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

NASA Astrophysics Data System (ADS)

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

2014-01-01

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

Combining fungal biopesticides and insecticide-treated bednets to enhance malaria control.

PubMed

Hancock, Penelope A

2009-10-01

In developing strategies to control malaria vectors, there is increased interest in biological methods that do not cause instant vector mortality, but have sublethal and lethal effects at different ages and stages in the mosquito life cycle. These techniques, particularly if integrated with other vector control interventions, may produce substantial reductions in malaria transmission due to the total effect of alterations to multiple life history parameters at relevant points in the life-cycle and transmission-cycle of the vector. To quantify this effect, an analytically tractable gonotrophic cycle model of mosquito-malaria interactions is developed that unites existing continuous and discrete feeding cycle approaches. As a case study, the combined use of fungal biopesticides and insecticide treated bednets (ITNs) is considered. Low values of the equilibrium EIR and human prevalence were obtained when fungal biopesticides and ITNs were combined, even for scenarios where each intervention acting alone had relatively little impact. The effect of the combined interventions on the equilibrium EIR was at least as strong as the multiplicative effect of both interventions. For scenarios representing difficult conditions for malaria control, due to high transmission intensity and widespread insecticide resistance, the effect of the combined interventions on the equilibrium EIR was greater than the multiplicative effect, as a result of synergistic interactions between the interventions. Fungal biopesticide application was found to be most effective when ITN coverage was high, producing significant reductions in equilibrium prevalence for low levels of biopesticide coverage. By incorporating biological mechanisms relevant to vectorial capacity, continuous-time vector population models can increase their applicability to integrated vector management.

A vectorized algorithm for 3D dynamics of a tethered satellite

NASA Technical Reports Server (NTRS)

Wilson, Howard B.

1989-01-01

Equations of motion characterizing the three dimensional motion of a tethered satellite during the retrieval phase are studied. The mathematical model involves an arbitrary number of point masses connected by weightless cords. Motion occurs in a gravity gradient field. The formulation presented accounts for general functions describing support point motion, rate of tether retrieval, and arbitrary forces applied to the point masses. The matrix oriented program language MATLAB is used to produce an efficient vectorized formulation for computing natural frequencies and mode shapes for small oscillations about the static equilibrium configuration; and for integrating the nonlinear differential equations governing large amplitude motions. An example of time response pertaining to the skip rope effect is investigated.

A geometrically nonlinear theory of elastic plates

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

Legendre submanifolds in contact manifolds as attractors and geometric nonequilibrium thermodynamics

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

Goto, Shin-itiro, E-mail: sgoto@ims.ac.jp

It has been proposed that equilibrium thermodynamics is described on Legendre submanifolds in contact geometry. It is shown in this paper that Legendre submanifolds embedded in a contact manifold can be expressed as attractors in phase space for a certain class of contact Hamiltonian vector fields. By giving a physical interpretation that points outside the Legendre submanifold can represent nonequilibrium states of thermodynamic variables, in addition to that points of a given Legendre submanifold can represent equilibrium states of the variables, this class of contact Hamiltonian vector fields is physically interpreted as a class of relaxation processes, in which thermodynamicmore » variables achieve an equilibrium state from a nonequilibrium state through a time evolution, a typical nonequilibrium phenomenon. Geometric properties of such vector fields on contact manifolds are characterized after introducing a metric tensor field on a contact manifold. It is also shown that a contact manifold and a strictly convex function induce a lower dimensional dually flat space used in information geometry where a geometrization of equilibrium statistical mechanics is constructed. Legendre duality on contact manifolds is explicitly stated throughout.« less

Splitting of inviscid fluxes for real gases

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing; Vanleer, Bram; Shuen, Jian-Shun

1988-01-01

Flux-vector and flux-difference splittings for the inviscid terms of the compressible flow equations are derived under the assumption of a general equation of state for a real gas in equilibrium. No necessary assumptions, approximations or auxiliary quantities are introduced. The formulas derived include several particular cases known for ideal gases and readily apply to curvilinear coordinates. Applications of the formulas in a TVD algorithm to one-dimensional shock-tube and nozzle problems show their quality and robustness.

Splitting of inviscid fluxes for real gases

NASA Technical Reports Server (NTRS)

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

1990-01-01

Flux-vector and flux-difference splittings for the inviscid terms of the compressible flow equations are derived under the assumption of a general equation of state for a real gas in equilibrium. No necessary assumptions, approximations for auxiliary quantities are introduced. The formulas derived include several particular cases known for ideal gases and readily apply to curvilinear coordinates. Applications of the formulas in a TVD algorithm to one-dimensional shock-tube and nozzle problems show their quality and robustness.

Density-dependent host choice by disease vectors: epidemiological implications of the ideal free distribution.

PubMed

Basáñez, María-Gloria; Razali, Karina; Renz, Alfons; Kelly, David

2007-03-01

The proportion of vector blood meals taken on humans (the human blood index, h) appears as a squared term in classical expressions of the basic reproduction ratio (R(0)) for vector-borne infections. Consequently, R(0) varies non-linearly with h. Estimates of h, however, constitute mere snapshots of a parameter that is predicted, from evolutionary theory, to vary with vector and host abundance. We test this prediction using a population dynamics model of river blindness assuming that, before initiation of vector control or chemotherapy, recorded measures of vector density and human infection accurately represent endemic equilibrium. We obtain values of h that satisfy the condition that the effective reproduction ratio (R(e)) must equal 1 at equilibrium. Values of h thus obtained decrease with vector density, decrease with the vector:human ratio and make R(0) respond non-linearly rather than increase linearly with vector density. We conclude that if vectors are less able to obtain human blood meals as their density increases, antivectorial measures may not lead to proportional reductions in R(0) until very low vector levels are achieved. Density dependence in the contact rate of infectious diseases transmitted by insects may be an important non-linear process with implications for their epidemiology and control.

Vaccination strategies for SIR vector-transmitted diseases.

PubMed

Cruz-Pacheco, Gustavo; Esteva, Lourdes; Vargas, Cristobal

2014-08-01

Vector-borne diseases are one of the major public health problems in the world with the fastest spreading rate. Control measures have been focused on vector control, with poor results in most cases. Vaccines should help to reduce the diseases incidence, but vaccination strategies should also be defined. In this work, we propose a vector-transmitted SIR disease model with age-structured population subject to a vaccination program. We find an expression for the age-dependent basic reproductive number R(0), and we show that the disease-free equilibrium is locally stable for R(0) ≤ 1, and a unique endemic equilibrium exists for R(0) > 1. We apply the theoretical results to public data to evaluate vaccination strategies, immunization levels, and optimal age of vaccination for dengue disease.

User's guide for vectorized code EQUIL for calculating equilibrium chemistry on Control Data STAR-100 computer

NASA Technical Reports Server (NTRS)

Kumar, A.; Graves, R. A., Jr.; Weilmuenster, K. J.

1980-01-01

A vectorized code, EQUIL, was developed for calculating the equilibrium chemistry of a reacting gas mixture on the Control Data STAR-100 computer. The code provides species mole fractions, mass fractions, and thermodynamic and transport properties of the mixture for given temperature, pressure, and elemental mass fractions. The code is set up for the electrons H, He, C, O, N system of elements. In all, 24 chemical species are included.

Hybrid state vector methods for structural dynamic and aeroelastic boundary value problems

NASA Technical Reports Server (NTRS)

Lehman, L. L.

1982-01-01

A computational technique is developed that is suitable for performing preliminary design aeroelastic and structural dynamic analyses of large aspect ratio lifting surfaces. The method proves to be quite general and can be adapted to solving various two point boundary value problems. The solution method, which is applicable to both fixed and rotating wing configurations, is based upon a formulation of the structural equilibrium equations in terms of a hybrid state vector containing generalized force and displacement variables. A mixed variational formulation is presented that conveniently yields a useful form for these state vector differential equations. Solutions to these equations are obtained by employing an integrating matrix method. The application of an integrating matrix provides a discretization of the differential equations that only requires solutions of standard linear matrix systems. It is demonstrated that matrix partitioning can be used to reduce the order of the required solutions. Results are presented for several example problems in structural dynamics and aeroelasticity to verify the technique and to demonstrate its use. These problems examine various types of loading and boundary conditions and include aeroelastic analyses of lifting surfaces constructed from anisotropic composite materials.

Formation of magnetic discontinuities through viscous relaxation

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

Kumar, Sanjay; Bhattacharyya, R.; Smolarkiewicz, P. K.

2014-05-15

According to Parker's magnetostatic theorem, tangential discontinuities in magnetic field, or current sheets (CSs), are generally unavoidable in an equilibrium magnetofluid with infinite electrical conductivity and complex magnetic topology. These CSs are due to a failure of a magnetic field in achieving force-balance everywhere and preserving its topology while remaining in a spatially continuous state. A recent work [Kumar, Bhattacharyya, and Smolarkiewicz, Phys. Plasmas 20, 112903 (2013)] demonstrated this CS formation utilizing numerical simulations in terms of the vector magnetic field. The magnetohydrodynamic simulations presented here complement the above work by demonstrating CS formation by employing a novel approach ofmore » describing the magnetofluid evolution in terms of magnetic flux surfaces instead of the vector magnetic field. The magnetic flux surfaces being the possible sites on which CSs develop, this approach provides a direct visualization of the CS formation, helpful in understanding the governing dynamics. The simulations confirm development of tangential discontinuities through a favorable contortion of magnetic flux surfaces, as the magnetofluid undergoes a topology-preserving viscous relaxation from an initial non-equilibrium state with twisted magnetic field. A crucial finding of this work is in its demonstration of CS formation at spatial locations away from the magnetic nulls.« less

Well-posed two-temperature constitutive equations for stable dense fluid shock waves using molecular dynamics and generalizations of Navier-Stokes-Fourier continuum mechanics.

PubMed

Hoover, Wm G; Hoover, Carol G

2010-04-01

Guided by molecular dynamics simulations, we generalize the Navier-Stokes-Fourier constitutive equations and the continuum motion equations to include both transverse and longitudinal temperatures. To do so we partition the contributions of the heat transfer, the work done, and the heat flux vector between the longitudinal and transverse temperatures. With shockwave boundary conditions time-dependent solutions of these equations converge to give stationary shockwave profiles. The profiles include anisotropic temperature and can be fitted to molecular dynamics results, demonstrating the utility and simplicity of a two-temperature description of far-from-equilibrium states.

Dielectric permeability tensor and linear waves in spin-1/2 quantum kinetics with non-trivial equilibrium spin-distribution functions

NASA Astrophysics Data System (ADS)

Andreev, Pavel A.; Kuz'menkov, L. S.

2017-11-01

A consideration of waves propagating parallel to the external magnetic field is presented. The dielectric permeability tensor is derived from the quantum kinetic equations with non-trivial equilibrium spin-distribution functions in the linear approximation on the amplitude of wave perturbations. It is possible to consider the equilibrium spin-distribution functions with nonzero z-projection proportional to the difference of the Fermi steps of electrons with the chosen spin direction, while x- and y-projections are equal to zero. It is called the trivial equilibrium spin-distribution functions. In the general case, x- and y-projections of the spin-distribution functions are nonzero which is called the non-trivial regime. A corresponding equilibrium solution is found in Andreev [Phys. Plasmas 23, 062103 (2016)]. The contribution of the nontrivial part of the spin-distribution function appears in the dielectric permeability tensor in the additive form. It is explicitly found here. A corresponding modification in the dispersion equation for the transverse waves is derived. The contribution of the nontrivial part of the spin-distribution function in the spectrum of transverse waves is calculated numerically. It is found that the term caused by the nontrivial part of the spin-distribution function can be comparable with the classic terms for the relatively small wave vectors and frequencies above the cyclotron frequency. In a majority of regimes, the extra spin caused term dominates over the spin term found earlier, except the small frequency regime, where their contributions in the whistler spectrum are comparable. A decrease of the left-hand circularly polarized wave frequency, an increase of the high-frequency right-hand circularly polarized wave frequency, and a decrease of frequency changing by an increase of frequency at the growth of the wave vector for the whistler are found. A considerable decrease of the spin wave frequency is found either. It results in an increase of module of the negative group velocity of the spin wave. The found dispersion equations are used for obtaining of an effective quantum hydrodynamics reproducing these results. This generalization requires the introduction of the corresponding equation of state for the thermal part of the spin current in the spin evolution equation.

MHD thrust vectoring of a rocket engine

NASA Astrophysics Data System (ADS)

Labaune, Julien; Packan, Denis; Tholin, Fabien; Chemartin, Laurent; Stillace, Thierry; Masson, Frederic

2016-09-01

In this work, the possibility to use MagnetoHydroDynamics (MHD) to vectorize the thrust of a solid propellant rocket engine exhaust is investigated. Using a magnetic field for vectoring offers a mass gain and a reusability advantage compared to standard gimbaled, elastomer-joint systems. Analytical and numerical models were used to evaluate the flow deviation with a 1 Tesla magnetic field inside the nozzle. The fluid flow in the resistive MHD approximation is calculated using the KRONOS code from ONERA, coupling the hypersonic CFD platform CEDRE and the electrical code SATURNE from EDF. A critical parameter of these simulations is the electrical conductivity, which was evaluated using a set of equilibrium calculations with 25 species. Two models were used: local thermodynamic equilibrium and frozen flow. In both cases, chlorine captures a large fraction of free electrons, limiting the electrical conductivity to a value inadequate for thrust vectoring applications. However, when using chlorine-free propergols with 1% in mass of alkali, an MHD thrust vectoring of several degrees was obtained.

Differential renormalization-group generators for static and dynamic critical phenomena

NASA Astrophysics Data System (ADS)

Chang, T. S.; Vvedensky, D. D.; Nicoll, J. F.

1992-09-01

The derivation of differential renormalization-group (DRG) equations for applications to static and dynamic critical phenomena is reviewed. The DRG approach provides a self-contained closed-form representation of the Wilson renormalization group (RG) and should be viewed as complementary to the Callan-Symanzik equations used in field-theoretic approaches to the RG. The various forms of DRG equations are derived to illustrate the general mathematical structure of each approach and to point out the advantages and disadvantages for performing practical calculations. Otherwise, the review focuses upon the one-particle-irreducible DRG equations derived by Nicoll and Chang and by Chang, Nicoll, and Young; no attempt is made to provide a general treatise of critical phenomena. A few specific examples are included to illustrate the utility of the DRG approach: the large- n limit of the classical n-vector model (the spherical model), multi- or higher-order critical phenomena, and crit ical dynamics far from equilibrium. The large- n limit of the n-vector model is used to introduce the application of DRG equations to a well-known example, with exact solution obtained for the nonlinear trajectories, generating functions for nonlinear scaling fields, and the equation of state. Trajectory integrals and nonlinear scaling fields within the framework of ɛ-expansions are then discussed for tricritical crossover, and briefly for certain aspects of multi- or higher-order critical points, including the derivation of the Helmholtz free energy and the equation of state. The discussion then turns to critical dynamics with a development of the path integral formulation for general dynamic processes. This is followed by an application to a model far-from-equilibrium system that undergoes a phase transformation analogous to a second-order critical point, the Schlögl model for a chemical instability.

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

NASA Technical Reports Server (NTRS)

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

2001-01-01

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

Electromagnetic fluctuation spectra of collective oscillations in magnetized Maxwellian plasmas for parallel wave vectors

NASA Astrophysics Data System (ADS)

Vafin, S.; Schlickeiser, R.; Yoon, P. H.

2016-05-01

The general electromagnetic fluctuation theory for magnetized plasmas is used to calculate the steady-state wave number spectra and total electromagnetic field strength of low-frequency collective weakly damped eigenmodes with parallel wavevectors in a Maxwellian electron-proton plasma. These result from the equilibrium of spontaneous emission and collisionless damping, and they represent the minimum electromagnetic fluctuations guaranteed in quiet thermal space plasmas, including the interstellar and interplanetary medium. Depending on the plasma beta, the ratio of |δB |/B0 can be as high as 10-12 .

Comparative study of high-resolution shock-capturing schemes for a real gas

NASA Technical Reports Server (NTRS)

Montagne, J.-L.; Yee, H. C.; Vinokur, M.

1987-01-01

Recently developed second-order explicit shock-capturing methods, in conjunction with generalized flux-vector splittings, and a generalized approximate Riemann solver for a real gas are studied. The comparisons are made on different one-dimensional Riemann (shock-tube) problems for equilibrium air with various ranges of Mach numbers, densities and pressures. Six different Riemann problems are considered. These tests provide a check on the validity of the generalized formulas, since theoretical prediction of their properties appears to be difficult because of the non-analytical form of the state equation. The numerical results in the supersonic and low-hypersonic regimes indicate that these produce good shock-capturing capability and that the shock resolution is only slightly affected by the state equation of equilibrium air. The difference in shock resolution between the various methods varies slightly from one Riemann problem to the other, but the overall accuracy is very similar. For the one-dimensional case, the relative efficiency in terms of operation count for the different methods is within 30%. The main difference between the methods lies in their versatility in being extended to multidimensional problems with efficient implicit solution procedures.

Variational Koopman models: Slow collective variables and molecular kinetics from short off-equilibrium simulations

NASA Astrophysics Data System (ADS)

Wu, Hao; Nüske, Feliks; Paul, Fabian; Klus, Stefan; Koltai, Péter; Noé, Frank

2017-04-01

Markov state models (MSMs) and master equation models are popular approaches to approximate molecular kinetics, equilibria, metastable states, and reaction coordinates in terms of a state space discretization usually obtained by clustering. Recently, a powerful generalization of MSMs has been introduced, the variational approach conformation dynamics/molecular kinetics (VAC) and its special case the time-lagged independent component analysis (TICA), which allow us to approximate slow collective variables and molecular kinetics by linear combinations of smooth basis functions or order parameters. While it is known how to estimate MSMs from trajectories whose starting points are not sampled from an equilibrium ensemble, this has not yet been the case for TICA and the VAC. Previous estimates from short trajectories have been strongly biased and thus not variationally optimal. Here, we employ the Koopman operator theory and the ideas from dynamic mode decomposition to extend the VAC and TICA to non-equilibrium data. The main insight is that the VAC and TICA provide a coefficient matrix that we call Koopman model, as it approximates the underlying dynamical (Koopman) operator in conjunction with the basis set used. This Koopman model can be used to compute a stationary vector to reweight the data to equilibrium. From such a Koopman-reweighted sample, equilibrium expectation values and variationally optimal reversible Koopman models can be constructed even with short simulations. The Koopman model can be used to propagate densities, and its eigenvalue decomposition provides estimates of relaxation time scales and slow collective variables for dimension reduction. Koopman models are generalizations of Markov state models, TICA, and the linear VAC and allow molecular kinetics to be described without a cluster discretization.

The distribution of the zeros of the Hermite-Padé polynomials for a pair of functions forming a Nikishin system

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

Rakhmanov, E A; Suetin, S P

2013-09-30

The distribution of the zeros of the Hermite-Padé polynomials of the first kind for a pair of functions with an arbitrary even number of common branch points lying on the real axis is investigated under the assumption that this pair of functions forms a generalized complex Nikishin system. It is proved (Theorem 1) that the zeros have a limiting distribution, which coincides with the equilibrium measure of a certain compact set having the S-property in a harmonic external field. The existence problem for S-compact sets is solved in Theorem 2. The main idea of the proof of Theorem 1 consists in replacing a vector equilibrium problem in potentialmore » theory by a scalar problem with an external field and then using the general Gonchar-Rakhmanov method, which was worked out in the solution of the '1/9'-conjecture. The relation of the result obtained here to some results and conjectures due to Nuttall is discussed. Bibliography: 51 titles.« less

Vector-borne diseases models with residence times - A Lagrangian perspective.

PubMed

Bichara, Derdei; Castillo-Chavez, Carlos

2016-11-01

A multi-patch and multi-group modeling framework describing the dynamics of a class of diseases driven by the interactions between vectors and hosts structured by groups is formulated. Hosts' dispersal is modeled in terms of patch-residence times with the nonlinear dynamics taking into account the effective patch-host size. The residence times basic reproduction number R 0 is computed and shown to depend on the relative environmental risk of infection. The model is robust, that is, the disease free equilibrium is globally asymptotically stable (GAS) if R 0 ≤1 and a unique interior endemic equilibrium is shown to exist that is GAS whenever R 0 >1 whenever the configuration of host-vector interactions is irreducible. The effects of patchiness and groupness, a measure of host-vector heterogeneous structure, on the basic reproduction number R 0 , are explored. Numerical simulations are carried out to highlight the effects of residence times on disease prevalence. Copyright © 2016 Elsevier Inc. All rights reserved.

Conservative-variable average states for equilibrium gas multi-dimensional fluxes

NASA Technical Reports Server (NTRS)

Iannelli, G. S.

1992-01-01

Modern split component evaluations of the flux vector Jacobians are thoroughly analyzed for equilibrium-gas average-state determinations. It is shown that all such derivations satisfy a fundamental eigenvalue consistency theorem. A conservative-variable average state is then developed for arbitrary equilibrium-gas equations of state and curvilinear-coordinate fluxes. Original expressions for eigenvalues, sound speed, Mach number, and eigenvectors are then determined for a general average Jacobian, and it is shown that the average eigenvalues, Mach number, and eigenvectors may not coincide with their classical pointwise counterparts. A general equilibrium-gas equation of state is then discussed for conservative-variable computational fluid dynamics (CFD) Euler formulations. The associated derivations lead to unique compatibility relations that constrain the pressure Jacobian derivatives. Thereafter, alternative forms for the pressure variation and average sound speed are developed in terms of two average pressure Jacobian derivatives. Significantly, no additional degree of freedom exists in the determination of these two average partial derivatives of pressure. Therefore, they are simultaneously computed exactly without any auxiliary relation, hence without any geometric solution projection or arbitrary scale factors. Several alternative formulations are then compared and key differences highlighted with emphasis on the determination of the pressure variation and average sound speed. The relevant underlying assumptions are identified, including some subtle approximations that are inherently employed in published average-state procedures. Finally, a representative test case is discussed for which an intrinsically exact average state is determined. This exact state is then compared with the predictions of recent methods, and their inherent approximations are appropriately quantified.

Effects of energy conservation on equilibrium properties of hot asymmetric nuclear matter

NASA Astrophysics Data System (ADS)

Zhang, Zhen; Ko, Che Ming

2018-01-01

Based on the relativistic Vlasov-Uehling-Uhlenbeck transport model, which includes relativistic scalar and vector potentials on baryons, we consider an N -Δ -π system in a box with periodic boundary conditions to study the effects of energy conservation in particle production and absorption processes on the equilibrium properties of the system. The density and temperature of the matter in the box are taken to be similar to the hot dense matter formed in heavy ion collisions at intermediate energies. We find that to maintain the equilibrium numbers of N ,Δ , and π , which depend on the mean-field potentials of N and Δ , we must include these potentials in the energy conservation condition that determines the momenta of outgoing particles after a scattering or decay process. We further find that the baryon scalar potentials mainly affect the Δ and pion equilibrium numbers, while the baryon vector potentials have considerable effect on the effective charged pion ratio at equilibrium. Our results thus indicate that it is essential to include in the transport model the effect of potentials in the energy conservation of a scattering or decay process, which is ignored in most transport models, for studying pion production in heavy ion collisions.

Thrust and torque vector characteristics of axially-symmetric E-sail

NASA Astrophysics Data System (ADS)

Bassetto, Marco; Mengali, Giovanni; Quarta, Alessandro A.

2018-05-01

The Electric Solar Wind Sail is an innovative propulsion system concept that gains propulsive acceleration from the interaction with charged particles released by the Sun. The aim of this paper is to obtain analytical expressions for the thrust and torque vectors of a spinning sail of given shape. Under the only assumption that each tether belongs to a plane containing the spacecraft spin axis, a general analytical relation is found for the thrust and torque vectors as a function of the spacecraft attitude relative to an orbital reference frame. The results are then applied to the noteworthy situation of a Sun-facing sail, that is, when the spacecraft spin axis is aligned with the Sun-spacecraft line, which approximatively coincides with the solar wind direction. In that case, the paper discusses the equilibrium shape of the generic conducting tether as a function of the sail geometry and the spin rate, using both a numerical and an analytical (approximate) approach. As a result, the structural characteristics of the conducting tether are related to the spacecraft geometric parameters.

Multi-stage Vector-Borne Zoonoses Models: A Global Analysis.

PubMed

Bichara, Derdei; Iggidr, Abderrahman; Smith, Laura

2018-04-25

A class of models that describes the interactions between multiple host species and an arthropod vector is formulated and its dynamics investigated. A host-vector disease model where the host's infection is structured into n stages is formulated and a complete global dynamics analysis is provided. The basic reproduction number acts as a sharp threshold, that is, the disease-free equilibrium is globally asymptotically stable (GAS) whenever [Formula: see text] and that a unique interior endemic equilibrium exists and is GAS if [Formula: see text]. We proceed to extend this model with m host species, capturing a class of zoonoses where the cross-species bridge is an arthropod vector. The basic reproduction number of the multi-host-vector, [Formula: see text], is derived and shown to be the sum of basic reproduction numbers of the model when each host is isolated with an arthropod vector. It is shown that the disease will persist in all hosts as long as it persists in one host. Moreover, the overall basic reproduction number increases with respect to the host and that bringing the basic reproduction number of each isolated host below unity in each host is not sufficient to eradicate the disease in all hosts. This is a type of "amplification effect," that is, for the considered vector-borne zoonoses, the increase in host diversity increases the basic reproduction number and therefore the disease burden.

A Progression of Static Equilibrium Laboratory Exercises

NASA Astrophysics Data System (ADS)

Kutzner, Mickey; Kutzner, Andrew

2013-10-01

Although simple architectural structures like bridges, catwalks, cantilevers, and Stonehenge have been integral in human societies for millennia, as have levers and other simple tools, modern students of introductory physics continue to grapple with Newton's conditions for static equilibrium. As formulated in typical introductory physics textbooks, these two conditions appear as ΣF=0(1) and Στ=0,(2) where each torque τ is defined as the cross product between the lever arm vector r and the corresponding applied force F, τ =r×F,(3) having magnitude, τ =Frsinθ.(4) The angle θ here is between the two vectors F and r. In Eq. (1), upward (downward) forces are considered positive (negative). In Eq. (2), counterclockwise (clockwise) torques are considered positive (negative). Equation (1) holds that the vector sum of the external forces acting on an object must be zero to prevent linear accelerations; Eq. (2) states that the vector sum of torques due to external forces about any axis must be zero to prevent angular accelerations. In our view these conditions can be problematic for students because a) the equations contain the unfamiliar summation notation Σ, b) students are uncertain of the role of torques in causing rotations, and c) it is not clear why the sum of torques is zero regardless of the choice of axis. Gianino5 describes an experiment using MBL and a force sensor to convey the meaning of torque as applied to a rigid-body lever system without exploring quantitative aspects of the conditions for static equilibrium.

Thermodynamic equilibrium with acceleration and the Unruh effect

NASA Astrophysics Data System (ADS)

Becattini, F.

2018-04-01

We address the problem of thermodynamic equilibrium with constant acceleration along the velocity field lines in a quantum relativistic statistical mechanics framework. We show that for a free scalar quantum field, after vacuum subtraction, all mean values vanish when the local temperature T is as low as the Unruh temperature TU=A /2 π where A is the magnitude of the acceleration four-vector. We argue that the Unruh temperature is an absolute lower bound for the temperature of any accelerated fluid at global thermodynamic equilibrium. We discuss the conditions of this bound to be applicable in a local thermodynamic equilibrium situation.

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

PubMed

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.

A Class of High-Resolution Explicit and Implicit Shock-Capturing Methods

NASA Technical Reports Server (NTRS)

Yee, H. C.

1994-01-01

The development of shock-capturing finite difference methods for hyperbolic conservation laws has been a rapidly growing area for the last decade. Many of the fundamental concepts, state-of-the-art developments and applications to fluid dynamics problems can only be found in meeting proceedings, scientific journals and internal reports. This paper attempts to give a unified and generalized formulation of a class of high-resolution, explicit and implicit shock capturing methods, and to illustrate their versatility in various steady and unsteady complex shock waves, perfect gases, equilibrium real gases and nonequilibrium flow computations. These numerical methods are formulated for the purpose of ease and efficient implementation into a practical computer code. The various constructions of high-resolution shock-capturing methods fall nicely into the present framework and a computer code can be implemented with the various methods as separate modules. Included is a systematic overview of the basic design principle of the various related numerical methods. Special emphasis will be on the construction of the basic nonlinear, spatially second and third-order schemes for nonlinear scalar hyperbolic conservation laws and the methods of extending these nonlinear scalar schemes to nonlinear systems via the approximate Riemann solvers and flux-vector splitting approaches. Generalization of these methods to efficiently include real gases and large systems of nonequilibrium flows will be discussed. Some perbolic conservation laws to problems containing stiff source terms and terms and shock waves are also included. The performance of some of these schemes is illustrated by numerical examples for one-, two- and three-dimensional gas-dynamics problems. The use of the Lax-Friedrichs numerical flux to obtain high-resolution shock-capturing schemes is generalized. This method can be extended to nonlinear systems of equations without the use of Riemann solvers or flux-vector splitting approaches and thus provides a large savings for multidimensional, equilibrium real gases and nonequilibrium flow computations.

The NEUF-DIX space project - Non-EquilibriUm Fluctuations during DIffusion in compleX liquids.

PubMed

Baaske, Philipp; Bataller, Henri; Braibanti, Marco; Carpineti, Marina; Cerbino, Roberto; Croccolo, Fabrizio; Donev, Aleksandar; Köhler, Werner; Ortiz de Zárate, José M; Vailati, Alberto

2016-12-01

Diffusion and thermal diffusion processes in a liquid mixture are accompanied by long-range non-equilibrium fluctuations, whose amplitude is orders of magnitude larger than that of equilibrium fluctuations. The mean-square amplitude of the non-equilibrium fluctuations presents a scale-free power law behavior q -4 as a function of the wave vector q, but the divergence of the amplitude of the fluctuations at small wave vectors is prevented by the presence of gravity. In microgravity conditions the non-equilibrium fluctuations are fully developed and span all the available length scales up to the macroscopic size of the systems in the direction parallel to the applied gradient. Available theoretical models are based on linearized hydrodynamics and provide an adequate description of the statics and dynamics of the fluctuations in the presence of small temperature/concentration gradients and under stationary or quasi-stationary conditions. We describe a project aimed at the investigation of Non-EquilibriUm Fluctuations during DIffusion in compleX liquids (NEUF-DIX). The focus of the project is on the investigation in micro-gravity conditions of the non-equilibrium fluctuations in complex liquids, trying to tackle several challenging problems that emerged during the latest years, such as the theoretical predictions of Casimir-like forces induced by non-equilibrium fluctuations; the understanding of the non-equilibrium fluctuations in multi-component mixtures including a polymer, both in relation to the transport coefficients and to their behavior close to a glass transition; the understanding of the non-equilibrium fluctuations in concentrated colloidal suspensions, a problem closely related with the detection of Casimir forces; and the investigation of the development of fluctuations during transient diffusion. We envision to parallel these experiments with state-of-the-art multi-scale simulations.

Global asymptotic stability of plant-seed bank models.

PubMed

Eager, Eric Alan; Rebarber, Richard; Tenhumberg, Brigitte

2014-07-01

Many plant populations have persistent seed banks, which consist of viable seeds that remain dormant in the soil for many years. Seed banks are important for plant population dynamics because they buffer against environmental perturbations and reduce the probability of extinction. Viability of the seeds in the seed bank can depend on the seed's age, hence it is important to keep track of the age distribution of seeds in the seed bank. In this paper we construct a general density-dependent plant-seed bank model where the seed bank is age-structured. We consider density dependence in both seedling establishment and seed production, since previous work has highlighted that overcrowding can suppress both of these processes. Under certain assumptions on the density dependence, we prove that there is a globally stable equilibrium population vector which is independent of the initial state. We derive an analytical formula for the equilibrium population using methods from feedback control theory. We apply these results to a model for the plant species Cirsium palustre and its seed bank.

Comparison of Flux-Surface Aligned Curvilinear Coordinate Systems and Neoclassical Magnetic Field Predictions

NASA Astrophysics Data System (ADS)

Collart, T. G.; Stacey, W. M.

2015-11-01

Several methods are presented for extending the traditional analytic ``circular'' representation of flux-surface aligned curvilinear coordinate systems to more accurately describe equilibrium plasma geometry and magnetic fields in DIII-D. The formalism originally presented by Miller is extended to include different poloidal variations in the upper and lower hemispheres. A coordinate system based on separate Fourier expansions of major radius and vertical position greatly improves accuracy in edge plasma structure representation. Scale factors and basis vectors for a system formed by expanding the circular model minor radius can be represented using linear combinations of Fourier basis functions. A general method for coordinate system orthogonalization is presented and applied to all curvilinear models. A formalism for the magnetic field structure in these curvilinear models is presented, and the resulting magnetic field predictions are compared against calculations performed in a Cartesian system using an experimentally based EFIT prediction for the Grad-Shafranov equilibrium. Supported by: US DOE under DE-FG02-00ER54538.

An implicit flux-split algorithm to calculate hypersonic flowfields in chemical equilibrium

NASA Technical Reports Server (NTRS)

Palmer, Grant

1987-01-01

An implicit, finite-difference, shock-capturing algorithm that calculates inviscid, hypersonic flows in chemical equilibrium is presented. The flux vectors and flux Jacobians are differenced using a first-order, flux-split technique. The equilibrium composition of the gas is determined by minimizing the Gibbs free energy at every node point. The code is validated by comparing results over an axisymmetric hemisphere against previously published results. The algorithm is also applied to more practical configurations. The accuracy, stability, and versatility of the algorithm have been promising.

Stability boundaries for command augmentation systems

NASA Technical Reports Server (NTRS)

Shrivastava, P. C.

1987-01-01

The Stability Augmentation System (SAS) is a special case of the Command Augmentation System (CAS). Control saturation imposes bounds on achievable commands. The state equilibrium depends only on the open loop dynamics and control deflection. The control magnitude to achieve a desired command equilibrium is independent of the feedback gain. A feedback controller provides the desired response, maintains the system equilibrium under disturbances, but it does not affect the equilibrium values of states and control. The saturation boundaries change with commands, but the location of the equilibrium points in the saturated region remains unchanged. Nonzero command vectors yield saturation boundaries that are asymmetric with respect to the state equilibrium. Except for the saddle point case with MCE control law, the stability boundaries change with commands. For the cases of saddle point and unstable nodes, the region of stability decreases with increasing command magnitudes.

Two Introductions of Lyme Disease into Connecticut: A Geospatial Analysis of Human Cases from 1984 to 2012.

PubMed

Xue, Ling; Scoglio, Caterina; McVey, D Scott; Boone, Rebecca; Cohnstaedt, Lee W

2015-09-01

Lyme disease has become the most prevalent vector-borne disease in the United States and results in morbidity in humans, especially children. We used historical case distributions to explain vector-borne disease introductions and subsequent geographic expansion in the absence of disease vector data. We used geographic information system analysis of publicly available Connecticut Department of Public Health case data from 1984, 1985, and 1991 to 2012 for the 169 towns in Connecticut to identify the yearly clusters of Lyme disease cases. Our analysis identified the spatial and temporal origins of two separate introductions of Lyme disease into Connecticut and identified the subsequent direction and rate of spread. We defined both epidemic clusters of cases using significant long-term spatial autocorrelation. The incidence-weighted geographic mean analysis indicates a northern trend of geographic expansion for both epidemic clusters. In eastern Connecticut, as the epidemic progressed, the yearly shift in the geographic mean (rate of epidemic expansion) decreased each year until spatial equilibrium was reached in 2007. The equilibrium indicates a transition from epidemic Lyme disease spread to stable endemic transmission, and we associate this with a reduction in incidence. In western Connecticut, the parabolic distribution of the yearly geographic mean indicates that following the establishment of Lyme disease (1988) the epidemic quickly expanded northward and established equilibrium in 2009.

The multiscale coarse-graining method. II. Numerical implementation for coarse-grained molecular models

PubMed Central

Noid, W. G.; Liu, Pu; Wang, Yanting; Chu, Jhih-Wei; Ayton, Gary S.; Izvekov, Sergei; Andersen, Hans C.; Voth, Gregory A.

2008-01-01

The multiscale coarse-graining (MS-CG) method [S. Izvekov and G. A. Voth, J. Phys. Chem. B 109, 2469 (2005);J. Chem. Phys. 123, 134105 (2005)] employs a variational principle to determine an interaction potential for a CG model from simulations of an atomically detailed model of the same system. The companion paper proved that, if no restrictions regarding the form of the CG interaction potential are introduced and if the equilibrium distribution of the atomistic model has been adequately sampled, then the MS-CG variational principle determines the exact many-body potential of mean force (PMF) governing the equilibrium distribution of CG sites generated by the atomistic model. In practice, though, CG force fields are not completely flexible, but only include particular types of interactions between CG sites, e.g., nonbonded forces between pairs of sites. If the CG force field depends linearly on the force field parameters, then the vector valued functions that relate the CG forces to these parameters determine a set of basis vectors that span a vector subspace of CG force fields. The companion paper introduced a distance metric for the vector space of CG force fields and proved that the MS-CG variational principle determines the CG force force field that is within that vector subspace and that is closest to the force field determined by the many-body PMF. The present paper applies the MS-CG variational principle for parametrizing molecular CG force fields and derives a linear least squares problem for the parameter set determining the optimal approximation to this many-body PMF. Linear systems of equations for these CG force field parameters are derived and analyzed in terms of equilibrium structural correlation functions. Numerical calculations for a one-site CG model of methanol and a molecular CG model of the EMIM+∕NO3− ionic liquid are provided to illustrate the method. PMID:18601325

Dynamic scaling for the growth of non-equilibrium fluctuations during thermophoretic diffusion in microgravity

DOE PAGES

Cerbino, Roberto; Sun, Yifei; Donev, Aleksandar; ...

2015-09-30

Diffusion processes are widespread in biological and chemical systems, where they play a fundamental role in the exchange of substances at the cellular level and in determining the rate of chemical reactions. Recently, the classical picture that portrays diffusion as random uncorrelated motion of molecules has been revised, when it was shown that giant non-equilibrium fluctuations develop during diffusion processes. Under microgravity conditions and at steady-state, non-equilibrium fluctuations exhibit scale invariance and their size is only limited by the boundaries of the system. Here in this work, we investigate the onset of non-equilibrium concentration fluctuations induced by thermophoretic diffusion inmore » microgravity, a regime not accessible to analytical calculations but of great relevance for the understanding of several natural and technological processes. A combination of state of the art simulations and experiments allows us to attain a fully quantitative description of the development of fluctuations during transient diffusion in microgravity. Both experiments and simulations show that during the onset the fluctuations exhibit scale invariance at large wave vectors. In a broader range of wave vectors simulations predict a spinodal-like growth of fluctuations, where the amplitude and length-scale of the dominant mode are determined by the thickness of the diffuse layer.« less

Dynamic scaling for the growth of non-equilibrium fluctuations during thermophoretic diffusion in microgravity

PubMed Central

Cerbino, Roberto; Sun, Yifei; Donev, Aleksandar; Vailati, Alberto

2015-01-01

Diffusion processes are widespread in biological and chemical systems, where they play a fundamental role in the exchange of substances at the cellular level and in determining the rate of chemical reactions. Recently, the classical picture that portrays diffusion as random uncorrelated motion of molecules has been revised, when it was shown that giant non-equilibrium fluctuations develop during diffusion processes. Under microgravity conditions and at steady-state, non-equilibrium fluctuations exhibit scale invariance and their size is only limited by the boundaries of the system. In this work, we investigate the onset of non-equilibrium concentration fluctuations induced by thermophoretic diffusion in microgravity, a regime not accessible to analytical calculations but of great relevance for the understanding of several natural and technological processes. A combination of state of the art simulations and experiments allows us to attain a fully quantitative description of the development of fluctuations during transient diffusion in microgravity. Both experiments and simulations show that during the onset the fluctuations exhibit scale invariance at large wave vectors. In a broader range of wave vectors simulations predict a spinodal-like growth of fluctuations, where the amplitude and length-scale of the dominant mode are determined by the thickness of the diffuse layer. PMID:26419420

Dynamic scaling for the growth of non-equilibrium fluctuations during thermophoretic diffusion in microgravity.

PubMed

Cerbino, Roberto; Sun, Yifei; Donev, Aleksandar; Vailati, Alberto

2015-09-30

Diffusion processes are widespread in biological and chemical systems, where they play a fundamental role in the exchange of substances at the cellular level and in determining the rate of chemical reactions. Recently, the classical picture that portrays diffusion as random uncorrelated motion of molecules has been revised, when it was shown that giant non-equilibrium fluctuations develop during diffusion processes. Under microgravity conditions and at steady-state, non-equilibrium fluctuations exhibit scale invariance and their size is only limited by the boundaries of the system. In this work, we investigate the onset of non-equilibrium concentration fluctuations induced by thermophoretic diffusion in microgravity, a regime not accessible to analytical calculations but of great relevance for the understanding of several natural and technological processes. A combination of state of the art simulations and experiments allows us to attain a fully quantitative description of the development of fluctuations during transient diffusion in microgravity. Both experiments and simulations show that during the onset the fluctuations exhibit scale invariance at large wave vectors. In a broader range of wave vectors simulations predict a spinodal-like growth of fluctuations, where the amplitude and length-scale of the dominant mode are determined by the thickness of the diffuse layer.

A model for the coevolution of immunity and immune evasion in vector-borne diseases with implications for the epidemiology of malaria.

PubMed

Koella, Jacob C; Boëte, C

2003-05-01

We describe a model of host-parasite coevolution, where the interaction depends on the investments by the host in its immune response and by the parasite in its ability to suppress (or evade) its host's immune response. We base our model on the interaction between malaria parasites and their mosquito hosts and thus describe the epidemiological dynamics with the Macdonald-Ross equation of malaria epidemiology. The qualitative predictions of the model are most sensitive to the cost of the immune response and to the intensity of transmission. If transmission is weak or the cost of immunity is low, the system evolves to a coevolutionarily stable equilibrium at intermediate levels of investment (and, generally, at a low frequency of resistance). At a higher cost of immunity and as transmission intensifies, the system is not evolutionarily stable but rather cycles around intermediate levels of investment. At more intense transmission, neither host nor parasite invests any resources in dominating its partner so that no resistance is observed in the population. These results may help to explain the lack of encapsulated malaria parasites generally observed in natural populations of mosquito vectors, despite strong selection pressure for resistance in areas of very intense transmission.

Numerical computation of gravitational field for general axisymmetric objects

NASA Astrophysics Data System (ADS)

Fukushima, Toshio

2016-10-01

We developed a numerical method to compute the gravitational field of a general axisymmetric object. The method (I) numerically evaluates a double integral of the ring potential by the split quadrature method using the double exponential rules, and (II) derives the acceleration vector by numerically differentiating the numerically integrated potential by Ridder's algorithm. Numerical comparison with the analytical solutions for a finite uniform spheroid and an infinitely extended object of the Miyamoto-Nagai density distribution confirmed the 13- and 11-digit accuracy of the potential and the acceleration vector computed by the method, respectively. By using the method, we present the gravitational potential contour map and/or the rotation curve of various axisymmetric objects: (I) finite uniform objects covering rhombic spindles and circular toroids, (II) infinitely extended spheroids including Sérsic and Navarro-Frenk-White spheroids, and (III) other axisymmetric objects such as an X/peanut-shaped object like NGC 128, a power-law disc with a central hole like the protoplanetary disc of TW Hya, and a tear-drop-shaped toroid like an axisymmetric equilibrium solution of plasma charge distribution in an International Thermonuclear Experimental Reactor-like tokamak. The method is directly applicable to the electrostatic field and will be easily extended for the magnetostatic field. The FORTRAN 90 programs of the new method and some test results are electronically available.

An Optimization Principle for Deriving Nonequilibrium Statistical Models of Hamiltonian Dynamics

NASA Astrophysics Data System (ADS)

Turkington, Bruce

2013-08-01

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

Auxiliary principle technique and iterative algorithm for a perturbed system of generalized multi-valued mixed quasi-equilibrium-like problems.

PubMed

Rahaman, Mijanur; Pang, Chin-Tzong; Ishtyak, Mohd; Ahmad, Rais

2017-01-01

In this article, we introduce a perturbed system of generalized mixed quasi-equilibrium-like problems involving multi-valued mappings in Hilbert spaces. To calculate the approximate solutions of the perturbed system of generalized multi-valued mixed quasi-equilibrium-like problems, firstly we develop a perturbed system of auxiliary generalized multi-valued mixed quasi-equilibrium-like problems, and then by using the celebrated Fan-KKM technique, we establish the existence and uniqueness of solutions of the perturbed system of auxiliary generalized multi-valued mixed quasi-equilibrium-like problems. By deploying an auxiliary principle technique and an existence result, we formulate an iterative algorithm for solving the perturbed system of generalized multi-valued mixed quasi-equilibrium-like problems. Lastly, we study the strong convergence analysis of the proposed iterative sequences under monotonicity and some mild conditions. These results are new and generalize some known results in this field.

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

ERIC Educational Resources Information Center

Bindel, Thomas H.

2012-01-01

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

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

NASA Technical Reports Server (NTRS)

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.

Electromagnetic fluctuations for anisotropic media and the generalized Kirchhoff's law

NASA Technical Reports Server (NTRS)

Yueh, Simon H.; Kwok, R.

1993-01-01

In this paper the polarimetric emission parameters for anisotropic media are derived using the generalized Kirchhoff's law for media with a uniform temperature and the fluctuation-dissipation theory for media with a temperature profile. Both finite-size objects and half-space media are considered. When the object has a uniform temperature across its body, the Kirchhoff's law, based on the condition of energy conservation in thermal equilibrium is generalized to obtain the emission parameters of an anisotropic medium, which can be interpreted as the absorptivity or the absorption cross section of the complementary object with a permittivity that is the transpose of the original object. When the medium has a nonuniform temperature distribution, the fluctuation-dissipation theory is applied for deriving the covariances between vector components of the thermal currents and, consequently, the covariances of the polarizations of electric fields radiated by the thermal currents. To verify the formulas derived from the fluctuation-dissipation theory, we let the temperature of the object be a constant and show that the results reduce to those obtained from the generalized Kirchhoff's law.

Entropy Production in Field Theories without Time-Reversal Symmetry: Quantifying the Non-Equilibrium Character of Active Matter

NASA Astrophysics Data System (ADS)

Nardini, Cesare; Fodor, Étienne; Tjhung, Elsen; van Wijland, Frédéric; Tailleur, Julien; Cates, Michael E.

2017-04-01

Active-matter systems operate far from equilibrium because of the continuous energy injection at the scale of constituent particles. At larger scales, described by coarse-grained models, the global entropy production rate S quantifies the probability ratio of forward and reversed dynamics and hence the importance of irreversibility at such scales: It vanishes whenever the coarse-grained dynamics of the active system reduces to that of an effective equilibrium model. We evaluate S for a class of scalar stochastic field theories describing the coarse-grained density of self-propelled particles without alignment interactions, capturing such key phenomena as motility-induced phase separation. We show how the entropy production can be decomposed locally (in real space) or spectrally (in Fourier space), allowing detailed examination of the spatial structure and correlations that underly departures from equilibrium. For phase-separated systems, the local entropy production is concentrated mainly on interfaces, with a bulk contribution that tends to zero in the weak-noise limit. In homogeneous states, we find a generalized Harada-Sasa relation that directly expresses the entropy production in terms of the wave-vector-dependent deviation from the fluctuation-dissipation relation between response functions and correlators. We discuss extensions to the case where the particle density is coupled to a momentum-conserving solvent and to situations where the particle current, rather than the density, should be chosen as the dynamical field. We expect the new conceptual tools developed here to be broadly useful in the context of active matter, allowing one to distinguish when and where activity plays an essential role in the dynamics.

N-Player Quantum Games in an EPR Setting

PubMed Central

Chappell, James M.; Iqbal, Azhar; Abbott, Derek

2012-01-01

The -player quantum games are analyzed that use an Einstein-Podolsky-Rosen (EPR) experiment, as the underlying physical setup. In this setup, a player’s strategies are not unitary transformations as in alternate quantum game-theoretic frameworks, but a classical choice between two directions along which spin or polarization measurements are made. The players’ strategies thus remain identical to their strategies in the mixed-strategy version of the classical game. In the EPR setting the quantum game reduces itself to the corresponding classical game when the shared quantum state reaches zero entanglement. We find the relations for the probability distribution for -qubit GHZ and W-type states, subject to general measurement directions, from which the expressions for the players’ payoffs and mixed Nash equilibrium are determined. Players’ payoff matrices are then defined using linear functions so that common two-player games can be easily extended to the -player case and permit analytic expressions for the Nash equilibrium. As a specific example, we solve the Prisoners’ Dilemma game for general . We find a new property for the game that for an even number of players the payoffs at the Nash equilibrium are equal, whereas for an odd number of players the cooperating players receive higher payoffs. By dispensing with the standard unitary transformations on state vectors in Hilbert space and using instead rotors and multivectors, based on Clifford’s geometric algebra (GA), it is shown how the N-player case becomes tractable. The new mathematical approach presented here has wide implications in the areas of quantum information and quantum complexity, as it opens up a powerful way to tractably analyze N-partite qubit interactions. PMID:22606258

Mathematical model of temephos resistance in Aedes aegypti mosquito population

NASA Astrophysics Data System (ADS)

Aldila, D.; Nuraini, N.; Soewono, E.; Supriatna, A. K.

2014-03-01

Aedes aegypti is the main vector of dengue disease in many tropical and sub-tropical countries. Dengue became major public concern in these countries due to the unavailability of vaccine or drugs for dengue disease in the market. Hence, the only way to control the spread of DF and DHF is by controlling the vectors carrying the disease, for instance with fumigation, temephos or genetic manipulation. Many previous studies conclude that Aedes aegypti may develop resistance to many kind of insecticide, including temephos. Mathematical model for transmission of temephos resistance in Aedes aegypti population is discussed in this paper. Nontrivial equilibrium point of the system and the corresponding existence are shown analytically. The model analysis have shown epidemiological trends condition that permits the coexistence of nontrivial equilibrium is given analytically. Numerical results are given to show parameter sensitivity and some cases of worsening effect values for illustrating possible conditions in the field.

Chaotic Behavior of a Generalized Sprott E Differential System

NASA Astrophysics Data System (ADS)

Oliveira, Regilene; Valls, Claudia

A chaotic system with only one equilibrium, a stable node-focus, was introduced by Wang and Chen [2012]. This system was found by adding a nonzero constant b to the Sprott E system [Sprott, 1994]. The coexistence of three types of attractors in this autonomous system was also considered by Braga and Mello [2013]. Adding a second parameter to the Sprott E differential system, we get the autonomous system ẋ = ayz + b,ẏ = x2 - y,ż = 1 - 4x, where a,b ∈ ℝ are parameters and a≠0. In this paper, we consider theoretically some global dynamical aspects of this system called here the generalized Sprott E differential system. This polynomial differential system is relevant because it is the first polynomial differential system in ℝ3 with two parameters exhibiting, besides the point attractor and chaotic attractor, coexisting stable limit cycles, demonstrating that this system is truly complicated and interesting. More precisely, we show that for b sufficiently small this system can exhibit two limit cycles emerging from the classical Hopf bifurcation at the equilibrium point p = (1/4, 1/16, 0). We also give a complete description of its dynamics on the Poincaré sphere at infinity by using the Poincaré compactification of a polynomial vector field in ℝ3, and we show that it has no first integrals in the class of Darboux functions.

Recent update of the RPLUS2D/3D codes

NASA Technical Reports Server (NTRS)

Tsai, Y.-L. Peter

1991-01-01

The development of the RPLUS2D/3D codes is summarized. These codes utilize LU algorithms to solve chemical non-equilibrium flows in a body-fitted coordinate system. The motivation behind the development of these codes is the need to numerically predict chemical non-equilibrium flows for the National AeroSpace Plane Program. Recent improvements include vectorization method, blocking algorithms for geometric flexibility, out-of-core storage for large-size problems, and an LU-SW/UP combination for CPU-time efficiency and solution quality.

An upwind, kinetic flux-vector splitting method for flows in chemical and thermal non-equilibrium

NASA Technical Reports Server (NTRS)

Eppard, W. M.; Grossman, B.

1993-01-01

We have developed new upwind kinetic difference schemes for flows with non-equilibrium thermodynamics and chemistry. These schemes are derived from the Boltzmann equation with the resulting Euler schemes developed as moments of the discretized Boltzmann scheme with a locally Maxwellian velocity distribution. Splitting the velocity distribution at the Boltzmann level is seen to result in a flux-split Euler scheme and is called Kinetic Flux Vector Splitting (KFVS). Extensions to flows with finite-rate chemistry and vibrational relaxation is accomplished utilizing nonequilibrium kinetic theory. Computational examples are presented comparing KFVS with the schemes of Van Leer and Roe for a quasi-one-dimensional flow through a supersonic diffuser, inviscid flow through two-dimensional inlet, and viscous flow over a cone at zero angle-of-attack. Calculations are also shown for the transonic flow over a bump in a channel and the transonic flow over an NACA 0012 airfoil. The results show that even though the KFVS scheme is a Riemann solver at the kinetic level, its behavior at the Euler level is more similar to the existing flux-vector splitting algorithms than to the flux-difference splitting scheme of Roe.

Equilibrium Spline Interface (ESI) for magnetic confinement codes

NASA Astrophysics Data System (ADS)

Li, Xujing; Zakharov, Leonid E.

2017-12-01

A compact and comprehensive interface between magneto-hydrodynamic (MHD) equilibrium codes and gyro-kinetic, particle orbit, MHD stability, and transport codes is presented. Its irreducible set of equilibrium data consists of three (in the 2-D case with occasionally one extra in the 3-D case) functions of coordinates and four 1-D radial profiles together with their first and mixed derivatives. The C reconstruction routines, accessible also from FORTRAN, allow the calculation of basis functions and their first derivatives at any position inside the plasma and in its vicinity. After this all vector fields and geometric coefficients, required for the above mentioned types of codes, can be calculated using only algebraic operations with no further interpolation or differentiation.

Silk-Elastinlike Copolymers for Breast Cancer Gene Therapy

DTIC Science & Technology

2005-05-01

linearized expression vector were mixed hydrolysis of the sample in 6 N HCI at 110 ’C for 20 h. at a high monomer-to-vector molar ratio in the presence of...measurements were taken for each sample GAGTA(GA(GTGC(GGTGTA(GAGTTCCTGCGATrT’GC( for calculation of q. TAcCAC(;AGTA(;(;CGTACCGCGAGG’AGGAGTGCC(;,GGTC The...P (Pro), proline ; Q (Gln), steps are to examine the influence of polymer molecular glutamine; Q, weight equilibrium swelling ratios of hydrogels

Extending the length and time scales of Gram-Schmidt Lyapunov vector computations

NASA Astrophysics Data System (ADS)

Costa, Anthony B.; Green, Jason R.

2013-08-01

Lyapunov vectors have found growing interest recently due to their ability to characterize systems out of thermodynamic equilibrium. The computation of orthogonal Gram-Schmidt vectors requires multiplication and QR decomposition of large matrices, which grow as N2 (with the particle count). This expense has limited such calculations to relatively small systems and short time scales. Here, we detail two implementations of an algorithm for computing Gram-Schmidt vectors. The first is a distributed-memory message-passing method using Scalapack. The second uses the newly-released MAGMA library for GPUs. We compare the performance of both codes for Lennard-Jones fluids from N=100 to 1300 between Intel Nahalem/Infiniband DDR and NVIDIA C2050 architectures. To our best knowledge, these are the largest systems for which the Gram-Schmidt Lyapunov vectors have been computed, and the first time their calculation has been GPU-accelerated. We conclude that Lyapunov vector calculations can be significantly extended in length and time by leveraging the power of GPU-accelerated linear algebra.

Relativistic distribution function for particles with spin at local thermodynamical equilibrium

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

Becattini, F., E-mail: becattini@fi.infn.it; INFN Sezione di Firenze, Florence; Universität Frankfurt, Frankfurt am Main

2013-11-15

We present an extension of relativistic single-particle distribution function for weakly interacting particles at local thermodynamical equilibrium including spin degrees of freedom, for massive spin 1/2 particles. We infer, on the basis of the global equilibrium case, that at local thermodynamical equilibrium particles acquire a net polarization proportional to the vorticity of the inverse temperature four-vector field. The obtained formula for polarization also implies that a steady gradient of temperature entails a polarization orthogonal to particle momentum. The single-particle distribution function in momentum space extends the so-called Cooper–Frye formula to particles with spin 1/2 and allows us to predict theirmore » polarization in relativistic heavy ion collisions at the freeze-out. -- Highlights: •Single-particle distribution function in local thermodynamical equilibrium with spin. •Polarization of spin 1/2 particles in a fluid at local thermodynamical equilibrium. •Prediction of a new effect: a steady gradient of temperature induces a polarization. •Application to the calculation of polarization in relativistic heavy ion collisions.« less

Reverse Mössbauer effect as a possible source of “hot” molecules absorbed in crystalline solids at low temperature

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

Demontis, Pierfranco; Suffritti, Giuseppe B., E-mail: pino@uniss.it

2016-09-07

As an attempt to explain some of the many anomalies and unresolved problems which have been reported about the dynamic behavior of particles and molecules absorbed in crystalline solids, the “reverse Mössbauer effect” (RME) is proposed. RME theory posits that a particle in non-equilibrium state with respect to a crystal (colliding with the crystal or absorbed in it, but set out of thermal equilibrium by some external cause) is scattered by the whole crystal with a momentum proportional to a vector representing a reciprocal lattice point. The scattering is expected to occur with a well-defined probability and the momentum transferablemore » to the particle is expected to follow a predictable distribution. The RME theory, in practice, is an extension of the Bragg–von Laue scattering law to high-energy colliding particles, in general, and can be applied to any particle or molecule colliding with the surface of a crystalline solid or absorbed in it, but not in thermal equilibrium with the crystal lattice. We verified the RME theory by considering a well-defined unresolved problem. In an experimental study about methane adsorbed in the zeolite Na-ZSM-5 [H. Jobic, Chem. Phys. Lett. 170, 217 (1990)] reporting neutron inelastic-scattering spectra (recoiled bands) at 10 K, the translational kinetic energy of methane resulted to be much higher than equilibrium expected value, namely, about 85 K (or 7.3 meV). The author concluded that “the interpretation of this unusual behavior has yet to be found.” In the present study, on the basis of the RME, an explanation of this behavior is put forward.« less

The Gibbs Variational Method in Thermodynamics of Equilibrium Plasma: 1. General Conditions of Equilibrium and Stability for One-Component Charged Gas

DTIC Science & Technology

2018-04-01

systems containing ionized gases. 2. Gibbs Method in the Integral Form As per the Gibbs general methodology , based on the concept of heterogeneous...ARL-TR-8348 ● APR 2018 US Army Research Laboratory The Gibbs Variational Method in Thermodynamics of Equilibrium Plasma: 1...ARL-TR-8348 ● APR 2018 US Army Research Laboratory The Gibbs Variational Method in Thermodynamics of Equilibrium Plasma: 1. General

Generalized Poisson-Kac Processes: Basic Properties and Implications in Extended Thermodynamics and Transport

NASA Astrophysics Data System (ADS)

Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro

2016-04-01

We introduce a new class of stochastic processes in Rn,{{{mathbb R}}^n}, referred to as generalized Poisson-Kac (GPK) processes, that generalizes the Poisson-Kac telegrapher's random motion in higher dimensions. These stochastic processes possess finite propagation velocity, almost everywhere smooth trajectories, and converge in the Kac limit to Brownian motion. GPK processes are defined by coupling the selection of a bounded velocity vector from a family of N distinct ones with a Markovian dynamics controlling probabilistically this selection. This model can be used as a probabilistic tool for a stochastically consistent formulation of extended thermodynamic theories far from equilibrium.

Artificial equilibrium points for a generalized sail in the elliptic restricted three-body problem

NASA Astrophysics Data System (ADS)

Aliasi, Generoso; Mengali, Giovanni; Quarta, Alessandro A.

2012-10-01

Different types of propulsion systems with continuous and purely radial thrust, whose modulus depends on the distance from a massive body, may be conveniently described within a single mathematical model by means of the concept of generalized sail. This paper discusses the existence and stability of artificial equilibrium points maintained by a generalized sail within an elliptic restricted three-body problem. Similar to the classical case in the absence of thrust, a generalized sail guarantees the existence of equilibrium points belonging only to the orbital plane of the two primaries. The geometrical loci of existing artificial equilibrium points are shown to coincide with those obtained for the circular three body problem when a non-uniformly rotating and pulsating coordinate system is chosen to describe the spacecraft motion. However, the generalized sail has to provide a periodically variable acceleration to maintain a given artificial equilibrium point. A linear stability analysis of the artificial equilibrium points is provided by means of the Floquet theory.

Description of the General Equilibrium Model of Ecosystem Services (GEMES)

Treesearch

Travis Warziniack; David Finnoff; Jenny Apriesnig

2017-01-01

This paper serves as documentation for the General Equilibrium Model of Ecosystem Services (GEMES). GEMES is a regional computable general equilibrium model that is composed of values derived from natural capital and ecosystem services. It models households, producing sectors, and governments, linked to one another through commodity and factor markets. GEMES was...

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

NASA Astrophysics Data System (ADS)

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.

Gyrokinetic Magnetohydrodynamics and the Associated Equilibrium

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

A class of high resolution explicit and implicit shock-capturing methods

NASA Technical Reports Server (NTRS)

Yee, H. C.

1989-01-01

An attempt is made to give a unified and generalized formulation of a class of high resolution, explicit and implicit shock capturing methods, and to illustrate their versatility in various steady and unsteady complex shock wave computations. Included is a systematic review of the basic design principle of the various related numerical methods. Special emphasis is on the construction of the basis nonlinear, spatially second and third order schemes for nonlinear scalar hyperbolic conservation laws and the methods of extending these nonlinear scalar schemes to nonlinear systems via the approximate Riemann solvers and the flux vector splitting approaches. Generalization of these methods to efficiently include equilibrium real gases and large systems of nonequilibrium flows are discussed. Some issues concerning the applicability of these methods that were designed for homogeneous hyperbolic conservation laws to problems containing stiff source terms and shock waves are also included. The performance of some of these schemes is illustrated by numerical examples for 1-, 2- and 3-dimensional gas dynamics problems.

Convergence of neural networks for programming problems via a nonsmooth Lojasiewicz inequality.

PubMed

Forti, Mauro; Nistri, Paolo; Quincampoix, Marc

2006-11-01

This paper considers a class of neural networks (NNs) for solving linear programming (LP) problems, convex quadratic programming (QP) problems, and nonconvex QP problems where an indefinite quadratic objective function is subject to a set of affine constraints. The NNs are characterized by constraint neurons modeled by ideal diodes with vertical segments in their characteristic, which enable to implement an exact penalty method. A new method is exploited to address convergence of trajectories, which is based on a nonsmooth Lojasiewicz inequality for the generalized gradient vector field describing the NN dynamics. The method permits to prove that each forward trajectory of the NN has finite length, and as a consequence it converges toward a singleton. Furthermore, by means of a quantitative evaluation of the Lojasiewicz exponent at the equilibrium points, the following results on convergence rate of trajectories are established: (1) for nonconvex QP problems, each trajectory is either exponentially convergent, or convergent in finite time, toward a singleton belonging to the set of constrained critical points; (2) for convex QP problems, the same result as in (1) holds; moreover, the singleton belongs to the set of global minimizers; and (3) for LP problems, each trajectory converges in finite time to a singleton belonging to the set of global minimizers. These results, which improve previous results obtained via the Lyapunov approach, are true independently of the nature of the set of equilibrium points, and in particular they hold even when the NN possesses infinitely many nonisolated equilibrium points.

A generalized graph-theoretical matrix of heterosystems and its application to the VMV procedure.

PubMed

Mozrzymas, Anna

2011-12-14

The extensions of generalized (molecular) graph-theoretical matrix and vector-matrix-vector procedure are considered. The elements of the generalized matrix are redefined in order to describe molecules containing heteroatoms and multiple bonds. The adjacency, distance, detour and reciprocal distance matrices of heterosystems, and corresponding vectors are derived from newly defined generalized graph matrix. The topological indices, which are most widely used in predicting physicochemical and biological properties/activities of various compounds, can be calculated from the new generalized vector-matrix-vector invariant. Copyright © 2011 Elsevier Ltd. All rights reserved.

Innovative Interactive Lecture Demonstrations Using Wireless Force Sensors and Accelerometers for Introductory Physics Courses

NASA Astrophysics Data System (ADS)

Yoder, G.; Cook, J.

2010-12-01

Interactive lecture demonstrations1-6 (ILDs) are a powerful tool designed to help instructors bring state-of-the-art teaching pedagogies into the college-level introductory physics classroom. ILDs have been shown to improve students' conceptual understanding, and many examples have been created and published by Sokoloff and Thornton.6 We have used the new technology of Vernier's Wireless Dynamics Sensor System (WDSS)7 to develop three new ILDs for the first-semester introductory physics (calculus-based or algebra-based) classroom. These three are the Force Board, to demonstrate the vector nature of forces, addition of vectors, and the first condition of equilibrium; the Torque Board, to demonstrate torque and the second condition for equilibrium; and the Circular Motion Board, to discover the nature of the acceleration an object exhibiting uniform circular motion. With the WDSS, all three of these ILDs are easy to set up and use in any classroom or laboratory situation, and allow more instructors to utilize the technique of interactive lecture demonstrations.

Non-Equilibrium Green’s Function Study of Transport in Disordered Double-Layer Graphene Systems

DTIC Science & Technology

2011-01-01

particles like electrons and holes. The Pauli exclusion principle prevents fermions from occupying the same quantum state, limiting the expectation...sity approximation. In Eq. 6.2, µ represents a vector that isolates each of the Cartesian components of the pairing vector, σµ represents the Pauli spin...devices on SiO2,” Nat. Nano, vol. 3, pp. 206–209, 2008. [35] X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung , E

Generalized non-equilibrium vertex correction method in coherent medium theory for quantum transport simulation of disordered nanoelectronics

NASA Astrophysics Data System (ADS)

Yan, Jiawei; Ke, Youqi

In realistic nanoelectronics, disordered impurities/defects are inevitable and play important roles in electron transport. However, due to the lack of effective quantum transport method, the important effects of disorders remain poorly understood. Here, we report a generalized non-equilibrium vertex correction (NVC) method with coherent potential approximation to treat the disorder effects in quantum transport simulation. With this generalized NVC method, any averaged product of two single-particle Green's functions can be obtained by solving a set of simple linear equations. As a result, the averaged non-equilibrium density matrix and various important transport properties, including averaged current, disordered induced current fluctuation and the averaged shot noise, can all be efficiently computed in a unified scheme. Moreover, a generalized form of conditionally averaged non-equilibrium Green's function is derived to incorporate with density functional theory to enable first-principles simulation. We prove the non-equilibrium coherent potential equals the non-equilibrium vertex correction. Our approach provides a unified, efficient and self-consistent method for simulating non-equilibrium quantum transport through disorder nanoelectronics. Shanghaitech start-up fund.

Extending the length and time scales of Gram–Schmidt Lyapunov vector computations

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

Costa, Anthony B., E-mail: acosta@northwestern.edu; Green, Jason R., E-mail: jason.green@umb.edu; Department of Chemistry, University of Massachusetts Boston, Boston, MA 02125

Lyapunov vectors have found growing interest recently due to their ability to characterize systems out of thermodynamic equilibrium. The computation of orthogonal Gram–Schmidt vectors requires multiplication and QR decomposition of large matrices, which grow as N{sup 2} (with the particle count). This expense has limited such calculations to relatively small systems and short time scales. Here, we detail two implementations of an algorithm for computing Gram–Schmidt vectors. The first is a distributed-memory message-passing method using Scalapack. The second uses the newly-released MAGMA library for GPUs. We compare the performance of both codes for Lennard–Jones fluids from N=100 to 1300 betweenmore » Intel Nahalem/Infiniband DDR and NVIDIA C2050 architectures. To our best knowledge, these are the largest systems for which the Gram–Schmidt Lyapunov vectors have been computed, and the first time their calculation has been GPU-accelerated. We conclude that Lyapunov vector calculations can be significantly extended in length and time by leveraging the power of GPU-accelerated linear algebra.« less

Temperature Effect on the Dispersion Relation of Nonequilibrium Exciton-Polariton Condensates in a CuBr Microcavity

NASA Astrophysics Data System (ADS)

Nakayama, Masaaki; Tamura, Kazuki

2018-05-01

We observed the dispersion relation of nonequilibrium exciton-polariton condensates at 10 and 80 K in a CuBr microcavity using angle-resolved photoluminescence spectroscopy. The dispersion relation consists of dispersionless and dispersive parts in small and large in-plane wave vector regions, respectively. It was found that the cutoff wave vector of the dispersionless region at 80 K is larger than that at 10 K. From quantitative analysis of the dispersion relation based on a theory for nonequilibrium condensation, we show that the larger cutoff wave vector results from an increase in the effective relaxation rate of the Bogoliubov mode in equilibrium condensation; namely, a degree of nonequilibrium at 80 K is higher than that at 10 K.

Mathematics, Vol. 2.

ERIC Educational Resources Information Center

Bureau of Naval Personnel, Washington, DC.

The second of three volumes of a mathematics training course for Navy personnel, this document contains material primarily found at the college level. Beginning with logarithms and trigonometry, the text moves into vectors and static equilibrium (physics). Coordinate geometry, conic sections, and the tangents, normals, and slopes of curves follow.…

Chemical Principles Revisited: Chemical Equilibrium.

ERIC Educational Resources Information Center

Mickey, Charles D.

1980-01-01

Describes: (1) Law of Mass Action; (2) equilibrium constant and ideal behavior; (3) general form of the equilibrium constant; (4) forward and reverse reactions; (5) factors influencing equilibrium; (6) Le Chatelier's principle; (7) effects of temperature, changing concentration, and pressure on equilibrium; and (8) catalysts and equilibrium. (JN)

A generalized nonlocal vector calculus

NASA Astrophysics Data System (ADS)

Alali, Bacim; Liu, Kuo; Gunzburger, Max

2015-10-01

A nonlocal vector calculus was introduced in Du et al. (Math Model Meth Appl Sci 23:493-540, 2013) that has proved useful for the analysis of the peridynamics model of nonlocal mechanics and nonlocal diffusion models. A formulation is developed that provides a more general setting for the nonlocal vector calculus that is independent of particular nonlocal models. It is shown that general nonlocal calculus operators are integral operators with specific integral kernels. General nonlocal calculus properties are developed, including nonlocal integration by parts formula and Green's identities. The nonlocal vector calculus introduced in Du et al. (Math Model Meth Appl Sci 23:493-540, 2013) is shown to be recoverable from the general formulation as a special example. This special nonlocal vector calculus is used to reformulate the peridynamics equation of motion in terms of the nonlocal gradient operator and its adjoint. A new example of nonlocal vector calculus operators is introduced, which shows the potential use of the general formulation for general nonlocal models.

Time, space and equilibrium means of continuous vector functions on the phase space of a dynamical system

NASA Astrophysics Data System (ADS)

Gurevich, Boris M.; Tempel'man, Arcady A.

2010-05-01

For a dynamical system \\tau with 'time' \\mathbb Z^d and compact phase space X, we introduce three subsets of the space \\mathbb R^m related to a continuous function f\\colon X\\to\\mathbb R^m: the set of time means of f and two sets of space means of f, namely those corresponding to all \\tau-invariant probability measures and those corresponding to some equilibrium measures on X. The main results concern topological properties of these sets of means and their mutual position. Bibliography: 18 titles.

Motion control of rigid bodies in SE(3)

NASA Astrophysics Data System (ADS)

Roza, Ashton

This thesis investigates the control of motion for a general class of vehicles that rotate and translate in three-space, and are propelled by a thrust vector which has fixed direction in body frame. The thesis addresses the problems of path following and position control. For path following, a feedback linearization controller is presented that makes the vehicle follow an arbitrary closed curve while simultaneously allowing the designer to specify the velocity profile of the vehicle on the path and its heading. For position control, a two-stage approach is presented that decouples position control from attitude control, allowing for a modular design and yielding almost global asymptotic stability of any desired hovering equilibrium. The effectiveness of the proposed method is verified both in simulation and experimentally by means of a hardware-in-the-loop setup emulating a co-axial helicopter.

Balancing Beams--For a Few Moments

ERIC Educational Resources Information Center

Kibble, Bob

2008-01-01

A 2 m long wooden beam provides an ideal demonstration tool for exploring moments. A class set is cheap and can be used at introductory and advanced levels. This article explores how such beams can be used to support learning about moments, equilibrium, vectors, and simultaneous equations. (Contains 7 figures.)

How random is a random vector?

NASA Astrophysics Data System (ADS)

Eliazar, Iddo

2015-12-01

Over 80 years ago Samuel Wilks proposed that the "generalized variance" of a random vector is the determinant of its covariance matrix. To date, the notion and use of the generalized variance is confined only to very specific niches in statistics. In this paper we establish that the "Wilks standard deviation" -the square root of the generalized variance-is indeed the standard deviation of a random vector. We further establish that the "uncorrelation index" -a derivative of the Wilks standard deviation-is a measure of the overall correlation between the components of a random vector. Both the Wilks standard deviation and the uncorrelation index are, respectively, special cases of two general notions that we introduce: "randomness measures" and "independence indices" of random vectors. In turn, these general notions give rise to "randomness diagrams"-tangible planar visualizations that answer the question: How random is a random vector? The notion of "independence indices" yields a novel measure of correlation for Lévy laws. In general, the concepts and results presented in this paper are applicable to any field of science and engineering with random-vectors empirical data.

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

NASA Astrophysics Data System (ADS)

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

2017-08-01

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

General stochastic variational formulation for the oligopolistic market equilibrium problem with excesses

NASA Astrophysics Data System (ADS)

Barbagallo, Annamaria; Di Meglio, Guglielmo; Mauro, Paolo

2017-07-01

The aim of the paper is to study, in a Hilbert space setting, a general random oligopolistic market equilibrium problem in presence of both production and demand excesses and to characterize the random Cournot-Nash equilibrium principle by means of a stochastic variational inequality. Some existence results are presented.

Field-induced metastability of the modulation wave vector in a magnetic soliton lattice

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

Zhu, M.; Peng, J.; Hong, T.

We present magnetic-field-induced metastability of the magnetic soliton lattice in a bilayer ruthenate Ca 3(Ru 1–xFe x) 2O 7(x=0.05) through single-crystal neutron diffraction study. We show that the incommensurability of the modulation wave vector at zero field strongly depends on the history of magnetic field at low temperature, and that the equilibrium ground state can be achieved by warming above a characteristic temperature T g~37K. Lastly, we suggest that such metastability might be associated with the domain wall pinning by the magnetic Fe dopants.

Field-induced metastability of the modulation wave vector in a magnetic soliton lattice

DOE PAGES

Zhu, M.; Peng, J.; Hong, T.; ...

2017-04-19

We present magnetic-field-induced metastability of the magnetic soliton lattice in a bilayer ruthenate Ca 3(Ru 1–xFe x) 2O 7(x=0.05) through single-crystal neutron diffraction study. We show that the incommensurability of the modulation wave vector at zero field strongly depends on the history of magnetic field at low temperature, and that the equilibrium ground state can be achieved by warming above a characteristic temperature T g~37K. Lastly, we suggest that such metastability might be associated with the domain wall pinning by the magnetic Fe dopants.

Langevin Dynamics with Spatial Correlations as a Model for Electron-Phonon Coupling

NASA Astrophysics Data System (ADS)

Tamm, A.; Caro, M.; Caro, A.; Samolyuk, G.; Klintenberg, M.; Correa, A. A.

2018-05-01

Stochastic Langevin dynamics has been traditionally used as a tool to describe nonequilibrium processes. When utilized in systems with collective modes, traditional Langevin dynamics relaxes all modes indiscriminately, regardless of their wavelength. We propose a generalization of Langevin dynamics that can capture a differential coupling between collective modes and the bath, by introducing spatial correlations in the random forces. This allows modeling the electronic subsystem in a metal as a generalized Langevin bath endowed with a concept of locality, greatly improving the capabilities of the two-temperature model. The specific form proposed here for the spatial correlations produces a physical wave-vector and polarization dependency of the relaxation produced by the electron-phonon coupling in a solid. We show that the resulting model can be used for describing the path to equilibration of ions and electrons and also as a thermostat to sample the equilibrium canonical ensemble. By extension, the family of models presented here can be applied in general to any dense system, solids, alloys, and dense plasmas. As an example, we apply the model to study the nonequilibrium dynamics of an electron-ion two-temperature Ni crystal.

Effect of a Perturbation on the Chemical Equilibrium: Comparison with Le Chatelier's Principle

ERIC Educational Resources Information Center

Torres, Emilio Martinez

2007-01-01

This article develops a general thermodynamic treatment to predict the direction of shift in a chemical equilibrium when it is subjected to a stress. This treatment gives an inequality that relates the change in the perturbed variable and the change that the equilibrium shift produces in the conjugated variable. To illustrate the generality of…

N-player stochastic differential games

NASA Technical Reports Server (NTRS)

Varaiya, P.

1976-01-01

The paper presents conditions which guarantee that the control strategies adopted by N players constitute an efficient solution, an equilibrium, or a core solution. The system dynamics are described by an Ito equation, and all players have perfect information. When the set of instantaneous joint costs and velocity vectors is convex, the conditions are necessary.

Gibbsian Stationary Non-equilibrium States

NASA Astrophysics Data System (ADS)

De Carlo, Leonardo; Gabrielli, Davide

2017-09-01

We study the structure of stationary non-equilibrium states for interacting particle systems from a microscopic viewpoint. In particular we discuss two different discrete geometric constructions. We apply both of them to determine non reversible transition rates corresponding to a fixed invariant measure. The first one uses the equivalence of this problem with the construction of divergence free flows on the transition graph. Since divergence free flows are characterized by cyclic decompositions we can generate families of models from elementary cycles on the configuration space. The second construction is a functional discrete Hodge decomposition for translational covariant discrete vector fields. According to this, for example, the instantaneous current of any interacting particle system on a finite torus can be canonically decomposed in a gradient part, a circulation term and an harmonic component. All the three components are associated with functions on the configuration space. This decomposition is unique and constructive. The stationary condition can be interpreted as an orthogonality condition with respect to an harmonic discrete vector field and we use this decomposition to construct models having a fixed invariant measure.

Vector critical points and generalized quasi-efficient solutions in nonsmooth multi-objective programming.

PubMed

Wang, Zhen; Li, Ru; Yu, Guolin

2017-01-01

In this work, several extended approximately invex vector-valued functions of higher order involving a generalized Jacobian are introduced, and some examples are presented to illustrate their existences. The notions of higher-order (weak) quasi-efficiency with respect to a function are proposed for a multi-objective programming. Under the introduced generalization of higher-order approximate invexities assumptions, we prove that the solutions of generalized vector variational-like inequalities in terms of the generalized Jacobian are the generalized quasi-efficient solutions of nonsmooth multi-objective programming problems. Moreover, the equivalent conditions are presented, namely, a vector critical point is a weakly quasi-efficient solution of higher order with respect to a function.

Generalized Finsler geometric continuum physics with applications in fracture and phase transformations

NASA Astrophysics Data System (ADS)

Clayton, J. D.

2017-02-01

A theory of deformation of continuous media based on concepts from Finsler differential geometry is presented. The general theory accounts for finite deformations, nonlinear elasticity, and changes in internal state of the material, the latter represented by elements of a state vector of generalized Finsler space whose entries consist of one or more order parameter(s). Two descriptive representations of the deformation gradient are considered. The first invokes an additive decomposition and is applied to problems involving localized inelastic deformation mechanisms such as fracture. The second invokes a multiplicative decomposition and is applied to problems involving distributed deformation mechanisms such as phase transformations or twinning. Appropriate free energy functions are posited for each case, and Euler-Lagrange equations of equilibrium are derived. Solutions are obtained for specific problems of tensile fracture of an elastic cylinder and for amorphization of a crystal under spherical and uniaxial compression. The Finsler-based approach is demonstrated to be more general and potentially more physically descriptive than existing hyperelasticity models couched in Riemannian geometry or Euclidean space, without incorporation of supplementary ad hoc equations or spurious fitting parameters. Predictions for single crystals of boron carbide ceramic agree qualitatively, and in many instances quantitatively, with results from physical experiments and atomic simulations involving structural collapse and failure of the crystal along its c-axis.

Equilibrium polymerization on the equivalent-neighbor lattice

NASA Technical Reports Server (NTRS)

Kaufman, Miron

1989-01-01

The equilibrium polymerization problem is solved exactly on the equivalent-neighbor lattice. The Flory-Huggins (Flory, 1986) entropy of mixing is exact for this lattice. The discrete version of the n-vector model is verified when n approaches 0 is equivalent to the equal reactivity polymerization process in the whole parameter space, including the polymerized phase. The polymerization processes for polymers satisfying the Schulz (1939) distribution exhibit nonuniversal critical behavior. A close analogy is found between the polymerization problem of index the Schulz r and the Bose-Einstein ideal gas in d = -2r dimensions, with the critical polymerization corresponding to the Bose-Einstein condensation.

Integrated Power and Attitude Control for a Spacecraft with Flywheels and Control Moment Gyroscopes

NASA Technical Reports Server (NTRS)

Roithmayr, Carlos M.; Karlgaard, Christopher D.; Kumar, Renjith R.; Bose, David M.

2003-01-01

A law is designed for simultaneous control of the orientation of an Earth-pointing spacecraft, the energy stored by counter-rotating flywheels, and the angular momentum of the flywheels and control moment gyroscopes used together as all integrated set of actuators for attitude control. General. nonlinear equations of motion are presented in vector-dyadic form, and used to obtain approximate expressions which are then linearized in preparation for design of control laws that include feedback of flywheel kinetic energy error as it means of compensating for damping exerted by rotor bearings. Two flywheel 'steering laws' are developed such that torque commanded by all attitude control law is achieved while energy is stored or discharged at the required rate. Using the International Space Station as an example, numerical simulations are performed to demonstrate control about a torque equilibrium attitude and illustrate the benefits of kinetic energy error feedback.

A simple fitness proxy for structured populations with continuous traits, with case studies on the evolution of haplo-diploids and genetic dimorphisms.

PubMed

Metz, J A J; Leimar, O

2011-03-01

For structured populations in equilibrium with everybody born equal, ln(R (0)) is a useful fitness proxy for evolutionarily steady strategy (ESS) and most adaptive dynamics calculations, with R (0) the average lifetime number of offspring in the clonal and haploid cases, and half the average lifetime number of offspring fathered or mothered for Mendelian diploids. When individuals have variable birth states, as is, for example, the case in spatial models, R (0) is itself an eigenvalue, which usually cannot be expressed explicitly in the trait vectors under consideration. In that case, Q(Y| X):=-det (I-L(Y| X)) can often be used as fitness proxy, with L the next-generation matrix for a potential mutant characterized by the trait vector Y in the (constant) environment engendered by a resident characterized by X. If the trait space is connected, global uninvadability can be determined from it. Moreover, it can be used in all the usual local calculations like the determination of evolutionarily singular trait vectors and their local invadability and attractivity. We conclude with three extended case studies demonstrating the usefulness of Q: the calculation of ESSs under haplo-diploid genetics (I), of evolutionarily steady genetic dimorphisms (ESDs) with a priori proportionality of macro- and micro-gametic outputs (an assumption that is generally made but the fulfilment of which is a priori highly exceptional) (II), and of ESDs without such proportionality (III). These case studies should also have some interest in their own right for the spelled out calculation recipes and their underlying modelling methodology.

A unified development of several techniques for the representation of random vectors and data sets

NASA Technical Reports Server (NTRS)

Bundick, W. T.

1973-01-01

Linear vector space theory is used to develop a general representation of a set of data vectors or random vectors by linear combinations of orthonormal vectors such that the mean squared error of the representation is minimized. The orthonormal vectors are shown to be the eigenvectors of an operator. The general representation is applied to several specific problems involving the use of the Karhunen-Loeve expansion, principal component analysis, and empirical orthogonal functions; and the common properties of these representations are developed.

N-Player Stochastic Differential Games. [control theory

NASA Technical Reports Server (NTRS)

Varaiya, P.

1974-01-01

Conditions are described which guarantee that the control strategies adopted by N players constitute an efficient solution, an equilibrium, or a core solution. The system dynamics are described by an Ito equation, and all players have perfect information. It was found that when the set of instantaneous joint costs and velocity vectors is convex, the conditions are necessary.

Generalized vector calculus on convex domain

NASA Astrophysics Data System (ADS)

Agrawal, Om P.; Xu, Yufeng

2015-06-01

In this paper, we apply recently proposed generalized integral and differential operators to develop generalized vector calculus and generalized variational calculus for problems defined over a convex domain. In particular, we present some generalization of Green's and Gauss divergence theorems involving some new operators, and apply these theorems to generalized variational calculus. For fractional power kernels, the formulation leads to fractional vector calculus and fractional variational calculus for problems defined over a convex domain. In special cases, when certain parameters take integer values, we obtain formulations for integer order problems. Two examples are presented to demonstrate applications of the generalized variational calculus which utilize the generalized vector calculus developed in the paper. The first example leads to a generalized partial differential equation and the second example leads to a generalized eigenvalue problem, both in two dimensional convex domains. We solve the generalized partial differential equation by using polynomial approximation. A special case of the second example is a generalized isoperimetric problem. We find an approximate solution to this problem. Many physical problems containing integer order integrals and derivatives are defined over arbitrary domains. We speculate that future problems containing fractional and generalized integrals and derivatives in fractional mechanics will be defined over arbitrary domains, and therefore, a general variational calculus incorporating a general vector calculus will be needed for these problems. This research is our first attempt in that direction.

Extended vector-tensor theories

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

Kimura, Rampei; Naruko, Atsushi; Yoshida, Daisuke, E-mail: rampei@th.phys.titech.ac.jp, E-mail: naruko@th.phys.titech.ac.jp, E-mail: yoshida@th.phys.titech.ac.jp

Recently, several extensions of massive vector theory in curved space-time have been proposed in many literatures. In this paper, we consider the most general vector-tensor theories that contain up to two derivatives with respect to metric and vector field. By imposing a degeneracy condition of the Lagrangian in the context of ADM decomposition of space-time to eliminate an unwanted mode, we construct a new class of massive vector theories where five degrees of freedom can propagate, corresponding to three for massive vector modes and two for massless tensor modes. We find that the generalized Proca and the beyond generalized Procamore » theories up to the quartic Lagrangian, which should be included in this formulation, are degenerate theories even in curved space-time. Finally, introducing new metric and vector field transformations, we investigate the properties of thus obtained theories under such transformations.« less

Flux Jacobian matrices and generaled Roe average for an equilibrium real gas

NASA Technical Reports Server (NTRS)

Vinokur, Marcel

1988-01-01

Inviscid flux Jacobian matrices and their properties used in numerical solutions of conservation laws are extended to general, equilibrium gas laws. Exact and approximate generalizations of the Roe average are presented. Results are given for one-dimensional flow, and then extended to three-dimensional flow with time-varying grids.

Fradkin-Bacry-Ruegg-Souriau perihelion vector for Gorringe-Leach equations

NASA Astrophysics Data System (ADS)

Grandati, Yves; Bérard, Alain; Mohrbach, Hervé

2010-02-01

We show that every generalized Gorringe-Leach equation admits an associated Fradkin-Bacry-Ruegg-Souriau’s vector which, in general, is only a piecewise conserved quantity. In the case of dualizable generalized Gorringe-Leach equations, which include the case of conservative motions in central power law potentials, the image sets of the FBRS vectors for dual classes are dual images of each other.

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

NASA Technical Reports Server (NTRS)

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.

The assisted prediction modelling frame with hybridisation and ensemble for business risk forecasting and an implementation

NASA Astrophysics Data System (ADS)

Li, Hui; Hong, Lu-Yao; Zhou, Qing; Yu, Hai-Jie

2015-08-01

The business failure of numerous companies results in financial crises. The high social costs associated with such crises have made people to search for effective tools for business risk prediction, among which, support vector machine is very effective. Several modelling means, including single-technique modelling, hybrid modelling, and ensemble modelling, have been suggested in forecasting business risk with support vector machine. However, existing literature seldom focuses on the general modelling frame for business risk prediction, and seldom investigates performance differences among different modelling means. We reviewed researches on forecasting business risk with support vector machine, proposed the general assisted prediction modelling frame with hybridisation and ensemble (APMF-WHAE), and finally, investigated the use of principal components analysis, support vector machine, random sampling, and group decision, under the general frame in forecasting business risk. Under the APMF-WHAE frame with support vector machine as the base predictive model, four specific predictive models were produced, namely, pure support vector machine, a hybrid support vector machine involved with principal components analysis, a support vector machine ensemble involved with random sampling and group decision, and an ensemble of hybrid support vector machine using group decision to integrate various hybrid support vector machines on variables produced from principle components analysis and samples from random sampling. The experimental results indicate that hybrid support vector machine and ensemble of hybrid support vector machines were able to produce dominating performance than pure support vector machine and support vector machine ensemble.

Vector calculus in non-integer dimensional space and its applications to fractal media

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2015-02-01

We suggest a generalization of vector calculus for the case of non-integer dimensional space. The first and second orders operations such as gradient, divergence, the scalar and vector Laplace operators for non-integer dimensional space are defined. For simplification we consider scalar and vector fields that are independent of angles. We formulate a generalization of vector calculus for rotationally covariant scalar and vector functions. This generalization allows us to describe fractal media and materials in the framework of continuum models with non-integer dimensional space. As examples of application of the suggested calculus, we consider elasticity of fractal materials (fractal hollow ball and fractal cylindrical pipe with pressure inside and outside), steady distribution of heat in fractal media, electric field of fractal charged cylinder. We solve the correspondent equations for non-integer dimensional space models.

One-electron densities of freely rotating Wigner molecules

NASA Astrophysics Data System (ADS)

Cioslowski, Jerzy

2017-12-01

A formalism enabling computation of the one-particle density of a freely rotating assembly of identical particles that vibrate about their equilibrium positions with amplitudes much smaller than their average distances is presented. It produces densities as finite sums of products of angular and radial functions, the length of the expansion being determined by the interplay between the point-group and permutational symmetries of the system in question. Obtaining from a convolution of the rotational and bosonic components of the parent wavefunction, the angular functions are state-dependent. On the other hand, the radial functions are Gaussians with maxima located at the equilibrium lengths of the position vectors of individual particles and exponents depending on the scalar products of these vectors and the eigenvectors of the corresponding Hessian as well as the respective eigenvalues. Although the new formalism is particularly useful for studies of the Wigner molecules formed by electrons subject to weak confining potentials, it is readily adaptable to species (such as ´balliums’ and Coulomb crystals) composed of identical particles with arbitrary spin statistics and permutational symmetry. Several examples of applications of the present approach to the harmonium atoms within the strong-correlation regime are given.

Wind and Temperature Spectrometry of the Upper Atmosphere in Low-Earth Orbit

NASA Technical Reports Server (NTRS)

Herrero, Federico

2011-01-01

Wind and Temperature Spectrometry (WATS) is a new approach to measure the full wind vector, temperature, and relative densities of major neutral species in the Earth's thermosphere. The method uses an energy-angle spectrometer moving through the tenuous upper atmosphere to measure directly the angular and energy distributions of the air stream that enters the spectrometer. The angular distribution gives the direction of the total velocity of the air entering the spectrometer, and the energy distribution gives the magnitude of the total velocity. The wind velocity vector is uniquely determined since the measured total velocity depends on the wind vector and the orbiting velocity vector. The orbiting spectrometer moves supersonically, Mach 8 or greater, through the air and must point within a few degrees of its orbital velocity vector (the ram direction). Pointing knowledge is critical; for example, pointing errors 0.1 lead to errors of about 10 m/s in the wind. The WATS method may also be applied without modification to measure the ion-drift vector, ion temperature, and relative ion densities of major ionic species in the ionosphere. In such an application it may be called IDTS: Ion-Drift Temperature Spectrometry. A spectrometer-based coordinate system with one axis instantaneously pointing along the ram direction makes it possible to transform the Maxwellian velocity distribution of the air molecules to a Maxwellian energy-angle distribution for the molecular flux entering the spectrometer. This implementation of WATS is called the gas kinetic method (GKM) because it is applied to the case of the Maxwellian distribution. The WATS method follows from the recognition that in a supersonic platform moving at 8,000 m/s, the measurement of small wind velocities in the air on the order of a few 100 m/s and less requires precise knowledge of the angle of incidence of the neutral atoms and molecules. The same is true for the case of ion-drift measurements. WATS also provides a general approach that can obtain non-equilibrium distributions as may exist in the upper regions of the thermosphere, above 500 km and into the exosphere. Finally, WATS serves as a mass spectrometer, with very low mass resolution of roughly 1 part in 3, but easily separating atomic oxygen from molecular nitrogen.

Experience with a vectorized general circulation weather model on Star-100

NASA Technical Reports Server (NTRS)

Soll, D. B.; Habra, N. R.; Russell, G. L.

1977-01-01

A version of an atmospheric general circulation model was vectorized to run on a CDC STAR 100. The numerical model was coded and run in two different vector languages, CDC and LRLTRAN. A factor of 10 speed improvement over an IBM 360/95 was realized. Efficient use of the STAR machine required some redesigning of algorithms and logic. This precludes the application of vectorizing compilers on the original scalar code to achieve the same results. Vector languages permit a more natural and efficient formulation for such numerical codes.

Reviving the shear-free perfect fluid conjecture in general relativity

NASA Astrophysics Data System (ADS)

Sikhonde, Muzikayise E.; Dunsby, Peter K. S.

2017-12-01

Employing a Mathematica symbolic computer algebra package called xTensor, we present (1+3) -covariant special case proofs of the shear-free perfect fluid conjecture in general relativity. We first present the case where the pressure is constant, and where the acceleration is parallel to the vorticity vector. These cases were first presented in their covariant form by Senovilla et al. We then provide a covariant proof for the case where the acceleration and vorticity vectors are orthogonal, which leads to the existence of a Killing vector along the vorticity. This Killing vector satisfies the new constraint equations resulting from the vanishing of the shear. Furthermore, it is shown that in order for the conjecture to be true, this Killing vector must have a vanishing spatially projected directional covariant derivative along the velocity vector field. This in turn implies the existence of another basic vector field along the direction of the vorticity for the conjecture to hold. Finally, we show that in general, there exists a basic vector field parallel to the acceleration for which the conjecture is true.

Orthonormal vector general polynomials derived from the Cartesian gradient of the orthonormal Zernike-based polynomials.

PubMed

Mafusire, Cosmas; Krüger, Tjaart P J

2018-06-01

The concept of orthonormal vector circle polynomials is revisited by deriving a set from the Cartesian gradient of Zernike polynomials in a unit circle using a matrix-based approach. The heart of this model is a closed-form matrix equation of the gradient of Zernike circle polynomials expressed as a linear combination of lower-order Zernike circle polynomials related through a gradient matrix. This is a sparse matrix whose elements are two-dimensional standard basis transverse Euclidean vectors. Using the outer product form of the Cholesky decomposition, the gradient matrix is used to calculate a new matrix, which we used to express the Cartesian gradient of the Zernike circle polynomials as a linear combination of orthonormal vector circle polynomials. Since this new matrix is singular, the orthonormal vector polynomials are recovered by reducing the matrix to its row echelon form using the Gauss-Jordan elimination method. We extend the model to derive orthonormal vector general polynomials, which are orthonormal in a general pupil by performing a similarity transformation on the gradient matrix to give its equivalent in the general pupil. The outer form of the Gram-Schmidt procedure and the Gauss-Jordan elimination method are then applied to the general pupil to generate the orthonormal vector general polynomials from the gradient of the orthonormal Zernike-based polynomials. The performance of the model is demonstrated with a simulated wavefront in a square pupil inscribed in a unit circle.

The quest for the next information processing technology

NASA Astrophysics Data System (ADS)

Welser, Jeffrey J.; Bourianoff, George I.; Zhirnov, Victor V.; Cavin, Ralph Keary

2008-01-01

Fundamental physical considerations indicate that the scaling of devices that use electron charge as the information carrier will limit within the next one to two decades. The Nanoelectronics Research Initiative (NRI), a joint industry-government program, has been developed to fund university research seeking devices that utilize alternative physical information carriers or non-equilibrium switching mechanisms to continue the historical cost and performance trends of information technology. Three research centers have been established to pursue five research vectors that have been identified as critical to the effort to replace the electronic switch. A brief history and rationale for NRI is given and the projects currently underway are described in the context of the five research vectors.

Anomaly on Superspace of Time Series Data

NASA Astrophysics Data System (ADS)

Capozziello, Salvatore; Pincak, Richard; Kanjamapornkul, Kabin

2017-11-01

We apply the G-theory and anomaly of ghost and antighost fields in the theory of supersymmetry to study a superspace over time series data for the detection of hidden general supply and demand equilibrium in the financial market. We provide proof of the existence of a general equilibrium point over 14 extradimensions of the new G-theory compared with the M-theory of the 11 dimensions model of Edward Witten. We found that the process of coupling between nonequilibrium and equilibrium spinor fields of expectation ghost fields in the superspace of time series data induces an infinitely long exact sequence of cohomology from a short exact sequence of moduli state space model. If we assume that the financial market is separated into two topological spaces of supply and demand as the D-brane and anti-D-brane model, then we can use a cohomology group to compute the stability of the market as a stable point of the general equilibrium of the interaction between D-branes of the market. We obtain the result that the general equilibrium will exist if and only if the 14th Batalin-Vilkovisky cohomology group with the negative dimensions underlying 14 major hidden factors influencing the market is zero.

Learning with LOGO: Logo and Vectors.

ERIC Educational Resources Information Center

Lough, Tom; Tipps, Steve

1986-01-01

This is the first of a two-part series on the general concept of vector space. Provides tool procedures to allow investigation of vector properties, vector addition and subtraction, and X and Y components. Lists several sources of additional vector ideas. (JM)

Full-field drift Hamiltonian particle orbits in 3D geometry

NASA Astrophysics Data System (ADS)

Cooper, W. A.; Graves, J. P.; Brunner, S.; Isaev, M. Yu

2011-02-01

A Hamiltonian/Lagrangian theory to describe guiding centre orbit drift motion which is canonical in the Boozer coordinate frame has been extended to include full electromagnetic perturbed fields in anisotropic pressure 3D equilibria with nested magnetic flux surfaces. A redefinition of the guiding centre velocity to eliminate the motion due to finite equilibrium radial magnetic fields and the choice of a gauge condition that sets the radial component of the electromagnetic vector potential to zero are invoked to guarantee that the Boozer angular coordinates retain the canonical structure. The canonical momenta are identified and the guiding centre particle radial drift motion and parallel gyroradius evolution are derived. The particle coordinate position is linearly modified by wave-particle interactions. All the nonlinear wave-wave interactions appear explicitly only in the evolution of the parallel gyroradius. The radial variation of the electrostatic potential is related to the binormal component of the displacement vector for MHD-type perturbations. The electromagnetic vector potential projections can then be determined from the electrostatic potential and the radial component of the MHD displacement vector.

Higher-dimensional generalizations of the Watanabe–Strogatz transform for vector models of synchronization

NASA Astrophysics Data System (ADS)

Lohe, M. A.

2018-06-01

We generalize the Watanabe–Strogatz (WS) transform, which acts on the Kuramoto model in d  =  2 dimensions, to a higher-dimensional vector transform which operates on vector oscillator models of synchronization in any dimension , for the case of identical frequency matrices. These models have conserved quantities constructed from the cross ratios of inner products of the vector variables, which are invariant under the vector transform, and have trajectories which lie on the unit sphere S d‑1. Application of the vector transform leads to a partial integration of the equations of motion, leaving independent equations to be solved, for any number of nodes N. We discuss properties of complete synchronization and use the reduced equations to derive a stability condition for completely synchronized trajectories on S d‑1. We further generalize the vector transform to a mapping which acts in and in particular preserves the unit ball , and leaves invariant the cross ratios constructed from inner products of vectors in . This mapping can be used to partially integrate a system of vector oscillators with trajectories in , and for d  =  2 leads to an extension of the Kuramoto system to a system of oscillators with time-dependent amplitudes and trajectories in the unit disk. We find an inequivalent generalization of the Möbius map which also preserves but leaves invariant a different set of cross ratios, this time constructed from the vector norms. This leads to a different extension of the Kuramoto model with trajectories in the complex plane that can be partially integrated by means of fractional linear transformations.

Equivalent model of a dually-fed machine for electric drive control systems

NASA Astrophysics Data System (ADS)

Ostrovlyanchik, I. Yu; Popolzin, I. Yu

2018-05-01

The article shows that the mathematical model of a dually-fed machine is complicated because of the presence of a controlled voltage source in the rotor circuit. As a method of obtaining a mathematical model, the method of a generalized two-phase electric machine is applied and a rotating orthogonal coordinate system is chosen that is associated with the representing vector of a stator current. In the chosen coordinate system in the operator form the differential equations of electric equilibrium for the windings of the generalized machine (the Kirchhoff equation) are written together with the expression for the moment, which determines the electromechanical energy transformation in the machine. Equations are transformed so that they connect the currents of the windings, that determine the moment of the machine, and the voltages on these windings. The structural diagram of the machine is assigned to the written equations. Based on the written equations and accepted assumptions, expressions were obtained for the balancing the EMF of windings, and on the basis of these expressions an equivalent mathematical model of a dually-fed machine is proposed, convenient for use in electric drive control systems.

General Equilibrium Models: Improving the Microeconomics Classroom

ERIC Educational Resources Information Center

Nicholson, Walter; Westhoff, Frank

2009-01-01

General equilibrium models now play important roles in many fields of economics including tax policy, environmental regulation, international trade, and economic development. The intermediate microeconomics classroom has not kept pace with these trends, however. Microeconomics textbooks primarily focus on the insights that can be drawn from the…

Analysis and Experimentation of Control Strategies for Underactuated Spacecraft

DTIC Science & Technology

2009-09-01

control techniques that provide time -invariant global asymptotic stability of the fully actuated spacecraft system of equations. Although these control ...momentum wheel actuators in finite time under the restriction that the total angular momentum vector of the system is zero. This control methodology...can be stabilizable to an arbitrarily small region about the equilibrium of the system via time -invariant smooth state feedback control

Nonlinear analogue of the May−Wigner instability transition

PubMed Central

Fyodorov, Yan V.; Khoruzhenko, Boris A.

2016-01-01

We study a system of N≫1 degrees of freedom coupled via a smooth homogeneous Gaussian vector field with both gradient and divergence-free components. In the absence of coupling, the system is exponentially relaxing to an equilibrium with rate μ. We show that, while increasing the ratio of the coupling strength to the relaxation rate, the system experiences an abrupt transition from a topologically trivial phase portrait with a single equilibrium into a topologically nontrivial regime characterized by an exponential number of equilibria, the vast majority of which are expected to be unstable. It is suggested that this picture provides a global view on the nature of the May−Wigner instability transition originally discovered by local linear stability analysis. PMID:27274077

BCS superconductors: The out-of-equilibrium response to a laser pulse

NASA Astrophysics Data System (ADS)

Avella, Adolfo

2018-05-01

The dynamics of a 2D d-wave BCS superconductor driven out-of-equilibrium by a perpendicularly-impinging polarized laser pulse is analyzed on varying the laser pulse characteristics. The observed effects include: oscillations both in the amplitude and in the phase of the superconducting order parameter, suppression of the superconductivity, but also its enhancement with a strong dependence on all varying parameters and, in particular, on the polarization in plane of the applied vector potential and on the value of its frequency. This study opens up the possibility to distinguish very clearly the behavior of the nodal and anti-nodal non-thermal excitations and to tackle some of the puzzling results of the current experimental scenario in the field.

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

PubMed

Wu, Wei; Wang, Jin

2013-09-28

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

Detection of a sudden change of the field time series based on the Lorenz system.

PubMed

Da, ChaoJiu; Li, Fang; Shen, BingLu; Yan, PengCheng; Song, Jian; Ma, DeShan

2017-01-01

We conducted an exploratory study of the detection of a sudden change of the field time series based on the numerical solution of the Lorenz system. First, the time when the Lorenz path jumped between the regions on the left and right of the equilibrium point of the Lorenz system was quantitatively marked and the sudden change time of the Lorenz system was obtained. Second, the numerical solution of the Lorenz system was regarded as a vector; thus, this solution could be considered as a vector time series. We transformed the vector time series into a time series using the vector inner product, considering the geometric and topological features of the Lorenz system path. Third, the sudden change of the resulting time series was detected using the sliding t-test method. Comparing the test results with the quantitatively marked time indicated that the method could detect every sudden change of the Lorenz path, thus the method is effective. Finally, we used the method to detect the sudden change of the pressure field time series and temperature field time series, and obtained good results for both series, which indicates that the method can apply to high-dimension vector time series. Mathematically, there is no essential difference between the field time series and vector time series; thus, we provide a new method for the detection of the sudden change of the field time series.

Assessment of tautomer distribution using the condensed reaction graph approach

NASA Astrophysics Data System (ADS)

Gimadiev, T. R.; Madzhidov, T. I.; Nugmanov, R. I.; Baskin, I. I.; Antipin, I. S.; Varnek, A.

2018-03-01

We report the first direct QSPR modeling of equilibrium constants of tautomeric transformations (logK T ) in different solvents and at different temperatures, which do not require intermediate assessment of acidity (basicity) constants for all tautomeric forms. The key step of the modeling consisted in the merging of two tautomers in one sole molecular graph ("condensed reaction graph") which enables to compute molecular descriptors characterizing entire equilibrium. The support vector regression method was used to build the models. The training set consisted of 785 transformations belonging to 11 types of tautomeric reactions with equilibrium constants measured in different solvents and at different temperatures. The models obtained perform well both in cross-validation (Q2 = 0.81 RMSE = 0.7 logK T units) and on two external test sets. Benchmarking studies demonstrate that our models outperform results obtained with DFT B3LYP/6-311 ++ G(d,p) and ChemAxon Tautomerizer applicable only in water at room temperature.

Weak Acid Ionization Constants and the Determination of Weak Acid-Weak Base Reaction Equilibrium Constants in the General Chemistry Laboratory

ERIC Educational Resources Information Center

Nyasulu, Frazier; McMills, Lauren; Barlag, Rebecca

2013-01-01

A laboratory to determine the equilibrium constants of weak acid negative weak base reactions is described. The equilibrium constants of component reactions when multiplied together equal the numerical value of the equilibrium constant of the summative reaction. The component reactions are weak acid ionization reactions, weak base hydrolysis…

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

NASA Astrophysics Data System (ADS)

Sefcik, Jan

1998-05-01

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

Degree of coupling and efficiency of energy converters far-from-equilibrium

NASA Astrophysics Data System (ADS)

Vroylandt, Hadrien; Lacoste, David; Verley, Gatien

2018-02-01

In this paper, we introduce a real symmetric and positive semi-definite matrix, which we call the non-equilibrium conductance matrix, and which generalizes the Onsager response matrix for a system in a non-equilibrium stationary state. We then express the thermodynamic efficiency in terms of the coefficients of this matrix using a parametrization similar to the one used near equilibrium. This framework, then valid arbitrarily far from equilibrium allows to set bounds on the thermodynamic efficiency by a universal function depending only on the degree of coupling between input and output currents. It also leads to new general power-efficiency trade-offs valid for macroscopic machines that are compared to trade-offs previously obtained from uncertainty relations. We illustrate our results on an unicycle heat to heat converter and on a discrete model of a molecular motor.

Computer Assisted Instruction in Economics: An Approach for Illustrating General Equilibrium Concepts.

ERIC Educational Resources Information Center

Gillespie, Robert W.

A market exchange simulation utilizing the PLATO computer-assisted instructional system at the University of Illinois has been designed to teach students the principles of a general equilibrium system. It serves a laboratory function which supplements traditional instruction by stimulating students' interests and providing them with illustrations…

A general equilibrium model of a production economy with asset markets

NASA Astrophysics Data System (ADS)

Raberto, Marco; Teglio, Andrea; Cincotti, Silvano

2006-10-01

In this paper, a general equilibrium model of a monetary production economy is presented. The model is characterized by three classes of agents: a representative firm, heterogeneous households, and the government. Two markets (i.e., a labour market and a goods market, are considered) and two assets are traded in exchange of money, namely, government bonds and equities. Households provide the labour force and decide on consumption and savings, whereas the firm provides consumption goods and demands labour. The government receives taxes from households and pays interests on debt. The Walrasian equilibrium is derived analytically. The dynamics through quantity constrained equilibria out from the Walrasian equilibrium is also studied by means of computer simulations.

Black holes in vector-tensor theories and their thermodynamics

NASA Astrophysics Data System (ADS)

Fan, Zhong-Ying

2018-01-01

In this paper, we study Einstein gravity either minimally or non-minimally coupled to a vector field which breaks the gauge symmetry explicitly in general dimensions. We first consider a minimal theory which is simply the Einstein-Proca theory extended with a quartic self-interaction term for the vector field. We obtain its general static maximally symmetric black hole solution and study the thermodynamics using Wald formalism. The aspects of the solution are much like a Reissner-Nordstrøm black hole in spite of that a global charge cannot be defined for the vector. For non-minimal theories, we obtain a lot of exact black hole solutions, depending on the parameters of the theories. In particular, many of the solutions are general static and have maximal symmetry. However, there are some subtleties and ambiguities in the derivation of the first laws because the existence of an algebraic degree of freedom of the vector in general invalids the Wald entropy formula. The thermodynamics of these solutions deserves further studies.

Energy-exchange collisions of dark-bright-bright vector solitons.

PubMed

Radhakrishnan, R; Manikandan, N; Aravinthan, K

2015-12-01

We find a dark component guiding the practically interesting bright-bright vector one-soliton to two different parametric domains giving rise to different physical situations by constructing a more general form of three-component dark-bright-bright mixed vector one-soliton solution of the generalized Manakov model with nine free real parameters. Moreover our main investigation of the collision dynamics of such mixed vector solitons by constructing the multisoliton solution of the generalized Manakov model with the help of Hirota technique reveals that the dark-bright-bright vector two-soliton supports energy-exchange collision dynamics. In particular the dark component preserves its initial form and the energy-exchange collision property of the bright-bright vector two-soliton solution of the Manakov model during collision. In addition the interactions between bound state dark-bright-bright vector solitons reveal oscillations in their amplitudes. A similar kind of breathing effect was also experimentally observed in the Bose-Einstein condensates. Some possible ways are theoretically suggested not only to control this breathing effect but also to manage the beating, bouncing, jumping, and attraction effects in the collision dynamics of dark-bright-bright vector solitons. The role of multiple free parameters in our solution is examined to define polarization vector, envelope speed, envelope width, envelope amplitude, grayness, and complex modulation of our solution. It is interesting to note that the polarization vector of our mixed vector one-soliton evolves in sphere or hyperboloid depending upon the initial parametric choices.

Siphon flows in isolated magnetic flux tubes. III - The equilibrium path of the flux-tube arch

NASA Technical Reports Server (NTRS)

Thomas, John H.; Montesinos, Benjamin

1990-01-01

It is shown how to calculate the equilibrium path of a thin magnetic flux tube in a stratified, nonmagnetic atmosphere when the flux tube contains a steady siphon flow. The equilbrium path of a static thin flux tube in an infinite stratified atmosphere generally takes the form of a symmetric arch of finite width, with the flux tube becoming vertical at either end of the arch. A siphon flow within the flux tube increases the curvature of the arched equilibrium path in order that the net magnetic tension force can balance the inertial force of the flow, which tries to straighten the flux tube. Thus, a siphon flow reduces the width of the arched equilibrium path, with faster flows producing narrower arches. The effect of the siphon flow on the equilibrium path is generally greater for flux tubes of weaker magnetic field strength. Examples of the equilibrium are shown for both isothemal and adiabatic siphon flows in thin flux tubes in an isothermal external atmosphere.

Radiative heat transfer and nonequilibrium Casimir-Lifshitz force in many-body systems with planar geometry

NASA Astrophysics Data System (ADS)

Latella, Ivan; Ben-Abdallah, Philippe; Biehs, Svend-Age; Antezza, Mauro; Messina, Riccardo

2017-05-01

A general theory of photon-mediated energy and momentum transfer in N -body planar systems out of thermal equilibrium is introduced. It is based on the combination of the scattering theory and the fluctuational-electrodynamics approach in many-body systems. By making a Landauer-like formulation of the heat transfer problem, explicit formulas for the energy transmission coefficients between two distinct slabs as well as the self-coupling coefficients are derived and expressed in terms of the reflection and transmission coefficients of the single bodies. We also show how to calculate local equilibrium temperatures in such systems. An analogous formulation is introduced to quantify momentum transfer coefficients describing Casimir-Lifshitz forces out of thermal equilibrium. Forces at thermal equilibrium are readily obtained as a particular case. As an illustration of this general theoretical framework, we show on three-body systems how the presence of a fourth slab can impact equilibrium temperatures in heat-transfer problems and equilibrium positions resulting from the forces acting on the system.

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

PubMed

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

2013-07-21

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

A new problem in mathematical physics associated with the problem of coherent phase transformation

NASA Astrophysics Data System (ADS)

Grinfeld, M. A.

1985-06-01

The description of heterogeneous coherent phase equilibria in an elastic single component system is shown to lead, in the approximation of small intrinsic deformation, to a new problem in mathematical physics with an unknown bound. The low order terms of the resulting system of equilibrium equations coincide with the equations of the classical linear theory of elasticity (generally speaking, anisotropic); however, the problem remains strongly nonlinear overall, inasmuch as it contains an unknown bound and a boundary condition on it which is quadratic with respect to translation. The formulas obtained are used to find certain explicit solutions to the boundary problems. As an example, the problem of heterogeneous equilibria in an infinite rectangular isotropic beam with free faces and constant loading on the surfaces x squared = const can be examined. A modeling problem for the asymptote of small intrinsic deformation during coherent phase transformation is presented as a scalar analog of the vector problem considered initially.

Split Octonion Reformulation for Electromagnetic Chiral Media of Massive Dyons

NASA Astrophysics Data System (ADS)

Chanyal, B. C.

2017-12-01

In an explicit, unified, and covariant formulation of an octonion algebra, we study and generalize the electromagnetic chiral fields equations of massive dyons with the split octonionic representation. Starting with 2×2 Zorn’s vector matrix realization of split-octonion and its dual Euclidean spaces, we represent the unified structure of split octonionic electric and magnetic induction vectors for chiral media. As such, in present paper, we describe the chiral parameter and pairing constants in terms of split octonionic matrix representation of Drude-Born-Fedorov constitutive relations. We have expressed a split octonionic electromagnetic field vector for chiral media, which exhibits the unified field structure of electric and magnetic chiral fields of dyons. The beauty of split octonionic representation of Zorn vector matrix realization is that, the every scalar and vector components have its own meaning in the generalized chiral electromagnetism of dyons. Correspondingly, we obtained the alternative form of generalized Proca-Maxwell’s equations of massive dyons in chiral media. Furthermore, the continuity equations, Poynting theorem and wave propagation for generalized electromagnetic fields of chiral media of massive dyons are established by split octonionic form of Zorn vector matrix algebra.

A Newton method for the magnetohydrodynamic equilibrium equations

NASA Astrophysics Data System (ADS)

Oliver, Hilary James

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

Integrating Transgenic Vector Manipulation with Clinical Interventions to Manage Vector-Borne Diseases.

PubMed

Okamoto, Kenichi W; Gould, Fred; Lloyd, Alun L

2016-03-01

Many vector-borne diseases lack effective vaccines and medications, and the limitations of traditional vector control have inspired novel approaches based on using genetic engineering to manipulate vector populations and thereby reduce transmission. Yet both the short- and long-term epidemiological effects of these transgenic strategies are highly uncertain. If neither vaccines, medications, nor transgenic strategies can by themselves suffice for managing vector-borne diseases, integrating these approaches becomes key. Here we develop a framework to evaluate how clinical interventions (i.e., vaccination and medication) can be integrated with transgenic vector manipulation strategies to prevent disease invasion and reduce disease incidence. We show that the ability of clinical interventions to accelerate disease suppression can depend on the nature of the transgenic manipulation deployed (e.g., whether vector population reduction or replacement is attempted). We find that making a specific, individual strategy highly effective may not be necessary for attaining public-health objectives, provided suitable combinations can be adopted. However, we show how combining only partially effective antimicrobial drugs or vaccination with transgenic vector manipulations that merely temporarily lower vector competence can amplify disease resurgence following transient suppression. Thus, transgenic vector manipulation that cannot be sustained can have adverse consequences-consequences which ineffective clinical interventions can at best only mitigate, and at worst temporarily exacerbate. This result, which arises from differences between the time scale on which the interventions affect disease dynamics and the time scale of host population dynamics, highlights the importance of accounting for the potential delay in the effects of deploying public health strategies on long-term disease incidence. We find that for systems at the disease-endemic equilibrium, even modest perturbations induced by weak interventions can exhibit strong, albeit transient, epidemiological effects. This, together with our finding that under some conditions combining strategies could have transient adverse epidemiological effects suggests that a relatively long time horizon may be necessary to discern the efficacy of alternative intervention strategies.

Integrating Transgenic Vector Manipulation with Clinical Interventions to Manage Vector-Borne Diseases

PubMed Central

Okamoto, Kenichi W.; Gould, Fred; Lloyd, Alun L.

2016-01-01

Many vector-borne diseases lack effective vaccines and medications, and the limitations of traditional vector control have inspired novel approaches based on using genetic engineering to manipulate vector populations and thereby reduce transmission. Yet both the short- and long-term epidemiological effects of these transgenic strategies are highly uncertain. If neither vaccines, medications, nor transgenic strategies can by themselves suffice for managing vector-borne diseases, integrating these approaches becomes key. Here we develop a framework to evaluate how clinical interventions (i.e., vaccination and medication) can be integrated with transgenic vector manipulation strategies to prevent disease invasion and reduce disease incidence. We show that the ability of clinical interventions to accelerate disease suppression can depend on the nature of the transgenic manipulation deployed (e.g., whether vector population reduction or replacement is attempted). We find that making a specific, individual strategy highly effective may not be necessary for attaining public-health objectives, provided suitable combinations can be adopted. However, we show how combining only partially effective antimicrobial drugs or vaccination with transgenic vector manipulations that merely temporarily lower vector competence can amplify disease resurgence following transient suppression. Thus, transgenic vector manipulation that cannot be sustained can have adverse consequences—consequences which ineffective clinical interventions can at best only mitigate, and at worst temporarily exacerbate. This result, which arises from differences between the time scale on which the interventions affect disease dynamics and the time scale of host population dynamics, highlights the importance of accounting for the potential delay in the effects of deploying public health strategies on long-term disease incidence. We find that for systems at the disease-endemic equilibrium, even modest perturbations induced by weak interventions can exhibit strong, albeit transient, epidemiological effects. This, together with our finding that under some conditions combining strategies could have transient adverse epidemiological effects suggests that a relatively long time horizon may be necessary to discern the efficacy of alternative intervention strategies. PMID:26962871

A substructure coupling procedure applicable to general linear time-invariant dynamic systems

NASA Technical Reports Server (NTRS)

Howsman, T. G.; Craig, R. R., Jr.

1984-01-01

A substructure synthesis procedure applicable to structural systems containing general nonconservative terms is presented. In their final form, the nonself-adjoint substructure equations of motion are cast in state vector form through the use of a variational principle. A reduced-order mode for each substructure is implemented by representing the substructure as a combination of a small number of Ritz vectors. For the method presented, the substructure Ritz vectors are identified as a truncated set of substructure eigenmodes, which are typically complex, along with a set of generalized real attachment modes. The formation of the generalized attachment modes does not require any knowledge of the substructure flexible modes; hence, only the eigenmodes used explicitly as Ritz vectors need to be extracted from the substructure eigenproblem. An example problem is presented to illustrate the method.

Fluctuation-dissipation relation and stationary distribution of an exactly solvable many-particle model for active biomatter far from equilibrium.

PubMed

Netz, Roland R

2018-05-14

An exactly solvable, Hamiltonian-based model of many massive particles that are coupled by harmonic potentials and driven by stochastic non-equilibrium forces is introduced. The stationary distribution and the fluctuation-dissipation relation are derived in closed form for the general non-equilibrium case. Deviations from equilibrium are on one hand characterized by the difference of the obtained stationary distribution from the Boltzmann distribution; this is possible because the model derives from a particle Hamiltonian. On the other hand, the difference between the obtained non-equilibrium fluctuation-dissipation relation and the standard equilibrium fluctuation-dissipation theorem allows us to quantify non-equilibrium in an alternative fashion. Both indicators of non-equilibrium behavior, i.e., deviations from the Boltzmann distribution and deviations from the equilibrium fluctuation-dissipation theorem, can be expressed in terms of a single non-equilibrium parameter α that involves the ratio of friction coefficients and random force strengths. The concept of a non-equilibrium effective temperature, which can be defined by the relation between fluctuations and the dissipation, is by comparison with the exactly derived stationary distribution shown not to hold, even if the effective temperature is made frequency dependent. The analysis is not confined to close-to-equilibrium situations but rather is exact and thus holds for arbitrarily large deviations from equilibrium. Also, the suggested harmonic model can be obtained from non-linear mechanical network systems by an expansion in terms of suitably chosen deviatory coordinates; the obtained results should thus be quite general. This is demonstrated by comparison of the derived non-equilibrium fluctuation dissipation relation with experimental data on actin networks that are driven out of equilibrium by energy-consuming protein motors. The comparison is excellent and allows us to extract the non-equilibrium parameter α from experimental spectral response and fluctuation data.

Fluctuation-dissipation relation and stationary distribution of an exactly solvable many-particle model for active biomatter far from equilibrium

NASA Astrophysics Data System (ADS)

Netz, Roland R.

2018-05-01

An exactly solvable, Hamiltonian-based model of many massive particles that are coupled by harmonic potentials and driven by stochastic non-equilibrium forces is introduced. The stationary distribution and the fluctuation-dissipation relation are derived in closed form for the general non-equilibrium case. Deviations from equilibrium are on one hand characterized by the difference of the obtained stationary distribution from the Boltzmann distribution; this is possible because the model derives from a particle Hamiltonian. On the other hand, the difference between the obtained non-equilibrium fluctuation-dissipation relation and the standard equilibrium fluctuation-dissipation theorem allows us to quantify non-equilibrium in an alternative fashion. Both indicators of non-equilibrium behavior, i.e., deviations from the Boltzmann distribution and deviations from the equilibrium fluctuation-dissipation theorem, can be expressed in terms of a single non-equilibrium parameter α that involves the ratio of friction coefficients and random force strengths. The concept of a non-equilibrium effective temperature, which can be defined by the relation between fluctuations and the dissipation, is by comparison with the exactly derived stationary distribution shown not to hold, even if the effective temperature is made frequency dependent. The analysis is not confined to close-to-equilibrium situations but rather is exact and thus holds for arbitrarily large deviations from equilibrium. Also, the suggested harmonic model can be obtained from non-linear mechanical network systems by an expansion in terms of suitably chosen deviatory coordinates; the obtained results should thus be quite general. This is demonstrated by comparison of the derived non-equilibrium fluctuation dissipation relation with experimental data on actin networks that are driven out of equilibrium by energy-consuming protein motors. The comparison is excellent and allows us to extract the non-equilibrium parameter α from experimental spectral response and fluctuation data.

Mass transport properties of the tetrahydronaphthalene/n-dodecane mixture measured by investigating non-equilibrium fluctuations

NASA Astrophysics Data System (ADS)

Croccolo, Fabrizio; Scheffold, Frank; Bataller, Henri

2013-04-01

We present preliminary near-field light scattering (NFS) data concerning the analysis of the static power spectrum and of the relaxation time constant as a function of the wave vector for non-equilibrium fluctuations (NEFs). The goal of these measurements is to obtain information about the Soret and the mass diffusion coefficients of a binary mixture undergoing thermodiffusion. In particular, we show how the interaction between NEFs and the gravity force gives rise to a critical wavelength that provides additional information about the Soret coefficient. We suggest that a quantitative analysis can be performed by means of this non-invasive optical technique. In our setup, the sample is monitored parallel to the imposed temperature gradient, thus being insensitive to the refractive index profile along the vertical axis, while at the same time we are able to detect the light scattered by the refractive index fluctuations in horizontal planes. We select a shadowgraph layout for the NFS setup due to the extremely small wave vectors we aim to analyze. From a double-frame differential analysis of the acquired images, we obtain both the static power spectrum and the dynamics of NEFs. As a proof-of-principle experiment, we present Soret and diffusion coefficient data on a liquid mixture of tetrahydronaphthalene/n-dodecane.

Equilibrium theory of island biogeography: A review

Treesearch

Angela D. Yu; Simon A. Lei

2001-01-01

The topography, climatic pattern, location, and origin of islands generate unique patterns of species distribution. The equilibrium theory of island biogeography creates a general framework in which the study of taxon distribution and broad island trends may be conducted. Critical components of the equilibrium theory include the species-area relationship, island-...

Proper Conformal Killing Vectors in Kantowski-Sachs Metric

NASA Astrophysics Data System (ADS)

Hussain, Tahir; Farhan, Muhammad

2018-04-01

This paper deals with the existence of proper conformal Killing vectors (CKVs) in Kantowski-Sachs metric. Subject to some integrability conditions, the general form of vector filed generating CKVs and the conformal factor is presented. The integrability conditions are solved generally as well as in some particular cases to show that the non-conformally flat Kantowski-Sachs metric admits two proper CKVs, while it admits a 15-dimensional Lie algebra of CKVs in the case when it becomes conformally flat. The inheriting conformal Killing vectors (ICKVs), which map fluid lines conformally, are also investigated.

Quantum corrections to the generalized Proca theory via a matter field

NASA Astrophysics Data System (ADS)

Amado, André; Haghani, Zahra; Mohammadi, Azadeh; Shahidi, Shahab

2017-09-01

We study the quantum corrections to the generalized Proca theory via matter loops. We consider two types of interactions, linear and nonlinear in the vector field. Calculating the one-loop correction to the vector field propagator, three- and four-point functions, we show that the non-linear interactions are harmless, although they renormalize the theory. The linear matter-vector field interactions introduce ghost degrees of freedom to the generalized Proca theory. Treating the theory as an effective theory, we calculate the energy scale up to which the theory remains healthy.

The Sequential Implementation of Array Processors when there is Directional Uncertainty

DTIC Science & Technology

1975-08-01

University of Washington kindly supplied office space and ccputing facilities. -The author hat, benefited greatly from discussions with several other...if i Q- inverse of Q I L general observation space R general vector of observation _KR general observation vector of dimension K Exiv] "Tf -- ’ -"-T’T...7" i ’i ’:"’ - ’ ; ’ ’ ’ ’ ’ ’" ’"- Glossary of Symbols (continued) R. ith observation 1 Rm real vector space of dimension m R(T) autocorrelation

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

NASA Astrophysics Data System (ADS)

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.

The generalized formula for angular velocity vector of the moving coordinate system

NASA Astrophysics Data System (ADS)

Ermolin, Vladislav S.; Vlasova, Tatyana V.

2018-05-01

There are various ways for introducing the concept of the instantaneous angular velocity vector. In this paper we propose a method based on introducing of this concept by construction of the solution for the system of kinematic equations. These equations connect the function vectors defining the motion of the basis, and their derivatives. Necessary and sufficient conditions for the existence and uniqueness of the solution of this system are established. The instantaneous angular velocity vector is a solution of the algebraic system of equations. It is built explicitly. The derived formulas for the angular velocity vector generalize the earlier results, both for a basis of an affine oblique coordinate system and for an orthonormal basis.

Elastic theory of origami-based metamaterials

NASA Astrophysics Data System (ADS)

Brunck, V.; Lechenault, F.; Reid, A.; Adda-Bedia, M.

2016-03-01

Origami offers the possibility for new metamaterials whose overall mechanical properties can be programed by acting locally on each crease. Starting from a thin plate and having knowledge about the properties of the material and the folding procedure, one would like to determine the shape taken by the structure at rest and its mechanical response. In this article, we introduce a vector deformation field acting on the imprinted network of creases that allows us to express the geometrical constraints of rigid origami structures in a simple and systematic way. This formalism is then used to write a general covariant expression of the elastic energy of n -creases meeting at a single vertex. Computations of the equilibrium states are then carried out explicitly in two special cases: the generalized waterbomb base and the Miura-Ori. For the waterbomb, we show a generic bistability for any number of creases. For the Miura folding, however, we uncover a phase transition from monostable to bistable states that explains the efficient deployability of this structure for a given range of geometrical and mechanical parameters. Moreover, the analysis shows that geometric frustration induces residual stresses in origami structures that should be taken into account in determining their mechanical response. This formalism can be extended to a general crease network, ordered or otherwise, and so opens new perspectives for the mechanics and the physics of origami-based metamaterials.

Conformal field theory out of equilibrium: a review

NASA Astrophysics Data System (ADS)

Bernard, Denis; Doyon, Benjamin

2016-06-01

We provide a pedagogical review of the main ideas and results in non-equilibrium conformal field theory and connected subjects. These concern the understanding of quantum transport and its statistics at and near critical points. Starting with phenomenological considerations, we explain the general framework, illustrated by the example of the Heisenberg quantum chain. We then introduce the main concepts underlying conformal field theory (CFT), the emergence of critical ballistic transport, and the CFT scattering construction of non-equilibrium steady states. Using this we review the theory for energy transport in homogeneous one-dimensional critical systems, including the complete description of its large deviations and the resulting (extended) fluctuation relations. We generalize some of these ideas to one-dimensional critical charge transport and to the presence of defects, as well as beyond one-dimensional criticality. We describe non-equilibrium transport in free-particle models, where connections are made with generalized Gibbs ensembles, and in higher-dimensional and non-integrable quantum field theories, where the use of the powerful hydrodynamic ideas for non-equilibrium steady states is explained. We finish with a list of open questions. The review does not assume any advanced prior knowledge of conformal field theory, large-deviation theory or hydrodynamics.

Temperature in and out of equilibrium: A review of concepts, tools and attempts

NASA Astrophysics Data System (ADS)

Puglisi, A.; Sarracino, A.; Vulpiani, A.

2017-11-01

We review the general aspects of the concept of temperature in equilibrium and non-equilibrium statistical mechanics. Although temperature is an old and well-established notion, it still presents controversial facets. After a short historical survey of the key role of temperature in thermodynamics and statistical mechanics, we tackle a series of issues which have been recently reconsidered. In particular, we discuss different definitions and their relevance for energy fluctuations. The interest in such a topic has been triggered by the recent observation of negative temperatures in condensed matter experiments. Moreover, the ability to manipulate systems at the micro and nano-scale urges to understand and clarify some aspects related to the statistical properties of small systems (as the issue of temperature's ;fluctuations;). We also discuss the notion of temperature in a dynamical context, within the theory of linear response for Hamiltonian systems at equilibrium and stochastic models with detailed balance, and the generalized fluctuation-response relations, which provide a hint for an extension of the definition of temperature in far-from-equilibrium systems. To conclude we consider non-Hamiltonian systems, such as granular materials, turbulence and active matter, where a general theoretical framework is still lacking.

Using the Logarithmic Concentration Diagram, Log "C", to Teach Acid-Base Equilibrium

ERIC Educational Resources Information Center

Kovac, Jeffrey

2012-01-01

Acid-base equilibrium is one of the most important and most challenging topics in a typical general chemistry course. This article introduces an alternative to the algebraic approach generally used in textbooks, the graphical log "C" method. Log "C" diagrams provide conceptual insight into the behavior of aqueous acid-base systems and allow…

Detection of a sudden change of the field time series based on the Lorenz system

PubMed Central

Li, Fang; Shen, BingLu; Yan, PengCheng; Song, Jian; Ma, DeShan

2017-01-01

We conducted an exploratory study of the detection of a sudden change of the field time series based on the numerical solution of the Lorenz system. First, the time when the Lorenz path jumped between the regions on the left and right of the equilibrium point of the Lorenz system was quantitatively marked and the sudden change time of the Lorenz system was obtained. Second, the numerical solution of the Lorenz system was regarded as a vector; thus, this solution could be considered as a vector time series. We transformed the vector time series into a time series using the vector inner product, considering the geometric and topological features of the Lorenz system path. Third, the sudden change of the resulting time series was detected using the sliding t-test method. Comparing the test results with the quantitatively marked time indicated that the method could detect every sudden change of the Lorenz path, thus the method is effective. Finally, we used the method to detect the sudden change of the pressure field time series and temperature field time series, and obtained good results for both series, which indicates that the method can apply to high-dimension vector time series. Mathematically, there is no essential difference between the field time series and vector time series; thus, we provide a new method for the detection of the sudden change of the field time series. PMID:28141832

Perspective: Maximum caliber is a general variational principle for dynamical systems

NASA Astrophysics Data System (ADS)

Dixit, Purushottam D.; Wagoner, Jason; Weistuch, Corey; Pressé, Steve; Ghosh, Kingshuk; Dill, Ken A.

2018-01-01

We review here Maximum Caliber (Max Cal), a general variational principle for inferring distributions of paths in dynamical processes and networks. Max Cal is to dynamical trajectories what the principle of maximum entropy is to equilibrium states or stationary populations. In Max Cal, you maximize a path entropy over all possible pathways, subject to dynamical constraints, in order to predict relative path weights. Many well-known relationships of non-equilibrium statistical physics—such as the Green-Kubo fluctuation-dissipation relations, Onsager's reciprocal relations, and Prigogine's minimum entropy production—are limited to near-equilibrium processes. Max Cal is more general. While it can readily derive these results under those limits, Max Cal is also applicable far from equilibrium. We give examples of Max Cal as a method of inference about trajectory distributions from limited data, finding reaction coordinates in bio-molecular simulations, and modeling the complex dynamics of non-thermal systems such as gene regulatory networks or the collective firing of neurons. We also survey its basis in principle and some limitations.

Perspective: Maximum caliber is a general variational principle for dynamical systems.

PubMed

Dixit, Purushottam D; Wagoner, Jason; Weistuch, Corey; Pressé, Steve; Ghosh, Kingshuk; Dill, Ken A

2018-01-07

We review here Maximum Caliber (Max Cal), a general variational principle for inferring distributions of paths in dynamical processes and networks. Max Cal is to dynamical trajectories what the principle of maximum entropy is to equilibrium states or stationary populations. In Max Cal, you maximize a path entropy over all possible pathways, subject to dynamical constraints, in order to predict relative path weights. Many well-known relationships of non-equilibrium statistical physics-such as the Green-Kubo fluctuation-dissipation relations, Onsager's reciprocal relations, and Prigogine's minimum entropy production-are limited to near-equilibrium processes. Max Cal is more general. While it can readily derive these results under those limits, Max Cal is also applicable far from equilibrium. We give examples of Max Cal as a method of inference about trajectory distributions from limited data, finding reaction coordinates in bio-molecular simulations, and modeling the complex dynamics of non-thermal systems such as gene regulatory networks or the collective firing of neurons. We also survey its basis in principle and some limitations.

Advanced Techniques for Scene Analysis

DTIC Science & Technology

2010-06-01

robustness prefers a bigger intergration window to handle larger motions. The advantage of pyramidal implementation is that, while each motion vector dL...labeled SAR images. Now the previous algorithm leads to a more dedicated classifier for the particular target; however, our algorithm trades generality for...accuracy is traded for generality. 7.3.2 I-RELIEF Feature weighting transforms the original feature vector x into a new feature vector x′ by assigning each

Students' Understanding of Equilibrium and Stability: The Case of Dynamic Systems

ERIC Educational Resources Information Center

Canu, Michaël; de Hosson, Cécile; Duque, Mauricio

2016-01-01

Engineering students in control courses have been observed to lack an understanding of equilibrium and stability, both of which are crucial concepts in this discipline. The introduction of these concepts is generally based on the study of classical examples from Newtonian mechanics supplemented with a control system. Equilibrium and stability are…

The Equilibrium Constant for Bromothymol Blue: A General Chemistry Laboratory Experiment Using Spectroscopy

ERIC Educational Resources Information Center

Klotz, Elsbeth; Doyle, Robert; Gross, Erin; Mattson, Bruce

2011-01-01

A simple, inexpensive, and environmentally friendly undergraduate laboratory experiment is described in which students use visible spectroscopy to determine a numerical value for an equilibrium constant, K[subscript c]. The experiment correlates well with the lecture topic of equilibrium even though the subject of the study is an acid-base…

Using a Spreadsheet Scroll Bar to Solve Equilibrium Concentrations

ERIC Educational Resources Information Center

Raviolo, Andres

2012-01-01

A simple, conceptual method is described for using the spreadsheet scroll bar to find the composition of a system at chemical equilibrium. Simulation of any kind of chemical equilibrium can be carried out using this method, and the effects of different disturbances can be predicted. This simulation, which can be used in general chemistry…

Production of heavy sterile neutrinos from vector boson decay at electroweak temperatures

NASA Astrophysics Data System (ADS)

Lello, Louis; Boyanovsky, Daniel; Pisarski, Robert D.

2017-02-01

In the standard model extended with a seesaw mass matrix, we study the production of sterile neutrinos from the decay of vector bosons at temperatures near the masses of the electroweak bosons. We derive a general quantum kinetic equation for the production of sterile neutrinos and their effective mixing angles, which is applicable over a wide range of temperature, to all orders in interactions of the standard model and to leading order in a small mixing angle for the neutrinos. We emphasize the relation between the production rate and Landau damping at one-loop order and show that production rates and effective mixing angles depend sensitively upon the neutrino's helicity. Sterile neutrinos with positive helicity interact more weakly with the medium than those with negative helicity, and their effective mixing angle is not modified significantly. Negative helicity states couple more strongly to the vector bosons, but their mixing angle is strongly suppressed by the medium. Consequently, if the mass of the sterile neutrino is ≲8.35 MeV , there are fewer states with negative helicity produced than those with positive helicity. There is an Mikheyev-Smirnov-Wolfenstein-type resonance in the absence of lepton asymmetry, but due to screening by the damping rate, the production rate is not enhanced. Sterile neutrinos with negative helicity freeze out at Tf-≃5 GeV , whereas positive helicity neutrinos freeze out at Tf+≃8 GeV , with both distributions far from thermal. As the temperature decreases, due to competition between a decreasing production rate and an increasing mixing angle, the distribution function for states with negative helicity is broader in momentum and hotter than that for those with positive helicity. Sterile neutrinos produced via vector boson decay do not satisfy the abundance, lifetime, and cosmological constraints to be the sole dark matter component in the Universe. Massive sterile neutrinos produced via vector boson decay might solve the 7Li problem, albeit at the very edge of the possible parameter space. A heavy sterile neutrino with a mass of a few MeV could decay into light sterile neutrinos, of a few keV in mass, that contribute to warm dark matter. We argue that heavy sterile neutrinos with lifetime ≤1 /H0 reach local thermodynamic equilibrium.

Production of heavy sterile neutrinos from vector boson decay at electroweak temperatures

DOE PAGES

Lello, Louis; Boyanovsky, Daniel; Pisarski, Robert D.

2017-02-22

Here, in the standard model extended with a seesaw mass matrix, we study the production of sterile neutrinos from the decay of vector bosons at temperatures near the masses of the electroweak bosons. We derive a general quantum kinetic equation for the production of sterile neutrinos and their effective mixing angles, which is applicable over a wide range of temperature, to all orders in interactions of the standard model and to leading order in a small mixing angle for the neutrinos. We emphasize the relation between the production rate and Landau damping at one-loop order and show that production rates and effective mixing angles depend sensitively upon the neutrino’s helicity. Sterile neutrinos with positive helicity interact more weakly with the medium than those with negative helicity, and their effective mixing angle is not modified significantly. Negative helicity states couple more strongly to the vector bosons, but their mixing angle is strongly suppressed by the medium. Consequently, if the mass of the sterile neutrino is ≲ 8.35 MeV , there are fewer states with negative helicity produced than those with positive helicity. There is an Mikheyev-Smirnov-Wolfenstein-type resonance in the absence of lepton asymmetry, but due to screening by the damping rate, the production rate is not enhanced. Sterile neutrinos with negative helicity freeze out at Tmore » $$-\\atop{f}$$ ≃ 5 GeV , whereas positive helicity neutrinos freeze out at T$$+\\atop{f}$$≃ 8 GeV , with both distributions far from thermal. As the temperature decreases, due to competition between a decreasing production rate and an increasing mixing angle, the distribution function for states with negative helicity is broader in momentum and hotter than that for those with positive helicity. Sterile neutrinos produced via vector boson decay do not satisfy the abundance, lifetime, and cosmological constraints to be the sole dark matter component in the Universe. Massive sterile neutrinos produced via vector boson decay might solve the 7Li problem, albeit at the very edge of the possible parameter space. A heavy sterile neutrino with a mass of a few MeV could decay into light sterile neutrinos, of a few keV in mass, that contribute to warm dark matter. In conclusion, we argue that heavy sterile neutrinos with lifetime ≤1/H 0 reach local thermodynamic equilibrium.« less

Distributed Nash Equilibrium Seeking for Generalized Convex Games with Shared Constraints

NASA Astrophysics Data System (ADS)

Sun, Chao; Hu, Guoqiang

2018-05-01

In this paper, we deal with the problem of finding a Nash equilibrium for a generalized convex game. Each player is associated with a convex cost function and multiple shared constraints. Supposing that each player can exchange information with its neighbors via a connected undirected graph, the objective of this paper is to design a Nash equilibrium seeking law such that each agent minimizes its objective function in a distributed way. Consensus and singular perturbation theories are used to prove the stability of the system. A numerical example is given to show the effectiveness of the proposed algorithms.

Equivalence of equations describing trace element distribution during equilibrium partial melting

NASA Technical Reports Server (NTRS)

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

1976-01-01

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

Quasiclassical description of a superconductor with a spin density wave

NASA Astrophysics Data System (ADS)

Moor, A.; Volkov, A. F.; Efetov, K. B.

2011-04-01

We derive equations for the quasiclassical Green’s functions ǧ within a simple model of a two-band superconductor with a spin density wave (SDW). The elements of the matrix ǧ are the retarded, advanced, and Keldysh functions, each of which is an 8×8 matrix in the Gor’kov-Nambu, the spin, and the band space. In equilibrium, these equations are a generalization of the Eilenberger equation. On the basis of the derived equations, we analyze the Knight shift, the proximity, and the dc Josephson effects in the superconductors under consideration. The Knight shift is shown to depend on the orientation of the external magnetic field with respect to the direction of the vector of the magnetization of the SDW. The proximity effect is analyzed for an interface between a superconductor with the SDW and a normal metal. The function describing both superconducting and magnetic correlations is shown to penetrate the normal metal or a metal with the SDW due to the proximity effect. The dc Josephson current in an SSDW/N/SSDW junction is also calculated as a function of the phase difference φ. It is shown that in our model, the Josephson current does not depend on the mutual orientation of the magnetic moments in the superconductors SSDW and is proportional to sinφ. The dissipationless spin current jsp depends on the angle α between the magnetization vectors in the same way (jsp~sinα) and is not zero above the superconducting transition temperature.

Deviations from Equilibrium in Daytime Atmospheric Boundary Layer Turbulence arising from Nonstationary Mesoscale Forcing

NASA Astrophysics Data System (ADS)

Jayaraman, Balaji; Brasseur, James; Haupt, Sue; Lee, Jared

2016-11-01

LES of the "canonical" daytime atmospheric boundary layer (ABL) over flat topography is developed as an equilibrium ABL with steady surface heat flux, Q0 and steady unidirectional "geostrophic" wind vector Vg above a capping inversion. A strong inversion layer in daytime ABL acts as a "lid" that sharply separates 3D "microscale" ABL turbulence at the O(10) m scale from the quasi-2D "mesoscale" turbulent weather eddies (O(100) km scale). While "canonical" ABL is equilibrium, quasi-stationary and characterized statistically by the ratio of boundary layer depth (zi) to Obukhov length scale (- L) , the real mesoscale influences (Ug and Q0) that force a true daytime ABL are nonstationary at both diurnal and sub-diurnal time scales. We study the consequences of this non-stationarity on ABL dynamics by forcing ABL LES with realistic WRF simulations over flat Kansas terrain. Considering horizontal homogeneity, we relate the mesoscale and geostrophic winds, Ug and Vg, and systematically study the ABL turbulence response to non-steady variations in Q0 and Ug. We observe significant deviations from equilibrium, that manifest in many ways, such as the formation of "roll" eddies purely from changes in mesoscale wind direction that are normally associated with increased surface heat flux. Support from DOE. Compute resources from Penn State ICS.

Vectorized Jiles-Atherton hysteresis model

NASA Astrophysics Data System (ADS)

Szymański, Grzegorz; Waszak, Michał

2004-01-01

This paper deals with vector hysteresis modeling. A vector model consisting of individual Jiles-Atherton components placed along principal axes is proposed. The cross-axis coupling ensures general vector model properties. Minor loops are obtained using scaling method. The model is intended for efficient finite element method computations defined in terms of magnetic vector potential. Numerical efficiency is ensured by differential susceptibility approach.

Versatile generation of optical vector fields and vector beams using a non-interferometric approach.

PubMed

Tripathi, Santosh; Toussaint, Kimani C

2012-05-07

We present a versatile, non-interferometric method for generating vector fields and vector beams which can produce all the states of polarization represented on a higher-order Poincaré sphere. The versatility and non-interferometric nature of this method is expected to enable exploration of various exotic properties of vector fields and vector beams. To illustrate this, we study the propagation properties of some vector fields and find that, in general, propagation alters both their intensity and polarization distribution, and more interestingly, converts some vector fields into vector beams. In the article, we also suggest a modified Jones vector formalism to represent vector fields and vector beams.

Calculation of secondary-electron escape currents from inclined-spacecraft surfaces in a magnetic field

NASA Technical Reports Server (NTRS)

Laframboise, J. G.

1985-01-01

In low Earth orbit, the geomagnetic field B(vector) is strong enough that secondary electrons emitted from spacecraft surfaces have an average gyroradius much smaller than typical dimensions of large spacecraft. This implies that escape of secondaries will be strongly inhibited on surfaces which are nearly parallel to B(vector), even if a repelling electric field exists outside them. This effect is likely to make an important contribution to the current balance and hence the equilibrium potential of such surfaces, making high voltage charging of them more likely. Numerically calculated escaping secondary electron fluxes are presented for these conditions. For use in numerical spacecraft charging simulations, an analytic curve fit to these results is given which is accurate to within 3% of the emitted current.

Quasiperiodicity in time evolution of the Bloch vector under the thermal Jaynes-Cummings model

NASA Astrophysics Data System (ADS)

Azuma, Hiroo; Ban, Masashi

2014-07-01

We study a quasiperiodic structure in the time evolution of the Bloch vector, whose dynamics is governed by the thermal Jaynes-Cummings model (JCM). Putting the two-level atom into a certain pure state and the cavity field into a mixed state in thermal equilibrium at initial time, we let the whole system evolve according to the JCM Hamiltonian. During this time evolution, motion of the Bloch vector seems to be in disorder. Because of the thermal photon distribution, both a norm and a direction of the Bloch vector change hard at random. In this paper, taking a different viewpoint compared with ones that we have been used to, we investigate quasiperiodicity of the Bloch vector’s trajectories. Introducing the concept of the quasiperiodic motion, we can explain the confused behaviour of the system as an intermediate state between periodic and chaotic motions. More specifically, we discuss the following two facts: (1) If we adjust the time interval Δt properly, figures consisting of plotted dots at the constant time interval acquire scale invariance under replacement of Δt by sΔt, where s(>1) is an arbitrary real but not transcendental number. (2) We can compute values of the time variable t, which let |Sz(t)| (the absolute value of the z-component of the Bloch vector) be very small, with the Diophantine approximation (a rational approximation of an irrational number).

A general equilibrium model of ecosystem services in a river basin

Treesearch

Travis Warziniack

2014-01-01

This study builds a general equilibrium model of ecosystem services, with sectors of the economy competing for use of the environment. The model recognizes that production processes in the real world require a combination of natural and human inputs, and understanding the value of these inputs and their competing uses is necessary when considering policies of resource...

Are Equity and Efficiency Irreconcilable Goals in Education? A General Equilibrium Analysis of Basic Education Finance in China

ERIC Educational Resources Information Center

Ding, Weili; Lu, Ming

2007-01-01

Lacking guidance of general equilibrium (GE) theories in public economics and the corresponding proper mechanisms, China has not surprisingly witnessed an inequality in educational expenditures across regions as well as insufficiency of funds for education in poor areas. It is wrongly thought that what happens is due to the decentralized financing…

Bioproducts and environmental quality: Biofuels, greenhouse gases, and water quality

NASA Astrophysics Data System (ADS)

Ren, Xiaolin

Promoting bio-based products is one oft-proposed solution to reduce GHG emissions because the feedstocks capture carbon, offsetting at least partially the carbon discharges resulting from use of the products. However, several life cycle analyses point out that while biofuels may emit less life cycle net carbon emissions than fossil fuels, they may exacerbate other parts of biogeochemical cycles, notably nutrient loads in the aquatic environment. In three essays, this dissertation explores the tradeoff between GHG emissions and nitrogen leaching associated with biofuel production using general equilibrium models. The first essay develops a theoretical general equilibrium model to calculate the second-best GHG tax with the existence of a nitrogen leaching distortion. The results indicate that the second-best GHG tax could be higher or lower than the first-best tax rates depending largely on the elasticity of substitution between fossil fuel and biofuel. The second and third essays employ computable general equilibrium models to further explore the tradeoff between GHG emissions and nitrogen leaching. The computable general equilibrium models also incorporate multiple biofuel pathways, i.e., biofuels made from different feedstocks using different processes, to identify the cost-effective combinations of biofuel pathways under different policies, and the corresponding economic and environmental impacts.

Teaching Chemical Equilibrium and Thermodynamics in Undergraduate General Chemistry Classes.

ERIC Educational Resources Information Center

Banerjee, Anil C.

1995-01-01

Discusses some of the conceptual difficulties encountered by undergraduate students in learning certain aspects of chemical equilibrium and thermodynamics. Discusses teaching strategies for dealing with these difficulties. (JRH)

14 CFR 29.471 - General.

Code of Federal Regulations, 2010 CFR

2010-01-01

... equilibrium. For limit ground loads— (1) The limit ground loads obtained in the landing conditions in this... equilibrium with linear and angular inertia loads in a rational or conservative manner. (b) Critical centers...

Finite-deformation phase-field chemomechanics for multiphase, multicomponent solids

NASA Astrophysics Data System (ADS)

Svendsen, Bob; Shanthraj, Pratheek; Raabe, Dierk

2018-03-01

The purpose of this work is the development of a framework for the formulation of geometrically non-linear inelastic chemomechanical models for a mixture of multiple chemical components diffusing among multiple transforming solid phases. The focus here is on general model formulation. No specific model or application is pursued in this work. To this end, basic balance and constitutive relations from non-equilibrium thermodynamics and continuum mixture theory are combined with a phase-field-based description of multicomponent solid phases and their interfaces. Solid phase modeling is based in particular on a chemomechanical free energy and stress relaxation via the evolution of phase-specific concentration fields, order-parameter fields (e.g., related to chemical ordering, structural ordering, or defects), and local internal variables. At the mixture level, differences or contrasts in phase composition and phase local deformation in phase interface regions are treated as mixture internal variables. In this context, various phase interface models are considered. In the equilibrium limit, phase contrasts in composition and local deformation in the phase interface region are determined via bulk energy minimization. On the chemical side, the equilibrium limit of the current model formulation reduces to a multicomponent, multiphase, generalization of existing two-phase binary alloy interface equilibrium conditions (e.g., KKS). On the mechanical side, the equilibrium limit of one interface model considered represents a multiphase generalization of Reuss-Sachs conditions from mechanical homogenization theory. Analogously, other interface models considered represent generalizations of interface equilibrium conditions consistent with laminate and sharp-interface theory. In the last part of the work, selected existing models are formulated within the current framework as special cases and discussed in detail.

Kinetic attractor phase diagrams of active nematic suspensions: the dilute regime.

PubMed

Forest, M Gregory; Wang, Qi; Zhou, Ruhai

2015-08-28

Large-scale simulations by the authors of the kinetic-hydrodynamic equations for active polar nematics revealed a variety of spatio-temporal attractors, including steady and unsteady, banded (1d) and cellular (2d) spatial patterns. These particle scale activation-induced attractors arise at dilute nanorod volume fractions where the passive equilibrium phase is isotropic, whereas all previous model simulations have focused on the semi-dilute, nematic equilibrium regime and mostly on low-moment orientation tensor and polarity vector models. Here we extend our previous results to complete attractor phase diagrams for active nematics, with and without an explicit polar potential, to map out novel spatial and dynamic transitions, and to identify some new attractors, over the parameter space of dilute nanorod volume fraction and nanorod activation strength. The particle-scale activation parameter corresponds experimentally to a tunable force dipole strength (so-called pushers with propulsion from the rod tail) generated by active rod macromolecules, e.g., catalysis with the solvent phase, ATP-induced propulsion, or light-activated propulsion. The simulations allow 2d spatial variations in all flow and orientational variables and full spherical orientational degrees of freedom; the attractors correspond to numerical integration of a coupled system of 125 nonlinear PDEs in 2d plus time. The phase diagrams with and without the polar interaction potential are remarkably similar, implying that polar interactions among the rodlike particles are not essential to long-range spatial and temporal correlations in flow, polarity, and nematic order. As a general rule, above a threshold, low volume fractions induce 1d banded patterns, whereas higher yet still dilute volume fractions yield 2d patterns. Again as a general rule, varying activation strength at fixed volume fraction induces novel dynamic transitions. First, stationary patterns saturate the instability of the isotropic state, consisting of discrete 1d banded or 2d cellular patterns depending on nanorod volume fraction. Increasing activation strength further induces a sequence of attractor bifurcations, including oscillations superimposed on the 1d and 2d stationary patterns, a uniform translational motion of 1d and 2d oscillating patterns, and periodic switching between 1d and 2d patterns. These results imply that active macromolecular suspensions are capable of long-range spatial and dynamic organization at isotropic equilibrium concentrations, provided particle-scale activation is sufficiently strong.

Mutation-selection equilibrium in games with mixed strategies.

PubMed

Tarnita, Corina E; Antal, Tibor; Nowak, Martin A

2009-11-07

We develop a new method for studying stochastic evolutionary game dynamics of mixed strategies. We consider the general situation: there are n pure strategies whose interactions are described by an nxn payoff matrix. Players can use mixed strategies, which are given by the vector (p(1),...,p(n)). Each entry specifies the probability to use the corresponding pure strategy. The sum over all entries is one. Therefore, a mixed strategy is a point in the simplex S(n). We study evolutionary dynamics in a well-mixed population of finite size. Individuals reproduce proportional to payoff. We consider the case of weak selection, which means the payoff from the game is only a small contribution to overall fitness. Reproduction can be subject to mutation; a mutant adopts a randomly chosen mixed strategy. We calculate the average abundance of every mixed strategy in the stationary distribution of the mutation-selection process. We find the crucial conditions that specify if a strategy is favored or opposed by selection. One condition holds for low mutation rate, another for high mutation rate. The result for any mutation rate is a linear combination of those two. As a specific example we study the Hawk-Dove game. We prove general statements about the relationship between games with pure and with mixed strategies.

Effect of a Perturbation on the Chemical Equilibrium: Comparison with Le Châtelier's Principle

NASA Astrophysics Data System (ADS)

Martínez Torres, Emilio

2007-03-01

This article develops a general thermodynamic treatment to predict the direction of shift in a chemical equilibrium when it is subjected to a stress. This treatment gives an inequality that relates the change in the perturbed variable and the change that the equilibrium shift produces in the conjugated variable. To illustrate the generality of this approach, it has been applied to predict the direction of shift caused by changes of pressure, volume, and amount of substance. In this last case, the well-known unexpected shift in the ammonia synthesis equilibrium upon addition of nitrogen is easily explained. From the above referred inequality and the stability criteria of thermodynamics some conclusions have been obtained about the direction of shift in terms of extensive and extensive variables. This article is suitable for physical chemistry courses.

Universal laws of human society's income distribution

NASA Astrophysics Data System (ADS)

Tao, Yong

2015-10-01

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

Decay width of hadronic molecule structure for quarks

NASA Astrophysics Data System (ADS)

Chen, Xiaozhao; Lü, Xiaofu

2018-06-01

Based on the general form of the Bethe-Salpeter wave functions for the bound states consisting of two vector fields, we obtain the general formulas for the decay widths of molecular states composed of two heavy vector mesons with arbitrary spin and parity into a heavy meson plus a light meson. In this approach, our attention is still focused on the internal structure of heavy vector mesons in the molecular state. According to the molecule state model of exotic meson, we give the generalized Bethe-Salpeter wave function of molecular state as a four-quark state. Then the observed Y (3940 ) state is considered as a molecular state consisting of two heavy vector mesons D*0D¯*0 and the strong Y (3940 )→J /ψ ω decay width is calculated. The numerical result is consistent with the experimental values.

Condition of Mechanical Equilibrium at the Phase Interface with Arbitrary Geometry

NASA Astrophysics Data System (ADS)

Zubkov, V. V.; Zubkova, A. V.

2017-09-01

The authors produced an expression for the mechanical equilibrium condition at the phase interface within the force definition of surface tension. This equilibrium condition is the most general one from the mathematical standpoint and takes into account the three-dimensional aspect of surface tension. Furthermore, the formula produced allows describing equilibrium on the fractal surface of the interface. The authors used the fractional integral model of fractal distribution and took the fractional order integrals over Euclidean space instead of integrating over the fractal set.

Flux Jacobian Matrices For Equilibrium Real Gases

NASA Technical Reports Server (NTRS)

Vinokur, Marcel

1990-01-01

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

Geometry of generalized depolarizing channels

NASA Astrophysics Data System (ADS)

Burrell, Christian K.

2009-10-01

A generalized depolarizing channel acts on an N -dimensional quantum system to compress the “Bloch ball” in N2-1 directions; it has a corresponding compression vector. We investigate the geometry of these compression vectors and prove a conjecture of Dixit and Sudarshan [Phys. Rev. A 78, 032308 (2008)], namely, that when N=2d (i.e., the system consists of d qubits), and we work in the Pauli basis then the set of all compression vectors forms a simplex. We extend this result by investigating the geometry in other bases; in particular we find precisely when the set of all compression vectors forms a simplex.

Geometry of generalized depolarizing channels

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

Burrell, Christian K.

2009-10-15

A generalized depolarizing channel acts on an N-dimensional quantum system to compress the 'Bloch ball' in N{sup 2}-1 directions; it has a corresponding compression vector. We investigate the geometry of these compression vectors and prove a conjecture of Dixit and Sudarshan [Phys. Rev. A 78, 032308 (2008)], namely, that when N=2{sup d} (i.e., the system consists of d qubits), and we work in the Pauli basis then the set of all compression vectors forms a simplex. We extend this result by investigating the geometry in other bases; in particular we find precisely when the set of all compression vectors formsmore » a simplex.« less

Nonlinear Viscoelastic Mechanics of Cross-linked Rubbers

NASA Technical Reports Server (NTRS)

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

2002-01-01

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

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

NASA Technical Reports Server (NTRS)

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

2002-01-01

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

Realistic soft tissue deformation strategies for real time surgery simulation.

PubMed

Shen, Yunhe; Zhou, Xiangmin; Zhang, Nan; Tamma, Kumar; Sweet, Robert

2008-01-01

A volume-preserving deformation method (VPDM) is developed in complement with the mass-spring method (MSM) to improve the deformation quality of the MSM to model soft tissue in surgical simulation. This method can also be implemented as a stand-alone model. The proposed VPDM satisfies the Newton's laws of motion by obtaining the resultant vectors form an equilibrium condition. The proposed method has been tested in virtual surgery systems with haptic rendering demands.

Large-Scale Parallel Simulations of Turbulent Combustion using Combined Dimension Reduction and Tabulation of Chemistry

DTIC Science & Technology

2012-05-22

tabulation of the reduced space is performed using the In Situ Adaptive Tabulation ( ISAT ) algorithm. In addition, we use x2f mpi – a Fortran library...for parallel vector-valued function evaluation (used with ISAT in this context) – to efficiently redistribute the chemistry workload among the...Constrained-Equilibrium (RCCE) method, and tabulation of the reduced space is performed using the In Situ Adaptive Tabulation ( ISAT ) algorithm. In addition

Parametric FEM for geometric biomembranes

NASA Astrophysics Data System (ADS)

Bonito, Andrea; Nochetto, Ricardo H.; Sebastian Pauletti, M.

2010-05-01

We consider geometric biomembranes governed by an L2-gradient flow for bending energy subject to area and volume constraints (Helfrich model). We give a concise derivation of a novel vector formulation, based on shape differential calculus, and corresponding discretization via parametric FEM using quadratic isoparametric elements and a semi-implicit Euler method. We document the performance of the new parametric FEM with a number of simulations leading to dumbbell, red blood cell and toroidal equilibrium shapes while exhibiting large deformations.

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

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

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

Semiexperimental equilibrium structures for building blocks of organic and biological molecules: the B2PLYP route.

PubMed

Penocchio, Emanuele; Piccardo, Matteo; Barone, Vincenzo

2015-10-13

The B2PLYP double hybrid functional, coupled with the correlation-consistent triple-ζ cc-pVTZ (VTZ) basis set, has been validated in the framework of the semiexperimental (SE) approach for deriving accurate equilibrium structures of molecules containing up to 15 atoms. A systematic comparison between new B2PLYP/VTZ results and several equilibrium SE structures previously determined at other levels, in particular B3LYP/SNSD and CCSD(T) with various basis sets, has put in evidence the accuracy and the remarkable stability of such model chemistry for both equilibrium structures and vibrational corrections. New SE equilibrium structures for phenylacetylene, pyruvic acid, peroxyformic acid, and phenyl radical are discussed and compared with literature data. Particular attention has been devoted to the discussion of systems for which lack of sufficient experimental data prevents a complete SE determination. In order to obtain an accurate equilibrium SE structure for these situations, the so-called templating molecule approach is discussed and generalized with respect to our previous work. Important applications are those involving biological building blocks, like uracil and thiouracil. In addition, for more general situations the linear regression approach has been proposed and validated.

Numerical simulation of weakly ionized hypersonic flow over reentry capsules

NASA Astrophysics Data System (ADS)

Scalabrin, Leonardo C.

The mathematical and numerical formulation employed in the development of a new multi-dimensional Computational Fluid Dynamics (CFD) code for the simulation of weakly ionized hypersonic flows in thermo-chemical non-equilibrium over reentry configurations is presented. The flow is modeled using the Navier-Stokes equations modified to include finite-rate chemistry and relaxation rates to compute the energy transfer between different energy modes. The set of equations is solved numerically by discretizing the flowfield using unstructured grids made of any mixture of quadrilaterals and triangles in two-dimensions or hexahedra, tetrahedra, prisms and pyramids in three-dimensions. The partial differential equations are integrated on such grids using the finite volume approach. The fluxes across grid faces are calculated using a modified form of the Steger-Warming Flux Vector Splitting scheme that has low numerical dissipation inside boundary layers. The higher order extension of inviscid fluxes in structured grids is generalized in this work to be used in unstructured grids. Steady state solutions are obtained by integrating the solution over time implicitly. The resulting sparse linear system is solved by using a point implicit or by a line implicit method in which a tridiagonal matrix is assembled by using lines of cells that are formed starting at the wall. An algorithm that assembles these lines using completely general unstructured grids is developed. The code is parallelized to allow simulation of computationally demanding problems. The numerical code is successfully employed in the simulation of several hypersonic entry flows over space capsules as part of its validation process. Important quantities for the aerothermodynamics design of capsules such as aerodynamic coefficients and heat transfer rates are compared to available experimental and flight test data and other numerical results yielding very good agreement. A sensitivity analysis of predicted radiative heating of a space capsule to several thermo-chemical non-equilibrium models is also performed.

Generalized decompositions of dynamic systems and vector Lyapunov functions

NASA Astrophysics Data System (ADS)

Ikeda, M.; Siljak, D. D.

1981-10-01

The notion of decomposition is generalized to provide more freedom in constructing vector Lyapunov functions for stability analysis of nonlinear dynamic systems. A generalized decomposition is defined as a disjoint decomposition of a system which is obtained by expanding the state-space of a given system. An inclusion principle is formulated for the solutions of the expansion to include the solutions of the original system, so that stability of the expansion implies stability of the original system. Stability of the expansion can then be established by standard disjoint decompositions and vector Lyapunov functions. The applicability of the new approach is demonstrated using the Lotka-Volterra equations.

The Influence of the Orbital Evolution of Main Belt Asteroids on Their Spin Vectors

NASA Astrophysics Data System (ADS)

Skoglöv, E.; Erikson, A.

2002-11-01

It was found that certain features in the observed spin vector distribution of main belt asteroids can be explained by the differences in the dynamical spin vector evolution between objects with high and low orbital inclinations. In particular, the deficiency of high-inclination objects whose spin vectors are close to the ecliptic plane can be accounted for. The present spin vector distribution of main belt asteroids is due to several factors connected with their collisional and dynamical evolution. In this paper, the influence of the orbital evolution on the spin axis of asteroids is examined in the case of 25 objects with typical main belt orbital evolution and 125 synthetic objects, during an integration over a time period of 1 Myr. This investigation produced the following general results: • The difference between maximum and minimum obliquity increases in an approximately linear fashion with increasing orbital inclination of the studied objects. • The inclination is the major factor influencing the magnitude of the obliquity variation. This variation is generally larger for asteroids with their initial spin vectors located close to the orbital plane. • In general, the regular obliquity differences are relatively insensitive to differences in the shape, composition, and spin rate of the asteroids. The result is compared with the properties of the observed spin vectors for 73 main belt asteroids and good agreement is found between the above results and the existing spin vector distribution.

Relativistic stars in vector-tensor theories

NASA Astrophysics Data System (ADS)

Kase, Ryotaro; Minamitsuji, Masato; Tsujikawa, Shinji

2018-04-01

We study relativistic star solutions in second-order generalized Proca theories characterized by a U (1 )-breaking vector field with derivative couplings. In the models with cubic and quartic derivative coupling, the mass and radius of stars become larger than those in general relativity for negative derivative coupling constants. This phenomenon is mostly attributed to the increase of star radius induced by a slower decrease of the matter pressure compared to general relativity. There is a tendency that the relativistic star with a smaller mass is not gravitationally bound for a low central density and hence is dynamically unstable, but that with a larger mass is gravitationally bound. On the other hand, we show that the intrinsic vector-mode couplings give rise to general relativistic solutions with a trivial field profile, so the mass and radius are not modified from those in general relativity.

Generalized thermodynamic relations for a system experiencing heat and mass diffusion in the far-from-equilibrium realm based on steepest entropy ascent.

PubMed

Li, Guanchen; von Spakovsky, Michael R

2016-09-01

This paper presents a nonequilibrium thermodynamic model for the relaxation of a local, isolated system in nonequilibrium using the principle of steepest entropy ascent (SEA), which can be expressed as a variational principle in thermodynamic state space. The model is able to arrive at the Onsager relations for such a system. Since no assumption of local equilibrium is made, the conjugate fluxes and forces are intrinsic to the subspaces of the system's state space and are defined using the concepts of hypoequilibrium state and nonequilibrium intensive properties, which describe the nonmutual equilibrium status between subspaces of the thermodynamic state space. The Onsager relations are shown to be a thermodynamic kinematic feature of the system independent of the specific details of the micromechanical dynamics. Two kinds of relaxation processes are studied with different constraints (i.e., conservation laws) corresponding to heat and mass diffusion. Linear behavior in the near-equilibrium region as well as nonlinear behavior in the far-from-equilibrium region are discussed. Thermodynamic relations in the equilibrium and near-equilibrium realm, including the Gibbs relation, the Clausius inequality, and the Onsager relations, are generalized to the far-from-equilibrium realm. The variational principle in the space spanned by the intrinsic conjugate fluxes and forces is expressed via the quadratic dissipation potential. As an application, the model is applied to the heat and mass diffusion of a system represented by a single-particle ensemble, which can also be applied to a simple system of many particles. Phenomenological transport coefficients are also derived in the near-equilibrium realm.

Visualizing vector field topology in fluid flows

NASA Technical Reports Server (NTRS)

Helman, James L.; Hesselink, Lambertus

1991-01-01

Methods of automating the analysis and display of vector field topology in general and flow topology in particular are discussed. Two-dimensional vector field topology is reviewed as the basis for the examination of topology in three-dimensional separated flows. The use of tangent surfaces and clipping in visualizing vector field topology in fluid flows is addressed.

ms2: A molecular simulation tool for thermodynamic properties

NASA Astrophysics Data System (ADS)

Deublein, Stephan; Eckl, Bernhard; Stoll, Jürgen; Lishchuk, Sergey V.; Guevara-Carrion, Gabriela; Glass, Colin W.; Merker, Thorsten; Bernreuther, Martin; Hasse, Hans; Vrabec, Jadran

2011-11-01

This work presents the molecular simulation program ms2 that is designed for the calculation of thermodynamic properties of bulk fluids in equilibrium consisting of small electro-neutral molecules. ms2 features the two main molecular simulation techniques, molecular dynamics (MD) and Monte-Carlo. It supports the calculation of vapor-liquid equilibria of pure fluids and multi-component mixtures described by rigid molecular models on the basis of the grand equilibrium method. Furthermore, it is capable of sampling various classical ensembles and yields numerous thermodynamic properties. To evaluate the chemical potential, Widom's test molecule method and gradual insertion are implemented. Transport properties are determined by equilibrium MD simulations following the Green-Kubo formalism. ms2 is designed to meet the requirements of academia and industry, particularly achieving short response times and straightforward handling. It is written in Fortran90 and optimized for a fast execution on a broad range of computer architectures, spanning from single processor PCs over PC-clusters and vector computers to high-end parallel machines. The standard Message Passing Interface (MPI) is used for parallelization and ms2 is therefore easily portable to different computing platforms. Feature tools facilitate the interaction with the code and the interpretation of input and output files. The accuracy and reliability of ms2 has been shown for a large variety of fluids in preceding work. Program summaryProgram title:ms2 Catalogue identifier: AEJF_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJF_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Special Licence supplied by the authors No. of lines in distributed program, including test data, etc.: 82 794 No. of bytes in distributed program, including test data, etc.: 793 705 Distribution format: tar.gz Programming language: Fortran90 Computer: The simulation tool ms2 is usable on a wide variety of platforms, from single processor machines over PC-clusters and vector computers to vector-parallel architectures. (Tested with Fortran compilers: gfortran, Intel, PathScale, Portland Group and Sun Studio.) Operating system: Unix/Linux, Windows Has the code been vectorized or parallelized?: Yes. Message Passing Interface (MPI) protocol Scalability. Excellent scalability up to 16 processors for molecular dynamics and >512 processors for Monte-Carlo simulations. RAM:ms2 runs on single processors with 512 MB RAM. The memory demand rises with increasing number of processors used per node and increasing number of molecules. Classification: 7.7, 7.9, 12 External routines: Message Passing Interface (MPI) Nature of problem: Calculation of application oriented thermodynamic properties for rigid electro-neutral molecules: vapor-liquid equilibria, thermal and caloric data as well as transport properties of pure fluids and multi-component mixtures. Solution method: Molecular dynamics, Monte-Carlo, various classical ensembles, grand equilibrium method, Green-Kubo formalism. Restrictions: No. The system size is user-defined. Typical problems addressed by ms2 can be solved by simulating systems containing typically 2000 molecules or less. Unusual features: Feature tools are available for creating input files, analyzing simulation results and visualizing molecular trajectories. Additional comments: Sample makefiles for multiple operation platforms are provided. Documentation is provided with the installation package and is available at http://www.ms-2.de. Running time: The running time of ms2 depends on the problem set, the system size and the number of processes used in the simulation. Running four processes on a "Nehalem" processor, simulations calculating VLE data take between two and twelve hours, calculating transport properties between six and 24 hours.

A Functional Central Limit Theorem for the Becker-Döring Model

NASA Astrophysics Data System (ADS)

Sun, Wen

2018-04-01

We investigate the fluctuations of the stochastic Becker-Döring model of polymerization when the initial size of the system converges to infinity. A functional central limit problem is proved for the vector of the number of polymers of a given size. It is shown that the stochastic process associated to fluctuations is converging to the strong solution of an infinite dimensional stochastic differential equation (SDE) in a Hilbert space. We also prove that, at equilibrium, the solution of this SDE is a Gaussian process. The proofs are based on a specific representation of the evolution equations, the introduction of a convenient Hilbert space and several technical estimates to control the fluctuations, especially of the first coordinate which interacts with all components of the infinite dimensional vector representing the state of the process.

Gravity Perception in a Cladoceran-zooplankter: Anatomy of Antennal Socket Setae of Daphnia Magna

NASA Technical Reports Server (NTRS)

Meyers, D. G.

1985-01-01

Night orientation in Daphnia magna was recently associated with setae on the basal socket of the swimming antennae. Daphnids are suspected of maintaining nocturnal equilibrium by monitoring the gravity vector through upward setal deflections caused by sinking between antennal swimming strokes. Setae appear to be hydrodynamic rheoceptors that sense the gravity vector indirectly by mechanoreceptivity to the direction and velocity of water currents. Neuroanatomical stains have revealed cell bodies at the base of the setal shafts, dendritic connections through to the distal ends of the shafts, and axonal tracts around the antennal socket connecting with an additional cell body and continuing toward the brain. These anatomical observations combined with previous scanning electron microscopy studies suggest that the setae are similar to mechanoreceptors and propreceptors used by higher crustaceans to sense water currents and gravity, and maintained balance.

Wigner functions for fermions in strong magnetic fields

NASA Astrophysics Data System (ADS)

Sheng, Xin-li; Rischke, Dirk H.; Vasak, David; Wang, Qun

2018-02-01

We compute the covariant Wigner function for spin-(1/2) fermions in an arbitrarily strong magnetic field by exactly solving the Dirac equation at non-zero fermion-number and chiral-charge densities. The Landau energy levels as well as a set of orthonormal eigenfunctions are found as solutions of the Dirac equation. With these orthonormal eigenfunctions we construct the fermion field operators and the corresponding Wigner-function operator. The Wigner function is obtained by taking the ensemble average of the Wigner-function operator in global thermodynamical equilibrium, i.e., at constant temperature T and non-zero fermion-number and chiral-charge chemical potentials μ and μ_5, respectively. Extracting the vector and axial-vector components of the Wigner function, we reproduce the currents of the chiral magnetic and separation effect in an arbitrarily strong magnetic field.

Applicability of Markets to Global Scheduling in Grids: Critical Examination of General Equilibrium Theory and Market Folklore

NASA Technical Reports Server (NTRS)

Nakai, Junko; VanDerWijngaart, Rob F.

2003-01-01

Markets are often considered superior to other global scheduling mechanisms for distributed computing systems. This claim is supported by: a casual observation from our every-day life that markets successfully equilibrate supply and demand, and the features of markets which originate in the general equilibrium theory, e.g., efficiency and the lack of necessity of 2 central controller. This paper describes why such beliefs in markets are not warranted. It does so by examining the general equilibrium theory, in terms of scope, abstraction, and interpretation. Not only does the general equilibrium theory fail to provide a satisfactory explanation of actual economies, including a computing-resource economy, it also falls short of supplying theoretical foundations for commonly held views of market desirability. This paper also points out that the argument for the desirability of markets involves circular reasoning and that the desirability can be established only vis-a-vis a scheduling goal. Finally, recasting the conclusion of Arrow's Impossibility Theorem as that for global scheduling, we conclude that there exists no market-based scheduler that is rational (in the sense defined in microeconomic theory), takes into account utility of more than one user, and yet yields a Pareto-optimal outcome for arbitrary user utility functions.

Answer Sets in a Fuzzy Equilibrium Logic

NASA Astrophysics Data System (ADS)

Schockaert, Steven; Janssen, Jeroen; Vermeir, Dirk; de Cock, Martine

Since its introduction, answer set programming has been generalized in many directions, to cater to the needs of real-world applications. As one of the most general “classical” approaches, answer sets of arbitrary propositional theories can be defined as models in the equilibrium logic of Pearce. Fuzzy answer set programming, on the other hand, extends answer set programming with the capability of modeling continuous systems. In this paper, we combine the expressiveness of both approaches, and define answer sets of arbitrary fuzzy propositional theories as models in a fuzzification of equilibrium logic. We show that the resulting notion of answer set is compatible with existing definitions, when the syntactic restrictions of the corresponding approaches are met. We furthermore locate the complexity of the main reasoning tasks at the second level of the polynomial hierarchy. Finally, as an illustration of its modeling power, we show how fuzzy equilibrium logic can be used to find strong Nash equilibria.

Thyra Abstract Interface Package

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

Bartlett, Roscoe A.

2005-09-01

Thrya primarily defines a set of abstract C++ class interfaces needed for the development of abstract numerical atgorithms (ANAs) such as iterative linear solvers, transient solvers all the way up to optimization. At the foundation of these interfaces are abstract C++ classes for vectors, vector spaces, linear operators and multi-vectors. Also included in the Thyra package is C++ code for creating concrete vector, vector space, linear operator, and multi-vector subclasses as well as other utilities to aid in the development of ANAs. Currently, very general and efficient concrete subclass implementations exist for serial and SPMD in-core vectors and multi-vectors. Codemore » also currently exists for testing objects and providing composite objects such as product vectors.« less

Isobaric molecular dynamics version of the generalized replica exchange method (gREM): Liquid–vapor equilibrium

DOE PAGES

Malolepsza, Edyta; Secor, Maxim; Keyes, Tom

2015-09-23

A prescription for sampling isobaric generalized ensembles with molecular dynamics is presented and applied to the generalized replica exchange method (gREM), which was designed for simulating first-order phase transitions. The properties of the isobaric gREM ensemble are discussed and a study is presented of the liquid-vapor equilibrium of the guest molecules given for gas hydrate formation with the mW water model. As a result, phase diagrams, critical parameters, and a law of corresponding states are obtained.

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

NASA Astrophysics Data System (ADS)

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

2016-03-01

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

Generalized adsorption isotherms for molecular and dissociative adsorption of a polar molecular species on two polar surface geometries: Perovskite (100) (Pm-3m) and fluorite (111) (Fm-3m)

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

Danielson, Thomas; Hin, Celine; Savara, Aditya

Lattice based kinetic Monte Carlo (KMC) simulations have been used to determine a functional form for the second order adsorption isotherms on two commonly investigated crystal surfaces: the (111) fluorite surface and the (100) perovskite surface which has the same geometric symmetry as the NaCl (100) surface. The functional form is generalized to be applicable to all values of the equilibrium constant by a shift along the pressure axis. Functions have been determined for estimating the pressure at which a desired coverage would be achieved and for estimating the coverage at a certain pressure. The generalized form has been calculatedmore » by investigating the surface adsorbate coverage across a range of thermodynamic equilibrium constants that span the range 10-26 to 1013. Finally, the equations have been shown to be general for any value of the adsorption equilibrium constant.« less

Generalized adsorption isotherms for molecular and dissociative adsorption of a polar molecular species on two polar surface geometries: Perovskite (100) (Pm-3m) and fluorite (111) (Fm-3m)

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

Danielson, Thomas; Hin, Celine; Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061

Lattice based kinetic Monte Carlo simulations have been used to determine a functional form for the second order adsorption isotherms on two commonly investigated crystal surfaces: the (111) fluorite surface and the (100) perovskite surface which has the same geometric symmetry as the NaCl (100) surface. The functional form is generalized to be applicable to all values of the equilibrium constant by a shift along the pressure axis. Functions have been determined for estimating the pressure at which a desired coverage would be achieved and, conversely, for estimating the coverage at a certain pressure. The generalized form has been calculatedmore » by investigating the surface adsorbate coverage across a range of thermodynamic equilibrium constants that span the range 10{sup −26} to 10{sup 13}. The equations have been shown to be general for any value of the adsorption equilibrium constant.« less

Generalized adsorption isotherms for molecular and dissociative adsorption of a polar molecular species on two polar surface geometries: Perovskite (100) (Pm-3m) and fluorite (111) (Fm-3m)

DOE PAGES

Danielson, Thomas; Hin, Celine; Savara, Aditya

2016-08-10

Lattice based kinetic Monte Carlo (KMC) simulations have been used to determine a functional form for the second order adsorption isotherms on two commonly investigated crystal surfaces: the (111) fluorite surface and the (100) perovskite surface which has the same geometric symmetry as the NaCl (100) surface. The functional form is generalized to be applicable to all values of the equilibrium constant by a shift along the pressure axis. Functions have been determined for estimating the pressure at which a desired coverage would be achieved and for estimating the coverage at a certain pressure. The generalized form has been calculatedmore » by investigating the surface adsorbate coverage across a range of thermodynamic equilibrium constants that span the range 10-26 to 1013. Finally, the equations have been shown to be general for any value of the adsorption equilibrium constant.« less

Generalized sidelobe canceller beamforming method for ultrasound imaging.

PubMed

Wang, Ping; Li, Na; Luo, Han-Wu; Zhu, Yong-Kun; Cui, Shi-Gang

2017-03-01

A modified generalized sidelobe canceller (IGSC) algorithm is proposed to enhance the resolution and robustness against the noise of the traditional generalized sidelobe canceller (GSC) and coherence factor combined method (GSC-CF). In the GSC algorithm, weighting vector is divided into adaptive and non-adaptive parts, while the non-adaptive part does not block all the desired signal. A modified steer vector of the IGSC algorithm is generated by the projection of the non-adaptive vector on the signal space constructed by the covariance matrix of received data. The blocking matrix is generated based on the orthogonal complementary space of the modified steer vector and the weighting vector is updated subsequently. The performance of IGSC was investigated by simulations and experiments. Through simulations, IGSC outperformed GSC-CF in terms of spatial resolution by 0.1 mm regardless there is noise or not, as well as the contrast ratio respect. The proposed IGSC can be further improved by combining with CF. The experimental results also validated the effectiveness of the proposed algorithm with dataset provided by the University of Michigan.

Weaving Knotted Vector Fields with Tunable Helicity.

PubMed

Kedia, Hridesh; Foster, David; Dennis, Mark R; Irvine, William T M

2016-12-30

We present a general construction of divergence-free knotted vector fields from complex scalar fields, whose closed field lines encode many kinds of knots and links, including torus knots, their cables, the figure-8 knot, and its generalizations. As finite-energy physical fields, they represent initial states for fields such as the magnetic field in a plasma, or the vorticity field in a fluid. We give a systematic procedure for calculating the vector potential, starting from complex scalar functions with knotted zero filaments, thus enabling an explicit computation of the helicity of these knotted fields. The construction can be used to generate isolated knotted flux tubes, filled by knots encoded in the lines of the vector field. Lastly, we give examples of manifestly knotted vector fields with vanishing helicity. Our results provide building blocks for analytical models and simulations alike.

Black hole perturbations in vector-tensor theories: the odd-mode analysis

NASA Astrophysics Data System (ADS)

Kase, Ryotaro; Minamitsuji, Masato; Tsujikawa, Shinji; Zhang, Ying-li

2018-02-01

In generalized Proca theories with vector-field derivative couplings, a bunch of hairy black hole solutions have been derived on a static and spherically symmetric background. In this paper, we formulate the odd-parity black hole perturbations in generalized Proca theories by expanding the corresponding action up to second order and investigate whether or not black holes with vector hair suffer ghost or Laplacian instabilities. We show that the models with cubic couplings G3(X), where X=‑AμAμ/2 with a vector field Aμ, do not provide any additional stability condition as in General Relativity. On the other hand, the exact charged stealth Schwarzschild solution with a nonvanishing longitudinal vector component A1, which originates from the coupling to the Einstein tensor GμνAμ Aν equivalent to the quartic coupling G4(X) containing a linear function of X, is unstable in the vicinity of the event horizon. The same instability problem also persists for hairy black holes arising from general quartic power-law couplings G4(X) ⊃ β4 Xn with the nonvanishing A1, while the other branch with A1=0 can be consistent with conditions for the absence of ghost and Laplacian instabilities. We also discuss the case of other exact and numerical black hole solutions associated with intrinsic vector-field derivative couplings and show that there exists a wide range of parameter spaces in which the solutions suffer neither ghost nor Laplacian instabilities against odd-parity perturbations.

WARP3D-Release 10.8: Dynamic Nonlinear Analysis of Solids using a Preconditioned Conjugate Gradient Software Architecture

NASA Technical Reports Server (NTRS)

Koppenhoefer, Kyle C.; Gullerud, Arne S.; Ruggieri, Claudio; Dodds, Robert H., Jr.; Healy, Brian E.

1998-01-01

This report describes theoretical background material and commands necessary to use the WARP3D finite element code. WARP3D is under continuing development as a research code for the solution of very large-scale, 3-D solid models subjected to static and dynamic loads. Specific features in the code oriented toward the investigation of ductile fracture in metals include a robust finite strain formulation, a general J-integral computation facility (with inertia, face loading), an element extinction facility to model crack growth, nonlinear material models including viscoplastic effects, and the Gurson-Tver-gaard dilatant plasticity model for void growth. The nonlinear, dynamic equilibrium equations are solved using an incremental-iterative, implicit formulation with full Newton iterations to eliminate residual nodal forces. The history integration of the nonlinear equations of motion is accomplished with Newmarks Beta method. A central feature of WARP3D involves the use of a linear-preconditioned conjugate gradient (LPCG) solver implemented in an element-by-element format to replace a conventional direct linear equation solver. This software architecture dramatically reduces both the memory requirements and CPU time for very large, nonlinear solid models since formation of the assembled (dynamic) stiffness matrix is avoided. Analyses thus exhibit the numerical stability for large time (load) steps provided by the implicit formulation coupled with the low memory requirements characteristic of an explicit code. In addition to the much lower memory requirements of the LPCG solver, the CPU time required for solution of the linear equations during each Newton iteration is generally one-half or less of the CPU time required for a traditional direct solver. All other computational aspects of the code (element stiffnesses, element strains, stress updating, element internal forces) are implemented in the element-by- element, blocked architecture. This greatly improves vectorization of the code on uni-processor hardware and enables straightforward parallel-vector processing of element blocks on multi-processor hardware.

Dynamics of the microaggregate composition of chernozem in relation to changes in the content of organic matter

NASA Astrophysics Data System (ADS)

Kryshchenko, V. S.; Zamulina, I. V.; Rybyanets, T. V.; Kravtsova, N. E.; Biryukova, O. A.; Golozubov, O. M.

2016-06-01

Monitoring of soil dispersivity and humus state has been performed in the stationary profile of ordinary chernozem in the Botanic Garden of the Southern Federal University in 2009-2014. The contents of physical clay and sand are almost stable in time, which indicates a quasi-static (climax) equilibrium in the soil. Another (reversible dynamic) process occurs simultaneously: seasonal and annual variation in the mass fractions of clay and silt in physical clay. Variations of humus content in the whole soil and in its physical clay are also observed on the background of seasonal changes in precipitation and temperature. A procedure has been developed for the analysis of the polydisperse soil system with consideration for the quasi-static and dynamic equilibriums. A two-vector coordinate system has been introduced, which consists of scales for changes in the contents of physical clay and physical sand in 100 g of soil and changes in the fractions of clay and silt in 100 g of physical clay. Co-measurements of two dispersivity series of soil samples—actual dynamic and calculated under quasi-static equilibrium (ideal)—have been performed. Dynamic equilibrium coefficients, which cumulatively reflect the varying proportions of physical clay and physical sand in the soil and the mass fractions of clay and silt in physical clay, have been calculated.

Van der Waals interactions between planar substrate and tubular lipid membranes undergoing pearling instability

NASA Astrophysics Data System (ADS)

Valchev, G. S.; Djondjorov, P. A.; Vassilev, V. M.; Dantchev, D. M.

2017-10-01

In the current article we study the behavior of the van der Waals force between a planar substrate and an axisymmetric bilayer lipid membrane undergoing pearling instability, caused by uniform hydrostatic pressure difference. To do so, the recently suggested "surface integration approach" is used, which can be considered a generalization of the well known and widely used Derjaguin approximation. The static equilibrium shape after the occurrence of the instability is described in the framework of Helfrich's spontaneous curvature model. Some specific classes of exact analytical solutions to the corresponding shape equation are considered, and the components of the respective position vectors given in terms of elliptic integrals and Jacobi elliptic functions. The mutual orientation between the interacting objects is chosen such that the axis of revolution of the distorted cylinder be parallel to the plane bounding the substrate. Based on the discussed models and approaches we made some estimations for the studied force in real experimentally realizable systems, thus showing the possibility of pearling as an useful technique for reduction of the adhesion in variety of industrial processes using lipid membranes as carriers.

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

NASA Astrophysics Data System (ADS)

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.

A General Method for Automatic Computation of Equilibrium Compositions and Theoretical Rocket Performance of Propellants

NASA Technical Reports Server (NTRS)

Gordon, Sanford; Zeleznik, Frank J.; Huff, Vearl N.

1959-01-01

A general computer program for chemical equilibrium and rocket performance calculations was written for the IBM 650 computer with 2000 words of drum storage, 60 words of high-speed core storage, indexing registers, and floating point attachments. The program is capable of carrying out combustion and isentropic expansion calculations on a chemical system that may include as many as 10 different chemical elements, 30 reaction products, and 25 pressure ratios. In addition to the equilibrium composition, temperature, and pressure, the program calculates specific impulse, specific impulse in vacuum, characteristic velocity, thrust coefficient, area ratio, molecular weight, Mach number, specific heat, isentropic exponent, enthalpy, entropy, and several thermodynamic first derivatives.

Global stability of a multiple delayed viral infection model with general incidence rate and an application to HIV infection.

PubMed

Ji, Yu

2015-06-01

In this paper, the dynamical behavior of a viral infection model with general incidence rate and two time delays is studied. By using the Lyapunov functional and LaSalle invariance principle, the global stabilities of the infection-free equilibrium and the endemic equilibrium are obtained. We obtain a threshold of the global stability for the uninfected equilibrium, which means the disease will be under control eventually. These results can be applied to a variety of viral infections of disease that would make it possible to devise optimal treatment strategies. Numerical simulations with application to HIV infection are given to verify the analytical results.

Semi-automatic feedback using concurrence between mixture vectors for general databases

NASA Astrophysics Data System (ADS)

Larabi, Mohamed-Chaker; Richard, Noel; Colot, Olivier; Fernandez-Maloigne, Christine

2001-12-01

This paper describes how a query system can exploit the basic knowledge by employing semi-automatic relevance feedback to refine queries and runtimes. For general databases, it is often useless to call complex attributes, because we have not sufficient information about images in the database. Moreover, these images can be topologically very different from one to each other and an attribute that is powerful for a database category may be very powerless for the other categories. The idea is to use very simple features, such as color histogram, correlograms, Color Coherence Vectors (CCV), to fill out the signature vector. Then, a number of mixture vectors is prepared depending on the number of very distinctive categories in the database. Knowing that a mixture vector is a vector containing the weight of each attribute that will be used to compute a similarity distance. We post a query in the database using successively all the mixture vectors defined previously. We retain then the N first images for each vector in order to make a mapping using the following information: Is image I present in several mixture vectors results? What is its rank in the results? These informations allow us to switch the system on an unsupervised relevance feedback or user's feedback (supervised feedback).

Optimal source coding, removable noise elimination, and natural coordinate system construction for general vector sources using replicator neural networks

NASA Astrophysics Data System (ADS)

Hecht-Nielsen, Robert

1997-04-01

A new universal one-chart smooth manifold model for vector information sources is introduced. Natural coordinates (a particular type of chart) for such data manifolds are then defined. Uniformly quantized natural coordinates form an optimal vector quantization code for a general vector source. Replicator neural networks (a specialized type of multilayer perceptron with three hidden layers) are the introduced. As properly configured examples of replicator networks approach minimum mean squared error (e.g., via training and architecture adjustment using randomly chosen vectors from the source), these networks automatically develop a mapping which, in the limit, produces natural coordinates for arbitrary source vectors. The new concept of removable noise (a noise model applicable to a wide variety of real-world noise processes) is then discussed. Replicator neural networks, when configured to approach minimum mean squared reconstruction error (e.g., via training and architecture adjustment on randomly chosen examples from a vector source, each with randomly chosen additive removable noise contamination), in the limit eliminate removable noise and produce natural coordinates for the data vector portions of the noise-corrupted source vectors. Consideration regarding selection of the dimension of a data manifold source model and the training/configuration of replicator neural networks are discussed.

Studying non-equilibrium many-body dynamics using one-dimensional Bose gases

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

Langen, Tim; Gring, Michael; Kuhnert, Maximilian

2014-12-04

Non-equilibrium dynamics of isolated quantum many-body systems play an important role in many areas of physics. However, a general answer to the question of how these systems relax is still lacking. We experimentally study the dynamics of ultracold one-dimensional (1D) Bose gases. This reveals the existence of a quasi-steady prethermalized state which differs significantly from the thermal equilibrium of the system. Our results demonstrate that the dynamics of non-equilibrium quantum many-body systems is a far richer process than has been assumed in the past.

Shape characteristics of equilibrium and non-equilibrium fractal clusters.

PubMed

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 between the viscosity and hydrodynamic radii, as potential measures of shape anisotropy. We also find a strong correlation between anisotropy and effective fractal dimension. These observations should provide new practical methods for quantifying the nature of particle clustering in diverse contexts.

Quantized Overcomplete Expansions: Analysis, Synthesis and Algorithms

DTIC Science & Technology

1995-07-01

would be in the spirit of the Lempel - Ziv algorithm . The decoder would have to be aware of changes in the dictionary, but depending on the nature of the...37 3.4 A General Vector Compression Algorithm Based on Frames : : : : : : : : : : 40 ii 3.4.1 Design Considerations...x3.3. Along with exploring general properties of matching pursuit, we are interested in its application to compressing data vectors in RN. A general

A Damage-Dependent Finite Element Analysis for Fiber-Reinforced Composite Laminates

NASA Technical Reports Server (NTRS)

Coats, Timothy W.; Harris, Charles E.

1998-01-01

A progressive damage methodology has been developed to predict damage growth and residual strength of fiber-reinforced composite structure with through penetrations such as a slit. The methodology consists of a damage-dependent constitutive relationship based on continuum damage mechanics. Damage is modeled using volume averaged strain-like quantities known as internal state variables and is represented in the equilibrium equations as damage induced force vectors instead of the usual degradation and modification of the global stiffness matrix.

Implementation of Premixed Equilibrium Chemistry Capability in OVERFLOW

NASA Technical Reports Server (NTRS)

Olsen, M. E.; Liu, Y.; Vinokur, M.; Olsen, T.

2003-01-01

An implementation of premixed equilibrium chemistry has been completed for the OVERFLOW code, a chimera capable, complex geometry flow code widely used to predict transonic flowfields. The implementation builds on the computational efficiency and geometric generality of the solver.

Implementation of Premixed Equilibrium Chemistry Capability in OVERFLOW

NASA Technical Reports Server (NTRS)

Olsen, Mike E.; Liu, Yen; Vinokur, M.; Olsen, Tom

2004-01-01

An implementation of premixed equilibrium chemistry has been completed for the OVERFLOW code, a chimera capable, complex geometry flow code widely used to predict transonic flowfields. The implementation builds on the computational efficiency and geometric generality of the solver.

Non-equilibrium thermodynamics, maximum entropy production and Earth-system evolution.

PubMed

Kleidon, Axel

2010-01-13

The present-day atmosphere is in a unique state far from thermodynamic equilibrium. This uniqueness is for instance reflected in the high concentration of molecular oxygen and the low relative humidity in the atmosphere. Given that the concentration of atmospheric oxygen has likely increased throughout Earth-system history, we can ask whether this trend can be generalized to a trend of Earth-system evolution that is directed away from thermodynamic equilibrium, why we would expect such a trend to take place and what it would imply for Earth-system evolution as a whole. The justification for such a trend could be found in the proposed general principle of maximum entropy production (MEP), which states that non-equilibrium thermodynamic systems maintain steady states at which entropy production is maximized. Here, I justify and demonstrate this application of MEP to the Earth at the planetary scale. I first describe the non-equilibrium thermodynamic nature of Earth-system processes and distinguish processes that drive the system's state away from equilibrium from those that are directed towards equilibrium. I formulate the interactions among these processes from a thermodynamic perspective and then connect them to a holistic view of the planetary thermodynamic state of the Earth system. In conclusion, non-equilibrium thermodynamics and MEP have the potential to provide a simple and holistic theory of Earth-system functioning. This theory can be used to derive overall evolutionary trends of the Earth's past, identify the role that life plays in driving thermodynamic states far from equilibrium, identify habitability in other planetary environments and evaluate human impacts on Earth-system functioning. This journal is © 2010 The Royal Society

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

NASA Technical Reports Server (NTRS)

Lerche, I.; Low, B. C.

1980-01-01

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

Metric of two balancing Kerr particles in physical parametrization

NASA Astrophysics Data System (ADS)

Manko, V. S.; Ruiz, E.

2015-11-01

The present paper aims at elaborating a completely physical representation for the general 4-parameter family of the extended double-Kerr spacetimes describing two spinning sources in gravitational equilibrium. This involved problem is solved in a concise analytical form by using the individual Komar masses and angular momenta as arbitrary parameters, and the simplest equatorially symmetric specialization of the general expressions obtained by us yields the physical representation for the well-known Dietz-Hoenselaers superextreme case of two balancing identical Kerr constituents. The existence of the physically meaningful "black-hole-superextreme-object" equilibrium configurations permitted by the general solution may be considered as a clear indication that the spin-spin repulsion force might actually be by far stronger than expected earlier, when only the balance between two superextreme Kerr sources was thought possible. We also present the explicit analytical formulas relating the equilibrium states in the double-Kerr and double-Reissner-Nordström configurations.

General equilibrium incidence of energy taxation

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

Solow, J.L.

1984-04-01

The pervasiveness of energy in the economy and the numerous ways in which energy taxation can distort resource allocations implies the necessity of a general equilibrium approach to the question of energy tax incidence. The author presents a general equilibrium model that accounts for domestic energy production and energy imports, direct energy consumption and use of energy as an intermediate good, and production of energy intensive and nonenergy intensive goods. He examines the incidence of three broadly-based energy taxation policies: a tax on all energy consumption, a subsidy to domestic energy production, and a tariff on energy imports. The subsidy,more » although not a revenue raising measure, is included because, like the other policies, it acts to reduce energy imports. Such a measure may be of interest by reducing reliance on unstable foreign sources of supply. 12 references, 3 tables.« less

A Variational Method in Out-of-Equilibrium Physical Systems

PubMed Central

Pinheiro, Mario J.

2013-01-01

We propose a new variational principle for out-of-equilibrium dynamic systems that are fundamentally based on the method of Lagrange multipliers applied to the total entropy of an ensemble of particles. However, we use the fundamental equation of thermodynamics on differential forms, considering U and S as 0-forms. We obtain a set of two first order differential equations that reveal the same formal symplectic structure shared by classical mechanics, fluid mechanics and thermodynamics. From this approach, a topological torsion current emerges of the form , where Aj and ωk denote the components of the vector potential (gravitational and/or electromagnetic) and where ω denotes the angular velocity of the accelerated frame. We derive a special form of the Umov-Poynting theorem for rotating gravito-electromagnetic systems. The variational method is then applied to clarify the working mechanism of particular devices. PMID:24316718

Magnetofermionic condensate in two dimensions

PubMed Central

Kulik, L. V.; Zhuravlev, A. S.; Dickmann, S.; Gorbunov, A. V.; Timofeev, V. B.; Kukushkin, I. V.; Schmult, S.

2016-01-01

Coherent condensate states of particles obeying either Bose or Fermi statistics are in the focus of interest in modern physics. Here we report on condensation of collective excitations with Bose statistics, cyclotron magnetoexcitons, in a high-mobility two-dimensional electron system in a magnetic field. At low temperatures, the dense non-equilibrium ensemble of long-lived triplet magnetoexcitons exhibits both a drastic reduction in the viscosity and a steep enhancement in the response to the external electromagnetic field. The observed effects are related to formation of a super-absorbing state interacting coherently with the electromagnetic field. Simultaneously, the electrons below the Fermi level form a super-emitting state. The effects are explicable from the viewpoint of a coherent condensate phase in a non-equilibrium system of two-dimensional fermions with a fully quantized energy spectrum. The condensation occurs in the space of vectors of magnetic translations, a property providing a completely new landscape for future physical investigations. PMID:27848969

Coronal emission-line polarization from the statistical equilibrium of magnetic sublevels. II. Fe XIV 5303 A

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

House, L.L.; Querfeld, C.W.; Rees, D.E.

1982-04-15

Coronal magnetic fields influence in the intensity and linear polarization of light scattered by coronal Fe XIV ions. To interpret polarization measurements of Fe XIV 5303 A coronal emission requires a detailed understanding of the dependence of the emitted Stokes vector on coronal magnetic field direction, electron density, and temperature and on height of origin. The required dependence is included in the solutions of statistical equilibrium for the ion which are solved explicitly for 34 magnetic sublevels in both the ground and four excited terms. The full solutions are reduced to equivalent simple analytic forms which clearly show the requiredmore » dependence on coronal conditions. The analytic forms of the reduced solutions are suitable for routine analysis of 5303 green line polarimetric data obtained at Pic du Midi and from the Solar Maximum Mission Coronagraph/Polarimeter.« less

Spontaneity and Equilibrium: Why "?G < 0 Denotes a Spontaneous Process" and "?G = 0 Means the System Is at Equilibrium" Are Incorrect

ERIC Educational Resources Information Center

Raff, Lionel M.

2014-01-01

The fundamental criteria for chemical reactions to be spontaneous in a given direction are generally incorrectly stated as ?G < 0 or ?A < 0 in most introductory chemistry textbooks and even in some more advanced texts. Similarly, the criteria for equilibrium are also misstated as being ?G = 0 or ?A = 0. Following a brief review of the…

Response solutions and quasi-periodic degenerate bifurcations for quasi-periodically forced systems

NASA Astrophysics Data System (ADS)

Si, Wen; Si, Jianguo

2018-06-01

This paper includes two parts. In the first part, we first focus on quasi-periodic time dependent perturbations of one-dimensional quasi-periodically forced systems with degenerate equilibrium. We study the system in two cases, for one of which system admits a response solution under a non-resonant condition on the frequency vector weaker than Brjuno–Rüssmann’s and for another of which system also admits a response solution without any non-resonant conditions. Next, we investigate the existence of response solutions of a quasi-periodic perturbed system with degenerate (including completely degenerate) equilibrium under Brjuno–Rüssmann’s non-resonant condition by using the Herman method. In the second part, we consider, firstly, the quasi-periodic perturbation of a universal unfolding of one-dimensional degenerate vector field . Secondly, we consider the perturbation of a universal unfolding of normal two-dimensional Hamiltonian system with completely degenerate equilibrium. With KAM theory and singularity theory, we show that these two classes of universal unfolding can persist on large Cantor sets under Brjuno–Rüssmann’s non-resonant condition, which implies all the invariant tori in the integrable part and all the bifurcation scenario can survive on large Cantor sets. The result for Hamiltonian system can apply directly to the response context for quasi-periodically forced systems. Our results in this paper can be regarded as an improvement with respect to several results in various literature (Broer et al 2005 Nonlinearity 18 1735–69 Broer et al 2006 J. Differ. Equ. 222 233–62 Wagener 2005 J. Differ. Equ. 216 216–81 Xu 2010 J. Differ. Equ. 250 551–71 Xu and Jiang 2010 Ergod. Theor. Dynam. Syst. 31 599–611 Lu and Xu 2014 Nonlinear Differ. Equ. Appl. 21 361–70). This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 11171185, 11571201).

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

NASA Astrophysics Data System (ADS)

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

2014-08-01

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

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

PubMed

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

2014-08-14

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

Equilibrium Distribution Functions: Another Look.

ERIC Educational Resources Information Center

Waite, Boyd A.

1986-01-01

Discusses equilibrium distribution functions and provides an alternative "derivation" that allows the student, with the help of a computer, to gain intuitive insight as to the nature of distributions in general and the precise nature of the dominance of the Boltzmann distribution. (JN)

Machine learning predictions of molecular properties: Accurate many-body potentials and nonlocality in chemical space

DOE PAGES

Hansen, Katja; Biegler, Franziska; Ramakrishnan, Raghunathan; ...

2015-06-04

Simultaneously accurate and efficient prediction of molecular properties throughout chemical compound space is a critical ingredient toward rational compound design in chemical and pharmaceutical industries. Aiming toward this goal, we develop and apply a systematic hierarchy of efficient empirical methods to estimate atomization and total energies of molecules. These methods range from a simple sum over atoms, to addition of bond energies, to pairwise interatomic force fields, reaching to the more sophisticated machine learning approaches that are capable of describing collective interactions between many atoms or bonds. In the case of equilibrium molecular geometries, even simple pairwise force fields demonstratemore » prediction accuracy comparable to benchmark energies calculated using density functional theory with hybrid exchange-correlation functionals; however, accounting for the collective many-body interactions proves to be essential for approaching the “holy grail” of chemical accuracy of 1 kcal/mol for both equilibrium and out-of-equilibrium geometries. This remarkable accuracy is achieved by a vectorized representation of molecules (so-called Bag of Bonds model) that exhibits strong nonlocality in chemical space. The same representation allows us to predict accurate electronic properties of molecules, such as their polarizability and molecular frontier orbital energies.« less

Machine Learning Predictions of Molecular Properties: Accurate Many-Body Potentials and Nonlocality in Chemical Space

PubMed Central

2015-01-01

Simultaneously accurate and efficient prediction of molecular properties throughout chemical compound space is a critical ingredient toward rational compound design in chemical and pharmaceutical industries. Aiming toward this goal, we develop and apply a systematic hierarchy of efficient empirical methods to estimate atomization and total energies of molecules. These methods range from a simple sum over atoms, to addition of bond energies, to pairwise interatomic force fields, reaching to the more sophisticated machine learning approaches that are capable of describing collective interactions between many atoms or bonds. In the case of equilibrium molecular geometries, even simple pairwise force fields demonstrate prediction accuracy comparable to benchmark energies calculated using density functional theory with hybrid exchange-correlation functionals; however, accounting for the collective many-body interactions proves to be essential for approaching the “holy grail” of chemical accuracy of 1 kcal/mol for both equilibrium and out-of-equilibrium geometries. This remarkable accuracy is achieved by a vectorized representation of molecules (so-called Bag of Bonds model) that exhibits strong nonlocality in chemical space. In addition, the same representation allows us to predict accurate electronic properties of molecules, such as their polarizability and molecular frontier orbital energies. PMID:26113956

Dynamic relaxation of a levitated nanoparticle from a non-equilibrium steady state.

PubMed

Gieseler, Jan; Quidant, Romain; Dellago, Christoph; Novotny, Lukas

2014-05-01

Fluctuation theorems are a generalization of thermodynamics on small scales and provide the tools to characterize the fluctuations of thermodynamic quantities in non-equilibrium nanoscale systems. They are particularly important for understanding irreversibility and the second law in fundamental chemical and biological processes that are actively driven, thus operating far from thermal equilibrium. Here, we apply the framework of fluctuation theorems to investigate the important case of a system relaxing from a non-equilibrium state towards equilibrium. Using a vacuum-trapped nanoparticle, we demonstrate experimentally the validity of a fluctuation theorem for the relative entropy change occurring during relaxation from a non-equilibrium steady state. The platform established here allows non-equilibrium fluctuation theorems to be studied experimentally for arbitrary steady states and can be extended to investigate quantum fluctuation theorems as well as systems that do not obey detailed balance.

Three sympatric clusters of the malaria vector Anopheles culicifacies E (Diptera: Culicidae) detected in Sri Lanka.

PubMed

Harischandra, Iresha Nilmini; Dassanayake, Ranil Samantha; De Silva, Bambaranda Gammacharige Don Nissanka Kolitha

2016-01-04

The disease re-emergence threat from the major malaria vector in Sri Lanka, Anopheles culicifacies, is currently increasing. To predict malaria vector dynamics, knowledge of population genetics and gene flow is required, but this information is unavailable for Sri Lanka. This study was carried out to determine the population structure of An. culicifacies E in Sri Lanka. Eight microsatellite markers were used to examine An. culicifacies E collected from six sites in Sri Lanka during 2010-2012. Standard population genetic tests and analyses, genetic differentiation, Hardy-Weinberg equilibrium, linkage disequilibrium, Bayesian cluster analysis, AMOVA, SAMOVA and isolation-by-distance were conducted using five polymorphic loci. Five microsatellite loci were highly polymorphic with high allelic richness. Hardy-Weinberg Equilibrium (HWE) was significantly rejected for four loci with positive F(IS) values in the pooled population (p < 0.0100). Three loci showed high deviations in all sites except Kataragama, which was in agreement with HWE for all loci except one locus (p < 0.0016). Observed heterozygosity was less than the expected values for all sites except Kataragama, where reported negative F(IS) values indicated a heterozygosity excess. Genetic differentiation was observed for all sampling site pairs and was not supported by the isolation by distance model. Bayesian clustering analysis identified the presence of three sympatric clusters (gene pools) in the studied population. Significant genetic differentiation was detected in cluster pairs with low gene flow and isolation by distance was not detected between clusters. Furthermore, the results suggested the presence of a barrier to gene flow that divided the populations into two parts with the central hill region of Sri Lanka as the dividing line. Three sympatric clusters were detected among An. culicifacies E specimens isolated in Sri Lanka. There was no effect of geographic distance on genetic differentiation and the central mountain ranges in Sri Lanka appeared to be a barrier to gene flow.

Three dimensional PNS solutions of hypersonic internal flows with equilibrium chemistry

NASA Technical Reports Server (NTRS)

Liou, May-Fun

1989-01-01

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

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

NASA Astrophysics Data System (ADS)

Ozaki, H.

2004-01-01

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

Analytical Study on the Saturated Polarization Under Electric Field and Phase Equilibrium of Three-Phase Polycrystalline Ferroelectrics by Using the Generalized Inverse-Pole-Figure Model

NASA Astrophysics Data System (ADS)

Ju, Kyong-Sik; Ryo, Hyok-Su; Pak, Sung-Nam; Pak, Chang-Su; Ri, Sung-Guk; Ri, Dok-Hwan

2018-07-01

By using the generalized inverse-pole-figure model, the numbers of crystalline particles involved in different domain-switching near the triple tetragonal-rhombohedral-orthorhombic (T-R-O) points of three-phase polycrystalline ferroelectrics have been analytically calculated and domain-switching which can bring out phase transformations has been considered. Through polarization by an electric field, different numbers of crystalline particles can be involved in different phase transformations. According to the phase equilibrium conditions, the phase equilibrium compositions of the three phases coexisting near the T-R-O triple point have been evaluated from the results of the numbers of crystalline particles involved in different phase transformations.

Stock markets as Minority Games: cognitive heterogeneity and equilibrium emergence

NASA Astrophysics Data System (ADS)

Brandouy, O.

2005-04-01

Standard finance theory generally assumes homogeneous agents relatively to their preferences, heuristics and investment strategies. We propose to study, in an agent-based simulation, the emergence of equilibrium under various heterogeneous conditions. Market interaction is stylized with the Minority Game representation. It is shown that inductive rational equilibrium emerges even though agents do not share the same representations of the value. This may lead to consider again the roots of EMH and REH.

Unique equilibrium states for Bonatti–Viana diffeomorphisms

NASA Astrophysics Data System (ADS)

Climenhaga, Vaughn; Fisher, Todd; Thompson, Daniel J.

2018-06-01

We show that the robustly transitive diffeomorphisms constructed by Bonatti and Viana have unique equilibrium states for natural classes of potentials. In particular, we characterize the SRB measure as the unique equilibrium state for a suitable geometric potential. The techniques developed are applicable to a wide class of DA diffeomorphisms, and persist under C 1 perturbations of the map. These results are an application of general machinery developed by the first and last named authors.

Equilibrium distribution of heavy quarks in fokker-planck dynamics

PubMed

Walton; Rafelski

2000-01-03

We obtain an explicit generalization, within Fokker-Planck dynamics, of Einstein's relation between drag, diffusion, and the equilibrium distribution for a spatially homogeneous system, considering both the transverse and longitudinal diffusion for dimension n>1. We provide a complete characterization of the equilibrium distribution in terms of the drag and diffusion transport coefficients. We apply this analysis to charm quark dynamics in a thermal quark-gluon plasma for the case of collisional equilibration.

Experiments with a Regional Vector-Vorticity Model, and Comparison with Other Models

NASA Astrophysics Data System (ADS)

Konor, C. S.; Dazlich, D. A.; Jung, J.; Randall, D. A.

2017-12-01

The Vector-Vorticity Model (VVM) is an anelastic model with a unique dynamical core that predicts the three-dimensional vorticity instead of the three-dimensional momentum. The VVM is used in the CRMs of the Global Quasi-3D Multiscale Modeling Framework, which is discussed by Joon-Hee Jung and collaborators elsewhere in this session. We are updating the physics package of the VVM, replacing it with the physics package of the System for Atmosphere Modeling (SAM). The new physics package includes a double-moment microphysics, Mellor-Yamada turbulence, Monin-Obukov surface fluxes, and the RRTMG radiation parameterization. We briefly describe the VVM and show results from standard test cases, including TWP-ICE. We compare the results with those obtained using the earlier physics. We also show results from experiments on convection aggregation in radiative-convective equilibrium, and compare with those obtained using both SAM and the Regional Atmospheric Modeling System (RAMS).

Preventing Superinfection in Malaria Spreads with Repellent and Medical Treatment Policy

NASA Astrophysics Data System (ADS)

Fitri, Fanny; Aldila, Dipo

2018-03-01

Malaria is a kind of a vector-borne disease. That means this disease needs a vector (in this case, the anopheles mosquito) to spread. In this article, a mathematical model for malaria disease spread will be discussed. The model is constructed as a seven-dimensional of a non-linear ordinary differential equation. The interventions of treatment for infected humans and use of repellent are included in the model to see how these interventions could be considered as alternative ways to control the spread of malaria. Analysis will be made of the disease-free equilibrium point along with its local stability criteria, construction of the next generation matrix which followed with the sensitivity analysis of basic reproduction number. We found that both medical treatment and repellent intervention succeeded in reducing the basic reproduction number as the endemic indicator of the model. Finally, some numerical simulations are given to give a better interpretation of the analytical results.

A Concept of Cross-Ferroic Plasma Turbulence

PubMed Central

Inagaki, S.; Kobayashi, T.; Kosuga, Y.; Itoh, S.-I.; Mitsuzono, T.; Nagashima, Y.; Arakawa, H.; Yamada, T.; Miwa, Y.; Kasuya, N.; Sasaki, M.; Lesur, M.; Fujisawa, A.; Itoh, K.

2016-01-01

The variety of scalar and vector fields in laboratory and nature plasmas is formed by plasma turbulence. Drift-wave fluctuations, driven by density gradients in magnetized plasmas, are known to relax the density gradient while they can generate flows. On the other hand, the sheared flow in the direction of magnetic fields causes Kelvin-Helmholtz type instabilities, which mix particle and momentum. These different types of fluctuations coexist in laboratory and nature, so that the multiple mechanisms for structural formation exist in extremely non-equilibrium plasmas. Here we report the discovery of a new order in plasma turbulence, in which chained structure formation is realized by cross-interaction between inhomogeneities of scalar and vector fields. The concept of cross-ferroic turbulence is developed, and the causal relation in the multiple mechanisms behind structural formation is identified, by measuring the relaxation rate and dissipation power caused by the complex turbulence-driven flux. PMID:26917218

Supplier Short Term Load Forecasting Using Support Vector Regression and Exogenous Input

NASA Astrophysics Data System (ADS)

Matijaš, Marin; Vukićcević, Milan; Krajcar, Slavko

2011-09-01

In power systems, task of load forecasting is important for keeping equilibrium between production and consumption. With liberalization of electricity markets, task of load forecasting changed because each market participant has to forecast their own load. Consumption of end-consumers is stochastic in nature. Due to competition, suppliers are not in a position to transfer their costs to end-consumers; therefore it is essential to keep forecasting error as low as possible. Numerous papers are investigating load forecasting from the perspective of the grid or production planning. We research forecasting models from the perspective of a supplier. In this paper, we investigate different combinations of exogenous input on the simulated supplier loads and show that using points of delivery as a feature for Support Vector Regression leads to lower forecasting error, while adding customer number in different datasets does the opposite.

Normalization in Lie algebras via mould calculus and applications

NASA Astrophysics Data System (ADS)

Paul, Thierry; Sauzin, David

2017-11-01

We establish Écalle's mould calculus in an abstract Lie-theoretic setting and use it to solve a normalization problem, which covers several formal normal form problems in the theory of dynamical systems. The mould formalism allows us to reduce the Lie-theoretic problem to a mould equation, the solutions of which are remarkably explicit and can be fully described by means of a gauge transformation group. The dynamical applications include the construction of Poincaré-Dulac formal normal forms for a vector field around an equilibrium point, a formal infinite-order multiphase averaging procedure for vector fields with fast angular variables (Hamiltonian or not), or the construction of Birkhoff normal forms both in classical and quantum situations. As a by-product we obtain, in the case of harmonic oscillators, the convergence of the quantum Birkhoff form to the classical one, without any Diophantine hypothesis on the frequencies of the unperturbed Hamiltonians.

Cigarette taxes and respiratory cancers: new evidence from panel co-integration analysis.

PubMed

Liu, Echu; Yu, Wei-Choun; Hsieh, Hsin-Ling

2011-01-01

Using a set of state-level longitudinal data from 1954 through 2005, this study investigates the "long-run equilibrium" relationship between cigarette excise taxes and the mortality rates of respiratory cancers in the United States. Statistical tests show that both cigarette excise taxes in real terms and mortality rates from respiratory cancers contain unit roots and are co-integrated. Estimates of co-integrating vectors indicated that a 10 percent increase in real cigarette excise tax rate leads to a 2.5 percent reduction in respiratory cancer mortality rate, implying a decline of 3,922 deaths per year, on a national level in the long run. These effects are statistically significant at the one percent level. Moreover, estimates of co-integrating vectors show that higher cigarette excise tax rates lead to lower mortality rates in most states; however, this relationship does not hold for Alaska, Florida, Hawaii, and Texas.

Computations of ideal and real gas high altitude plume flows

NASA Technical Reports Server (NTRS)

Feiereisen, William J.; Venkatapathy, Ethiraj

1988-01-01

In the present work, complete flow fields around generic space vehicles in supersonic and hypersonic flight regimes are studied numerically. Numerical simulation is performed with a flux-split, time asymptotic viscous flow solver that incorporates a generalized equilibrium chemistry model. Solutions to generic problems at various altitude and flight conditions show the complexity of the flow, the equilibrium chemical dissociation and its effect on the overall flow field. Viscous ideal gas solutions are compared against equilibrium gas solutions to illustrate the effect of equilibrium chemistry. Improved solution accuracy is achieved through adaptive grid refinement.

A Comparison Between a Synthetic Over-Sampling Equilibrium and Observed Subsets of Data for Epidemic Vector Classification

NASA Astrophysics Data System (ADS)

Fusco, Terence; Bi, Yaxin; Nugent, Chris; Wu, Shengli

2016-08-01

We can see that the data imputation approach using the Regression CTA has performed more favourably when compared with the alternative methods on this dataset. We now have the evidence to show that this method is viable moving forward with further research in this area. The weighted distribution experiments have provided us with a more balanced and appropriate ratio for snail density classification purposes when using either the 3 or 5 category combination. The most desirable results are found when using 3 categories of SD with the weighted distribution of classes being 20-60-20. This information reflects the optimum classification accuracy across the data range and can be applied to any novel environment feature dataset pertaining to Schistosomiasis vector classification. ITSVM has provided us with a method of labelling SD data which we can use for classification with epidemic disease prediction research. The confidence level selection enables consistent labelling accuracy for bespoke requirements when classifying the data from each year. The SMOTE Equilibrium proposed method has yielded a slight increase with each multiple of synthetic instances that are compounded to the training dataset. The reduction of overfitting and increase of data instances has shown a gradual classification accuracy increase across the data for each year. We will now test to see what the optimum synthetic instance incremental increase is across our data and apply this to our experiments with this research.

Stability properties of a general class of nonlinear dynamical systems

NASA Astrophysics Data System (ADS)

Gléria, I. M.; Figueiredo, A.; Rocha Filho, T. M.

2001-05-01

We establish sufficient conditions for the boundedness of the trajectories and the stability of the fixed points in a class of general nonlinear systems, the so-called quasi-polynomial vector fields, with the help of a natural embedding of such systems in a family of generalized Lotka-Volterra (LV) equations. A purely algebraic procedure is developed to determine such conditions. We apply our method to obtain new results for LV systems, by a reparametrization in time variable, and to study general nonlinear vector fields, originally far from the LV format.

Cosmology in generalized Proca theories

NASA Astrophysics Data System (ADS)

De Felice, Antonio; Heisenberg, Lavinia; Kase, Ryotaro; Mukohyama, Shinji; Tsujikawa, Shinji; Zhang, Ying-li

2016-06-01

We consider a massive vector field with derivative interactions that propagates only the 3 desired polarizations (besides two tensor polarizations from gravity) with second-order equations of motion in curved space-time. The cosmological implications of such generalized Proca theories are investigated for both the background and the linear perturbation by taking into account the Lagrangian up to quintic order. In the presence of a matter fluid with a temporal component of the vector field, we derive the background equations of motion and show the existence of de Sitter solutions relevant to the late-time cosmic acceleration. We also obtain conditions for the absence of ghosts and Laplacian instabilities of tensor, vector, and scalar perturbations in the small-scale limit. Our results are applied to concrete examples of the general functions in the theory, which encompass vector Galileons as a specific case. In such examples, we show that the de Sitter fixed point is always a stable attractor and study viable parameter spaces in which the no-ghost and stability conditions are satisfied during the cosmic expansion history.

Turning Passive Brownian Motion Into Active Motion

NASA Astrophysics Data System (ADS)

Sevilla, Francisco J.; VáSquez-Arzola, Alejandro; Puga-Cital, Enrique

We consider out-of-equilibrium phenomena, specifically, the pattern of motion of active particles. These particles absorb energy from the environment and transform it into self-locomotion, generally, through complex mechanisms. Though the out-of-equilibrium nature of on the motion of these systems is well recognized, is generally difficult to pinpoint how far from equilibrium these systems are. In this work we elucidate the out-of-equilibrium nature of non-interacting, trapped, active particles, whose pattern of motion is described by a run-and-tumble dynamics. We show that the stationary distributions of these run-and-tumble particles, moving under the effects of an external potential, is equivalent to the stationary distribution of non-interacting, passive Brownian particles moving in the same potential but in an inhomogeneous source of heat. The interest in this topic has recently regrown due to the experimental possibility to design man-made active particles that emulate the ones that exist in the biological realm. F.J.S kindly acknowledges support from Grant UNAM-DGAPA-PAPIIT-IN113114.

Stage-structured infection transmission and a spatial epidemic: a model for Lyme disease.

PubMed

Caraco, Thomas; Glavanakov, Stephan; Chen, Gang; Flaherty, Joseph E; Ohsumi, Toshiro K; Szymanski, Boleslaw K

2002-09-01

A greater understanding of the rate at which emerging disease advances spatially has both ecological and applied significance. Analyzing the spread of vector-borne disease can be relatively complex when the vector's acquisition of a pathogen and subsequent transmission to a host occur in different life stages. A contemporary example is Lyme disease. A long-lived tick vector acquires infection during the larval blood meal and transmits it as a nymph. We present a reaction-diffusion model for the ecological dynamics governing the velocity of the current epidemic's spread. We find that the equilibrium density of infectious tick nymphs (hence the risk of human disease) can depend on density-independent survival interacting with biotic effects on the tick's stage structure. The local risk of infection reaches a maximum at an intermediate level of adult tick mortality and at an intermediate rate of juvenile tick attacks on mammalian hosts. If the juvenile tick attack rate is low, an increase generates both a greater density of infectious nymphs and an increased spatial velocity. However, if the juvenile attack rate is relatively high, nymph density may decline while the epidemic's velocity still increases. Velocities of simulated two-dimensional epidemics correlate with the model pathogen's basic reproductive number (R0), but calculating R0 involves parameters of both host infection dynamics and the vector's stage-structured dynamics.

Non-Equilibrium Properties from Equilibrium Free Energy Calculations

NASA Technical Reports Server (NTRS)

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.

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

Lello, Louis; Boyanovsky, Daniel; Pisarski, Robert D.

Here, in the standard model extended with a seesaw mass matrix, we study the production of sterile neutrinos from the decay of vector bosons at temperatures near the masses of the electroweak bosons. We derive a general quantum kinetic equation for the production of sterile neutrinos and their effective mixing angles, which is applicable over a wide range of temperature, to all orders in interactions of the standard model and to leading order in a small mixing angle for the neutrinos. We emphasize the relation between the production rate and Landau damping at one-loop order and show that production rates and effective mixing angles depend sensitively upon the neutrino’s helicity. Sterile neutrinos with positive helicity interact more weakly with the medium than those with negative helicity, and their effective mixing angle is not modified significantly. Negative helicity states couple more strongly to the vector bosons, but their mixing angle is strongly suppressed by the medium. Consequently, if the mass of the sterile neutrino is ≲ 8.35 MeV , there are fewer states with negative helicity produced than those with positive helicity. There is an Mikheyev-Smirnov-Wolfenstein-type resonance in the absence of lepton asymmetry, but due to screening by the damping rate, the production rate is not enhanced. Sterile neutrinos with negative helicity freeze out at Tmore » $$-\\atop{f}$$ ≃ 5 GeV , whereas positive helicity neutrinos freeze out at T$$+\\atop{f}$$≃ 8 GeV , with both distributions far from thermal. As the temperature decreases, due to competition between a decreasing production rate and an increasing mixing angle, the distribution function for states with negative helicity is broader in momentum and hotter than that for those with positive helicity. Sterile neutrinos produced via vector boson decay do not satisfy the abundance, lifetime, and cosmological constraints to be the sole dark matter component in the Universe. Massive sterile neutrinos produced via vector boson decay might solve the 7Li problem, albeit at the very edge of the possible parameter space. A heavy sterile neutrino with a mass of a few MeV could decay into light sterile neutrinos, of a few keV in mass, that contribute to warm dark matter. In conclusion, we argue that heavy sterile neutrinos with lifetime ≤1/H 0 reach local thermodynamic equilibrium.« less

Some properties of correlations of quantum lattice systems in thermal equilibrium

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

Fröhlich, Jürg, E-mail: juerg@phys.ethz.ch; Ueltschi, Daniel, E-mail: daniel@ueltschi.org

Simple proofs of uniqueness of the thermodynamic limit of KMS states and of the decay of equilibrium correlations are presented for a large class of quantum lattice systems at high temperatures. New quantum correlation inequalities for general Heisenberg models are described. Finally, a simplified derivation of a general result on power-law decay of correlations in 2D quantum lattice systems with continuous symmetries is given, extending results of McBryan and Spencer for the 2D classical XY model.

Rotating charged black holes accelerated by an electric field

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

Bicak, Jiri; Kofron, David; Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Am Muehlenberg 1, D-14476 Golm

The Ernst method of removing nodal singularities from the charged C-metric representing a uniformly accelerated black hole with mass m, charge q and acceleration A by 'adding' an electric field E is generalized. Utilizing the new form of the C-metric found recently, Ernst's simple 'equilibrium condition' mA=qE valid for small accelerations is generalized for arbitrary A. The nodal singularity is removed also in the case of accelerating and rotating charged black holes, and the corresponding equilibrium condition is determined.

Serendipity in dark photon searches

NASA Astrophysics Data System (ADS)

Ilten, Philip; Soreq, Yotam; Williams, Mike; Xue, Wei

2018-06-01

Searches for dark photons provide serendipitous discovery potential for other types of vector particles. We develop a framework for recasting dark photon searches to obtain constraints on more general theories, which includes a data-driven method for determining hadronic decay rates. We demonstrate our approach by deriving constraints on a vector that couples to the B-L current, a leptophobic B boson that couples directly to baryon number and to leptons via B- γ kinetic mixing, and on a vector that mediates a protophobic force. Our approach can easily be generalized to any massive gauge boson with vector couplings to the Standard Model fermions, and software to perform any such recasting is provided at https://gitlab.com/philten/darkcast .

Extrapolation methods for vector sequences

NASA Technical Reports Server (NTRS)

Smith, David A.; Ford, William F.; Sidi, Avram

1987-01-01

This paper derives, describes, and compares five extrapolation methods for accelerating convergence of vector sequences or transforming divergent vector sequences to convergent ones. These methods are the scalar epsilon algorithm (SEA), vector epsilon algorithm (VEA), topological epsilon algorithm (TEA), minimal polynomial extrapolation (MPE), and reduced rank extrapolation (RRE). MPE and RRE are first derived and proven to give the exact solution for the right 'essential degree' k. Then, Brezinski's (1975) generalization of the Shanks-Schmidt transform is presented; the generalized form leads from systems of equations to TEA. The necessary connections are then made with SEA and VEA. The algorithms are extended to the nonlinear case by cycling, the error analysis for MPE and VEA is sketched, and the theoretical support for quadratic convergence is discussed. Strategies for practical implementation of the methods are considered.

Effect of difference of cupula and endolymph densities on the dynamics of semicircular canal.

PubMed

Kondrachuk, A V; Sirenko, S P; Boyle, R

2008-01-01

The effect of different densities of a cupula and endolymph on the dynamics of the semicircular canals is considered within the framework of a simplified one-dimensional mathematical model where the canal is approximated by a torus. If the densities are equal, the model is represented by Steinhausen's phenomenological equation. The difference of densities results in the complex dynamics of the cupulo-endolymphatic system, and leads to a dependence on the orientation of both the gravity vector relative to the canal plane and the axis of rotation, as well as on the distance between the axis of rotation and the center of the semicircular canal. Our analysis focused on two cases of canal stimulation: rotation with a constant velocity and a time-dependent (harmonically oscillating) angular velocity. Two types of spatial orientation of the axis of rotation, the axis of canal symmetry, and the vector of gravity were considered: i) the gravity vector and axis of rotation lie in the canal plane, and ii) the axis of rotation and gravity vector are normal to the canal plane. The difference of the cupula and endolymph densities reveals new features of cupula dynamics, for instance--a shift of the cupula to a new position of equilibrium that depends on the gravity vector and the parameters of head rotation, and the onset of cupula oscillations with multiple frequencies that results in the distortion of cupula dynamics relative to harmonic stimulation. Factors that might influence the density difference effects and the conditions under which these effects occur are discussed.

GENERIC Integrators: Structure Preserving Time Integration for Thermodynamic Systems

NASA Astrophysics Data System (ADS)

Öttinger, Hans Christian

2018-04-01

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

Effective gravitational couplings for cosmological perturbations in generalized Proca theories

NASA Astrophysics Data System (ADS)

De Felice, Antonio; Heisenberg, Lavinia; Kase, Ryotaro; Mukohyama, Shinji; Tsujikawa, Shinji; Zhang, Ying-li

2016-08-01

We consider the finite interactions of the generalized Proca theory including the sixth-order Lagrangian and derive the full linear perturbation equations of motion on the flat Friedmann-Lemaître-Robertson-Walker background in the presence of a matter perfect fluid. By construction, the propagating degrees of freedom (besides the matter perfect fluid) are two transverse vector perturbations, one longitudinal scalar, and two tensor polarizations. The Lagrangians associated with intrinsic vector modes neither affect the background equations of motion nor the second-order action of tensor perturbations, but they do give rise to nontrivial modifications to the no-ghost condition of vector perturbations and to the propagation speeds of vector and scalar perturbations. We derive the effective gravitational coupling Geff with matter density perturbations under a quasistatic approximation on scales deep inside the sound horizon. We find that the existence of intrinsic vector modes allows a possibility for reducing Geff. In fact, within the parameter space, Geff can be even smaller than the Newton gravitational constant G at the late cosmological epoch, with a peculiar phantom dark energy equation of state (without ghosts). The modifications to the slip parameter η and the evolution of the growth rate f σ8 are discussed as well. Thus, dark energy models in the framework of generalized Proca theories can be observationally distinguished from the Λ CDM model according to both cosmic growth and expansion history. Furthermore, we study the evolution of vector perturbations and show that outside the vector sound horizon the perturbations are nearly frozen and start to decay with oscillations after the horizon entry.

Training Extract, AFSC 113X0B, Flight Engineer, Helicopter Qualified.

DTIC Science & Technology

1982-12-01

TRAINING .................................................................. 1I0 SE. GENERAL rLIGHT RULES A 9 C t | 7. PeRFORM INSPECIIOIS 12 7A... TRAINING .................................................................. lIC 6E. GENERAL FLIGHT RULES A a C...ME"BERS PERFORMING I-A I PROGRAM GENERATED VECTOR IMEMBERS/ NO TYPE VECTOR MEAN - SC DESCRIPTION I TN. SEP J.6 2.J TRAINING EMPHASIS RATINSS I IIOS

Curved manifolds with conserved Runge-Lenz vectors

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

Ngome, J.-P.

2009-12-15

van Holten's algorithm is used to construct Runge-Lenz-type conserved quantities, induced by Killing tensors, on curved manifolds. For the generalized Taub-Newman-Unti-Tamburino metric, the most general external potential such that the combined system admits a conserved Runge-Lenz-type vector is found. In the multicenter case, the subclass of two-center metric exhibits a conserved Runge-Lenz-type scalar.

Curved manifolds with conserved Runge-Lenz vectors

NASA Astrophysics Data System (ADS)

Ngome, J.-P.

2009-12-01

van Holten's algorithm is used to construct Runge-Lenz-type conserved quantities, induced by Killing tensors, on curved manifolds. For the generalized Taub-Newman-Unti-Tamburino metric, the most general external potential such that the combined system admits a conserved Runge-Lenz-type vector is found. In the multicenter case, the subclass of two-center metric exhibits a conserved Runge-Lenz-type scalar.

Energy shift and Casimir-Polder force for an atom out of thermal equilibrium near a dielectric substrate

NASA Astrophysics Data System (ADS)

Zhou, Wenting; Yu, Hongwei

2014-09-01

We study the energy shift and the Casimir-Polder force of an atom out of thermal equilibrium near the surface of a dielectric substrate. We first generalize, adopting the local source hypothesis, the formalism proposed by Dalibard, Dupont-Roc, and Cohen-Tannoudji [J. Phys. (Paris) 43, 1617 (1982), 10.1051/jphys:0198200430110161700; J. Phys. (Paris) 45, 637 (1984), 10.1051/jphys:01984004504063700], which separates the contributions of thermal fluctuations and radiation reaction to the energy shift and allows a distinct treatment of atoms in the ground and excited states, to the case out of thermal equilibrium, and then we use the generalized formalism to calculate the energy shift and the Casimir-Polder force of an isotropically polarizable neutral atom. We identify the effects of the thermal fluctuations that originate from the substrate and the environment and discuss in detail how the Casimir-Polder force out of thermal equilibrium behaves in three different distance regions in both the low-temperature limit and the high-temperature limit for both the ground-state and excited-state atoms, with special attention devoted to the distinctive features as opposed to thermal equilibrium. In particular, we recover the distinctive behavior of the atom-wall force out of thermal equilibrium at large distances in the low-temperature limit recently found in a different theoretical framework, and furthermore we give a concrete region where this behavior holds.

Differential Calculus on h-Deformed Spaces

NASA Astrophysics Data System (ADS)

Herlemont, Basile; Ogievetsky, Oleg

2017-10-01

We construct the rings of generalized differential operators on the h-deformed vector space of gl-type. In contrast to the q-deformed vector space, where the ring of differential operators is unique up to an isomorphism, the general ring of h-deformed differential operators {Diff}_{h},σ(n) is labeled by a rational function σ in n variables, satisfying an over-determined system of finite-difference equations. We obtain the general solution of the system and describe some properties of the rings {Diff}_{h},σ(n).

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

Dupertuis, M.A.; Proctor, M.; Acklin, B.

Energy balance and reciprocity relations are studied for harmonic inhomogeneous plane waves that are incident upon a stack of continuous absorbing dielectric media that are macroscopically characterized by their electric and magnetic permittivities and their conductivities. New cross terms between parallel electric and parallel magnetic modes are identified in the fully generalized Poynting vector. The symmetry and the relations between the general Fresnel coefficients are investigated in the context of energy balance at the interface. The contributions of the so-called mixed Poynting vector are discussed in detail. In particular a new transfer matrix is introduced for energy fluxes in thin-filmmore » optics based on the Poynting and mixed Poynting vectors. Finally, the study of reciprocity relations leads to a generalization of a theorem of reversibility for conducting and dielectric media. 16 refs.« less

Equilibrium Solutions of the Logarithmic Hamiltonian Leapfrog for the N-body Problem

NASA Astrophysics Data System (ADS)

Minesaki, Yukitaka

2018-04-01

We prove that a second-order logarithmic Hamiltonian leapfrog for the classical general N-body problem (CGNBP) designed by Mikkola and Tanikawa and some higher-order logarithmic Hamiltonian methods based on symmetric multicompositions of the logarithmic algorithm exactly reproduce the orbits of elliptic relative equilibrium solutions in the original CGNBP. These methods are explicit symplectic methods. Before this proof, only some implicit discrete-time CGNBPs proposed by Minesaki had been analytically shown to trace the orbits of elliptic relative equilibrium solutions. The proof is therefore the first existence proof for explicit symplectic methods. Such logarithmic Hamiltonian methods with a variable time step can also precisely retain periodic orbits in the classical general three-body problem, which generic numerical methods with a constant time step cannot do.

Global asymptotic stability to a generalized Cohen-Grossberg BAM neural networks of neutral type delays.

PubMed

Zhang, Zhengqiu; Liu, Wenbin; Zhou, Dongming

2012-01-01

In this paper, we first discuss the existence of a unique equilibrium point of a generalized Cohen-Grossberg BAM neural networks of neutral type delays by means of the Homeomorphism theory and inequality technique. Then, by applying the existence result of an equilibrium point and constructing a Lyapunov functional, we study the global asymptotic stability of the equilibrium solution to the above Cohen-Grossberg BAM neural networks of neutral type. In our results, the hypothesis for boundedness in the existing paper, which discussed Cohen-Grossberg neural networks of neutral type on the activation functions, are removed. Finally, we give an example to demonstrate the validity of our global asymptotic stability result for the above neural networks. Copyright © 2011 Elsevier Ltd. All rights reserved.

Characterization of Weak Convergence of Probability-Valued Solutions of General One-Dimensional Kinetic Equations

NASA Astrophysics Data System (ADS)

Perversi, Eleonora; Regazzini, Eugenio

2015-05-01

For a general inelastic Kac-like equation recently proposed, this paper studies the long-time behaviour of its probability-valued solution. In particular, the paper provides necessary and sufficient conditions for the initial datum in order that the corresponding solution converges to equilibrium. The proofs rest on the general CLT for independent summands applied to a suitable Skorokhod representation of the original solution evaluated at an increasing and divergent sequence of times. It turns out that, roughly speaking, the initial datum must belong to the standard domain of attraction of a stable law, while the equilibrium is presentable as a mixture of stable laws.

Closed set of the uniqueness conditions and bifurcation criteria in generalized coupled thermoplasticity for small deformations

NASA Astrophysics Data System (ADS)

Śloderbach, Zdzisław

2016-05-01

This paper reports the results of a study into global and local conditions of uniqueness and the criteria excluding the possibility of bifurcation of the equilibrium state for small strains. The conditions and criteria are derived on the basis of an analysis of the problem of uniqueness of a solution involving the basic incremental boundary problem of coupled generalized thermo-elasto-plasticity. This work forms a follow-up of previous research (Śloderbach in Bifurcations criteria for equilibrium states in generalized thermoplasticity, IFTR Reports, 1980, Arch Mech 3(35):337-349, 351-367, 1983), but contains a new derivation of global and local criteria excluding a possibility of bifurcation of an equilibrium state regarding a comparison body dependent on the admissible fields of stress rate. The thermal elasto-plastic coupling effects, non-associated laws of plastic flow and influence of plastic strains on thermoplastic properties of a body were taken into account in this work. Thus, the mathematical problem considered here is not a self-conjugated problem.

Model-based analysis of coupled equilibrium-kinetic processes: indirect kinetic studies of thermodynamic parameters using the dynamic data.

PubMed

Emami, Fereshteh; Maeder, Marcel; Abdollahi, Hamid

2015-05-07

Thermodynamic studies of equilibrium chemical reactions linked with kinetic procedures are mostly impossible by traditional approaches. In this work, the new concept of generalized kinetic study of thermodynamic parameters is introduced for dynamic data. The examples of equilibria intertwined with kinetic chemical mechanisms include molecular charge transfer complex formation reactions, pH-dependent degradation of chemical compounds and tautomerization kinetics in micellar solutions. Model-based global analysis with the possibility of calculating and embedding the equilibrium and kinetic parameters into the fitting algorithm has allowed the complete analysis of the complex reaction mechanisms. After the fitting process, the optimal equilibrium and kinetic parameters together with an estimate of their standard deviations have been obtained. This work opens up a promising new avenue for obtaining equilibrium constants through the kinetic data analysis for the kinetic reactions that involve equilibrium processes.

Progress Toward an Efficient and General CFD Tool for Propulsion Design/Analysis

NASA Technical Reports Server (NTRS)

Cox, C. F.; Cinnella, P.; Westmoreland, S.

1996-01-01

The simulation of propulsive flows inherently involves chemical activity. Recent years have seen substantial strides made in the development of numerical schemes for reacting flowfields, in particular those involving finite-rate chemistry. However, finite-rate calculations are computationally intensive and require knowledge of the actual kinetics, which are not always known with sufficient accuracy. Alternatively, flow simulations based on the assumption of local chemical equilibrium are capable of obtaining physically reasonable results at far less computational cost. The present study summarizes the development of efficient numerical techniques for the simulation of flows in local chemical equilibrium, whereby a 'Black Box' chemical equilibrium solver is coupled to the usual gasdynamic equations. The generalization of the methods enables the modelling of any arbitrary mixture of thermally perfect gases, including air, combustion mixtures and plasmas. As demonstration of the potential of the methodologies, several solutions, involving reacting and perfect gas flows, will be presented. Included is a preliminary simulation of the SSME startup transient. Future enhancements to the proposed techniques will be discussed, including more efficient finite-rate and hybrid (partial equilibrium) schemes. The algorithms that have been developed and are being optimized provide for an efficient and general tool for the design and analysis of propulsion systems.

Selection vector filter framework

NASA Astrophysics Data System (ADS)

Lukac, Rastislav; Plataniotis, Konstantinos N.; Smolka, Bogdan; Venetsanopoulos, Anastasios N.

2003-10-01

We provide a unified framework of nonlinear vector techniques outputting the lowest ranked vector. The proposed framework constitutes a generalized filter class for multichannel signal processing. A new class of nonlinear selection filters are based on the robust order-statistic theory and the minimization of the weighted distance function to other input samples. The proposed method can be designed to perform a variety of filtering operations including previously developed filtering techniques such as vector median, basic vector directional filter, directional distance filter, weighted vector median filters and weighted directional filters. A wide range of filtering operations is guaranteed by the filter structure with two independent weight vectors for angular and distance domains of the vector space. In order to adapt the filter parameters to varying signal and noise statistics, we provide also the generalized optimization algorithms taking the advantage of the weighted median filters and the relationship between standard median filter and vector median filter. Thus, we can deal with both statistical and deterministic aspects of the filter design process. It will be shown that the proposed method holds the required properties such as the capability of modelling the underlying system in the application at hand, the robustness with respect to errors in the model of underlying system, the availability of the training procedure and finally, the simplicity of filter representation, analysis, design and implementation. Simulation studies also indicate that the new filters are computationally attractive and have excellent performance in environments corrupted by bit errors and impulsive noise.

Resonant behaviour of MHD waves on magnetic flux tubes. III - Effect of equilibrium flow

NASA Technical Reports Server (NTRS)

Goossens, Marcel; Hollweg, Joseph V.; Sakurai, Takashi

1992-01-01

The Hollweg et al. (1990) analysis of MHD surface waves in a stationary equilibrium is extended. The conservation laws and jump conditions at Alfven and slow resonance points obtained by Sakurai et al. (1990) are generalized to include an equilibrium flow, and the assumption that the Eulerian perturbation of total pressure is constant is recovered as the special case of the conservation law for an equilibrium with straight magnetic field lines and flow along the magnetic field lines. It is shown that the conclusions formulated by Hollweg et al. are still valid for the straight cylindrical case. The effect of curvature is examined.

Hybrid function projective synchronization in complex dynamical networks

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

Wei, Qiang; Wang, Xing-yuan, E-mail: wangxy@dlut.edu.cn; Hu, Xiao-peng

2014-02-15

This paper investigates hybrid function projective synchronization in complex dynamical networks. When the complex dynamical networks could be synchronized up to an equilibrium or periodic orbit, a hybrid feedback controller is designed to realize the different component of vector of node could be synchronized up to different desired scaling function in complex dynamical networks with time delay. Hybrid function projective synchronization (HFPS) in complex dynamical networks with constant delay and HFPS in complex dynamical networks with time-varying coupling delay are researched, respectively. Finally, the numerical simulations show the effectiveness of theoretical analysis.

Proceedings of Workshop on Atmospheric Density and Aerodynamic Drag Models for Air Force Operations Held at Air Force Geophysics Laboratory on 20-22 October 1987. Volume 1

DTIC Science & Technology

1990-02-13

considered with these production processes in a simple photochemical equilibrium calculation , we are able to determine the contribution each makes to the...Hessian matrix of second derivatives (which is required in the Newton-Raphson procedure) by the vector product of the gradient (VJ) and its transpose...was focused on the altitude region 80-250 Km. Papers were presented in the folowing areas: Air Force requirements , physics of density and drag

Relations between dissipated work and Rényi divergences in the generalized Gibbs ensemble

NASA Astrophysics Data System (ADS)

Wei, Bo-Bo

2018-04-01

In this work, we show that the dissipation in a many-body system under an arbitrary nonequilibrium process is related to the Rényi divergences between two states along the forward and reversed dynamics under a very general family of initial conditions. This relation generalizes the links between dissipated work and Rényi divergences to quantum systems with conserved quantities whose equilibrium state is described by the generalized Gibbs ensemble. The relation is applicable for quantum systems with conserved quantities and can be applied to protocols driving the system between integrable and chaotic regimes. We demonstrate our ideas by considering the one-dimensional transverse quantum Ising model and the Jaynes-Cummings model which are driven out of equilibrium.

Large General Purpose Frame for Studying Force Vectors

ERIC Educational Resources Information Center

Heid, Christy; Rampolla, Donald

2011-01-01

Many illustrations and problems on the vector nature of forces have weights and forces in a vertical plane. One of the common devices for studying the vector nature of forces is a horizontal "force table," in which forces are produced by weights hanging vertically and transmitted to cords in a horizontal plane. Because some students have…

Teaching Chemical Equilibrium with the Jigsaw Technique

ERIC Educational Resources Information Center

Doymus, Kemal

2008-01-01

This study investigates the effect of cooperative learning (jigsaw) versus individual learning methods on students' understanding of chemical equilibrium in a first-year general chemistry course. This study was carried out in two different classes in the department of primary science education during the 2005-2006 academic year. One of the classes…

Understanding Thermal Equilibrium through Activities

ERIC Educational Resources Information Center

Pathare, Shirish; Huli, Saurabhee; Nachane, Madhura; Ladage, Savita; Pradhan, Hemachandra

2015-01-01

Thermal equilibrium is a basic concept in thermodynamics. In India, this concept is generally introduced at the first year of undergraduate education in physics and chemistry. In our earlier studies (Pathare and Pradhan 2011 "Proc. episteme-4 Int. Conf. to Review Research on Science Technology and Mathematics Education" pp 169-72) we…

Strategies Reported Used by Instructors to Address Student Alternate Conceptions in Chemical Equilibrium

ERIC Educational Resources Information Center

Piquette, Jeff S.; Heikkinen, Henry W.

2005-01-01

This study explores general-chemistry instructors' awareness of and ability to identify and address common student learning obstacles in chemical equilibrium. Reported instructor strategies directed at remediating student alternate conceptions were investigated and compared with successful, literature-based conceptual change methods. Fifty-two…

Education Policy and Intergenerational Transfers in Equilibrium. NBER Working Paper No. 18782

ERIC Educational Resources Information Center

Abbott, Brant; Gallipoli, Giovanni; Meghir, Costas; Violante, Giovanni L.

2013-01-01

This paper compares partial and general equilibrium effects of alternative financial aid policies intended to promote college participation. We build an overlapping generations life-cycle, heterogeneous-agent, incomplete-markets model with education, labor supply, and consumption/saving decisions. Altruistic parents make inter vivos transfers to…

Bright solitons in non-equilibrium coherent quantum matter

PubMed Central

Pinsker, F.; Flayac, H.

2016-01-01

We theoretically demonstrate a mechanism for bright soliton generation in spinor non-equilibrium Bose–Einstein condensates made of atoms or quasi-particles such as polaritons in semiconductor microcavities. We give analytical expressions for bright (half) solitons as minimizing functions of a generalized non-conservative Lagrangian elucidating the unique features of inter and intra-competition in non-equilibrium systems. The analytical results are supported by a detailed numerical analysis that further shows the rich soliton dynamics inferred by their instability and mutual cross-interactions. PMID:26997892

Computing Properties Of Chemical Mixtures At Equilibrium

NASA Technical Reports Server (NTRS)

Mcbride, B. J.; Gordon, S.

1995-01-01

Scientists and engineers need data on chemical equilibrium compositions to calculate theoretical thermodynamic properties of chemical systems. Information essential in design and analysis of such equipment as compressors, turbines, nozzles, engines, shock tubes, heat exchangers, and chemical-processing equipment. CET93 is general program that calculates chemical equilibrium compositions and properties of mixtures for any chemical system for which thermodynamic data are available. Includes thermodynamic data for more than 1,300 gaseous and condensed species and thermal-transport data for 151 gases. Written in FORTRAN 77.

Integral Equation for the Equilibrium State of Colliding Electron Beams

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

Warnock, Robert L.

2002-11-11

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

One-dimensional Vlasov-Maxwell equilibrium for the force-free Harris sheet.

PubMed

Harrison, Michael G; Neukirch, Thomas

2009-04-03

In this Letter, the first nonlinear force-free Vlasov-Maxwell equilibrium is presented. One component of the equilibrium magnetic field has the same spatial structure as the Harris sheet, but whereas the Harris sheet is kept in force balance by pressure gradients, in the force-free solution presented here force balance is maintained by magnetic shear. Magnetic pressure, plasma pressure and plasma density are constant. The method used to find the equilibrium is based on the analogy of the one-dimensional Vlasov-Maxwell equilibrium problem to the motion of a pseudoparticle in a two-dimensional conservative potential. The force-free solution can be generalized to a complete family of equilibria that describe the transition between the purely pressure-balanced Harris sheet to the force-free Harris sheet.

Intermittent many-body dynamics at equilibrium

NASA Astrophysics Data System (ADS)

Danieli, C.; Campbell, D. K.; Flach, S.

2017-06-01

The equilibrium value of an observable defines a manifold in the phase space of an ergodic and equipartitioned many-body system. A typical trajectory pierces that manifold infinitely often as time goes to infinity. We use these piercings to measure both the relaxation time of the lowest frequency eigenmode of the Fermi-Pasta-Ulam chain, as well as the fluctuations of the subsequent dynamics in equilibrium. The dynamics in equilibrium is characterized by a power-law distribution of excursion times far off equilibrium, with diverging variance. Long excursions arise from sticky dynamics close to q -breathers localized in normal mode space. Measuring the exponent allows one to predict the transition into nonergodic dynamics. We generalize our method to Klein-Gordon lattices where the sticky dynamics is due to discrete breathers localized in real space.

Black holes in vector-tensor theories

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

Heisenberg, Lavinia; Kase, Ryotaro; Tsujikawa, Shinji

We study static and spherically symmetric black hole (BH) solutions in second-order generalized Proca theories with nonminimal vector field derivative couplings to the Ricci scalar, the Einstein tensor, and the double dual Riemann tensor. We find concrete Lagrangians which give rise to exact BH solutions by imposing two conditions of the two identical metric components and the constant norm of the vector field. These exact solutions are described by either Reissner-Nordström (RN), stealth Schwarzschild, or extremal RN solutions with a non-trivial longitudinal mode of the vector field. We then numerically construct BH solutions without imposing these conditions. For cubic andmore » quartic Lagrangians with power-law couplings which encompass vector Galileons as the specific cases, we show the existence of BH solutions with the difference between two non-trivial metric components. The quintic-order power-law couplings do not give rise to non-trivial BH solutions regular throughout the horizon exterior. The sixth-order and intrinsic vector-mode couplings can lead to BH solutions with a secondary hair. For all the solutions, the vector field is regular at least at the future or past horizon. The deviation from General Relativity induced by the Proca hair can be potentially tested by future measurements of gravitational waves in the nonlinear regime of gravity.« less

Search for Tensor, Vector, and Scalar Polarizations in the Stochastic Gravitational-Wave Background

NASA Astrophysics Data System (ADS)

Abbott, B. P.; Abbott, R.; Abbott, T. D.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R. X.; Adya, V. B.; Affeldt, C.; Afrough, M.; Agarwal, B.; Agathos, M.; Agatsuma, K.; Aggarwal, N.; Aguiar, O. D.; Aiello, L.; Ain, A.; Ajith, P.; Allen, B.; Allen, G.; Allocca, A.; Altin, P. A.; Amato, A.; Ananyeva, A.; Anderson, S. B.; Anderson, W. G.; Angelova, S. V.; Antier, S.; Appert, S.; Arai, K.; Araya, M. C.; Areeda, J. S.; Arnaud, N.; Ascenzi, S.; Ashton, G.; Ast, M.; Aston, S. M.; Astone, P.; Atallah, D. V.; Aufmuth, P.; Aulbert, C.; AultONeal, K.; Austin, C.; Avila-Alvarez, A.; Babak, S.; Bacon, P.; Bader, M. K. M.; Bae, S.; Baker, P. T.; Baldaccini, F.; Ballardin, G.; Ballmer, S. W.; Banagiri, S.; Barayoga, J. C.; Barclay, S. E.; Barish, B. C.; Barker, D.; Barkett, K.; Barone, F.; Barr, B.; Barsotti, L.; Barsuglia, M.; Barta, D.; Bartlett, J.; Bartos, I.; Bassiri, R.; Basti, A.; Batch, J. C.; Bawaj, M.; Bayley, J. C.; Bazzan, M.; Bécsy, B.; Beer, C.; Bejger, M.; Belahcene, I.; Bell, A. S.; Berger, B. K.; Bergmann, G.; Bero, J. J.; Berry, C. P. L.; Bersanetti, D.; Bertolini, A.; Betzwieser, J.; Bhagwat, S.; Bhandare, R.; Bilenko, I. A.; Billingsley, G.; Billman, C. R.; Birch, J.; Birney, R.; Birnholtz, O.; Biscans, S.; Biscoveanu, S.; Bisht, A.; Bitossi, M.; Biwer, C.; Bizouard, M. A.; Blackburn, J. K.; Blackman, J.; Blair, C. D.; Blair, D. G.; Blair, R. M.; Bloemen, S.; Bock, O.; Bode, N.; Boer, M.; Bogaert, G.; Bohe, A.; Bondu, F.; Bonilla, E.; Bonnand, R.; Boom, B. A.; Bork, R.; Boschi, V.; Bose, S.; Bossie, K.; Bouffanais, Y.; Bozzi, A.; Bradaschia, C.; Brady, P. R.; Branchesi, M.; Brau, J. E.; Briant, T.; Brillet, A.; Brinkmann, M.; Brisson, V.; Brockill, P.; Broida, J. E.; Brooks, A. F.; Brown, D. A.; Brown, D. D.; Brunett, S.; Buchanan, C. C.; Buikema, A.; Bulik, T.; Bulten, H. J.; Buonanno, A.; Buskulic, D.; Buy, C.; Byer, R. L.; Cabero, M.; Cadonati, L.; Cagnoli, G.; Cahillane, C.; Calderón Bustillo, J.; Callister, T. A.; Calloni, E.; Camp, J. B.; Canepa, M.; Canizares, P.; Cannon, K. C.; Cao, H.; Cao, J.; Capano, C. D.; Capocasa, E.; Carbognani, F.; Caride, S.; Carney, M. F.; Diaz, J. Casanueva; Casentini, C.; Caudill, S.; Cavaglià, M.; Cavalier, F.; Cavalieri, R.; Cella, G.; Cepeda, C. B.; Cerdá-Durán, P.; Cerretani, G.; Cesarini, E.; Chamberlin, S. J.; Chan, M.; Chao, S.; Charlton, P.; Chase, E.; Chassande-Mottin, E.; Chatterjee, D.; Cheeseboro, B. D.; Chen, H. Y.; Chen, X.; Chen, Y.; Cheng, H.-P.; Chia, H.; Chincarini, A.; Chiummo, A.; Chmiel, T.; Cho, H. S.; Cho, M.; Chow, J. H.; Christensen, N.; Chu, Q.; Chua, A. J. K.; Chua, S.; Chung, A. K. W.; Chung, S.; Ciani, G.; Ciolfi, R.; Cirelli, C. E.; Cirone, A.; Clara, F.; Clark, J. A.; Clearwater, P.; Cleva, F.; Cocchieri, C.; Coccia, E.; Cohadon, P.-F.; Cohen, D.; Colla, A.; Collette, C. G.; Cominsky, L. R.; Constancio, M.; Conti, L.; Cooper, S. J.; Corban, P.; Corbitt, T. R.; Cordero-Carrión, I.; Corley, K. R.; Cornish, N.; Corsi, A.; Cortese, S.; Costa, C. A.; Coughlin, E.; Coughlin, M. W.; Coughlin, S. B.; Coulon, J.-P.; Countryman, S. T.; Couvares, P.; Covas, P. B.; Cowan, E. E.; Coward, D. M.; Cowart, M. J.; Coyne, D. C.; Coyne, R.; Creighton, J. D. E.; Creighton, T. D.; Cripe, J.; Crowder, S. G.; Cullen, T. J.; Cumming, A.; Cunningham, L.; Cuoco, E.; Canton, T. Dal; Dálya, G.; Danilishin, S. L.; D'Antonio, S.; Danzmann, K.; Dasgupta, A.; Da Silva Costa, C. F.; Dattilo, V.; Dave, I.; Davier, M.; Davis, D.; Daw, E. J.; Day, B.; De, S.; DeBra, D.; Degallaix, J.; De Laurentis, M.; Deléglise, S.; Del Pozzo, W.; Demos, N.; Denker, T.; Dent, T.; De Pietri, R.; Dergachev, V.; De Rosa, R.; DeRosa, R. T.; De Rossi, C.; DeSalvo, R.; de Varona, O.; Devenson, J.; Dhurandhar, S.; Díaz, M. C.; Di Fiore, L.; Di Giovanni, M.; Di Girolamo, T.; Di Lieto, A.; Di Pace, S.; Di Palma, I.; Di Renzo, F.; Doctor, Z.; Dolique, V.; Donovan, F.; Dooley, K. L.; Doravari, S.; Dorrington, I.; Douglas, R.; Dovale Álvarez, M.; Downes, T. P.; Drago, M.; Dreissigacker, C.; Driggers, J. C.; Du, Z.; Ducrot, M.; Dupej, P.; Dwyer, S. E.; Edo, T. B.; Edwards, M. C.; Effler, A.; Eggenstein, H.-B.; Ehrens, P.; Eichholz, J.; Eikenberry, S. S.; Eisenstein, R. A.; Essick, R. C.; Estevez, D.; Etienne, Z. B.; Etzel, T.; Evans, M.; Evans, T. M.; Factourovich, M.; Fafone, V.; Fair, H.; Fairhurst, S.; Fan, X.; Farinon, S.; Farr, B.; Farr, W. M.; Fauchon-Jones, E. J.; Favata, M.; Fays, M.; Fee, C.; Fehrmann, H.; Feicht, J.; Fejer, M. M.; Fernandez-Galiana, A.; Ferrante, I.; Ferreira, E. C.; Ferrini, F.; Fidecaro, F.; Finstad, D.; Fiori, I.; Fiorucci, D.; Fishbach, M.; Fisher, R. P.; Fitz-Axen, M.; Flaminio, R.; Fletcher, M.; Fong, H.; Font, J. A.; Forsyth, P. W. F.; Forsyth, S. S.; Fournier, J.-D.; Frasca, S.; Frasconi, F.; Frei, Z.; Freise, A.; Frey, R.; Frey, V.; Fries, E. M.; Fritschel, P.; Frolov, V. V.; Fulda, P.; Fyffe, M.; Gabbard, H.; Gadre, B. U.; Gaebel, S. M.; Gair, J. R.; Gammaitoni, L.; Ganija, M. R.; Gaonkar, S. G.; Garcia-Quiros, C.; Garufi, F.; Gateley, B.; Gaudio, S.; Gaur, G.; Gayathri, V.; Gehrels, N.; Gemme, G.; Genin, E.; Gennai, A.; George, D.; George, J.; Gergely, L.; Germain, V.; Ghonge, S.; Ghosh, Abhirup; Ghosh, Archisman; Ghosh, S.; Giaime, J. A.; Giardina, K. D.; Giazotto, A.; Gill, K.; Glover, L.; Goetz, E.; Goetz, R.; Gomes, S.; Goncharov, B.; González, G.; Gonzalez Castro, J. M.; Gopakumar, A.; Gorodetsky, M. L.; Gossan, S. E.; Gosselin, M.; Gouaty, R.; Grado, A.; Graef, C.; Granata, M.; Grant, A.; Gras, S.; Gray, C.; Greco, G.; Green, A. C.; Gretarsson, E. M.; Groot, P.; Grote, H.; Grunewald, S.; Gruning, P.; Guidi, G. M.; Guo, X.; Gupta, A.; Gupta, M. K.; Gushwa, K. E.; Gustafson, E. K.; Gustafson, R.; Halim, O.; Hall, B. R.; Hall, E. D.; Hamilton, E. Z.; Hammond, G.; Haney, M.; Hanke, M. M.; Hanks, J.; Hanna, C.; Hannam, M. D.; Hannuksela, O. A.; Hanson, J.; Hardwick, T.; Harms, J.; Harry, G. M.; Harry, I. W.; Hart, M. J.; Haster, C.-J.; Haughian, K.; Healy, J.; Heidmann, A.; Heintze, M. C.; Heitmann, H.; Hello, P.; Hemming, G.; Hendry, M.; Heng, I. S.; Hennig, J.; Heptonstall, A. W.; Heurs, M.; Hild, S.; Hinderer, T.; Hoak, D.; Hofman, D.; Holt, K.; Holz, D. E.; Hopkins, P.; Horst, C.; Hough, J.; Houston, E. A.; Howell, E. J.; Hreibi, A.; Hu, Y. M.; Huerta, E. A.; Huet, D.; Hughey, B.; Husa, S.; Huttner, S. H.; Huynh-Dinh, T.; Indik, N.; Inta, R.; Intini, G.; Isa, H. N.; Isac, J.-M.; Isi, M.; Iyer, B. R.; Izumi, K.; Jacqmin, T.; Jani, K.; Jaranowski, P.; Jawahar, S.; Jiménez-Forteza, F.; Johnson, W. W.; Jones, D. I.; Jones, R.; Jonker, R. J. G.; Ju, L.; Junker, J.; Kalaghatgi, C. V.; Kalogera, V.; Kamai, B.; Kandhasamy, S.; Kang, G.; Kanner, J. B.; Kapadia, S. J.; Karki, S.; Karvinen, K. S.; Kasprzack, M.; Katolik, M.; Katsavounidis, E.; Katzman, W.; Kaufer, S.; Kawabe, K.; Kéfélian, F.; Keitel, D.; Kemball, A. J.; Kennedy, R.; Kent, C.; Key, J. S.; Khalili, F. Y.; Khan, I.; Khan, S.; Khan, Z.; Khazanov, E. A.; Kijbunchoo, N.; Kim, Chunglee; Kim, J. C.; Kim, K.; Kim, W.; Kim, W. S.; Kim, Y.-M.; Kimbrell, S. J.; King, E. J.; King, P. J.; Kinley-Hanlon, M.; Kirchhoff, R.; Kissel, J. S.; Kleybolte, L.; Klimenko, S.; Knowles, T. D.; Koch, P.; Koehlenbeck, S. M.; Koley, S.; Kondrashov, V.; Kontos, A.; Korobko, M.; Korth, W. Z.; Kowalska, I.; Kozak, D. B.; Krämer, C.; Kringel, V.; Królak, A.; Kuehn, G.; Kumar, P.; Kumar, R.; Kumar, S.; Kuo, L.; Kutynia, A.; Kwang, S.; Lackey, B. D.; Lai, K. H.; Landry, M.; Lang, R. N.; Lange, J.; Lantz, B.; Lanza, R. K.; Lartaux-Vollard, A.; Lasky, P. D.; Laxen, M.; Lazzarini, A.; Lazzaro, C.; Leaci, P.; Leavey, S.; Lee, C. H.; Lee, H. K.; Lee, H. M.; Lee, H. W.; Lee, K.; Lehmann, J.; Lenon, A.; Leonardi, M.; Leroy, N.; Letendre, N.; Levin, Y.; Li, T. G. F.; Linker, S. D.; Littenberg, T. B.; Liu, J.; Lo, R. K. L.; Lockerbie, N. A.; London, L. T.; Lord, J. E.; Lorenzini, M.; Loriette, V.; Lormand, M.; Losurdo, G.; Lough, J. D.; Lousto, C. O.; Lovelace, G.; Lück, H.; Lumaca, D.; Lundgren, A. P.; Lynch, R.; Ma, Y.; Macas, R.; Macfoy, S.; Machenschalk, B.; MacInnis, M.; Macleod, D. M.; Magaña Hernandez, I.; Magaña-Sandoval, F.; Magaña Zertuche, L.; Magee, R. M.; Majorana, E.; Maksimovic, I.; Man, N.; Mandic, V.; Mangano, V.; Mansell, G. L.; Manske, M.; Mantovani, M.; Marchesoni, F.; Marion, F.; Márka, S.; Márka, Z.; Markakis, C.; Markosyan, A. S.; Markowitz, A.; Maros, E.; Marquina, A.; Martelli, F.; Martellini, L.; Martin, I. W.; Martin, R. M.; Martynov, D. V.; Mason, K.; Massera, E.; Masserot, A.; Massinger, T. J.; Masso-Reid, M.; Mastrogiovanni, S.; Matas, A.; Matichard, F.; Matone, L.; Mavalvala, N.; Mazumder, N.; McCarthy, R.; McClelland, D. E.; McCormick, S.; McCuller, L.; McGuire, S. C.; McIntyre, G.; McIver, J.; McManus, D. J.; McNeill, L.; McRae, T.; McWilliams, S. T.; Meacher, D.; Meadors, G. D.; Mehmet, M.; Meidam, J.; Mejuto-Villa, E.; Melatos, A.; Mendell, G.; Mercer, R. A.; Merilh, E. L.; Merzougui, M.; Meshkov, S.; Messenger, C.; Messick, C.; Metzdorff, R.; Meyers, P. M.; Miao, H.; Michel, C.; Middleton, H.; Mikhailov, E. E.; Milano, L.; Miller, A. L.; Miller, B. B.; Miller, J.; Millhouse, M.; Milovich-Goff, M. C.; Minazzoli, O.; Minenkov, Y.; Ming, J.; Mishra, C.; Mitra, S.; Mitrofanov, V. P.; Mitselmakher, G.; Mittleman, R.; Moffa, D.; Moggi, A.; Mogushi, K.; Mohan, M.; Mohapatra, S. R. P.; Montani, M.; Moore, C. J.; Moraru, D.; Moreno, G.; Morriss, S. R.; Mours, B.; Mow-Lowry, C. M.; Mueller, G.; Muir, A. W.; Mukherjee, Arunava; Mukherjee, D.; Mukherjee, S.; Mukund, N.; Mullavey, A.; Munch, J.; Muñiz, E. A.; Muratore, M.; Murray, P. G.; Napier, K.; Nardecchia, I.; Naticchioni, L.; Nayak, R. K.; Neilson, J.; Nelemans, G.; Nelson, T. J. N.; Nery, M.; Neunzert, A.; Nevin, L.; Newport, J. M.; Newton, G.; Ng, K. K. Y.; Nguyen, T. T.; Nichols, D.; Nielsen, A. B.; Nissanke, S.; Nitz, A.; Noack, A.; Nocera, F.; Nolting, D.; North, C.; Nuttall, L. K.; Oberling, J.; O'Dea, G. D.; Ogin, G. H.; Oh, J. J.; Oh, S. H.; Ohme, F.; Okada, M. A.; Oliver, M.; Oppermann, P.; Oram, Richard J.; O'Reilly, B.; Ormiston, R.; Ortega, L. F.; O'Shaughnessy, R.; Ossokine, S.; Ottaway, D. J.; Overmier, H.; Owen, B. J.; Pace, A. E.; Page, J.; Page, M. A.; Pai, A.; Pai, S. A.; Palamos, J. R.; Palashov, O.; Palomba, C.; Pal-Singh, A.; Pan, Howard; Pan, Huang-Wei; Pang, B.; Pang, P. T. H.; Pankow, C.; Pannarale, F.; Pant, B. C.; Paoletti, F.; Paoli, A.; Papa, M. A.; Parida, A.; Parker, W.; Pascucci, D.; Pasqualetti, A.; Passaquieti, R.; Passuello, D.; Patil, M.; Patricelli, B.; Pearlstone, B. L.; Pedraza, M.; Pedurand, R.; Pekowsky, L.; Pele, A.; Penn, S.; Perez, C. J.; Perreca, A.; Perri, L. M.; Pfeiffer, H. P.; Phelps, M.; Piccinni, O. J.; Pichot, M.; Piergiovanni, F.; Pierro, V.; Pillant, G.; Pinard, L.; Pinto, I. M.; Pirello, M.; Pitkin, M.; Poe, M.; Poggiani, R.; Popolizio, P.; Porter, E. K.; Post, A.; Powell, J.; Prasad, J.; Pratt, J. W. W.; Pratten, G.; Predoi, V.; Prestegard, T.; Prijatelj, M.; Principe, M.; Privitera, S.; Prodi, G. A.; Prokhorov, L. G.; Puncken, O.; Punturo, M.; Puppo, P.; Pürrer, M.; Qi, H.; Quetschke, V.; Quintero, E. A.; Quitzow-James, R.; Raab, F. J.; Rabeling, D. S.; Radkins, H.; Raffai, P.; Raja, S.; Rajan, C.; Rajbhandari, B.; Rakhmanov, M.; Ramirez, K. E.; Ramos-Buades, A.; Rapagnani, P.; Raymond, V.; Razzano, M.; Read, J.; Regimbau, T.; Rei, L.; Reid, S.; Reitze, D. H.; Ren, W.; Reyes, S. D.; Ricci, F.; Ricker, P. M.; Rieger, S.; Riles, K.; Rizzo, M.; Robertson, N. A.; Robie, R.; Robinet, F.; Rocchi, A.; Rolland, L.; Rollins, J. G.; Roma, V. J.; Romano, J. D.; Romano, R.; Romel, C. L.; Romie, J. H.; Rosińska, D.; Ross, M. P.; Rowan, S.; Rüdiger, A.; Ruggi, P.; Rutins, G.; Ryan, K.; Sachdev, S.; Sadecki, T.; Sadeghian, L.; Sakellariadou, M.; Salconi, L.; Saleem, M.; Salemi, F.; Samajdar, A.; Sammut, L.; Sampson, L. M.; Sanchez, E. J.; Sanchez, L. E.; Sanchis-Gual, N.; Sandberg, V.; Sanders, J. R.; Sassolas, B.; Saulson, P. R.; Sauter, O.; Savage, R. L.; Sawadsky, A.; Schale, P.; Scheel, M.; Scheuer, J.; Schmidt, J.; Schmidt, P.; Schnabel, R.; Schofield, R. M. S.; Schönbeck, A.; Schreiber, E.; Schuette, D.; Schulte, B. W.; Schutz, B. F.; Schwalbe, S. G.; Scott, J.; Scott, S. M.; Seidel, E.; Sellers, D.; Sengupta, A. S.; Sentenac, D.; Sequino, V.; Sergeev, A.; Shaddock, D. A.; Shaffer, T. J.; Shah, A. A.; Shahriar, M. S.; Shaner, M. B.; Shao, L.; Shapiro, B.; Shawhan, P.; Sheperd, A.; Shoemaker, D. H.; Shoemaker, D. M.; Siellez, K.; Siemens, X.; Sieniawska, M.; Sigg, D.; Silva, A. D.; Singer, L. P.; Singh, A.; Singhal, A.; Sintes, A. M.; Slagmolen, B. J. J.; Smith, B.; Smith, J. R.; Smith, R. J. E.; Somala, S.; Son, E. J.; Sonnenberg, J. A.; Sorazu, B.; Sorrentino, F.; Souradeep, T.; Spencer, A. P.; Srivastava, A. K.; Staats, K.; Staley, A.; Steinke, M.; Steinlechner, J.; Steinlechner, S.; Steinmeyer, D.; Stevenson, S. P.; Stone, R.; Stops, D. J.; Strain, K. A.; Stratta, G.; Strigin, S. E.; Strunk, A.; Sturani, R.; Stuver, A. L.; Summerscales, T. Z.; Sun, L.; Sunil, S.; Suresh, J.; Sutton, P. J.; Swinkels, B. L.; Szczepańczyk, M. J.; Tacca, M.; Tait, S. C.; Talbot, C.; Talukder, D.; Tanner, D. B.; Tao, D.; Tápai, M.; Taracchini, A.; Tasson, J. D.; Taylor, J. A.; Taylor, R.; Tewari, S. V.; Theeg, T.; Thies, F.; Thomas, E. G.; Thomas, M.; Thomas, P.; Thorne, K. A.; Thrane, E.; Tiwari, S.; Tiwari, V.; Tokmakov, K. V.; Toland, K.; Tonelli, M.; Tornasi, Z.; Torres-Forné, A.; Torrie, C. I.; Töyrä, D.; Travasso, F.; Traylor, G.; Trinastic, J.; Tringali, M. C.; Trozzo, L.; Tsang, K. W.; Tse, M.; Tso, R.; Tsukada, L.; Tsuna, D.; Tuyenbayev, D.; Ueno, K.; Ugolini, D.; Unnikrishnan, C. S.; Urban, A. L.; Usman, S. A.; Vahlbruch, H.; Vajente, G.; Valdes, G.; van Bakel, N.; van Beuzekom, M.; van den Brand, J. F. J.; Van Den Broeck, C.; Vander-Hyde, D. C.; van der Schaaf, L.; van Heijningen, J. V.; van Veggel, A. A.; Vardaro, M.; Varma, V.; Vass, S.; Vasúth, M.; Vecchio, A.; Vedovato, G.; Veitch, J.; Veitch, P. J.; Venkateswara, K.; Venugopalan, G.; Verkindt, D.; Vetrano, F.; Viceré, A.; Viets, A. D.; Vinciguerra, S.; Vine, D. J.; Vinet, J.-Y.; Vitale, S.; Vo, T.; Vocca, H.; Vorvick, C.; Vyatchanin, S. P.; Wade, A. R.; Wade, L. E.; Wade, M.; Walet, R.; Walker, M.; Wallace, L.; Walsh, S.; Wang, G.; Wang, H.; Wang, J. Z.; Wang, W. H.; Wang, Y. F.; Ward, R. L.; Warner, J.; Was, M.; Watchi, J.; Weaver, B.; Wei, L.-W.; Weinert, M.; Weinstein, A. J.; Weiss, R.; Wen, L.; Wessel, E. K.; Weßels, P.; Westerweck, J.; Westphal, T.; Wette, K.; Whelan, J. T.; Whiting, B. F.; Whittle, C.; Wilken, D.; Williams, D.; Williams, R. D.; Williamson, A. R.; Willis, J. L.; Willke, B.; Wimmer, M. H.; Winkler, W.; Wipf, C. C.; Wittel, H.; Woan, G.; Woehler, J.; Wofford, J.; Wong, K. W. K.; Worden, J.; Wright, J. L.; Wu, D. S.; Wysocki, D. M.; Xiao, S.; Yamamoto, H.; Yancey, C. C.; Yang, L.; Yap, M. J.; Yazback, M.; Yu, Hang; Yu, Haocun; Yvert, M.; ZadroŻny, A.; Zanolin, M.; Zelenova, T.; Zendri, J.-P.; Zevin, M.; Zhang, L.; Zhang, M.; Zhang, T.; Zhang, Y.-H.; Zhao, C.; Zhou, M.; Zhou, Z.; Zhu, S. J.; Zhu, X. J.; Zucker, M. E.; Zweizig, J.; LIGO Scientific Collaboration; Virgo Collaboration

2018-05-01

The detection of gravitational waves with Advanced LIGO and Advanced Virgo has enabled novel tests of general relativity, including direct study of the polarization of gravitational waves. While general relativity allows for only two tensor gravitational-wave polarizations, general metric theories can additionally predict two vector and two scalar polarizations. The polarization of gravitational waves is encoded in the spectral shape of the stochastic gravitational-wave background, formed by the superposition of cosmological and individually unresolved astrophysical sources. Using data recorded by Advanced LIGO during its first observing run, we search for a stochastic background of generically polarized gravitational waves. We find no evidence for a background of any polarization, and place the first direct bounds on the contributions of vector and scalar polarizations to the stochastic background. Under log-uniform priors for the energy in each polarization, we limit the energy densities of tensor, vector, and scalar modes at 95% credibility to Ω0T<5.58 ×10-8 , Ω0V<6.35 ×10-8 , and Ω0S<1.08 ×10-7 at a reference frequency f0=25 Hz .

Cosmology in generalized Proca theories

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

Felice, Antonio De; Mukohyama, Shinji; Heisenberg, Lavinia

2016-06-01

We consider a massive vector field with derivative interactions that propagates only the 3 desired polarizations (besides two tensor polarizations from gravity) with second-order equations of motion in curved space-time. The cosmological implications of such generalized Proca theories are investigated for both the background and the linear perturbation by taking into account the Lagrangian up to quintic order. In the presence of a matter fluid with a temporal component of the vector field, we derive the background equations of motion and show the existence of de Sitter solutions relevant to the late-time cosmic acceleration. We also obtain conditions for themore » absence of ghosts and Laplacian instabilities of tensor, vector, and scalar perturbations in the small-scale limit. Our results are applied to concrete examples of the general functions in the theory, which encompass vector Galileons as a specific case. In such examples, we show that the de Sitter fixed point is always a stable attractor and study viable parameter spaces in which the no-ghost and stability conditions are satisfied during the cosmic expansion history.« less

Vector and axial-vector decomposition of Einstein's gravitational action

NASA Astrophysics Data System (ADS)

Soh, Kwang S.

1991-08-01

Vector and axial-vector gravitational fields are introduced to express the Einstein action in the manner of electromagnetism. Their conformal scaling properties are examined, and the resemblance between the general coordinate and electromagnetic gauge transformation is elucidated. The chiral formulation of the gravitational action is constructed. I am deeply grateful to Professor S. Hawking, and Professor G. Lloyd for warm hospitality at DAMTP, and Darwin College, University of Cambridge, respectively. I also appreciate much help received from Dr. Q.-H. Park.

An improved EMD method for modal identification and a combined static-dynamic method for damage detection

NASA Astrophysics Data System (ADS)

Yang, Jinping; Li, Peizhen; Yang, Youfa; Xu, Dian

2018-04-01

Empirical mode decomposition (EMD) is a highly adaptable signal processing method. However, the EMD approach has certain drawbacks, including distortions from end effects and mode mixing. In the present study, these two problems are addressed using an end extension method based on the support vector regression machine (SVRM) and a modal decomposition method based on the characteristics of the Hilbert transform. The algorithm includes two steps: using the SVRM, the time series data are extended at both endpoints to reduce the end effects, and then, a modified EMD method using the characteristics of the Hilbert transform is performed on the resulting signal to reduce mode mixing. A new combined static-dynamic method for identifying structural damage is presented. This method combines the static and dynamic information in an equilibrium equation that can be solved using the Moore-Penrose generalized matrix inverse. The combination method uses the differences in displacements of the structure with and without damage and variations in the modal force vector. Tests on a four-story, steel-frame structure were conducted to obtain static and dynamic responses of the structure. The modal parameters are identified using data from the dynamic tests and improved EMD method. The new method is shown to be more accurate and effective than the traditional EMD method. Through tests with a shear-type test frame, the higher performance of the proposed static-dynamic damage detection approach, which can detect both single and multiple damage locations and the degree of the damage, is demonstrated. For structures with multiple damage, the combined approach is more effective than either the static or dynamic method. The proposed EMD method and static-dynamic damage detection method offer improved modal identification and damage detection, respectively, in structures.

ON THE DYNAMICAL DERIVATION OF EQUILIBRIUM STATISTICAL MECHANICS

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

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

1960-12-01

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

A Class of Solvable Stopping Games

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

Alvarez, Luis H. R.

We consider a class of Dynkin games in the case where the underlying process evolves according to a one-dimensional but otherwise general diffusion. We establish general conditions under which both the value and the saddle point equilibrium exist and under which the exercise boundaries characterizing the saddle point strategy can be explicitly characterized in terms of a pair of standard first order necessary conditions for optimality. We also analyze those cases where an extremal pair of boundaries exists and investigate the overall impact of increased volatility on the equilibrium stopping strategies and their values.

Entropic Description of Gas Hydrate Ice-Liquid Equilibrium via Enhanced Sampling of Coexisting Phases

NASA Astrophysics Data System (ADS)

Małolepsza, Edyta; Kim, Jaegil; Keyes, Tom

2015-05-01

Metastable β ice holds small guest molecules in stable gas hydrates, so its solid-liquid equilibrium is of interest. However, aqueous crystal-liquid transitions are very difficult to simulate. A new molecular dynamics algorithm generates trajectories in a generalized N P T ensemble and equilibrates states of coexisting phases with a selectable enthalpy. With replicas spanning the range between β ice and liquid water, we find the statistical temperature from the enthalpy histograms and characterize the transition by the entropy, introducing a general computational procedure for first-order transitions.

Geometric approach to nuclear pasta phases

NASA Astrophysics Data System (ADS)

Kubis, Sebastian; Wójcik, Włodzimierz

2016-12-01

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

Entropic description of gas hydrate ice/liquid equilibrium via enhanced sampling of coexisting phases

DOE PAGES

Malolepsza, Edyta; Kim, Jaegil; Keyes, Tom

2015-04-28

Metastable β ice holds small guest molecules in stable gas hydrates, so its solid/liquid equilibrium is of interest. However, aqueous crystal/liquid transitions are very difficult to simulate. A new MD algorithm generates trajectories in a generalized NPT ensemble and equilibrates states of coexisting phases with a selectable enthalpy. Furthermore, with replicas spanning the range between β ice and liquid water we find the statistical temperature from the enthalpy histograms and characterize the transition by the entropy, introducing a general computational procedure for first-order transitions.

IONIZATION EQUILIBRIUM TIMESCALES IN COLLISIONAL PLASMAS

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

Smith, Randall K.; Hughes, John P., E-mail: rsmith@cfa.harvard.ed, E-mail: jph@physics.rutgers.ed

2010-07-20

Astrophysical shocks or bursts from a photoionizing source can disturb the typical collisional plasma found in galactic interstellar media or the intergalactic medium. The spectrum emitted by this plasma contains diagnostics that have been used to determine the time since the disturbing event, although this determination becomes uncertain as the elements in the plasma return to ionization equilibrium. A general solution for the equilibrium timescale for each element arises from the elegant eigenvector method of solution to the problem of a non-equilibrium plasma described by Masai and Hughes and Helfand. In general, the ionization evolution of an element Z inmore » a constant electron temperature plasma is given by a coupled set of Z + 1 first-order differential equations. However, they can be recast as Z uncoupled first-order differential equations using an eigenvector basis for the system. The solution is then Z separate exponential functions, with the time constants given by the eigenvalues of the rate matrix. The smallest of these eigenvalues gives the scale of the slowest return to equilibrium independent of the initial conditions, while conversely the largest eigenvalue is the scale of the fastest change in the ion population. These results hold for an ionizing plasma, a recombining plasma, or even a plasma with random initial conditions, and will allow users of these diagnostics to determine directly if their best-fit result significantly limits the timescale since a disturbance or is so close to equilibrium as to include an arbitrarily long time.« less

On the LHC sensitivity for non-thermalised hidden sectors

NASA Astrophysics Data System (ADS)

Kahlhoefer, Felix

2018-04-01

We show under rather general assumptions that hidden sectors that never reach thermal equilibrium in the early Universe are also inaccessible for the LHC. In other words, any particle that can be produced at the LHC must either have been in thermal equilibrium with the Standard Model at some point or must be produced via the decays of another hidden sector particle that has been in thermal equilibrium. To reach this conclusion, we parametrise the cross section connecting the Standard Model to the hidden sector in a very general way and use methods from linear programming to calculate the largest possible number of LHC events compatible with the requirement of non-thermalisation. We find that even the HL-LHC cannot possibly produce more than a few events with energy above 10 GeV involving states from a non-thermalised hidden sector.

Connecting Solubility, Equilibrium, and Periodicity in a Green, Inquiry Experiment for the General Chemistry Laboratory

ERIC Educational Resources Information Center

Cacciatore, Kristen L.; Amado, Jose; Evans, Jason J.; Sevian, Hannah

2008-01-01

We present a novel first-year chemistry laboratory experiment that connects solubility, equilibrium, and chemical periodicity concepts. It employs a unique format that asks students to replicate experiments described in different sample lab reports, each lacking some essential information, rather than follow a scripted procedure. This structure is…

Equilibrium Partitioning Sediment Benchmarks (ESBs) for the Protection of Benthic Organisms: Procedures for the Determination of the Freely Dissolved Interstitial Water Concentrations of Nonionic Organics

EPA Science Inventory

This document describes procedures to determine the concentrations of nonionic organic chemicals in sediment interstitial waters. In previous ESB documents, the general equilibrium partitioning (EqP) approach was chosen for the derivation of sediment benchmarks because it account...

Systematic Approach to Calculate the Concentration of Chemical Species in Multi-Equilibrium Problems

ERIC Educational Resources Information Center

Baeza-Baeza, Juan Jose; Garcia-Alvarez-Coque, Maria Celia

2011-01-01

A general systematic approach is proposed for the numerical calculation of multi-equilibrium problems. The approach involves several steps: (i) the establishment of balances involving the chemical species in solution (e.g., mass balances, charge balance, and stoichiometric balance for the reaction products), (ii) the selection of the unknowns (the…

Using the Science Writing Heuristic to Improve Students' Understanding of General Equilibrium

ERIC Educational Resources Information Center

Rudd, James A., II; Greenbowe, Thomas J.; Hand, Brian M.

2007-01-01

This study compared the performance of students using the Science Writing Heuristic (SWH) approach and students using a standard or traditional laboratory curriculum on lecture exams and a laboratory practical exam on a specific topic, chemical equilibrium. The SWH helps students do inquiry science laboratory work by structuring the laboratory…

Exact results in nonequilibrium statistical mechanics: Formalism and applications in chemical kinetics and single-molecule free energy estimation

NASA Astrophysics Data System (ADS)

Adib, Artur B.

In the last two decades or so, a collection of results in nonequilibrium statistical mechanics that departs from the traditional near-equilibrium framework introduced by Lars Onsager in 1931 has been derived, yielding new fundamental insights into far-from-equilibrium processes in general. Apart from offering a more quantitative statement of the second law of thermodynamics, some of these results---typified by the so-called "Jarzynski equality"---have also offered novel means of estimating equilibrium quantities from nonequilibrium processes, such as free energy differences from single-molecule "pulling" experiments. This thesis contributes to such efforts by offering three novel results in nonequilibrium statistical mechanics: (a) The entropic analog of the Jarzynski equality; (b) A methodology for estimating free energies from "clamp-and-release" nonequilibrium processes; and (c) A directly measurable symmetry relation in chemical kinetics similar to (but more general than) chemical detailed balance. These results share in common the feature of remaining valid outside Onsager's near-equilibrium regime, and bear direct applicability in protein folding kinetics as well as in single-molecule free energy estimation.

SSM/I and ECMWF Wind Vector Comparison

NASA Technical Reports Server (NTRS)

Wentz, Frank J.; Ashcroft, Peter D.

1996-01-01

Wentz was the first to convincingly show that satellite microwave radiometers have the potential to measure the oceanic wind vector. The most compelling evidence for this conclusion was the monthly wind vector maps derived solely from a statistical analysis of Special Sensor Microwave Imager (SSM/I) observations. In a qualitative sense, these maps clearly showed the general circulation over the world's oceans. In this report we take a closer look at the SSM/I monthly wind vector maps and compare them to European Center for Medium-Range Weather Forecasts (ECMWF) wind fields. This investigation leads both to an empirical comparison of SSM/I calculated wind vectors with ECMWF wind vectors, and to an examination of possible reasons that the SSM/I calculated wind vector direction would be inherently more reliable at some locations than others.

General Relativity Exactly Described by Use of Newton's Laws within a Curved Geometry

NASA Astrophysics Data System (ADS)

Savickas, David

2014-03-01

The connection between general relativity and Newtonian mechanics is shown to be much closer than generally recognized. When Newton's second law is written in a curved geometry by using the physical components of a vector as defined in tensor calculus, and by replacing distance within the momentum's velocity by the vector metric ds in a curved geometry, the second law can then be easily shown to be exactly identical to the geodesic equation of motion occurring in general relativity. By using a time whose vector direction is constant, as similarly occurs in Newtonian mechanics, this equation can be separated into two equations one of which is a curved three-dimensional equation of motion and the other is an equation for energy. For the gravitational field of an isolated particle, they yield the Schwarzschild equations. They can be used to describe gravitation for any array of masses for which the Newtonian gravitational potential is known, and is applied here to describe motion in the gravitational field of a thin mass-rod.

Beyond generalized Proca theories

NASA Astrophysics Data System (ADS)

Heisenberg, Lavinia; Kase, Ryotaro; Tsujikawa, Shinji

2016-09-01

We consider higher-order derivative interactions beyond second-order generalized Proca theories that propagate only the three desired polarizations of a massive vector field besides the two tensor polarizations from gravity. These new interactions follow the similar construction criteria to those arising in the extension of scalar-tensor Horndeski theories to Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories. On the isotropic cosmological background, we show the existence of a constraint with a vanishing Hamiltonian that removes the would-be Ostrogradski ghost. We study the behavior of linear perturbations on top of the isotropic cosmological background in the presence of a matter perfect fluid and find the same number of propagating degrees of freedom as in generalized Proca theories (two tensor polarizations, two transverse vector modes, and two scalar modes). Moreover, we obtain the conditions for the avoidance of ghosts and Laplacian instabilities of tensor, vector, and scalar perturbations. We observe key differences in the scalar sound speed, which is mixed with the matter sound speed outside the domain of generalized Proca theories.

Quadratic obstructions to small-time local controllability for scalar-input systems

NASA Astrophysics Data System (ADS)

Beauchard, Karine; Marbach, Frédéric

2018-03-01

We consider nonlinear finite-dimensional scalar-input control systems in the vicinity of an equilibrium. When the linearized system is controllable, the nonlinear system is smoothly small-time locally controllable: whatever m > 0 and T > 0, the state can reach a whole neighborhood of the equilibrium at time T with controls arbitrary small in Cm-norm. When the linearized system is not controllable, we prove that: either the state is constrained to live within a smooth strict manifold, up to a cubic residual, or the quadratic order adds a signed drift with respect to it. This drift holds along a Lie bracket of length (2 k + 1), is quantified in terms of an H-k-norm of the control, holds for controls small in W 2 k , ∞-norm and these spaces are optimal. Our proof requires only C3 regularity of the vector field. This work underlines the importance of the norm used in the smallness assumption on the control, even in finite dimension.

Static elastica formulations of a pine conveying fluid

NASA Astrophysics Data System (ADS)

Thompson, J. M. T.; Lunn, T. S.

1981-07-01

An elastic pipe in an equilibrium configuration of arbitrary large deflection discharging fluid from its end experiences static centrifugal and frictional drag forces along its complete length. These are, however, entirely equivalent to an end follower force of magnitude ρ AV2. This equivalence is examined in detail by using the intrinsic field equations which are suitable for closed form solutions in terms of elliptic integrals. Once the pipe moves it also experiences gyroscopic Coriolis forces along its length, but these are not considered in this static examination. It is shown in detail how a discharging pipe with end forces and moments is statically equivalent to a beam or strut with the same end forces and moments plus the reversed momentum vector ρ AV2. It is seen that a cantilevered pipe with a free end can have no statical equilibrium states at all, at either large or small deflections, while pipes with constrained ends have large static deflections identical to those of the equivalent struts.

Dynamics and Control of Attitude, Power, and Momentum for a Spacecraft Using Flywheels and Control Moment Gyroscopes

NASA Technical Reports Server (NTRS)

Roithmayr, Carlos M.; Karlgaard, Christopher D.; Kumar, Renjith R.; Seywald, Hans; Bose, David M.

2003-01-01

Several laws are designed for simultaneous control of the orientation of an Earth-pointing spacecraft, the energy stored by counter-rotating flywheels, and the angular momentum of the flywheels and control moment gyroscopes used together as an integrated set of actuators for attitude control. General, nonlinear equations of motion are presented in vector-dyadic form, and used to obtain approximate expressions which are then linearized in preparation for design of control laws that include feedback of flywheel kinetic energy error as a means of compensating for damping exerted by rotor bearings. Two flywheel steering laws are developed such that torque commanded by an attitude control law is achieved while energy is stored or discharged at the required rate. Using the International Space Station as an example, numerical simulations are performed to demonstrate control about a torque equilibrium attitude, and illustrate the benefits of kinetic energy error feedback. Control laws for attitude hold are also developed, and used to show the amount of propellant that can be saved when flywheels assist the CMGs. Nonlinear control laws for large-angle slew maneuvers perform well, but excessive momentum is required to reorient a vehicle like the International Space Station.

Non-equilibrium quantum heat machines

NASA Astrophysics Data System (ADS)

Alicki, Robert; Gelbwaser-Klimovsky, David

2015-11-01

Standard heat machines (engine, heat pump, refrigerator) are composed of a system (working fluid) coupled to at least two equilibrium baths at different temperatures and periodically driven by an external device (piston or rotor) sometimes called the work reservoir. The aim of this paper is to go beyond this scheme by considering environments which are stationary but cannot be decomposed into a few baths at thermal equilibrium. Such situations are important, for example in solar cells, chemical machines in biology, various realizations of laser cooling or nanoscopic machines driven by laser radiation. We classify non-equilibrium baths depending on their thermodynamic behavior and show that the efficiency of heat machines powered by them is limited by the generalized Carnot bound.

Liapunov stability analysis of hybrid dynamical systems in the neighborhood of nontrivial equilibrium

NASA Technical Reports Server (NTRS)

Meirovitch, L.

1973-01-01

This paper is concerned with the stability of a hybrid dynamical system in the neighborhood of a nontrivial equilibrium, where the system consists of one rigid part and n elastic members. The body moves in a central-force field with its mass center describing a circular orbit. The nontrivial equilibrium is defined by steady rotation of the system at an angular velocity equal to the orbital velocity, with the elastic members being in deformed state. A Liapunov stability analysis is performed by assuming small perturbations about the nontrivial equilibrium, where the latter is generally defined by nonlinear differential equations. The theory is applied to a gravity-gradient stabilized satellite with flexible appendages.

Thermal conductance at the interface between crystals using equilibrium and nonequilibrium molecular dynamics

NASA Astrophysics Data System (ADS)

Merabia, Samy; Termentzidis, Konstantinos

2012-09-01

In this article, we compare the results of nonequilibrium (NEMD) and equilibrium (EMD) molecular dynamics methods to compute the thermal conductance at the interface between solids. We propose to probe the thermal conductance using equilibrium simulations measuring the decay of the thermally induced energy fluctuations of each solid. We also show that NEMD and EMD give generally speaking inconsistent results for the thermal conductance: Green-Kubo simulations probe the Landauer conductance between two solids which assumes phonons on both sides of the interface to be at equilibrium. On the other hand, we show that NEMD give access to the out-of-equilibrium interfacial conductance consistent with the interfacial flux describing phonon transport in each solid. The difference may be large and reaches typically a factor 5 for interfaces between usual semiconductors. We analyze finite size effects for the two determinations of the interfacial thermal conductance, and show that the equilibrium simulations suffer from severe size effects as compared to NEMD. We also compare the predictions of the two above-mentioned methods—EMD and NEMD—regarding the interfacial conductance of a series of mass mismatched Lennard-Jones solids. We show that the Kapitza conductance obtained with EMD can be well described using the classical diffuse mismatch model (DMM). On the other hand, NEMD simulation results are consistent with an out-of-equilibrium generalization of the acoustic mismatch model (AMM). These considerations are important in rationalizing previous results obtained using molecular dynamics, and help in pinpointing the physical scattering mechanisms taking place at atomically perfect interfaces between solids, which is a prerequisite to understand interfacial heat transfer across real interfaces.

Stochastic thermodynamics of quantum maps with and without equilibrium.

PubMed

Barra, Felipe; Lledó, Cristóbal

2017-11-01

We study stochastic thermodynamics for a quantum system of interest whose dynamics is described by a completely positive trace-preserving (CPTP) map as a result of its interaction with a thermal bath. We define CPTP maps with equilibrium as CPTP maps with an invariant state such that the entropy production due to the action of the map on the invariant state vanishes. Thermal maps are a subgroup of CPTP maps with equilibrium. In general, for CPTP maps, the thermodynamic quantities, such as the entropy production or work performed on the system, depend on the combined state of the system plus its environment. We show that these quantities can be written in terms of system properties for maps with equilibrium. The relations that we obtain are valid for arbitrary coupling strengths between the system and the thermal bath. The fluctuations of thermodynamic quantities are considered in the framework of a two-point measurement scheme. We derive the entropy production fluctuation theorem for general maps and a fluctuation relation for the stochastic work on a system that starts in the Gibbs state. Some simplifications for the probability distributions in the case of maps with equilibrium are presented. We illustrate our results by considering spin 1/2 systems under thermal maps, nonthermal maps with equilibrium, maps with nonequilibrium steady states, and concatenations of them. Finally, and as an important application, we consider a particular limit in which the concatenation of maps generates a continuous time evolution in Lindblad form for the system of interest, and we show that the concept of maps with and without equilibrium translates into Lindblad equations with and without quantum detailed balance, respectively. The consequences for the thermodynamic quantities in this limit are discussed.

Stochastic thermodynamics of quantum maps with and without equilibrium

NASA Astrophysics Data System (ADS)

Barra, Felipe; Lledó, Cristóbal

2017-11-01

We study stochastic thermodynamics for a quantum system of interest whose dynamics is described by a completely positive trace-preserving (CPTP) map as a result of its interaction with a thermal bath. We define CPTP maps with equilibrium as CPTP maps with an invariant state such that the entropy production due to the action of the map on the invariant state vanishes. Thermal maps are a subgroup of CPTP maps with equilibrium. In general, for CPTP maps, the thermodynamic quantities, such as the entropy production or work performed on the system, depend on the combined state of the system plus its environment. We show that these quantities can be written in terms of system properties for maps with equilibrium. The relations that we obtain are valid for arbitrary coupling strengths between the system and the thermal bath. The fluctuations of thermodynamic quantities are considered in the framework of a two-point measurement scheme. We derive the entropy production fluctuation theorem for general maps and a fluctuation relation for the stochastic work on a system that starts in the Gibbs state. Some simplifications for the probability distributions in the case of maps with equilibrium are presented. We illustrate our results by considering spin 1/2 systems under thermal maps, nonthermal maps with equilibrium, maps with nonequilibrium steady states, and concatenations of them. Finally, and as an important application, we consider a particular limit in which the concatenation of maps generates a continuous time evolution in Lindblad form for the system of interest, and we show that the concept of maps with and without equilibrium translates into Lindblad equations with and without quantum detailed balance, respectively. The consequences for the thermodynamic quantities in this limit are discussed.

Some Applications Of Semigroups And Computer Algebra In Discrete Structures

NASA Astrophysics Data System (ADS)

Bijev, G.

2009-11-01

An algebraic approach to the pseudoinverse generalization problem in Boolean vector spaces is used. A map (p) is defined, which is similar to an orthogonal projection in linear vector spaces. Some other important maps with properties similar to those of the generalized inverses (pseudoinverses) of linear transformations and matrices corresponding to them are also defined and investigated. Let Ax = b be an equation with matrix A and vectors x and b Boolean. Stochastic experiments for solving the equation, which involves the maps defined and use computer algebra methods, have been made. As a result, the Hamming distance between vectors Ax = p(b) and b is equal or close to the least possible. We also share our experience in using computer algebra systems for teaching discrete mathematics and linear algebra and research. Some examples for computations with binary relations using Maple are given.

Comparison of SOM point densities based on different criteria.

PubMed

Kohonen, T

1999-11-15

Point densities of model (codebook) vectors in self-organizing maps (SOMs) are evaluated in this article. For a few one-dimensional SOMs with finite grid lengths and a given probability density function of the input, the numerically exact point densities have been computed. The point density derived from the SOM algorithm turned out to be different from that minimizing the SOM distortion measure, showing that the model vectors produced by the basic SOM algorithm in general do not exactly coincide with the optimum of the distortion measure. A new computing technique based on the calculus of variations has been introduced. It was applied to the computation of point densities derived from the distortion measure for both the classical vector quantization and the SOM with general but equal dimensionality of the input vectors and the grid, respectively. The power laws in the continuum limit obtained in these cases were found to be identical.

3D hydrophobic moment vectors as a tool to characterize the surface polarity of amphiphilic peptides.

PubMed

Reißer, Sabine; Strandberg, Erik; Steinbrecher, Thomas; Ulrich, Anne S

2014-06-03

The interaction of membranes with peptides and proteins is largely determined by their amphiphilic character. Hydrophobic moments of helical segments are commonly derived from their two-dimensional helical wheel projections, and the same is true for β-sheets. However, to the best of our knowledge, there exists no method to describe structures in three dimensions or molecules with irregular shape. Here, we define the hydrophobic moment of a molecule as a vector in three dimensions by evaluating the surface distribution of all hydrophilic and lipophilic regions over any given shape. The electrostatic potential on the molecular surface is calculated based on the atomic point charges. The resulting hydrophobic moment vector is specific for the instantaneous conformation, and it takes into account all structural characteristics of the molecule, e.g., partial unfolding, bending, and side-chain torsion angles. Extended all-atom molecular dynamics simulations are then used to calculate the equilibrium hydrophobic moments for two antimicrobial peptides, gramicidin S and PGLa, under different conditions. We show that their effective hydrophobic moment vectors reflect the distribution of polar and nonpolar patches on the molecular surface and the calculated electrostatic surface potential. A comparison of simulations in solution and in lipid membranes shows how the peptides undergo internal conformational rearrangement upon binding to the bilayer surface. A good correlation with solid-state NMR data indicates that the hydrophobic moment vector can be used to predict the membrane binding geometry of peptides. This method is available as a web application on http://www.ibg.kit.edu/HM/. Copyright © 2014 Biophysical Society. Published by Elsevier Inc. All rights reserved.

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

PubMed

Khantuleva, Tatiana A; Shalymov, Dmitry S

2017-03-06

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

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

NASA Astrophysics Data System (ADS)

Khantuleva, Tatiana A.; Shalymov, Dmitry S.

2017-03-01

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

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

PubMed Central

Khantuleva, Tatiana A.

2017-01-01

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

Under What Conditions Can Equilibrium Gas-Particle Partitioning Be Expected to Hold in the Atmosphere?

PubMed

Mai, Huajun; Shiraiwa, Manabu; Flagan, Richard C; Seinfeld, John H

2015-10-06

The prevailing treatment of secondary organic aerosol formation in atmospheric models is based on the assumption of instantaneous gas-particle equilibrium for the condensing species, yet compelling experimental evidence indicates that organic aerosols can exhibit the properties of highly viscous, semisolid particles, for which gas-particle equilibrium may be achieved slowly. The approach to gas-particle equilibrium partitioning is controlled by gas-phase diffusion, interfacial transport, and particle-phase diffusion. Here we evaluate the controlling processes and the time scale to achieve gas-particle equilibrium as a function of the volatility of the condensing species, its surface accommodation coefficient, and its particle-phase diffusivity. For particles in the size range of typical atmospheric organic aerosols (∼50-500 nm), the time scale to establish gas-particle equilibrium is generally governed either by interfacial accommodation or particle-phase diffusion. The rate of approach to equilibrium varies, depending on whether the bulk vapor concentration is constant, typical of an open system, or decreasing as a result of condensation into the particles, typical of a closed system.

Derivation of the chemical-equilibrium rate coefficient using scattering theory

NASA Technical Reports Server (NTRS)

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.

Coherent states for the relativistic harmonic oscillator

NASA Technical Reports Server (NTRS)

Aldaya, Victor; Guerrero, J.

1995-01-01

Recently we have obtained, on the basis of a group approach to quantization, a Bargmann-Fock-like realization of the Relativistic Harmonic Oscillator as well as a generalized Bargmann transform relating fock wave functions and a set of relativistic Hermite polynomials. Nevertheless, the relativistic creation and annihilation operators satisfy typical relativistic commutation relations of the Lie product (vector-z, vector-z(sup dagger)) approximately equals Energy (an SL(2,R) algebra). Here we find higher-order polarization operators on the SL(2,R) group, providing canonical creation and annihilation operators satisfying the Lie product (vector-a, vector-a(sup dagger)) = identity vector 1, the eigenstates of which are 'true' coherent states.

Cosmology in beyond-generalized Proca theories

NASA Astrophysics Data System (ADS)

Nakamura, Shintaro; Kase, Ryotaro; Tsujikawa, Shinji

2017-05-01

The beyond-generalized Proca theories are the extension of second-order massive vector-tensor theories (dubbed generalized Proca theories) with two transverse vector modes and one longitudinal scalar besides two tensor polarizations. Even with this extension, the propagating degrees of freedom remain unchanged on the isotropic cosmological background without an Ostrogradski instability. We study the cosmology in beyond-generalized Proca theories by paying particular attention to the dynamics of late-time cosmic acceleration and resulting observational consequences. We derive conditions for avoiding ghosts and instabilities of tensor, vector, and scalar perturbations and discuss viable parameter spaces in concrete models allowing the dark energy equation of state smaller than -1 . The propagation speeds of those perturbations are subject to modifications beyond the domain of generalized Proca theories. There is a mixing between scalar and matter sound speeds, but such a mixing is suppressed during most of the cosmic expansion history without causing a new instability. On the other hand, we find that derivative interactions arising in beyond-generalized Proca theories give rise to important modifications to the cosmic growth history. The growth rate of matter perturbations can be compatible with the redshift-space distortion data due to the realization of gravitational interaction weaker than that in generalized Proca theories. Thus, it is possible to distinguish the dark energy model in beyond-generalized Proca theories from the counterpart in generalized Proca theories as well as from the Λ CDM model.

LeChâtelier's Principle in the Sciences

NASA Astrophysics Data System (ADS)

Thomsen, Volker B. E.

2000-02-01

LeChâtelier's principle of chemical equilibrium is actually a very general statement about systems in equilibrium and their behavior when subjected to external force or stress. Although one almost never finds mention of his name or law in other sciences, analogous principles and concepts do exist. In this note we examine some of the similar forms taken by this chemical principle in the fields of physics, geology, biology, and economics. Lenz's law in physics is an example of electromagnetic equilibrium and the geological principle of isostatic uplift concerns mechanical equilibrium. Both are strictly consequences of conservation of energy. LeChâtelier's principle deals with thermodynamic equilibrium and involves both the first and second laws of thermodynamics. The concept of homeostasis in biology and the economic law of supply and demand are both equilibrium-like principles, but involve systems in the steady state. However, all these principles involve the stability of the system under consideration and the analogies presented may be useful in the teaching of LeChâtelier's principle.

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

PubMed

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

2013-10-07

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

Mathematical and computational studies of equilibrium capillary free surfaces

NASA Technical Reports Server (NTRS)

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

1977-01-01

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

Dynamical quantum phase transitions: a review

NASA Astrophysics Data System (ADS)

Heyl, Markus

2018-05-01

Quantum theory provides an extensive framework for the description of the equilibrium properties of quantum matter. Yet experiments in quantum simulators have now opened up a route towards the generation of quantum states beyond this equilibrium paradigm. While these states promise to show properties not constrained by equilibrium principles, such as the equal a priori probability of the microcanonical ensemble, identifying the general properties of nonequilibrium quantum dynamics remains a major challenge, especially in view of the lack of conventional concepts such as free energies. The theory of dynamical quantum phase transitions attempts to identify such general principles by lifting the concept of phase transitions to coherent quantum real-time evolution. This review provides a pedagogical introduction to this field. Starting from the general setting of nonequilibrium dynamics in closed quantum many-body systems, we give the definition of dynamical quantum phase transitions as phase transitions in time with physical quantities becoming nonanalytic at critical times. We summarize the achieved theoretical advances as well as the first experimental observations, and furthermore provide an outlook to major open questions as well as future directions of research.

Dynamical quantum phase transitions: a review.

PubMed

Heyl, Markus

2018-05-01

Quantum theory provides an extensive framework for the description of the equilibrium properties of quantum matter. Yet experiments in quantum simulators have now opened up a route towards the generation of quantum states beyond this equilibrium paradigm. While these states promise to show properties not constrained by equilibrium principles, such as the equal a priori probability of the microcanonical ensemble, identifying the general properties of nonequilibrium quantum dynamics remains a major challenge, especially in view of the lack of conventional concepts such as free energies. The theory of dynamical quantum phase transitions attempts to identify such general principles by lifting the concept of phase transitions to coherent quantum real-time evolution. This review provides a pedagogical introduction to this field. Starting from the general setting of nonequilibrium dynamics in closed quantum many-body systems, we give the definition of dynamical quantum phase transitions as phase transitions in time with physical quantities becoming nonanalytic at critical times. We summarize the achieved theoretical advances as well as the first experimental observations, and furthermore provide an outlook to major open questions as well as future directions of research.

General equilibrium effects of a supply side GHG mitigation option under the Clean Development Mechanism.

PubMed

Timilsina, Govinda R; Shrestha, Ram M

2006-09-01

The Clean Development Mechanism (CDM) under the Kyoto Protocol to the United Nations Framework Convention on Climate Change is considered a key instrument to encourage developing countries' participation in the mitigation of global climate change. Reduction of greenhouse gas (GHG) emissions through the energy supply and demand side activities are the main options to be implemented under the CDM. This paper analyses the general equilibrium effects of a supply side GHG mitigation option-the substitution of thermal power with hydropower--in Thailand under the CDM. A static multi-sector general equilibrium model has been developed for the purpose of this study. The key finding of the study is that the substitution of electricity generation from thermal power plants with that from hydropower plants would increase economic welfare in Thailand. The supply side option would, however, adversely affect the gross domestic product (GDP) and the trade balance. The percentage changes in economic welfare, GDP and trade balance increase with the level of substitution and the price of certified emission reduction (CER) units.

IRREVERSIBLE PROCESSES IN A PLASMA

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

Balescu, R.

1959-04-01

ABS>The characteristic divergences caused by long-range phenomena in gases can be eliminated in equilibrium situations by partial summations of terms individually divergent but whose sum converges. It is shown how the recently developed diagram technique enables treatment of non-equilibrium cases by a rigorous asymptotic method. The general ideas underlying the approach are briefly indicated. (T.R. H.)

Microeconomics, Socialization, and Norms. Program Report No. 79-B22.

ERIC Educational Resources Information Center

Field, Alexander J.

Microeconomic theory encompasses two basic theoretical concepts. First is the theory of general competitive equilibrium in a market economy, which holds that the actions of any one agent cannot affect prices or quantities for the system as a whole. The second is that when the conditions of competitive equilibrium do not apply, theories of games…

Chief Characteristics and Advantages of Tailless Airplanes

NASA Technical Reports Server (NTRS)

Dufaure De Lajarte, A

1936-01-01

This study will be concerned with the critical examination of two main questions, mainly, susceptibility of centering and more generally, the conditions of static stability, longitudinal equilibrium, and the question of dynamic stability, or at least the damping of longitudinal vibrations about a position of equilibrium that may result from a small variation in the angle of attack.

An Application of Variational Theory to an Integrated Walrasian Model of Exchange, Consumption and Production

NASA Astrophysics Data System (ADS)

Donato, M. B.; Milasi, M.; Vitanza, C.

2010-09-01

An existence result of a Walrasian equilibrium for an integrated model of exchange, consumption and production is obtained. The equilibrium model is characterized in terms of a suitable generalized quasi-variational inequality; so the existence result comes from an original technique which takes into account tools of convex and set-valued analysis.

Spontaneity and Equilibrium II: Multireaction Systems

ERIC Educational Resources Information Center

Raff, Lionel M.

2014-01-01

The thermodynamic criteria for spontaneity and equilibrium in multireaction systems are developed and discussed. When N reactions are occurring simultaneously, it is shown that G and A will depend upon N independent reaction coordinates, ?a (a = 1,2, ..., N), in addition to T and p for G or T and V for A. The general criteria for spontaneity and…

Point Defect Distributions in ZnSe Crystals: Effects of Gravity Vector Orientation During Physical Vapor Transport Growth

NASA Technical Reports Server (NTRS)

Su, Ching-Hua; Feth, S.; Hirschfeld, D.; Smith, T. M.; Wang, Ling Jun; Volz, M. P.; Lehoczky, S. L.

1999-01-01

ZnSe crystals were grown by the physical vapor transport technique under horizontal and vertical (stabilized and destabilized) configurations. Secondary ion mass spectroscopy and photoluminescence measurements were performed on the grown ZnSe samples to map the distributions of [Si], [Fe], [Cu], [Al] and [Li or Na] impurities as well as Zn vacancy, [V (sub Zn)]. Annealings of ZnSe under controlled Zn pressures were studied to correlate the measured photoluminescence emission intensity to the equilibrium Zn partial pressure. In the horizontal grown crystals the segregations of [Si], [Fe], [Al] and [V (sub Zn)] were observed along the gravity vector direction whereas in the vertically stabilized grown crystal the segregation of these point defects was radially symmetrical. No apparent pattern was observed on the measured distributions in the vertically destabilized grown crystal. The observed segregations in the three growth configurations were interpreted based on the possible buoyancy-driven convection in the vapor phase.

Non performing loans (NPLs) in a crisis economy: Long-run equilibrium analysis with a real time VEC model for Greece (2001-2015)

NASA Astrophysics Data System (ADS)

Konstantakis, Konstantinos N.; Michaelides, Panayotis G.; Vouldis, Angelos T.

2016-06-01

As a result of domestic and international factors, the Greek economy faced a severe crisis which is directly comparable only to the Great Recession. In this context, a prominent victim of this situation was the country's banking system. This paper attempts to shed light on the determining factors of non-performing loans in the Greek banking sector. The analysis presents empirical evidence from the Greek economy, using aggregate data on a quarterly basis, in the time period 2001-2015, fully capturing the recent recession. In this work, we use a relevant econometric framework based on a real time Vector Autoregressive (VAR)-Vector Error Correction (VEC) model, which captures the dynamic interdependencies among the variables used. Consistent with international evidence, the empirical findings show that both macroeconomic and financial factors have a significant impact on non-performing loans in the country. Meanwhile, the deteriorating credit quality feeds back into the economy leading to a self-reinforcing negative loop.

General equilibrium second-order hydrodynamic coefficients for free quantum fields

NASA Astrophysics Data System (ADS)

Buzzegoli, M.; Grossi, E.; Becattini, F.

2017-10-01

We present a systematic calculation of the corrections of the stress-energy tensor and currents of the free boson and Dirac fields up to second order in thermal vorticity, which is relevant for relativistic hydrodynamics. These corrections are non-dissipative because they survive at general thermodynamic equilibrium with non vanishing mean values of the conserved generators of the Lorentz group, i.e. angular momenta and boosts. Their equilibrium nature makes it possible to express the relevant coefficients by means of correlators of the angular-momentum and boost operators with stress-energy tensor and current, thus making simpler to determine their so-called "Kubo formulae". We show that, at least for free fields, the corrections are of quantum origin and we study several limiting cases and compare our results with previous calculations. We find that the axial current of the free Dirac field receives corrections proportional to the vorticity independently of the anomalous term.

Equivalency principle for magnetoelectroelastic multiferroics with arbitrary microstructure: The phase field approach

NASA Astrophysics Data System (ADS)

Ni, Yong; He, Linghui; Khachaturyan, Armen G.

2010-07-01

A phase field method is proposed to determine the equilibrium fields of a magnetoelectroelastic multiferroic with arbitrarily distributed constitutive constants under applied loadings. This method is based on a developed generalized Eshelby's equivalency principle, in which the elastic strain, electrostatic, and magnetostatic fields at the equilibrium in the original heterogeneous system are exactly the same as those in an equivalent homogeneous magnetoelectroelastic coupled or uncoupled system with properly chosen distributed effective eigenstrain, polarization, and magnetization fields. Finding these effective fields fully solves the equilibrium elasticity, electrostatics, and magnetostatics in the original heterogeneous multiferroic. The paper formulates a variational principle proving that the effective fields are minimizers of appropriate close-form energy functional. The proposed phase field approach produces the energy minimizing effective fields (and thus solving the general multiferroic problem) as a result of artificial relaxation process described by the Ginzburg-Landau-Khalatnikov kinetic equations.

Nonequilibrium Entropy in a Shock

DOE PAGES

Margolin, Len G.

2017-07-19

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

A dynamic analysis of the motion of a low-wing general aviation aircraft about its calculated equilibrium flat spin mode

NASA Technical Reports Server (NTRS)

Tischler, M. B.; Barlow, J. B.

1980-01-01

The properties of the flat spin mode of a general aviation configuration have been studied through analysis of rotary balance data, numerical simulation, and analytical study of the equilibrium state. The equilibrium state is predicted well from rotary balance data. The variations of yawing moment and pitching moment as functions of sideslip have been shown to be of great importance in obtaining accurate modeling. These dependencies are not presently available with sufficient accuracy from previous tests or theories. The stability of the flat spin mode has been examined extensively using numerical linearization, classical perturbation methods, and reduced order modeling. The stability exhibited by the time histories and the eigenvalue analyses is shown to be strongly dependent on certain static cross derivatives and more so on the dynamic derivatives. Explicit stability criteria are obtained from the reduced order models.

Nonequilibrium Entropy in a Shock

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

Margolin, Len G.

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

Addition of equilibrium air to an upwind Navier-Stokes code and other first steps toward a more generalized flow solver

NASA Technical Reports Server (NTRS)

Rosen, Bruce S.

1991-01-01

An upwind three-dimensional volume Navier-Stokes code is modified to facilitate modeling of complex geometries and flow fields represented by proposed National Aerospace Plane concepts. Code enhancements include an equilibrium air model, a generalized equilibrium gas model and several schemes to simplify treatment of complex geometric configurations. The code is also restructured for inclusion of an arbitrary number of independent and dependent variables. This latter capability is intended for eventual use to incorporate nonequilibrium/chemistry gas models, more sophisticated turbulence and transition models, or other physical phenomena which will require inclusion of additional variables and/or governing equations. Comparisons of computed results with experimental data and results obtained using other methods are presented for code validation purposes. Good correlation is obtained for all of the test cases considered, indicating the success of the current effort.

A study of the linear free energy model for DNA structures using the generalized Hamiltonian formalism

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

Yavari, M., E-mail: yavari@iaukashan.ac.ir

2016-06-15

We generalize the results of Nesterenko [13, 14] and Gogilidze and Surovtsev [15] for DNA structures. Using the generalized Hamiltonian formalism, we investigate solutions of the equilibrium shape equations for the linear free energy model.

Mathematical Theory of Generalized Duality Quantum Computers Acting on Vector-States

NASA Astrophysics Data System (ADS)

Cao, Huai-Xin; Long, Gui-Lu; Guo, Zhi-Hua; Chen, Zheng-Li

2013-06-01

Following the idea of duality quantum computation, a generalized duality quantum computer (GDQC) acting on vector-states is defined as a tuple consisting of a generalized quantum wave divider (GQWD) and a finite number of unitary operators as well as a generalized quantum wave combiner (GQWC). It is proved that the GQWD and GQWC of a GDQC are an isometry and a co-isometry, respectively, and mutually dual. It is also proved that every GDQC gives a contraction, called a generalized duality quantum gate (GDQG). A classification of GDQCs is given and the properties of GDQGs are discussed. Some applications are obtained, including two orthogonal duality quantum computer algorithms for unsorted database search and an understanding of the Mach-Zehnder interferometer.

Entropy is in Flux V3.4

NASA Astrophysics Data System (ADS)

Kadanoff, Leo P.

2017-05-01

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

Kirchhoff's Laws Revisited for Protein Dynamics

NASA Astrophysics Data System (ADS)

Atilgan, Alirana; Baysal, Canan

2001-03-01

We monitor the collective motions of the proteins, and relate the topological characteristics to the flexibility and stability of the protein molecule.^1,2 For modeling purposes, we follow the backbone topology of a compact globular protein and pick the C^α atom at each residue. To define the non-bonded contacts, the first coordination sphere of each C^α with 7 Åradius is considered. Now, C^α's are the nodes and the contacts are the branches; thus, we create an equivalent connected digraph from a folded protein. We accordingly consider first the equilibrium of each residue: A Δ f = 0, then the compatibility equation between the fluctuation of a residue and fluctuations of its contacting bonds: A^T Δ R = Δ r; and finally the constitutive relation for each bonded and nonbonded contact: K Δ r + C dotΔ r = Δ f. In this formulation, A is the incidence matrix of the connected digraph of the protein molecule, K and C are diagonal matrices whose entries are, respectively, the rigidities and the viscous dissipations of the contacts. In addition, the forces at each bond f, positional movements of each residue R, and the bond displacements r are analogous to the branch current vector, node-to-datum voltage vector, and branch voltage vector, respectively, of the circuit theory; and, therefore, the equilibrium and the compatibility equations are the Kirchhoff's Law of Currents and Voltages, respectively. For homogeneous, elastic interactions, the global rigidity of a protein is represented by the Kirchhoff Matrix, that is the incidence matrix multiplied by its transpose. This procedure lends a great helping hand to elucidate the structural dynamic mechanisms for biological activities.^3,4 Illustrative examples are presented and validated by experimental results, and the qualitative differences between one- and three-dimensional formulations are discussed. 1. Bahar, I., Atilgan A.R., Demirel, M.C., and Erman, B., Phys. Rev. Lett., 80, 2733, 1998. 2. Yilmaz, L.S. and Atilgan, A.R., J. Chem. Phys., 113, 4454, 2000. 3. Bahar, I., Erman, B., Jernigan, R.L., Atilgan, A.R., and Covell, D., J. Mol. Biol., 285, 1023, 1999. 4. Baysal, C. and Atilgan, A.R., Proteins, to appear, 2001.

Global Solutions to Repulsive Hookean Elastodynamics

NASA Astrophysics Data System (ADS)

Hu, Xianpeng; Masmoudi, Nader

2017-01-01

The global existence of classical solutions to the three dimensional repulsive Hookean elastodynamics around an equilibrium is considered. By linearization and Hodge's decomposition, the compressible part of the velocity, the density, and the compressible part of the transpose of the deformation gradient satisfy Klein-Gordon equations with speed {√{2}}, while the incompressible parts of the velocity and of the transpose of the deformation gradient satisfy wave equations with speed one. The space-time resonance method combined with the vector field method is used in a novel way to obtain the decay of the solution and hence global existence.

Dynamics of climate-based malaria transmission model with age-structured human population

NASA Astrophysics Data System (ADS)

Addawe, Joel; Pajimola, Aprimelle Kris

2016-10-01

In this paper, we proposed to study the dynamics of malaria transmission with periodic birth rate of the vector and an age-structure for the human population. The human population is divided into two compartments: pre-school (0-5 years) and the rest of the human population. We showed the existence of a disease-free equilibrium point. Using published epidemiological parameters, we use numerical simulations to show potential effect of climate change in the dynamics of age-structured malaria transmission. Numerical simulations suggest that there exists an asymptotically attractive solution that is positive and periodic.

Stability of equilibrium solutions of Hamiltonian systems with n-degrees of freedom and single resonance in the critical case

NASA Astrophysics Data System (ADS)

dos Santos, Fabio; Vidal, Claudio

2018-04-01

In this paper we give new results for the stability of one equilibrium solution of an autonomous analytic Hamiltonian system in a neighborhood of the equilibrium point with n-degrees of freedom. Our Main Theorem generalizes several results existing in the literature and mainly we give information in the critical cases (i.e., the condition of stability and instability is not fulfilled). In particular, our Main Theorem provides necessary and sufficient conditions for stability of the equilibrium solutions under the existence of a single resonance. Using analogous tools used in the Main Theorem for the critical case, we study the stability or instability of degenerate equilibrium points in Hamiltonian systems with one degree of freedom. We apply our results to the stability of Hamiltonians of the type of cosmological models as in planar as in the spatial case.

Revealing missing charges with generalised quantum fluctuation relations.

PubMed

Mur-Petit, J; Relaño, A; Molina, R A; Jaksch, D

2018-05-22

The non-equilibrium dynamics of quantum many-body systems is one of the most fascinating problems in physics. Open questions range from how they relax to equilibrium to how to extract useful work from them. A critical point lies in assessing whether a system has conserved quantities (or 'charges'), as these can drastically influence its dynamics. Here we propose a general protocol to reveal the existence of charges based on a set of exact relations between out-of-equilibrium fluctuations and equilibrium properties of a quantum system. We apply these generalised quantum fluctuation relations to a driven quantum simulator, demonstrating their relevance to obtain unbiased temperature estimates from non-equilibrium measurements. Our findings will help guide research on the interplay of quantum and thermal fluctuations in quantum simulation, in studying the transition from integrability to chaos and in the design of new quantum devices.

Linear and angular coherence momenta in the classical second-order coherence theory of vector electromagnetic fields.

PubMed

Wang, Wei; Takeda, Mitsuo

2006-09-01

A new concept of vector and tensor densities is introduced into the general coherence theory of vector electromagnetic fields that is based on energy and energy-flow coherence tensors. Related coherence conservation laws are presented in the form of continuity equations that provide new insights into the propagation of second-order correlation tensors associated with stationary random classical electromagnetic fields.

A general theory of linear cosmological perturbations: scalar-tensor and vector-tensor theories

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

Lagos, Macarena; Baker, Tessa; Ferreira, Pedro G.

We present a method for parametrizing linear cosmological perturbations of theories of gravity, around homogeneous and isotropic backgrounds. The method is sufficiently general and systematic that it can be applied to theories with any degrees of freedom (DoFs) and arbitrary gauge symmetries. In this paper, we focus on scalar-tensor and vector-tensor theories, invariant under linear coordinate transformations. In the case of scalar-tensor theories, we use our framework to recover the simple parametrizations of linearized Horndeski and ''Beyond Horndeski'' theories, and also find higher-derivative corrections. In the case of vector-tensor theories, we first construct the most general quadratic action for perturbationsmore » that leads to second-order equations of motion, which propagates two scalar DoFs. Then we specialize to the case in which the vector field is time-like (à la Einstein-Aether gravity), where the theory only propagates one scalar DoF. As a result, we identify the complete forms of the quadratic actions for perturbations, and the number of free parameters that need to be defined, to cosmologically characterize these two broad classes of theories.« less

Design of a universal two-layered neural network derived from the PLI theory

NASA Astrophysics Data System (ADS)

Hu, Chia-Lun J.

2004-05-01

The if-and-only-if (IFF) condition that a set of M analog-to-digital vector-mapping relations can be learned by a one-layered-feed-forward neural network (OLNN) is that all the input analog vectors dichotomized by the i-th output bit must be positively, linearly independent, or PLI. If they are not PLI, then the OLNN just cannot learn no matter what learning rules is employed because the solution of the connection matrix does not exist mathematically. However, in this case, one can still design a parallel-cascaded, two-layered, perceptron (PCTLP) to acheive this general mapping goal. The design principle of this "universal" neural network is derived from the major mathematical properties of the PLI theory - changing the output bits of the dependent relations existing among the dichotomized input vectors to make the PLD relations PLI. Then with a vector concatenation technique, the required mapping can still be learned by this PCTLP system with very high efficiency. This paper will report in detail the mathematical derivation of the general design principle and the design procedures of the PCTLP neural network system. It then will be verified in general by a practical numerical example.

Search for Tensor, Vector, and Scalar Polarizations in the Stochastic Gravitational-Wave Background.

PubMed

Abbott, B P; Abbott, R; Abbott, T D; Acernese, F; Ackley, K; Adams, C; Adams, T; Addesso, P; Adhikari, R X; Adya, V B; Affeldt, C; Afrough, M; Agarwal, B; Agathos, M; Agatsuma, K; Aggarwal, N; Aguiar, O D; Aiello, L; Ain, A; Ajith, P; Allen, B; Allen, G; Allocca, A; Altin, P A; Amato, A; Ananyeva, A; Anderson, S B; Anderson, W G; Angelova, S V; Antier, S; Appert, S; Arai, K; Araya, M C; Areeda, J S; Arnaud, N; Ascenzi, S; Ashton, G; Ast, M; Aston, S M; Astone, P; Atallah, D V; Aufmuth, P; Aulbert, C; AultONeal, K; Austin, C; Avila-Alvarez, A; Babak, S; Bacon, P; Bader, M K M; Bae, S; Baker, P T; Baldaccini, F; Ballardin, G; Ballmer, S W; Banagiri, S; Barayoga, J C; Barclay, S E; Barish, B C; Barker, D; Barkett, K; Barone, F; Barr, B; Barsotti, L; Barsuglia, M; Barta, D; Bartlett, J; Bartos, I; Bassiri, R; Basti, A; Batch, J C; Bawaj, M; Bayley, J C; Bazzan, M; Bécsy, B; Beer, C; Bejger, M; Belahcene, I; Bell, A S; Berger, B K; Bergmann, G; Bero, J J; Berry, C P L; Bersanetti, D; Bertolini, A; Betzwieser, J; Bhagwat, S; Bhandare, R; Bilenko, I A; Billingsley, G; Billman, C R; Birch, J; Birney, R; Birnholtz, O; Biscans, S; Biscoveanu, S; Bisht, A; Bitossi, M; Biwer, C; Bizouard, M A; Blackburn, J K; Blackman, J; Blair, C D; Blair, D G; Blair, R M; Bloemen, S; Bock, O; Bode, N; Boer, M; Bogaert, G; Bohe, A; Bondu, F; Bonilla, E; Bonnand, R; Boom, B A; Bork, R; Boschi, V; Bose, S; Bossie, K; Bouffanais, Y; Bozzi, A; Bradaschia, C; Brady, P R; Branchesi, M; Brau, J E; Briant, T; Brillet, A; Brinkmann, M; Brisson, V; Brockill, P; Broida, J E; Brooks, A F; Brown, D A; Brown, D D; Brunett, S; Buchanan, C C; Buikema, A; Bulik, T; Bulten, H J; Buonanno, A; Buskulic, D; Buy, C; Byer, R L; Cabero, M; Cadonati, L; Cagnoli, G; Cahillane, C; Calderón Bustillo, J; Callister, T A; Calloni, E; Camp, J B; Canepa, M; Canizares, P; Cannon, K C; Cao, H; Cao, J; Capano, C D; Capocasa, E; Carbognani, F; Caride, S; Carney, M F; Diaz, J Casanueva; Casentini, C; Caudill, S; Cavaglià, M; Cavalier, F; Cavalieri, R; Cella, G; Cepeda, C B; Cerdá-Durán, P; Cerretani, G; Cesarini, E; Chamberlin, S J; Chan, M; Chao, S; Charlton, P; Chase, E; Chassande-Mottin, E; Chatterjee, D; Cheeseboro, B D; Chen, H Y; Chen, X; Chen, Y; Cheng, H-P; Chia, H; Chincarini, A; Chiummo, A; Chmiel, T; Cho, H S; Cho, M; Chow, J H; Christensen, N; Chu, Q; Chua, A J K; Chua, S; Chung, A K W; Chung, S; Ciani, G; Ciolfi, R; Cirelli, C E; Cirone, A; Clara, F; Clark, J A; Clearwater, P; Cleva, F; Cocchieri, C; Coccia, E; Cohadon, P-F; Cohen, D; Colla, A; Collette, C G; Cominsky, L R; Constancio, M; Conti, L; Cooper, S J; Corban, P; Corbitt, T R; Cordero-Carrión, I; Corley, K R; Cornish, N; Corsi, A; Cortese, S; Costa, C A; Coughlin, E; Coughlin, M W; Coughlin, S B; Coulon, J-P; Countryman, S T; Couvares, P; Covas, P B; Cowan, E E; Coward, D M; Cowart, M J; Coyne, D C; Coyne, R; Creighton, J D E; Creighton, T D; Cripe, J; Crowder, S G; Cullen, T J; Cumming, A; Cunningham, L; Cuoco, E; Canton, T Dal; Dálya, G; Danilishin, S L; 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Messenger, C; Messick, C; Metzdorff, R; Meyers, P M; Miao, H; Michel, C; Middleton, H; Mikhailov, E E; Milano, L; Miller, A L; Miller, B B; Miller, J; Millhouse, M; Milovich-Goff, M C; Minazzoli, O; Minenkov, Y; Ming, J; Mishra, C; Mitra, S; Mitrofanov, V P; Mitselmakher, G; Mittleman, R; Moffa, D; Moggi, A; Mogushi, K; Mohan, M; Mohapatra, S R P; Montani, M; Moore, C J; Moraru, D; Moreno, G; Morriss, S R; Mours, B; Mow-Lowry, C M; Mueller, G; Muir, A W; Mukherjee, Arunava; Mukherjee, D; Mukherjee, S; Mukund, N; Mullavey, A; Munch, J; Muñiz, E A; Muratore, M; Murray, P G; Napier, K; Nardecchia, I; Naticchioni, L; Nayak, R K; Neilson, J; Nelemans, G; Nelson, T J N; Nery, M; Neunzert, A; Nevin, L; Newport, J M; Newton, G; Ng, K K Y; Nguyen, T T; Nichols, D; Nielsen, A B; Nissanke, S; Nitz, A; Noack, A; Nocera, F; Nolting, D; North, C; Nuttall, L K; Oberling, J; O'Dea, G D; Ogin, G H; Oh, J J; Oh, S H; Ohme, F; Okada, M A; Oliver, M; Oppermann, P; Oram, Richard J; O'Reilly, B; Ormiston, R; 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2018-05-18

The detection of gravitational waves with Advanced LIGO and Advanced Virgo has enabled novel tests of general relativity, including direct study of the polarization of gravitational waves. While general relativity allows for only two tensor gravitational-wave polarizations, general metric theories can additionally predict two vector and two scalar polarizations. The polarization of gravitational waves is encoded in the spectral shape of the stochastic gravitational-wave background, formed by the superposition of cosmological and individually unresolved astrophysical sources. Using data recorded by Advanced LIGO during its first observing run, we search for a stochastic background of generically polarized gravitational waves. We find no evidence for a background of any polarization, and place the first direct bounds on the contributions of vector and scalar polarizations to the stochastic background. Under log-uniform priors for the energy in each polarization, we limit the energy densities of tensor, vector, and scalar modes at 95% credibility to Ω_{0}^{T}<5.58×10^{-8}, Ω_{0}^{V}<6.35×10^{-8}, and Ω_{0}^{S}<1.08×10^{-7} at a reference frequency f_{0}=25  Hz.

Detecting temperature fluctuations at equilibrium.

PubMed

Dixit, Purushottam D

2015-05-21

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

He I lines in B stars - Comparison of non-local thermodynamic equilibrium models with observations

NASA Technical Reports Server (NTRS)

Heasley, J. N.; Timothy, J. G.; Wolff, S. C.

1982-01-01

Profiles of He gamma-gamma 4026, 4387, 4471, 4713, 5876, and 6678 have been obtained in 17 stars of spectral type B0-B5. Parameters of the nonlocal thermodynamic equilibrium models appropriate to each star are determined from the Stromgren index and fits to H-alpha line profiles. These parameters yield generally good fits to the observed He I line profiles, with the best fits being found for the blue He I lines where departures from local thermodynamic equilibrium are relatively small. For the two red lines it is found that, in the early B stars and in stars with log g less than 3.5, both lines are systematically stronger than predicted by the nonlocal thermodynamic equilibrium models.

Generalized dark-bright vector soliton solution to the mixed coupled nonlinear Schrödinger equations.

PubMed

Manikandan, N; Radhakrishnan, R; Aravinthan, K

2014-08-01

We have constructed a dark-bright N-soliton solution with 4N+3 real parameters for the physically interesting system of mixed coupled nonlinear Schrödinger equations. Using this as well as an asymptotic analysis we have investigated the interaction between dark-bright vector solitons. Each colliding dark-bright one-soliton at the asymptotic limits includes more coupling parameters not only in the polarization vector but also in the amplitude part. Our present solution generalizes the dark-bright soliton in the literature with parametric constraints. By exploiting the role of such coupling parameters we are able to control certain interaction effects, namely beating, breathing, bouncing, attraction, jumping, etc., without affecting other soliton parameters. Particularly, the results of the interactions between the bound state dark-bright vector solitons reveal oscillations in their amplitudes under certain parametric choices. A similar kind of effect was also observed experimentally in the BECs. We have also characterized the solutions with complicated structure and nonobvious wrinkle to define polarization vector, envelope speed, envelope width, envelope amplitude, grayness, and complex modulation. It is interesting to identify that the polarization vector of the dark-bright one-soliton evolves on a spherical surface instead of a hyperboloid surface as in the bright-bright case of the mixed coupled nonlinear Schrödinger equations.

Stellar dynamics around a massive black hole - II. Resonant relaxation

NASA Astrophysics Data System (ADS)

Sridhar, S.; Touma, Jihad R.

2016-06-01

We present a first-principles theory of resonant relaxation (RR) of a low-mass stellar system orbiting a more massive black hole (MBH). We first extend the kinetic theory of Gilbert to include the Keplerian field of a black hole of mass M•. Specializing to a Keplerian stellar system of mass M ≪ M•, we use the orbit-averaging method of Sridhar & Touma to derive a kinetic equation for RR. This describes the collisional evolution of a system of N ≫ 1 Gaussian rings in a reduced 5-dim space, under the combined actions of self-gravity, 1 post-Newtonian (PN) and 1.5 PN relativistic effects of the MBH and an arbitrary external potential. In general geometries, RR is driven by both apsidal and nodal resonances, so the distinction between scalar RR and vector RR disappears. The system passes through a sequence of quasi-steady secular collisionless equilibria, driven by irreversible two-ring correlations that accrue through gravitational interactions, both direct and collective. This correlation function is related to a `wake function', which is the linear response of the system to the perturbation of a chosen ring. The wake function is easier to appreciate, and satisfies a simpler equation, than the correlation function. We discuss general implications for the interplay of secular dynamics and non-equilibrium statistical mechanics in the evolution of Keplerian stellar systems towards secular thermodynamic equilibria, and set the stage for applications to the RR of axisymmetric discs in Paper III.

Generalizations of Tikhonov's regularized method of least squares to non-Euclidean vector norms

NASA Astrophysics Data System (ADS)

Volkov, V. V.; Erokhin, V. I.; Kakaev, V. V.; Onufrei, A. Yu.

2017-09-01

Tikhonov's regularized method of least squares and its generalizations to non-Euclidean norms, including polyhedral, are considered. The regularized method of least squares is reduced to mathematical programming problems obtained by "instrumental" generalizations of the Tikhonov lemma on the minimal (in a certain norm) solution of a system of linear algebraic equations with respect to an unknown matrix. Further studies are needed for problems concerning the development of methods and algorithms for solving reduced mathematical programming problems in which the objective functions and admissible domains are constructed using polyhedral vector norms.

The futility of utility: how market dynamics marginalize Adam Smith

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2000-10-01

Economic theorizing is based on the postulated, nonempiric notion of utility. Economists assume that prices, dynamics, and market equilibria are supposed to be derived from utility. The results are supposed to represent mathematically the stabilizing action of Adam Smith's invisible hand. In deterministic excess demand dynamics I show the following. A utility function generally does not exist mathematically due to nonintegrable dynamics when production/investment are accounted for, resolving Mirowski's thesis. Price as a function of demand does not exist mathematically either. All equilibria are unstable. I then explain how deterministic chaos can be distinguished from random noise at short times. In the generalization to liquid markets and finance theory described by stochastic excess demand dynamics, I also show the following. Market price distributions cannot be rescaled to describe price movements as ‘equilibrium’ fluctuations about a systematic drift in price. Utility maximization does not describe equilibrium. Maximization of the Gibbs entropy of the observed price distribution of an asset would describe equilibrium, if equilibrium could be achieved, but equilibrium does not describe real, liquid markets (stocks, bonds, foreign exchange). There are three inconsistent definitions of equilibrium used in economics and finance, only one of which is correct. Prices in unregulated free markets are unstable against both noise and rising or falling expectations: Adam Smith's stabilizing invisible hand does not exist, either in mathematical models of liquid market data, or in real market data.

Large-scale adenovirus and poxvirus-vectored vaccine manufacturing to enable clinical trials.

PubMed

Kallel, Héla; Kamen, Amine A

2015-05-01

Efforts to make vaccines against infectious diseases and immunotherapies for cancer have evolved to utilize a variety of heterologous expression systems such as viral vectors. These vectors are often attenuated or engineered to safely deliver genes encoding antigens of different pathogens. Adenovirus and poxvirus vectors are among the viral vectors that are most frequently used to develop prophylactic vaccines against infectious diseases as well as therapeutic cancer vaccines. This mini-review describes the trends and processes in large-scale production of adenovirus and poxvirus vectors to meet the needs of clinical applications. We briefly describe the general principles for the production and purification of adenovirus and poxvirus viral vectors. Currently, adenovirus and poxvirus vector manufacturing methods rely on well-established cell culture technologies. Several improvements have been evaluated to increase the yield and to reduce the overall manufacturing cost, such as cultivation at high cell densities and continuous downstream processing. Additionally, advancements in vector characterization will greatly facilitate the development of novel vectored vaccine candidates. Copyright © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Weakly charged generalized Kerr-NUT-(A)dS spacetimes

NASA Astrophysics Data System (ADS)

Frolov, Valeri P.; Krtouš, Pavel; Kubizňák, David

2017-08-01

We find an explicit solution of the source free Maxwell equations in a generalized Kerr-NUT-(A)dS spacetime in all dimensions. This solution is obtained as a linear combination of the closed conformal Killing-Yano tensor hab, which is present in such a spacetime, and a derivative of the primary Killing vector, associated with hab. For the vanishing cosmological constant the obtained solution reduces to the Wald's electromagnetic field generated from the primary Killing vector.

Invariant object recognition based on the generalized discrete radon transform

NASA Astrophysics Data System (ADS)

Easley, Glenn R.; Colonna, Flavia

2004-04-01

We introduce a method for classifying objects based on special cases of the generalized discrete Radon transform. We adjust the transform and the corresponding ridgelet transform by means of circular shifting and a singular value decomposition (SVD) to obtain a translation, rotation and scaling invariant set of feature vectors. We then use a back-propagation neural network to classify the input feature vectors. We conclude with experimental results and compare these with other invariant recognition methods.

A realistic host-vector transmission model for describing malaria prevalence pattern.

PubMed

Mandal, Sandip; Sinha, Somdatta; Sarkar, Ram Rup

2013-12-01

Malaria continues to be a major public health concern all over the world even after effective control policies have been employed, and considerable understanding of the disease biology have been attained, from both the experimental and modelling perspective. Interactions between different general and local processes, such as dependence on age and immunity of the human host, variations of temperature and rainfall in tropical and sub-tropical areas, and continued presence of asymptomatic infections, regulate the host-vector interactions, and are responsible for the continuing disease prevalence pattern.In this paper, a general mathematical model of malaria transmission is developed considering short and long-term age-dependent immunity of human host and its interaction with pathogen-infected mosquito vector. The model is studied analytically and numerically to understand the role of different parameters related to mosquitoes and humans. To validate the model with a disease prevalence pattern in a particular region, real epidemiological data from the north-eastern part of India was used, and the effect of seasonal variation in mosquito density was modelled based on local climactic data. The model developed based on general features of host-vector interactions, and modified simply incorporating local environmental factors with minimal changes, can successfully explain the disease transmission process in the region. This provides a general approach toward modelling malaria that can be adapted to control future outbreaks of malaria.

Role of grain size and particle velocity distribution in secondary electron emission in space plasmas

NASA Technical Reports Server (NTRS)

Chow, V. W.; Mendis, D. A.; Rosenberg, M.

1993-01-01

By virtue of being generally immersed in a plasma environment, cosmic dust is necessarily electrically charged. The fact that secondary emission plays an important role in determining the equilibrium grain potential has long been recognized, but the fact that the grain size plays a crucial role in this equilibrium potential, when secondary emission is important, has not been widely appreciated. Using both conducting and insulating spherical grains of various sizes and also both Maxwellian and generalized Lorentzian plasmas (which are believed to represent certain space plasmas), we have made a detailed study of this problem. In general, we find that the secondary emission yield delta increases with decreasing size and becomes very large for grains whose dimensions are comparable to the primary electron penetration depth, such as in the case of the very small grains observed at comet Halley and inferred in the interstellar medium. Moreover, we observed that delta is larger for insulators and equilibrium potentials are generally more positive when the plasma has a broad non-Maxwellian tail. Interestingly, we find that for thermal energies that are expected in several cosmic regions, grains of different sizes can have opposite charge, the smaller ones being positive while the larger ones are negative. This may have important consequences for grain accretion in polydisperse dusty space plasmas.

A Two-Layer Least Squares Support Vector Machine Approach to Credit Risk Assessment

NASA Astrophysics Data System (ADS)

Liu, Jingli; Li, Jianping; Xu, Weixuan; Shi, Yong

Least squares support vector machine (LS-SVM) is a revised version of support vector machine (SVM) and has been proved to be a useful tool for pattern recognition. LS-SVM had excellent generalization performance and low computational cost. In this paper, we propose a new method called two-layer least squares support vector machine which combines kernel principle component analysis (KPCA) and linear programming form of least square support vector machine. With this method sparseness and robustness is obtained while solving large dimensional and large scale database. A U.S. commercial credit card database is used to test the efficiency of our method and the result proved to be a satisfactory one.

Pre-existing immunity against vaccine vectors – friend or foe?

PubMed Central

Saxena, Manvendra; Van, Thi Thu Hao; Baird, Fiona J.; Coloe, Peter J.

2013-01-01

Over the last century, the successful attenuation of multiple bacterial and viral pathogens has led to an effective, robust and safe form of vaccination. Recently, these vaccines have been evaluated as delivery vectors for heterologous antigens, as a means of simultaneous vaccination against two pathogens. The general consensus from published studies is that these vaccine vectors have the potential to be both safe and efficacious. However, some of the commonly employed vectors, for example Salmonella and adenovirus, often have pre-existing immune responses in the host and this has the potential to modify the subsequent immune response to a vectored antigen. This review examines the literature on this topic, and concludes that for bacterial vectors there can in fact, in some cases, be an enhancement in immunogenicity, typically humoral, while for viral vectors pre-existing immunity is a hindrance for subsequent induction of cell-mediated responses. PMID:23175507

Using Beads and Divided Containers to Study Kinetic and Equilibrium Isotope Effects in the Laboratory and in the Classroom

ERIC Educational Resources Information Center

Campbell, Dean J.; Brewer, Emily R.; Martinez, Keri A.; Fitzjarrald, Tamara J.

2017-01-01

The purpose of this laboratory experiment is to study fundamental concepts of kinetics and equilibria and the isotope effects associated with both of these concepts. The concepts of isotopes in introductory and general chemistry courses are typically used within the contexts of atomic weights and radioactivity. Kinetic and equilibrium isotope…

Stresses in non-equilibrium fluids: Exact formulation and coarse-grained theory.

PubMed

Krüger, Matthias; Solon, Alexandre; Démery, Vincent; Rohwer, Christian M; Dean, David S

2018-02-28

Starting from the stochastic equation for the density operator, we formulate the exact (instantaneous) stress tensor for interacting Brownian particles and show that its average value agrees with expressions derived previously. We analyze the relation between the stress tensor and forces due to external potentials and observe that, out of equilibrium, particle currents give rise to extra forces. Next, we derive the stress tensor for a Landau-Ginzburg theory in generic, non-equilibrium situations, finding an expression analogous to that of the exact microscopic stress tensor, and discuss the computation of out-of-equilibrium (classical) Casimir forces. Subsequently, we give a general form for the stress tensor which is valid for a large variety of energy functionals and which reproduces the two mentioned cases. We then use these relations to study the spatio-temporal correlations of the stress tensor in a Brownian fluid, which we compute to leading order in the interaction potential strength. We observe that, after integration over time, the spatial correlations generally decay as power laws in space. These are expected to be of importance for driven confined systems. We also show that divergence-free parts of the stress tensor do not contribute to the Green-Kubo relation for the viscosity.

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

PubMed Central

Omar, Mohamed A.

2014-01-01

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

Stresses in non-equilibrium fluids: Exact formulation and coarse-grained theory

NASA Astrophysics Data System (ADS)

Krüger, Matthias; Solon, Alexandre; Démery, Vincent; Rohwer, Christian M.; Dean, David S.

2018-02-01

Starting from the stochastic equation for the density operator, we formulate the exact (instantaneous) stress tensor for interacting Brownian particles and show that its average value agrees with expressions derived previously. We analyze the relation between the stress tensor and forces due to external potentials and observe that, out of equilibrium, particle currents give rise to extra forces. Next, we derive the stress tensor for a Landau-Ginzburg theory in generic, non-equilibrium situations, finding an expression analogous to that of the exact microscopic stress tensor, and discuss the computation of out-of-equilibrium (classical) Casimir forces. Subsequently, we give a general form for the stress tensor which is valid for a large variety of energy functionals and which reproduces the two mentioned cases. We then use these relations to study the spatio-temporal correlations of the stress tensor in a Brownian fluid, which we compute to leading order in the interaction potential strength. We observe that, after integration over time, the spatial correlations generally decay as power laws in space. These are expected to be of importance for driven confined systems. We also show that divergence-free parts of the stress tensor do not contribute to the Green-Kubo relation for the viscosity.

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

PubMed

Omar, Mohamed A

2014-01-01

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

Multiphase, multicomponent phase behavior prediction

NASA Astrophysics Data System (ADS)

Dadmohammadi, Younas

Accurate prediction of phase behavior of fluid mixtures in the chemical industry is essential for designing and operating a multitude of processes. Reliable generalized predictions of phase equilibrium properties, such as pressure, temperature, and phase compositions offer an attractive alternative to costly and time consuming experimental measurements. The main purpose of this work was to assess the efficacy of recently generalized activity coefficient models based on binary experimental data to (a) predict binary and ternary vapor-liquid equilibrium systems, and (b) characterize liquid-liquid equilibrium systems. These studies were completed using a diverse binary VLE database consisting of 916 binary and 86 ternary systems involving 140 compounds belonging to 31 chemical classes. Specifically the following tasks were undertaken: First, a comprehensive assessment of the two common approaches (gamma-phi (gamma-ϕ) and phi-phi (ϕ-ϕ)) used for determining the phase behavior of vapor-liquid equilibrium systems is presented. Both the representation and predictive capabilities of these two approaches were examined, as delineated form internal and external consistency tests of 916 binary systems. For the purpose, the universal quasi-chemical (UNIQUAC) model and the Peng-Robinson (PR) equation of state (EOS) were used in this assessment. Second, the efficacy of recently developed generalized UNIQUAC and the nonrandom two-liquid (NRTL) for predicting multicomponent VLE systems were investigated. Third, the abilities of recently modified NRTL model (mNRTL2 and mNRTL1) to characterize liquid-liquid equilibria (LLE) phase conditions and attributes, including phase stability, miscibility, and consolute point coordinates, were assessed. The results of this work indicate that the ϕ-ϕ approach represents the binary VLE systems considered within three times the error of the gamma-ϕ approach. A similar trend was observed for the for the generalized model predictions using quantitative structure-property parameter generalizations (QSPR). For ternary systems, where all three constituent binary systems were available, the NRTL-QSPR, UNIQUAC-QSPR, and UNIFAC-6 models produce comparable accuracy. For systems where at least one constituent binary is missing, the UNIFAC-6 model produces larger errors than the QSPR generalized models. In general, the LLE characterization results indicate the accuracy of the modified models in reproducing the findings of the original NRTL model.

O Electromagnetic Power Waves and Power Density Components.

NASA Astrophysics Data System (ADS)

Petzold, Donald Wayne

1980-12-01

On January 10, 1884 Lord Rayleigh presented a paper entitled "On the Transfer of Energy in the Electromagnetic Field" to the Royal Society of London. This paper had been authored by the late Fellow of Trinity College, Cambridge, Professor J. H. Poynting and in it he claimed that there was a general law for the transfer of electromagnetic energy. He argued that associated with each point in space is a quantity, that has since been called the Poynting vector, that is a measure of the rate of energy flow per unit area. His analysis was concerned with the integration of this power density vector at all points over an enclosing surface of a specific volume. The interpretation of this Poynting vector as a true measure of the local power density was viewed with great skepticism unless the vector was integrated over a closed surface, as the development of the concept required. However, within the last decade or so Shadowitz indicates that a number of prominent authors have argued that the criticism of the interpretation of Poynting's vector as a local power density vector is unjustified. The present paper is not concerned with these arguments but instead is concerned with a decomposition of Poynting's power density vector into two and only two components: one vector which has the same direction as Poynting's vector and which is called the forward power density vector, and another vector, directed opposite to the Poynting vector and called the reverse power density vector. These new local forward and reverse power density vectors will be shown to be dependent upon forward and reverse power wave vectors and these vectors in turn will be related to newly defined forward and reverse components of the electric and magnetic fields. The sum of these forward and reverse power density vectors, which is simply the original Poynting vector, is associated with the total electromagnetic energy traveling past the local point. Another vector which is the difference between the forward and reverse power density vectors and which will be shown to be associated with the total electric and magnetic field energy densities existing at a local point will also be introduced. These local forward and reverse power density vectors may be integrated over a surface to determine the forward and reverse powers and from these results problems related to maximum power transfer or efficiency of electromagnetic energy transmission in space may be studied in a manner similar to that presently being done with transmission lines, wave guides, and more recently with two port multiport lumped parameter systems. These new forward and reverse power density vectors at a point in space are analogous to the forward and revoltages or currents and power waves as used with the transmission line, waveguide, or port. These power wave vectors in space are a generalization of the power waves as developed by Penfield, Youla, and Kurokawa and used with the scattering parameters associated with transmission lines, waveguides and ports.

Epidemiological Implications of Host Biodiversity and Vector Biology: Key Insights from Simple Models.

PubMed

Dobson, Andrew D M; Auld, Stuart K J R

2016-04-01

Models used to investigate the relationship between biodiversity change and vector-borne disease risk often do not explicitly include the vector; they instead rely on a frequency-dependent transmission function to represent vector dynamics. However, differences between classes of vector (e.g., ticks and insects) can cause discrepancies in epidemiological responses to environmental change. Using a pair of disease models (mosquito- and tick-borne), we simulated substitutive and additive biodiversity change (where noncompetent hosts replaced or were added to competent hosts, respectively), while considering different relationships between vector and host densities. We found important differences between classes of vector, including an increased likelihood of amplified disease risk under additive biodiversity change in mosquito models, driven by higher vector biting rates. We also draw attention to more general phenomena, such as a negative relationship between initial infection prevalence in vectors and likelihood of dilution, and the potential for a rise in density of infected vectors to occur simultaneously with a decline in proportion of infected hosts. This has important implications; the density of infected vectors is the most valid metric for primarily zoonotic infections, while the proportion of infected hosts is more relevant for infections where humans are a primary host.

A Harris-Todaro Agent-Based Model to Rural-Urban Migration

NASA Astrophysics Data System (ADS)

Espíndola, Aquino L.; Silveira, Jaylson J.; Penna, T. J. P.

2006-09-01

The Harris-Todaro model of the rural-urban migration process is revisited under an agent-based approach. The migration of the workers is interpreted as a process of social learning by imitation, formalized by a computational model. By simulating this model, we observe a transitional dynamics with continuous growth of the urban fraction of overall population toward an equilibrium. Such an equilibrium is characterized by stabilization of rural-urban expected wages differential (generalized Harris-Todaro equilibrium condition), urban concentration and urban unemployment. These classic results obtained originally by Harris and Todaro are emergent properties of our model.

[Lymphoscintigrams with anatomical landmarks obtained with vector graphics].

PubMed

Rubini, Giuseppe; Antonica, Filippo; Renna, Maria Antonia; Ferrari, Cristina; Iuele, Francesca; Stabile Ianora, Antonio Amato; Losco, Matteo; Niccoli Asabella, Artor

2012-11-01

Nuclear medicine images are difficult to interpret because they do not include anatomical details. The aim of this study was to obtain lymphoscintigrams with anatomical landmarks that could be easily interpreted by General Physicians. Traditional lymphoscintigrams were processed with Adobe© Photoshop® CS6 and converted into vector images created by Illustrator®. The combination with a silhouette vector improved image interpretation, without resulting in longer radiation exposure or acquisition times.

A Heuristic Approach to Examining Volatile Equilibrium at Titan's Surface

NASA Technical Reports Server (NTRS)

Samuelson, Robert E.

1999-01-01

R. D. Lorenz, J. I. Lunine, and C. P. McKay have shown in a manuscript accepted for publication that, for a given ethane abundance and surface temperature, the nitrogen and methane abundances in Titan's atmosphere can be calculated, yielding a surface pressure that can be compared with the observed value. This is potentially a very valuable tool for examining the evolution of Titan's climatology. Its validity does depend on two important assumptions, however: 1) that the atmosphere of Titan is in global radiative equilibrium, and 2) that volatiles present are in vapor equilibrium with the surface. The former assumption has been shown to be likely, but the latter has not. Water vapor in the Earth's atmosphere, in fact, is generally not very close to equilibrium in a global sense. In the present work a heuristic approach is used to examine the likelihood that methane vapor is in equilibrium with Titan's surface. Plausible climate scenerios are examined that are consistent with methane vapor abundances derived from Voyager IRIS data. Simple precipitation and surface diffusion models are incorporated into the analysis. It is tentatively inferred that methane may be in surface equilibrium near the poles, but that equilibrium at low latitudes is more difficult to establish.

Equilibrium analysis of a yellow Fever dynamical model with vaccination.

PubMed

Martorano Raimundo, Silvia; Amaku, Marcos; Massad, Eduardo

2015-01-01

We propose an equilibrium analysis of a dynamical model of yellow fever transmission in the presence of a vaccine. The model considers both human and vector populations. We found thresholds parameters that affect the development of the disease and the infectious status of the human population in the presence of a vaccine whose protection may wane over time. In particular, we derived a threshold vaccination rate, above which the disease would be eradicated from the human population. We show that if the mortality rate of the mosquitoes is greater than a given threshold, then the disease is naturally (without intervention) eradicated from the population. In contrast, if the mortality rate of the mosquitoes is less than that threshold, then the disease is eradicated from the populations only when the growing rate of humans is less than another threshold; otherwise, the disease is eradicated only if the reproduction number of the infection after vaccination is less than 1. When this reproduction number is greater than 1, the disease will be eradicated from the human population if the vaccination rate is greater than a given threshold; otherwise, the disease will establish itself among humans, reaching a stable endemic equilibrium. The analysis presented in this paper can be useful, both to the better understanding of the disease dynamics and also for the planning of vaccination strategies.

Signal detection using support vector machines in the presence of ultrasonic speckle

NASA Astrophysics Data System (ADS)

Kotropoulos, Constantine L.; Pitas, Ioannis

2002-04-01

Support Vector Machines are a general algorithm based on guaranteed risk bounds of statistical learning theory. They have found numerous applications, such as in classification of brain PET images, optical character recognition, object detection, face verification, text categorization and so on. In this paper we propose the use of support vector machines to segment lesions in ultrasound images and we assess thoroughly their lesion detection ability. We demonstrate that trained support vector machines with a Radial Basis Function kernel segment satisfactorily (unseen) ultrasound B-mode images as well as clinical ultrasonic images.

Thermodynamic integration of the free energy along a reaction coordinate in Cartesian coordinates

NASA Astrophysics Data System (ADS)

den Otter, W. K.

2000-05-01

A generalized formulation of the thermodynamic integration (TI) method for calculating the free energy along a reaction coordinate is derived. Molecular dynamics simulations with a constrained reaction coordinate are used to sample conformations. These are then projected onto conformations with a higher value of the reaction coordinate by means of a vector field. The accompanying change in potential energy plus the divergence of the vector field constitute the derivative of the free energy. Any vector field meeting some simple requirements can be used as the basis of this TI expression. Two classes of vector fields are of particular interest here. The first recovers the conventional TI expression, with its cumbersome dependence on a full set of generalized coordinates. As the free energy is a function of the reaction coordinate only, it should in principle be possible to derive an expression depending exclusively on the definition of the reaction coordinate. This objective is met by the second class of vector fields to be discussed. The potential of mean constraint force (PMCF) method, after averaging over the unconstrained momenta, falls in this second class. The new method is illustrated by calculations on the isomerization of n-butane, and is compared with existing methods.

GPU Accelerated Vector Median Filter

NASA Technical Reports Server (NTRS)

Aras, Rifat; Shen, Yuzhong

2011-01-01

Noise reduction is an important step for most image processing tasks. For three channel color images, a widely used technique is vector median filter in which color values of pixels are treated as 3-component vectors. Vector median filters are computationally expensive; for a window size of n x n, each of the n(sup 2) vectors has to be compared with other n(sup 2) - 1 vectors in distances. General purpose computation on graphics processing units (GPUs) is the paradigm of utilizing high-performance many-core GPU architectures for computation tasks that are normally handled by CPUs. In this work. NVIDIA's Compute Unified Device Architecture (CUDA) paradigm is used to accelerate vector median filtering. which has to the best of our knowledge never been done before. The performance of GPU accelerated vector median filter is compared to that of the CPU and MPI-based versions for different image and window sizes, Initial findings of the study showed 100x improvement of performance of vector median filter implementation on GPUs over CPU implementations and further speed-up is expected after more extensive optimizations of the GPU algorithm .

Latitudinal oscillations of plasma within the Io torus

NASA Technical Reports Server (NTRS)

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

1980-01-01

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

Equilibrium stochastic dynamics of a Brownian particle in inhomogeneous space: Derivation of an alternative model

NASA Astrophysics Data System (ADS)

Bhattacharyay, A.

2018-03-01

An alternative equilibrium stochastic dynamics for a Brownian particle in inhomogeneous space is derived. Such a dynamics can model the motion of a complex molecule in its conformation space when in equilibrium with a uniform heat bath. The derivation is done by a simple generalization of the formulation due to Zwanzig for a Brownian particle in homogeneous heat bath. We show that, if the system couples to different number of bath degrees of freedom at different conformations then the alternative model gets derived. We discuss results of an experiment by Faucheux and Libchaber which probably has indicated possible limitation of the Boltzmann distribution as equilibrium distribution of a Brownian particle in inhomogeneous space and propose experimental verification of the present theory using similar methods.

Nuclear spin polarized H and D by means of spin-exchange optical pumping

NASA Astrophysics Data System (ADS)

Stenger, Jörn; Grosshauser, Carsten; Kilian, Wolfgang; Nagengast, Wolfgang; Ranzenberger, Bernd; Rith, Klaus; Schmidt, Frank

1998-01-01

Optically pumped spin-exchange sources for polarized hydrogen and deuterium atoms have been demonstrated to yield high atomic flow and high electron spin polarization. For maximum nuclear polarization the source has to be operated in spin temperature equilibrium, which has already been demonstrated for hydrogen. In spin temperature equilibrium the nuclear spin polarization PI equals the electron spin polarization PS for hydrogen and is even larger than PS for deuterium. We discuss the general properties of spin temperature equilibrium for a sample of deuterium atoms. One result are the equations PI=4PS/(3+PS2) and Pzz=PSṡPI, where Pzz is the nuclear tensor polarization. Furthermore we demonstrate that the deuterium atoms from our source are in spin temperature equilibrium within the experimental accuracy.

Equilibrium pricing in an order book environment: Case study for a spin model

NASA Astrophysics Data System (ADS)

Meudt, Frederik; Schmitt, Thilo A.; Schäfer, Rudi; Guhr, Thomas

2016-07-01

When modeling stock market dynamics, the price formation is often based on an equilibrium mechanism. In real stock exchanges, however, the price formation is governed by the order book. It is thus interesting to check if the resulting stylized facts of a model with equilibrium pricing change, remain the same or, more generally, are compatible with the order book environment. We tackle this issue in the framework of a case study by embedding the Bornholdt-Kaizoji-Fujiwara spin model into the order book dynamics. To this end, we use a recently developed agent based model that realistically incorporates the order book. We find realistic stylized facts. We conclude for the studied case that equilibrium pricing is not needed and that the corresponding assumption of a ;fundamental; price may be abandoned.

Examples of equilibrium and non-equilibrium behavior in evolutionary systems

NASA Astrophysics Data System (ADS)

Soulier, Arne

With this thesis, we want to shed some light into the darkness of our understanding of simply defined statistical mechanics systems and the surprisingly complex dynamical behavior they exhibit. We will do so by presenting in turn one equilibrium and then one non-equilibrium system with evolutionary dynamics. In part 1, we will present the seceder-model, a newly developed system that cannot equilibrate. We will then study several properties of the system and obtain an idea of the richness of the dynamics of the seceder model, which is particular impressive given the minimal amount of modeling necessary in its setup. In part 2, we will present extensions to the directed polymer in random media problem on a hypercube and its connection to the Eigen model of evolution. Our main interest will be the influence of time-dependent and time-independent changes in the fitness landscape viewed by an evolving population. This part contains the equilibrium dynamics. The stochastic models and the topic of evolution and non-equilibrium in general will allow us to point out similarities to the various lines of thought in game theory.

Some General Thoughts about Broken Symmetry.

DTIC Science & Technology

1981-01-21

to what extent one may generalize to random systems and to ’dissipative structures’. Thermal equilibrium broken symmetry is characterized by an order...stable defects. We conjecture what may be the consequences of relaxing these assumptions. (Author)

Vectorized Monte Carlo methods for reactor lattice analysis

NASA Technical Reports Server (NTRS)

Brown, F. B.

1984-01-01

Some of the new computational methods and equivalent mathematical representations of physics models used in the MCV code, a vectorized continuous-enery Monte Carlo code for use on the CYBER-205 computer are discussed. While the principal application of MCV is the neutronics analysis of repeating reactor lattices, the new methods used in MCV should be generally useful for vectorizing Monte Carlo for other applications. For background, a brief overview of the vector processing features of the CYBER-205 is included, followed by a discussion of the fundamentals of Monte Carlo vectorization. The physics models used in the MCV vectorized Monte Carlo code are then summarized. The new methods used in scattering analysis are presented along with details of several key, highly specialized computational routines. Finally, speedups relative to CDC-7600 scalar Monte Carlo are discussed.

The Total Gaussian Class of Quasiprobabilities and its Relation to Squeezed-State Excitations

NASA Technical Reports Server (NTRS)

Wuensche, Alfred

1996-01-01

The class of quasiprobabilities obtainable from the Wigner quasiprobability by convolutions with the general class of Gaussian functions is investigated. It can be described by a three-dimensional, in general, complex vector parameter with the property of additivity when composing convolutions. The diagonal representation of this class of quasiprobabilities is connected with a generalization of the displaced Fock states in direction of squeezing. The subclass with real vector parameter is considered more in detail. It is related to the most important kinds of boson operator ordering. The properties of a specific set of discrete excitations of squeezed coherent states are given.

Z2×Z2 generalizations of 𝒩 =2 super Schrödinger algebras and their representations

NASA Astrophysics Data System (ADS)

Aizawa, N.; Segar, J.

2017-11-01

We generalize the real and chiral N =2 super Schrödinger algebras to Z2×Z2-graded Lie superalgebras. This is done by D-module presentation, and as a consequence, the D-module presentations of Z2×Z2-graded superalgebras are identical to the ones of super Schrödinger algebras. We then generalize the calculus over the Grassmann number to Z2×Z2 setting. Using it and the standard technique of Lie theory, we obtain a vector field realization of Z2×Z2-graded superalgebras. A vector field realization of the Z2×Z2 generalization of N =1 super Schrödinger algebra is also presented.

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

NASA Technical Reports Server (NTRS)

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

1986-01-01

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

Identifying Liquid-Gas System Misconceptions and Addressing Them Using a Laboratory Exercise on Pressure-Temperature Diagrams of a Mixed Gas Involving Liquid-Vapor Equilibrium

ERIC Educational Resources Information Center

Yoshikawa, Masahiro; Koga, Nobuyoshi

2016-01-01

This study focuses on students' understandings of a liquid-gas system with liquid-vapor equilibrium in a closed system using a pressure-temperature ("P-T") diagram. By administrating three assessment questions concerning the "P-T" diagrams of liquid-gas systems to students at the beginning of undergraduate general chemistry…

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

Pugliese, D.; Stuchlík, Z., E-mail: d.pugliese.physics@gmail.com, E-mail: zdenek.stuchlik@physics.cz

We analyze the possibility that several instability points may be formed, due to the Paczyński mechanism of violation of mechanical equilibrium, in the orbiting matter around a supermassive Kerr black hole. We consider a recently proposed model of a ringed accretion disk, made up by several tori (rings) that can be corotating or counter-rotating relative to the Kerr attractor due to the history of the accretion process. Each torus is governed by the general relativistic hydrodynamic Boyer condition of equilibrium configurations of rotating perfect fluids. We prove that the number of the instability points is generally limited and depends onmore » the dimensionless spin of the rotating attractor.« less

Scalar products of Bethe vectors in models with {\\mathfrak{gl}}(2| 1) symmetry 1. Super-analog of Reshetikhin formula

NASA Astrophysics Data System (ADS)

Hutsalyuk, A.; Liashyk, A.; Pakuliak, S. Z.; Ragoucy, E.; Slavnov, N. A.

2016-11-01

We study the scalar products of Bethe vectors in integrable models solvable by the nested algebraic Bethe ansatz and possessing {gl}(2| 1) symmetry. Using explicit formulas of the monodromy matrix entries’ multiple actions onto Bethe vectors we obtain a representation for the scalar product in the most general case. This explicit representation appears to be a sum over partitions of the Bethe parameters. It can be used for the analysis of scalar products involving on-shell Bethe vectors. As a by-product, we obtain a determinant representation for the scalar products of generic Bethe vectors in integrable models with {gl}(1| 1) symmetry. Dedicated to the memory of Petr Petrovich Kulish.

First passage analysis of the folding of a β-sheet miniprotein: is it more realistic than the standard equilibrium approach?

PubMed

Kalgin, Igor V; Chekmarev, Sergei F; Karplus, Martin

2014-04-24

Simulations of first-passage folding of the antiparallel β-sheet miniprotein beta3s, which has been intensively studied under equilibrium conditions by A. Caflisch and co-workers, show that the kinetics and dynamics are significantly different from those for equilibrium folding. Because the folding of a protein in a living system generally corresponds to the former (i.e., the folded protein is stable and unfolding is a rare event), the difference is of interest. In contrast to equilibrium folding, the Ch-curl conformations become very rare because they contain unfavorable parallel β-strand arrangements, which are difficult to form dynamically due to the distant N- and C-terminal strands. At the same time, the formation of helical conformations becomes much easier (particularly in the early stage of folding) due to short-range contacts. The hydrodynamic descriptions of the folding reaction have also revealed that while the equilibrium flow field presented a collection of local vortices with closed "streamlines", the first-passage folding is characterized by a pronounced overall flow from the unfolded states to the native state. The flows through the locally stable structures Cs-or and Ns-or, which are conformationally close to the native state, are negligible due to detailed balance established between these structures and the native state. Although there are significant differences in the general picture of the folding process from the equilibrium and first-passage folding simulations, some aspects of the two are in agreement. The rate of transitions between the clusters of characteristic protein conformations in both cases decreases approximately exponentially with the distance between the clusters in the hydrogen bond distance space of collective variables, and the folding time distribution in the first-passage segments of the equilibrium trajectory is in good agreement with that for the first-passage folding simulations.

First Passage Analysis of the Folding of a β-Sheet Miniprotein: Is it More Realistic Than the Standard Equilibrium Approach?

PubMed Central

2015-01-01

Simulations of first-passage folding of the antiparallel β-sheet miniprotein beta3s, which has been intensively studied under equilibrium conditions by A. Caflisch and co-workers, show that the kinetics and dynamics are significantly different from those for equilibrium folding. Because the folding of a protein in a living system generally corresponds to the former (i.e., the folded protein is stable and unfolding is a rare event), the difference is of interest. In contrast to equilibrium folding, the Ch-curl conformations become very rare because they contain unfavorable parallel β-strand arrangements, which are difficult to form dynamically due to the distant N- and C-terminal strands. At the same time, the formation of helical conformations becomes much easier (particularly in the early stage of folding) due to short-range contacts. The hydrodynamic descriptions of the folding reaction have also revealed that while the equilibrium flow field presented a collection of local vortices with closed ”streamlines”, the first-passage folding is characterized by a pronounced overall flow from the unfolded states to the native state. The flows through the locally stable structures Cs-or and Ns-or, which are conformationally close to the native state, are negligible due to detailed balance established between these structures and the native state. Although there are significant differences in the general picture of the folding process from the equilibrium and first-passage folding simulations, some aspects of the two are in agreement. The rate of transitions between the clusters of characteristic protein conformations in both cases decreases approximately exponentially with the distance between the clusters in the hydrogen bond distance space of collective variables, and the folding time distribution in the first-passage segments of the equilibrium trajectory is in good agreement with that for the first-passage folding simulations. PMID:24669953

Stability of Horndeski vector-tensor interactions

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

Jiménez, Jose Beltrán; Durrer, Ruth; Heisenberg, Lavinia

2013-10-01

We study the Horndeski vector-tensor theory that leads to second order equations of motion and contains a non-minimally coupled abelian gauge vector field. This theory is remarkably simple and consists of only 2 terms for the vector field, namely: the standard Maxwell kinetic term and a coupling to the dual Riemann tensor. Furthermore, the vector sector respects the U(1) gauge symmetry and the theory contains only one free parameter, M{sup 2}, that controls the strength of the non-minimal coupling. We explore the theory in a de Sitter spacetime and study the presence of instabilities and show that it corresponds tomore » an attractor solution in the presence of the vector field. We also investigate the cosmological evolution and stability of perturbations in a general FLRW spacetime. We find that a sufficient condition for the absence of ghosts is M{sup 2} > 0. Moreover, we study further constraints coming from imposing the absence of Laplacian instabilities. Finally, we study the stability of the theory in static and spherically symmetric backgrounds (in particular, Schwarzschild and Reissner-Nordström-de Sitter). We find that the theory, quite generally, do have ghosts or Laplacian instabilities in regions of spacetime where the non-minimal interaction dominates over the Maxwell term. We also calculate the propagation speed in these spacetimes and show that superluminality is a quite generic phenomenon in this theory.« less

Shape functions for velocity interpolation in general hexahedral cells

USGS Publications Warehouse

Naff, R.L.; Russell, T.F.; Wilson, J.D.

2002-01-01

Numerical methods for grids with irregular cells require discrete shape functions to approximate the distribution of quantities across cells. For control-volume mixed finite-element (CVMFE) methods, vector shape functions approximate velocities and vector test functions enforce a discrete form of Darcy's law. In this paper, a new vector shape function is developed for use with irregular, hexahedral cells (trilinear images of cubes). It interpolates velocities and fluxes quadratically, because as shown here, the usual Piola-transformed shape functions, which interpolate linearly, cannot match uniform flow on general hexahedral cells. Truncation-error estimates for the shape function are demonstrated. CVMFE simulations of uniform and non-uniform flow with irregular meshes show first- and second-order convergence of fluxes in the L2 norm in the presence and absence of singularities, respectively.

FPGA Implementation of Generalized Hebbian Algorithm for Texture Classification

PubMed Central

Lin, Shiow-Jyu; Hwang, Wen-Jyi; Lee, Wei-Hao

2012-01-01

This paper presents a novel hardware architecture for principal component analysis. The architecture is based on the Generalized Hebbian Algorithm (GHA) because of its simplicity and effectiveness. The architecture is separated into three portions: the weight vector updating unit, the principal computation unit and the memory unit. In the weight vector updating unit, the computation of different synaptic weight vectors shares the same circuit for reducing the area costs. To show the effectiveness of the circuit, a texture classification system based on the proposed architecture is physically implemented by Field Programmable Gate Array (FPGA). It is embedded in a System-On-Programmable-Chip (SOPC) platform for performance measurement. Experimental results show that the proposed architecture is an efficient design for attaining both high speed performance and low area costs. PMID:22778640

Teaching Chemical Equilibrium with the Jigsaw Technique

NASA Astrophysics Data System (ADS)

Doymus, Kemal

2008-03-01

This study investigates the effect of cooperative learning (jigsaw) versus individual learning methods on students’ understanding of chemical equilibrium in a first-year general chemistry course. This study was carried out in two different classes in the department of primary science education during the 2005-2006 academic year. One of the classes was randomly assigned as the non-jigsaw group (control) and other as the jigsaw group (cooperative). Students participating in the jigsaw group were divided into four “home groups” since the topic chemical equilibrium is divided into four subtopics (Modules A, B, C and D). Each of these home groups contained four students. The groups were as follows: (1) Home Group A (HGA), representin g the equilibrium state and quantitative aspects of equilibrium (Module A), (2) Home Group B (HGB), representing the equilibrium constant and relationships involving equilibrium constants (Module B), (3) Home Group C (HGC), representing Altering Equilibrium Conditions: Le Chatelier’s principle (Module C), and (4) Home Group D (HGD), representing calculations with equilibrium constants (Module D). The home groups then broke apart, like pieces of a jigsaw puzzle, and the students moved into jigsaw groups consisting of members from the other home groups who were assigned the same portion of the material. The jigsaw groups were then in charge of teaching their specific subtopic to the rest of the students in their learning group. The main data collection tool was a Chemical Equilibrium Achievement Test (CEAT), which was applied to both the jigsaw and non-jigsaw groups The results indicated that the jigsaw group was more successful than the non-jigsaw group (individual learning method).

The DIII-D Map -- An Area-Preserving Map for Trajectories of Magnetic Field Lines in the DIII-D Tokamak

NASA Astrophysics Data System (ADS)

Punjabi, Alkesh; Ali, Halima; Boozer, Allen; Evans, Todd

2007-11-01

The EFIT data for the DIII-D shot 115467 3000 ms is used to calculate the generating function for an area-preserving map for trajectories of magnetic field lines in the DIII-D. We call this map the DIII-D map. The generating function is a bivariate polynomial in base vectors &1/2circ;cos(θ) and &1/2circ;sin(θ). ψ is toroidal flux and θ is poloidal angle. The generating function is calculated using a canonical transformation from (ψ,θ) to physical coordinates (R,Z) in the DIII-D [1] and nonlinear regression. The equilibrium generating function gives an excellent representation of the equilibrium flux surfaces in the DIII-D. The DIII-D map is then used to calculate effects of the magnetic perturbations in the DIII-D. Preliminary results of the DIII-D map will be presented. This work is supported by US DOE OFES DE-FG02-01ER54624 and DE-FG02-04ER54793. [1] A. Punjabi, H. Ali, T. Evans, and A. Boozer, Phys Lett A 364 140--145 (2007).

Isotropic–Nematic Phase Transitions in Gravitational Systems. II. Higher Order Multipoles

NASA Astrophysics Data System (ADS)

Takács, Ádám; Kocsis, Bence

2018-04-01

The gravitational interaction among bodies orbiting in a spherical potential leads to the rapid relaxation of the orbital planes’ distribution, a process called vector resonant relaxation. We examine the statistical equilibrium of this process for a system of bodies with similar semimajor axes and eccentricities. We extend the previous model of Roupas et al. by accounting for the multipole moments beyond the quadrupole, which dominate the interaction for radially overlapping orbits. Nevertheless, we find no qualitative differences between the behavior of the system with respect to the model restricted to the quadrupole interaction. The equilibrium distribution resembles a counterrotating disk at low temperature and a spherical structure at high temperature. The system exhibits a first-order phase transition between the disk and the spherical phase in the canonical ensemble if the total angular momentum is below a critical value. We find that the phase transition erases the high-order multipoles, i.e., small-scale structure in angular momentum space, most efficiently. The system admits a maximum entropy and a maximum energy, which lead to the existence of negative temperature equilibria.

On a Class of Hairy Square Barriers and Gamow Vectors

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

Fernandez-Garcia, N.

The second order Darboux-Gamow transformation is applied to deform square one dimensional barriers in non-relativistic quantum mechanics. The initial and the new 'hairy' potentials have the same transmission probabilities (for the appropriate parameters). In general, new Gamow vectors are constructed as Darboux deformations of the initial ones.

Hidden symmetries and equilibrium properties of multiplicative white-noise stochastic processes

NASA Astrophysics Data System (ADS)

González Arenas, Zochil; Barci, Daniel G.

2012-12-01

Multiplicative white-noise stochastic processes continue to attract attention in a wide area of scientific research. The variety of prescriptions available for defining them makes the development of general tools for their characterization difficult. In this work, we study equilibrium properties of Markovian multiplicative white-noise processes. For this, we define the time reversal transformation for such processes, taking into account that the asymptotic stationary probability distribution depends on the prescription. Representing the stochastic process in a functional Grassmann formalism, we avoid the necessity of fixing a particular prescription. In this framework, we analyze equilibrium properties and study hidden symmetries of the process. We show that, using a careful definition of the equilibrium distribution and taking into account the appropriate time reversal transformation, usual equilibrium properties are satisfied for any prescription. Finally, we present a detailed deduction of a covariant supersymmetric formulation of a multiplicative Markovian white-noise process and study some of the constraints that it imposes on correlation functions using Ward-Takahashi identities.

Competitive Cyber-Insurance and Internet Security

NASA Astrophysics Data System (ADS)

Shetty, Nikhil; Schwartz, Galina; Felegyhazi, Mark; Walrand, Jean

This paper investigates how competitive cyber-insurers affect network security and welfare of the networked society. In our model, a user's probability to incur damage (from being attacked) depends on both his security and the network security, with the latter taken by individual users as given. First, we consider cyberinsurers who cannot observe (and thus, affect) individual user security. This asymmetric information causes moral hazard. Then, for most parameters, no equilibrium exists: the insurance market is missing. Even if an equilibrium exists, the insurance contract covers only a minor fraction of the damage; network security worsens relative to the no-insurance equilibrium. Second, we consider insurers with perfect information about their users' security. Here, user security is perfectly enforceable (zero cost); each insurance contract stipulates the required user security. The unique equilibrium contract covers the entire user damage. Still, for most parameters, network security worsens relative to the no-insurance equilibrium. Although cyber-insurance improves user welfare, in general, competitive cyber-insurers fail to improve network security.

Macroscopic Fluctuation Theory for Stationary Non-Equilibrium States

NASA Astrophysics Data System (ADS)

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

2002-05-01

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

Universality of electronic friction. II. Equivalence of the quantum-classical Liouville equation approach with von Oppen's nonequilibrium Green's function methods out of equilibrium

NASA Astrophysics Data System (ADS)

Dou, Wenjie; Subotnik, Joseph E.

2018-02-01

In a recent publication [W. Dou et al., Phys. Rev. Lett. 119, 046001 (2017), 10.1103/PhysRevLett.119.046001], using the quantum-classical Liouville equation (QCLE), we derived a very general form for the electronic friction felt by a molecule moving near one or many metal surfaces. Moreover, we have already proved the equivalence of the QCLE electronic friction with the Head-Gordon-Tully model as well as a generalized version of von Oppen's nonequilibrium Green's function (NEGF) method at equilibrium [W. Dou and J. E. Subotnik, Phys. Rev. B 96, 104305 (2017), 10.1103/PhysRevB.96.104305]. In the present paper, we now further prove the equivalence between the QCLE friction and the NEGF friction for the case of multiple metal surfaces and an out-of-equilibrium electronic current without electron-electron interactions. The present results reinforce our recent claim that there is only one universal electronic friction tensor arising from the Born-Oppenheimer approximation.

Geologic map of the Agnesi quadrangle (V-45), Venus

USGS Publications Warehouse

Hansen, Vicki L.; Tharalson, Erik R.

2014-01-01

Two general classes of hypotheses have emerged to address the near random spatial distribution of ~970 apparently pristine impact craters across the surface of Venus: (1) catastrophic/episodic resurfacing and (2) equilibrium/evolutionary resurfacing. Catastrophic/episodic hypotheses propose that a global-scale, temporally punctuated event or events dominated Venus’ evolution and that the generally uniform impact crater distribution (Schaber and others, 1992; Phillips and others, 1992; Herrick and others, 1997) reflects craters that accumulated during relative global quiescence since that event (for example, Strom and others, 1994; Herrick, 1994; Turcotte and others, 1999). Equilibrium/evolutionary hypotheses suggest instead that the near random crater distribution results from relatively continuous, but spatially localized, resurfacing in which volcanic and (or) tectonic processes occur across the planet through time, although the style of operative processes may have varied temporally and spatially (for example, Phillips and others, 1992; Guest and Stofan, 1999; Hansen and Young, 2007). Geologic relations within the map area allow us to test the catastrophic/episodic versus equilibrium/evolutionary resurfacing hypotheses.

Cooperativity in self-limiting equilibrium self-associating systems

NASA Astrophysics Data System (ADS)

Freed, Karl F.

2012-11-01

A wide variety of highly cooperative self-assembly processes in biological and synthetic systems involve the assembly of a large number (m) of units into clusters, with m narrowly peaked about a large size m0 ≫ 1 and with a second peak centered about the m = 1 unassembled monomers. While very specific models have been proposed for the assembly of, for example, viral capsids and core-shell micelles of ß-casein, no available theory describes a thermodynamically general mechanism for this double peaked, highly cooperative equilibrium assembly process. This study provides a general mechanism for these cooperative processes by developing a minimal Flory-Huggins type theory. Beginning from the simplest non-cooperative, free association model in which the equilibrium constant for addition of a monomer to a cluster is independent of cluster size, the new model merely allows more favorable growth for clusters of intermediate sizes. The theory is illustrated by computing the phase diagram for cases of self-assembly on cooling or heating and for the mass distribution of the two phases.

A Nonequilibrium Rate Formula for Collective Motions of Complex Molecular Systems

NASA Astrophysics Data System (ADS)

Yanao, Tomohiro; Koon, Wang Sang; Marsden, Jerrold E.

2010-09-01

We propose a compact reaction rate formula that accounts for a non-equilibrium distribution of residence times of complex molecules, based on a detailed study of the coarse-grained phase space of a reaction coordinate. We take the structural transition dynamics of a six-atom Morse cluster between two isomers as a prototype of multi-dimensional molecular reactions. Residence time distribution of one of the isomers shows an exponential decay, while that of the other isomer deviates largely from the exponential form and has multiple peaks. Our rate formula explains such equilibrium and non-equilibrium distributions of residence times in terms of the rates of diffusions of energy and the phase of the oscillations of the reaction coordinate. Rapid diffusions of energy and the phase generally give rise to the exponential decay of residence time distribution, while slow diffusions give rise to a non-exponential decay with multiple peaks. We finally make a conjecture about a general relationship between the rates of the diffusions and the symmetry of molecular mass distributions.

Exact mapping between different dynamics of isotropically trapped quantum gases

NASA Astrophysics Data System (ADS)

Wamba, Etienne; Pelster, Axel; Anglin, James R.

2016-05-01

Experiments on trapped quantum gases can probe challenging regimes of quantum many-body dynamics, where strong interactions or non-equilibrium states prevent exact theoretical treatment. In this talk, we present a class of exact mappings between all the observables of different experiments, under the experimentally attainable conditions that the gas particles interact via a homogeneously scaling two-body potential which is in general time-dependent, and are confined in an isotropic harmonic trap. We express our result through an identity relating second-quantized field operators in the Heisenberg picture of quantum mechanics which makes it general. It applies to arbitrary measurements on possibly multi-component Bose or Fermi gases in arbitrary initial quantum states, no matter how highly excited or far from equilibrium. We use an example to show how the results of two different and currently feasible experiments can be mapped onto each other by our spacetime transformation. DAMOP sorting category: 6.11 Nonlinear dynamics and out-of-equilibrium trapped gases EW acknowledge the financial support from the Alexander von Humboldt foundation.

On Nash Equilibrium and Evolutionarily Stable States That Are Not Characterised by the Folk Theorem

PubMed Central

Li, Jiawei; Kendall, Graham

2015-01-01

In evolutionary game theory, evolutionarily stable states are characterised by the folk theorem because exact solutions to the replicator equation are difficult to obtain. It is generally assumed that the folk theorem, which is the fundamental theory for non-cooperative games, defines all Nash equilibria in infinitely repeated games. Here, we prove that Nash equilibria that are not characterised by the folk theorem do exist. By adopting specific reactive strategies, a group of players can be better off by coordinating their actions in repeated games. We call it a type-k equilibrium when a group of k players coordinate their actions and they have no incentive to deviate from their strategies simultaneously. The existence and stability of the type-k equilibrium in general games is discussed. This study shows that the sets of Nash equilibria and evolutionarily stable states have greater cardinality than classic game theory has predicted in many repeated games. PMID:26288088

A Generalized Multi-Phase Framework for Modeling Cavitation in Cryogenic Fluids

NASA Technical Reports Server (NTRS)

Dorney, Dan (Technical Monitor); Hosangadi, Ashvin; Ahuja, Vineet

2003-01-01

A generalized multi-phase formulation for cavitation in fluids operating at temperatures elevated relative to their critical temperatures is presented. The thermal effects and the accompanying property variations due to phase change are modeled rigorously. Thermal equilibrium is assumed and fluid thermodynamic properties are specified along the saturation line using the NIST-12 databank. Fundamental changes in the physical characteristics of the cavity when thermal effects become pronounced are identified; the cavity becomes more porous, the interface less distinct, and has increased entrainment when temperature variations are present. Quantitative estimates of temperature and pressure depressions in both liquid nitrogen and liquid hydrogen were computed and compared with experimental data of Hord for hydrofoils. Excellent estimates of the leading edge temperature and pressure depression were obtained while the comparisons in the cavity closure region were reasonable. Liquid nitrogen cavities were consistently found to be in thermal equilibrium while liquid hydrogen cavities exhibited small, but distinct, non-equilibrium effects.

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

NASA Astrophysics Data System (ADS)

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

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

Electronic energy transfer through non-adiabatic vibrational-electronic resonance. I. Theory for a dimer

NASA Astrophysics Data System (ADS)

Tiwari, Vivek; Peters, William K.; Jonas, David M.

2017-10-01

Non-adiabatic vibrational-electronic resonance in the excited electronic states of natural photosynthetic antennas drastically alters the adiabatic framework, in which electronic energy transfer has been conventionally studied, and suggests the possibility of exploiting non-adiabatic dynamics for directed energy transfer. Here, a generalized dimer model incorporates asymmetries between pigments, coupling to the environment, and the doubly excited state relevant for nonlinear spectroscopy. For this generalized dimer model, the vibrational tuning vector that drives energy transfer is derived and connected to decoherence between singly excited states. A correlation vector is connected to decoherence between the ground state and the doubly excited state. Optical decoherence between the ground and singly excited states involves linear combinations of the correlation and tuning vectors. Excitonic coupling modifies the tuning vector. The correlation and tuning vectors are not always orthogonal, and both can be asymmetric under pigment exchange, which affects energy transfer. For equal pigment vibrational frequencies, the nonadiabatic tuning vector becomes an anti-correlated delocalized linear combination of intramolecular vibrations of the two pigments, and the nonadiabatic energy transfer dynamics become separable. With exchange symmetry, the correlation and tuning vectors become delocalized intramolecular vibrations that are symmetric and antisymmetric under pigment exchange. Diabatic criteria for vibrational-excitonic resonance demonstrate that anti-correlated vibrations increase the range and speed of vibronically resonant energy transfer (the Golden Rule rate is a factor of 2 faster). A partial trace analysis shows that vibronic decoherence for a vibrational-excitonic resonance between two excitons is slower than their purely excitonic decoherence.

Electronic energy transfer through non-adiabatic vibrational-electronic resonance. I. Theory for a dimer.

PubMed

Tiwari, Vivek; Peters, William K; Jonas, David M

2017-10-21

Non-adiabatic vibrational-electronic resonance in the excited electronic states of natural photosynthetic antennas drastically alters the adiabatic framework, in which electronic energy transfer has been conventionally studied, and suggests the possibility of exploiting non-adiabatic dynamics for directed energy transfer. Here, a generalized dimer model incorporates asymmetries between pigments, coupling to the environment, and the doubly excited state relevant for nonlinear spectroscopy. For this generalized dimer model, the vibrational tuning vector that drives energy transfer is derived and connected to decoherence between singly excited states. A correlation vector is connected to decoherence between the ground state and the doubly excited state. Optical decoherence between the ground and singly excited states involves linear combinations of the correlation and tuning vectors. Excitonic coupling modifies the tuning vector. The correlation and tuning vectors are not always orthogonal, and both can be asymmetric under pigment exchange, which affects energy transfer. For equal pigment vibrational frequencies, the nonadiabatic tuning vector becomes an anti-correlated delocalized linear combination of intramolecular vibrations of the two pigments, and the nonadiabatic energy transfer dynamics become separable. With exchange symmetry, the correlation and tuning vectors become delocalized intramolecular vibrations that are symmetric and antisymmetric under pigment exchange. Diabatic criteria for vibrational-excitonic resonance demonstrate that anti-correlated vibrations increase the range and speed of vibronically resonant energy transfer (the Golden Rule rate is a factor of 2 faster). A partial trace analysis shows that vibronic decoherence for a vibrational-excitonic resonance between two excitons is slower than their purely excitonic decoherence.

[Adeno-associated viral vectors: methods for production and purification for gene therapy applications].

PubMed

Mena-Enriquez, Mayra; Flores-Contreras, Lucia; Armendáriz-Borunda, Juan

2012-01-01

Viral vectors based on adeno-associated virus (AAV) are widely used in gene therapy protocols, because they have characteristics that make them valuable for the treatment of genetic and chronic degenerative diseases. AAV2 serotype had been the best characterized to date. However, the AAV vectors developed from other serotypes is of special interest, since they have organ-specific tropism which increases their potential for transgene delivery to target cells for performing their therapeutic effects. This article summarizes AAV generalities, methods for their production and purification. It also discusses the use of these vectors in vitro, in vivo and their application in gene therapy clinical trials.

On Finsler spacetimes with a timelike Killing vector field

NASA Astrophysics Data System (ADS)

Caponio, Erasmo; Stancarone, Giuseppe

2018-04-01

We study Finsler spacetimes and Killing vector fields taking care of the fact that the generalised metric tensor associated to the Lorentz–Finsler function L is in general well defined only on a subset of the slit tangent bundle. We then introduce a new class of Finsler spacetimes endowed with a timelike Killing vector field that we call stationary splitting Finsler spacetimes. We characterize when a Finsler spacetime with a timelike Killing vector field is locally a stationary splitting. Finally, we show that the causal structure of a stationary splitting is the same of one of two Finslerian static spacetimes naturally associated to the stationary splitting.

Stability of differential susceptibility and infectivity epidemic models

PubMed Central

Bonzi, B.; Fall, A. A.; Iggidr, Abderrahman; Sallet, Gauthier

2011-01-01

We introduce classes of differential susceptibility and infectivity epidemic models. These models address the problem of flows between the different susceptible, infectious and infected compartments and differential death rates as well. We prove the global stability of the disease free equilibrium when the basic reproduction ratio ≤ 1 and the existence and uniqueness of an endemic equilibrium when > 1. We also prove the global asymptotic stability of the endemic equilibrium for a differential susceptibility and staged progression infectivity model, when > 1. Our results encompass and generalize those of [18, 22]. AMS Subject Classification : 34A34,34D23,34D40,92D30 PMID:20148330

Equilibrium figures inside the dark-matter ring and the shapes of elliptical galaxies

NASA Astrophysics Data System (ADS)

Kondratyev, B. P.; Trubitsyna, N. G.; Kireeva, E. N.

We solve the general problem of the theory of equilibrium figures and analyze two classes of liquid rotating gravitating figures residing inside a gravitating ring or torus. These figures form families of sequences of generalized oblate spheroids and triaxial ellipsoids, which at the lower limit of the tidal parameter α = 0 have the form of the Maclaurin spheroids and the Jacobi ellipsoids. In intermediate cases 0 < α ≤ αmax each new sequence of axisymmetric equilibrium figures has two non-rotating boundary spheroids. At the upper limit αmax/(π Gρ ) = 0.1867 the sequence degenerates into a single non-rotating spheroid with the eccentricity {e cr} ≈ 0.96 corresponding to the flattening limit of elliptical galaxies (E7). We also perform a detailed study of the sequences of generalized triaxial ellipsoids and find bifurcation points of triaxial ellipsoids in the sequences of generalized spheroids. We use this method to explain the shapes of E-galaxies. According to observations, very slowly rotating oblate E-type galaxies are known that have the shapes, which, because of instability, cannot be supported by velocity dispersion anisotropy exclusively. The hypothesis of a massive dark-matter outer ring requires no extreme anisotropy of pressure; it not only explains the shape of these elliptical galaxies, but also sheds new light on the riddle of the ellipticity limit (E7) of elliptical galaxies.

Attitude Determination Using Two Vector Measurements

NASA Technical Reports Server (NTRS)

Markley, F. Landis

1998-01-01

Many spacecraft attitude determination methods use exactly two vector measurements. The two vectors are typically the unit vector to the Sun and the Earth's magnetic field vector for coarse "sun-mag" attitude determination or unit vectors to two stars tracked by two star trackers for fine attitude determination. TRIAD, the earliest published algorithm for determining spacecraft attitude from two vector measurements, has been widely used in both ground-based and onboard attitude determination. Later attitude determination methods have been based on Wahba's optimality criterion for n arbitrarily weighted observations. The solution of Wahba's problem is somewhat difficult in the general case, but there is a simple closed-form solution in the two-observation case. This solution reduces to the TRIAD solution for certain choices of measurement weights. This paper presents and compares these algorithms as well as sub-optimal algorithms proposed by Bar-Itzhack, Harman, and Reynolds. Some new results will be presented, but the paper is primarily a review and tutorial.

Applicability of initial optimal maternal and fetal electrocardiogram combination vectors to subsequent recordings

NASA Astrophysics Data System (ADS)

Yan, Hua-Wen; Huang, Xiao-Lin; Zhao, Ying; Si, Jun-Feng; Liu, Tie-Bing; Liu, Hong-Xing

2014-11-01

A series of experiments are conducted to confirm whether the vectors calculated for an early section of a continuous non-invasive fetal electrocardiogram (fECG) recording can be directly applied to subsequent sections in order to reduce the computation required for real-time monitoring. Our results suggest that it is generally feasible to apply the initial optimal maternal and fetal ECG combination vectors to extract the fECG and maternal ECG in subsequent recorded sections.

Global climate change and vector-borne diseases

USGS Publications Warehouse

Ginsberg, H.S.

2002-01-01

Global warming will have different effects on different diseases because of the complex and idiosynchratic interactions between vectors, hosts, and pathogens that influence transmission dynamics of each pathogen. Human activities, including urbanization, rapid global travel, and vector management, have profound effects on disease transmission that can operate on more rapid time scales than does global climate change. The general concern about global warming encouraging the spread of tropical diseases is legitimate, but the effects vary among diseases, and the ecological implications are difficult to predict.

New QCD sum rules based on canonical commutation relations

NASA Astrophysics Data System (ADS)

Hayata, Tomoya

2012-04-01

New derivation of QCD sum rules by canonical commutators is developed. It is the simple and straightforward generalization of Thomas-Reiche-Kuhn sum rule on the basis of Kugo-Ojima operator formalism of a non-abelian gauge theory and a suitable subtraction of UV divergences. By applying the method to the vector and axial vector current in QCD, the exact Weinberg’s sum rules are examined. Vector current sum rules and new fractional power sum rules are also discussed.

Cosmology for quadratic gravity in generalized Weyl geometry

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

Jiménez, Jose Beltrán; Heisenberg, Lavinia; Koivisto, Tomi S.

A class of vector-tensor theories arises naturally in the framework of quadratic gravity in spacetimes with linear vector distortion. Requiring the absence of ghosts for the vector field imposes an interesting condition on the allowed connections with vector distortion: the resulting one-parameter family of connections generalises the usual Weyl geometry with polar torsion. The cosmology of this class of theories is studied, focusing on isotropic solutions wherein the vector field is dominated by the temporal component. De Sitter attractors are found and inhomogeneous perturbations around such backgrounds are analysed. In particular, further constraints on the models are imposed by excludingmore » pathologies in the scalar, vector and tensor fluctuations. Various exact background solutions are presented, describing a constant and an evolving dark energy, a bounce and a self-tuning de Sitter phase. However, the latter two scenarios are not viable under a closer scrutiny.« less

Computational Investigation of Fluidic Counterflow Thrust Vectoring

NASA Technical Reports Server (NTRS)

Hunter, Craig A.; Deere, Karen A.

1999-01-01

A computational study of fluidic counterflow thrust vectoring has been conducted. Two-dimensional numerical simulations were run using the computational fluid dynamics code PAB3D with two-equation turbulence closure and linear Reynolds stress modeling. For validation, computational results were compared to experimental data obtained at the NASA Langley Jet Exit Test Facility. In general, computational results were in good agreement with experimental performance data, indicating that efficient thrust vectoring can be obtained with low secondary flow requirements (less than 1% of the primary flow). An examination of the computational flowfield has revealed new details about the generation of a countercurrent shear layer, its relation to secondary suction, and its role in thrust vectoring. In addition to providing new information about the physics of counterflow thrust vectoring, this work appears to be the first documented attempt to simulate the counterflow thrust vectoring problem using computational fluid dynamics.

A Novel Gradient Vector Flow Snake Model Based on Convex Function for Infrared Image Segmentation

PubMed Central

Zhang, Rui; Zhu, Shiping; Zhou, Qin

2016-01-01

Infrared image segmentation is a challenging topic because infrared images are characterized by high noise, low contrast, and weak edges. Active contour models, especially gradient vector flow, have several advantages in terms of infrared image segmentation. However, the GVF (Gradient Vector Flow) model also has some drawbacks including a dilemma between noise smoothing and weak edge protection, which decrease the effect of infrared image segmentation significantly. In order to solve this problem, we propose a novel generalized gradient vector flow snakes model combining GGVF (Generic Gradient Vector Flow) and NBGVF (Normally Biased Gradient Vector Flow) models. We also adopt a new type of coefficients setting in the form of convex function to improve the ability of protecting weak edges while smoothing noises. Experimental results and comparisons against other methods indicate that our proposed snakes model owns better ability in terms of infrared image segmentation than other snakes models. PMID:27775660

Material quality assessment of silk nanofibers based on swarm intelligence

NASA Astrophysics Data System (ADS)

Brandoli Machado, Bruno; Nunes Gonçalves, Wesley; Martinez Bruno, Odemir

2013-02-01

In this paper, we propose a novel approach for texture analysis based on artificial crawler model. Our method assumes that each agent can interact with the environment and each other. The evolution process converges to an equilibrium state according to the set of rules. For each textured image, the feature vector is composed by signatures of the live agents curve at each time. Experimental results revealed that combining the minimum and maximum signatures into one increase the classification rate. In addition, we pioneer the use of autonomous agents for characterizing silk fibroin scaffolds. The results strongly suggest that our approach can be successfully employed for texture analysis.

Magnetic dynamo action in two-dimensional turbulent magneto-hydrodynamics

NASA Technical Reports Server (NTRS)

Fyfe, D.; Joyce, G.; Montgomery, D.

1977-01-01

Two-dimensional magnetohydrodynamic turbulence is explored by means of numerical simulation. Previous analytical theory, based on non-dissipative constants of the motion in a truncated Fourier representation, is verified by following the evolution of highly non-equilibrium initial conditions numerically. Dynamo action (conversion of a significant fraction of turbulent kinetic energy into long-wavelength magnetic field energy) is observed. It is conjectured that in the presence of dissipation and external forcing, a dual cascade will be observed for zero-helicity situations. Energy will cascade to higher wavenumbers simultaneously with a cascade of mean square vector potential to lower wavenumbers, leading to an omni-directional magnetic energy spectrum.

Photons in dense nuclear matter: Random-phase approximation

NASA Astrophysics Data System (ADS)

Stetina, Stephan; Rrapaj, Ermal; Reddy, Sanjay

2018-04-01

We present a comprehensive and pedagogic discussion of the properties of photons in cold and dense nuclear matter based on the resummed one-loop photon self-energy. Correlations among electrons, muons, protons, and neutrons in β equilibrium that arise as a result of electromagnetic and strong interactions are consistently taken into account within the random phase approximation. Screening effects, damping, and collective excitations are systematically studied in a fully relativistic setup. Our study is relevant to the linear response theory of dense nuclear matter, calculations of transport properties of cold dense matter, and investigations of the production and propagation of hypothetical vector bosons such as the dark photons.

Influence of the extrinsic curvature on two-dimensional nematic films.

PubMed

Napoli, Gaetano; Vergori, Luigi

2018-05-01

Nematic films are thin fluid structures, ideally two dimensional, endowed with an in-plane degenerate nematic order. In this paper we examine a generalization of the classical Plateau problem to an axisymmetric nematic film bounded by two coaxial parallel rings. At equilibrium, the shape of the nematic film results from the competition between surface tension, which favors the minimization of the area, and the nematic elasticity, which instead promotes the alignment of the molecules along a common direction. We find two classes of equilibrium solutions in which the molecules are uniformly aligned along the meridians or parallels. Depending on two dimensionless parameters, one related to the geometry of the film and the other to the constitutive moduli, the Gaussian curvature of the equilibrium shape may be everywhere negative, vanishing, or positive. The stability of these equilibrium configurations is investigated.

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

Ivanov, A. A., E-mail: aai@a5.kiam.ru; Martynov, A. A., E-mail: martynov@a5.kiam.ru; Medvedev, S. Yu., E-mail: medvedev@a5.kiam.ru

In the MHD tokamak plasma theory, the plasma pressure is usually assumed to be isotropic. However, plasma heating by neutral beam injection and RF heating can lead to a strong anisotropy of plasma parameters and rotation of the plasma. The development of MHD equilibrium theory taking into account the plasma inertia and anisotropic pressure began a long time ago, but until now it has not been consistently applied in computational codes for engineering calculations of the plasma equilibrium and evolution in tokamak. This paper contains a detailed derivation of the axisymmetric plasma equilibrium equation in the most general form (withmore » arbitrary rotation and anisotropic pressure) and description of the specialized version of the SPIDER code. The original method of calculation of the equilibrium with an anisotropic pressure and a prescribed rotational transform profile is proposed. Examples of calculations and discussion of the results are also presented.« less

Coupling of Higgs and Leggett modes in non-equilibrium superconductors.

PubMed

Krull, H; Bittner, N; Uhrig, G S; Manske, D; Schnyder, A P

2016-06-21

In equilibrium systems amplitude and phase collective modes are decoupled, as they are mutually orthogonal excitations. The direct detection of these Higgs and Leggett collective modes by linear-response measurements is not possible, because they do not couple directly to the electromagnetic field. In this work, using numerical exact simulations we show for the case of two-gap superconductors, that optical pump-probe experiments excite both Higgs and Leggett modes out of equilibrium. We find that this non-adiabatic excitation process introduces a strong interaction between the collective modes, which is absent in equilibrium. Moreover, we propose a type of pump-probe experiment, which allows to probe and coherently control the Higgs and Leggett modes, and thus the order parameter directly. These findings go beyond two-band superconductors and apply to general collective modes in quantum materials.

Overshoot in biological systems modelled by Markov chains: a non-equilibrium dynamic phenomenon.

PubMed

Jia, Chen; Qian, Minping; Jiang, Daquan

2014-08-01

A number of biological systems can be modelled by Markov chains. Recently, there has been an increasing concern about when biological systems modelled by Markov chains will perform a dynamic phenomenon called overshoot. In this study, the authors found that the steady-state behaviour of the system will have a great effect on the occurrence of overshoot. They showed that overshoot in general cannot occur in systems that will finally approach an equilibrium steady state. They further classified overshoot into two types, named as simple overshoot and oscillating overshoot. They showed that except for extreme cases, oscillating overshoot will occur if the system is far from equilibrium. All these results clearly show that overshoot is a non-equilibrium dynamic phenomenon with energy consumption. In addition, the main result in this study is validated with real experimental data.

Influence of the extrinsic curvature on two-dimensional nematic films

NASA Astrophysics Data System (ADS)

Napoli, Gaetano; Vergori, Luigi

2018-05-01

Nematic films are thin fluid structures, ideally two dimensional, endowed with an in-plane degenerate nematic order. In this paper we examine a generalization of the classical Plateau problem to an axisymmetric nematic film bounded by two coaxial parallel rings. At equilibrium, the shape of the nematic film results from the competition between surface tension, which favors the minimization of the area, and the nematic elasticity, which instead promotes the alignment of the molecules along a common direction. We find two classes of equilibrium solutions in which the molecules are uniformly aligned along the meridians or parallels. Depending on two dimensionless parameters, one related to the geometry of the film and the other to the constitutive moduli, the Gaussian curvature of the equilibrium shape may be everywhere negative, vanishing, or positive. The stability of these equilibrium configurations is investigated.

Figuring the Acceleration of the Simple Pendulum

NASA Astrophysics Data System (ADS)

Lieberherr, Martin

2011-12-01

The centripetal acceleration has been known since Huygens' (1659) and Newton's (1684) time.1,2 The physics to calculate the acceleration of a simple pendulum has been around for more than 300 years, and a fairly complete treatise has been given by C. Schwarz in this journal.3 But sentences like "the acceleration is always directed towards the equilibrium position" beside the picture of a swing on a circular arc can still be found in textbooks, as e.g. in Ref. 4. Vectors have been invented by Grassmann (1844)5 and are conveniently used to describe the acceleration in curved orbits, but acceleration is more often treated as a scalar with or without sign, as the words acceleration/deceleration suggest. The component tangential to the orbit is enough to deduce the period of the simple pendulum, but it is not enough to discuss the forces on the pendulum, as has been pointed out by Santos-Benito and A. Gras-Marti.6 A suitable way to address this problem is a nice figure with a catch for classroom discussions or homework. When I plotted the acceleration vectors of the simple pendulum in their proper positions, pictures as in Fig. 1 appeared on the screen. The endpoints of the acceleration vectors, if properly scaled, seemed to lie on a curve with a familiar shape: a cardioid. Is this true or just an illusion?

Reciprocity relationships in vector acoustics and their application to vector field calculations.

PubMed

Deal, Thomas J; Smith, Kevin B

2017-08-01

The reciprocity equation commonly stated in underwater acoustics relates pressure fields and monopole sources. It is often used to predict the pressure measured by a hydrophone for multiple source locations by placing a source at the hydrophone location and calculating the field everywhere for that source. A similar equation that governs the orthogonal components of the particle velocity field is needed to enable this computational method to be used for acoustic vector sensors. This paper derives a general reciprocity equation that accounts for both monopole and dipole sources. This vector-scalar reciprocity equation can be used to calculate individual components of the received vector field by altering the source type used in the propagation calculation. This enables a propagation model to calculate the received vector field components for an arbitrary number of source locations with a single model run for each vector field component instead of requiring one model run for each source location. Application of the vector-scalar reciprocity principle is demonstrated with analytic solutions for a range-independent environment and with numerical solutions for a range-dependent environment using a parabolic equation model.

Micromechanics of Composite Materials Governed by Vector Constitutive Laws

NASA Technical Reports Server (NTRS)

Bednarcyk, Brett A.; Aboudi, Jacob; Arnold, Steven M.

2017-01-01

The high-fidelity generalized method of cells micromechanics theory has been extended for the prediction of the effective property tensor and the corresponding local field distributions for composites whose constituents are governed by vector constitutive laws. As shown, the shear analogy, which can predict effective transverse properties, is not valid in the general three-dimensional case. Consequently, a general derivation is presented that is applicable to both continuously and discontinuously reinforced composites with arbitrary vector constitutive laws and periodic microstructures. Results are given for thermal and electric problems, effective properties and local field distributions, ordered and random microstructures, as well as complex geometries including woven composites. Comparisons of the theory's predictions are made to test data, numerical analysis, and classical expressions from the literature. Further, classical methods cannot provide the local field distributions in the composite, and it is demonstrated that, as the percolation threshold is approached, their predictions are increasingly unreliable. XXXX It has been observed that the bonding between the fibers and matrix in composite materials can be imperfect. In the context of thermal conductivity, such imperfect interfaces have been investigated in micromechanical models by Dunn and Taya (1993), Duan and Karihaloo (2007), Nan et al. (1997) and Hashin (2001). The present HFGMC micromechanical method, derived for perfectly bonded composite materials governed by vector constitutive laws, can be easily generalized to include the effects of weak bonding between the constituents. Such generalizations, in the context of the mechanical micromechanics problem, involve introduction of a traction-separation law at the fiber/matrix interface and have been presented by Aboudi (1987), Bednarcyk and Arnold (2002), Bednarcyk et al. (2004) and Aboudi et al. (2013) and will be addressed in the future.

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

Rapid equilibrium sampling initiated from nonequilibrium data.

PubMed

Huang, Xuhui; Bowman, Gregory R; Bacallado, Sergio; Pande, Vijay S

2009-11-24

Simulating the conformational dynamics of biomolecules is extremely difficult due to the rugged nature of their free energy landscapes and multiple long-lived, or metastable, states. Generalized ensemble (GE) algorithms, which have become popular in recent years, attempt to facilitate crossing between states at low temperatures by inducing a random walk in temperature space. Enthalpic barriers may be crossed more easily at high temperatures; however, entropic barriers will become more significant. This poses a problem because the dominant barriers to conformational change are entropic for many biological systems, such as the short RNA hairpin studied here. We present a new efficient algorithm for conformational sampling, called the adaptive seeding method (ASM), which uses nonequilibrium GE simulations to identify the metastable states, and seeds short simulations at constant temperature from each of them to quantitatively determine their equilibrium populations. Thus, the ASM takes advantage of the broad sampling possible with GE algorithms but generally crosses entropic barriers more efficiently during the seeding simulations at low temperature. We show that only local equilibrium is necessary for ASM, so very short seeding simulations may be used. Moreover, the ASM may be used to recover equilibrium properties from existing datasets that failed to converge, and is well suited to running on modern computer clusters.

Rigid rotators. [deriving the time-independent energy states associated with rotational motions of the molecule

NASA Technical Reports Server (NTRS)

1976-01-01

The two-particle, steady-state Schroedinger equation is transformed to center of mass and internuclear distance vector coordinates, leading to the free particle wave equation for the kinetic energy motion of the molecule and a decoupled wave equation for a single particle of reduced mass moving in a spherical potential field. The latter describes the vibrational and rotational energy modes of the diatomic molecule. For fixed internuclear distance, this becomes the equation of rigid rotator motion. The classical partition function for the rotator is derived and compared with the quantum expression. Molecular symmetry effects are developed from the generalized Pauli principle that the steady-state wave function of any system of fundamental particles must be antisymmetric. Nuclear spin and spin quantum functions are introduced and ortho- and para-states of rotators, along with their degeneracies, are defined. Effects of nuclear spin on entropy are deduced. Next, rigid polyatomic rotators are considered and the partition function for this case is derived. The patterns of rotational energy levels for nonlinear molecules are discussed for the spherical symmetric top, for the prolate symmetric top, for the oblate symmetric top, and for the asymmetric top. Finally, the equilibrium energy and specific heat of rigid rotators are derived.

A generalized electro-elastic theory of polymer networks

NASA Astrophysics Data System (ADS)

Cohen, Noy

2018-01-01

A rigorous multi-scale analysis of the electromechanical coupling in dielectric polymers is conducted. The body couples stemming from a misalignment between the electric field and the electric-dipole density vector are studied and the conservation laws for polymer networks are derived. Using variational principles, expressions for the polarization and the stress are determined. Interestingly, it is found that the stress tensor resulting from coupled loadings in which the electric field is misaligned with the principal stretch directions is not symmetric and the asymmetry arises from the body couples. Next, the electro-mechanical response of a chain is analyzed. The deformations of the individual polymer chains are related to the macroscopic deformation via two highly non-linear constraints - the first pertaining to the compatibility of the local deformations with the imposed macroscopic one and the second stems from the symmetric part of the stress at equilibrium. In accord with the proposed framework, an amended three-chains model is introduced. The predictions of this model are found to be in excellent agreement with experimental findings. Lastly, the behavior of a polymer subjected to a simple shear and an electric field is studied. The offset between the electric field and the principal directions gives rise to body couples, a polarization that is not aligned with the electric field, and an asymmetric stress tensor.

Super-Alfvénic Propagation and Damping of Reconnection Onset Signatures

NASA Astrophysics Data System (ADS)

Sharma Pyakurel, P.; Shay, M. A.; Haggerty, C. C.; Parashar, T. N.; Drake, J. F.; Cassak, P. A.; Gary, S. Peter

2018-01-01

The quadrupolar out-of-plane Hall magnetic field generated during collisionless reconnection propagates away from the x line as a kinetic Alfvén wave (KAW). While it has been shown that this KAW carries substantial Poynting flux and propagates super-Alfvenically, how this KAW damps as it propagates away from the x line is not well understood. In this study, this damping is examined using kinetic particle-in-cell simulations of antiparallel symmetric magnetic reconnection in a one-dimensional current sheet equilibrium. In the reconnection simulations, the KAW wave vector has a typical magnitude comparable to an inverse fluid Larmor radius (effectively an inverse ion Larmor radius) and a direction of 85-89° relative to the local magnetic field. We find that the damping of the reconnection KAW is consistent with linear Landau damping results from a numerical Vlasov dispersion solver. This knowledge allows us to generalize our damping predictions to regions in the magnetotail and solar corona where the magnetic geometry can be approximated as a current sheet. For the magnetotail, the KAW from reconnection will not damp away before propagating the approximately 20 Earth radii associated with global magnetotail distances. For the solar corona, on the other hand, these KAWs will completely damp before reaching the distances comparable to the flare loop length.

Approximate reduction of linear population models governed by stochastic differential equations: application to multiregional models.

PubMed

Sanz, Luis; Alonso, Juan Antonio

2017-12-01

In this work we develop approximate aggregation techniques in the context of slow-fast linear population models governed by stochastic differential equations and apply the results to the treatment of populations with spatial heterogeneity. Approximate aggregation techniques allow one to transform a complex system involving many coupled variables and in which there are processes with different time scales, by a simpler reduced model with a fewer number of 'global' variables, in such a way that the dynamics of the former can be approximated by that of the latter. In our model we contemplate a linear fast deterministic process together with a linear slow process in which the parameters are affected by additive noise, and give conditions for the solutions corresponding to positive initial conditions to remain positive for all times. By letting the fast process reach equilibrium we build a reduced system with a lesser number of variables, and provide results relating the asymptotic behaviour of the first- and second-order moments of the population vector for the original and the reduced system. The general technique is illustrated by analysing a multiregional stochastic system in which dispersal is deterministic and the rate growth of the populations in each patch is affected by additive noise.

Dual-scale topology optoelectronic processor.

PubMed

Marsden, G C; Krishnamoorthy, A V; Esener, S C; Lee, S H

1991-12-15

The dual-scale topology optoelectronic processor (D-STOP) is a parallel optoelectronic architecture for matrix algebraic processing. The architecture can be used for matrix-vector multiplication and two types of vector outer product. The computations are performed electronically, which allows multiplication and summation concepts in linear algebra to be generalized to various nonlinear or symbolic operations. This generalization permits the application of D-STOP to many computational problems. The architecture uses a minimum number of optical transmitters, which thereby reduces fabrication requirements while maintaining area-efficient electronics. The necessary optical interconnections are space invariant, minimizing space-bandwidth requirements.

Stable solutions of inflation driven by vector fields

NASA Astrophysics Data System (ADS)

Emami, Razieh; Mukohyama, Shinji; Namba, Ryo; Zhang, Ying-li

2017-03-01

Many models of inflation driven by vector fields alone have been known to be plagued by pathological behaviors, namely ghost and/or gradient instabilities. In this work, we seek a new class of vector-driven inflationary models that evade all of the mentioned instabilities. We build our analysis on the Generalized Proca Theory with an extension to three vector fields to realize isotropic expansion. We obtain the conditions required for quasi de-Sitter solutions to be an attractor analogous to the standard slow-roll one and those for their stability at the level of linearized perturbations. Identifying the remedy to the existing unstable models, we provide a simple example and explicitly show its stability. This significantly broadens our knowledge on vector inflationary scenarios, reviving potential phenomenological interests for this class of models.

An experimental investigation of thrust vectoring two-dimensional convergent-divergent nozzles installed in a twin-engine fighter model at high angles of attack

NASA Technical Reports Server (NTRS)

Capone, Francis J.; Mason, Mary L.; Leavitt, Laurence D.

1990-01-01

An investigation was conducted in the Langley 16-Foot Transonic Tunnel to determine thrust vectoring capability of subscale 2-D convergent-divergent exhaust nozzles installed on a twin engine general research fighter model. Pitch thrust vectoring was accomplished by downward rotation of nozzle upper and lower flaps. The effects of nozzle sidewall cutback were studied for both unvectored and pitch vectored nozzles. A single cutback sidewall was employed for yaw thrust vectoring. This investigation was conducted at Mach numbers ranging from 0 to 1.20 and at angles of attack from -2 to 35 deg. High pressure air was used to simulate jet exhaust and provide values of nozzle pressure ratio up to 9.

Novel method of finding extreme edges in a convex set of N-dimension vectors

NASA Astrophysics Data System (ADS)

Hu, Chia-Lun J.

2001-11-01

As we published in the last few years, for a binary neural network pattern recognition system to learn a given mapping {Um mapped to Vm, m=1 to M} where um is an N- dimension analog (pattern) vector, Vm is a P-bit binary (classification) vector, the if-and-only-if (IFF) condition that this network can learn this mapping is that each i-set in {Ymi, m=1 to M} (where Ymithere existsVmiUm and Vmi=+1 or -1, is the i-th bit of VR-m).)(i=1 to P and there are P sets included here.) Is POSITIVELY, LINEARLY, INDEPENDENT or PLI. We have shown that this PLI condition is MORE GENERAL than the convexity condition applied to a set of N-vectors. In the design of old learning machines, we know that if a set of N-dimension analog vectors form a convex set, and if the machine can learn the boundary vectors (or extreme edges) of this set, then it can definitely learn the inside vectors contained in this POLYHEDRON CONE. This paper reports a new method and new algorithm to find the boundary vectors of a convex set of ND analog vectors.

Supersymmetric solutions of N =(1 ,1 ) general massive supergravity

NASA Astrophysics Data System (ADS)

Deger, N. S.; Nazari, Z.; Sarıoǧlu, Ö.

2018-05-01

We construct supersymmetric solutions of three-dimensional N =(1 ,1 ) general massive supergravity (GMG). Solutions with a null Killing vector are, in general, pp-waves. We identify those that appear at critical points of the model, some of which do not exist in N =(1 ,1 ) new massive supergravity (NMG). In the timelike case, we find that many solutions are common with NMG, but there is a new class that is genuine to GMG, two members of which are stationary Lifshitz and timelike squashed AdS spacetimes. We also show that in addition to the fully supersymmetric AdS vacuum, there is a second AdS background with a nonzero vector field that preserves 1 /4 supersymmetry.

From density to interface fluctuations: The origin of wavelength dependence in surface tension

NASA Astrophysics Data System (ADS)

Hiester, Thorsten

2008-12-01

The height-height correlation function for a fluctuating interface between two coexisting bulk phases is derived by means of general equilibrium properties of the corresponding density-density correlation function. A wavelength-dependent surface tension γ(q) can be defined and expressed in terms of the direct correlation function c(r,r') , the equilibrium density profile ρ0(r) , and an operator which relates density to surface configurations. Neither the concept of an effective interface Hamiltonian nor the difference in pressure is needed to determine the general structure of the height-height correlations or γ(q) , respectively. This result generalizes the Mecke-Dietrich surface tension γMD(q) [Phys. Rev. E 59, 6766 (1999)] and modifies recently published criticism concerning γMD(q) [Tarazona, Checa, and Chacón, Phys. Rev. Lett. 99, 196101 (2007)].

A diagram for evaluating multiple aspects of model performance in simulating vector fields

NASA Astrophysics Data System (ADS)

Xu, Zhongfeng; Hou, Zhaolu; Han, Ying; Guo, Weidong

2016-12-01

Vector quantities, e.g., vector winds, play an extremely important role in climate systems. The energy and water exchanges between different regions are strongly dominated by wind, which in turn shapes the regional climate. Thus, how well climate models can simulate vector fields directly affects model performance in reproducing the nature of a regional climate. This paper devises a new diagram, termed the vector field evaluation (VFE) diagram, which is a generalized Taylor diagram and able to provide a concise evaluation of model performance in simulating vector fields. The diagram can measure how well two vector fields match each other in terms of three statistical variables, i.e., the vector similarity coefficient, root mean square length (RMSL), and root mean square vector difference (RMSVD). Similar to the Taylor diagram, the VFE diagram is especially useful for evaluating climate models. The pattern similarity of two vector fields is measured by a vector similarity coefficient (VSC) that is defined by the arithmetic mean of the inner product of normalized vector pairs. Examples are provided, showing that VSC can identify how close one vector field resembles another. Note that VSC can only describe the pattern similarity, and it does not reflect the systematic difference in the mean vector length between two vector fields. To measure the vector length, RMSL is included in the diagram. The third variable, RMSVD, is used to identify the magnitude of the overall difference between two vector fields. Examples show that the VFE diagram can clearly illustrate the extent to which the overall RMSVD is attributed to the systematic difference in RMSL and how much is due to the poor pattern similarity.

Effects of internal yaw-vectoring devices on the static performance of a pitch-vectoring nonaxisymmetric convergent-divergent nozzle

NASA Technical Reports Server (NTRS)

Asbury, Scott C.

1993-01-01

An investigation was conducted in the static test facility of the Langley 16-Foot Transonic Tunnel to evaluate the internal performance of a nonaxisymmetric convergent divergent nozzle designed to have simultaneous pitch and yaw thrust vectoring capability. This concept utilized divergent flap deflection for thrust vectoring in the pitch plane and flow-turning deflectors installed within the divergent flaps for yaw thrust vectoring. Modifications consisting of reducing the sidewall length and deflecting the sidewall outboard were investigated as means to increase yaw-vectoring performance. This investigation studied the effects of multiaxis (pitch and yaw) thrust vectoring on nozzle internal performance characteristics. All tests were conducted with no external flow, and nozzle pressure ratio was varied from 2.0 to approximately 13.0. The results indicate that this nozzle concept can successfully generate multiaxis thrust vectoring. Deflection of the divergent flaps produced resultant pitch vector angles that, although dependent on nozzle pressure ratio, were nearly equal to the geometric pitch vector angle. Losses in resultant thrust due to pitch vectoring were small or negligible. The yaw deflectors produced resultant yaw vector angles up to 21 degrees that were controllable by varying yaw deflector rotation. However, yaw deflector rotation resulted in significant losses in thrust ratios and, in some cases, nozzle discharge coefficient. Either of the sidewall modifications generally reduced these losses and increased maximum resultant yaw vector angle. During multiaxis (simultaneous pitch and yaw) thrust vectoring, little or no cross coupling between the thrust vectoring processes was observed.

Equilibrium, confinement and stability of runaway electrons in tokamaks

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

Spong, D A

1976-03-01

Some of the ramifications of the runaway population in tokamak experiments are investigated. Consideration is given both to the normal operating regime of tokamaks where only a small fraction of high energy runaways are present and to the strong runaway regime where runaways are thought to carry a significant portion of the toroidal current. In particular, the areas to be examined are the modeling of strong runaway discharges, single particle orbit characteristics of runaways, macroscopic beam-plasma equilibria, and stability against kink modes. A simple one-dimensional, time-dependent model has been constructed in relation to strong runaway discharges. Single particle orbits aremore » analyzed in relation to both the strong runaway regime and the weak regime. The effects of vector E x vector B drifts are first considered in strong runaway discharges and are found to lead to a slow inward shrinkage of the beam. Macroscopic beam-plasma equilibria are treated assuming a pressureless relativistic beam with inertia and using an ideal MHD approximation for the plasma. The stability of a toroidal relativistic beam against kink perturbations is examined using several models. (MOW)« less

Potential theory of radiation

NASA Technical Reports Server (NTRS)

Chiu, Huei-Huang

1989-01-01

A theoretical method is being developed by which the structure of a radiation field can be predicted by a radiation potential theory, similar to a classical potential theory. The introduction of a scalar potential is justified on the grounds that the spectral intensity vector is irrotational. The vector is also solenoidal in the limits of a radiation field in complete radiative equilibrium or in a vacuum. This method provides an exact, elliptic type equation that will upgrade the accuracy and the efficiency of the current CFD programs required for the prediction of radiation and flow fields. A number of interesting results emerge from the present study. First, a steady state radiation field exhibits an optically modulated inverse square law distribution character. Secondly, the unsteady radiation field is structured with two conjugate scalar potentials. Each is governed by a Klein-Gordon equation with a frictional force and a restoring force. This steady potential field structure and the propagation of radiation potentials are consistent with the well known results of classical electromagnetic theory. The extension of the radiation potential theory for spray combustion and hypersonic flow is also recommended.

Real-time radiography of Titan 4 Solid Rocket Motor Upgrade (SRMU) static firing test QM-2

NASA Astrophysics Data System (ADS)

Dolan, K. W.; Curnow, G. M.; Perkins, D. E.; Schneberk, D. J.; Costerus, B. W.; Lachapell, M. J.; Turner, D. E.; Wallace, P. W.

1994-03-01

Real-time radiography was successfully applied to the Titan-4 Solid Rocket Motor Upgrade (SRMU) static firing test QM-2 conducted February 22, 1993 at Phillips Laboratory, Edwards AFB, CA. The real-time video data obtained in this test gave the first incontrovertible evidence that the molten slag pool is low (less than 5 to 6 inches in depth referenced to the bottom of the aft dome cavity) before T + 55 seconds, builds fairly linearly from this point in time reaching a quasi-equilibrium depth of 16 to 17 inches at about T + 97 seconds, which is well below the top of the vectored nozzle, and maintains that level until T + 125 near the end motor burn. From T + 125 seconds to motor burn-out at T + 140 seconds the slag pool builds to a maximum depth of about 20 to 21 inches, still well below the top of the nozzle. The molten slag pool was observed to interact with motions of the vectored nozzle, and exhibit slosh and wave mode oscillations. A few slag ejection events were also observed.

[What makes an insect a vector?].

PubMed

Kampen, Helge

2009-01-01

Blood-feeding insects transmit numerous viruses, bacteria, protozoans and helminths to vertebrates. The developmental cycles of the microorganisms in their vectors and the mechanisms of transmission are generally extremely complex and the result of a long-lasting coevolution of vector and vectored pathogen based on mutual adaptation. The conditions necessary for an insect to become a vector are multiple but require an innate vector competence as a genetic basis. Next to the vector competence plenty of entomological, ecological and pathogen-related factors are decisive, given the availability of infection sources. The various modes of pathogen transmission by vectors are connected to the developmental routes of the microorganisms in their vectors. In particular, pathogens transmitted by saliva encounter a lot of cellular and acellular barriers during their migration from the insect's midgut through the hemocele into the salivary fluid, including components of the insect's immune system. With regard to intracellular development, receptor-mediated invasion mechanisms are of relevance. As an environmental factor, the temperature has a paramount impact on the vectorial roles of hematophagous insects. Not only has it a considerable influence on the duration of a pathogen's development in its vector (extrinsic incubation period) but it can render putatively vector-incompetent insects to vectors ("leaky gut" phenomenon). Equally crucial are behavioural aspects of both the insect and the pathogen such as blood host preferences, seasonal appearance and circadian biting activity on the vector's side and diurnal/nocturnal periodicity on the pathogen's side which facilitate a contact in the first place.

Bethe vectors for XXX-spin chain

NASA Astrophysics Data System (ADS)

Burdík, Čestmír; Fuksa, Jan; Isaev, Alexei

2014-11-01

The paper deals with algebraic Bethe ansatz for XXX-spin chain. Generators of Yang-Baxter algebra are expressed in basis of free fermions and used to calculate explicit form of Bethe vectors. Their relation to N-component models is used to prove conjecture about their form in general. Some remarks on inhomogeneous XXX-spin chain are included.

Protection against California 2002 NDV strain afforded by adenovirus vectored vaccine expressing Fusion or Hemagglutination-neuraminidase genes

USDA-ARS?s Scientific Manuscript database

Vectored vaccines expressing the combination of the hemagglutinin-neuraminidase (HN) and fusion (F) genes generally have better clinical protection against Newcastle disease virus (NDV) than when either the F and HN genes are expressed alone. Interestingly, the protection induced by F is usually bet...

Kac determinant and singular vector of the level N representation of Ding-Iohara-Miki algebra

NASA Astrophysics Data System (ADS)

Ohkubo, Yusuke

2018-05-01

In this paper, we obtain the formula for the Kac determinant of the algebra arising from the level N representation of the Ding-Iohara-Miki algebra. It is also discovered that its singular vectors correspond to generalized Macdonald functions (the q-deformed version of the AFLT basis).

Energy theorem for (2+1)-dimensional gravity.

NASA Astrophysics Data System (ADS)

Menotti, P.; Seminara, D.

1995-05-01

We prove a positive energy theorem in (2+1)-dimensional gravity for open universes and any matter energy-momentum tensor satisfying the dominant energy condition. We consider on the space-like initial value surface a family of widening Wilson loops and show that the energy-momentum of the enclosed subsystem is a future directed time-like vector whose mass is an increasing function of the loop, until it reaches the value 1/4G corresponding to a deficit angle of 2π. At this point the energy-momentum of the system evolves, depending on the nature of a zero norm vector appearing in the evolution equations, either into a time-like vector of a universe which closes kinematically or into a Gott-like universe whose energy momentum vector, as first recognized by Deser, Jackiw, and 't Hooft (1984) is space-like. This treatment generalizes results obtained by Carroll, Fahri, Guth, and Olum (1994) for a system of point-like spinless particle, to the most general form of matter whose energy-momentum tensor satisfies the dominant energy condition. The treatment is also given for the anti-de Sitter (2+1)-dimensional gravity.

On A Nonlinear Generalization of Sparse Coding and Dictionary Learning.

PubMed

Xie, Yuchen; Ho, Jeffrey; Vemuri, Baba

2013-01-01

Existing dictionary learning algorithms are based on the assumption that the data are vectors in an Euclidean vector space ℝ d , and the dictionary is learned from the training data using the vector space structure of ℝ d and its Euclidean L 2 -metric. However, in many applications, features and data often originated from a Riemannian manifold that does not support a global linear (vector space) structure. Furthermore, the extrinsic viewpoint of existing dictionary learning algorithms becomes inappropriate for modeling and incorporating the intrinsic geometry of the manifold that is potentially important and critical to the application. This paper proposes a novel framework for sparse coding and dictionary learning for data on a Riemannian manifold, and it shows that the existing sparse coding and dictionary learning methods can be considered as special (Euclidean) cases of the more general framework proposed here. We show that both the dictionary and sparse coding can be effectively computed for several important classes of Riemannian manifolds, and we validate the proposed method using two well-known classification problems in computer vision and medical imaging analysis.

On A Nonlinear Generalization of Sparse Coding and Dictionary Learning

PubMed Central

Xie, Yuchen; Ho, Jeffrey; Vemuri, Baba

2013-01-01

Existing dictionary learning algorithms are based on the assumption that the data are vectors in an Euclidean vector space ℝd, and the dictionary is learned from the training data using the vector space structure of ℝd and its Euclidean L2-metric. However, in many applications, features and data often originated from a Riemannian manifold that does not support a global linear (vector space) structure. Furthermore, the extrinsic viewpoint of existing dictionary learning algorithms becomes inappropriate for modeling and incorporating the intrinsic geometry of the manifold that is potentially important and critical to the application. This paper proposes a novel framework for sparse coding and dictionary learning for data on a Riemannian manifold, and it shows that the existing sparse coding and dictionary learning methods can be considered as special (Euclidean) cases of the more general framework proposed here. We show that both the dictionary and sparse coding can be effectively computed for several important classes of Riemannian manifolds, and we validate the proposed method using two well-known classification problems in computer vision and medical imaging analysis. PMID:24129583

Towards Microeconomic Resource Sharing in End System Multicast Networks Based on Walrasian General Equilibrium

NASA Astrophysics Data System (ADS)

Rezvani, Mohammad Hossein; Analoui, Morteza

2010-11-01

We have designed a competitive economical mechanism for application level multicast in which a number of independent services are provided to the end-users by a number of origin servers. Each offered service can be thought of as a commodity and the origin servers and the users who relay the service to their downstream nodes can thus be thought of as producers of the economy. Also, the end-users can be viewed as consumers of the economy. The proposed mechanism regulates the price of each service in such a way that general equilibrium holds. So, all allocations will be Pareto optimal in the sense that the social welfare of the users is maximized.

Fate of polychlorinated biphenyls in a contaminated lake ecosystem: combining equilibrium passive sampling of sediment and water with total concentration measurements of biota.

PubMed

Mäenpää, Kimmo; Leppänen, Matti T; Figueiredo, Kaisa; Mayer, Philipp; Gilbert, Dorothea; Jahnke, Annika; Gil-Allué, Carmen; Akkanen, Jarkko; Nybom, Inna; Herve, Sirpa

2015-11-01

Equilibrium sampling devices can be applied to study and monitor the exposure and fate of hydrophobic organic chemicals on a thermodynamic basis. They can be used to determine freely dissolved concentrations and chemical activity ratios and to predict equilibrium partitioning concentrations of hydrophobic organic chemicals in biota lipids. The authors' aim was to assess the equilibrium status of polychlorinated biphenyls (PCBs) in a contaminated lake ecosystem and along its discharge course using equilibrium sampling devices for measurements in sediment and water and by also analyzing biota. The authors used equilibrium sampling devices (silicone rubber and polyethylene [PE]) to determine freely dissolved concentrations and chemical activities of PCBs in the water column and sediment porewater and calculated for both phases the corresponding equilibrium concentrations and chemical activities in model lipids. Overall, the studied ecosystem appeared to be in disequilibrium for the studied phases: sediment, water, and biota. Chemical activities of PCBs were higher in sediment than in water, which implies that the sediment functioned as a partitioning source of PCBs and that net diffusion occurred from the sediment to the water column. Measured lipid-normalized PCB concentrations in biota were generally below equilibrium lipid concentrations relative to the sediment (CLip ⇌Sed ) or water (CLip ⇌W ), indicating that PCB levels in the organisms were below the maximum partitioning levels. The present study shows the application versatility of equilibrium sampling devices in the field and facilitates a thermodynamic understanding of exposure and fate of PCBs in a contaminated lake and its discharge course. © 2015 SETAC.

Integrated pest management and allocation of control efforts for vector-borne diseases

USGS Publications Warehouse

Ginsberg, H.S.

2001-01-01

Applications of various control methods were evaluated to determine how to integrate methods so as to minimize the number of human cases of vector-borne diseases. These diseases can be controlled by lowering the number of vector-human contacts (e.g., by pesticide applications or use of repellents), or by lowering the proportion of vectors infected with pathogens (e.g., by lowering or vaccinating reservoir host populations). Control methods should be combined in such a way as to most efficiently lower the probability of human encounter with an infected vector. Simulations using a simple probabilistic model of pathogen transmission suggest that the most efficient way to integrate different control methods is to combine methods that have the same effect (e.g., combine treatments that lower the vector population; or combine treatments that lower pathogen prevalence in vectors). Combining techniques that have different effects (e.g., a technique that lowers vector populations with a technique that lowers pathogen prevalence in vectors) will be less efficient than combining two techniques that both lower vector populations or combining two techniques that both lower pathogen prevalence, costs being the same. Costs of alternative control methods generally differ, so the efficiency of various combinations at lowering human contact with infected vectors should be estimated at available funding levels. Data should be collected from initial trials to improve the effects of subsequent interventions on the number of human cases.

A Maximal Element Theorem in FWC-Spaces and Its Applications

PubMed Central

Hu, Qingwen; Miao, Yulin

2014-01-01

A maximal element theorem is proved in finite weakly convex spaces (FWC-spaces, in short) which have no linear, convex, and topological structure. Using the maximal element theorem, we develop new existence theorems of solutions to variational relation problem, generalized equilibrium problem, equilibrium problem with lower and upper bounds, and minimax problem in FWC-spaces. The results represented in this paper unify and extend some known results in the literature. PMID:24782672

Reconstruction of interatomic vectors by principle component analysis of nuclear magnetic resonance data in multiple alignments

NASA Astrophysics Data System (ADS)

Hus, Jean-Christophe; Bruschweiler, Rafael

2002-07-01

A general method is presented for the reconstruction of interatomic vector orientations from nuclear magnetic resonance (NMR) spectroscopic data of tensor interactions of rank 2, such as dipolar coupling and chemical shielding anisotropy interactions, in solids and partially aligned liquid-state systems. The method, called PRIMA, is based on a principal component analysis of the covariance matrix of the NMR parameters collected for multiple alignments. The five nonzero eigenvalues and their eigenvectors efficiently allow the approximate reconstruction of the vector orientations of the underlying interactions. The method is demonstrated for an isotropic distribution of sample orientations as well as for finite sets of orientations and internuclear vectors encountered in protein systems.

The optical analogy for vector fields

NASA Technical Reports Server (NTRS)

Parker, E. N. (Editor)

1991-01-01

This paper develops the optical analogy for a general vector field. The optical analogy allows the examination of certain aspects of a vector field that are not otherwise readily accessible. In particular, in the cases of a stationary Eulerian flow v of an ideal fluid and a magnetostatic field B, the vectors v and B have surface loci in common with their curls. The intrinsic discontinuities around local maxima in absolute values of v and B take the form of vortex sheets and current sheets, respectively, the former playing a fundamental role in the development of hydrodyamic turbulence and the latter playing a major role in heating the X-ray coronas of stars and galaxies.

Improvements in Block-Krylov Ritz Vectors and the Boundary Flexibility Method of Component Synthesis

NASA Technical Reports Server (NTRS)

Carney, Kelly Scott

1997-01-01

A method of dynamic substructuring is presented which utilizes a set of static Ritz vectors as a replacement for normal eigenvectors in component mode synthesis. This set of Ritz vectors is generated in a recurrence relationship, proposed by Wilson, which has the form of a block-Krylov subspace. The initial seed to the recurrence algorithm is based upon the boundary flexibility vectors of the component. Improvements have been made in the formulation of the initial seed to the Krylov sequence, through the use of block-filtering. A method to shift the Krylov sequence to create Ritz vectors that will represent the dynamic behavior of the component at target frequencies, the target frequency being determined by the applied forcing functions, has been developed. A method to terminate the Krylov sequence has also been developed. Various orthonormalization schemes have been developed and evaluated, including the Cholesky/QR method. Several auxiliary theorems and proofs which illustrate issues in component mode synthesis and loss of orthogonality in the Krylov sequence have also been presented. The resulting methodology is applicable to both fixed and free- interface boundary components, and results in a general component model appropriate for any type of dynamic analysis. The accuracy is found to be comparable to that of component synthesis based upon normal modes, using fewer generalized coordinates. In addition, the block-Krylov recurrence algorithm is a series of static solutions and so requires significantly less computation than solving the normal eigenspace problem. The requirement for less vectors to form the component, coupled with the lower computational expense of calculating these Ritz vectors, combine to create a method more efficient than traditional component mode synthesis.

Bluetongue Disease Risk Assessment Based on Observed and Projected Culicoides obsoletus spp. Vector Densities

PubMed Central

Brugger, Katharina; Rubel, Franz

2013-01-01

Bluetongue is an arboviral disease of ruminants causing significant economic losses. Our risk assessment is based on the epidemiological key parameter, the basic reproduction number. It is defined as the number of secondary cases caused by one primary case in a fully susceptible host population, in which values greater than one indicate the possibility, i.e., the risk, for a major disease outbreak. In the course of the Bluetongue virus serotype 8 (BTV-8) outbreak in Europe in 2006 we developed such a risk assessment for the University of Veterinary Medicine Vienna, Austria. Basic reproduction numbers were calculated using a well-known formula for vector-borne diseases considering the population densities of hosts (cattle and small ruminants) and vectors (biting midges of the Culicoides obsoletus spp.) as well as temperature dependent rates. The latter comprise the biting and mortality rate of midges as well as the reciprocal of the extrinsic incubation period. Most important, but generally unknown, is the spatio-temporal distribution of the vector density. Therefore, we established a continuously operating daily monitoring to quantify the seasonal cycle of the vector population by a statistical model. We used cross-correlation maps and Poisson regression to describe vector densities by environmental temperature and precipitation. Our results comprise time series of observed and simulated Culicoides obsoletus spp. counts as well as basic reproduction numbers for the period 2009–2011. For a spatio-temporal risk assessment we projected our results from the location of Vienna to the entire region of Austria. We compiled both daily maps of vector densities and the basic reproduction numbers, respectively. Basic reproduction numbers above one were generally found between June and August except in the mountainous regions of the Alps. The highest values coincide with the locations of confirmed BTV cases. PMID:23560090

Thermodynamics of stoichiometric biochemical networks in living systems far from equilibrium.

PubMed

Qian, Hong; Beard, Daniel A

2005-04-22

The principles of thermodynamics apply to both equilibrium and nonequilibrium biochemical systems. The mathematical machinery of the classic thermodynamics, however, mainly applies to systems in equilibrium. We introduce a thermodynamic formalism for the study of metabolic biochemical reaction (open, nonlinear) networks in both time-dependent and time-independent nonequilibrium states. Classical concepts in equilibrium thermodynamics-enthalpy, entropy, and Gibbs free energy of biochemical reaction systems-are generalized to nonequilibrium settings. Chemical motive force, heat dissipation rate, and entropy production (creation) rate, key concepts in nonequilibrium systems, are introduced. Dynamic equations for the thermodynamic quantities are presented in terms of the key observables of a biochemical network: stoichiometric matrix Q, reaction fluxes J, and chemical potentials of species mu without evoking empirical rate laws. Energy conservation and the Second Law are established for steady-state and dynamic biochemical networks. The theory provides the physiochemical basis for analyzing large-scale metabolic networks in living organisms.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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