrium Dynamics in a Small Open Economy

OpenAIRE

Paula Hernandez-Verme; Wen-Yao Wang

2009-01-01

We model a typical Asian-crisis-economy using dynamic general equilibrium tech-niques. Exchange rates obtain from nontrivial fiat-currencies demands. Sudden stops/bank-panics are possible, and key for evaluating the merits of alternative ex-change rate regimes. Strategic complementarities contribute to the severe indetermi-nacy of the continuum of equilibria. The scope for existence and indeterminacy of equilibria and dynamic properties are associated with the underlying policy regime. Bindin...

Non-equilibrium supramolecular polymerization.

Science.gov (United States)

Sorrenti, Alessandro; Leira-Iglesias, Jorge; Markvoort, Albert J; de Greef, Tom F A; Hermans, Thomas M

2017-09-18

Supramolecular polymerization has been traditionally focused on the thermodynamic equilibrium state, where one-dimensional assemblies reside at the global minimum of the Gibbs free energy. The pathway and rate to reach the equilibrium state are irrelevant, and the resulting assemblies remain unchanged over time. In the past decade, the focus has shifted to kinetically trapped (non-dissipative non-equilibrium) structures that heavily depend on the method of preparation (i.e., pathway complexity), and where the assembly rates are of key importance. Kinetic models have greatly improved our understanding of competing pathways, and shown how to steer supramolecular polymerization in the desired direction (i.e., pathway selection). The most recent innovation in the field relies on energy or mass input that is dissipated to keep the system away from the thermodynamic equilibrium (or from other non-dissipative states). This tutorial review aims to provide the reader with a set of tools to identify different types of self-assembled states that have been explored so far. In particular, we aim to clarify the often unclear use of the term "non-equilibrium self-assembly" by subdividing systems into dissipative, and non-dissipative non-equilibrium states. Examples are given for each of the states, with a focus on non-dissipative non-equilibrium states found in one-dimensional supramolecular polymerization.

The Enskog Equation for Confined Elastic Hard Spheres

Science.gov (United States)

Maynar, P.; García de Soria, M. I.; Brey, J. Javier

2018-03-01

A kinetic equation for a system of elastic hard spheres or disks confined by a hard wall of arbitrary shape is derived. It is a generalization of the modified Enskog equation in which the effects of the confinement are taken into account and it is supposed to be valid up to moderate densities. From the equation, balance equations for the hydrodynamic fields are derived, identifying the collisional transfer contributions to the pressure tensor and heat flux. A Lyapunov functional, H[f], is identified. For any solution of the kinetic equation, H decays monotonically in time until the system reaches the inhomogeneous equilibrium distribution, that is a Maxwellian distribution with a density field consistent with equilibrium statistical mechanics.

Catalysis of Silver catfish Major Hepatic Glutathione Transferase proceeds via rapid equilibrium sequential random Mechanism

Directory of Open Access Journals (Sweden)

Ayodele O. Kolawole

Full Text Available Fish hepatic glutathione transferases are connected with the elimination of intracellular pollutants and detoxification of organic micro-pollutants in their aquatic ecosystem. The two-substrate steady state kinetic mechanism of Silver catfish (Synodontis eupterus major hepatic glutathione transferases purified to apparent homogeneity was explored. The enzyme was dimeric enzyme with a monomeric size of 25.6 kDa. Initial-velocity studies and Product inhibition patterns by methyl glutathione and chloride with respect to GSH-CDNB; GSH-ρ-nitrophenylacetate; and GSH-Ethacrynic acid all conforms to a rapid equilibrium sequential random Bi Bi kinetic mechanism rather than steady state sequential random Bi Bi kinetic. α was 2.96 ± 0.35 for the model. The pH profile of Vmax/KM (with saturating 1-chloro-2,4-dinitrobenzene and variable GSH concentrations showed apparent pKa value of 6.88 and 9.86. Inhibition studies as a function of inhibitor concentration show that the enzyme is a homodimer and near neutral GST. The enzyme poorly conjugates 4-hydroxylnonenal and cumene hydroperoxide and may not be involved in oxidative stress protection. The seGST is unique and overwhelmingly shows characteristics similar to those of homodimeric class Pi GSTs, as was indicated by its kinetic mechanism, substrate specificity and inhibition studies. The rate- limiting step, probably the product release, of the reaction is viscosity-dependent and is consequential if macro-viscosogen or micro-viscosogen. Keywords: Silver catfish, Glutathione transferase, Steady-state, Kinetic mechanism, Inhibition

Equilibrium econophysics: A unified formalism for neoclassical economics and equilibrium thermodynamics

Science.gov (United States)

Sousa, Tânia; Domingos, Tiago

2006-11-01

We develop a unified conceptual and mathematical structure for equilibrium econophysics, i.e., the use of concepts and tools of equilibrium thermodynamics in neoclassical microeconomics and vice versa. Within this conceptual structure the results obtained in microeconomic theory are: (1) the definition of irreversibility in economic behavior; (2) the clarification that the Engel curve and the offer curve are not descriptions of real processes dictated by the maximization of utility at constant endowment; (3) the derivation of a relation between elasticities proving that economic elasticities are not all independent; (4) the proof that Giffen goods do not exist in a stable equilibrium; (5) the derivation that ‘economic integrability’ is equivalent to the generalized Le Chatelier principle and (6) the definition of a first order phase transition, i.e., a transition between separate points in the utility function. In thermodynamics the results obtained are: (1) a relation between the non-dimensional isothermal and adiabatic compressibilities and the increase or decrease in the thermodynamic potentials; (2) the distinction between mathematical integrability and optimization behavior and (3) the generalization of the Clapeyron equation.

Analysis of non-equilibrium phenomena in inductively coupled plasma generators

Energy Technology Data Exchange (ETDEWEB)

Zhang, W.; Panesi, M., E-mail: mpanesi@illinois.edu [University of Illinois at Urbana-Champaign, Urbana, Illinois 61822 (United States); Lani, A. [Von Karman Institute for Fluid Dynamics, Rhode-Saint-Genèse (Belgium)

2016-07-15

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.

Force-dominated non-equilibrium oxidation kinetics of tantalum

International Nuclear Information System (INIS)

Kar, Prasenjit; Wang, Ke; Liang, Hong

2008-01-01

Using a combined electrochemical and mechanical manipulation technique, we compared the equilibrium and non-equilibrium oxidation processes and states of tantalum. Experimentally, a setup was developed with an electrochemical system attached to a sliding mechanical configuration capable of friction force measurement. The surface chemistry of a sliding surface, i.e., tantalum, was modified through the electrolyte. The mechanically applied force was fixed and the dynamics of the surface was monitored in situ through a force sensor. The formation of non-equilibrium oxidation states of tantalum was found in oxidation limiting environment of acetic acid. An oxidative environment of deionized water saturated with KCl was used as comparison. We proposed a modified Arrhenius-Eyring equation in which the mechanical factor was considered. We found that the mechanical energy induced the non-stable-state reactions leading to metastable oxidation states of tantalum. This equation can be used to predict mechanochemical reactions that are important in many industrial applications

Out-of-equilibrium quantum fields with conserved charge

International Nuclear Information System (INIS)

Bedingham, D.J.

2004-01-01

We study the out-of-equilibrium evolution of an O(2)-invariant scalar field in which a conserved charge is stored. We apply a loop expansion of the 2-particle irreducible effective action to 3-loop order. Equations of motion are derived which conserve both total charge and total energy yet allow for the effects of scattering whereby charge and energy can transfer between modes. Working in 1+1 dimensions we solve the equations of motion numerically for a system knocked out of equilibrium by a sudden temperature quench. We examine the initial stages of the charge and energy redistribution. This provides a basis from which we can understand the formation of Bose-Einstein condensates from first principles

Cation distributions on rapidly solidified cobalt ferrite

Science.gov (United States)

De Guire, Mark R.; Kalonji, Gretchen; O'Handley, Robert C.

1990-01-01

The cation distributions in two rapidly solidified cobalt ferrites have been determined using Moessbauer spectroscopy at 4.2 K in an 8-T magnetic field. The samples were obtained by gas atomization of a Co0-Fe2O3-P2O5 melt. The degree of cation disorder in both cases was greater than is obtainable by cooling unmelted cobalt ferrite. The more rapidly cooled sample exhibited a smaller departure from the equilibrium cation distribution than did the more slowly cooled sample. This result is explained on the basis of two competing effects of rapid solidification: high cooling rate of the solid, and large undercooling.

Magnetotail equilibrium theory - The general three-dimensional solution

Science.gov (United States)

Birn, J.

1987-01-01

The general magnetostatic equilibrium problem for the geomagnetic tail is reduced to the solution of ordinary differential equations and ordinary integrals. The theory allows the integration of the self-consistent magnetotail equilibrium field from the knowledge of four functions of two space variables: the neutral sheet location, the total pressure, the magnetic field strength, and the z component of the magnetic field at the neutral sheet.

Chemical Equilibrium as Balance of the Thermodynamic Forces

OpenAIRE

Zilbergleyt, B.

2004-01-01

The article sets forth comprehensive basics of thermodynamics of chemical equilibrium as balance of the thermodynamic forces. Based on the linear equations of irreversible thermodynamics, De Donder definition of the thermodynamic force, and Le Chatelier's principle, new thermodynamics of chemical equilibrium offers an explicit account for multiple chemical interactions within the system. Basic relations between energetic characteristics of chemical transformations and reaction extents are bas...

Structural Stability of Tokamak Equilibrium: Transport Barriers

Energy Technology Data Exchange (ETDEWEB)

Solano, E. R.

2001-07-01

A generalised theory of structural stability of differential equations is introduced and applied to the Grad-Shafranov equation. It is discussed how the formation and loss of transport barrier could be associated with the appearance/disappearance of equilibria. The equilibrium conjecture is presented: transport barriers are associated with locally diamagnetic regions in the plasma, and affected by the paramagnetism of the bootstrap current. (Author) 18 refs.

Flux Jacobian Matrices For Equilibrium Real Gases

Science.gov (United States)

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.

Transonic flow of steam with non-equilibrium and homogenous condensation

Science.gov (United States)

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.

Relation between the conditions of helium ion implantation and helium void equilibrium parameters

International Nuclear Information System (INIS)

Neklyudov, I.M.; Rybalko, V.F.; Ruzhitskij, V.V.; Tolstolutskaya, G.D.

1981-01-01

The conditions of helium thermodynamic equilibrium in a system of voids produced by helium ion bombardment of a metal sample are studied. As an initial equation for description of the equilibrium the Clapeyron equation was used. The equation is obtained relating basic parameters of helium voids (average diameter and density) to irradiation parameters (dose, ion energy (straggling)) and properties of the metal (surface tension coefficient, yield strength). Comparison of the calculations with experimental data on helium in nickel found in literature shows that the equation yields satisfactory resutls for the dose range 1.10 16 -1x10 17 cm -2 and temperatures T [ru

Generalized rate-equation analysis of excitation exchange between silicon nanoclusters and erbium ions

International Nuclear Information System (INIS)

Kenyon, A. J.; Wojdak, M.; Ahmad, I.; Loh, W. H.; Oton, C. J.

2008-01-01

We discuss the use of rate equations to analyze the sensitization of erbium luminescence by silicon nanoclusters. In applying the general form of second-order coupled rate-equations to the Si nanocluster-erbium system, we find that the photoluminescence dynamics cannot be described using a simple rate equation model. Both rise and fall times exhibit a stretched exponential behavior, which we propose arises from a combination of a strongly distance-dependent nanocluster-erbium interaction, along with the finite size distribution and indirect band gap of the silicon nanoclusters. Furthermore, the low fraction of erbium ions that can be excited nonresonantly is a result of the small number of ions coupled to nanoclusters

An approximate method for calculating composition of the non-equilibrium explosion products of hydrocarbons and oxygen

International Nuclear Information System (INIS)

Shargatov, V A; Gubin, S A; Okunev, D Yu

2016-01-01

We develop a method for calculating the changes in composition of the explosion products in the case where the complete chemical equilibrium is absent but the bimolecular reactions are in quasi-equilibrium with the exception bimolecular reactions with one of the components of the mixture. We investigate the possibility of using the method of 'quasiequilibrium' for mixtures of hydrocarbons and oxygen. The method is based on the assumption of the existence of the partial chemical equilibrium in the explosion products. Without significant loss of accuracy to the solution of stiff differential equations detailed kinetic mechanism can be replaced by one or two differential equation and a system of algebraic equations. This method is always consistent with the detailed mechanism and can be used separately or in conjunction with the solution of a stiff system for chemically non-equilibrium mixtures replacing it when bimolecular reactions are near to equilibrium. (paper)

Estimating long-run equilibrium real exchange rates: short-lived shocks with long-lived impacts on Pakistan.

Science.gov (United States)

Zardad, Asma; Mohsin, Asma; Zaman, Khalid

2013-12-01

The purpose of this study is to investigate the factors that affect real exchange rate volatility for Pakistan through the co-integration and error correction model over a 30-year time period, i.e. between 1980 and 2010. The study employed the autoregressive conditional heteroskedasticity (ARCH), generalized autoregressive conditional heteroskedasticity (GARCH) and Vector Error Correction model (VECM) to estimate the changes in the volatility of real exchange rate series, while an error correction model was used to determine the short-run dynamics of the system. The study is limited to a few variables i.e., productivity differential (i.e., real GDP per capita relative to main trading partner); terms of trade; trade openness and government expenditures in order to manage robust data. The result indicates that real effective exchange rate (REER) has been volatile around its equilibrium level; while, the speed of adjustment is relatively slow. VECM results confirm long run convergence of real exchange rate towards its equilibrium level. Results from ARCH and GARCH estimation shows that real shocks volatility persists, so that shocks die out rather slowly, and lasting misalignment seems to have occurred.

The stability of second sound waves in a rotating Darcy–Brinkman porous layer in local thermal non-equilibrium

Energy Technology Data Exchange (ETDEWEB)

Eltayeb, I A; Elbashir, T B A, E-mail: ieltayeb@squ.edu.om, E-mail: elbashir@squ.edu.om [Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, Muscat 123 (Oman)

2017-08-15

The linear and nonlinear stabilities of second sound waves in a rotating porous Darcy–Brinkman layer in local thermal non-equilibrium are studied when the heat flux in the solid obeys the Cattaneo law. The simultaneous action of the Brinkman effect (effective viscosity) and rotation is shown to destabilise the layer, as compared to either of them acting alone, for both stationary and overstable modes. The effective viscosity tends to favour overstable modes while rotation tends to favour stationary convection. Rapid rotation invokes a negative viscosity effect that suppresses the stabilising effect of porosity so that the stability characteristics resemble those of the classical rotating Benard layer. A formal weakly nonlinear analysis yields evolution equations of the Landau–Stuart type governing the slow time development of the amplitudes of the unstable waves. The equilibrium points of the evolution equations are analysed and the overall development of the amplitudes is examined. Both overstable and stationary modes can exhibit supercritical stability; supercritical instability, subcritical instability and stability are not possible. The dependence of the supercritical stability on the relative values of the six dimensionless parameters representing thermal non-equilibrium, rotation, porosity, relaxation time, thermal diffusivities and Brinkman effect is illustrated as regions in regime diagrams in the parameter space. The dependence of the heat transfer and the mean heat flux on the parameters of the problem is also discussed. (paper)

Slope-velocity equilibrium and evolution of surface roughness on a stony hillslope

Science.gov (United States)

Nearing, Mark A.; Polyakov, Viktor O.; Nichols, Mary H.; Hernandez, Mariano; Li, Li; Zhao, Ying; Armendariz, Gerardo

2017-06-01

Slope-velocity equilibrium is hypothesized as a state that evolves naturally over time due to the interaction between overland flow and surface morphology, wherein steeper areas develop a relative increase in physical and hydraulic roughness such that flow velocity is a unique function of overland flow rate independent of slope gradient. This study tests this hypothesis under controlled conditions. Artificial rainfall was applied to 2 m by 6 m plots at 5, 12, and 20 % slope gradients. A series of simulations were made with two replications for each treatment with measurements of runoff rate, velocity, rock cover, and surface roughness. Velocities measured at the end of each experiment were a unique function of discharge rates, independent of slope gradient or rainfall intensity. Physical surface roughness was greater at steeper slopes. The data clearly showed that there was no unique hydraulic coefficient for a given slope, surface condition, or rainfall rate, with hydraulic roughness greater at steeper slopes and lower intensities. This study supports the hypothesis of slope-velocity equilibrium, implying that use of hydraulic equations, such as Chezy and Manning, in hillslope-scale runoff models is problematic because the coefficients vary with both slope and rainfall intensity.

Deviation from local thermodynamic equilibrium in a cesium-seeded argon plasma

International Nuclear Information System (INIS)

Stefanov, B.; Zarkova, L.

1985-11-01

The possibility of deviations from local thermodynamic equilibrium of a cesium seeded argon plasma has been analyzed. A four level model of cesium has been employed. Overpopulations of the ground state and the first excited state as well as the corresponding reduction of the electron density are calculated for cylindrical discharge structures by solving stationary rate equations. Numerical results are presented. These results indicate that in a large regime of plasma conditions the LTE assumption is valid for electron temperatures larger than 3000 K. (orig.)

The compressive behaviour and constitutive equation of polyimide foam in wide strain rate and temperature

Directory of Open Access Journals (Sweden)

Yoshimoto Akifumi

2015-01-01

Full Text Available These days, polymer foams, such as polyurethane foam and polystyrene foam, are used in various situations as a thermal insulator or shock absorber. In general, however, their strength is insufficient in high temperature environments because of their low glass transition temperature. Polyimide is a polymer which has a higher glass transition temperature and high strength. Its mechanical properties do not vary greatly, even in low temperature environments. Therefore, polyimide foam is expected to be used in the aerospace industry. Thus, the constitutive equation of polyimide foam that can be applied across a wide range of strain rates and ambient temperature is very useful. In this study, a series of compression tests at various strain rates, from 10−3 to 103 s−1 were carried out in order to examine the effect of strain rate on the compressive properties of polyimide foam. The flow stress of polyimide foam increased rapidly at dynamic strain rates. The effect of ambient temperature on the properties of polyimide foam was also investigated at temperature from − 190 °C to 270°∘C. The flow stress decreased with increasing temperature.

A toroidal plasma MHD equilibrium code 'EQUCIR version 1'

International Nuclear Information System (INIS)

Ninomiya, Hiromasa; Shinya, Kichiro; Kameari, Akihisa.

1980-10-01

A new free-boundary toroidal MHD equilibrium code ''EQUCIR version 1'' has been developed. The central problems approached by this code is as follows: 1) The magnetic flux distribution of a plasma at equilibrium is determined in the given external field. 2) A set of circuit equations between the plasma and the external conductors are constructed. These circuit equations and the Grad-Shafranov equation are solved self-consistently and the time evolutions of plasma equilibria and currents in external conductors are determined at the same time. 3) The currents in the external conductors are determined so that the plasma cross-section and plasma parameters are to be maintained with desired ones. It is shown that this code is very useful for study of the tokamak plasma equilibria, for design of the poloidal coil system and for investigation of experimental results. (author)

Non-equilibrium mean-field theories on scale-free networks

International Nuclear Information System (INIS)

Caccioli, Fabio; Dall'Asta, Luca

2009-01-01

Many non-equilibrium processes on scale-free networks present anomalous critical behavior that is not explained by standard mean-field theories. We propose a systematic method to derive stochastic equations for mean-field order parameters that implicitly account for the degree heterogeneity. The method is used to correctly predict the dynamical critical behavior of some binary spin models and reaction–diffusion processes. The validity of our non-equilibrium theory is further supported by showing its relation with the generalized Landau theory of equilibrium critical phenomena on networks

Dynamics and feedback control of plasma equilibrium position in a tokamak

International Nuclear Information System (INIS)

Burenko, O.

1983-01-01

A brief history of the beginnings of nuclear fusion research involving toroidal closed-system magnetic plasma containment is presented. A tokamak machine is defined mathematically for the purposes of plasma equilibrium position perturbation analysis. The perturbation equations of a tokamak plasma equilibrium position are developed. Solution of the approximated perturbation equations is carried out. A unique, simple, and useful plasma displacement dynamics transfer function of a tokamak is developed. The dominant time constants of the dynamics transfer function are determined in a symbolic form. This symbolic form of the dynamics transfer function makes it possible to study the stability of a tokamak's plasma equilibrium position. Knowledge of the dynamics transfer function permits systematic syntheses of the required plasma displacement feedback control systems

Rate equation analysis of hydrogen uptake on Si (100) surfaces

International Nuclear Information System (INIS)

Inanaga, S.; Rahman, F.; Khanom, F.; Namiki, A.

2005-01-01

We have studied the uptake process of H on Si (100) surfaces by means of rate equation analysis. Flowers' quasiequilibrium model for adsorption and desorption of H [M. C. Flowers, N. B. H. Jonathan, A. Morris, and S. Wright, Surf. Sci. 396, 227 (1998)] is extended so that in addition to the H abstraction (ABS) and β 2 -channel thermal desorption (TD) the proposed rate equation further includes the adsorption-induced desorption (AID) and β 1 -TD. The validity of the model is tested by the experiments of ABS and AID rates in the reaction system H+D/Si (100). Consequently, we find it can well reproduce the experimental results, validating the proposed model. We find the AID rate curve as a function of surface temperature T s exhibits a clear anti-correlation with the bulk dangling bond density versus T s curve reported in the plasma-enhanced chemical vapor deposition (CVD) for amorphous Si films. The significance of the H chemistry in plasma-enhanced CVD is discussed

Lattice Boltzmann method with the cell-population equilibrium

International Nuclear Information System (INIS)

Zhou Xiaoyang; Cheng Bing; Shi Baochang

2008-01-01

The central problem of the lattice Boltzmann method (LBM) is to construct a discrete equilibrium. In this paper, a multi-speed 1D cell-model of Boltzmann equation is proposed, in which the cell-population equilibrium, a direct non-negative approximation to the continuous Maxwellian distribution, plays an important part. By applying the explicit one-order Chapman–Enskog distribution, the model reduces the transportation and collision, two basic evolution steps in LBM, to the transportation of the non-equilibrium distribution. Furthermore, 1D dam-break problem is performed and the numerical results agree well with the analytic solutions

Rapid Fourier space solution of linear partial integro-differential equations in toroidal magnetic confinement geometries

International Nuclear Information System (INIS)

McMillan, B.F.; Jolliet, S.; Tran, T.M.; Villard, L.; Bottino, A.; Angelino, P.

2010-01-01

Fluctuating quantities in magnetic confinement geometries often inherit a strong anisotropy along the field lines. One technique for describing these structures is the use of a certain set of Fourier components on the tori of nested flux surfaces. We describe an implementation of this approach for solving partial differential equations, like Poisson's equation, where a different set of Fourier components may be chosen on each surface according to the changing safety factor profile. Allowing the resolved components to change to follow the anisotropy significantly reduces the total number of degrees of freedom in the description. This can permit large gains in computational performance. We describe, in particular, how this approach can be applied to rapidly solve the gyrokinetic Poisson equation in a particle code, ORB5 (Jolliet et al. (2007) [5]), with a regular (non-field-aligned) mesh. (authors)

Modified Ammonia Removal Model Based on Equilibrium and Mass Transfer Principles

International Nuclear Information System (INIS)

Shanableh, A.; Imteaz, M.

2010-01-01

Yoon et al. 1 presented an approximate mathematical model to describe ammonia removal from an experimental batch reactor system with gaseous headspace. The development of the model was initially based on assuming instantaneous equilibrium between ammonia in the aqueous and gas phases. In the model, a 'saturation factor, β' was defined as a constant and used to check whether the equilibrium assumption was appropriate. The authors used the trends established by the estimated β values to conclude that the equilibrium assumption was not valid. The authors presented valuable experimental results obtained using a carefully designed system and the model used to analyze the results accounted for the following effects: speciation of ammonia between NH 3 and NH 4 + as a function of pH: temperature dependence of the reactions constants; and air flow rate. In this article, an alternative model based on the exact solution of the governing mass-balance differential equations was developed and used to describe ammonia removal without relying on the use of the saturation factor. The modified model was also extended to mathematically describe the pH dependence of the ammonia removal rate, in addition to accounting for the speciation of ammonia, temperature dependence of reactions constants, and air flow rate. The modified model was used to extend the analysis of the original experimental data presented by Yoon et al. 1 and the results matched the theory in an excellent manner

Molecular equilibrium with condensation

International Nuclear Information System (INIS)

Sharp, C.M.; Huebner, W.F.

1990-01-01

Minimization of the Gibbs energy of formation for species of chemical elements and compounds in their gas and condensed phases determines their relative abundances in a mixture in chemical equilibrium. The procedure is more general and more powerful than previous abundance determinations in multiphase astrophysical mixtures. Some results for astrophysical equations of state are presented, and the effects of condensation on opacity are briefly indicated. 18 refs

Computing diffusivities from particle models out of equilibrium

Science.gov (United States)

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.

Justification of the averaging method for parabolic equations containing rapidly oscillating terms with large amplitudes

International Nuclear Information System (INIS)

Levenshtam, V B

2006-01-01

We justify the averaging method for abstract parabolic equations with stationary principal part that contain non-linearities (subordinate to the principal part) some of whose terms are rapidly oscillating in time with zero mean and are proportional to the square root of the frequency of oscillation. Our interest in the exponent 1/2 is motivated by the fact that terms proportional to lower powers of the frequency have no influence on the average. For linear equations of the same type, we justify an algorithm for the study of the stability of solutions in the case when the stationary averaged problem has eigenvalues on the imaginary axis (the critical case)

A model for non-equilibrium, non-homogeneous two-phase critical flow

International Nuclear Information System (INIS)

Bassel, Wageeh Sidrak; Ting, Daniel Kao Sun

1999-01-01

Critical two phase flow is a very important phenomena in nuclear reactor technology for the analysis of loss of coolant accident. Several recent papers, Lee and Shrock (1990), Dagan (1993) and Downar (1996) , among others, treat the phenomena using complex models which require heuristic parameters such as relaxation constants or interfacial transfer models. In this paper a mathematical model for one dimensional non equilibrium and non homogeneous two phase flow in constant area duct is developed. The model is constituted of three conservation equations type mass ,momentum and energy. Two important variables are defined in the model: equilibrium constant in the energy equation and the impulse function in the momentum equation. In the energy equation, the enthalpy of the liquid phase is determined by a linear interpolation function between the liquid phase enthalpy at inlet condition and the saturated liquid enthalpy at local pressure. The interpolation coefficient is the equilibrium constant. The momentum equation is expressed in terms of the impulse function. It is considered that there is slip between the liquid and vapor phases, the liquid phase is in metastable state and the vapor phase is in saturated stable state. The model is not heuristic in nature and does not require complex interface transfer models. It is proved numerically that for the critical condition the partial derivative of two phase pressure drop with respect to the local pressure or to phase velocity must be zero.This criteria is demonstrated by numerical examples. The experimental work of Fauske (1962) and Jeandey (1982) were analyzed resulting in estimated numerical values for important parameters like slip ratio, equilibrium constant and two phase frictional drop. (author)

Violations of local equilibrium and linear response in classical lattice systems

International Nuclear Information System (INIS)

Aoki, Kenichiro; Kusnezov, Dimitri

2003-01-01

We quantitatively and systematically analyze how local equilibrium, and linear response in transport are violated as systems move far from equilibrium. This is done by studying heat flow in classical lattice models with and without bulk transport behavior, in 1-3 dimensions, at various temperatures. Equations of motion for the system are integrated numerically to construct the non-equilibrium steady states. Linear response and local equilibrium assumptions are seen to break down in a similar manner. We quantify the breakdown through the analysis of both microscopic and macroscopic observables and examine its transformation properties under general redefinitions of the non-equilibrium temperature

Rate equation simulation of temporal characteristics of a pulsed dye ...

Indian Academy of Sciences (India)

-dependent, two-dimensional (in space) rate equation model of a .... fluorescence band of the dye is divided into ten wavelength segments of variable sizes. ... qualitative and reasonably good quantitative agreement with experimental results.

Technical note: Evaluation of the simultaneous measurements of mesospheric OH, HO2, and O3 under a photochemical equilibrium assumption - a statistical approach

Science.gov (United States)

Kulikov, Mikhail Y.; Nechaev, Anton A.; Belikovich, Mikhail V.; Ermakova, Tatiana S.; Feigin, Alexander M.

2018-05-01

This Technical Note presents a statistical approach to evaluating simultaneous measurements of several atmospheric components under the assumption of photochemical equilibrium. We consider simultaneous measurements of OH, HO2, and O3 at the altitudes of the mesosphere as a specific example and their daytime photochemical equilibrium as an evaluating relationship. A simplified algebraic equation relating local concentrations of these components in the 50-100 km altitude range has been derived. The parameters of the equation are temperature, neutral density, local zenith angle, and the rates of eight reactions. We have performed a one-year simulation of the mesosphere and lower thermosphere using a 3-D chemical-transport model. The simulation shows that the discrepancy between the calculated evolution of the components and the equilibrium value given by the equation does not exceed 3-4 % in the full range of altitudes independent of season or latitude. We have developed a statistical Bayesian evaluation technique for simultaneous measurements of OH, HO2, and O3 based on the equilibrium equation taking into account the measurement error. The first results of the application of the technique to MLS/Aura data (Microwave Limb Sounder) are presented in this Technical Note. It has been found that the satellite data of the HO2 distribution regularly demonstrate lower altitudes of this component's mesospheric maximum. This has also been confirmed by model HO2 distributions and comparison with offline retrieval of HO2 from the daily zonal means MLS radiance.

Improved decay rates for solutions for a multidimensional generalized Benjamin-Bona-Mahony equation

KAUST Repository

Said-Houari, Belkacem

2014-01-01

In this paper, we study the decay rates of solutions for the generalized Benjamin-Bona-Mahony equation in multi-dimensional space. For initial data in some L1-weighted spaces, we prove faster decay rates of the solutions. More precisely, using the Fourier transform and the energy method, we show the global existence and the convergence rates of the solutions under the smallness assumption on the initial data and we give better decay rates of the solutions. This result improves early works in J. Differential Equations 158(2) (1999), 314-340 and Nonlinear Anal. 75(7) (2012), 3385-3392. © 2014-IOS Press.

Realization of radioactive equilibrium in the KRISS radon chamber

International Nuclear Information System (INIS)

Lee, Mo Sung; Park, Tae Soon; Lee, Jong Man

2013-01-01

The maintenance of radioactive equilibrium between radon and its decay products in a radon chamber is necessary to calibrate radon decay product monitors. In this study, the activity concentrations of radon decay products have been measured, and mosquito-repellent incense has been used to produce aerosol particles in the chamber. Filter papers with 8 μm pore size were used to collect aerosol in the chamber. The activity concentrations of radon decay products have been evaluated by the Modified Tsivoglou Method. The correction factors due to the differences in counting time requirements of the Modified Tsivoglou Method and the time delay between consecutive measurements have been determined. Finally, the radioactive equilibrium has been confirmed by applying the Bateman equation. - Highlights: • The activity concentrations of radon decay products are evaluated by the Modified Tsivoglou Method. • Mosquito-repellent incense is used to produce aerosol particles in the radon chamber. • The radioactive equilibrium in the chamber was achieved within 2 days and confirmed by the Bateman equation

Fluid dynamics of out of equilibrium boost invariant plasmas

Science.gov (United States)

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.

Out of equilibrium transport through an Anderson impurity: probing scaling laws within the equation of motion approach.

Science.gov (United States)

Balseiro, C A; Usaj, G; Sánchez, M J

2010-10-27

We study non-equilibrium electron transport through a quantum impurity coupled to metallic leads using the equation of motion technique at finite temperature T. Assuming that the interactions are taking place solely in the impurity and focusing on the infinite Hubbard limit, we compute the out of equilibrium density of states and the differential conductance G(2)(T, V) in order to test several scaling laws. We find that G(2)(T, V)/G(2)(T, 0) is a universal function of both eV/T(K) and T/T(K), T(K) being the Kondo temperature. The effect of an in-plane magnetic field on the splitting of the zero bias anomaly in the differential conductance is also analyzed. For a Zeeman splitting Δ, the computed differential conductance peak splitting depends only on Δ/T(K), and for large fields approaches the value of 2Δ. Besides studying the traditional two leads setup, we also consider other configurations that mimic recent experiments, namely, an impurity embedded in a mesoscopic wire and the presence of a third weakly coupled lead. In these cases, a double peak structure of the Kondo resonance is clearly obtained in the differential conductance while the amplitude of the highest peak is shown to decrease as ln(eV/T(K)). Several features of these results are in qualitative agreement with recent experimental observations reported on quantum dots.

An improved flux-split algorithm applied to hypersonic flows in chemical equilibrium

Science.gov (United States)

Palmer, Grant

1988-01-01

An explicit, finite-difference, shock-capturing numerical algorithm is presented and applied to hypersonic flows assumed to be in thermochemical equilibrium. Real-gas chemistry is either loosely coupled to the gasdynamics by way of a Gibbs free energy minimization package or fully coupled using species mass conservation equations with finite-rate chemical reactions. A scheme is developed that maintains stability in the explicit, finite-rate formulation while allowing relatively high time steps. The codes use flux vector splitting to difference the inviscid fluxes and employ real-gas corrections to viscosity and thermal conductivity. Numerical results are compared against existing ballistic range and flight data. Flows about complex geometries are also computed.

Balance Mass Flux and Velocity Across the Equilibrium Line in Ice Drainage Systems of Greenland

Science.gov (United States)

Zwally, H. Jay; Giovinetto, Mario B.; Koblinsky, Chester J. (Technical Monitor)

2001-01-01

Estimates of balance mass flux and the depth-averaged ice velocity through the cross-section aligned with the equilibrium line are produced for each of six drainage systems in Greenland. (The equilibrium line, which lies at approximately 1200 m elevation on the ice sheet, is the boundary between the area of net snow accumulation at higher elevations and the areas of net melting at lower elevations around the ice sheet.) Ice drainage divides and six major drainage systems are delineated using surface topography from ERS (European Remote Sensing) radar altimeter data. The net accumulation rate in the accumulation zone bounded by the equilibrium line is 399 Gt/yr and net ablation rate in the remaining area is 231 Gt/yr. (1 GigaTon of ice is 1090 kM(exp 3). The mean balance mass flux and depth-averaged ice velocity at the cross-section aligned with the modeled equilibrium line are 0.1011 Gt kM(exp -2)/yr and 0.111 km/yr, respectively, with little variation in these values from system to system. The ratio of the ice mass above the equilibrium line to the rate of mass output implies an effective exchange time of approximately 6000 years for total mass exchange. The range of exchange times, from a low of 3 ka in the SE drainage system to 14 ka in the NE, suggests a rank as to which regions of the ice sheet may respond more rapidly to climate fluctuations.

Potential in stochastic differential equations: novel construction

International Nuclear Information System (INIS)

Ao, P

2004-01-01

There is a whole range of emergent phenomena in a complex network such as robustness, adaptiveness, multiple-equilibrium, hysteresis, oscillation and feedback. Those non-equilibrium behaviours can often be described by a set of stochastic differential equations. One persistent important question is the existence of a potential function. Here we demonstrate that a dynamical structure built into stochastic differential equation allows us to construct such a global optimization potential function. We present an explicit construction procedure to obtain the potential and relevant quantities. In the procedure no reference to the Fokker-Planck equation is needed. The availability of the potential suggests that powerful statistical mechanics tools can be used in nonequilibrium situations. (letter to the editor)

Multicomponent equations of state for electrolytes

DEFF Research Database (Denmark)

Lin, Yi; Thomsen, Kaj; Hemptinne, Jean-Charles de

2007-01-01

. The parameters in the equations of state were fitted to experimental data consisting of apparent molar volumes, osmotic coefficients, mean ionic activity coefficients, and solid-liquid equilibrium data. The results of the parameter fitting are presented. The ability of the equations of state to reproduce...

The Gibbs-Thomson equation for a spherical coherent precipitate with applications to nucleation

International Nuclear Information System (INIS)

Rottman, C.; Voorhees, P.W.; Johnson, W.C.

1988-01-01

The conditions for interfacial thermodynamic equilibrium form the basis for the derivation of a number of basic equations in materials science, including the various forms of the Gibbs-Thomson equation. The equilibrium conditions pertaining to a curved interface in a two-phase fluid system are well-known. In contrast, the conditions for thermodynamic equilibrium at a curved interface in nonhydrostatically stressed solids have only recently been examined. These conditions can be much different from those at a fluid interface and, as a result, the Gibbs-Thomson equation appropriate to coherent solids is likely to be considerably different from that for fluids. In this paper, the authors first derive the conditions necessary for thermodynamic equilibrium at the precipitate-matrix interface of a coherent spherical precipitate. The authors' derivation of these equilibrium conditions includes a correction to the equilibrium conditions of Johnson and Alexander for a spherical precipitate in an isotropic matrix. They then use these conditions to derive the dependence of the interfacial precipitate and matrix concentrations on precipitate radius (Gibbs-Thomson equation) for a such a precipitate. In addition, these relationships are then used to calculate the critical radius for the nucleation of a coherent misfitting precipitate

Equilibrium and nonequilibrium solvation and solute electronic structure

International Nuclear Information System (INIS)

Kim, H.J.; Hynes, J.T.

1990-01-01

When a molecular solute is immersed in a polar and polarizable solvent, the electronic wave function of the solute system is altered compared to its vacuum value; the solute electronic structure is thus solvent-dependent. Further, the wave function will be altered depending upon whether the polarization of the solvent is or is not in equilibrium with the solute charge distribution. More precisely, while the solvent electronic polarization should be in equilibrium with the solute electronic wave function, the much more sluggish solvent orientational polarization need not be. We call this last situation non-equilibrium solvation. We outline a nonlinear Schroedinger equation approach to these issues

CO2/H2O adsorption equilibrium and rates on metal-organic frameworks: HKUST-1 and Ni/DOBDC.

Science.gov (United States)

Liu, Jian; Wang, Yu; Benin, Annabelle I; Jakubczak, Paulina; Willis, Richard R; LeVan, M Douglas

2010-09-07

Metal-organic frameworks (MOFs) have recently attracted intense research interest because of their permanent porous structures, huge surface areas, and potential applications as novel adsorbents and catalysts. In order to provide a basis for consideration of MOFs for removal of carbon dioxide from gases containing water vapor, such as flue gas, we have studied adsorption equilibrium of CO(2), H(2)O vapor, and their mixtures and also rates of CO(2) adsorption in two MOFs: HKUST-1 (CuBTC) and Ni/DOBDC (CPO-27-Ni or Ni/MOF-74). The MOFs were synthesized via solvothermal methods, and the as-synthesized products were solvent exchanged and regenerated before experiments. Pure component adsorption equilibria and CO(2)/H(2)O binary adsorption equilibria were studied using a volumetric system. The effects of H(2)O adsorption on CO(2) adsorption for both MOF samples were determined, and the results for 5A and NaX zeolites were included for comparison. The hydrothermal stabilities for the two MOFs over the course of repetitive measurements of H(2)O and CO(2)/H(2)O mixture equilibria were also studied. CO(2) adsorption rates from helium for the MOF samples were investigated by using a unique concentration-swing frequency response (CSFR) system. Mass transfer into the MOFs is rapid with the controlling resistance found to be macropore diffusion, and rate parameters were established for the mechanism.

Validation of resting metabolic rate prediction equations for teenagers

Directory of Open Access Journals (Sweden)

Paulo Henrique Santos da Fonseca

2007-09-01

Full Text Available The resting metabolic rate (RMR can be defi ned as the minimum rate of energy spent and represents the main component of the energetic outlay. The purpose of this study is to validate equations to predict the resting metabolic rate in teenagers (103 individuals, being 51 girls and 52 boys, with age between 10 and 17 years from Florianópolis – SC – Brazil. It was measured: the body weight, body height, skinfolds and obtained the lean and body fat mass through bioimpedance. The nonproteic RMR was measured by Weir’s equation (1949, utilizing AeroSport TEEM-100 gas analyzer. The studied equations were: Harry and Benedict (1919, Schofi eld (1985, WHO/FAO/UNU (1985, Henry and Rees (1991, Molnár et al. (1998, Tverskaya et al. (1998 and Müller et al. (2004. In order to study the cross-validation of the RMR prediction equations and its standard measure (Weir 1949, the following statistics procedure were calculated: Pearson’s correlation (r ≥ 0.70, the “t” test with the signifi cance level of p0.05 in relation to the standard measure, with exception of the equations suggested for Tverskaya et al. (1998, and the two models of Müller et al (2004. Even though there was not a signifi cant difference, only the models considered for Henry and Rees (1991, and Molnár et al. (1995 had gotten constant error variation under 5%. All the equations analyzed in the study in girls had not reached criterion of correlation values of 0.70 with the indirect calorimetry. Analyzing the prediction equations of RMR in boys, all of them had moderate correlation coeffi cients with the indirect calorimetry, however below 0.70. Only the equation developed for Tverskaya et al. (1998 presented differences (p ABSTRACT0,05 em relação à medida padrão (Weir 1949, com exceção das equações sugeridas por Tverskaya et al. (1998 e os dois modelos de Müller et al (2004. Mesmo não havendo diferença signifi cativa, somente os modelos propostos por Henry e Rees (1991

High freight rates hinder oil markets' return to equilibrium

International Nuclear Information System (INIS)

Anon

2005-01-01

Hurricane damage to refineries in the US has created shortages of refined products there, boosting imports and sending freight rates across the Atlantic to record levels. The situation was made worse for a time by a strike at France's main oil terminals in the Mediterranean, which prevented some oil tankers from being rapidly redeployed to routes across the Atlantic. Worldscale (WS) rates for routes from the UK and Europe to the US Atlantic and Gulf Coasts rose well above WS500 for clean tonnage during October. High rates were nevertheless not simply confined to product tankers crossing the Atlantic. Rates for crude tankers to the US have also risen, and tightness has begun to appear in some other markets as well. The net result has been to slow down the movement of oil from regions of surplus to those of scarcity, depressing prices in the former and keeping them at high levels in the latter. Atlantic tanker markets look like remaining tight for the rest of the year and perhaps beyond. (author)

Squeezing corrections to the Bloch equations

International Nuclear Information System (INIS)

Abundo, M.; Accardi, L.

1991-01-01

The general analysis of quantum noise shows that a squeezing noise can produce quadratic nonlinearities in the Langevin equations leading to the Bloch equations. These quadratic nonlinearities are governed by the imaginary part of the off-diagonal terms of the covariance of the noise (the squeezing terms) and imply a correction to the usual form of the Bloch equations. Here the case of spin-one nuclei subjected to squeezing noises of particular type is studied numerically. It is shown that the corrections to the Bloch equations, suggested by the theory, to the behaviour of the macroscopic nuclear polarization in a scale of times of the order of the relaxation time can be quite substantial. In the equilibrium regime, even if the qualitative behaviour of the system is the same (exponential decay), the numerical equilibrium values predicted by the theory are consistently different from those predicted by the usual Bloch equation. It is suggested that this difference might be used to test experimentally the observable effects of squeezing noises

Equations to Estimate Creatinine Excretion Rate : The CKD Epidemiology Collaboration

NARCIS (Netherlands)

Ix, Joachim H.; Wassel, Christina L.; Stevens, Lesley A.; Beck, Gerald J.; Froissart, Marc; Navis, Gerjan; Rodby, Roger; Torres, Vicente E.; Zhang, Yaping (Lucy); Greene, Tom; Levey, Andrew S.

Background and objectives Creatinine excretion rate (CER) indicates timed urine collection accuracy. Although equations to estimate CER exist, their bias and precision are untested and none simultaneously include age, sex, race, and weight. Design, setting, participants, & measurements Participants

Asymptotic equilibrium diffusion analysis of time-dependent Monte Carlo methods for grey radiative transfer

International Nuclear Information System (INIS)

Densmore, Jeffery D.; Larsen, Edward W.

2004-01-01

The equations of nonlinear, time-dependent radiative transfer are known to yield the equilibrium diffusion equation as the leading-order solution of an asymptotic analysis when the mean-free path and mean-free time of a photon become small. We apply this same analysis to the Fleck-Cummings, Carter-Forest, and N'kaoua Monte Carlo approximations for grey (frequency-independent) radiative transfer. Although Monte Carlo simulation usually does not require the discretizations found in deterministic transport techniques, Monte Carlo methods for radiative transfer require a time discretization due to the nonlinearities of the problem. If an asymptotic analysis of the equations used by a particular Monte Carlo method yields an accurate time-discretized version of the equilibrium diffusion equation, the method should generate accurate solutions if a time discretization is chosen that resolves temperature changes, even if the time steps are much larger than the mean-free time of a photon. This analysis is of interest because in many radiative transfer problems, it is a practical necessity to use time steps that are large compared to a mean-free time. Our asymptotic analysis shows that: (i) the N'kaoua method has the equilibrium diffusion limit, (ii) the Carter-Forest method has the equilibrium diffusion limit if the material temperature change during a time step is small, and (iii) the Fleck-Cummings method does not have the equilibrium diffusion limit. We include numerical results that verify our theoretical predictions

Technical note: Use of a simplified equation for estimating glomerular filtration rate in beef cattle.

Science.gov (United States)

Murayama, I; Miyano, A; Sasaki, Y; Hirata, T; Ichijo, T; Satoh, H; Sato, S; Furuhama, K

2013-11-01

This study was performed to clarify whether a formula (Holstein equation) based on a single blood sample and the isotonic, nonionic, iodine contrast medium iodixanol in Holstein dairy cows can apply to the estimation of glomerular filtration rate (GFR) for beef cattle. To verify the application of iodixanol in beef cattle, instead of the standard tracer inulin, both agents were coadministered as a bolus intravenous injection to identical animals at doses of 10 mg of I/kg of BW and 30 mg/kg. Blood was collected 30, 60, 90, and 120 min after the injection, and the GFR was determined by the conventional multisample strategies. The GFR values from iodixanol were well consistent with those from inulin, and no effects of BW, age, or parity on GFR estimates were noted. However, the GFR in cattle weighing less than 300 kg, aged<1 yr old, largely fluctuated, presumably due to the rapid ruminal growth and dynamic changes in renal function at young adult ages. Using clinically healthy cattle and those with renal failure, the GFR values estimated from the Holstein equation were in good agreement with those by the multisample method using iodixanol (r=0.89, P=0.01). The results indicate that the simplified Holstein equation using iodixanol can be used for estimating the GFR of beef cattle in the same dose regimen as Holstein dairy cows, and provides a practical and ethical alternative.

Magnetohydrodynamic equilibrium with spheroidal plasma-vacuum interface

International Nuclear Information System (INIS)

Kaneko, Shobu; Chiyoda, Katsuji; Hirota, Isao.

1983-01-01

The Grad-Shafranov equations for an oblate and a prolate spheroidal plasmas are solved analytically under the assumptions, Bsub(phi) = 0 and dp/dpsi = constant. Here Bsub(phi) is the toroidal magnetic field, p is the kinetic pressure, and psi is the magnetic flux function. The plasmas in magnetohydrodynamic equilibrium are shown to be toroidal. The equilibrium magnetic-field configurations outside the spheroidal plasmas are considerably different from that of a spherical plasma. A line cusp or two point cusps appear outside the oblate or the prolate spheroidal plasma, respectively. (author)

Lower hybrid wave current ramp-up and plasma equilibrium

International Nuclear Information System (INIS)

Gong Xueyu

1996-01-01

Questions on lower hybrid driven current and plasma equilibrium are studied. With the induced electric field taken into account, a system of self-consistent equations is obtained. This theory has been applied to some moments of the current ramp-up phase for the Tokamak Engineering Test Breeder (TETB) to study the lower hybrid current drive and MHD equilibrium. So, better electron current and safety factor profiles are obtained

Calculation of the form of an equilibrium poloidal magnetic field contained in a polytropic star

International Nuclear Information System (INIS)

Brundrit, G.B.; Miketinac, M.J.

1976-01-01

This program is designed to integrate the exact equations which determine the distribution of the density of a self-gravitating, axisymmetric polytrope of infinite conductivity containing a poloidal magnetic field. In addition, other properties of an equilibrium configuration such as mass, volume and radius are calculated. The program can also provide at very small extra cost the rates of change of the density with respect to changes of the polytropic index n and the parameter lambda which characterizes the poloidal magnetic field. Mathematically, the problem can be formulated as a boundary value problem for three coupled equations, two of which are second order, non-linear, two-dimensional partial differential equations. The solution is obtained numerically by an adaptation of the Stoeckl's finite difference-finite expansion method. In fact, the present program is a major modification of the program TOROID. The numerical scheme developed in the program is valid for all polytropes whose polytropic index n is greater than or equal to one. The other parameter of the theory, lambda, is unrestricted, i.e. the program permits the study of stars whose matnetic energy is a 'sizeable' percentage of their gravitational energy. Also, the program, with minor modifications, could be used for calculating equilibrium configurations of (a) (uniformly or non-uniformly) rotating polytropes pervaded by poloidal magnetic fields or (b) (rotation) polytropes containing poloidal magnetic fields. However, the greatest use of the present program is expected to arise in attempts to construct equilibrium configurations of polytropes containing mixed poloidal toroidal magnetic fields. (Auth.)

Thermodynamic and transport properties of gaseous tetrafluoromethane in chemical equilibrium

Science.gov (United States)

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.

Generalized quantum master equations in and out of equilibrium: When can one win?

International Nuclear Information System (INIS)

Kelly, Aaron; Markland, Thomas E.; Montoya-Castillo, Andrés; Wang, Lu

2016-01-01

Generalized quantum master equations (GQMEs) are an important tool in modeling chemical and physical processes. For a large number of problems, it has been shown that exact and approximate quantum dynamics methods can be made dramatically more efficient, and in the latter case more accurate, by proceeding via the GQME formalism. However, there are many situations where utilizing the GQME approach with an approximate method has been observed to return the same dynamics as using that method directly. Here, for systems both in and out of equilibrium, we provide a more detailed understanding of the conditions under which using an approximate method can yield benefits when combined with the GQME formalism. In particular, we demonstrate the necessary manipulations, which are satisfied by exact quantum dynamics, that are required to recast the memory kernel in a form that can be analytically shown to yield the same result as a direct application of the dynamics regardless of the approximation used. By considering the connections between these forms of the kernel, we derive the conditions that approximate methods must satisfy if they are to offer different results when used in conjunction with the GQME formalism. These analytical results thus provide new insights as to when proceeding via the GQME approach can be used to improve the accuracy of simulations.

Relativistic phenomenological equations and transformation laws of relative coefficients

Directory of Open Access Journals (Sweden)

Patrizia Rogolino

2017-06-01

Full Text Available The aim of this paper is to derive the phenomenological equations in the context of special relativistic non-equilibrium thermodynamics with internal variables. In particular, after introducing some results developed in our previous paper, by means of classical non-equilibrium thermodynamic procedure and under suitable assumptions on the entropy density production, the phenomenological equations and transformation laws of phenomenological coefficients are derived. Finally, some symmetries of aforementioned coefficients are obtained.

Local Equilibrium and Retardation Revisited.

Science.gov (United States)

Hansen, Scott K; Vesselinov, Velimir V

2018-01-01

In modeling solute transport with mobile-immobile mass transfer (MIMT), it is common to use an advection-dispersion equation (ADE) with a retardation factor, or retarded ADE. This is commonly referred to as making the local equilibrium assumption (LEA). Assuming local equilibrium, Eulerian textbook treatments derive the retarded ADE, ostensibly exactly. However, other authors have presented rigorous mathematical derivations of the dispersive effect of MIMT, applicable even in the case of arbitrarily fast mass transfer. We resolve the apparent contradiction between these seemingly exact derivations by adopting a Lagrangian point of view. We show that local equilibrium constrains the expected time immobile, whereas the retarded ADE actually embeds a stronger, nonphysical, constraint: that all particles spend the same amount of every time increment immobile. Eulerian derivations of the retarded ADE thus silently commit the gambler's fallacy, leading them to ignore dispersion due to mass transfer that is correctly modeled by other approaches. We then present a particle tracking simulation illustrating how poor an approximation the retarded ADE may be, even when mobile and immobile plumes are continually near local equilibrium. We note that classic "LEA" (actually, retarded ADE validity) criteria test for insignificance of MIMT-driven dispersion relative to hydrodynamic dispersion, rather than for local equilibrium. Published 2017. This article is a U.S. Government work and is in the public domain in the USA.

Wall ablation of heated compound-materials into non-equilibrium discharge plasmas

Science.gov (United States)

Wang, Weizong; Kong, Linghan; Geng, Jinyue; Wei, Fuzhi; Xia, Guangqing

2017-02-01

The discharge properties of the plasma bulk flow near the surface of heated compound-materials strongly affects the kinetic layer parameters modeled and manifested in the Knudsen layer. This paper extends the widely used two-layer kinetic ablation model to the ablation controlled non-equilibrium discharge due to the fact that the local thermodynamic equilibrium (LTE) approximation is often violated as a result of the interaction between the plasma and solid walls. Modifications to the governing set of equations, to account for this effect, are derived and presented by assuming that the temperature of the electrons deviates from that of the heavy particles. The ablation characteristics of one typical material, polytetrafluoroethylene (PTFE) are calculated with this improved model. The internal degrees of freedom as well as the average particle mass and specific heat ratio of the polyatomic vapor, which strongly depends on the temperature, pressure and plasma non-equilibrium degree and plays a crucial role in the accurate determination of the ablation behavior by this model, are also taken into account. Our assessment showed the significance of including such modifications related to the non-equilibrium effect in the study of vaporization of heated compound materials in ablation controlled arcs. Additionally, a two-temperature magneto-hydrodynamic (MHD) model accounting for the thermal non-equilibrium occurring near the wall surface is developed and applied into an ablation-dominated discharge for an electro-thermal chemical launch device. Special attention is paid to the interaction between the non-equilibrium plasma and the solid propellant surface. Both the mass exchange process caused by the wall ablation and plasma species deposition as well as the associated momentum and energy exchange processes are taken into account. A detailed comparison of the results of the non-equilibrium model with those of an equilibrium model is presented. The non-equilibrium results

Solving QCD evolution equations in rapidity space with Markovian Monte Carlo

CERN Document Server

Golec-Biernat, K; Placzek, W; Skrzypek, M

2009-01-01

This work covers methodology of solving QCD evolution equation of the parton distribution using Markovian Monte Carlo (MMC) algorithms in a class of models ranging from DGLAP to CCFM. One of the purposes of the above MMCs is to test the other more sophisticated Monte Carlo programs, the so-called Constrained Monte Carlo (CMC) programs, which will be used as a building block in the parton shower MC. This is why the mapping of the evolution variables (eikonal variable and evolution time) into four-momenta is also defined and tested. The evolution time is identified with the rapidity variable of the emitted parton. The presented MMCs are tested independently, with ~0.1% precision, against the non-MC program APCheb especially devised for this purpose.

Guiding Center Equations in Toroidal Equilibria

International Nuclear Information System (INIS)

White, Roscoe; Zakharov, Leonid

2002-01-01

Guiding center equations for particle motion in a general toroidal magnetic equilibrium configuration are derived using magnetic coordinates. Previous derivations made use of Boozer coordinates, in which the poloidal and toroidal angle variables are chosen so that the Jacobian is inversely proportional to the square of the magnetic field. It is shown that the equations for guiding center motion in any equilibrium possessing nested flux surfaces have exactly the same simple form as those derived in this special case. This allows the use of more spatially uniform coordinates instead of the Boozer coordinates, greatly increasing the accuracy of calculations in large beta and strongly shaped equilibria

A strictly hyperbolic equilibrium phase transition model

International Nuclear Information System (INIS)

Allaire, G; Faccanoni, G; Kokh, S.

2007-01-01

This Note is concerned with the strict hyperbolicity of the compressible Euler equations equipped with an equation of state that describes the thermodynamical equilibrium between the liquid phase and the vapor phase of a fluid. The proof is valid for a very wide class of fluids. The argument only relies on smoothness assumptions and on the classical thermodynamical stability assumptions, that requires a definite negative Hessian matrix for each phase entropy as a function of the specific volume and internal energy. (authors)

Center manifolds for a class of degenerate evolution equations and existence of small-amplitude kinetic shocks

Science.gov (United States)

Pogan, Alin; Zumbrun, Kevin

2018-06-01

We construct center manifolds for a class of degenerate evolution equations including the steady Boltzmann equation and related kinetic models, establishing in the process existence and behavior of small-amplitude kinetic shock and boundary layers. Notably, for Boltzmann's equation, we show that elements of the center manifold decay in velocity at near-Maxwellian rate, in accord with the formal Chapman-Enskog picture of near-equilibrium flow as evolution along the manifold of Maxwellian states, or Grad moment approximation via Hermite polynomials in velocity. Our analysis is from a classical dynamical systems point of view, with a number of interesting modifications to accommodate ill-posedness of the underlying evolution equation.

Some recent developments in non-equilibrium statistical physics

Indian Academy of Sciences (India)

: ... This canonical prescription is the starting point for studying a system in ... abilistic approach to non-equilibrium dynamics by treating the case of Markovian ..... equation in this network between the incoming flux and the outgoing flux at each.

Non-equilibrium relaxation and near-arrest dynamics in colloidal suspensions

International Nuclear Information System (INIS)

Medina-Noyola, M; RamIrez-Gonzalez, Pedro

2009-01-01

In this work we propose a theory to describe the irreversible diffusive relaxation of the local concentration of a colloidal dispersion that proceeds toward its stable thermodynamic equilibrium state, but which may in the process be trapped in metastable or dynamically arrested states. The central assumption of this theory is that the irreversible relaxation of the macroscopically observed mean value n-bar(r,t) of the local concentration of colloidal particles is described by a diffusion equation involving a local mobility b*(r,t) that depends not only on the mean value n-bar(r,t) but also on the covariance σ(r,r';t)≡δn(r,t)δn(r',t)-bar of the fluctuations δn(r,t)≡n(r,t)-n-bar(r,t). This diffusion equation must hence be solved simultaneously with the relaxation equation for the covariance σ(r,r';t), and here we also derive the corresponding relaxation equation. The dependence of the local mobility b*(r,t) on the mean value and the covariance is determined by a self-consistent set of equations involving now the spatially and temporally non-local time-dependent correlation functions, which in a uniform system in equilibrium reduces to the self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics. The resulting general theory considers the possibility that these relaxation processes occur under the influence of external fields, such as gravitational forces acting in the process of sedimentation. In this paper, however, we describe a simpler application, in which the system remains spatially uniform during the irreversible relaxation process, and discuss the general features of the glass transition scenario predicted by this non-equilibrium theory.

A detailed analysis of inviscid flux splitting algorithms for real gases with equilibrium or finite-rate chemistry

Science.gov (United States)

Shuen, Jian-Shun; Liou, Meng-Sing; Van Leer, Bram

1989-01-01

The extension of the known flux-vector and flux-difference splittings to real gases via rigorous mathematical procedures is demonstrated. Formulations of both equilibrium and finite-rate chemistry for real-gas flows are described, with emphasis on derivations of finite-rate chemistry. Split-flux formulas from other authors are examined. A second-order upwind-based TVD scheme is adopted to eliminate oscillations and to obtain a sharp representation of discontinuities.

The reactions of neutral iron clusters with D2O: Deconvolution of equilibrium constants from multiphoton processes

International Nuclear Information System (INIS)

Weiller, B.H.; Bechthold, P.S.; Parks, E.K.; Pobo, L.G.; Riley, S.J.

1989-01-01

The chemical reactions of neutral iron clusters with D 2 O are studied in a continuous flow tube reactor by molecular beam sampling and time-of-flight mass spectrometry with laser photoionization. Product distributions are invariant to a four-fold change in reaction time demonstrating that equilibrium is attained between free and adsorbed D 2 O. The observed negative temperature dependence is consistent with an exothermic, molecular addition reaction at equilibrium. Under our experimental conditions, there is significant photodesorption of D 2 O (Fe/sub n/(D 2 O)/sub m/ + hν → Fe/sub n/ + m D 2 O) along with ionization due to absorption of multiple photons from the ionizing laser. Using a simple model based on a rate equation analysis, we are able to quantitatively deconvolute this desorption process from the equilibrium constants. 8 refs., 1 fig

Computer program to solve two-dimensional shock-wave interference problems with an equilibrium chemically reacting air model

Science.gov (United States)

Glass, Christopher E.

1990-08-01

The computer program EASI, an acronym for Equilibrium Air Shock Interference, was developed to calculate the inviscid flowfield, the maximum surface pressure, and the maximum heat flux produced by six shock wave interference patterns on a 2-D, cylindrical configuration. Thermodynamic properties of the inviscid flowfield are determined using either an 11-specie, 7-reaction equilibrium chemically reacting air model or a calorically perfect air model. The inviscid flowfield is solved using the integral form of the conservation equations. Surface heating calculations at the impingement point for the equilibrium chemically reacting air model use variable transport properties and specific heat. However, for the calorically perfect air model, heating rate calculations use a constant Prandtl number. Sample calculations of the six shock wave interference patterns, a listing of the computer program, and flowcharts of the programming logic are included.

Validity of predictive equations for basal metabolic rate in Japanese adults.

Science.gov (United States)

Miyake, Rieko; Tanaka, Shigeho; Ohkawara, Kazunori; Ishikawa-Takata, Kazuko; Hikihara, Yuki; Taguri, Emiko; Kayashita, Jun; Tabata, Izumi

2011-01-01

Many predictive equations for basal metabolic rate (BMR) based on anthropometric measurements, age, and sex have been developed, mainly for healthy Caucasians. However, it has been reported that many of these equations, used widely, overestimate BMR not only for Asians, but also for Caucasians. The present study examined the accuracy of several predictive equations for BMR in Japanese subjects. In 365 healthy Japanese male and female subjects, aged 18 to 79 y, BMR was measured in the post-absorptive state using a mask and Douglas bag. Six predictive equations were examined. Total error was used as an index of the accuracy of each equation's prediction. Predicted BMR values by Dietary Reference Intakes for Japanese (Japan-DRI), Adjusted Dietary Reference Intakes for Japanese (Adjusted-DRI), and Ganpule equations were not significantly different from the measured BMR in either sex. On the other hand, Harris-Benedict, Schofield, and Food and Agriculture Organization of the United Nations/World Health Organization/United Nations University equations were significantly higher than the measured BMR in both sexes. The prediction error by Japan-DRI, Adjusted-DRI, and Harris-Benedict equations was significantly correlated with body weight in both sexes. Total error using the Ganpule equation was low in both males and females (125 and 99 kcal/d, respectively). In addition, total error using the Adjusted-DRI equation was low in females (95 kcal/d). Thus, the Ganpule equation was the most accurate in predicting BMR in our healthy Japanese subjects, because the difference between the predicted and measured BMR was relatively small, and body weight had no effect on the prediction error.

Shape characteristics of equilibrium and non-equilibrium fractal clusters.

Science.gov (United States)

Mansfield, Marc L; Douglas, Jack F

2013-07-28

It is often difficult in practice to discriminate between equilibrium and non-equilibrium nanoparticle or colloidal-particle clusters that form through aggregation in gas or solution phases. Scattering studies often permit the determination of an apparent fractal dimension, but both equilibrium and non-equilibrium clusters in three dimensions frequently have fractal dimensions near 2, so that it is often not possible to discriminate on the basis of this geometrical property. A survey of the anisotropy of a wide variety of polymeric structures (linear and ring random and self-avoiding random walks, percolation clusters, lattice animals, diffusion-limited aggregates, and Eden clusters) based on the principal components of both the radius of gyration and electric polarizability tensor indicates, perhaps counter-intuitively, that self-similar equilibrium clusters tend to be intrinsically anisotropic at all sizes, while non-equilibrium processes such as diffusion-limited aggregation or Eden growth tend to be isotropic in the large-mass limit, providing a potential means of discriminating these clusters experimentally if anisotropy could be determined along with the fractal dimension. Equilibrium polymer structures, such as flexible polymer chains, are normally self-similar due to the existence of only a single relevant length scale, and are thus anisotropic at all length scales, while non-equilibrium polymer structures that grow irreversibly in time eventually become isotropic if there is no difference in the average growth rates in different directions. There is apparently no proof of these general trends and little theoretical insight into what controls the universal anisotropy in equilibrium polymer structures of various kinds. This is an obvious topic of theoretical investigation, as well as a matter of practical interest. To address this general problem, we consider two experimentally accessible ratios, one between the hydrodynamic and gyration radii, the other

Speeding up compositional reservoir simulation through an efficient implementation of phase equilibrium calculation

DEFF Research Database (Denmark)

Belkadi, Abdelkrim; Yan, Wei; Moggia, Elsa

2013-01-01

Compositional reservoir simulations are widely used to simulate reservoir processes with strong compositional effects, such as gas injection. The equations of state (EoS) based phase equilibrium calculation is a time consuming part in this type of simulations. The phase equilibrium problem can....... Application of the shadow region method to skip stability analysis can further cut the phase equilibrium calculation time. Copyright 2013, Society of Petroleum Engineers....

Nash Equilibrium of an Energy Saving Strategy with Dual Rate Transmission in Wireless Regional Area Network

Directory of Open Access Journals (Sweden)

Zhanqiang Huo

2017-01-01

Full Text Available Wireless regional area network (WRAN adopts centralized network architecture and is currently one of the most typical cognitive radio networks. In order to reduce the energy consumption of the communication networks with the constraint of spectrum resource utilization, a working sleep mechanism is introduced into the base station (BS, and a novel energy saving strategy with dual rate transmission is proposed. Combining the multiple-vacation queue and priority queue, using the quasi-birth-death process and the matrix-geometric solution method, we assess the average latency and the forced termination probability of secondary user packets, as well as the energy saving ratio and the channel utilization of system. Based on the revenue-expenditure structure, a profit function is built, and then the Nash equilibrium behavior and the socially optimal behavior are investigated. With the help of the particle swarm optimization, an intelligent optimization algorithm to search the socially optimal arrival rate of secondary user packets is presented. In order to unify the arrival rates of secondary user packets with Nash equilibrium and social optimization, a reasonable pricing policy is formulated. In addition, system experiments are carried out to verify the effectiveness of the energy saving strategy and the rationality of the pricing policy.

Hartman-Wintner growth results for sublinear functional differential equations

Directory of Open Access Journals (Sweden)

John A. D. Appleby

2017-01-01

Full Text Available This article determines the rate of growth to infinity of scalar autonomous nonlinear functional and Volterra differential equations. In these equations, the right-hand side is a positive continuous linear functional of f(x. We assume f grows sublinearly, leading to subexponential growth in the solutions. The main results show that the solution of the functional differential equations are asymptotic to that of an auxiliary autonomous ordinary differential equation with right-hand side proportional to f. This happens provided f grows more slowly than l(x=x/log(x. The linear-logarithmic growth rate is also shown to be critical: if f grows more rapidly than l, the ODE dominates the FDE; if f is asymptotic to a constant multiple of l, the FDE and ODE grow at the same rate, modulo a constant non-unit factor; if f grows more slowly than l, the ODE and FDE grow at exactly the same rate. A partial converse of the last result is also proven. In the case when the growth rate is slower than that of the ODE, sharp bounds on the growth rate are determined. The Volterra and finite memory equations can have differing asymptotic behaviour and we explore the source of these differences.

Rapid changes in the range limits of Scots pine 4000 years ago

International Nuclear Information System (INIS)

Gear, A.J.; Huntley, B.

1991-01-01

Paleoecological data provide estimates of response rates to past climate changes. Fossil Pinus sylvestris stumps in far northern Scotland demonstrate former presence of pine trees where conventional pollen evidence of pine forests is lacking. Radiocarbon, dendrochronological, and fine temporal-resolution palynological data show that pine forest were present for about four centuries some 4,000 years ago; the forests expanded and then retreated rapidly some 70 to 80 kilometers. Despite the rapidity of this response to climate change, it occurred at rates slower by an order of magnitude than those necessary to maintain equilibrium with forecast climate changes attributed to the greenhouse effect

Nakedly singular non-vacuum gravitating equilibrium states

Science.gov (United States)

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.

Algorithm For Hypersonic Flow In Chemical Equilibrium

Science.gov (United States)

Palmer, Grant

1989-01-01

Implicit, finite-difference, shock-capturing algorithm calculates inviscid, hypersonic flows in chemical equilibrium. Implicit formulation chosen because overcomes limitation on mathematical stability encountered in explicit formulations. For dynamical portion of problem, Euler equations written in conservation-law form in Cartesian coordinate system for two-dimensional or axisymmetric flow. For chemical portion of problem, equilibrium state of gas at each point in computational grid determined by minimizing local Gibbs free energy, subject to local conservation of molecules, atoms, ions, and total enthalpy. Major advantage: resulting algorithm naturally stable and captures strong shocks without help of artificial-dissipation terms to damp out spurious numerical oscillations.

Reformulation of nonlinear integral magnetostatic equations for rapid iterative convergence

International Nuclear Information System (INIS)

Bloomberg, D.S.; Castelli, V.

1985-01-01

The integral equations of magnetostatics, conventionally given in terms of the field variables M and H, are reformulated with M and B. Stability criteria and convergence rates of the eigenvectors of the linear iteration matrices are evaluated. The relaxation factor β in the MH approach varies inversely with permeability μ, and nonlinear problems with high permeability converge slowly. In contrast, MB iteration is stable for β 3 , the number of iterations is reduced by two orders of magnitude over the conventional method, and at higher permeabilities the reduction is proportionally greater. The dependence of MB convergence rate on β, degree of saturation, element aspect ratio, and problem size is found numerically. An analytical result for the MB convergence rate for small nonlinear problems is found to be accurate for βless than or equal to1.2. The results are generally valid for two- and three-dimensional integral methods and are independent of the particular discretization procedures used to compute the field matrix

A simple algebraic cancer equation: calculating how cancers may arise with normal mutation rates

Directory of Open Access Journals (Sweden)

Shibata Darryl

2010-01-01

Full Text Available Abstract Background The purpose of this article is to present a relatively easy to understand cancer model where transformation occurs when the first cell, among many at risk within a colon, accumulates a set of driver mutations. The analysis of this model yields a simple algebraic equation, which takes as inputs the number of stem cells, mutation and division rates, and the number of driver mutations, and makes predictions about cancer epidemiology. Methods The equation [p = 1 - (1 - (1 - (1 - udkNm ] calculates the probability of cancer (p and contains five parameters: the number of divisions (d, the number of stem cells (N × m, the number of critical rate-limiting pathway driver mutations (k, and the mutation rate (u. In this model progression to cancer "starts" at conception and mutations accumulate with cell division. Transformation occurs when a critical number of rate-limiting pathway mutations first accumulates within a single stem cell. Results When applied to several colorectal cancer data sets, parameter values consistent with crypt stem cell biology and normal mutation rates were able to match the increase in cancer with aging, and the mutation frequencies found in cancer genomes. The equation can help explain how cancer risks may vary with age, height, germline mutations, and aspirin use. APC mutations may shorten pathways to cancer by effectively increasing the numbers of stem cells at risk. Conclusions The equation illustrates that age-related increases in cancer frequencies may result from relatively normal division and mutation rates. Although this equation does not encompass all of the known complexity of cancer, it may be useful, especially in a teaching setting, to help illustrate relationships between small and large cancer features.

Ventilation rate in equilibrium factor measurements with solid state nuclear track detectors (SSNTD)

International Nuclear Information System (INIS)

Gil, L.R.; Leitao, R.M.S.; Marques, A.; Rivera, A.

1994-08-01

Ventilation rate values are calculated from track density measurements in solid state nuclear track detectors (SSNTD), both when ventilation is the main cause of radioactive disequilibrium in radon progeny and when it shares importance with other agents. The method consists in exposing a SSNTD of high intrinsic efficiency (CR-39) in filtered and unfiltered conditions and, in addition, covered with a thin Aluminium foil, to stop alpha particles from 218 Po and 222 Rn. No calibrations are required but, when necessary, independent measurements of the loss rates of radioactivity to aerosol and to walls have to perform. Ventilation rates depend upon geometry detection efficiencies for alpha particles, here obtained by Monte Carlo simulation, taking into account the space distribution of emission positions. This may lead to sizeable corrections in ventilation and equilibrium factor values. Since geometric detection efficiencies depend upon alpha-particle ranges in air, the influences of barometric variables are also discussed. (author). 7 refs

Three-dimensional stellarator equilibrium as an ohmic steady state

International Nuclear Information System (INIS)

Park, W.; Monticello, D.A.; Strauss, H.; Manickam, J.

1985-07-01

A stable three-dimensional stellarator equilibrium can be obtained numerically by a time-dependent relaxation method using small values of dissipation. The final state is an ohmic steady state which approaches an ohmic equilibrium in the limit of small dissipation coefficients. We describe a method to speed up the relaxation process and a method to implement the B vector . del p = 0 condition. These methods are applied to obtain three-dimensional heliac equilibria using the reduced heliac equations

An equilibrium model for tungsten fuzz in an eroding plasma environment

International Nuclear Information System (INIS)

Doerner, R.P.; Baldwin, M.J.; Stangeby, P.C.

2011-01-01

A model equating the growth rate of tungsten fuzz on a plasma-exposed surface to the erosion rate of the fuzzy surface is developed to predict the likelihood of tungsten fuzz formation in the steady-state environment of toroidal confinement devices. To date this question has not been answered because the operational conditions in existing magnetic confinement machines do not necessarily replicate those expected in future fusion reactors (i.e. high-fluence operation, high temperature plasma-facing materials and edge plasma relatively free of condensable impurities). The model developed is validated by performing plasma exposure experiments at different incident ion energies (thereby varying the erosion rate) and measuring the resultant fuzz layer thickness. The results indicate that if the conditions exist for fuzz development in a steady-state plasma (surface temperature and energetic helium flux), then the erosion rate will determine the equilibrium thickness of the surface fuzz layer.

Quantum gas in the fast forward scheme of adiabatically expanding cavities: Force and equation of state

Science.gov (United States)

Babajanova, Gulmira; Matrasulov, Jasur; Nakamura, Katsuhiro

2018-04-01

With use of the scheme of fast forward which realizes quasistatic or adiabatic dynamics in shortened timescale, we investigate a thermally isolated ideal quantum gas confined in a rapidly dilating one-dimensional (1D) cavity with the time-dependent size L =L (t ) . In the fast-forward variants of equation of states, i.e., Bernoulli's formula and Poisson's adiabatic equation, the force or 1D analog of pressure can be expressed as a function of the velocity (L ˙) and acceleration (L ̈) of L besides rapidly changing state variables like effective temperature (T ) and L itself. The force is now a sum of nonadiabatic (NAD) and adiabatic contributions with the former caused by particles moving synchronously with kinetics of L and the latter by ideal bulk particles insensitive to such a kinetics. The ratio of NAD and adiabatic contributions does not depend on the particle number (N ) in the case of the soft-wall confinement, whereas such a ratio is controllable in the case of hard-wall confinement. We also reveal the condition when the NAD contribution overwhelms the adiabatic one and thoroughly changes the standard form of the equilibrium equation of states.

Basic researches on thermo-hydraulic non-equilibrium phenomena related to nuclear reactor safety

International Nuclear Information System (INIS)

Sakurai, Akira; Kataoka, Isao; Aritomi, Masanori.

1989-01-01

A review was made of recent developments of fundamental researches on thermo-hydraulic non-equilibrium phenomena related to light water reactor safety, in relation to problems to be solved for the improvement of safety analysis codes. As for the problems related to flow con ditions, fundamental researches on basic conservation equations and constitutive equations for transient two-phase flow were reviewed. Regarding to the problems related to thermal non-equilibrium phenomena, fundamental researches on film boiling in pool and forced convection, transient boiling heat transfer and flow behavior caused by pressure transients were reviewed. (author)

arXiv Status of rates and rate equations for thermal leptogenesis

CERN Document Server

Biondini, Simone; Brambilla, Nora; Garny, Mathias; Ghiglieri, Jacopo; Hohenegger, Andreas; Laine, Mikko; Mendizabal, Sebastian; Millington, Peter; Salvio, Alberto; Vairo, Antonio

2018-02-28

In many realizations of leptogenesis, heavy right-handed neutrinos play the main role in the generation of an imbalance between matter and antimatter in the early Universe. Hence, it is relevant to address quantitatively their dynamics in a hot and dense environment by taking into account the various thermal aspects of the problem at hand. The strong washout regime offers an interesting framework to carry out calculations systematically and reduce theoretical uncertainties. Indeed, any matter-antimatter asymmetry generated when the temperature of the hot plasma $T$ exceeds the right-handed neutrino mass scale $M$ is efficiently erased, and one can focus on the temperature window $T \\ll M$. We review recent progresses in the thermal field theoretic derivation of the key ingredients for the leptogenesis mechanism: the right-handed neutrino production rate, the CP asymmetry in the heavy-neutrino decays and the washout rates. The derivation of evolution equations for the heavy-neutrino and lepton-asymmetry number...

Non-equilibrium dynamics from RPMD and CMD.

Science.gov (United States)

Welsch, Ralph; Song, Kai; Shi, Qiang; Althorpe, Stuart C; Miller, Thomas F

2016-11-28

We investigate the calculation of approximate non-equilibrium quantum time correlation functions (TCFs) using two popular path-integral-based molecular dynamics methods, ring-polymer molecular dynamics (RPMD) and centroid molecular dynamics (CMD). It is shown that for the cases of a sudden vertical excitation and an initial momentum impulse, both RPMD and CMD yield non-equilibrium TCFs for linear operators that are exact for high temperatures, in the t = 0 limit, and for harmonic potentials; the subset of these conditions that are preserved for non-equilibrium TCFs of non-linear operators is also discussed. Furthermore, it is shown that for these non-equilibrium initial conditions, both methods retain the connection to Matsubara dynamics that has previously been established for equilibrium initial conditions. Comparison of non-equilibrium TCFs from RPMD and CMD to Matsubara dynamics at short times reveals the orders in time to which the methods agree. Specifically, for the position-autocorrelation function associated with sudden vertical excitation, RPMD and CMD agree with Matsubara dynamics up to O(t 4 ) and O(t 1 ), respectively; for the position-autocorrelation function associated with an initial momentum impulse, RPMD and CMD agree with Matsubara dynamics up to O(t 5 ) and O(t 2 ), respectively. Numerical tests using model potentials for a wide range of non-equilibrium initial conditions show that RPMD and CMD yield non-equilibrium TCFs with an accuracy that is comparable to that for equilibrium TCFs. RPMD is also used to investigate excited-state proton transfer in a system-bath model, and it is compared to numerically exact calculations performed using a recently developed version of the Liouville space hierarchical equation of motion approach; again, similar accuracy is observed for non-equilibrium and equilibrium initial conditions.

Multi-equilibrium property of metabolic networks: SSI module

Directory of Open Access Journals (Sweden)

Chen Luonan

2011-06-01

Full Text Available Abstract Background Revealing the multi-equilibrium property of a metabolic network is a fundamental and important topic in systems biology. Due to the complexity of the metabolic network, it is generally a difficult task to study the problem as a whole from both analytical and numerical viewpoint. On the other hand, the structure-oriented modularization idea is a good choice to overcome such a difficulty, i.e. decomposing the network into several basic building blocks and then studying the whole network through investigating the dynamical characteristics of the basic building blocks and their interactions. Single substrate and single product with inhibition (SSI metabolic module is one type of the basic building blocks of metabolic networks, and its multi-equilibrium property has important influence on that of the whole metabolic networks. Results In this paper, we describe what the SSI metabolic module is, characterize the rates of the metabolic reactions by Hill kinetics and give a unified model for SSI modules by using a set of nonlinear ordinary differential equations with multi-variables. Specifically, a sufficient and necessary condition is first given to describe the injectivity of a class of nonlinear systems, and then, the sufficient condition is used to study the multi-equilibrium property of SSI modules. As a main theoretical result, for the SSI modules in which each reaction has no more than one inhibitor, a sufficient condition is derived to rule out multiple equilibria, i.e. the Jacobian matrix of its rate function is nonsingular everywhere. Conclusions In summary, we describe SSI modules and give a general modeling framework based on Hill kinetics, and provide a sufficient condition for ruling out multiple equilibria of a key type of SSI module.

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

International Nuclear Information System (INIS)

Snezhko, Alexey

2011-01-01

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. (topical review)

A numerical solution for a toroidal plasma in equilibrium

International Nuclear Information System (INIS)

Hintz, E.; Sudano, J.P.

1982-01-01

The iterative techniques alternating direction implicit (ADI), sucessive ove-relaxation (SOR) and Gauss-Seidel are applied to a nonlinear elliptical second order differential equation (Grand-Shafranov). This equation was solve with the free boundary conditions plasma-vacuum interface over a rectangular section in cylindrical coordinates R and Z. The current density profile, plasma pressure profile, magnetic and isobaric surfaces are numerically determined for a toroidal plasma in equilibrium. (L.C.) [pt

Methodology for benzodiazepine receptor binding assays at physiological temperature. Rapid change in equilibrium with falling temperature

International Nuclear Information System (INIS)

Dawson, R.M.

1986-01-01

Benzodiazepine receptors of rat cerebellum were assayed with [ 3 H]-labeled flunitrazepam at 37 0 C, and assays were terminated by filtration in a cold room according to one of three protocols: keeping each sample at 37 degrees C until ready for filtration, taking the batch of samples (30) into the cold room and filtering sequentially in the order 1-30, and taking the batch of 30 samples into the cold room and filtering sequentially in the order 30-1. the results for each protocol were substantially different from each other, indicating that rapid disruption of equilibrium occurred as the samples cooled in the cold room while waiting to be filtered. Positive or negative cooperativity of binding was apparent, and misleading effects of gamma-aminobutyric acid on the affinity of diazepam were observed, unless each sample was kept at 37 0 C until just prior to filtration

Vibrational energy flow in the villin headpiece subdomain: Master equation simulations

Energy Technology Data Exchange (ETDEWEB)

Leitner, David M., E-mail: dml@unr.edu, E-mail: stock@physik.uni-freiburg.de [Department of Chemistry and Chemical Physics Program, University of Nevada, Reno, Nevada 89557 (United States); Freiburg Institute for Advanced Studies (FRIAS), University of Freiburg, Freiburg (Germany); Buchenberg, Sebastian; Brettel, Paul [Biomolecular Dynamics, Institute of Physics, University of Freiburg, Freiburg (Germany); Stock, Gerhard, E-mail: dml@unr.edu, E-mail: stock@physik.uni-freiburg.de [Freiburg Institute for Advanced Studies (FRIAS), University of Freiburg, Freiburg (Germany); Biomolecular Dynamics, Institute of Physics, University of Freiburg, Freiburg (Germany)

2015-02-21

We examine vibrational energy flow in dehydrated and hydrated villin headpiece subdomain HP36 by master equation simulations. Transition rates used in the simulations are obtained from communication maps calculated for HP36. In addition to energy flow along the main chain, we identify pathways for energy transport in HP36 via hydrogen bonding between residues quite far in sequence space. The results of the master equation simulations compare well with all-atom non-equilibrium simulations to about 1 ps following initial excitation of the protein, and quite well at long times, though for some residues we observe deviations between the master equation and all-atom simulations at intermediate times from about 1–10 ps. Those deviations are less noticeable for hydrated than dehydrated HP36 due to energy flow into the water.

Vibrational energy flow in the villin headpiece subdomain: Master equation simulations

International Nuclear Information System (INIS)

Leitner, David M.; Buchenberg, Sebastian; Brettel, Paul; Stock, Gerhard

2015-01-01

We examine vibrational energy flow in dehydrated and hydrated villin headpiece subdomain HP36 by master equation simulations. Transition rates used in the simulations are obtained from communication maps calculated for HP36. In addition to energy flow along the main chain, we identify pathways for energy transport in HP36 via hydrogen bonding between residues quite far in sequence space. The results of the master equation simulations compare well with all-atom non-equilibrium simulations to about 1 ps following initial excitation of the protein, and quite well at long times, though for some residues we observe deviations between the master equation and all-atom simulations at intermediate times from about 1–10 ps. Those deviations are less noticeable for hydrated than dehydrated HP36 due to energy flow into the water

Rapid separation of pure 144Ce fraction from fuel dissolver solution for demonstration experiment on secular equilibrium

International Nuclear Information System (INIS)

Ashok Kumar, G.V.S.; Kumar, R.; Venkata Subramani, C.R.

2015-01-01

Radioactive equilibrium is a condition in which the activity ratio of parent to its daughter is maintained constant with time which occurs only when the parent half-life is greater than daughter half-life. It is transient equilibrium in the case of the ratio of their half-lives of parent to daughter being less than an order whereas it becomes secular equilibrium when it is more than an order. In the case of secular equilibrium, the ratio of the activities becomes unity whereas the same depends on the decay constants of the parent and daughter nuclide for the transient equilibrium. 144 Ce- 144 Pr pair is a good example for the demonstration of secular equilibrium

Stellar Equilibrium in Semiclassical Gravity.

Science.gov (United States)

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.

Supersymmetric Field Theory of Non-Equilibrium Thermodynamic System

OpenAIRE

Olemskoi, Alexander I.; Brazhnyi, Valerii A.

1998-01-01

On the basis of Langevin equation the optimal SUSY field scheme is formulated to discribe a non-equilibrium thermodynamic system with quenched disorder and non-ergodicity effects. Thermodynamic and isothermal susceptibilities, memory parameter and irreversible response are determined at different temperatures and quenched disorder intensities.

Approach to equilibrium in a pure superconductor. The relaxation of the Cooper pair density

Energy Technology Data Exchange (ETDEWEB)

Schid, A

1968-01-01

Electron-phonon and electron-electron collisions are the processes which determine the relaxation time r/sub R/ of the Cooper pair density. The case is considered for which the deviation of the pair density from equilibrium is small and where the equilibrium state is homogeneous. Starting from the Eliashberg equation one is able to reduce the problem to a quadrature once the equilibrium Green functions are known.

Out-of-equilibrium catalysis of chemical reactions by electronic tunnel currents.

Science.gov (United States)

Dzhioev, Alan A; Kosov, Daniel S; von Oppen, Felix

2013-04-07

We present an escape rate theory for current-induced chemical reactions. We use Keldysh nonequilibrium Green's functions to derive a Langevin equation for the reaction coordinate. Due to the out of equilibrium electronic degrees of freedom, the friction, noise, and effective temperature in the Langevin equation depend locally on the reaction coordinate. As an example, we consider the dissociation of diatomic molecules induced by the electronic current from a scanning tunnelling microscope tip. In the resonant tunnelling regime, the molecular dissociation involves two processes which are intricately interconnected: a modification of the potential energy barrier and heating of the molecule. The decrease of the molecular barrier (i.e., the current induced catalytic reduction of the barrier) accompanied by the appearance of the effective, reaction-coordinate-dependent temperature is an alternative mechanism for current-induced chemical reactions, which is distinctly different from the usual paradigm of pumping vibrational degrees of freedom.

Analysis and extension of the Furter equation, and its application in the simulation of saline extractive distillation columns

Directory of Open Access Journals (Sweden)

Ernesto O. Timmermann

Full Text Available ABSTRACT Simulation of saline extractive distillation columns is a difficult task owing to the high nonlinearity of the rigorous models that represent these systems. The use of simple models to obtain initial estimates of equilibrium compositions may improve the stability and rate of convergence. One of the simplest models to study the vapor-liquid equilibrium of binary liquid mixtures + salt systems is the Furter equation. This model was analyzed in the present work by means of the incorporation of activity coefficient models in the ratio of relative volatility. This approach allowed systematic extensions of the Furter equation and a brief review of the theoretical basis of the original equation. As a result of these extensions, two simple equations were proposed and tested with experimental data from 20 systems, including binary liquid mixtures + salt systems and binary liquid mixtures + ionic liquid systems. Finally, one of these proposed equations was incorporated into the GKTM software in order to assess the utility of these simple models in the simulation of saline extractive distillation columns. The obtained results showed a significant improvement over the previous algorithm.

Thermal non-equilibrium heat transfer in a porous cavity in the presence of bio-chemical heat source

Directory of Open Access Journals (Sweden)

Nazari Mohsen

2015-01-01

Full Text Available This paper is concerned with thermal non-equilibrium natural convection in a square cavity filled with a porous medium in the presence of a biomass which is transported in the cavity. The biomass can consume a secondary moving substrate. The physics of the presented problem is related to the analysis of heat and mass transfer in a composting process that controlled by internal heat generation. The intensity of the bio-heat source generated in the cavity is equal to the rate of consumption of the substrate by the biomass. It is assumed that the porous medium is homogeneous and isotropic. A two-field model that represents the fluid and solid phase temperature fields separately is used for energy equation. A simplified Monod model is introduced along with the governing equations to describe the consumption of the substrate by the biomass. In other word, the transient biochemical heat source which is dependent on a solute concentration is considered in the energy equations. Investigation of the biomass activity and bio-chemical heat generation in the case of thermal non-equilibrium assumption has not been considered in the literature and they are open research topics. The effects of thermal non-equilibrium model on heat transfer, flow pattern and biomass transfer are investigated. The effective parameters which have a direct impact on the generated bio-chemical heat source are also presented. The influences of the non-dimensional parameters such as fluid-to-solid conductivity ratio on the temperature distribution are presented.

Fractional hydrodynamic equations for fractal media

International Nuclear Information System (INIS)

Tarasov, Vasily E.

2005-01-01

We use the fractional integrals in order to describe dynamical processes in the fractal medium. We consider the 'fractional' continuous medium model for the fractal media and derive the fractional generalization of the equations of balance of mass density, momentum density, and internal energy. The fractional generalization of Navier-Stokes and Euler equations are considered. We derive the equilibrium equation for fractal media. The sound waves in the continuous medium model for fractional media are considered

Biosorption of lead ions on biosorbent prepared from plumb shells (spondias mombin): kinetics and equilibrium studies

International Nuclear Information System (INIS)

Adeogen, A.I.; Bello, O.S.; Adeboye, M.D.

2010-01-01

Plumb shell was used to prepare an adsorbent for biosorption of lead ions in aqueous solution at 25 degree C. The adsorption capacity of the adsorbent at equilibrium was found to increase from 2.8 to 49.0 mg/g with an increase in the initial lead ion concentration from 50 to 200 mg/L. Using the equilibrium and kinetics studies, isotherm of the lead ions on the biosorbent was determined and correlated with common isotherm equations. The equilibrium data for lead ion adsorption fitted well into the Freundlich equation, with a value of 0.76 (R2 = 0.9), with distribution coefficient of 4.90. The biosorption of lead ions on the adsorbent from plumb shells could best be described by the pseudo-second-order equation. The kinetic parameters of this best-fit model were calculated and discussed. (author)

Current-induced magnetization changes in a spin valve due to incoherent emission of non-equilibrium magnons

OpenAIRE

Kozub, V. I.; Caro, J.

2004-01-01

We describe spin transfer in a ferromagnet/normal metal/ferromagnet spin-valve point contact. Spin is transferred from the spin-polarized device current to the magnetization of the free layer by the mechanism of incoherent magnon emission by electrons. Our approach is based on the rate equation for the magnon occupation, using Fermi's golden rule for magnon emission and absorption and the non-equilibrium electron distribution for a biased spin valve. The magnon emission reduces the magnetizat...

Nonlinear equilibrium in Tokamaks including convective terms and viscosity

International Nuclear Information System (INIS)

Martin, P.; Castro, E.; Puerta, J.

2003-01-01

MHD equilibrium in tokamaks becomes very complex, when the non-linear convective term and viscosity are included in the momentum equation. In order to simplify the analysis, each new term has been separated in type gradient terms and vorticity depending terms. For the special case in which the vorticity vanishes, an extended Grad-Shafranov type equation can be obtained. However now the magnetic surface is not isobars or current surfaces as in the usual Grad-Shafranov treatment. The non-linear convective terms introduces gradient of Bernoulli type kinetic terms . Montgomery and other authors have shown the importance of the viscosity terms in tokamaks [1,2], here the treatment is carried out for the equilibrium condition, including generalized tokamaks coordinates recently described [3], which simplify the equilibrium analysis. Calculation of the new isobar surfaces is difficult and some computation have been carried out elsewhere for some particular cases [3]. Here, our analysis is extended discussing how the toroidal current density, plasma pressure and toroidal field are modified across the midplane because of the new terms (convective and viscous). New calculations and computations are also presented. (Author)

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

Science.gov (United States)

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.

Influence of quench rates on the properties of rapidly solidified ...

Indian Academy of Sciences (India)

Unknown

Abstract. FeNbCuSiB based materials were produced in the form of ribbons by rapid solidification techniques. The crystallization, magnetic, mechanical and corrosion behaviour were studied for the prepared materials as a function of quenching rate from liquid to the solid state. Higher quench rates produced a more ...

Fixation of waste materials in grouts: Part 3, Equation for critical flow rate

International Nuclear Information System (INIS)

Tallent, O.K.; McDaniel, E.W.; Spence, R.D.; Godsey, T.T.; Dodson, K.E.

1986-12-01

Critical flow rate data for grouts prepared from three distinctly different nuclear waste materials have been correlated. The wastes include Oak Ridge National Laboratory (ORNL) low-level waste (LLW) solution, Hanford Facility waste (HFW) solution, and cladding removal waste (CRW) slurry. Data for the three wastes have been correlated with a 0.96 coefficient of correlation by the following equation: log V/sub E/ = 0.289 + 0.707 log μ/sub E/, where V/sub E/ and μ/sub E/ denote critical flow rate in m 3 /min and apparent viscosity in Pa.s, respectively. The equation may be used to estimate critical flow rate for grouts prepared within the compositional range of the investigation. 5 refs., 4 figs., 7 tabs

Long-run and Cyclic Movements in the Unemployment Rate in Hong Kong: A Dynamic, General Equilibrium Approach

OpenAIRE

Michael K. Salemi

2007-01-01

Prior to the late 1990s, low unemployment was a standard feature of macroeconomic life in Hong Kong. Between 1985 and 1997, the unemployment rate averaged 2.5 percent. But the picture changed dramatically thereafter with the unemployment rate rising to 6.2 percent by 1999 and remaining above 5 percent through 2005. What caused the large and sustained increase? This paper provides some answers with an analysis based on a dynamic, general equilibrium model of a small, open economy in which wage...

Chimpanzee choice rates in competitive games match equilibrium game theory predictions.

Science.gov (United States)

Martin, Christopher Flynn; Bhui, Rahul; Bossaerts, Peter; Matsuzawa, Tetsuro; Camerer, Colin

2014-06-05

The capacity for strategic thinking about the payoff-relevant actions of conspecifics is not well understood across species. We use game theory to make predictions about choices and temporal dynamics in three abstract competitive situations with chimpanzee participants. Frequencies of chimpanzee choices are extremely close to equilibrium (accurate-guessing) predictions, and shift as payoffs change, just as equilibrium theory predicts. The chimpanzee choices are also closer to the equilibrium prediction, and more responsive to past history and payoff changes, than two samples of human choices from experiments in which humans were also initially uninformed about opponent payoffs and could not communicate verbally. The results are consistent with a tentative interpretation of game theory as explaining evolved behavior, with the additional hypothesis that chimpanzees may retain or practice a specialized capacity to adjust strategy choice during competition to perform at least as well as, or better than, humans have.

Cell membrane temperature rate sensitivity predicted from the Nernst equation.

Science.gov (United States)

Barnes, F S

1984-01-01

A hyperpolarized current is predicted from the Nernst equation for conditions of positive temperature derivatives with respect to time. This ion current, coupled with changes in membrane channel conductivities, is expected to contribute to a transient potential shift across the cell membrane for silent cells and to a change in firing rate for pacemaker cells.

Disorder trapping by rapidly moving phase interface in an undercooled liquid

Science.gov (United States)

Galenko, Peter; Danilov, Denis; Nizovtseva, Irina; Reuther, Klemens; Rettenmayr, Markus

2017-08-01

Non-equilibrium phenomena such as the disappearance of solute drag, the origin of solute trapping and evolution of disorder trapping occur during fast transformations with originating metastable phases [D.M. Herlach, P.K. Galenko, D. Holland-Moritz, Metastable solids from undrercooled melts (Elsevier, Amsterdam, 2007)]. In the present work, a theoretical investigation of disorder trapping by a rapidly moving phase interface is presented. Using a model of fast phase transformations, a system of governing equations for the diffusion of atoms, and the evolution of both long-range order parameter and phase field variable is formulated. First numerical solutions are carried out for a congruently melting binary alloy system.

The Kadomtsev endash Petviashvili equation under rapid forcing

International Nuclear Information System (INIS)

Moroz, I.M.

1997-01-01

We consider the initial value problem for the forced Kadomtsev endash Petviashvili equation (KP) when the forcing is assumed to be fast compared to the evolution of the unforced equation. This suggests the introduction of two time scales. Solutions to the forced KP are sought by expanding the dependent variable in powers of a small parameter, which is inversely related to the forcing time scale. The unforced system describes weakly nonlinear, weakly dispersive, weakly two-dimensional wave propagation and is studied in two forms, depending upon whether gravity dominates surface tension or vice versa. We focus on the effect that the forcing has on the one-lump solution to the KPI equation (where surface tension dominates) and on the one- and two-line soliton solutions to the KPII equation (when gravity dominates). Solutions to second order in the expansion are computed analytically for some specific choices of the forcing function, which are related to the choice of initial data. copyright 1997 American Institute of Physics

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

Science.gov (United States)

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.

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

Science.gov (United States)

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…

Hamilton's equations for a fluid membrane

International Nuclear Information System (INIS)

Capovilla, R; Guven, J; Rojas, E

2005-01-01

Consider a homogeneous fluid membrane described by the Helfrich-Canham energy, quadratic in the mean curvature of the membrane surface. The shape equation that determines equilibrium configurations is fourth order in derivatives and cubic in the mean curvature. We introduce a Hamiltonian formulation of this equation which dismantles it into a set of coupled first-order equations. This involves interpreting the Helfrich-Canham energy as an action; equilibrium surfaces are generated by the evolution of space curves. Two features complicate the implementation of a Hamiltonian framework. (i) The action involves second derivatives. This requires treating the velocity as a phase-space variable and the introduction of its conjugate momentum. The canonical Hamiltonian is constructed on this phase space. (ii) The action possesses a local symmetry-reparametrization invariance. The two labels we use to parametrize points on the surface are themselves physically irrelevant. This symmetry implies primary constraints, one for each label, that need to be implemented within the Hamiltonian. The two Lagrange multipliers associated with these constraints are identified as the components of the acceleration tangential to the surface. The conservation of the primary constraints implies two secondary constraints, fixing the tangential components of the momentum conjugate to the position. Hamilton's equations are derived and the appropriate initial conditions on the phase-space variables are identified. Finally, it is shown how the shape equation can be reconstructed from these equations

Altering the cooling rate dependence of phase formation during rapid solidification in the Nd{sub 2}Fe{sub 14}B system

Energy Technology Data Exchange (ETDEWEB)

Branagan, D.J. [USDOE, Ames, IA (United States). Ames Lab.]|[Iowa State Univ. of Science and Technology, Ames, IA (United States). Dept. of Materials Science and Engineering; McCallum, R.W. [USDOE, Ames, IA (United States). Ames Lab.]|[Iowa State Univ. of Science and Technology, Ames, IA (United States). Dept. of Materials Science and Engineering

1995-04-26

In order to evaluate the effects of additions on the solidification behavior of Nd{sub 2}Fe{sub 14}B, a stoichiometric alloy was modified with elemental additions of Ti or C and a compound addition of Ti with C. For each alloy, a series of wheel speed runs was undertaken, from which the optimum wheel speeds and optimum energy products were determined. On the BH{sub max} versus wheel speed plots, regions were identified in order to analyze the changes with cooling rates leading to phase formation brought about by the alloy modifications. The compilation of the regional data of the modified alloys showed their effects on altering the cooling rate dependence of phase formation. It was found that the regions of properitectic iron formation, glass formation, and the optimum cooling rate can be changed by more than a factor of two through appropriate alloying additions. The effects of the alloy modifications can be visualized in a convenient fashion through the use of a model continuous cooling transformation (CCT) diagram which represents phase formation during the solidification process under continuous cooling conditions for a wide range of cooling rates from rapid solidification to equilibrium cooling. ((orig.)).

Decay to Equilibrium for Energy-Reaction-Diffusion Systems

KAUST Repository

Haskovec, Jan

2018-02-06

We derive thermodynamically consistent models of reaction-diffusion equations coupled to a heat equation. While the total energy is conserved, the total entropy serves as a driving functional such that the full coupled system is a gradient flow. The novelty of the approach is the Onsager structure, which is the dual form of a gradient system, and the formulation in terms of the densities and the internal energy. In these variables it is possible to assume that the entropy density is strictly concave such that there is a unique maximizer (thermodynamical equilibrium) given linear constraints on the total energy and suitable density constraints. We consider two particular systems of this type, namely, a diffusion-reaction bipolar energy transport system, and a drift-diffusion-reaction energy transport system with confining potential. We prove corresponding entropy-entropy production inequalities with explicitly calculable constants and establish the convergence to thermodynamical equilibrium, first in entropy and later in L norm using Cziszár–Kullback–Pinsker type inequalities.

Decay to Equilibrium for Energy-Reaction-Diffusion Systems

KAUST Repository

Haskovec, Jan; Hittmeir, Sabine; Markowich, Peter A.; Mielke, Alexander

2018-01-01

We derive thermodynamically consistent models of reaction-diffusion equations coupled to a heat equation. While the total energy is conserved, the total entropy serves as a driving functional such that the full coupled system is a gradient flow. The novelty of the approach is the Onsager structure, which is the dual form of a gradient system, and the formulation in terms of the densities and the internal energy. In these variables it is possible to assume that the entropy density is strictly concave such that there is a unique maximizer (thermodynamical equilibrium) given linear constraints on the total energy and suitable density constraints. We consider two particular systems of this type, namely, a diffusion-reaction bipolar energy transport system, and a drift-diffusion-reaction energy transport system with confining potential. We prove corresponding entropy-entropy production inequalities with explicitly calculable constants and establish the convergence to thermodynamical equilibrium, first in entropy and later in L norm using Cziszár–Kullback–Pinsker type inequalities.

Non-equilibrium dynamics of disordered systems: understanding the broad continuum of relevant time scales via a strong-disorder RG in configuration space

International Nuclear Information System (INIS)

Monthus, Cecile; Garel, Thomas

2008-01-01

We show that an appropriate description of the non-equilibrium dynamics of disordered systems is obtained through a strong disorder renormalization procedure in configuration space that we define for any master equation with transitions rates W(C→C') between configurations. The idea is to eliminate iteratively the configuration with the highest exit rate W out (C)+Σ C' W(C→C') to obtain renormalized transition rates between the remaining configurations. The multiplicative structure of the new generated transition rates suggests that for a very broad class of disordered systems, the distribution of renormalized exit barriers defined as B out (C)≡-ln W out (C) will become broader and broader upon iteration, so that the strong disorder renormalization procedure should become asymptotically exact at large time scales. We have checked numerically this scenario for the non-equilibrium dynamics of a directed polymer in a two-dimensional random medium

Standardization of 125 Sb in equilibrium non-equilibrium situations with 125m Te

International Nuclear Information System (INIS)

Rodriguez Barquero, L.; Jimenez de Mingo, A.; Grau Carles, A.

1997-10-01

We study the stability of ''125 Sb in the following scintillators: HiSafeIII''TM, Insta- Gel reg s ign Plus and '' Ultima-Gold'' TM. Since ''125 m Te requires more than one year to reach the secular equilibrium with ''125 Sb, we cannot be sure, for a given sample, whether equilibrium is reached or not. In this report we present a new procedure that permits one calibrate mixtures of ''125 Sb+''125 m Te out of the equilibrium. The steps required for the radiochemical separation of the components are indicated. Finally, we study the evolution of counting rate when column yields are less than 100%. (Author)

Critical dynamics a field theory approach to equilibrium and non-equilibrium scaling behavior

CERN Document Server

Täuber, Uwe C

2014-01-01

Introducing a unified framework for describing and understanding complex interacting systems common in physics, chemistry, biology, ecology, and the social sciences, this comprehensive overview of dynamic critical phenomena covers the description of systems at thermal equilibrium, quantum systems, and non-equilibrium systems. Powerful mathematical techniques for dealing with complex dynamic systems are carefully introduced, including field-theoretic tools and the perturbative dynamical renormalization group approach, rapidly building up a mathematical toolbox of relevant skills. Heuristic and qualitative arguments outlining the essential theory behind each type of system are introduced at the start of each chapter, alongside real-world numerical and experimental data, firmly linking new mathematical techniques to their practical applications. Each chapter is supported by carefully tailored problems for solution, and comprehensive suggestions for further reading, making this an excellent introduction to critic...

Nonuniqueness of the two-temperature Saha equation and related considerations

International Nuclear Information System (INIS)

Giordano, D.; Capitelli, M.

2002-01-01

The present paper contains considerations relative to the long debated thermodynamic derivation of two-temperature Saha equations. The main focus of our discourse is on the dependence of the multitemperature equilibrium conditions on the constraints imposed on the thermodynamic system. We also examine the following key issues related to that dependence: correspondence between constraints and equilibrium-equation forms that have appeared in the literature; presumed dominance of the free-electron translational temperature in the two-temperature expression of the equilibrium constant of the ionization reaction A A + +e - ; disagreement between the derivation methods based on, respectively, the extended second law of classical thermodynamics and axiomatic thermodynamics; and plausibility of the existence of entropic constraints

Non-equilibrium scaling analysis of the Kondo model with voltage bias

International Nuclear Information System (INIS)

Fritsch, Peter; Kehrein, Stefan

2009-01-01

The quintessential description of Kondo physics in equilibrium is obtained within a scaling picture that shows the buildup of Kondo screening at low temperature. For the non-equilibrium Kondo model with a voltage bias, the key new feature are decoherence effects due to the current across the impurity. In the present paper, we show how one can develop a consistent framework for studying the non-equilibrium Kondo model within a scaling picture of infinitesimal unitary transformations (flow equations). Decoherence effects appear naturally in third order of the β-function and dominate the Hamiltonian flow for sufficiently large voltage bias. We work out the spin dynamics in non-equilibrium and compare it with finite temperature equilibrium results. In particular, we report on the behavior of the static spin susceptibility including leading logarithmic corrections and compare it with the celebrated equilibrium result as a function of temperature.

Foundations and models of pre-equilibrium decay

International Nuclear Information System (INIS)

Bunakov, V.E.

1980-01-01

A review is given of the presently existing microscopic, semi-phenomenologic and phenomenologic models used for the description of nuclear reactions. Their advantages and drawbacks are analyzed. A special attention is given to the analysis of pre-equilibrium decay phenomenological models based on the use of master equations (time-dependent versions of exciton models, intranuclear cascade, etc.). A version of the unified theory of nuclear reactions is discussed which makes use of quantum master equations for finite open systems. The conditions are formulated for the derivation of these equations from the time-dependent Schroedinger equation for the many-body problem. The various models of nuclear reactions used in practice are shown to be approximate solutions of master equations for finite open systems. From this point of view the analysis is carried out of these models' reliability in the description of experimental data. Possible modifications are considered which provide for better agreement between the different models and for the more exact description of experimental data. (author)

Do MincerianWage Equations Inform How Schooling Influences Productivity?

DEFF Research Database (Denmark)

Groth, Christian; Growiec, Jakub

2017-01-01

We study the links between the Mincerian wage equation (the cross-sectional relationship between wages and years of schooling) and the human capital production function (the causal effect of schooling on labor productivity). Based on a stylized Mincerian general equilibrium model with imperfect...... substitutability across skill types and ex ante identical workers, we demonstrate that the mechanism of compensating wage differentials renders the Mincerian wage equation uninformative for the human capital production function. Proper identification of the human capital production function should take...... into account the equilibrium allocation of individuals across skill types....

Thermodynamic theory of equilibrium fluctuations

International Nuclear Information System (INIS)

Mishin, Y.

2015-01-01

The postulational basis of classical thermodynamics has been expanded to incorporate equilibrium fluctuations. The main additional elements of the proposed thermodynamic theory are the concept of quasi-equilibrium states, a definition of non-equilibrium entropy, a fundamental equation of state in the entropy representation, and a fluctuation postulate describing the probability distribution of macroscopic parameters of an isolated system. Although these elements introduce a statistical component that does not exist in classical thermodynamics, the logical structure of the theory is different from that of statistical mechanics and represents an expanded version of thermodynamics. Based on this theory, we present a regular procedure for calculations of equilibrium fluctuations of extensive parameters, intensive parameters and densities in systems with any number of fluctuating parameters. The proposed fluctuation formalism is demonstrated by four applications: (1) derivation of the complete set of fluctuation relations for a simple fluid in three different ensembles; (2) fluctuations in finite-reservoir systems interpolating between the canonical and micro-canonical ensembles; (3) derivation of fluctuation relations for excess properties of grain boundaries in binary solid solutions, and (4) derivation of the grain boundary width distribution for pre-melted grain boundaries in alloys. The last two applications offer an efficient fluctuation-based approach to calculations of interface excess properties and extraction of the disjoining potential in pre-melted grain boundaries. Possible future extensions of the theory are outlined.

Rapid change of field line connectivity and reconnection in stochastic magnetic fields

International Nuclear Information System (INIS)

Huang, Yi-Min; Bhattacharjee, A.; Boozer, Allen H.

2014-01-01

Magnetic fields without a direction of continuous symmetry have the generic feature that neighboring field lines exponentiate away from each other and become stochastic, and hence the ideal constraint of preserving magnetic field line connectivity becomes exponentially sensitive to small deviations from ideal Ohm's law. The idea of breaking field line connectivity by stochasticity as a mechanism for fast reconnection is tested with numerical simulations based on reduced magnetohydrodynamics equations with a strong guide field line-tied to two perfectly conducting end plates. Starting from an ideally stable force-free equilibrium, the system is allowed to undergo resistive relaxation. Two distinct phases are found in the process of resistive relaxation. During the quasi-static phase, rapid change of field line connectivity and strong induced flow are found in regions of high field line exponentiation. However, although the field line connectivity of individual field lines can change rapidly, the overall pattern of field line mapping appears to deform gradually. From this perspective, field line exponentiation appears to cause enhanced diffusion rather than reconnection. In some cases, resistive quasi-static evolution can cause the ideally stable initial equilibrium to cross a stability threshold, leading to formation of intense current filaments and rapid change of field line mapping into a qualitatively different pattern. It is in this onset phase that the change of field line connectivity is more appropriately designated as magnetic reconnection. Our results show that rapid change of field line connectivity appears to be a necessary, but not a sufficient condition for fast reconnection.

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

Science.gov (United States)

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

Non-equilibrium effects in the plasmas

International Nuclear Information System (INIS)

Einfeld, D.

1975-01-01

Radial dependences of non-equilibrium effects of a He plasma were studied in a wall-stabilized short-time discharge. The electron density (nsub(e) = 2.5 x 10 22 m -3 ), the electron temperature and the equilibrium shift were determined by calculations of the continuum beam density and the beam densities of one He-I and one He-II line, respectively. In the discharge axis, the overpopulation factors of the ground state of He-I and He-II are about 75. As the distance to the axis increases, they increase for He-I and decrease for He-II. Except for the usual errors of measurement, the overpopulation factors found here correspond to those calculated from the balance equations (Drawin). (orig./AK) [de

Line radiative transfer and statistical equilibrium*

Directory of Open Access Journals (Sweden)

Kamp Inga

2015-01-01

Full Text Available Atomic and molecular line emission from protoplanetary disks contains key information of their detailed physical and chemical structures. To unravel those structures, we need to understand line radiative transfer in dusty media and the statistical equilibrium, especially of molecules. I describe here the basic principles of statistical equilibrium and illustrate them through the two-level atom. In a second part, the fundamentals of line radiative transfer are introduced along with the various broadening mechanisms. I explain general solution methods with their drawbacks and also specific difficulties encountered in solving the line radiative transfer equation in disks (e.g. velocity gradients. I am closing with a few special cases of line emission from disks: Radiative pumping, masers and resonance scattering.

Ward identity for non-equilibrium Fermi systems

Czech Academy of Sciences Publication Activity Database

Velický, B.; Kalvová, Anděla; Špička, Václav

2008-01-01

Roč. 77, č. 4 (2008), 041201/1-041201/4 ISSN 1098-0121 R&D Projects: GA ČR GC202/07/J051 Institutional research plan: CEZ:AV0Z10100520; CEZ:AV0Z10100521 Keywords : non-equilibrium * Green’s functions * quantum transport equations * Ward identity Subject RIV: BE - Theoretical Physics Impact factor: 3.322, year: 2008

Rate equation description of quantum noise in nanolasers with few emitters

DEFF Research Database (Denmark)

Mørk, Jesper; Lippi, G. L.

2018-01-01

Rate equations for micro- and nanocavity lasers are formulated which take account of the finite number of emitters, Purcell effects as well as stochastic effects of spontaneous emission quantum noise. Analytical results are derived for the intensity noise and intensity correlation properties, g(2...

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

Science.gov (United States)

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.

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

International Nuclear Information System (INIS)

Glavatskiy, K. S.

2015-01-01

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

The specification of cross exchange rate equations used to test Purchasing Power Parity

OpenAIRE

Hunter, J; Simpson, M

2004-01-01

The Article considers the speciÞcation of models used to test Pur- chasing Power Parity when applied to cross exchange rates. SpeciÞcally, conventional dynamic models used to test stationarity of the real exchange rate are likely to be misspeciÞed, except when the parameters of each ex- change rate equation are the same

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

Science.gov (United States)

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.

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

Science.gov (United States)

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.

Unified implicit kinetic scheme for steady multiscale heat transfer based on the phonon Boltzmann transport equation

Science.gov (United States)

Zhang, Chuang; Guo, Zhaoli; Chen, Songze

2017-12-01

An implicit kinetic scheme is proposed to solve the stationary phonon Boltzmann transport equation (BTE) for multiscale heat transfer problem. Compared to the conventional discrete ordinate method, the present method employs a macroscopic equation to accelerate the convergence in the diffusive regime. The macroscopic equation can be taken as a moment equation for phonon BTE. The heat flux in the macroscopic equation is evaluated from the nonequilibrium distribution function in the BTE, while the equilibrium state in BTE is determined by the macroscopic equation. These two processes exchange information from different scales, such that the method is applicable to the problems with a wide range of Knudsen numbers. Implicit discretization is implemented to solve both the macroscopic equation and the BTE. In addition, a memory reduction technique, which is originally developed for the stationary kinetic equation, is also extended to phonon BTE. Numerical comparisons show that the present scheme can predict reasonable results both in ballistic and diffusive regimes with high efficiency, while the memory requirement is on the same order as solving the Fourier law of heat conduction. The excellent agreement with benchmark and the rapid converging history prove that the proposed macro-micro coupling is a feasible solution to multiscale heat transfer problems.

Numerical solution of dynamic equilibrium models under Poisson uncertainty

DEFF Research Database (Denmark)

Posch, Olaf; Trimborn, Timo

2013-01-01

We propose a simple and powerful numerical algorithm to compute the transition process in continuous-time dynamic equilibrium models with rare events. In this paper we transform the dynamic system of stochastic differential equations into a system of functional differential equations of the retar...... solution to Lucas' endogenous growth model under Poisson uncertainty are used to compute the exact numerical error. We show how (potential) catastrophic events such as rare natural disasters substantially affect the economic decisions of households....

Non-equilibrium statistical physics with application to disordered systems

CERN Document Server

Cáceres, Manuel Osvaldo

2017-01-01

This textbook is the result of the enhancement of several courses on non-equilibrium statistics, stochastic processes, stochastic differential equations, anomalous diffusion and disorder. The target audience includes students of physics, mathematics, biology, chemistry, and engineering at undergraduate and graduate level with a grasp of the basic elements of mathematics and physics of the fourth year of a typical undergraduate course. The little-known physical and mathematical concepts are described in sections and specific exercises throughout the text, as well as in appendices. Physical-mathematical motivation is the main driving force for the development of this text. It presents the academic topics of probability theory and stochastic processes as well as new educational aspects in the presentation of non-equilibrium statistical theory and stochastic differential equations.. In particular it discusses the problem of irreversibility in that context and the dynamics of Fokker-Planck. An introduction on fluc...

Calculation of the equilibrium pH in a multiple-buffered aqueous solution based on partitioning of proton buffering: a new predictive formula.

Science.gov (United States)

Nguyen, Minhtri K; Kao, Liyo; Kurtz, Ira

2009-06-01

Upon the addition of protons to an aqueous solution containing multiple buffers, the final H+ concentration ([H+]) at equilibrium is determined by the partitioning of added H+ among the various buffer components. In the analysis of acid-base chemistry, the Henderson-Hasselbalch equation and the Stewart strong ion formulation can only describe (rather than predict) the equilibrium pH following a proton load since these formulas calculate the equilibrium pH only when the reactant concentrations at equilibrium(1) 1The term "equilibrium" refers to the steady state proton and reactant concentrations when the buffering of excess protons by the various buffers is complete. are already known. In this regard, it is simpler to directly measure the equilibrium pH rather than measure the equilibrium reactant concentrations to calculate the equilibrium pH. As these formulas cannot predict the final equilibrium [H+] following a proton load to a multiple-buffered aqueous solution, we developed a new quantitative approach for predicting the equilibrium [H+] that is based on the preequilibrium(2)2 The term "preequilibrium" refers to the initial proton and reactant concentrations immediately upon addition of protons and before the buffering of excess protons by the various buffers. concentrations of all buffers in an aqueous solution. The mathematical model used to derive our equation is based on proton transfer buffer equilibria without requiring the incorporation of electroneutrality considerations. The model consists of a quartic polynomial equation that is derived based solely on the partitioning of H+ among the various buffer components. We tested the accuracy of the model using aqueous solutions with various buffers and measured the equilibrium pH values following the addition of HCl. Our results confirmed the accuracy of our new equation (r2 = 1; measured pH vs. predicted pH), indicating that it quantitatively accounts for the underlying acid-base phenomenology.

Conditions of equilibrium of a rotating ideal fluid in the parametrized post-Newtonian formalism

International Nuclear Information System (INIS)

Bondarenko, N.P.

1986-01-01

Conditions of equilibrium of a rotating ideal fluid in parametrized post-Newtonian hydrodynamics are obtained by the variational method. They generalize the analogous equilibrium conditions in the post-Newtonian approximation of the general theory of relativity. A conservation law for the total energy is obtained by integrating the equations of motion

Validation of estimated glomerular filtration rate equations for Japanese children.

Science.gov (United States)

Gotoh, Yoshimitsu; Uemura, Osamu; Ishikura, Kenji; Sakai, Tomoyuki; Hamasaki, Yuko; Araki, Yoshinori; Hamda, Riku; Honda, Masataka

2018-01-25

The gold standard for evaluation of kidney function is renal inulin clearance (Cin). However, the methodology for Cin is complicated and difficult, especially for younger children and/or patients with bladder dysfunction. Therefore, we developed a simple and easier method for obtaining the estimated glomerular filtration rate (eGFR) using equations and values for several biomarkers, i.e., serum creatinine (Cr), serum cystatin C (cystC), serum beta-2 microglobulin (β 2 MG), and creatinine clearance (Ccr). The purpose of the present study was to validate these equations with a new data set. To validate each equation, we used data of 140 patients with CKD with clinical need for Cin, using the measured GFR (mGFR). We compared the results for each eGFR equation with the mGFR using mean error (ME), root mean square error (RMSE), P 30 , and Bland-Altman analysis. The ME of Cr, cystC, β 2 MG, and Ccr based on eGFR was 15.8 ± 13.0, 17.2 ± 16.5, 15.4 ± 14.3, and 10.6 ± 13.0 ml/min/1.73 m 2 , respectively. The RMSE was 29.5, 23.8, 20.9, and 16.7, respectively. The P 30 was 79.4, 71.1, 69.5, and 92.9%, respectively. The Bland-Altman bias analysis showed values of 4.0 ± 18.6, 5.3 ± 16.8, 12.7 ± 17.0, and 2.5 ± 17.2 ml/min/1.73 m 2 , respectively, for these parameters. The bias of each eGFR equation was not large. Therefore, each eGFR equation could be used.

Prediction of critical flow rates through power-operated relief valves

International Nuclear Information System (INIS)

Abdollahian, D.; Singh, A.

1983-01-01

Existing single-phase and two-phase critical flow models are used to predict the flow rates through the power-operated relief valves tested in the EPRI Safety and Relief Valve test program. For liquid upstream conditions, Homogeneous Equilibrium Model, Moody, Henry-Fauske and Burnell two-phase critical flow models are used for comparison with data. Under steam upstream conditions, the flow rates are predicted either by the single-phase isentropic equations or the Homogeneous Equilibrium Model, depending on the thermodynamic condition of the fluid at the choking plane. The results of the comparisons are used to specify discharge coefficients for different valves under steam and liquid upstream conditions and evaluate the existing approximate critical flow relations for a wide range of subcooled water and steam conditions

Bifurcation and Stability Analysis of the Equilibrium States in Thermodynamic Systems in a Small Vicinity of the Equilibrium Values of Parameters

Science.gov (United States)

Barsuk, Alexandr A.; Paladi, Florentin

2018-04-01

The dynamic behavior of thermodynamic system, described by one order parameter and one control parameter, in a small neighborhood of ordinary and bifurcation equilibrium values of the system parameters is studied. Using the general methods of investigating the branching (bifurcations) of solutions for nonlinear equations, we performed an exhaustive analysis of the order parameter dependences on the control parameter in a small vicinity of the equilibrium values of parameters, including the stability analysis of the equilibrium states, and the asymptotic behavior of the order parameter dependences on the control parameter (bifurcation diagrams). The peculiarities of the transition to an unstable state of the system are discussed, and the estimates of the transition time to the unstable state in the neighborhood of ordinary and bifurcation equilibrium values of parameters are given. The influence of an external field on the dynamic behavior of thermodynamic system is analyzed, and the peculiarities of the system dynamic behavior are discussed near the ordinary and bifurcation equilibrium values of parameters in the presence of external field. The dynamic process of magnetization of a ferromagnet is discussed by using the general methods of bifurcation and stability analysis presented in the paper.

Module description of TOKAMAK equilibrium code MEUDAS

International Nuclear Information System (INIS)

Suzuki, Masaei; Hayashi, Nobuhiko; Matsumoto, Taro; Ozeki, Takahisa

2002-01-01

The analysis of an axisymmetric MHD equilibrium serves as a foundation of TOKAMAK researches, such as a design of devices and theoretical research, the analysis of experiment result. For this reason, also in JAERI, an efficient MHD analysis code has been developed from start of TOKAMAK research. The free boundary equilibrium code ''MEUDAS'' which uses both the DCR method (Double-Cyclic-Reduction Method) and a Green's function can specify the pressure and the current distribution arbitrarily, and has been applied to the analysis of a broad physical subject as a code having rapidity and high precision. Also the MHD convergence calculation technique in ''MEUDAS'' has been built into various newly developed codes. This report explains in detail each module in ''MEUDAS'' for performing convergence calculation in solving the MHD equilibrium. (author)

Hydrostatic equilibrium of stars without electroneutrality constraint

Science.gov (United States)

Krivoruchenko, M. I.; Nadyozhin, D. K.; Yudin, A. V.

2018-04-01

The general solution of hydrostatic equilibrium equations for a two-component fluid of ions and electrons without a local electroneutrality constraint is found in the framework of Newtonian gravity theory. In agreement with the Poincaré theorem on analyticity and in the context of Dyson's argument, the general solution is demonstrated to possess a fixed (essential) singularity in the gravitational constant G at G =0 . The regular component of the general solution can be determined by perturbation theory in G starting from a locally neutral solution. The nonperturbative component obtained using the method of Wentzel, Kramers and Brillouin is exponentially small in the inner layers of the star and grows rapidly in the outward direction. Near the surface of the star, both components are comparable in magnitude, and their nonlinear interplay determines the properties of an electro- or ionosphere. The stellar charge varies within the limits of -0.1 to 150 C per solar mass. The properties of electro- and ionospheres are exponentially sensitive to variations of the fluid densities in the central regions of the star. The general solutions of two exactly solvable stellar models without a local electroneutrality constraint are also presented.

A framework for modelling gene regulation which accommodates non-equilibrium mechanisms.

Science.gov (United States)

Ahsendorf, Tobias; Wong, Felix; Eils, Roland; Gunawardena, Jeremy

2014-12-05

Gene regulation has, for the most part, been quantitatively analysed by assuming that regulatory mechanisms operate at thermodynamic equilibrium. This formalism was originally developed to analyse the binding and unbinding of transcription factors from naked DNA in eubacteria. Although widely used, it has made it difficult to understand the role of energy-dissipating, epigenetic mechanisms, such as DNA methylation, nucleosome remodelling and post-translational modification of histones and co-regulators, which act together with transcription factors to regulate gene expression in eukaryotes. Here, we introduce a graph-based framework that can accommodate non-equilibrium mechanisms. A gene-regulatory system is described as a graph, which specifies the DNA microstates (vertices), the transitions between microstates (edges) and the transition rates (edge labels). The graph yields a stochastic master equation for how microstate probabilities change over time. We show that this framework has broad scope by providing new insights into three very different ad hoc models, of steroid-hormone responsive genes, of inherently bounded chromatin domains and of the yeast PHO5 gene. We find, moreover, surprising complexity in the regulation of PHO5, which has not yet been experimentally explored, and we show that this complexity is an inherent feature of being away from equilibrium. At equilibrium, microstate probabilities do not depend on how a microstate is reached but, away from equilibrium, each path to a microstate can contribute to its steady-state probability. Systems that are far from equilibrium thereby become dependent on history and the resulting complexity is a fundamental challenge. To begin addressing this, we introduce a graph-based concept of independence, which can be applied to sub-systems that are far from equilibrium, and prove that history-dependent complexity can be circumvented when sub-systems operate independently. As epigenomic data become increasingly

Existing creatinine-based equations overestimate glomerular filtration rate in Indians.

Science.gov (United States)

Kumar, Vivek; Yadav, Ashok Kumar; Yasuda, Yoshinari; Horio, Masaru; Kumar, Vinod; Sahni, Nancy; Gupta, Krishan L; Matsuo, Seiichi; Kohli, Harbir Singh; Jha, Vivekanand

2018-02-01

Accurate estimation of glomerular filtration rate (GFR) is important for diagnosis and risk stratification in chronic kidney disease and for selection of living donors. Ethnic differences have required correction factors in the originally developed creatinine-based GFR estimation equations for populations around the world. Existing equations have not been validated in the vegetarian Indian population. We examined the performance of creatinine and cystatin-based GFR estimating equations in Indians. GFR was measured by urinary clearance of inulin. Serum creatinine was measured using IDMS-traceable Jaffe's and enzymatic assays, and cystatin C by colloidal gold immunoassay. Dietary protein intake was calculated by measuring urinary nitrogen appearance. Bias, precision and accuracy were calculated for the eGFR equations. A total of 130 participants (63 healthy kidney donors and 67 with CKD) were studied. About 50% were vegetarians, and the remainder ate meat 3.8 times every month. The average creatinine excretion were 14.7 mg/kg/day (95% CI: 13.5 to 15.9 mg/kg/day) and 12.4 mg/kg/day (95% CI: 11.2 to 13.6 mg/kg/day) in males and females, respectively. The average daily protein intake was 46.1 g/day (95% CI: 43.2 to 48.8 g/day). The mean mGFR in the study population was 51.66 ± 31.68 ml/min/1.73m 2 . All creatinine-based eGFR equations overestimated GFR (p < 0.01 for each creatinine based eGFR equation). However, eGFR by CKD-EPI Cys was not significantly different from mGFR (p = 0.38). The CKD-EPI Cys exhibited lowest bias [mean bias: -3.53 ± 14.70 ml/min/1.73m 2 (95% CI: -0.608 to -0.98)] and highest accuracy (P 30 : 74.6%). The GFR in the healthy population was 79.44 ± 20.19 (range: 41.90-134.50) ml/min/1.73m 2 . Existing creatinine-based GFR estimating equations overestimate GFR in Indians. An appropriately powered study is needed to develop either a correction factor or a new equation for accurate assessment of kidney function in the

Blade bowing effects on radial equilibrium of inlet flow in axial compressor cascades

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Han XU

2017-10-01

Full Text Available The circumferentially averaged equation of the inlet flow radial equilibrium in axial compressor was deduced. It indicates that the blade inlet radial pressure gradient is closely related to the radial component of the circumferential fluctuation (CF source item. Several simplified cascades with/without aerodynamic loading were numerically studied to investigate the effects of blade bowing on the inlet flow radial equilibrium. A data reduction program was conducted to obtain the CF source from three-dimensional (3D simulation results. Flow parameters at the passage inlet were focused on and each term in the radial equilibrium equation was discussed quantitatively. Results indicate that the inviscid blade force is the inducement of the inlet CF due to geometrical asymmetry. Blade bowing induces variation of the inlet CF, thus changes the radial pressure gradient and leads to flow migration before leading edge (LE in the cascades. Positive bowing drives the inlet flow to migrate from end walls to mid-span and negative bowing turns it to the reverse direction to build a new equilibrium. In addition, comparative studies indicate that the inlet Mach number and blade loading can efficiently impact the effectiveness of blade bowing on radial equilibrium in compressor design.

NON-EQUILIBRIUM IONIZATION MODELING OF THE CURRENT SHEET IN A SIMULATED SOLAR ERUPTION

International Nuclear Information System (INIS)

Shen Chengcai; Reeves, Katharine K.; Raymond, John C.; Murphy, Nicholas A.; Ko, Yuan-Kuen; Lin Jun; Mikić, Zoran; Linker, Jon A.

2013-01-01

The current sheet that extends from the top of flare loops and connects to an associated flux rope is a common structure in models of coronal mass ejections (CMEs). To understand the observational properties of CME current sheets, we generated predictions from a flare/CME model to be compared with observations. We use a simulation of a large-scale CME current sheet previously reported by Reeves et al. This simulation includes ohmic and coronal heating, thermal conduction, and radiative cooling in the energy equation. Using the results of this simulation, we perform time-dependent ionization calculations of the flow in a CME current sheet and construct two-dimensional spatial distributions of ionic charge states for multiple chemical elements. We use the filter responses from the Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory and the predicted intensities of emission lines to compute the count rates for each of the AIA bands. The results show differences in the emission line intensities between equilibrium and non-equilibrium ionization. The current sheet plasma is underionized at low heights and overionized at large heights. At low heights in the current sheet, the intensities of the AIA 94 Å and 131 Å channels are lower for non-equilibrium ionization than for equilibrium ionization. At large heights, these intensities are higher for non-equilibrium ionization than for equilibrium ionization inside the current sheet. The assumption of ionization equilibrium would lead to a significant underestimate of the temperature low in the current sheet and overestimate at larger heights. We also calculate the intensities of ultraviolet lines and predict emission features to be compared with events from the Ultraviolet Coronagraph Spectrometer on the Solar and Heliospheric Observatory, including a low-intensity region around the current sheet corresponding to this model

Equilibrium moisture content of OSB panels made from Eucalyptus urophylla clones

Directory of Open Access Journals (Sweden)

Lourival Marin Mendes

2014-12-01

Full Text Available This work aimed to verify the efficiency of Nelson's equation to estimate equilibrium moisture content of this material and provide a model for determination of moisture content of panels based on air relative moisture content, as well as to evaluate the effect of some processing variables on the equilibrium moisture content of OSB (Oriented Strand Board panels. The 25 x 25 mm samples were put in an acclimation room where they were kept at 30ºC and had their mass determined after stabilization at the relative air moisture contents of 40, 50, 60, 70, 80 and 90%. By the results obtained it was possible to conclude that: Nelson's equation tended to underestimate moisture values of the panel; the polynomial model adjusted based on the relative moisture of the air presented great potential to be used; although different behavior may be observed for the isotherms of treatments, there was no significant effect of the variables panel density, wood basic density, mat type and pressure temperature on mean equilibrium moisture content in desorption 1, adsorption and desorption 2.

Time-dependent integral transport equation kernels, leakage rates and collision rates for plane and spherical geometry

International Nuclear Information System (INIS)

Henderson, D.L.

1987-01-01

Time-dependent integral transport equation flux and current kernels for plane and spherical geometry are derived for homogeneous media. Using the multiple collision formalism, isotropic sources that are delta distributions in time are considered for four different problems. The plane geometry flux kernel is applied to a uniformly distributed source within an infinite medium and to a surface source in a semi-infinite medium. The spherical flux kernel is applied to a point source in an infinite medium and to a point source at the origin of a finite sphere. The time-dependent first-flight leakage rates corresponding to the existing steady state first-flight escape probabilities are computed by the Laplace transform technique assuming a delta distribution source in time. The case of a constant source emitting neutrons over a time interval, Δt, for a spatially uniform source is obtained for a slab and a sphere. Time-dependent first-flight leakage rates are also determined for the general two region spherical medium problem for isotropic sources with a delta distribution in time uniformly distributed throughout both the inner and outer regions. The time-dependent collision rates due to the uncollided neutrons are computed for a slab and a sphere using the time-dependent first-flight leakage rates and the time-dependent continuity equation. The case of a constant source emitting neutrons over a time interval, Δt, is also considered

Asymptotic solution of the Vlasov and Poisson equations for an inhomogeneous plasma

International Nuclear Information System (INIS)

Croci, R.

1991-01-01

The asymptotic solutions to a class of inhomogeneous integral equations that reduce to algebraic equations when a parameter η goes to zero (the kernel becoming proportional to a Dirac δ function) are derived. This class includes the integral equations obtained from the system of Vlasov and Poisson equations for the Fourier transform in space and the Laplace transform in time of the electrostatic potential, when the equilibrium magnetic field is uniform and the equilibrium plasma density depends on ηx, with the co-ordinate z being the direction of the magnetic field. In this case the inhomogeneous term is given by the initial conditions and possibly by sources, and the Laplace-transform variable ω is the eigenvalue parameter. (Author)

The influence of thermal pressure on equilibrium models of hypermassive neutron star merger remnants

Energy Technology Data Exchange (ETDEWEB)

Kaplan, J. D.; Ott, C. D.; Roberts, L. [TAPIR, California Institute of Technology, Mailcode 350-17, Pasadena, CA 91125 (United States); O' Connor, E. P. [CITA, University of Toronto, 60 St. George Street, Toronto, ON M5S 3H8 (Canada); Kiuchi, K. [Yukawa Institute for Theoretical Physics, University of Kyoto, Kyoto (Japan); Duez, M., E-mail: cott@tapir.caltech.edu [Department of Physics and Astronomy, Washington State University, Pullman, WA (United States)

2014-07-20

The merger of two neutron stars leaves behind a rapidly spinning hypermassive object whose survival is believed to depend on the maximum mass supported by the nuclear equation of state (EOS), angular momentum redistribution by (magneto-)rotational instabilities, and spindown by gravitational waves. The high temperatures (∼5-40 MeV) prevailing in the merger remnant may provide thermal pressure support that could increase its maximum mass and, thus, its life on a neutrino-cooling timescale. We investigate the role of thermal pressure support in hypermassive merger remnants by computing sequences of spherically symmetric and axisymmetric uniformly and differentially rotating equilibrium solutions to the general-relativistic stellar structure equations. Using a set of finite-temperature nuclear EOS, we find that hot maximum-mass critically spinning configurations generally do not support larger baryonic masses than their cold counterparts. However, subcritically spinning configurations with mean density of less than a few times nuclear saturation density yield a significantly thermally enhanced mass. Even without decreasing the maximum mass, cooling and other forms of energy loss can drive the remnant to an unstable state. We infer secular instability by identifying approximate energy turning points in equilibrium sequences of constant baryonic mass parameterized by maximum density. Energy loss carries the remnant along the direction of decreasing gravitational mass and higher density until instability triggers collapse. Since configurations with more thermal pressure support are less compact and thus begin their evolution at a lower maximum density, they remain stable for longer periods after merger.

The influence of thermal pressure on equilibrium models of hypermassive neutron star merger remnants

International Nuclear Information System (INIS)

Kaplan, J. D.; Ott, C. D.; Roberts, L.; O'Connor, E. P.; Kiuchi, K.; Duez, M.

2014-01-01

The merger of two neutron stars leaves behind a rapidly spinning hypermassive object whose survival is believed to depend on the maximum mass supported by the nuclear equation of state (EOS), angular momentum redistribution by (magneto-)rotational instabilities, and spindown by gravitational waves. The high temperatures (∼5-40 MeV) prevailing in the merger remnant may provide thermal pressure support that could increase its maximum mass and, thus, its life on a neutrino-cooling timescale. We investigate the role of thermal pressure support in hypermassive merger remnants by computing sequences of spherically symmetric and axisymmetric uniformly and differentially rotating equilibrium solutions to the general-relativistic stellar structure equations. Using a set of finite-temperature nuclear EOS, we find that hot maximum-mass critically spinning configurations generally do not support larger baryonic masses than their cold counterparts. However, subcritically spinning configurations with mean density of less than a few times nuclear saturation density yield a significantly thermally enhanced mass. Even without decreasing the maximum mass, cooling and other forms of energy loss can drive the remnant to an unstable state. We infer secular instability by identifying approximate energy turning points in equilibrium sequences of constant baryonic mass parameterized by maximum density. Energy loss carries the remnant along the direction of decreasing gravitational mass and higher density until instability triggers collapse. Since configurations with more thermal pressure support are less compact and thus begin their evolution at a lower maximum density, they remain stable for longer periods after merger.

Asymptotic Expansions for Higher-Order Scalar Difference Equations

Directory of Open Access Journals (Sweden)

Pituk Mihály

2007-01-01

Full Text Available We give an asymptotic expansion of the solutions of higher-order Poincaré difference equation in terms of the characteristic solutions of the limiting equation. As a consequence, we obtain an asymptotic description of the solutions approaching a hyperbolic equilibrium of a higher-order nonlinear difference equation with sufficiently smooth nonlinearity. The proof is based on the inversion formula for the z -transform and the residue theorem.

Calculation of the equilibrium pH in a multiple-buffered aqueous solution based on partitioning of proton buffering: a new predictive formula

Science.gov (United States)

Nguyen, Minhtri K.; Kao, Liyo; Kurtz, Ira

2009-01-01

Upon the addition of protons to an aqueous solution containing multiple buffers, the final H+ concentration ([H+]) at equilibrium is determined by the partitioning of added H+ among the various buffer components. In the analysis of acid-base chemistry, the Henderson-Hasselbalch equation and the Stewart strong ion formulation can only describe (rather than predict) the equilibrium pH following a proton load since these formulas calculate the equilibrium pH only when the reactant concentrations at equilibrium1 1The term “equilibrium” refers to the steady state proton and reactant concentrations when the buffering of excess protons by the various buffers is complete. are already known. In this regard, it is simpler to directly measure the equilibrium pH rather than measure the equilibrium reactant concentrations to calculate the equilibrium pH. As these formulas cannot predict the final equilibrium [H+] following a proton load to a multiple-buffered aqueous solution, we developed a new quantitative approach for predicting the equilibrium [H+] that is based on the preequilibrium22The term “preequilibrium” refers to the initial proton and reactant concentrations immediately upon addition of protons and before the buffering of excess protons by the various buffers. concentrations of all buffers in an aqueous solution. The mathematical model used to derive our equation is based on proton transfer buffer equilibria without requiring the incorporation of electroneutrality considerations. The model consists of a quartic polynomial equation that is derived based solely on the partitioning of H+ among the various buffer components. We tested the accuracy of the model using aqueous solutions with various buffers and measured the equilibrium pH values following the addition of HCl. Our results confirmed the accuracy of our new equation (r2 = 1; measured pH vs. predicted pH), indicating that it quantitatively accounts for the underlying acid-base phenomenology. PMID

Macroscopic and microscopic description of HE-HI collisions; classical equations of motion calculations. [Rapidity, cross sections, central and noncentral collisions

Energy Technology Data Exchange (ETDEWEB)

Bodmer, A. R.

1978-01-01

The study of high energy heavy ion reactions includes the three principle a priori approaches used for central collisions, namely, hydrodynamics, cascade--Boltzman equation, and the classical equations of motion. While no clearly justified central or near central collisions are found, the classical equations of motion are used to illustrate some general features of these reactions. It is expected that the hot nuclear matter produced in such collisions is a dense, viscous, and thermally conductive fluid with important nonequilibrium and nonclassical features, rapidity, distribution, noncentral collisions, potential dependent effects for a given two-body scattering, and c.m. cross sections for a central collision with given parameters are among the properties considered. 12 references. (JFP)

Numerical computation of FCT equilibria by inverse equilibrium method

International Nuclear Information System (INIS)

Tokuda, Shinji; Tsunematsu, Toshihide; Takeda, Tatsuoki

1986-11-01

FCT (Flux Conserving Tokamak) equilibria were obtained numerically by the inverse equilibrium method. The high-beta tokamak ordering was used to get the explicit boundary conditions for FCT equilibria. The partial differential equation was reduced to the simultaneous quasi-linear ordinary differential equations by using the moment method. The regularity conditions for solutions at the singular point of the equations can be expressed correctly by this reduction and the problem to be solved becomes a tractable boundary value problem on the quasi-linear ordinary differential equations. This boundary value problem was solved by the method of quasi-linearization, one of the shooting methods. Test calculations show that this method provides high-beta tokamak equilibria with sufficiently high accuracy for MHD stability analysis. (author)

Effects of Non-Equilibrium Chemistry and Darcy-Forchheimer Flow of Pyrolysis Gas for a Charring Ablator

Science.gov (United States)

Chen, Yih-Kanq; Milos, Frank S.

2011-01-01

The Fully Implicit Ablation and Thermal Response code, FIAT, simulates pyrolysis and ablation of thermal protection materials and systems. The governing equations, which include energy conservation, a three-component decomposition model, and a surface energy balance, are solved with a moving grid. This work describes new modeling capabilities that are added to a special version of FIAT. These capabilities include a time-dependent pyrolysis gas flow momentum equation with Darcy-Forchheimer terms and pyrolysis gas species conservation equations with finite-rate homogeneous chemical reactions. The total energy conservation equation is also enhanced for consistency with these new additions. Parametric studies are performed using this enhanced version of FIAT. Two groups of analyses of Phenolic Impregnated Carbon Ablator (PICA) are presented. In the first group, an Orion flight environment for a proposed Lunar-return trajectory is considered. In the second group, various test conditions for arcjet models are examined. The central focus of these parametric studies is to understand the effect of pyrolysis gas momentum transfer on PICA material in-depth thermal responses with finite-rate, equilibrium, or frozen homogeneous gas chemistry. Results are presented, discussed, and compared with those predicted by the baseline PICA/FIAT ablation and thermal response model developed by the Orion Thermal Protection System Advanced Development Project.

Equilibrium state analysis of a nonneutral plasma under a uniform magnetic field

International Nuclear Information System (INIS)

Fernandez, J.E.; Molinari, V.G.; Sumini, M.A.

1990-01-01

By recourse to the Boltzmann H-theorem, the existence of a thermodynamic equilibrium state has been proved for a nonneutral plasma under an external magnetic field. The equation describing the density profile of ions or electrons has been found. The density equation has been numerically solved for a generic magnetic field and plasma frequency, giving a parametric limit for the confinement region. An appropriate change of variable allows to approximate the density equation whose analytical solution has been found. The approximated density closely fits the numerical solution of the original equation. (Author)

Exact Solutions of Fragmentation Equations with General Fragmentation Rates and Separable Particles Distribution Kernels

Directory of Open Access Journals (Sweden)

S. C. Oukouomi Noutchie

2014-01-01

Full Text Available We make use of Laplace transform techniques and the method of characteristics to solve fragmentation equations explicitly. Our result is a breakthrough in the analysis of pure fragmentation equations as this is the first instance where an exact solution is provided for the fragmentation evolution equation with general fragmentation rates. This paper is the key for resolving most of the open problems in fragmentation theory including “shattering” and the sudden appearance of infinitely many particles in some systems with initial finite particles number.

Isothermal phase (vapour + liquid) equilibrium data for binary mixtures of propene (R1270) with either 1,1,2,3,3,3-hexafluoro-1-propene (R1216) or 2,2,3-trifluoro-3-(trifluoromethyl)oxirane in the temperature range of (279 to 318) K

International Nuclear Information System (INIS)

Subramoney, Shalendra Clinton; Nelson, Wayne Michael; Courtial, Xavier; Naidoo, Paramespri; Coquelet, Christophe; Richon, Dominique; Ramjugernath, Deresh

2015-01-01

Highlights: • Phase equilibrium data for propene and hexafluoropropylene. • Phase equilibrium data for propene and hexafluoropropylene oxide. • Systems exhibit pressure-maximum azeotropes. • Data well correlated by Peng–Robinson equation of state with the Wong–Sandler mixing rule. - Abstract: Isothermal (vapour + liquid) equilibrium data (P–x–y) are presented for the 1-propene 1,1,2,3,3,3-hexafluoro-1-propene and the 1-propene + 2,2,3-trifluoro-3-(trifluoromethyl)oxirane binary systems. Both binary systems were studied at five temperatures, ranging from (279.36 to 318.09) K, at pressures up to 2 MPa. The experimental (vapour + liquid) equilibrium data were measured using an apparatus based on the “(static + analytic)” method incorporating a single movable Rapid On-Line Sampler-Injector to sample the liquid and vapour phases at equilibrium. The expanded uncertainties are approximated on average as T = 0.07 K, 0.008 MPa, and 0.007 and 0.009 for the temperature, pressure, and the liquid and vapour mole fractions, respectively. A homogenous maximum-pressure azeotrope was observed for both binary systems at all temperatures studied. The experimental data were correlated with the Peng–Robinson equation of state using the Mathias–Copeman alpha function, paired with the Wong–Sandler mixing rule and the Non-Random Two Liquid activity coefficient model. The model provided satisfactory representation of the phase equilibrium data measured

On the non-stationary generalized Langevin equation

Science.gov (United States)

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.

Modeling of two-phase flow with thermal and mechanical non-equilibrium

International Nuclear Information System (INIS)

Houdayer, G.; Pinet, B.; Le Coq, G.; Reocreux, M.; Rousseau, J.C.

1977-01-01

To improve two-phase flow modeling by taking into account thermal and mechanical non-equilibrium a joint effort on analytical experiment and physical modeling has been undertaken. A model describing thermal non-equilibrium effects is first presented. A correlation of mass transfer has been developed using steam water critical flow tests. This model has been used to predict in a satisfactory manner blowdown tests. It has been incorporated in CLYSTERE system code. To take into account mechanical non-equilibrium, a six equations model is written. To get information on the momentum transfers special nitrogen-water tests have been undertaken. The first results of these studies are presented

Development of a Thermal Equilibrium Prediction Algorithm

International Nuclear Information System (INIS)

Aviles-Ramos, Cuauhtemoc

2002-01-01

A thermal equilibrium prediction algorithm is developed and tested using a heat conduction model and data sets from calorimetric measurements. The physical model used in this study is the exact solution of a system of two partial differential equations that govern the heat conduction in the calorimeter. A multi-parameter estimation technique is developed and implemented to estimate the effective volumetric heat generation and thermal diffusivity in the calorimeter measurement chamber, and the effective thermal diffusivity of the heat flux sensor. These effective properties and the exact solution are used to predict the heat flux sensor voltage readings at thermal equilibrium. Thermal equilibrium predictions are carried out considering only 20% of the total measurement time required for thermal equilibrium. A comparison of the predicted and experimental thermal equilibrium voltages shows that the average percentage error from 330 data sets is only 0.1%. The data sets used in this study come from calorimeters of different sizes that use different kinds of heat flux sensors. Furthermore, different nuclear material matrices were assayed in the process of generating these data sets. This study shows that the integration of this algorithm into the calorimeter data acquisition software will result in an 80% reduction of measurement time. This reduction results in a significant cutback in operational costs for the calorimetric assay of nuclear materials. (authors)

A facilitated diffusion model constrained by the probability isotherm: a pedagogical exercise in intuitive non-equilibrium thermodynamics.

Science.gov (United States)

Chapman, Brian

2017-06-01

This paper seeks to develop a more thermodynamically sound pedagogy for students of biological transport than is currently available from either of the competing schools of linear non-equilibrium thermodynamics (LNET) or Michaelis-Menten kinetics (MMK). To this end, a minimal model of facilitated diffusion was constructed comprising four reversible steps: cis- substrate binding, cis → trans bound enzyme shuttling, trans -substrate dissociation and trans → cis free enzyme shuttling. All model parameters were subject to the second law constraint of the probability isotherm, which determined the unidirectional and net rates for each step and for the overall reaction through the law of mass action. Rapid equilibration scenarios require sensitive 'tuning' of the thermodynamic binding parameters to the equilibrium substrate concentration. All non-equilibrium scenarios show sigmoidal force-flux relations, with only a minority of cases having their quasi -linear portions close to equilibrium. Few cases fulfil the expectations of MMK relating reaction rates to enzyme saturation. This new approach illuminates and extends the concept of rate-limiting steps by focusing on the free energy dissipation associated with each reaction step and thereby deducing its respective relative chemical impedance. The crucial importance of an enzyme's being thermodynamically 'tuned' to its particular task, dependent on the cis- and trans- substrate concentrations with which it deals, is consistent with the occurrence of numerous isoforms for enzymes that transport a given substrate in physiologically different circumstances. This approach to kinetic modelling, being aligned with neither MMK nor LNET, is best described as intuitive non-equilibrium thermodynamics, and is recommended as a useful adjunct to the design and interpretation of experiments in biotransport.

Non-equilibrium physics at a holographic chiral phase transition

Energy Technology Data Exchange (ETDEWEB)

Evans, Nick; Kim, Keun-young [Southampton Univ. (United Kingdom). School of Physics and Astronomy; Kavli Institute for Theoretical Physics China, Beijing (China); Kalaydzhyan, Tigran; Kirsch, Ingo [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2010-11-15

The D3/D7 system holographically describes an N=2 gauge theory which spontaneously breaks a chiral symmetry by the formation of a quark condensate in the presence of a magnetic field. At finite temperature it displays a first order phase transition. We study out of equilibrium dynamics associated with this transition by placing probe D7 branes in a geometry describing a boost-invariant expanding or contracting plasma. We use an adiabatic approximation to track the evolution of the quark condensate in a heated system and reproduce the phase structure expected from equilibrium dynamics. We then study solutions of the full partial differential equation that describes the evolution of out of equilibrium configurations to provide a complete description of the phase transition including describing aspects of bubble formation. (orig.)

Thermodynamics of the Rhodamine B Lactone--Zwitterion Equilibrium.

Science.gov (United States)

Hinckley, Daniel A.; Seybold, Paul G.

1987-01-01

Discusses the benefits of thermochromic transformations for studying thermodynamic properties. Describes an experiment that uses a commercially available dye, attains equilibrium rapidly, employs a simple, single-beam spectrophotometer, and is suitable for both physical chemistry and introductory chemistry laboratories. (TW)

BGK-type models in strong reaction and kinetic chemical equilibrium regimes

International Nuclear Information System (INIS)

Monaco, R; Bianchi, M Pandolfi; Soares, A J

2005-01-01

A BGK-type procedure is applied to multi-component gases undergoing chemical reactions of bimolecular type. The relaxation process towards local Maxwellians, depending on mass and numerical densities of each species as well as common velocity and temperature, is investigated in two different cases with respect to chemical regimes. These cases are related to the strong reaction regime characterized by slow reactions, and to the kinetic chemical equilibrium regime where fast reactions take place. The consistency properties of both models are stated in detail. The trend to equilibrium is numerically tested and comparisons for the two regimes are performed within the hydrogen-air and carbon-oxygen reaction mechanism. In the spatial homogeneous case, it is also shown that the thermodynamical equilibrium of the models recovers satisfactorily the asymptotic equilibrium solutions to the reactive Euler equations

Morphodynamic Modeling of the Lower Yellow River, China: Flux (Equilibrium) Form or Entrainment (Nonequilibrium) Form of Sediment Mass Conservation?

Science.gov (United States)

An, C.; Parker, G.; Ma, H.; Naito, K.; Moodie, A. J.; Fu, X.

2017-12-01

Models of river morphodynamics consist of three elements: (1) a treatment of flow hydraulics, (2) a formulation relating some aspect of sediment transport to flow hydraulics, and (3) a description of sediment conservation. In the case of unidirectional river flow, the Exner equation of sediment conservation is commonly described in terms of a flux-based formulation, in which bed elevation variation is related to the streamwise gradient of sediment transport rate. An alternate formulation of the Exner equation, however, is the entrainment-based formulation in which bed elevation variation is related to the difference between the entrainment rate of bed sediment into suspension and the deposition rate of suspended sediment onto the bed. In the flux-based formulation, sediment transport is regarded to be in a local equilibrium state (i.e., sediment transport rate locally equals sediment transport capacity). However, the entrainment-based formulation does not require this constraint; the sediment transport rate may lag in space and time behind the changing flow conditions. In modeling the fine-grained Lower Yellow River, it is usual to treat sediment conservation in terms of an entrainment-based (nonequilibrium) rather than a flux-based (equilibrium) formulation with the consideration that fine-grained sediment may be entrained at one place but deposited only at some distant location downstream. However, the differences in prediction between the two formulations are still not well known, and the entrainment formulation may not always be necessary for the Lower Yellow River. Here we study this problem by comparing the results of flux-based and entrainment-based morphodynamics under conditions typical of the Yellow River, using sediment transport equations specifically designed for the Lower Yellow River. We find, somewhat unexpectedly, that in a treatment of a 200-km reach using uniform sediment, there is little difference between the two formulations unless the

Equilibrium models of trade equations : a critical review

OpenAIRE

Portugal, Marcelo Savino

1993-01-01

Neste artigo, revisa-se a literatura teórica sobre equações de comércio exterior, inclusive o modelo de comércio baseado na teoria da produção. Discute-se vários problemas comumente encontrados em trabalhos empíricos e também a literatura existente sobre equações relativas ao comércio exterior brasileiro. In this paper we review the theoretical literature on trade equation models, including the production theory approach. We discuss several empirical problems commonly found in the applied ...

Near-Nash equilibrium strategies for LQ differential games with inaccurate state information

Directory of Open Access Journals (Sweden)

2006-01-01

Full Text Available ε -Nash equilibrium or “near equilibrium” for a linear quadratic cost game is considered. Due to inaccurate state information, the standard solution for feedback Nash equilibrium cannot be applied. Instead, an estimation of the players' states is substituted into the optimal control strategies equation obtained for perfect state information. The magnitude of the ε in the ε -Nash equilibrium will depend on the quality of the estimation process. To illustrate this approach, a Luenberger-type observer is used in the numerical example to generate the players' state estimates in a two-player non-zero-sum LQ differential game.

Numerical Analysis Of Hooke Jeeves-Runge Kutta To Determine Reaction Rate Equation In Pyrrole Polymerization

International Nuclear Information System (INIS)

Gunawan, Indra; Sulistyo, Harry; Rochmad

2001-01-01

The numerical analysis of Hooke Jeeves Methods combined with Runge Kutta Methods is used to determine the exact model of reaction rate equation of pyrrole polymerization. Chemical polymerization of pyrrole was conducted with FeCI 3 / pyrrole solution at concentration ratio of 1.62 mole / mole and 2.18 mole / mole with varrying temperature of 28, 40, 50, and 60 o C. FeCl 3 acts as an oxidation agent to form pyrrole cation that will polymerize. The numerical analysis was done to examine the exact model of reaction rate equation which is derived from reaction equation of initiation, propagation, and termination. From its numerical analysis, it is found that the pyrrole polymerization follows third order of pyrrole cation concentration

Influence of Equilibrium Perpendicular Shear Flow on Peeling-ballooning Instabilities

Science.gov (United States)

Xi, P. W.; Xu, X. Q.

2011-10-01

The influence of perpendicular ExB shear flow on peeling-ballooning instabilities is investigated with BOUT++ code. In our simulation, a set of reduced MHD equations are solved for a very unstable equilibrium and a marginal unstable equilibrium in shifted-circular tokamak geometry. For ideal MHD cases without diamagnetic terms and resistivity, we find that flow shear shows dramatic stabilizing effect on peeling-ballooning modes and the stabilizing degree increases with mode number. When the flow shear is large enough, we find the curvature of growth rate verse mode number has the same shape like that for the case with only diamagnetic term, and this implies that diamagnetic term and the shear flow have the same mechanism acting on peeling-ballooning instabilities. The role of Kelvin-Helmholtz term is also investigated and we find it is destabilizing and the effect depends on both flow shear and mode number. For cases with both diamagnetic term and the applied shear flow, modes with intermediate mode number are strongest stabilized while high n and low n mode keep unstable. Based on these results, an ELM trigger sketch is proposed. Performed for USDoE by LLNL Contract DE-AC52-07NA27344.

Nonlinear electromagnetic gyrokinetic equations for rotating axisymmetric plasmas

International Nuclear Information System (INIS)

Artun, M.; Tang, W.M.

1994-03-01

The influence of sheared equilibrium flows on the confinement properties of tokamak plasmas is a topic of much current interest. A proper theoretical foundation for the systematic kinetic analysis of this important problem has been provided here by presented the derivation of a set of nonlinear electromagnetic gyrokinetic equations applicable to low frequency microinstabilities in a rotating axisymmetric plasma. The subsonic rotation velocity considered is in the direction of symmetry with the angular rotation frequency being a function of the equilibrium magnetic flux surface. In accordance with experimental observations, the rotation profile is chosen to scale with the ion temperature. The results obtained represent the shear flow generalization of the earlier analysis by Frieman and Chen where such flows were not taken into account. In order to make it readily applicable to gyrokinetic particle simulations, this set of equations is cast in a phase-space-conserving continuity equation form

Asymptotic Expansions for Higher-Order Scalar Difference Equations

Directory of Open Access Journals (Sweden)

Ravi P. Agarwal

2007-04-01

Full Text Available We give an asymptotic expansion of the solutions of higher-order Poincaré difference equation in terms of the characteristic solutions of the limiting equation. As a consequence, we obtain an asymptotic description of the solutions approaching a hyperbolic equilibrium of a higher-order nonlinear difference equation with sufficiently smooth nonlinearity. The proof is based on the inversion formula for the z -transform and the residue theorem.

An effective rate equation approach to reaction kinetics in small volumes: theory and application to biochemical reactions in nonequilibrium steady-state conditions.

Science.gov (United States)

Grima, R

2010-07-21

Chemical master equations provide a mathematical description of stochastic reaction kinetics in well-mixed conditions. They are a valid description over length scales that are larger than the reactive mean free path and thus describe kinetics in compartments of mesoscopic and macroscopic dimensions. The trajectories of the stochastic chemical processes described by the master equation can be ensemble-averaged to obtain the average number density of chemical species, i.e., the true concentration, at any spatial scale of interest. For macroscopic volumes, the true concentration is very well approximated by the solution of the corresponding deterministic and macroscopic rate equations, i.e., the macroscopic concentration. However, this equivalence breaks down for mesoscopic volumes. These deviations are particularly significant for open systems and cannot be calculated via the Fokker-Planck or linear-noise approximations of the master equation. We utilize the system-size expansion including terms of the order of Omega(-1/2) to derive a set of differential equations whose solution approximates the true concentration as given by the master equation. These equations are valid in any open or closed chemical reaction network and at both the mesoscopic and macroscopic scales. In the limit of large volumes, the effective mesoscopic rate equations become precisely equal to the conventional macroscopic rate equations. We compare the three formalisms of effective mesoscopic rate equations, conventional rate equations, and chemical master equations by applying them to several biochemical reaction systems (homodimeric and heterodimeric protein-protein interactions, series of sequential enzyme reactions, and positive feedback loops) in nonequilibrium steady-state conditions. In all cases, we find that the effective mesoscopic rate equations can predict very well the true concentration of a chemical species. This provides a useful method by which one can quickly determine the

[Estimating glomerular filtration rate in 2012: which adding value for the CKD-EPI equation?].

Science.gov (United States)

Delanaye, Pierre; Mariat, Christophe; Moranne, Olivier; Cavalier, Etienne; Flamant, Martin

2012-07-01

Measuring or estimating glomerular filtration rate (GFR) is still considered as the best way to apprehend global renal function. In 2009, the new Chronic Kidney Disease Epidemiology (CKD-EPI) equation has been proposed as a better estimator of GFR than the Modification of Diet in Renal Disease (MDRD) study equation. This new equation is supposed to underestimate GFR to a lesser degree in higher GFR levels. In this review, we will present and deeply discuss the performances of this equation. Based on articles published between 2009 and 2012, this review will underline advantages, notably the better knowledge of chronic kidney disease prevalence, but also limitations of this new equation, especially in some specific populations. We eventually insist on the fact that all these equations are estimations and nephrologists should remain cautious in their interpretation. Copyright © 2012 Association Société de néphrologie. Published by Elsevier SAS. All rights reserved.

Approach to equilibrium of a quantum system and generalization of the Montroll-Shuler equation for vibrational relaxation of a molecular oscillator

Science.gov (United States)

Kenkre, V. M.; Chase, M.

2017-08-01

The approach to equilibrium of a quantum mechanical system in interaction with a bath is studied from a practical as well as a conceptual point of view. Explicit memory functions are derived for given models of bath couplings. If the system is a harmonic oscillator representing a molecule in interaction with a reservoir, the generalized master equation derived becomes an extension into the coherent domain of the well-known Montroll-Shuler equation for vibrational relaxation and unimolecular dissociation. A generalization of the Bethe-Teller result regarding energy relaxation is found for short times. The theory has obvious applications to relaxation dynamics at ultra-short times as in observations on the femtosecond time scale and to the investigation of quantum coherence at those short times. While vibrational relaxation in chemical physics is a primary target of the study, another system of interest in condensed matter physics, an electron or hole in a lattice subjected to a strong DC electric field that gives rise to well-known Wannier-Stark ladders, is naturally addressed with the theory. Specific system-bath interactions are explored to obtain explicit details of the dynamics. General phenomenological descriptions of the reservoir are considered rather than specific microscopic realizations.

Velocity-based planning of rapid elbow movements expands the control scheme of the equilibrium point hypothesis.

Science.gov (United States)

Suzuki, Masataka; Yamazaki, Yoshihiko

2005-01-01

According to the equilibrium point hypothesis of voluntary motor control, control action of muscles is not explicitly computed, but rather arises as a consequence of interaction between moving equilibrium position, current kinematics and stiffness of the joint. This approach is attractive as it obviates the need to explicitly specify the forces controlling limb movements. However, many debatable aspects of this hypothesis remain in the manner of specification of the equilibrium point trajectory and muscle activation (or its stiffness), which elicits a restoring force toward the planned equilibrium trajectory. In this study, we expanded the framework of this hypothesis by assuming that the control system uses the velocity measure as the origin of subordinate variables scaling descending commands. The velocity command is translated into muscle control inputs by second order pattern generators, which yield reciprocal command and coactivation commands, and create alternating activation of the antagonistic muscles during movement and coactivation in the post-movement phase, respectively. The velocity command is also integrated to give a position command specifying a moving equilibrium point. This model is purely kinematics-dependent, since the descending commands needed to modulate the visco-elasticity of muscles are implicitly given by simple parametric specifications of the velocity command alone. The simulated movements of fast elbow single-joint movements corresponded well with measured data performed over a wide range of movement distances, in terms of both muscle excitations and kinematics. Our proposal on a synthesis for the equilibrium point approach and velocity command, may offer some insights into the control scheme of the single-joint arm movements.

Validation of equilibrium tools on the COMPASS tokamak

Energy Technology Data Exchange (ETDEWEB)

Urban, J., E-mail: urban@ipp.cas.cz [Institute of Plasma Physics ASCR, Za Slovankou 3, 182 00 Praha 8 (Czech Republic); Appel, L.C. [CCFE, Culham Science Centre, Abingdon, Oxfordshire (United Kingdom); Artaud, J.F. [CEA, IRFM, F-13108 Saint Paul Lez Durance (France); Faugeras, B. [Laboratoire J.A. Dieudonné, UMR 7351, Université de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice Cedex 02 (France); Havlicek, J. [Institute of Plasma Physics ASCR, Za Slovankou 3, 182 00 Praha 8 (Czech Republic); Department of Surface and Plasma Science, Faculty of Mathematics and Physics, Charles University in Prague, V Holešovičkách 2, 180 00 Praha 8 (Czech Republic); Komm, M. [Institute of Plasma Physics ASCR, Za Slovankou 3, 182 00 Praha 8 (Czech Republic); Lupelli, I. [CCFE, Culham Science Centre, Abingdon, Oxfordshire (United Kingdom); Peterka, M. [Institute of Plasma Physics ASCR, Za Slovankou 3, 182 00 Praha 8 (Czech Republic); Department of Surface and Plasma Science, Faculty of Mathematics and Physics, Charles University in Prague, V Holešovičkách 2, 180 00 Praha 8 (Czech Republic)

2015-10-15

Highlights: • Three equilibrium codes—EFIT++, FREEBIE and VacTH—have been successfully set up and validated on COMPASS. • FREEBIE can predictively calculate the equilibrium and corresponding poloidal field coil currents. • EFIT++ can reconstruct equilibria generated by FREEBIE from synthetic, optionally noisy diagnostic data. • VacTH is a promising tool for real time plasma shape reconstruction. • Optimized parameters are estimated for EFIT++ and VacTH by a statistical analysis. - Abstract: Various MHD (magnetohydrodynamic) equilibrium tools, some of which being recently developed or considerably updated, are used on the COMPASS tokamak at IPP Prague. MHD equilibrium is a fundamental property of the tokamak plasma, whose knowledge is required for many diagnostics and modelling tools. Proper benchmarking and validation of equilibrium tools is thus key for interpreting and planning tokamak experiments. We present here benchmarks and comparisons to experimental data of the EFIT++ reconstruction code (Appel et al., 2006), the free-boundary equilibrium code FREEBIE (Artaud and Kim, 2012), and a rapid plasma boundary reconstruction code VacTH (Faugeras et al., 2014). We demonstrate that FREEBIE can calculate the equilibrium and corresponding poloidal field (PF) coils currents consistently with EFIT++ reconstructions from experimental data. Both EFIT++ and VacTH can reconstruct equilibria generated by FREEBIE from synthetic, optionally noisy diagnostic data. Hence, VacTH is suitable for real-time control. Optimum reconstruction parameters are estimated.

Comment on 'A Forecasting Equation for the Canada-US Dollar Real Exchange Rate'

OpenAIRE

Kollmann, Robert

1993-01-01

This paper is a comment on the paper 'A Forecasting Equation for the Canada-US Dollar Exchange Rate' (Robert Amano and Simon van Norden, Bank of Canada). The comment was published in: The Exchange Rate and the Economy, Proceedings of 1992 Bank of Canada Conference; Bank of Canada, 1993, Ottawa (ISBN 0-660-15195-2), pp. 266-271.

Equilibrium of rotating and nonrotating plasmas in tokamaks

International Nuclear Information System (INIS)

Pustovitov, V.D.

2003-01-01

One studied plasma equilibrium in tokamak in case of toroidal rotation. Rotation associated centrifugal force is shown to result in decrease of equilibrium limit as to β. One analyzes unlike opinion and considers its supports. It is shown that in possible case of local improvement of equilibrium conditions associated with special selection of profile of plasma rotation rate, the combined integral effect turns to be negative one. But in case of typical conditions, decrease of equilibrium β caused by plasma rotation is negligible one and one may ignore effect of plasma rotation on its equilibrium for hot plasma [ru

Mechanical measurement of hydrogen bonded host-guest systems under non-equilibrium, near-physiological conditions.

Science.gov (United States)

Naranjo, Teresa; Cerrón, Fernando; Nieto-Ortega, Belén; Latorre, Alfonso; Somoza, Álvaro; Ibarra, Borja; Pérez, Emilio M

2017-09-01

Decades after the birth of supramolecular chemistry, there are many techniques to measure noncovalent interactions, such as hydrogen bonding, under equilibrium conditions. As ensembles of molecules rapidly lose coherence, we cannot extrapolate bulk data to single-molecule events under non-equilibrium conditions, more relevant to the dynamics of biological systems. We present a new method that exploits the high force resolution of optical tweezers to measure at the single molecule level the mechanical strength of a hydrogen bonded host-guest pair out of equilibrium and under near-physiological conditions. We utilize a DNA reporter to unambiguously isolate single binding events. The Hamilton receptor-cyanuric acid host-guest system is used as a test bed. The force required to dissociate the host-guest system is ∼17 pN and increases with the pulling rate as expected for a system under non-equilibrium conditions. Blocking one of the hydrogen bonding sites results in a significant decrease of the force-to-break by 1-2 pN, pointing out the ability of the method to resolve subtle changes in the mechanical strength of the binding due to the individual H-bonding components. We believe the method will prove to be a versatile tool to address important questions in supramolecular chemistry.

Clapeyron equation and phase equilibrium properties in higher dimensional charged topological dilaton AdS black holes with a nonlinear source

Energy Technology Data Exchange (ETDEWEB)

Li, Huai-Fan; Zhao, Hui-Hua; Zhang, Li-Chun; Zhao, Ren [Shanxi Datong University, Institute of Theoretical Physics, Datong (China); Shanxi Datong University, Department of Physics, Datong (China)

2017-05-15

Using Maxwell's equal area law, we discuss the phase transition of higher dimensional charged topological dilaton AdS black hole with a nonlinear source. The coexisting region of the two phases is found and we depict the coexistence region in the P-v diagrams. The two-phase equilibrium curves in the P-T diagrams are plotted, and we take the first order approximation of volume v in the calculation. To better compare with a general thermodynamic system, the Clapeyron equation is derived for a higher dimensional charged topological black hole with a nonlinear source. The latent heat of an isothermal phase transition is investigated. We also study the effect of the parameters of the black hole on the region of two-phase coexistence. The results show that the black hole may go through a small-large phase transition similar to those of usual non-gravity thermodynamic systems. (orig.)

Iterative solution of the Grad-Shafranov equation in symmetric magnetic coordinates

International Nuclear Information System (INIS)

Brambilla, Marco

2003-01-01

The inverse Grad-Shafranov equation for axisymmetric magnetohydrodynamic equilibria is reformulated in symmetric magnetic coordinates (in which magnetic field lines look 'straight', and the geometric toroidal angle is one of the coordinates). The poloidally averaged part of the equilibrium condition and Ampere law takes the form of two first-order ordinary differential equations, with the two arbitrary flux functions, pressure and force-free part of the current density, as sources. The condition for the coordinates to be flux coordinates, and the poloidally varying part of the equilibrium equation are similarly transformed into a set of first-order ordinary differential equations, with coefficients depending on the metric, and explicitly solved for the radial derivatives of the coefficients of the Fourier representation of the Cartesian coordinates in the poloidal angle. The derivation exploits the existence of Boozer-White coordinates, but does not require to find these coordinates explicitly; on the other hand, it offers a simple recipe to perform the transformation to Boozer-White coordinates, if required. Use of symmetric flux coordinates is advantageous for the formulation of many problems of equilibrium, stability, and wave propagation in tokamak plasmas, since these coordinates have the simplest metric of their class. It is also shown that in symmetric flux coordinates the Lagrangian equations of the drift motion of charged particles are automatically solved for the time derivatives, with right-hand sides closely related to the coefficients of the inverse Grad-Shafranov equation