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Sample records for langevin equation theory

  1. Boedeker's effective theory: From Langevin dynamics to Dyson-Schwinger equations

    SciTech Connect

    Zahlten, Claus Hernandez, Andres Schmidt, Michael G.

    2009-10-15

    The dynamics of weakly coupled, non-abelian gauge fields at high temperature is non-perturbative if the characteristic momentum scale is of order |k|{approx}g{sup 2}T. Such a situation is typical for the processes of electroweak baryon number violation in the early Universe. Boedeker has derived an effective theory that describes the dynamics of the soft field modes by means of a Langevin equation. This effective theory has been used for lattice calculations so far [G.D. Moore, Nucl. Phys. B568 (2000) 367. Available from: (); G.D. Moore, Phys. Rev. D62 (2000) 085011. Available from: ()]. In this work we provide a complementary, more analytic approach based on Dyson-Schwinger equations. Using methods known from stochastic quantitation, we recast Boedeker's Langevin equation in the form of a field theoretic path integral. We introduce gauge ghosts in order to help control possible gauge artefacts that might appear after truncation, and which leads to a BRST symmetric formulation and to corresponding Ward identities. A second set of Ward identities, reflecting the origin of the theory in a stochastic differential equation, is also obtained. Finally, Dyson-Schwinger equations are derived.

  2. Self-consistent generalized Langevin-equation theory for liquids of nonspherically interacting particles.

    PubMed

    Elizondo-Aguilera, L F; Zubieta Rico, P F; Ruiz-Estrada, H; Alarcón-Waess, O

    2014-11-01

    A self-consistent generalized Langevin-equation theory is proposed to describe the self- and collective dynamics of a liquid of linear Brownian particles. The equations of motion for the spherical harmonics projections of the collective and self-intermediate-scattering functions, F_{lm,lm}(k,t) and F_{lm,lm}^{S}(k,t), are derived as a contraction of the description involving the stochastic equations of the corresponding tensorial one-particle density n_{lm}(k,t) and the translational (α=T) and rotational (α=R) current densities j_{lm}^{α}(k,t). Similar to the spherical case, these dynamic equations require as an external input the equilibrium structural properties of the system contained in the projections of the static structure factor, denoted by S_{lm,lm}(k). Complementing these exact equations with simple (Vineyard-like) approximate relations for the collective and the self-memory functions we propose a closed self-consistent set of equations for the dynamic properties involved. In the long-time asymptotic limit, these equations become the so-called bifurcation equations, whose solutions (the nonergodicity parameters) can be written, extending the spherical case, in terms of one translational and one orientational scalar dynamic order parameter, γ_{T} and γ_{R}, which characterize the possible dynamical arrest transitions of the system. As a concrete illustrative application of this theory we determine the dynamic arrest diagram of the dipolar hard-sphere fluid. In qualitative agreement with mode coupling theory, the present self-consistent equations also predict three different regions in the state space spanned by the macroscopic control parameters η (volume fraction) and T* (scaled temperature): a region of fully ergodic states, a region of mixed states, in which the translational degrees of freedom become arrested while the orientational degrees of freedom remain ergodic, and a region of fully nonergodic states. PMID:25493790

  3. Langevin Equation for DNA Dynamics

    NASA Astrophysics Data System (ADS)

    Grych, David; Copperman, Jeremy; Guenza, Marina

    Under physiological conditions, DNA oligomers can contain well-ordered helical regions and also flexible single-stranded regions. We describe the site-specific motion of DNA with a modified Rouse-Zimm Langevin equation formalism that describes DNA as a coarse-grained polymeric chain with global structure and local flexibility. The approach has successfully described the protein dynamics in solution and has been extended to nucleic acids. Our approach provides diffusive mode analytical solutions for the dynamics of global rotational diffusion and internal motion. The internal DNA dynamics present a rich energy landscape that accounts for an interior where hydrogen bonds and base-stacking determine structure and experience limited solvent exposure. We have implemented several models incorporating different coarse-grained sites with anisotropic rotation, energy barrier crossing, and local friction coefficients that include a unique internal viscosity and our models reproduce dynamics predicted by atomistic simulations. The models reproduce bond autocorrelation along the sequence as compared to that directly calculated from atomistic molecular dynamics simulations. The Langevin equation approach captures the essence of DNA dynamics without a cumbersome atomistic representation.

  4. The complex chemical Langevin equation

    SciTech Connect

    Schnoerr, David; Sanguinetti, Guido; Grima, Ramon

    2014-07-14

    The chemical Langevin equation (CLE) is a popular simulation method to probe the stochastic dynamics of chemical systems. The CLE’s main disadvantage is its break down in finite time due to the problem of evaluating square roots of negative quantities whenever the molecule numbers become sufficiently small. We show that this issue is not a numerical integration problem, rather in many systems it is intrinsic to all representations of the CLE. Various methods of correcting the CLE have been proposed which avoid its break down. We show that these methods introduce undesirable artefacts in the CLE’s predictions. In particular, for unimolecular systems, these correction methods lead to CLE predictions for the mean concentrations and variance of fluctuations which disagree with those of the chemical master equation. We show that, by extending the domain of the CLE to complex space, break down is eliminated, and the CLE’s accuracy for unimolecular systems is restored. Although the molecule numbers are generally complex, we show that the “complex CLE” predicts real-valued quantities for the mean concentrations, the moments of intrinsic noise, power spectra, and first passage times, hence admitting a physical interpretation. It is also shown to provide a more accurate approximation of the chemical master equation of simple biochemical circuits involving bimolecular reactions than the various corrected forms of the real-valued CLE, the linear-noise approximation and a commonly used two moment-closure approximation.

  5. Self-guided Langevin dynamics via generalized Langevin equation.

    PubMed

    Wu, Xiongwu; Brooks, Bernard R; Vanden-Eijnden, Eric

    2016-03-01

    Self-guided Langevin dynamics (SGLD) is a molecular simulation method that enhances conformational search and sampling via acceleration of the low frequency motions of the system. This acceleration is produced via introduction of a guiding force which breaks down the detailed-balance property of the dynamics, implying that some reweighting is necessary to perform equilibrium sampling. Here, we eliminate the need of reweighing and show that the NVT and NPT ensembles are sampled exactly by a new version of self-guided motion involving a generalized Langevin equation (GLE) in which the random force is modified so as to restore detailed-balance. Through the examples of alanine dipeptide and argon liquid, we show that this SGLD-GLE method has enhanced conformational sampling capabilities compared with regular Langevin dynamics (LD) while being of comparable computational complexity. In particular, SGLD-GLE is fully size extensive and can be used in arbitrarily large systems, making it an appealing alternative to LD. © 2015 Wiley Periodicals, Inc. PMID:26183423

  6. Second-quantized molecular time scale generalized Langevin equation theory: Coupled oscillator model

    SciTech Connect

    McDowell, H.K.

    1986-11-15

    A second-quantized, coupled oscillator model is presented which explicitly displays the structure of a second-quantized MTGLE theory. The Adelman ansatz (J. Chem Phys. 75, 5837 (1981)) for a quantum MTGLE response function is shown to generate the correct response function for the model. This result paves the way for the development of a general second-quantized MTGLE theory.

  7. Distance fluctuation of a single molecule in Lennard-Jones liquid based on generalized Langevin equation and mode coupling theory

    NASA Astrophysics Data System (ADS)

    Li, Ping; Dong, Yunhong; Zhao, Nanrong; Hou, Zhonghuai

    2014-04-01

    Distance fluctuation of a single molecule, modeled as an idealized bead-spring chain, dissolved in a Lennard-Jones liquid is studied by using a multidimensional generalized Langevin equation, where the friction kernel ζ(t) is calculated from the kinetic mode coupling theory (MCT). Temporal behavior of the distance autocorrelation function shows three typical regimes of time dependence, starting with a constant, followed by a power law of t-α, and finally an exponential decay. Particular attentions are paid to the time span of the power law regime, which corresponds to anomalous subdiffusion behavior, and the MCT framework enables us to investigate thoroughly how this regime depends on microscopic details such as the bead-to-solvent mass ratio MR, chain spring frequency ω, and the chain length N. Interestingly, the exponent α is robust to be 1/2 against the change of these parameters, although the friction kernel ζ(t) shows nontrivial dependence on time. In addition, we find that the starting time of the power-law region t1 scales with Γ-1, with Γ = 4ω2/ζ0 where ζ0 is the zero-frequency friction which decreases rapidly with increasing bead mass. On the other hand, the ending time t2 is not sensitive to varying ω or ζ0, but it increases with N rapidly before it reaches a constant for N larger than some threshold value. Our work may provide a unified strategy starting from the microscopic level to understand the anomalous subdiffusive behavior regarding large scale conformational change of polymers or proteins.

  8. Langevin equation approach to reactor noise analysis: stochastic transport equation

    SciTech Connect

    Akcasu, A.Z. ); Stolle, A.M. )

    1993-01-01

    The application of the Langevin equation method to the study of fluctuations in the space- and velocity-dependent neutron density as well as in the detector outputs in nuclear reactors is presented. In this case, the Langevin equation is the stochastic linear neutron transport equation with a space- and velocity-dependent random neutron source, often referred to as the noise equivalent source (NES). The power spectral densities (PSDs) of the NESs in the transport equation, as well as in the accompanying detection rate equations, are obtained, and the cross- and auto-power spectral densities of the outputs of pairs of detectors are explicitly calculated. The transport-level expression for the R([omega]) ratio measured in the [sup 252]Cf source-driven noise analysis method is also derived. Finally, the implementation of the Langevin equation approach at different levels of approximation is discussed, and the stochastic one-speed transport and one-group P[sub 1] equations are derived by first integrating the stochastic transport equation over speed and then eliminating the angular dependence by a spherical harmonics expansion. By taking the large transport rate limit in the P[sub 1] description, the stochastic diffusion equation is obtained as well as the PSD of the NES in it. This procedure also leads directly to the stochastic Fick's law.

  9. Critical exponent of the fractional Langevin equation.

    PubMed

    Burov, S; Barkai, E

    2008-02-22

    We investigate the dynamical phase diagram of the fractional Langevin equation and show that critical exponents mark dynamical transitions in the behavior of the system. For a free and harmonically bound particle the critical exponent alpha(c)=0.402+/-0.002 marks a transition to a nonmonotonic underdamped phase. The critical exponent alpha(R)=0.441... marks a transition to a resonance phase, when an external oscillating field drives the system. Physically, we explain these behaviors using a cage effect, where the medium induces an elastic type of friction. Phase diagrams describing the underdamped, the overdamped and critical frequencies of the fractional oscillator, recently used to model single protein experiments, show behaviors vastly different from normal. PMID:18352535

  10. Probability Density Function Method for Langevin Equations with Colored Noise

    SciTech Connect

    Wang, Peng; Tartakovsky, Alexandre M.; Tartakovsky, Daniel M.

    2013-04-05

    We present a novel method to derive closed-form, computable PDF equations for Langevin systems with colored noise. The derived equations govern the dynamics of joint or marginal probability density functions (PDFs) of state variables, and rely on a so-called Large-Eddy-Diffusivity (LED) closure. We demonstrate the accuracy of the proposed PDF method for linear and nonlinear Langevin equations, describing the classical Brownian displacement and dispersion in porous media.

  11. Improving multilevel Monte Carlo for stochastic differential equations with application to the Langevin equation

    PubMed Central

    Müller, Eike H.; Scheichl, Rob; Shardlow, Tony

    2015-01-01

    This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the multilevel Monte Carlo (MLMC) method for stochastic differential equations (SDEs) and especially the Langevin equation. We use modified equations analysis as an alternative to strong-approximation theory for the integrator, and we apply this to introduce MLMC for Langevin-type equations with integrators based on operator splitting. We combine this with extrapolation and investigate the use of discrete random variables in place of the Gaussian increments, which is a well-known technique for the weak approximation of SDEs. We show that, for small-noise problems, discrete random variables can lead to an increase in efficiency of almost two orders of magnitude for practical levels of accuracy.

  12. Waveform characteristics of deep low-frequency earthquakes: time-series evolution based on the theory of the KM2O-Langevin equation

    NASA Astrophysics Data System (ADS)

    Takeo, Minoru; Ueda, Hiroko; Okabe, Yasunori; Matsuura, Masaya

    2006-04-01

    Since the 1970s, deep low-frequency earthquakes (DLF) with depths ranging 20-40 km have been observed just beneath the Japan Island Arc. Almost all of these earthquakes are recognized up to now have had magnitudes less than 2.5, so that we have little information concerning DLF. Employing the theory of KM2O-Langevin equations, we develop a new method to represent the characteristics of the coda parts of DLF, and propose a new concept of `average dissipation spectrum'. The new averaging algorithm for the KM2O-Langevin matrix function was applied in the analysis of DLF (M: 1.0), which occurred in Akita prefecture on 2001 July 11, and we succeeded in separating the characteristics of the source vibration system and the source excitation process into the averaged dissipation term and the fluctuation term, respectively. The gaps between the arrival times of the fluctuation term's peaks at three stations near the epicentre are slightly different than the gaps between the S-wave arrival times. Assuming a homogenous crust structure with an S-wave velocity of 4.3 km s-1 and assuming the depth of the second source to be the same as that of the hypocentre, the second source lies about 1.5 km, N 56°E of the hypocentre. We estimate the common characteristics of this DLF successfully by using the `average dissipation spectrum', which is made up of typical frequencies, θk, attenuation factors, Qk and amplitude factors, Ak. The common elements of (θk~ 1.5, Qk~-0.3) and (θk~ 3.25, Qk~-0.45) among all stations indicate the characteristics of the source dynamics of the Akita DLF. The major parts of the coda waves of DLF satisfy the stationary property, and the causality values for the linear and odd-degree non-linear transformations are relatively higher than those for the even-degree non-linear transformations. These characteristics are quite different from the characteristics of tectonic earthquakes. This quantitative property is common among all DLF.

  13. Simplified simulation of Boltzmann-Langevin equation

    SciTech Connect

    Ayik, S.; Randrup, J.

    1994-06-01

    We briefly recall the Boltzmann-Langevin model of nuclear dynamics. We then summarize recent progress in deriving approximate analytical expressions for the associated transport coefficients and describe a numerical method for simulating the stochastic evolution of the phase-space density.

  14. A path integral approach to the Langevin equation

    NASA Astrophysics Data System (ADS)

    Das, Ashok K.; Panda, Sudhakar; Santos, J. R. L.

    2015-02-01

    We study the Langevin equation with both a white noise and a colored noise. We construct the Lagrangian as well as the Hamiltonian for the generalized Langevin equation which leads naturally to a path integral description from first principles. This derivation clarifies the meaning of the additional fields introduced by Martin, Siggia and Rose in their functional formalism. We show that the transition amplitude, in this case, is the generating functional for correlation functions. We work out explicitly the correlation functions for the Markovian process of the Brownian motion of a free particle as well as for that of the non-Markovian process of the Brownian motion of a harmonic oscillator (Uhlenbeck-Ornstein model). The path integral description also leads to a simple derivation of the Fokker-Planck equation for the generalized Langevin equation.

  15. Bifurcation dynamics of the tempered fractional Langevin equation.

    PubMed

    Zeng, Caibin; Yang, Qigui; Chen, YangQuan

    2016-08-01

    Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings. PMID:27586627

  16. Bifurcation dynamics of the tempered fractional Langevin equation

    NASA Astrophysics Data System (ADS)

    Zeng, Caibin; Yang, Qigui; Chen, YangQuan

    2016-08-01

    Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings.

  17. Langevin equation model of dispersion in the convective boundary layer

    SciTech Connect

    Nasstrom, J S

    1998-08-01

    This dissertation presents the development and evaluation of a Lagrangian stochastic model of vertical dispersion of trace material in the convective boundary layer (CBL). This model is based on a Langevin equation of motion for a fluid particle, and assumes the fluid vertical velocity probability distribution is skewed and spatially homogeneous. This approach can account for the effect of large-scale, long-lived turbulent structures and skewed vertical velocity distributions found in the CBL. The form of the Langevin equation used has a linear (in velocity) deterministic acceleration and a skewed randomacceleration. For the case of homogeneous fluid velocity statistics, this ""linear-skewed" Langevin equation can be integrated explicitly, resulting in a relatively efficient numerical simulation method. It is shown that this approach is more efficient than an alternative using a "nonlinear-Gaussian" Langevin equation (with a nonlinear deterministic acceleration and a Gaussian random acceleration) assuming homogeneous turbulence, and much more efficient than alternative approaches using Langevin equation models assuming inhomogeneous turbulence. "Reflection" boundary conditions for selecting a new velocity for a particle that encounters a boundary at the top or bottom of the CBL were investigated. These include one method using the standard assumption that the magnitudes of the particle incident and reflected velocities are positively correlated, and two alternatives in which the magnitudes of these velocities are negatively correlated and uncorrelated. The constraint that spatial and velocity distributions of a well-mixed tracer must be the same as those of the fluid, was used to develop the Langevin equation models and the reflection boundary conditions. The two Langevin equation models and three reflection methods were successfully tested using cases for which exact, analytic statistical properties of particle velocity and position are known, including well

  18. Langevin equation approach to granular flow in a narrow pipe

    SciTech Connect

    Riethmueller, T.; Schimansky-Geier, L.; Rosenkranz, D.; Poeschel, T.

    1997-01-01

    The gravity-driven flow of granular material through a rough, narrow vertical pipe is described using the Langevin equation formalism. Above a critical particle density the homogeneous flow becomes unstable with respect to short-wave length perturbations. In correspondence with experimental observations, we find clogging and density waves in the flowing material.

  19. Boltzmann-Langevin theory of Coulomb drag

    NASA Astrophysics Data System (ADS)

    Chen, W.; Andreev, A. V.; Levchenko, A.

    2015-06-01

    We develop a Boltzmann-Langevin description of the Coulomb drag effect in clean double-layer systems with large interlayer separation d as compared to the average interelectron distance λF. Coulomb drag arises from density fluctuations with spatial scales of order d . At low temperatures, their characteristic frequencies exceed the intralayer equilibration rate of the electron liquid, and Coulomb drag may be treated in the collisionless approximation. As temperature is raised, the electron mean free path becomes short due to electron-electron scattering. This leads to local equilibration of electron liquid, and consequently drag is determined by hydrodynamic density modes. Our theory applies to both the collisionless and the hydrodynamic regimes, and it enables us to describe the crossover between them. We find that drag resistivity exhibits a nonmonotonic temperature dependence with multiple crossovers at distinct energy scales. At the lowest temperatures, Coulomb drag is dominated by the particle-hole continuum, whereas at higher temperatures of the collision-dominated regime it is governed by the plasmon modes. We observe that fast intralayer equilibration mediated by electron-electron collisions ultimately renders a stronger drag effect.

  20. Stochastic modeling of driver behavior by Langevin equations

    NASA Astrophysics Data System (ADS)

    Langner, Michael; Peinke, Joachim

    2015-06-01

    A procedure based on stochastic Langevin equations is presented and shows how a stochastic model of driver behavior can be estimated directly from given data. The Langevin analysis allows the separation of a given data-set into a stochastic diffusion- and a deterministic drift field. Form the drift field a potential can be derived. In particular the method is here applied on driving data from a simulator. We overcome typical problems like varying sampling rates, low noise levels, low data amounts, inefficient coordinate systems, and non-stationary situations. From the estimation of the drift- and diffusion vector-fields derived from the data, we show different ways how to set up Monte-Carlo simulations for the driver behavior.

  1. Quantum Non-Markovian Langevin Equations and Transport Coefficients

    SciTech Connect

    Sargsyan, V.V.; Antonenko, N.V.; Kanokov, Z.; Adamian, G.G.

    2005-12-01

    Quantum diffusion equations featuring explicitly time-dependent transport coefficients are derived from generalized non-Markovian Langevin equations. Generalized fluctuation-dissipation relations and analytic expressions for calculating the friction and diffusion coefficients in nuclear processes are obtained. The asymptotic behavior of the transport coefficients and correlation functions for a damped harmonic oscillator that is linearly coupled in momentum to a heat bath is studied. The coupling to a heat bath in momentum is responsible for the appearance of the diffusion coefficient in coordinate. The problem of regression of correlations in quantum dissipative systems is analyzed.

  2. The generalized Schrödinger–Langevin equation

    SciTech Connect

    Bargueño, Pedro; Miret-Artés, Salvador

    2014-07-15

    In this work, for a Brownian particle interacting with a heat bath, we derive a generalization of the so-called Schrödinger–Langevin or Kostin equation. This generalization is based on a nonlinear interaction model providing a state-dependent dissipation process exhibiting multiplicative noise. Two straightforward applications to the measurement process are then analyzed, continuous and weak measurements in terms of the quantum Bohmian trajectory formalism. Finally, it is also shown that the generalized uncertainty principle, which appears in some approaches to quantum gravity, can be expressed in terms of this generalized equation. -- Highlights: •We generalize the Kostin equation for arbitrary system–bath coupling. •This generalization is developed both in the Schrödinger and Bohmian formalisms. •We write the generalized Kostin equation for two measurement problems. •We reformulate the generalized uncertainty principle in terms of this equation.

  3. Langevin equation with fluctuating diffusivity: A two-state model

    NASA Astrophysics Data System (ADS)

    Miyaguchi, Tomoshige; Akimoto, Takuma; Yamamoto, Eiji

    2016-07-01

    Recently, anomalous subdiffusion, aging, and scatter of the diffusion coefficient have been reported in many single-particle-tracking experiments, though the origins of these behaviors are still elusive. Here, as a model to describe such phenomena, we investigate a Langevin equation with diffusivity fluctuating between a fast and a slow state. Namely, the diffusivity follows a dichotomous stochastic process. We assume that the sojourn time distributions of these two states are given by power laws. It is shown that, for a nonequilibrium ensemble, the ensemble-averaged mean-square displacement (MSD) shows transient subdiffusion. In contrast, the time-averaged MSD shows normal diffusion, but an effective diffusion coefficient transiently shows aging behavior. The propagator is non-Gaussian for short time and converges to a Gaussian distribution in a long-time limit; this convergence to Gaussian is extremely slow for some parameter values. For equilibrium ensembles, both ensemble-averaged and time-averaged MSDs show only normal diffusion and thus we cannot detect any traces of the fluctuating diffusivity with these MSDs. Therefore, as an alternative approach to characterizing the fluctuating diffusivity, the relative standard deviation (RSD) of the time-averaged MSD is utilized and it is shown that the RSD exhibits slow relaxation as a signature of the long-time correlation in the fluctuating diffusivity. Furthermore, it is shown that the RSD is related to a non-Gaussian parameter of the propagator. To obtain these theoretical results, we develop a two-state renewal theory as an analytical tool.

  4. Langevin equation with fluctuating diffusivity: A two-state model.

    PubMed

    Miyaguchi, Tomoshige; Akimoto, Takuma; Yamamoto, Eiji

    2016-07-01

    Recently, anomalous subdiffusion, aging, and scatter of the diffusion coefficient have been reported in many single-particle-tracking experiments, though the origins of these behaviors are still elusive. Here, as a model to describe such phenomena, we investigate a Langevin equation with diffusivity fluctuating between a fast and a slow state. Namely, the diffusivity follows a dichotomous stochastic process. We assume that the sojourn time distributions of these two states are given by power laws. It is shown that, for a nonequilibrium ensemble, the ensemble-averaged mean-square displacement (MSD) shows transient subdiffusion. In contrast, the time-averaged MSD shows normal diffusion, but an effective diffusion coefficient transiently shows aging behavior. The propagator is non-Gaussian for short time and converges to a Gaussian distribution in a long-time limit; this convergence to Gaussian is extremely slow for some parameter values. For equilibrium ensembles, both ensemble-averaged and time-averaged MSDs show only normal diffusion and thus we cannot detect any traces of the fluctuating diffusivity with these MSDs. Therefore, as an alternative approach to characterizing the fluctuating diffusivity, the relative standard deviation (RSD) of the time-averaged MSD is utilized and it is shown that the RSD exhibits slow relaxation as a signature of the long-time correlation in the fluctuating diffusivity. Furthermore, it is shown that the RSD is related to a non-Gaussian parameter of the propagator. To obtain these theoretical results, we develop a two-state renewal theory as an analytical tool. PMID:27575079

  5. Reconstruction of the modified discrete Langevin equation from persistent time series.

    PubMed

    Czechowski, Zbigniew

    2016-05-01

    The discrete Langevin-type equation, which can describe persistent processes, was introduced. The procedure of reconstruction of the equation from time series was proposed and tested on synthetic data, with short and long-tail distributions, generated by different Langevin equations. Corrections due to the finite sampling rates were derived. For an exemplary meteorological time series, an appropriate Langevin equation, which constitutes a stochastic macroscopic model of the phenomenon, was reconstructed. PMID:27249949

  6. Solving the generalized Langevin equation with the algebraically correlated noise

    NASA Astrophysics Data System (ADS)

    Srokowski, T.; Płoszajczak, M.

    1998-04-01

    We solve the Langevin equation with the memory kernel. The stochastic force possesses algebraic correlations, proportional to 1/t. The velocity autocorrelation function and related quantities characterizing transport properties are calculated with the assumption that the system is in thermal equilibrium. Stochastic trajectories are simulated numerically, using the kangaroo process as a noise generator. Results of this simulation resemble Lévy walks with divergent moments of the velocity distribution. We consider motion of a Brownian particle, both without any external potential and in the harmonic oscillator field, in particular the escape from a potential well. The results are compared with memory-free calculations for the Brownian particle.

  7. Is the Langevin phase equation an efficient model for oscillating neurons?

    NASA Astrophysics Data System (ADS)

    Ota, Keisuke; Tsunoda, Takamasa; Omori, Toshiaki; Watanabe, Shigeo; Miyakawa, Hiroyoshi; Okada, Masato; Aonishi, Toru

    2009-12-01

    The Langevin phase model is an important canonical model for capturing coherent oscillations of neural populations. However, little attention has been given to verifying its applicability. In this paper, we demonstrate that the Langevin phase equation is an efficient model for neural oscillators by using the machine learning method in two steps: (a) Learning of the Langevin phase model. We estimated the parameters of the Langevin phase equation, i.e., a phase response curve and the intensity of white noise from physiological data measured in the hippocampal CA1 pyramidal neurons. (b) Test of the estimated model. We verified whether a Fokker-Planck equation derived from the Langevin phase equation with the estimated parameters could capture the stochastic oscillatory behavior of the same neurons disturbed by periodic perturbations. The estimated model could predict the neural behavior, so we can say that the Langevin phase equation is an efficient model for oscillating neurons.

  8. On the environmental modes for the generalized Langevin equation

    NASA Astrophysics Data System (ADS)

    Kawai, Shinnosuke

    2015-09-01

    The generalized Langevin equation (GLE) is used widely in molecular science and time series analysis as it offers a convenient low-dimensional description for large systems. There the dynamical effect of the environment interacting with the low-dimensional system is expressed as friction and random force. The present paper aims to investigate explicit dynamical variables to describe the dynamical modes in the environment that are derived from the GLE and defined solely in terms of the time series of the observed variable. The formulation results in equations of motion without a memory term and hence offers a more intuitive description than the GLE. The framework provided by the present study is expected to elucidate a multi-dimensional dynamics hidden behind the time series of the observed quantity.

  9. Langevin Theory of Anomalous Brownian Motion Made Simple

    ERIC Educational Resources Information Center

    Tothova, Jana; Vasziova, Gabriela; Glod, Lukas; Lisy, Vladimir

    2011-01-01

    During the century from the publication of the work by Einstein (1905 "Ann. Phys." 17 549) Brownian motion has become an important paradigm in many fields of modern science. An essential impulse for the development of Brownian motion theory was given by the work of Langevin (1908 "C. R. Acad. Sci.", Paris 146 530), in which he proposed an…

  10. Fractional Langevin equation: overdamped, underdamped, and critical behaviors.

    PubMed

    Burov, S; Barkai, E

    2008-09-01

    The dynamical phase diagram of the fractional Langevin equation is investigated for a harmonically bound particle. It is shown that critical exponents mark dynamical transitions in the behavior of the system. Four different critical exponents are found. (i) alpha_{c}=0.402+/-0.002 marks a transition to a nonmonotonic underdamped phase, (ii) alpha_{R}=0.441... marks a transition to a resonance phase when an external oscillating field drives the system, and (iii) alpha_{chi_{1}}=0.527... and (iv) alpha_{chi_{2}}=0.707... mark transitions to a double-peak phase of the "loss" when such an oscillating field present. As a physical explanation we present a cage effect, where the medium induces an elastic type of friction. Phase diagrams describing over and underdamped regimes, with or without resonances, show behaviors different from normal. PMID:18850998

  11. Recovering hidden dynamical modes from the generalized Langevin equation.

    PubMed

    Kawai, Shinnosuke; Miyazaki, Yusuke

    2016-09-01

    In studying large molecular systems, insights can better be extracted by selecting a limited number of physical quantities for analysis rather than treating every atomic coordinate in detail. Some information may, however, be lost by projecting the total system onto a small number of coordinates. For such problems, the generalized Langevin equation (GLE) is shown to provide a useful framework to examine the interaction between the observed variables and their environment. Starting with the GLE obtained from the time series of the observed quantity, we perform a transformation to introduce a set of variables that describe dynamical modes existing in the environment. The introduced variables are shown to effectively recover the essential information of the total system that appeared to be lost by the projection. PMID:27608984

  12. Description of quantum noise by a Langevin equation

    NASA Technical Reports Server (NTRS)

    Metiu, H.; Schon, G.

    1984-01-01

    General features of the quantum noise problem expressed as the equations of motion for a particle coupled to a set of oscillators are investigated analytically. Account is taken of the properties of the companion oscillators by formulating quantum statistical correlation Langevin equations (QSLE). The frequency of the oscillators is then retained as a natural cut-off for the quantum noise. The QSLE is further extended to encompass the particle trajectory and is bounded by initial and final states of the oscillator. The states are expressed as the probability of existence at the moment of particle collision that takes the oscillator into a final state. Two noise sources then exist: a statistical uncertainty of the initial state and the quantum dynamical uncertainty associated with a transition from the initial to final state. Feynman's path-integral formulation is used to characterize the functional of the particle trajectory, which slows the particle. It is shown that the energy loss may be attributed to friction, which satisfies energy conservation laws.

  13. Dynamical simulation of neutron-induced fission of uranium isotopes using four-dimensional Langevin equations

    NASA Astrophysics Data System (ADS)

    Pahlavani, M. R.; Mirfathi, S. M.

    2016-04-01

    Four-dimensional Langevin equations have been suggested for the dynamical simulation of neutron-induced fission at low and medium excitation energies. The mass distribution of the fission fragments, the neutron multiplicity, and the fission cross section for the thermal and fast neutron-induced fission of 233U, 235U, and 238U is studied by considering energy dissipation of the compound nucleus through the fission using four-dimensional Langevin equations combined with a Monte Carlo simulation approach. The calculated results using this approach indicate reasonable agreement with available experimental data.

  14. Trajectory approach to the Schrödinger-Langevin equation with linear dissipation for ground states

    NASA Astrophysics Data System (ADS)

    Chou, Chia-Chun

    2015-11-01

    The Schrödinger-Langevin equation with linear dissipation is integrated by propagating an ensemble of Bohmian trajectories for the ground state of quantum systems. Substituting the wave function expressed in terms of the complex action into the Schrödinger-Langevin equation yields the complex quantum Hamilton-Jacobi equation with linear dissipation. We transform this equation into the arbitrary Lagrangian-Eulerian version with the grid velocity matching the flow velocity of the probability fluid. The resulting equation is simultaneously integrated with the trajectory guidance equation. Then, the computational method is applied to the harmonic oscillator, the double well potential, and the ground vibrational state of methyl iodide. The excellent agreement between the computational and the exact results for the ground state energies and wave functions shows that this study provides a synthetic trajectory approach to the ground state of quantum systems.

  15. Langevin equation with stochastic damping - Possible application to critical binary fluid

    NASA Technical Reports Server (NTRS)

    Jasnow, D.; Gerjuoy, E.

    1975-01-01

    We solve the familiar Langevin equation with stochastic damping to represent the motion of a Brownian particle in a fluctuating medium. A connection between the damping and the random driving forces is proposed which preserves quite generally the Einstein relation between the diffusion and mobility coefficients. We present an application to the case of a Brownian particle in a critical binary mixture.

  16. Critical comparison of Kramers' fission width with the stationary width from the Langevin equation

    SciTech Connect

    Sadhukhan, Jhilam; Pal, Santanu

    2009-06-15

    It is shown that Kramers' fission width, originally derived for a system with constant inertia, can be extended to systems with a deformation-dependent collective inertia, which is the case for nuclear fission. The predictions of Kramers' width for systems with variable inertia are found to be in very good agreement with the stationary fission widths obtained by solving the corresponding Langevin equations.

  17. Gaussian approximations for stochastic systems with delay: Chemical Langevin equation and application to a Brusselator system

    SciTech Connect

    Brett, Tobias Galla, Tobias

    2014-03-28

    We present a heuristic derivation of Gaussian approximations for stochastic chemical reaction systems with distributed delay. In particular, we derive the corresponding chemical Langevin equation. Due to the non-Markovian character of the underlying dynamics, these equations are integro-differential equations, and the noise in the Gaussian approximation is coloured. Following on from the chemical Langevin equation, a further reduction leads to the linear-noise approximation. We apply the formalism to a delay variant of the celebrated Brusselator model, and show how it can be used to characterise noise-driven quasi-cycles, as well as noise-triggered spiking. We find surprisingly intricate dependence of the typical frequency of quasi-cycles on the delay period.

  18. Dynamics of neutron-induced fission of 235U using four-dimensional Langevin equations

    NASA Astrophysics Data System (ADS)

    Pahlavani, M. R.; Mirfathi, S. M.

    2015-08-01

    Background: Langevin equations have been suggested as a key approach to the dynamical analysis of energy dissipation in excited nuclei, formed during heavy-ion fusion-fission reactions. Recently, a few researchers theoretically reported investigations of fission for light nuclei in a low excitation energy using the Langevin approach, without considering the contribution of pre- and post-scission particles and γ -ray emission. Purpose: We study the dynamical evolution of mass distribution of fission fragments, and neutron and γ -ray multiplicity for 236U as compound nuclei that are constructed after fusion of a neutron and 235U. Method: Energy dissipation of the compound nucleus through fission is calculated using the Langevin dynamical approach combined with a Monte Carlo method. Also the shape of the fissioning nucleus is restricted to "funny hills" parametrization. Results: Fission fragment mass distribution, neutron and γ -ray multiplicity, and the average kinetic energy of emitted neutrons and γ rays at a low excitation energy are calculated using a dynamical model, based on the four-dimensional Langevin equations. Conclusions: The theoretical results show reasonable agreement with experimental data and the proposed dynamical model can well explain the energy dissipation in low energy induced fission.

  19. New Kinematic Model in comparing with Langevin equation and Fokker Planck Equation

    NASA Astrophysics Data System (ADS)

    Lee, Kyoung; Wang, Zhijian; Gardner, Robin

    2010-03-01

    An analytic approximate solution of New Kinematic Model with the boundary conditions is developed for the incompressible packing condition in Pebble Bed Reactors. It is based on velocity description of the packing density in the hopper. The packing structure can be presented with a jamming phenomenon from flow types. The gravity-driven macroscopic motions are governed not only by the geometry and external boundary conditions of silos and hoppers, but by flow prosperities of granular materials, such as friction, viscosity and porosity. The analytical formulas for the quasi-linear diffusion and convection coefficients of the velocity profile are obtained. Since it was found that the New Kinematic Model is dependent upon the granular packing density distribution, we are motivated to study the Langevin equation with friction under the influence of the Gravitational field. We also discuss the relation with the Fokker Planck Equation using Detailed balance and Metropolis-Hastings Algorithm. Markov chain Monte Carlo methods are shown to be a non-Maxwellian distribution function with the mean velocity of the field particles having an effective temperature.

  20. Solving the Langevin equation with stochastic algebraically correlated noise

    NASA Astrophysics Data System (ADS)

    Płoszajczak, M.; Srokowski, T.

    1997-05-01

    The long time tail in the velocity and force autocorrelation function has been found recently in molecular dynamics simulations of peripheral collisions of ions. Simulation of those slowly decaying correlations in the stochastic transport theory requires the development of new methods of generating stochastic force of arbitrarily long correlation times. In this paper we propose a Markovian process, the multidimensional kangaroo process, which permits the description of various algebraically correlated stochastic processes.

  1. Dynamic scaling behaviors of linear fractal Langevin-type equation driven by nonconserved and conserved noise

    NASA Astrophysics Data System (ADS)

    Zhang, Zhe; Xun, Zhi-Peng; Wu, Ling; Chen, Yi-Li; Xia, Hui; Hao, Da-Peng; Tang, Gang

    2016-06-01

    In order to study the effects of the microscopic details of fractal substrates on the scaling behavior of the growth model, a generalized linear fractal Langevin-type equation, ∂h / ∂t =(- 1) m + 1 ν∇ mzrw h (zrw is the dynamic exponent of random walk on substrates), driven by nonconserved and conserved noise is proposed and investigated theoretically employing scaling analysis. Corresponding dynamic scaling exponents are obtained.

  2. Entropy production in non-equilibrium systems described by the generalized Langevin equation

    NASA Astrophysics Data System (ADS)

    Sevilla, Francisco J.; Piña-Perez, Omar

    2014-03-01

    The generalized Langevin equation for a charged particle under the influence of time-dependent external fields, is employed to study the effects of non-Markovian dissipative terms in the entropy production of non-equilibrium states exhibiting non-zero mass flux. We present results for the case in which the fluctuation-dissipation relation holds. FJS and OPP acknowledge financial support from PAPIIT-IN113114 and PAEP-UNAM respectively.

  3. A path-integral Langevin equation treatment of low-temperature doped helium clusters

    NASA Astrophysics Data System (ADS)

    Ing, Christopher; Hinsen, Konrad; Yang, Jing; Zeng, Toby; Li, Hui; Roy, Pierre-Nicholas

    2012-06-01

    We present an implementation of path integral molecular dynamics for sampling low temperature properties of doped helium clusters using Langevin dynamics. The robustness of the path integral Langevin equation and white-noise Langevin equation [M. Ceriotti, M. Parrinello, T. E. Markland, and D. E. Manolopoulos, J. Chem. Phys. 133, 124104 (2010)], 10.1063/1.3489925 sampling methods are considered for those weakly bound systems with comparison to path integral Monte Carlo (PIMC) in terms of efficiency and accuracy. Using these techniques, convergence studies are performed to confirm the systematic error reduction introduced by increasing the number of discretization steps of the path integral. We comment on the structural and energetic evolution of HeN-CO2 clusters from N = 1 to 20. To quantify the importance of both rotations and exchange in our simulations, we present a chemical potential and calculated band origin shifts as a function of cluster size utilizing PIMC sampling that includes these effects. This work also serves to showcase the implementation of path integral simulation techniques within the molecular modelling toolkit [K. Hinsen, J. Comp. Chem. 21, 79 (2000)], 10.1002/(SICI)1096-987X(20000130)21:2<79::AID-JCC1>3.0.CO;2-B, an open-source molecular simulation package.

  4. Stochastic resonance in the fractional Langevin equation driven by multiplicative noise and periodically modulated noise

    NASA Astrophysics Data System (ADS)

    Yu, Tao; Zhang, Lu; Luo, Mao-Kang

    2013-10-01

    First we study the time and frequency characteristics of fractional calculus, which reflect the memory and gain properties of fractional-order systems. Then, the fractional Langevin equation driven by multiplicative colored noise and periodically modulated noise is investigated in the over-damped case. Using the moment equation method, the exact analytical expression of the output amplitude is derived. Numerical results indicate that the output amplitude presents stochastic resonance driven by periodically modulated noise. For low frequency signal, the higher the system order is, the bigger the resonance intensity will be; while the result of high frequency signal is quite the contrary. This is consistent with the frequency characteristics of fractional calculus.

  5. Stochastic processes with finite correlation time: Modeling and application to the generalized Langevin equation

    NASA Astrophysics Data System (ADS)

    Srokowski, T.

    2001-09-01

    The kangaroo process (KP) is characterized by various forms of covariance and can serve as a useful model of random noises. We discuss properties of that process for the exponential, stretched exponential, and algebraic (power-law) covariances. Then we apply the KP as a model of noise in the generalized Langevin equation and simulate solutions by a Monte Carlo method. Some results appear to be incompatible with requirements of the fluctuation-dissipation theorem because probability distributions change when the process is inserted into the equation. We demonstrate how one can construct a model of noise free of that difficulty. This form of the KP is especially suitable for physical applications.

  6. Laws of Large Numbers and Langevin Approximations for Stochastic Neural Field Equations

    PubMed Central

    2013-01-01

    In this study, we consider limit theorems for microscopic stochastic models of neural fields. We show that the Wilson–Cowan equation can be obtained as the limit in uniform convergence on compacts in probability for a sequence of microscopic models when the number of neuron populations distributed in space and the number of neurons per population tend to infinity. This result also allows to obtain limits for qualitatively different stochastic convergence concepts, e.g., convergence in the mean. Further, we present a central limit theorem for the martingale part of the microscopic models which, suitably re-scaled, converges to a centred Gaussian process with independent increments. These two results provide the basis for presenting the neural field Langevin equation, a stochastic differential equation taking values in a Hilbert space, which is the infinite-dimensional analogue of the chemical Langevin equation in the present setting. On a technical level, we apply recently developed law of large numbers and central limit theorems for piecewise deterministic processes taking values in Hilbert spaces to a master equation formulation of stochastic neuronal network models. These theorems are valid for processes taking values in Hilbert spaces, and by this are able to incorporate spatial structures of the underlying model. Mathematics Subject Classification (2000): 60F05, 60J25, 60J75, 92C20. PMID:23343328

  7. Stochastic Oscillations of General Relativistic Disks Described by a Fractional Langevin Equation with Fractional Gaussian Noise

    NASA Astrophysics Data System (ADS)

    Zhi-Yun, Wang; Pei-Jie, Chen

    2016-06-01

    A generalized Langevin equation driven by fractional Brownian motion is used to describe the vertical oscillations of general relativistic disks. By means of numerical calculation method, the displacements, velocities and luminosities of oscillating disks are explicitly obtained for different Hurst exponent H. The results show that as H increases, the energies and luminosities of oscillating disk are enhanced, and the spectral slope at high frequencies of the power spectrum density of disk luminosity is also increased. This could explain the observational features related to the Intra Day Variability of the BL Lac objects.

  8. Collective behavior of globally coupled Langevin equations with colored noise in the presence of stochastic resonance

    NASA Astrophysics Data System (ADS)

    Yang, Bo; Zhang, Xiao; Zhang, Lu; Luo, Mao-Kang

    2016-08-01

    The long-time collective behavior of globally coupled Langevin equations in a dichotomous fluctuating potential driven by a periodic source is investigated. By describing the collective behavior using the moments of the mean field and single-particle displacements, we study stochastic resonance and synchronization using the exact steady-state solutions and related stability criteria. Based on the simulation results and the criterion of the stationary regime, the notable differences between the stationary and nonstationary regimes are demonstrated. For the stationary regime, stochastic resonance with synchronization is discussed, and for the nonstationary regime, the volatility clustering phenomenon is observed.

  9. Time-local Heisenberg-Langevin equations and the driven qubit

    NASA Astrophysics Data System (ADS)

    Whalen, S. J.; Carmichael, H. J.

    2016-06-01

    The time-local master equation for a driven boson system interacting with a boson environment is derived by way of a time-local Heisenberg-Langevin equation. Extension to the driven qubit fails—except for weak excitation—due to the lost linearity of the system-environment interaction. We show that a reported time-local master equation for the driven qubit is incorrect. As a corollary to our demonstration, we also uncover odd asymptotic behavior in the "repackaged" time-local dynamics of a system driven to a far-from-equilibrium steady state: the density operator becomes steady while time-dependent coefficients oscillate (with periodic singularities) forever.

  10. Anomalous diffusion in nonhomogeneous media: Power spectral density of signals generated by time-subordinated nonlinear Langevin equations

    NASA Astrophysics Data System (ADS)

    Kazakevičius, R.; Ruseckas, J.

    2015-11-01

    Subdiffusive behavior of one-dimensional stochastic systems can be described by time-subordinated Langevin equations. The corresponding probability density satisfies the time-fractional Fokker-Planck equations. In the homogeneous systems the power spectral density of the signals generated by such Langevin equations has power-law dependency on the frequency with the exponent smaller than 1. In this paper we consider nonhomogeneous systems and show that in such systems the power spectral density can have power-law behavior with the exponent equal to or larger than 1 in a wide range of intermediate frequencies.

  11. Generalized Langevin equation with colored noise description of the stochastic oscillations of accretion disks

    NASA Astrophysics Data System (ADS)

    Harko, Tiberiu; Leung, Chun Sing; Mocanu, Gabriela

    2014-05-01

    We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects interacting with their external medium based on a generalized Langevin equation with colored noise and on the fluctuation-dissipation theorems. The former accounts for the general memory and retarded effects of the frictional force. The presence of the memory effects influences the response of the disk to external random interactions, and it modifies the dynamical behavior of the disk, as well as the energy dissipation processes. The generalized Langevin equation of the motion of the disk in the vertical direction is studied numerically, and the vertical displacements, velocities, and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases. The power spectral distribution of the disk luminosity is also obtained. As a possible astrophysical application of the formalism we investigate the possibility that the intra-day variability of the active galactic nuclei may be due to the stochastic disk instabilities. The perturbations due to colored/nontrivially correlated noise induce a complicated disk dynamics, which could explain some astrophysical observational features related to disk variability.

  12. Correlation functions for the fractional generalized Langevin equation in the presence of internal and external noise

    SciTech Connect

    Sandev, Trifce; Metzler, Ralf; Department of Physics, Tampere University of Technology, FI-33101 Tampere ; Tomovski, Živorad

    2014-02-15

    We study generalized fractional Langevin equations in the presence of a harmonic potential. General expressions for the mean velocity and particle displacement, the mean squared displacement, position and velocity correlation functions, as well as normalized displacement correlation function are derived. We report exact results for the cases of internal and external friction, that is, when the driving noise is either internal and thus the fluctuation-dissipation relation is fulfilled or when the noise is external. The asymptotic behavior of the generalized stochastic oscillator is investigated, and the case of high viscous damping (overdamped limit) is considered. Additional behaviors of the normalized displacement correlation functions different from those for the regular damped harmonic oscillator are observed. In addition, the cases of a constant external force and the force free case are obtained. The validity of the generalized Einstein relation for this process is discussed. The considered fractional generalized Langevin equation may be used to model anomalous diffusive processes including single file-type diffusion.

  13. A Bohmian approach to the non-Markovian non-linear Schrödinger–Langevin equation

    SciTech Connect

    Vargas, Andrés F.; Morales-Durán, Nicolás; Bargueño, Pedro

    2015-05-15

    In this work, a non-Markovian non-linear Schrödinger–Langevin equation is derived from the system-plus-bath approach. After analyzing in detail previous Markovian cases, Bohmian mechanics is shown to be a powerful tool for obtaining the desired generalized equation.

  14. Nonequilibrium processes from generalized Langevin equations: Realistic nanoscale systems connected to two thermal baths

    NASA Astrophysics Data System (ADS)

    Ness, H.; Genina, A.; Stella, L.; Lorenz, C. D.; Kantorovich, L.

    2016-05-01

    We extend the generalized Langevin equation (GLE) method [L. Stella, C. D. Lorenz, and L. Kantorovich, Phys. Rev. B 89, 134303 (2014), 10.1103/PhysRevB.89.134303] to model a central classical region connected to two realistic thermal baths at two different temperatures. In such nonequilibrium conditions a heat flow is established, via the central system, in between the two baths. The GLE-2B (GLE two baths) scheme permits us to have a realistic description of both the dissipative central system and its surrounding baths. Following the original GLE approach, the extended Langevin dynamics scheme is modified to take into account two sets of auxiliary degrees of freedom corresponding to the mapping of the vibrational properties of each bath. These auxiliary variables are then used to solve the non-Markovian dissipative dynamics of the central region. The resulting algorithm is used to study a model of a short Al nanowire connected to two baths. The results of the simulations using the GLE-2B approach are compared to the results of other simulations that were carried out using standard thermostatting approaches (based on Markovian Langevin and Nosé-Hoover thermostats). We concentrate on the steady-state regime and study the establishment of a local temperature profile within the system. The conditions for obtaining a flat profile or a temperature gradient are examined in detail, in agreement with earlier studies. The results show that the GLE-2B approach is able to treat, within a single scheme, two widely different thermal transport regimes, i.e., ballistic systems, with no temperature gradient, and diffusive systems with a temperature gradient.

  15. Non-Gaussian statistics, classical field theory, and realizable Langevin models

    SciTech Connect

    Krommes, J.A.

    1995-11-01

    The direct-interaction approximation (DIA) to the fourth-order statistic Z {approximately}{l_angle}{lambda}{psi}{sup 2}){sup 2}{r_angle}, where {lambda} is a specified operator and {psi} is a random field, is discussed from several points of view distinct from that of Chen et al. [Phys. Fluids A 1, 1844 (1989)]. It is shown that the formula for Z{sub DIA} already appeared in the seminal work of Martin, Siggia, and Rose (Phys. Rev. A 8, 423 (1973)] on the functional approach to classical statistical dynamics. It does not follow from the original generalized Langevin equation (GLE) of Leith [J. Atmos. Sd. 28, 145 (1971)] and Kraichnan [J. Fluid Mech. 41, 189 (1970)] (frequently described as an amplitude representation for the DIA), in which the random forcing is realized by a particular superposition of products of random variables. The relationship of that GLE to renormalized field theories with non-Gaussian corrections (``spurious vertices``) is described. It is shown how to derive an improved representation, that realizes cumulants through O({psi}{sup 4}), by adding to the GLE a particular non-Gaussian correction. A Markovian approximation Z{sub DIA}{sup M} to Z{sub DIA} is derived. Both Z{sub DIA} and Z{sub DIA}{sup M} incorrectly predict a Gaussian kurtosis for the steady state of a solvable three-mode example.

  16. Bistable systems with stochastic noise: virtues and limits of effective one-dimensional Langevin equations

    NASA Astrophysics Data System (ADS)

    Lucarini, V.; Faranda, D.; Willeit, M.

    2012-01-01

    The understanding of the statistical properties and of the dynamics of multistable systems is gaining more and more importance in a vast variety of scientific fields. This is especially relevant for the investigation of the tipping points of complex systems. Sometimes, in order to understand the time series of given observables exhibiting bimodal distributions, simple one-dimensional Langevin models are fitted to reproduce the observed statistical properties, and used to investing-ate the projected dynamics of the observable. This is of great relevance for studying potential catastrophic changes in the properties of the underlying system or resonant behaviours like those related to stochastic resonance-like mechanisms. In this paper, we propose a framework for encasing this kind of studies, using simple box models of the oceanic circulation and choosing as observable the strength of the thermohaline circulation. We study the statistical properties of the transitions between the two modes of operation of the thermohaline circulation under symmetric boundary forcings and test their agreement with simplified one-dimensional phenomenological theories. We extend our analysis to include stochastic resonance-like amplification processes. We conclude that fitted one-dimensional Langevin models, when closely scrutinised, may result to be more ad-hoc than they seem, lacking robustness and/or well-posedness. They should be treated with care, more as an empiric descriptive tool than as methodology with predictive power.

  17. Internal noise-driven generalized Langevin equation from a nonlocal continuum model.

    PubMed

    Sarkar, Saikat; Chowdhury, Shubhankar Roy; Roy, Debasish; Vasu, Ram Mohan

    2015-08-01

    Starting with a micropolar formulation, known to account for nonlocal microstructural effects at the continuum level, a generalized Langevin equation (GLE) for a particle, describing the predominant motion of a localized region through a single displacement degree of freedom, is derived. The GLE features a memory-dependent multiplicative or internal noise, which appears upon recognizing that the microrotation variables possess randomness owing to an uncertainty principle. Unlike its classical version, the present GLE qualitatively reproduces the experimentally measured fluctuations in the steady-state mean square displacement of scattering centers in a polyvinyl alcohol slab. The origin of the fluctuations is traced to nonlocal spatial interactions within the continuum, a phenomenon that is ubiquitous across a broad class of response regimes in solids and fluids. This renders the proposed GLE a potentially useful model in such cases. PMID:26382386

  18. Internal noise-driven generalized Langevin equation from a nonlocal continuum model

    NASA Astrophysics Data System (ADS)

    Sarkar, Saikat; Chowdhury, Shubhankar Roy; Roy, Debasish; Vasu, Ram Mohan

    2015-08-01

    Starting with a micropolar formulation, known to account for nonlocal microstructural effects at the continuum level, a generalized Langevin equation (GLE) for a particle, describing the predominant motion of a localized region through a single displacement degree of freedom, is derived. The GLE features a memory-dependent multiplicative or internal noise, which appears upon recognizing that the microrotation variables possess randomness owing to an uncertainty principle. Unlike its classical version, the present GLE qualitatively reproduces the experimentally measured fluctuations in the steady-state mean square displacement of scattering centers in a polyvinyl alcohol slab. The origin of the fluctuations is traced to nonlocal spatial interactions within the continuum, a phenomenon that is ubiquitous across a broad class of response regimes in solids and fluids. This renders the proposed GLE a potentially useful model in such cases.

  19. A note on the fluctuation-dissipation relation for the generalized Langevin equation with hydrodynamic backflow

    NASA Astrophysics Data System (ADS)

    Tóthová, Jana; Lisý, Vladimír

    2016-07-01

    This paper is devoted to finding the fluctuation-dissipation relation (FDR) for the generalized Langevin equation (GLE) with the Boussinesq-Basset (BB) force in which the Stokes friction is generalized to a convolution of a memory kernel with the velocity of a Brownian particle. First, the solution of such GLE with hydrodynamic backflow is obtained. Using this solution, we find in a simple and easily controllable way the time correlation function of the thermal force driving the particles. If the GLE is used with the original BB force for pure liquids, the FDR known from the literature is corrected. It is shown that in this case the FDR contains, in addition to the known term ∼t - 3 / 2, a more slowly decaying contribution ∼t - 1 / 2.

  20. Behavior of molecules on interstellar grains - Application of the Langevin equation and iterative extended Hueckel

    NASA Technical Reports Server (NTRS)

    Aronowitz, S.; Chang, S.

    1980-01-01

    The Langevin equation was used to explore an adsorbate desorption mechanism. Calculations were performed using iterative extended Hueckel on a silica model site with various small adsorbates, e.g., H, CH, OH, NO, CO. It was found that barriers to free traversal from one site to another are substantial (about 3-10 eV). A bootstrap desorption mechanism for some molecules in the process of forming at a site also became apparent from the calculations. The desorption mechanisms appear to be somewhat balanced by a counterforce - the attraction of sites for the newly desorbed molecule. The order of attraction to a silica grain site for the diatomic molecules considered was OH greater than CH greater than CO greater than NO, when these entities were sufficiently distant. The nature of the silica grain and that of the 'cold' desorption mechanism, when considered together, suggest that the abundance of very small grains might be less common than anticipated.

  1. Behavior of Molecules on Interstellar Grains: Application of the Langevin Equation and Iterative Extended Huckel

    NASA Technical Reports Server (NTRS)

    Aronowitz. Sheldon

    1980-01-01

    The Langevin equation was used to explore an adsorbate desorption mechanism. Calculations were performed using iterative extended Huckel on a silica model site with various small adsorbates, e.g., H, CH, OH, NO, CO. It was found that barriers to free traversal from one site to another are substantial (approximately 3 - 10 eV). A bootstrap desorption mechanism for some molecules in the process of forming at a site also became apparent from the calculations. The desorption mechanisms appear to be somewhat balanced by a counterforce--the attraction of sites for the newly desorbed molecule. The order of attraction to a silica grain site for the diatomic molecules considered was OH > CH > CO > NO, when these entities were sufficiently distant. The nature of the silica grain and that of the "cold" desorption mechanism, when considered together, suggest that the abundance of very small grains might be less common than anticipated.

  2. Variational superposed Gaussian approximation for time-dependent solutions of Langevin equations

    NASA Astrophysics Data System (ADS)

    Hasegawa, Yoshihiko

    2015-04-01

    We propose a variational superposed Gaussian approximation (VSGA) for dynamical solutions of Langevin equations subject to applied signals, determining time-dependent parameters of superposed Gaussian distributions by the variational principle. We apply the proposed VSGA to systems driven by a chaotic signal, where the conventional Fourier method cannot be adopted, and calculate the time evolution of probability density functions (PDFs) and moments. Both white and colored Gaussian noises terms are included to describe fluctuations. Our calculations show that time-dependent PDFs obtained by VSGA agree excellently with those obtained by Monte Carlo simulations. The correlation between the chaotic input signal and the mean response are also calculated as a function of the noise intensity, which confirms the occurrence of aperiodic stochastic resonance with both white and colored noises.

  3. Tracer dispersion simulation in low wind speed conditions with a new 2D Langevin equation system

    NASA Astrophysics Data System (ADS)

    Anfossi, D.; Alessandrini, S.; Trini Castelli, S.; Ferrero, E.; Oettl, D.; Degrazia, G.

    The simulation of atmospheric dispersion in low wind speed conditions (LW) is still recognised as a challenge for modellers. Recently, a new system of two coupled Langevin equations that explicitly accounts for meandering has been proposed. It is based on the study of turbulence and dispersion properties in LW. The new system was implemented in the Lagrangian stochastic particle models LAMBDA and GRAL. In this paper we present simulations with this new approach applying it to the tracer experiments carried out in LW by Idaho National Engineering Laboratory (INEL, USA) in 1974 and by the Graz University of Technology and CNR-Torino near Graz in 2003. To assess the improvement obtained with the present model with respect to previous models not taking into account the meandering effect, the simulations for the INEL experiments were also performed with the old version of LAMBDA. The results of the comparisons clearly indicate that the new approach improves the simulation results.

  4. Adjoint design sensitivity analysis of reduced atomic systems using generalized Langevin equation for lattice structures

    SciTech Connect

    Kim, Min-Geun; Jang, Hong-Lae; Cho, Seonho

    2013-05-01

    An efficient adjoint design sensitivity analysis method is developed for reduced atomic systems. A reduced atomic system and the adjoint system are constructed in a locally confined region, utilizing generalized Langevin equation (GLE) for periodic lattice structures. Due to the translational symmetry of lattice structures, the size of time history kernel function that accounts for the boundary effects of the reduced atomic systems could be reduced to a single atom’s degrees of freedom. For the problems of highly nonlinear design variables, the finite difference method is impractical for its inefficiency and inaccuracy. However, the adjoint method is very efficient regardless of the number of design variables since one additional time integration is required for the adjoint GLE. Through numerical examples, the derived adjoint sensitivity turns out to be accurate and efficient through the comparison with finite difference sensitivity.

  5. Crossover behavior of stock returns and mean square displacements of particles governed by the Langevin equation

    NASA Astrophysics Data System (ADS)

    Ma, Wen-Jong; Wang, Shih-Chieh; Chen, Chi-Ning; Hu, Chin-Kun

    2013-06-01

    It is found that the mean square log-returns calculated from the high-frequency one-day moving average of US and Taiwan stocks with the time internal τ show ballistic behavior \\theta \\tau^{\\alpha_1} with the exponent \\alpha_1 \\approx 2 for small τ and show diffusion-like behavior D \\tau^{\\alpha_2} with the exponent \\alpha_2 \\approx 1 for large τ. Such a crossover behavior can be well described by the mean square displacements of particles governed by the Langevin equation of motion. Thus, θ and D can be considered, respectively, as the temperature-like and diffusivity-like kinetic parameters of the market, and they can be used to characterize the behavior of the market.

  6. Composite generalized Langevin equation for Brownian motion in different hydrodynamic and adhesion regimes.

    PubMed

    Yu, Hsiu-Yu; Eckmann, David M; Ayyaswamy, Portonovo S; Radhakrishnan, Ravi

    2015-05-01

    We present a composite generalized Langevin equation as a unified framework for bridging the hydrodynamic, Brownian, and adhesive spring forces associated with a nanoparticle at different positions from a wall, namely, a bulklike regime, a near-wall regime, and a lubrication regime. The particle velocity autocorrelation function dictates the dynamical interplay between the aforementioned forces, and our proposed methodology successfully captures the well-known hydrodynamic long-time tail with context-dependent scaling exponents and oscillatory behavior due to the binding interaction. Employing the reactive flux formalism, we analyze the effect of hydrodynamic variables on the particle trajectory and characterize the transient kinetics of a particle crossing a predefined milestone. The results suggest that both wall-hydrodynamic interactions and adhesion strength impact the particle kinetics. PMID:26066173

  7. Current-induced atomic dynamics, instabilities, and Raman signals: Quasiclassical Langevin equation approach

    NASA Astrophysics Data System (ADS)

    Lü, Jing-Tao; Brandbyge, Mads; Hedegård, Per; Todorov, Tchavdar N.; Dundas, Daniel

    2012-06-01

    We derive and employ a semiclassical Langevin equation obtained from path integrals to describe the ionic dynamics of a molecular junction in the presence of electrical current. The electronic environment serves as an effective nonequilibrium bath. The bath results in random forces describing Joule heating, current-induced forces including the nonconservative wind force, dissipative frictional forces, and an effective Lorentz-type force due to the Berry phase of the nonequilibrium electrons. Using a generic two-level molecular model, we highlight the importance of both current-induced forces and Joule heating for the stability of the system. We compare the impact of the different forces, and the wide-band approximation for the electronic structure on our result. We examine the current-induced instabilities (excitation of runaway “waterwheel” modes) and investigate the signature of these in the Raman signals.

  8. Biomolecular folding rates as understood from single-reaction-coordinate Langevin dynamics and Kramers' theory

    NASA Astrophysics Data System (ADS)

    Kabir, Md Adnan

    Langevin dynamics was used to model the folding and unfolding of simple, hairpin-like biomolecules whose ends are attached to laser-trapped beads, as occurs in optical tweezers experiments. The Langevin process was evolved numerically, using parameters motivated by real experimental systems. Folding trajectories were generated and analyzed to extract the folding rate as a function of the force applied to the beads. The observed rate was compared to the analytical predictions of Kramers' theory. Strong discrepancies were noted. The failure of the Kramers' theory was attributed to the slow dynamical response of the beads, which it does not account for. The results of this work highlight the necessity to include in the modeling the experimental systems that mediate force along the length of the biomolecule.

  9. Langevin Poisson-Boltzmann equation: point-like ions and water dipoles near a charged surface.

    PubMed

    Gongadze, Ekaterina; van Rienen, Ursula; Kralj-Iglič, Veronika; Iglič, Aleš

    2011-06-01

    Water ordering near a charged membrane surface is important for many biological processes such as binding of ligands to a membrane or transport of ions across it. In this work, the mean-field Poisson-Boltzmann theory for point-like ions, describing an electrolyte solution in contact with a planar charged surface, is modified by including the orientational ordering of water. Water molecules are considered as Langevin dipoles, while the number density of water is assumed to be constant everywhere in the electrolyte solution. It is shown that the dielectric permittivity of an electrolyte close to a charged surface is decreased due to the increased orientational ordering of water dipoles. The dielectric permittivity close to the charged surface is additionally decreased due to the finite size of ions and dipoles. PMID:21613667

  10. Analysis of porosity distribution of large-scale porous media and their reconstruction by Langevin equation.

    PubMed

    Jafari, G Reza; Sahimi, Muhammad; Rasaei, M Reza; Tabar, M Reza Rahimi

    2011-02-01

    Several methods have been developed in the past for analyzing the porosity and other types of well logs for large-scale porous media, such as oil reservoirs, as well as their permeability distributions. We developed a method for analyzing the porosity logs ϕ(h) (where h is the depth) and similar data that are often nonstationary stochastic series. In this method one first generates a new stationary series based on the original data, and then analyzes the resulting series. It is shown that the series based on the successive increments of the log y(h)=ϕ(h+δh)-ϕ(h) is a stationary and Markov process, characterized by a Markov length scale h(M). The coefficients of the Kramers-Moyal expansion for the conditional probability density function (PDF) P(y,h|y(0),h(0)) are then computed. The resulting PDFs satisfy a Fokker-Planck (FP) equation, which is equivalent to a Langevin equation for y(h) that provides probabilistic predictions for the porosity logs. We also show that the Hurst exponent H of the self-affine distributions, which have been used in the past to describe the porosity logs, is directly linked to the drift and diffusion coefficients that we compute for the FP equation. Also computed are the level-crossing probabilities that provide insight into identifying the high or low values of the porosity beyond the depth interval in which the data have been measured. PMID:21405908

  11. The Spatial Chemical Langevin and Reaction Diffusion Master Equations: Moments and Qualitative Solutions

    NASA Astrophysics Data System (ADS)

    Ghosh, Atiyo; Leier, Andre; Marquez-Lago, Tatiana

    2014-03-01

    Spatial stochastic effects are prevalent in many biological systems spanning a variety of scales, from intracellular (e.g. gene expression) to ecological (plankton aggregation). The most common ways of simulating such systems involve drawing sample paths from either the Reaction Diffusion Master Equation (RDME) or the Smoluchowski Equation, using methods such as Gillespie's Simulation Algorithm, Green's Function Reaction Dynamics and Single Particle Tracking. The simulation times of such techniques scale with the number of simulated particles, leading to much computational expense when considering large systems. The Spatial Chemical Langevin Equation (SCLE) can be simulated with fixed time intervals, independent of the number of particles, and can thus provide significant computational savings. However, very little work has been done to investigate the behavior of the SCLE. In this talk we summarize our findings on comparing the SCLE to the well-studied RDME. We use both analytical and numerical procedures to show when one should expect the moments of the SCLE to be close to the RDME, and also when they should differ.

  12. Generalized Langevin equation: An efficient approach to nonequilibrium molecular dynamics of open systems

    NASA Astrophysics Data System (ADS)

    Stella, L.; Lorenz, C. D.; Kantorovich, L.

    2014-04-01

    The generalized Langevin equation (GLE) has been recently suggested to simulate the time evolution of classical solid and molecular systems when considering general nonequilibrium processes. In this approach, a part of the whole system (an open system), which interacts and exchanges energy with its dissipative environment, is studied. Because the GLE is derived by projecting out exactly the harmonic environment, the coupling to it is realistic, while the equations of motion are non-Markovian. Although the GLE formalism has already found promising applications, e.g., in nanotribology and as a powerful thermostat for equilibration in classical molecular dynamics simulations, efficient algorithms to solve the GLE for realistic memory kernels are highly nontrivial, especially if the memory kernels decay nonexponentially. This is due to the fact that one has to generate a colored noise and take account of the memory effects in a consistent manner. In this paper, we present a simple, yet efficient, algorithm for solving the GLE for practical memory kernels and we demonstrate its capability for the exactly solvable case of a harmonic oscillator coupled to a Debye bath.

  13. Non-Gaussian statistics, classical field theory, and realizable Langevin models

    SciTech Connect

    Krommes, J.A.

    1996-05-01

    The direct-interaction approximation (DIA) to the fourth-order statistic {ital Z}{approximately}{l_angle}({lambda}{psi}{sup 2}){sup 2}{r_angle}, where {lambda} is a specified operator and {psi} is a random field, is discussed from several points of view distinct from that of Chen {ital et} {ital al}. [Phys. Fluids A {bold 1}, 1844 (1989)]. It is shown that the formula for {ital Z}{sub DIA} already appeared in the seminal work of Martin, Siggia, and Rose [Phys. Rev. A {bold 8}, 423 (1973)] on the functional approach to classical statistical dynamics. It does not follow from the original generalized Langevin equation (GLE) of Leith [J. Atmos. Sci. {bold 28}, 145 (1971)] and Kraichnan [J. Fluid Mech. {bold 41}, 189 (1970)] (frequently described as an amplitude representation for the DIA), in which the random forcing is realized by a particular superposition of products of random variables. The relationship of that GLE to renormalized field theories with non-Gaussian corrections ({open_quote}{open_quote}spurious vertices{close_quote}{close_quote}) is described. It is shown how to derive an improved representation, which realizes cumulants through {ital O}({psi}{sup 4}), by adding to the GLE a particular non-Gaussian correction. A Markovian approximation {ital Z}{sub DIA}{sup {ital M}} to {ital Z}{sub DIA} is derived. Both {ital Z}{sub DIA} and {ital Z}{sub DIA}{sup {ital M}} incorrectly predict a Gaussian kurtosis for the steady state of a solvable three-mode example. {copyright} {ital 1996 The American Physical Society.}

  14. AQUASOL: An efficient solver for the dipolar Poisson–Boltzmann–Langevin equation

    PubMed Central

    Koehl, Patrice; Delarue, Marc

    2010-01-01

    The Poisson–Boltzmann (PB) formalism is among the most popular approaches to modeling the solvation of molecules. It assumes a continuum model for water, leading to a dielectric permittivity that only depends on position in space. In contrast, the dipolar Poisson–Boltzmann–Langevin (DPBL) formalism represents the solvent as a collection of orientable dipoles with nonuniform concentration; this leads to a nonlinear permittivity function that depends both on the position and on the local electric field at that position. The differences in the assumptions underlying these two models lead to significant differences in the equations they generate. The PB equation is a second order, elliptic, nonlinear partial differential equation (PDE). Its response coefficients correspond to the dielectric permittivity and are therefore constant within each subdomain of the system considered (i.e., inside and outside of the molecules considered). While the DPBL equation is also a second order, elliptic, nonlinear PDE, its response coefficients are nonlinear functions of the electrostatic potential. Many solvers have been developed for the PB equation; to our knowledge, none of these can be directly applied to the DPBL equation. The methods they use may adapt to the difference; their implementations however are PBE specific. We adapted the PBE solver originally developed by Holst and Saied [J. Comput. Chem. 16, 337 (1995)] to the problem of solving the DPBL equation. This solver uses a truncated Newton method with a multigrid preconditioner. Numerical evidences suggest that it converges for the DPBL equation and that the convergence is superlinear. It is found however to be slow and greedy in memory requirement for problems commonly encountered in computational biology and computational chemistry. To circumvent these problems, we propose two variants, a quasi-Newton solver based on a simplified, inexact Jacobian and an iterative self-consistent solver that is based directly on

  15. AQUASOL: An efficient solver for the dipolar Poisson-Boltzmann-Langevin equation.

    PubMed

    Koehl, Patrice; Delarue, Marc

    2010-02-14

    The Poisson-Boltzmann (PB) formalism is among the most popular approaches to modeling the solvation of molecules. It assumes a continuum model for water, leading to a dielectric permittivity that only depends on position in space. In contrast, the dipolar Poisson-Boltzmann-Langevin (DPBL) formalism represents the solvent as a collection of orientable dipoles with nonuniform concentration; this leads to a nonlinear permittivity function that depends both on the position and on the local electric field at that position. The differences in the assumptions underlying these two models lead to significant differences in the equations they generate. The PB equation is a second order, elliptic, nonlinear partial differential equation (PDE). Its response coefficients correspond to the dielectric permittivity and are therefore constant within each subdomain of the system considered (i.e., inside and outside of the molecules considered). While the DPBL equation is also a second order, elliptic, nonlinear PDE, its response coefficients are nonlinear functions of the electrostatic potential. Many solvers have been developed for the PB equation; to our knowledge, none of these can be directly applied to the DPBL equation. The methods they use may adapt to the difference; their implementations however are PBE specific. We adapted the PBE solver originally developed by Holst and Saied [J. Comput. Chem. 16, 337 (1995)] to the problem of solving the DPBL equation. This solver uses a truncated Newton method with a multigrid preconditioner. Numerical evidences suggest that it converges for the DPBL equation and that the convergence is superlinear. It is found however to be slow and greedy in memory requirement for problems commonly encountered in computational biology and computational chemistry. To circumvent these problems, we propose two variants, a quasi-Newton solver based on a simplified, inexact Jacobian and an iterative self-consistent solver that is based directly on the PBE

  16. The Schrödinger-Langevin equation with and without thermal fluctuations

    NASA Astrophysics Data System (ADS)

    Katz, R.; Gossiaux, P. B.

    2016-05-01

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

  17. Anomalous polymer dynamics is non-Markovian: memory effects and the generalized Langevin equation formulation

    NASA Astrophysics Data System (ADS)

    Panja, Debabrata

    2010-06-01

    Any first course on polymer physics teaches that the dynamics of a tagged monomer of a polymer is anomalously subdiffusive, i.e., the mean-square displacement of a tagged monomer increases as tα for some α < 1 until the terminal relaxation time τ of the polymer. Beyond time τ the motion of the tagged monomer becomes diffusive. Classical examples of anomalous dynamics in polymer physics are single polymeric systems, such as phantom Rouse, self-avoiding Rouse, self-avoiding Zimm, reptation, translocation through a narrow pore in a membrane, and many-polymeric systems such as polymer melts. In this pedagogical paper I report that all these instances of anomalous dynamics in polymeric systems are robustly characterized by power-law memory kernels within a unified generalized Langevin equation (GLE) scheme, and therefore are non-Markovian. The exponents of the power-law memory kernels are related to the relaxation response of the polymers to local strains, and are derived from the equilibrium statistical physics of polymers. The anomalous dynamics of a tagged monomer of a polymer in these systems is then reproduced from the power-law memory kernels of the GLE via the fluctuation-dissipation theorem (FDT). Using this GLE formulation I further show that the characteristics of the drifts caused by a (weak) applied field on these polymeric systems are also obtained from the corresponding memory kernels.

  18. Higher-order time integration of Coulomb collisions in a plasma using Langevin equations

    SciTech Connect

    Dimits, A. M.; Cohen, B. I.; Caflisch, R. E.; Rosin, M. S.; Ricketson, L. F.

    2013-02-08

    The extension of Langevin-equation Monte-Carlo algorithms for Coulomb collisions from the conventional Euler-Maruyama time integration to the next higher order of accuracy, the Milstein scheme, has been developed, implemented, and tested. This extension proceeds via a formulation of the angular scattering directly as stochastic differential equations in the two fixed-frame spherical-coordinate velocity variables. Results from the numerical implementation show the expected improvement [O(Δt) vs. O(Δt1/2)] in the strong convergence rate both for the speed |v| and angular components of the scattering. An important result is that this improved convergence is achieved for the angular component of the scattering if and only if the “area-integral” terms in the Milstein scheme are included. The resulting Milstein scheme is of value as a step towards algorithms with both improved accuracy and efficiency. These include both algorithms with improved convergence in the averages (weak convergence) and multi-time-level schemes. The latter have been shown to give a greatly reduced cost for a given overall error level when compared with conventional Monte-Carlo schemes, and their performance is improved considerably when the Milstein algorithm is used for the underlying time advance versus the Euler-Maruyama algorithm. A new method for sampling the area integrals is given which is a simplification of an earlier direct method and which retains high accuracy. Lastly, this method, while being useful in its own right because of its relative simplicity, is also expected to considerably reduce the computational requirements for the direct conditional sampling of the area integrals that is needed for adaptive strong integration.

  19. Approximate method for stochastic chemical kinetics with two-time scales by chemical Langevin equations.

    PubMed

    Wu, Fuke; Tian, Tianhai; Rawlings, James B; Yin, George

    2016-05-01

    The frequently used reduction technique is based on the chemical master equation for stochastic chemical kinetics with two-time scales, which yields the modified stochastic simulation algorithm (SSA). For the chemical reaction processes involving a large number of molecular species and reactions, the collection of slow reactions may still include a large number of molecular species and reactions. Consequently, the SSA is still computationally expensive. Because the chemical Langevin equations (CLEs) can effectively work for a large number of molecular species and reactions, this paper develops a reduction method based on the CLE by the stochastic averaging principle developed in the work of Khasminskii and Yin [SIAM J. Appl. Math. 56, 1766-1793 (1996); ibid. 56, 1794-1819 (1996)] to average out the fast-reacting variables. This reduction method leads to a limit averaging system, which is an approximation of the slow reactions. Because in the stochastic chemical kinetics, the CLE is seen as the approximation of the SSA, the limit averaging system can be treated as the approximation of the slow reactions. As an application, we examine the reduction of computation complexity for the gene regulatory networks with two-time scales driven by intrinsic noise. For linear and nonlinear protein production functions, the simulations show that the sample average (expectation) of the limit averaging system is close to that of the slow-reaction process based on the SSA. It demonstrates that the limit averaging system is an efficient approximation of the slow-reaction process in the sense of the weak convergence. PMID:27155630

  20. Approximate method for stochastic chemical kinetics with two-time scales by chemical Langevin equations

    NASA Astrophysics Data System (ADS)

    Wu, Fuke; Tian, Tianhai; Rawlings, James B.; Yin, George

    2016-05-01

    The frequently used reduction technique is based on the chemical master equation for stochastic chemical kinetics with two-time scales, which yields the modified stochastic simulation algorithm (SSA). For the chemical reaction processes involving a large number of molecular species and reactions, the collection of slow reactions may still include a large number of molecular species and reactions. Consequently, the SSA is still computationally expensive. Because the chemical Langevin equations (CLEs) can effectively work for a large number of molecular species and reactions, this paper develops a reduction method based on the CLE by the stochastic averaging principle developed in the work of Khasminskii and Yin [SIAM J. Appl. Math. 56, 1766-1793 (1996); ibid. 56, 1794-1819 (1996)] to average out the fast-reacting variables. This reduction method leads to a limit averaging system, which is an approximation of the slow reactions. Because in the stochastic chemical kinetics, the CLE is seen as the approximation of the SSA, the limit averaging system can be treated as the approximation of the slow reactions. As an application, we examine the reduction of computation complexity for the gene regulatory networks with two-time scales driven by intrinsic noise. For linear and nonlinear protein production functions, the simulations show that the sample average (expectation) of the limit averaging system is close to that of the slow-reaction process based on the SSA. It demonstrates that the limit averaging system is an efficient approximation of the slow-reaction process in the sense of the weak convergence.

  1. Inclusion of trial functions in the Langevin equation path integral ground state method: Application to parahydrogen clusters and their isotopologues

    NASA Astrophysics Data System (ADS)

    Schmidt, Matthew; Constable, Steve; Ing, Christopher; Roy, Pierre-Nicholas

    2014-06-01

    We developed and studied the implementation of trial wavefunctions in the newly proposed Langevin equation Path Integral Ground State (LePIGS) method [S. Constable, M. Schmidt, C. Ing, T. Zeng, and P.-N. Roy, J. Phys. Chem. A 117, 7461 (2013)]. The LePIGS method is based on the Path Integral Ground State (PIGS) formalism combined with Path Integral Molecular Dynamics sampling using a Langevin equation based sampling of the canonical distribution. This LePIGS method originally incorporated a trivial trial wavefunction, ψT, equal to unity. The present paper assesses the effectiveness of three different trial wavefunctions on three isotopes of hydrogen for cluster sizes N = 4, 8, and 13. The trial wavefunctions of interest are the unity trial wavefunction used in the original LePIGS work, a Jastrow trial wavefunction that includes correlations due to hard-core repulsions, and a normal mode trial wavefunction that includes information on the equilibrium geometry. Based on this analysis, we opt for the Jastrow wavefunction to calculate energetic and structural properties for parahydrogen, orthodeuterium, and paratritium clusters of size N = 4 - 19, 33. Energetic and structural properties are obtained and compared to earlier work based on Monte Carlo PIGS simulations to study the accuracy of the proposed approach. The new results for paratritium clusters will serve as benchmark for future studies. This paper provides a detailed, yet general method for optimizing the necessary parameters required for the study of the ground state of a large variety of systems.

  2. Inclusion of trial functions in the Langevin equation path integral ground state method: Application to parahydrogen clusters and their isotopologues

    SciTech Connect

    Schmidt, Matthew; Constable, Steve; Ing, Christopher; Roy, Pierre-Nicholas

    2014-06-21

    We developed and studied the implementation of trial wavefunctions in the newly proposed Langevin equation Path Integral Ground State (LePIGS) method [S. Constable, M. Schmidt, C. Ing, T. Zeng, and P.-N. Roy, J. Phys. Chem. A 117, 7461 (2013)]. The LePIGS method is based on the Path Integral Ground State (PIGS) formalism combined with Path Integral Molecular Dynamics sampling using a Langevin equation based sampling of the canonical distribution. This LePIGS method originally incorporated a trivial trial wavefunction, ψ{sub T}, equal to unity. The present paper assesses the effectiveness of three different trial wavefunctions on three isotopes of hydrogen for cluster sizes N = 4, 8, and 13. The trial wavefunctions of interest are the unity trial wavefunction used in the original LePIGS work, a Jastrow trial wavefunction that includes correlations due to hard-core repulsions, and a normal mode trial wavefunction that includes information on the equilibrium geometry. Based on this analysis, we opt for the Jastrow wavefunction to calculate energetic and structural properties for parahydrogen, orthodeuterium, and paratritium clusters of size N = 4 − 19, 33. Energetic and structural properties are obtained and compared to earlier work based on Monte Carlo PIGS simulations to study the accuracy of the proposed approach. The new results for paratritium clusters will serve as benchmark for future studies. This paper provides a detailed, yet general method for optimizing the necessary parameters required for the study of the ground state of a large variety of systems.

  3. Molecular dynamics and analytical Langevin equation approach for the self-diffusion constant of an anisotropic fluid.

    PubMed

    Colmenares, Pedro J; López, Floralba; Olivares-Rivas, Wilmer

    2009-12-01

    We carried out a molecular-dynamics (MD) study of the self-diffusion tensor of a Lennard-Jones-type fluid, confined in a slit pore with attractive walls. We developed Bayesian equations, which modify the virtual layer sampling method proposed by Liu, Harder, and Berne (LHB) [P. Liu, E. Harder, and B. J. Berne, J. Phys. Chem. B 108, 6595 (2004)]. Additionally, we obtained an analytical solution for the corresponding nonhomogeneous Langevin equation. The expressions found for the mean-squared displacement in the layers contain naturally a modification due to the mean force in the transverse component in terms of the anisotropic diffusion constants and mean exit time. Instead of running a time consuming dual MD-Langevin simulation dynamics, as proposed by LHB, our expression was used to fit the MD data in the entire survival time interval not only for the parallel but also for the perpendicular direction. The only fitting parameter was the diffusion constant in each layer. PMID:20365134

  4. Molecular dynamics and analytical Langevin equation approach for the self-diffusion constant of an anisotropic fluid

    NASA Astrophysics Data System (ADS)

    Colmenares, Pedro J.; López, Floralba; Olivares-Rivas, Wilmer

    2009-12-01

    We carried out a molecular-dynamics (MD) study of the self-diffusion tensor of a Lennard-Jones-type fluid, confined in a slit pore with attractive walls. We developed Bayesian equations, which modify the virtual layer sampling method proposed by Liu, Harder, and Berne (LHB) [P. Liu, E. Harder, and B. J. Berne, J. Phys. Chem. B 108, 6595 (2004)]. Additionally, we obtained an analytical solution for the corresponding nonhomogeneous Langevin equation. The expressions found for the mean-squared displacement in the layers contain naturally a modification due to the mean force in the transverse component in terms of the anisotropic diffusion constants and mean exit time. Instead of running a time consuming dual MD-Langevin simulation dynamics, as proposed by LHB, our expression was used to fit the MD data in the entire survival time interval not only for the parallel but also for the perpendicular direction. The only fitting parameter was the diffusion constant in each layer.

  5. Distributional behaviors of time-averaged observables in the Langevin equation with fluctuating diffusivity: Normal diffusion but anomalous fluctuations

    NASA Astrophysics Data System (ADS)

    Akimoto, Takuma; Yamamoto, Eiji

    2016-06-01

    We consider the Langevin equation with dichotomously fluctuating diffusivity, where the diffusion coefficient changes dichotomously over time, in order to study fluctuations of time-averaged observables in temporally heterogeneous diffusion processes. We find that the time-averaged mean-square displacement (TMSD) can be represented by the occupation time of a state in the asymptotic limit of the measurement time and hence occupation time statistics is a powerful tool for calculating the TMSD in the model. We show that the TMSD increases linearly with time (normal diffusion) but the time-averaged diffusion coefficients are intrinsically random when the mean sojourn time for one of the states diverges, i.e., intrinsic nonequilibrium processes. Thus, we find that temporally heterogeneous environments provide anomalous fluctuations of time-averaged diffusivity, which have relevance to large fluctuations of the diffusion coefficients obtained by single-particle-tracking trajectories in experiments.

  6. Green functions and Langevin equations for nonlinear diffusion equations: A comment on ‘Markov processes, Hurst exponents, and nonlinear diffusion equations’ by Bassler et al.

    NASA Astrophysics Data System (ADS)

    Frank, T. D.

    2008-02-01

    We discuss two central claims made in the study by Bassler et al. [K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369 (2006) 343]. Bassler et al. claimed that Green functions and Langevin equations cannot be defined for nonlinear diffusion equations. In addition, they claimed that nonlinear diffusion equations are linear partial differential equations disguised as nonlinear ones. We review bottom-up and top-down approaches that have been used in the literature to derive Green functions for nonlinear diffusion equations and, in doing so, show that the first claim needs to be revised. We show that the second claim as well needs to be revised. To this end, we point out similarities and differences between non-autonomous linear Fokker-Planck equations and autonomous nonlinear Fokker-Planck equations. In this context, we raise the question whether Bassler et al.’s approach to financial markets is physically plausible because it necessitates the introduction of external traders and causes. Such external entities can easily be eliminated when taking self-organization principles and concepts of nonextensive thermostatistics into account and modeling financial processes by means of nonlinear Fokker-Planck equations.

  7. Notes on the Langevin model for turbulent diffusion of ``marked`` particles

    SciTech Connect

    Rodean, H.C.

    1994-01-26

    Three models for scalar diffusion in turbulent flow (eddy diffusivity, random displacement, and on the Langevin equation) are briefly described. These models random velocity increment based Fokker-Planck equation is introduced as are then examined in more detail in the reverse order. The Fokker-Planck equation is the Eulerian equivalent of the Lagrangian Langevin equation, and the derivation of e outlined. The procedure for obtaining the deterministic and stochastic components of the Langevin equation from Kolmogorov`s 1941 inertial range theory and the Fokker-Planck equation is described. it is noted that a unique form of the Langevin equation can be determined for diffusion in one dimension but not in two or three. The Langevin equation for vertical diffusion in the non-Gaussian convective boundary layer is presented and successively simplified for Gaussian inhomogeneous turbulence and Gaussian homogeneous turbulence in turn. The Langevin equation for Gaussian inhomogeneous turbulence is mathematically transformed into the random displacement model. It is shown how the Fokker-Planck equation for the random displacement model is identical in form to the partial differential equation for the eddy diffusivity model. It is noted that the Langevin model is applicable in two cases in which the other two are not valid: (1) very close in time and distance to the point of scalar release and (2) the non-Gaussian convective boundary layer. The two- and three-dimensional cases are considered in Part III.

  8. Fluctuations in reactive networks subject to extrinsic noise studied in the framework of the chemical Langevin equation

    NASA Astrophysics Data System (ADS)

    Berthoumieux, H.

    2016-07-01

    Theoretical and experimental studies have shown that the fluctuations of in vivo systems break the fluctuation-dissipation theorem. One can thus ask what information is contained in the correlation functions of protein concentrations and how they relate to the response of the reactive network to a perturbation. Answers to these questions are of prime importance to extract meaningful parameters from the in vivo fluorescence correlation spectroscopy data. In this paper we study the fluctuations of the concentration of a reactive species involved in a cyclic network that is in a nonequilibrium steady state perturbed by a noisy force, taking into account both the breaking of detailed balance and extrinsic noises. Using a generic model for the network and the extrinsic noise, we derive a chemical Langevin equation that describes the dynamics of the system, we determine the expressions of the correlation functions of the concentrations, and we estimate the deviation of the fluctuation-dissipation theorem and the range of parameters in which an effective temperature can be defined.

  9. Fluctuations in reactive networks subject to extrinsic noise studied in the framework of the chemical Langevin equation.

    PubMed

    Berthoumieux, H

    2016-07-01

    Theoretical and experimental studies have shown that the fluctuations of in vivo systems break the fluctuation-dissipation theorem. One can thus ask what information is contained in the correlation functions of protein concentrations and how they relate to the response of the reactive network to a perturbation. Answers to these questions are of prime importance to extract meaningful parameters from the in vivo fluorescence correlation spectroscopy data. In this paper we study the fluctuations of the concentration of a reactive species involved in a cyclic network that is in a nonequilibrium steady state perturbed by a noisy force, taking into account both the breaking of detailed balance and extrinsic noises. Using a generic model for the network and the extrinsic noise, we derive a chemical Langevin equation that describes the dynamics of the system, we determine the expressions of the correlation functions of the concentrations, and we estimate the deviation of the fluctuation-dissipation theorem and the range of parameters in which an effective temperature can be defined. PMID:27575151

  10. Self-assembly of nanocomponents into composite structures: Derivation and simulation of Langevin equations

    NASA Astrophysics Data System (ADS)

    Pankavich, S.; Shreif, Z.; Miao, Y.; Ortoleva, P.

    2009-05-01

    The kinetics of the self-assembly of nanocomponents into a virus, nanocapsule, or other composite structure is analyzed via a multiscale approach. The objective is to achieve predictability and to preserve key atomic-scale features that underlie the formation and stability of the composite structures. We start with an all-atom description, the Liouville equation, and the order parameters characterizing nanoscale features of the system. An equation of Smoluchowski type for the stochastic dynamics of the order parameters is derived from the Liouville equation via a multiscale perturbation technique. The self-assembly of composite structures from nanocomponents with internal atomic structure is analyzed and growth rates are derived. Applications include the assembly of a viral capsid from capsomers, a ribosome from its major subunits, and composite materials from fibers and nanoparticles. Our approach overcomes errors in other coarse-graining methods, which neglect the influence of the nanoscale configuration on the atomistic fluctuations. We account for the effect of order parameters on the statistics of the atomistic fluctuations, which contribute to the entropic and average forces driving order parameter evolution. This approach enables an efficient algorithm for computer simulation of self-assembly, whereas other methods severely limit the timestep due to the separation of diffusional and complexing characteristic times. Given that our approach does not require recalibration with each new application, it provides a way to estimate assembly rates and thereby facilitate the discovery of self-assembly pathways and kinetic dead-end structures.

  11. Self-assembly of nanocomponents into composite structures: derivation and simulation of Langevin equations.

    PubMed

    Pankavich, S; Shreif, Z; Miao, Y; Ortoleva, P

    2009-05-21

    The kinetics of the self-assembly of nanocomponents into a virus, nanocapsule, or other composite structure is analyzed via a multiscale approach. The objective is to achieve predictability and to preserve key atomic-scale features that underlie the formation and stability of the composite structures. We start with an all-atom description, the Liouville equation, and the order parameters characterizing nanoscale features of the system. An equation of Smoluchowski type for the stochastic dynamics of the order parameters is derived from the Liouville equation via a multiscale perturbation technique. The self-assembly of composite structures from nanocomponents with internal atomic structure is analyzed and growth rates are derived. Applications include the assembly of a viral capsid from capsomers, a ribosome from its major subunits, and composite materials from fibers and nanoparticles. Our approach overcomes errors in other coarse-graining methods, which neglect the influence of the nanoscale configuration on the atomistic fluctuations. We account for the effect of order parameters on the statistics of the atomistic fluctuations, which contribute to the entropic and average forces driving order parameter evolution. This approach enables an efficient algorithm for computer simulation of self-assembly, whereas other methods severely limit the timestep due to the separation of diffusional and complexing characteristic times. Given that our approach does not require recalibration with each new application, it provides a way to estimate assembly rates and thereby facilitate the discovery of self-assembly pathways and kinetic dead-end structures. PMID:19466829

  12. The generalized Langevin equation revisited: Analytical expressions for the persistence dynamics of a viscous fluid under a time dependent external force

    NASA Astrophysics Data System (ADS)

    Olivares-Rivas, Wilmer; Colmenares, Pedro J.

    2016-09-01

    The non-static generalized Langevin equation and its corresponding Fokker-Planck equation for the position of a viscous fluid particle were solved in closed form for a time dependent external force. Its solution for a constant external force was obtained analytically. The non-Markovian stochastic differential equation, associated to the dynamics of the position under a colored noise, was then applied to the description of the dynamics and persistence time of particles constrained within absorbing barriers. Comparisons with molecular dynamics were very satisfactory.

  13. Fluctuation analysis of time-averaged mean-square displacement for the Langevin equation with time-dependent and fluctuating diffusivity

    NASA Astrophysics Data System (ADS)

    Uneyama, Takashi; Miyaguchi, Tomoshige; Akimoto, Takuma

    2015-09-01

    The mean-square displacement (MSD) is widely utilized to study the dynamical properties of stochastic processes. The time-averaged MSD (TAMSD) provides some information on the dynamics which cannot be extracted from the ensemble-averaged MSD. In particular, the relative standard deviation (RSD) of the TAMSD can be utilized to study the long-time relaxation behavior. In this work, we consider a class of Langevin equations which are multiplicatively coupled to time-dependent and fluctuating diffusivities. Various interesting dynamics models such as entangled polymers and supercooled liquids can be interpreted as the Langevin equations with time-dependent and fluctuating diffusivities. We derive a general formula for the RSD of the TAMSD for the Langevin equation with the time-dependent and fluctuating diffusivity. We show that the RSD can be expressed in terms of the correlation function of the diffusivity. The RSD exhibits the crossover at the long time region. The crossover time is related to a weighted average relaxation time for the diffusivity. Thus the crossover time gives some information on the relaxation time of fluctuating diffusivity which cannot be extracted from the ensemble-averaged MSD. We discuss the universality and possible applications of the formula via some simple examples.

  14. Models for microtubule cargo transport coupling the Langevin equation to stochastic stepping motor dynamics: Caring about fluctuations

    NASA Astrophysics Data System (ADS)

    Bouzat, Sebastián

    2016-01-01

    One-dimensional models coupling a Langevin equation for the cargo position to stochastic stepping dynamics for the motors constitute a relevant framework for analyzing multiple-motor microtubule transport. In this work we explore the consistence of these models focusing on the effects of the thermal noise. We study how to define consistent stepping and detachment rates for the motors as functions of the local forces acting on them in such a way that the cargo velocity and run-time match previously specified functions of the external load, which are set on the base of experimental results. We show that due to the influence of the thermal fluctuations this is not a trivial problem, even for the single-motor case. As a solution, we propose a motor stepping dynamics which considers memory on the motor force. This model leads to better results for single-motor transport than the approaches previously considered in the literature. Moreover, it gives a much better prediction for the stall force of the two-motor case, highly compatible with the experimental findings. We also analyze the fast fluctuations of the cargo position and the influence of the viscosity, comparing the proposed model to the standard one, and we show how the differences on the single-motor dynamics propagate to the multiple motor situations. Finally, we find that the one-dimensional character of the models impede an appropriate description of the fast fluctuations of the cargo position at small loads. We show how this problem can be solved by considering two-dimensional models.

  15. Models for microtubule cargo transport coupling the Langevin equation to stochastic stepping motor dynamics: Caring about fluctuations.

    PubMed

    Bouzat, Sebastián

    2016-01-01

    One-dimensional models coupling a Langevin equation for the cargo position to stochastic stepping dynamics for the motors constitute a relevant framework for analyzing multiple-motor microtubule transport. In this work we explore the consistence of these models focusing on the effects of the thermal noise. We study how to define consistent stepping and detachment rates for the motors as functions of the local forces acting on them in such a way that the cargo velocity and run-time match previously specified functions of the external load, which are set on the base of experimental results. We show that due to the influence of the thermal fluctuations this is not a trivial problem, even for the single-motor case. As a solution, we propose a motor stepping dynamics which considers memory on the motor force. This model leads to better results for single-motor transport than the approaches previously considered in the literature. Moreover, it gives a much better prediction for the stall force of the two-motor case, highly compatible with the experimental findings. We also analyze the fast fluctuations of the cargo position and the influence of the viscosity, comparing the proposed model to the standard one, and we show how the differences on the single-motor dynamics propagate to the multiple motor situations. Finally, we find that the one-dimensional character of the models impede an appropriate description of the fast fluctuations of the cargo position at small loads. We show how this problem can be solved by considering two-dimensional models. PMID:26871095

  16. PDF model based on Langevin equation for polydispersed two-phase flows applied to a bluff-body gas-solid flow

    NASA Astrophysics Data System (ADS)

    Minier, Jean-Pierre; Peirano, Eric; Chibbaro, Sergio

    2004-07-01

    The aim of the paper is to discuss the main characteristics of a complete theoretical and numerical model for turbulent polydispersed two-phase flows, pointing out some specific issues. The theoretical details of the model have already been presented [Minier and Peirano, Phys. Rep. 352, 1 (2001)]. Consequently, the present work is mainly focused on complementary aspects that are often overlooked and that require particular attention. In particular, the following points are analyzed: the necessity to add an extra term in the equation for the velocity of the fluid seen in the case of two-way coupling, the theoretical and numerical evaluations of particle averages and the fulfillment of the particle mass-continuity constraint. The theoretical model is developed within the probability density function (PDF) formalism. The important physical choice of the state vector variables is first discussed and the model is then expressed as a stochastic differential equation written in continuous time (Langevin equations) for the velocity of the fluid seen. The interests and limitations of Langevin equations, compared to the single-phase case, are reviewed. From the numerical point of view, the model corresponds to a hybrid Eulerian/Lagrangian approach where the fluid and particle phases are simulated by different methods. Important aspects of the Monte Carlo particle/mesh numerical method are emphasized. Finally, the complete model is validated and its performance is assessed by simulating a bluff-body case with an important recirculation zone and in which two-way coupling is noticeable.

  17. Two critical issues in Langevin simulation of gas flows

    NASA Astrophysics Data System (ADS)

    Zhang, Jun; Fan, Jing

    2014-12-01

    A stochastic algorithm based on the Langevin equation has been recently proposed to simulate rarefied gas flows. Compared with the direct simulation Monte Carlo (DSMC) method, the Langevin method is more efficient in simulating small Knudsen number flows. While it is well-known that the cell sizes and time steps should be smaller than the mean free path and the mean collision time, respectively, in DSMC simulations, the Langevin equation uses a drift term and a diffusion term to describe molecule movements, so no direct molecular collisions have to be modeled. This enables the Langevin simulation to proceed with a much larger time step than that in the DSMC method. Two critical issues in Langevin simulation are addressed in this paper. The first issue is how to reproduce the transport properties as that described by kinetic theory. Transport coefficients predicted by Langevin equation are obtained by using Green-Kubo formulae. The second issue is numerical scheme with boundary conditions. We present two schemes corresponding to small time step and large time step, respectively. For small time step, the scheme is similar to DSMC method as the update of positions and velocities are uncoupled; for large time step, we present an analytical solution of the hitting time, which is the crucial factor for accurate simulation. Velocity-Couette flow, thermal-Couette flow, Rayleigh-Bénard flow and wall-confined problem are simulated by using these two schemes. Our study shows that Langevin simulation is a promising tool to investigate small Knudsen number flows.

  18. Two critical issues in Langevin simulation of gas flows

    SciTech Connect

    Zhang, Jun; Fan, Jing

    2014-12-09

    A stochastic algorithm based on the Langevin equation has been recently proposed to simulate rarefied gas flows. Compared with the direct simulation Monte Carlo (DSMC) method, the Langevin method is more efficient in simulating small Knudsen number flows. While it is well-known that the cell sizes and time steps should be smaller than the mean free path and the mean collision time, respectively, in DSMC simulations, the Langevin equation uses a drift term and a diffusion term to describe molecule movements, so no direct molecular collisions have to be modeled. This enables the Langevin simulation to proceed with a much larger time step than that in the DSMC method. Two critical issues in Langevin simulation are addressed in this paper. The first issue is how to reproduce the transport properties as that described by kinetic theory. Transport coefficients predicted by Langevin equation are obtained by using Green-Kubo formulae. The second issue is numerical scheme with boundary conditions. We present two schemes corresponding to small time step and large time step, respectively. For small time step, the scheme is similar to DSMC method as the update of positions and velocities are uncoupled; for large time step, we present an analytical solution of the hitting time, which is the crucial factor for accurate simulation. Velocity-Couette flow, thermal-Couette flow, Rayleigh-Bénard flow and wall-confined problem are simulated by using these two schemes. Our study shows that Langevin simulation is a promising tool to investigate small Knudsen number flows.

  19. Localised distributions and criteria for correctness in complex Langevin dynamics

    SciTech Connect

    Aarts, Gert; Giudice, Pietro; Seiler, Erhard

    2013-10-15

    Complex Langevin dynamics can solve the sign problem appearing in numerical simulations of theories with a complex action. In order to justify the procedure, it is important to understand the properties of the real and positive distribution, which is effectively sampled during the stochastic process. In the context of a simple model, we study this distribution by solving the Fokker–Planck equation as well as by brute force and relate the results to the recently derived criteria for correctness. We demonstrate analytically that it is possible that the distribution has support in a strip in the complexified configuration space only, in which case correct results are expected. -- Highlights: •Characterisation of the equilibrium distribution sampled in complex Langevin dynamics. •Connection between criteria for correctness and breakdown. •Solution of the Fokker–Planck equation in the case of real noise. •Analytical determination of support in complexified space.

  20. On the theory of Brownian motion with the Alder-Wainwright effect

    NASA Astrophysics Data System (ADS)

    Okabe, Yasunori

    1986-12-01

    The Stokes-Boussinesq-Langevin equation, which describes the time evolution of Brownian motion with the Alder-Wainwright effect, can be treated in the framework of the theory of KMO-Langevin equations which describe the time evolution of a real, stationary Gaussian process with T-positivity (reflection positivity) originating in axiomatic quantum field theory. After proving the fluctuation-dissipation theorems for KMO-Langevin equations, we obtain an explicit formula for the deviation from the classical Einstein relation that occurs in the Stokes-Boussinesq-Langevin equation with a white noise as its random force. We are interested in whether or not it can be measured experimentally.

  1. Gauge cooling for the singular-drift problem in the complex Langevin method — a test in Random Matrix Theory for finite density QCD

    NASA Astrophysics Data System (ADS)

    Nagata, Keitaro; Nishimura, Jun; Shimasaki, Shinji

    2016-07-01

    Recently, the complex Langevin method has been applied successfully to finite density QCD either in the deconfinement phase or in the heavy dense limit with the aid of a new technique called the gauge cooling. In the confinement phase with light quarks, however, convergence to wrong limits occurs due to the singularity in the drift term caused by small eigenvalues of the Dirac operator including the mass term. We propose that this singular-drift problem should also be overcome by the gauge cooling with different criteria for choosing the complexified gauge transformation. The idea is tested in chiral Random Matrix Theory for finite density QCD, where exact results are reproduced at zero temperature with light quarks. It is shown that the gauge cooling indeed changes drastically the eigenvalue distribution of the Dirac operator measured during the Langevin process. Despite its non-holomorphic nature, this eigenvalue distribution has a universal diverging behavior at the origin in the chiral limit due to a generalized Banks-Casher relation as we confirm explicitly.

  2. Nonlinear quantum equations: Classical field theory

    SciTech Connect

    Rego-Monteiro, M. A.; Nobre, F. D.

    2013-10-15

    An exact classical field theory for nonlinear quantum equations is presented herein. It has been applied recently to a nonlinear Schrödinger equation, and it is shown herein to hold also for a nonlinear generalization of the Klein-Gordon equation. These generalizations were carried by introducing nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard, linear equations, are recovered in the limit q→ 1. The main characteristic of this field theory consists on the fact that besides the usual Ψ(x(vector sign),t), a new field Φ(x(vector sign),t) needs to be introduced in the Lagrangian, as well. The field Φ(x(vector sign),t), which is defined by means of an additional equation, becomes Ψ{sup *}(x(vector sign),t) only when q→ 1. The solutions for the fields Ψ(x(vector sign),t) and Φ(x(vector sign),t) are found herein, being expressed in terms of a q-plane wave; moreover, both field equations lead to the relation E{sup 2}=p{sup 2}c{sup 2}+m{sup 2}c{sup 4}, for all values of q. The fact that such a classical field theory works well for two very distinct nonlinear quantum equations, namely, the Schrödinger and Klein-Gordon ones, suggests that this procedure should be appropriate for a wider class nonlinear equations. It is shown that the standard global gauge invariance is broken as a consequence of the nonlinearity.

  3. Langevin representation of Coulomb collisions for bi-Maxwellian plasmas

    SciTech Connect

    Hellinger, Petr

    2010-07-20

    Langevin model corresponding to the Fokker-Planck equation for bi-Maxwellian particle distribution functions is developed. Rosenbluth potentials and their derivatives are derived in the form of triple hypergeometric functions. The Langevin model is tested in the case of relaxation of the proton temperature anisotropy and implemented into the hybrid expanding box model. First results of this code are presented and discussed.

  4. Dynamical systems theory for the Gardner equation

    NASA Astrophysics Data System (ADS)

    Saha, Aparna; Talukdar, B.; Chatterjee, Supriya

    2014-02-01

    The Gardner equation ut+auux+bu2ux+μuxxx=0 is a generic mathematical model for weakly nonlinear and weakly dispersive wave propagation when the effects of higher-order nonlinearity become significant. Using the so-called traveling wave ansatz u (x,t)=φ(ξ), ξ =x-vt (where v is the velocity of the wave) we convert the (1+1)-dimensional partial differential equation to a second-order ordinary differential equation in ϕ with an arbitrary constant and treat the latter equation by the methods of the dynamical systems theory. With some special attention on the equilibrium points of the equation, we derive an analytical constraint for admissible values of the parameters a, b, and μ. From the Hamiltonian form of the system we confirm that, in addition to the usual bright soliton solution, the equation can be used to generate three different varieties of internal waves of which one is a dark soliton recently observed in water [A. Chabchoub et al., Phys. Rev. Lett. 110, 124101 (2013), 10.1103/PhysRevLett.110.124101].

  5. Dynamical systems theory for the Gardner equation.

    PubMed

    Saha, Aparna; Talukdar, B; Chatterjee, Supriya

    2014-02-01

    The Gardner equation u(t) + auu(x) + bu(2)u(x)+μu(xxx) = 0 is a generic mathematical model for weakly nonlinear and weakly dispersive wave propagation when the effects of higher-order nonlinearity become significant. Using the so-called traveling wave ansatz u(x,t) = φ(ξ), ξ = x-vt (where v is the velocity of the wave) we convert the (1+1)-dimensional partial differential equation to a second-order ordinary differential equation in ϕ with an arbitrary constant and treat the latter equation by the methods of the dynamical systems theory. With some special attention on the equilibrium points of the equation, we derive an analytical constraint for admissible values of the parameters a, b, and μ. From the Hamiltonian form of the system we confirm that, in addition to the usual bright soliton solution, the equation can be used to generate three different varieties of internal waves of which one is a dark soliton recently observed in water [A. Chabchoub et al., Phys. Rev. Lett. 110, 124101 (2013)]. PMID:25353592

  6. Graph theory and the Virasoro master equation

    SciTech Connect

    Obers, N.A.J.

    1991-01-01

    A brief history of affine Lie algebra, the Virasoro algebra and its culmination in the Virasoro master equation is given. By studying ansaetze of the master equation, the author obtains exact solutions and gains insight in the structure of large slices of affine-Virasoro space. He finds an isomorphism between the constructions in the ansatz SO(n){sub diag}, which is a set of unitary, generically irrational affine-Virasoro constructions on SO(n), and the unlabeled graphs of order n. On the one hand, the conformal constructions, are classified by the graphs, while, conversely, a group-theoretic and conformal field-theoretic identification is obtained for every graph of graph theory. He also defines a class of magic Lie group bases in which the Virasoro master equation admits a simple metric ansatz {l brace}g{sub metric}{r brace}, whose structure is visible in the high-level expansion. When a magic basis is real on compact g, the corresponding g{sub metric} is a large system of unitary, generically irrational conformal field theories. Examples in this class include the graph-theory ansatz SO(n){sub diag} in the Cartesian basis of SO(n), and the ansatz SU(n){sub metric} in the Pauli-like basis of SU(n). Finally, he defines the sine-area graphs' of SU(n), which label the conformal field theories of SU(n){sub metric}, and he notes that, in similar fashion, each magic basis of g defines a generalized graph theory on g which labels the conformal field theories of g{sub metric}.

  7. Graph theory and the Virasoro master equation

    SciTech Connect

    Obers, N.A.J.

    1991-04-01

    A brief history of affine Lie algebra, the Virasoro algebra and its culmination in the Virasoro master equations is given. By studying ansaetze of the master equation, we obtain exact solutions and gain insight in the structure of large slices of affine-Virasoro space. We find an isomorphism between the constructions in the ansatz SO(n){sub diag}, which is a set of unitary, generically irrational affine-Virasoro constructions on SO(n), and the unlabelled graphs, while, conversely, a group-theoretic and conformal field-theoretic identification is obtained for every graph of graph theory. We also define a class of magic'' Lie group bases in which the Virasoro master equation admits a simple metric ansatz (gmetric), whose structure is visible in the high-level expansion. When a magic basis is real on compact g, the corresponding g{sub metric} is a large system of unitary, generically irrational conformal field theories. Examples in this class include the graph-theory ansatz SO(n){sub diag} in the Cartesian basis of SO(n), and the ansatz SU(n){sub metric} in the Pauli-like basis of SU(n). Finally, we define the sine-area graphs'' of SU(n), which label the conformal field theories of SU(n){sub metric}, and we note that, in similar fashion, each magic basis of g defines a generalized graph theory on g which labels the conformal field theories of g{sub metric}. 24 figs., 4 tabs.

  8. New Langevin and gradient thermostats for rigid body dynamics

    NASA Astrophysics Data System (ADS)

    Davidchack, R. L.; Ouldridge, T. E.; Tretyakov, M. V.

    2015-04-01

    We introduce two new thermostats, one of Langevin type and one of gradient (Brownian) type, for rigid body dynamics. We formulate rotation using the quaternion representation of angular coordinates; both thermostats preserve the unit length of quaternions. The Langevin thermostat also ensures that the conjugate angular momenta stay within the tangent space of the quaternion coordinates, as required by the Hamiltonian dynamics of rigid bodies. We have constructed three geometric numerical integrators for the Langevin thermostat and one for the gradient thermostat. The numerical integrators reflect key properties of the thermostats themselves. Namely, they all preserve the unit length of quaternions, automatically, without the need of a projection onto the unit sphere. The Langevin integrators also ensure that the angular momenta remain within the tangent space of the quaternion coordinates. The Langevin integrators are quasi-symplectic and of weak order two. The numerical method for the gradient thermostat is of weak order one. Its construction exploits ideas of Lie-group type integrators for differential equations on manifolds. We numerically compare the discretization errors of the Langevin integrators, as well as the efficiency of the gradient integrator compared to the Langevin ones when used in the simulation of rigid TIP4P water model with smoothly truncated electrostatic interactions. We observe that the gradient integrator is computationally less efficient than the Langevin integrators. We also compare the relative accuracy of the Langevin integrators in evaluating various static quantities and give recommendations as to the choice of an appropriate integrator.

  9. New Langevin and gradient thermostats for rigid body dynamics.

    PubMed

    Davidchack, R L; Ouldridge, T E; Tretyakov, M V

    2015-04-14

    We introduce two new thermostats, one of Langevin type and one of gradient (Brownian) type, for rigid body dynamics. We formulate rotation using the quaternion representation of angular coordinates; both thermostats preserve the unit length of quaternions. The Langevin thermostat also ensures that the conjugate angular momenta stay within the tangent space of the quaternion coordinates, as required by the Hamiltonian dynamics of rigid bodies. We have constructed three geometric numerical integrators for the Langevin thermostat and one for the gradient thermostat. The numerical integrators reflect key properties of the thermostats themselves. Namely, they all preserve the unit length of quaternions, automatically, without the need of a projection onto the unit sphere. The Langevin integrators also ensure that the angular momenta remain within the tangent space of the quaternion coordinates. The Langevin integrators are quasi-symplectic and of weak order two. The numerical method for the gradient thermostat is of weak order one. Its construction exploits ideas of Lie-group type integrators for differential equations on manifolds. We numerically compare the discretization errors of the Langevin integrators, as well as the efficiency of the gradient integrator compared to the Langevin ones when used in the simulation of rigid TIP4P water model with smoothly truncated electrostatic interactions. We observe that the gradient integrator is computationally less efficient than the Langevin integrators. We also compare the relative accuracy of the Langevin integrators in evaluating various static quantities and give recommendations as to the choice of an appropriate integrator. PMID:25877569

  10. Brownian motion from Boltzmann's equation.

    NASA Technical Reports Server (NTRS)

    Montgomery, D.

    1971-01-01

    Two apparently disparate lines of inquiry in kinetic theory are shown to be equivalent: (1) Brownian motion as treated by the (stochastic) Langevin equation and Fokker-Planck equation; and (2) Boltzmann's equation. The method is to derive the kinetic equation for Brownian motion from the Boltzmann equation for a two-component neutral gas by a simultaneous expansion in the density and mass ratios.

  11. Undular bore theory for the Gardner equation.

    PubMed

    Kamchatnov, A M; Kuo, Y-H; Lin, T-C; Horng, T-L; Gou, S-C; Clift, R; El, G A; Grimshaw, R H J

    2012-09-01

    We develop modulation theory for undular bores (dispersive shock waves) in the framework of the Gardner, or extended Korteweg-de Vries (KdV), equation, which is a generic mathematical model for weakly nonlinear and weakly dispersive wave propagation, when effects of higher order nonlinearity become important. Using a reduced version of the finite-gap integration method we derive the Gardner-Whitham modulation system in a Riemann invariant form and show that it can be mapped onto the well-known modulation system for the Korteweg-de Vries equation. The transformation between the two counterpart modulation systems is, however, not invertible. As a result, the study of the resolution of an initial discontinuity for the Gardner equation reveals a rich phenomenology of solutions which, along with the KdV-type simple undular bores, include nonlinear trigonometric bores, solibores, rarefaction waves, and composite solutions representing various combinations of the above structures. We construct full parametric maps of such solutions for both signs of the cubic nonlinear term in the Gardner equation. Our classification is supported by numerical simulations. PMID:23031043

  12. Solving Kepler's equation via Smale's -theory

    NASA Astrophysics Data System (ADS)

    Avendano, Martín; Martín-Molina, Verónica; Ortigas-Galindo, Jorge

    2014-05-01

    We obtain an approximate solution of Kepler's equation for any and . Our solution is guaranteed, via Smale's -theory, to converge to the actual solution through Newton's method at quadratic speed, i.e. the -th iteration produces a value such that . The formula provided for is a piecewise rational function with conditions defined by polynomial inequalities, except for a small region near and , where a single cubic root is used. We also show that the root operation is unavoidable, by proving that no approximate solution can be computed in the entire region if only rational functions are allowed in each branch.

  13. Comparison of Kernel Equating and Item Response Theory Equating Methods

    ERIC Educational Resources Information Center

    Meng, Yu

    2012-01-01

    The kernel method of test equating is a unified approach to test equating with some advantages over traditional equating methods. Therefore, it is important to evaluate in a comprehensive way the usefulness and appropriateness of the Kernel equating (KE) method, as well as its advantages and disadvantages compared with several popular item…

  14. Analysis of multifrequency langevin composite ultrasonic transducers.

    PubMed

    Lin, Shuyu

    2009-09-01

    The multimode coupled vibration of Langevin composite ultrasonic transducers with conical metal mass of large cross-section is analyzed. The coupled resonance and anti-resonance frequency equations are derived and the effective electromechanical coupling coefficient is analyzed. The effect of the geometrical dimensions on the resonance frequency, the anti-resonance frequency, and the effective electromechanical coupling coefficient is studied. It is illustrated that when the radial dimension is large compared with the longitudinal dimension, the vibration of the Langevin transducer becomes a multifrequency multimode coupled vibration. Numerical methods are used to simulate the coupled vibration; the simulated results are in good agreement with those from the analytical results. Some Langevin transducers of large cross-section are designed and manufactured and their resonance frequencies are measured. It can be seen that the resonance frequencies obtained from the coupled resonance frequency equations are in good agreement with the measured results. It is expected that by properly choosing the dimensions, multifrequency Langevin transducers can be designed and used in ultrasonic cleaning, ultrasonic sonochemistry, and other applications. PMID:19812002

  15. Thermodynamic restrictions on the constitutive equations of electromagnetic theory

    NASA Technical Reports Server (NTRS)

    Coleman, B. D.; Dill, E. H.

    1971-01-01

    Thermodynamics second law restrictions on constitutive equations of electromagnetic theory for nonlinear materials with long-range gradually fading memory, considering dissipation principle consequences

  16. Ramond equations of motion in superstring field theory

    NASA Astrophysics Data System (ADS)

    Erler, Theodore; Konopka, Sebastian; Sachs, Ivo

    2015-11-01

    We extend the recently constructed NS superstring field theories in the small Hilbert space to give classical field equations for all superstring theories, including Ramond sectors. We also comment on the realization of supersymmetry in this framework.

  17. Langevin stabilization of molecular dynamics

    NASA Astrophysics Data System (ADS)

    Izaguirre, Jesús A.; Catarello, Daniel P.; Wozniak, Justin M.; Skeel, Robert D.

    2001-02-01

    In this paper we show the possibility of using very mild stochastic damping to stabilize long time step integrators for Newtonian molecular dynamics. More specifically, stable and accurate integrations are obtained for damping coefficients that are only a few percent of the natural decay rate of processes of interest, such as the velocity autocorrelation function. Two new multiple time stepping integrators, Langevin Molly (LM) and Brünger-Brooks-Karplus-Molly (BBK-M), are introduced in this paper. Both use the mollified impulse method for the Newtonian term. LM uses a discretization of the Langevin equation that is exact for the constant force, and BBK-M uses the popular Brünger-Brooks-Karplus integrator (BBK). These integrators, along with an extrapolative method called LN, are evaluated across a wide range of damping coefficient values. When large damping coefficients are used, as one would for the implicit modeling of solvent molecules, the method LN is superior, with LM closely following. However, with mild damping of 0.2 ps-1, LM produces the best results, allowing long time steps of 14 fs in simulations containing explicitly modeled flexible water. With BBK-M and the same damping coefficient, time steps of 12 fs are possible for the same system. Similar results are obtained for a solvated protein-DNA simulation of estrogen receptor ER with estrogen response element ERE. A parallel version of BBK-M runs nearly three times faster than the Verlet-I/r-RESPA (reversible reference system propagator algorithm) when using the largest stable time step on each one, and it also parallelizes well. The computation of diffusion coefficients for flexible water and ER/ERE shows that when mild damping of up to 0.2 ps-1 is used the dynamics are not significantly distorted.

  18. Langevin dynamics, entropic crowding, and stochastic cloaking.

    PubMed

    Eliazar, Iddo

    2011-12-01

    We consider a pack of independent probes--within a spatially inhomogeneous thermal bath consisting of a vast number of randomly moving particles--which are subjected to an external force. The stochastic dynamics of the probes are governed by Langevin's equation. The probes attain a steady state distribution which, in general, is different than the concentration of the particles in the spatially inhomogeneous thermal bath. In this paper we explore the state of "entropic crowding" in which the probes' distribution and the particles' concentration coincide--thus yielding maximal relative entropies of one with respect to the other. Entropic crowding can be attained by two scenarios which are analyzed in detail: (i) "entropically crowding thermal baths"--in which the particles crowd uniformly around the probes; (ii) "entropically crowding Langevin forces"--in which the probes crowd uniformly amongst the particles. Entropic crowding is equivalent to the optimal stochastic cloaking of the probes within the spatially inhomogeneous thermal bath. PMID:22304065

  19. THE BERNOULLI EQUATION AND COMPRESSIBLE FLOW THEORIES

    EPA Science Inventory

    The incompressible Bernoulli equation is an analytical relationship between pressure, kinetic energy, and potential energy. As perhaps the simplest and most useful statement for describing laminar flow, it buttresses numerous incompressible flow models that have been developed ...

  20. Behavioral Momentum Theory: Equations and Applications

    ERIC Educational Resources Information Center

    Nevin, John A.; Shahan, Timothy A.

    2011-01-01

    Behavioral momentum theory provides a quantitative account of how reinforcers experienced within a discriminative stimulus context govern the persistence of behavior that occurs in that context. The theory suggests that all reinforcers obtained in the presence of a discriminative stimulus increase resistance to change, regardless of whether those…

  1. Electron transfer dynamics: Zusman equation versus exact theory.

    PubMed

    Shi, Qiang; Chen, Liping; Nan, Guangjun; Xu, Ruixue; Yan, YiJing

    2009-04-28

    The Zusman equation has been widely used to study the effect of solvent dynamics on electron transfer reactions. However, application of this equation is limited by the classical treatment of the nuclear degrees of freedom. In this paper, we revisit the Zusman equation in the framework of the exact hierarchical equations of motion formalism, and show that a high temperature approximation of the hierarchical theory is equivalent to the Zusman equation in describing electron transfer dynamics. Thus the exact hierarchical formalism naturally extends the Zusman equation to include quantum nuclear dynamics at low temperatures. This new finding has also inspired us to rescale the original hierarchical equations and incorporate a filtering algorithm to efficiently propagate the hierarchical equations. Numerical exact results are also presented for the electron transfer reaction dynamics and rate constant calculations. PMID:19405605

  2. Item Response Theory Equating Using Bayesian Informative Priors.

    ERIC Educational Resources Information Center

    de la Torre, Jimmy; Patz, Richard J.

    This paper seeks to extend the application of Markov chain Monte Carlo (MCMC) methods in item response theory (IRT) to include the estimation of equating relationships along with the estimation of test item parameters. A method is proposed that incorporates estimation of the equating relationship in the item calibration phase. Item parameters from…

  3. Reprint of : The Boltzmann--Langevin approach: A simple quantum-mechanical derivation

    NASA Astrophysics Data System (ADS)

    Nagaev, K. E.

    2016-08-01

    We present a simple quantum-mechanical derivation of correlation function of Langevin sources in the semiclassical Boltzmann-Langevin equation. The specific case of electron-phonon scattering is considered. It is shown that the assumption of weak scattering leads to the Poisson nature of the scattering fluxes.

  4. The Boltzmann-Langevin approach: A simple quantum-mechanical derivation

    NASA Astrophysics Data System (ADS)

    Nagaev, K. E.

    2015-11-01

    We present a simple quantum-mechanical derivation of correlation function of Langevin sources in the semiclassical Boltzmann-Langevin equation. The specific case of electron-phonon scattering is considered. It is shown that the assumption of weak scattering leads to the Poisson nature of the scattering fluxes.

  5. Fokker-Planck equation of Schramm-Loewner evolution.

    PubMed

    Najafi, M N

    2015-08-01

    In this paper we statistically analyze the Fokker-Planck (FP) equation of Schramm-Loewner evolution (SLE) and its variant SLE(κ,ρc). After exploring the derivation and the properties of the Langevin equation of the tip of the SLE trace, we obtain the long- and short-time behaviors of the chordal SLE traces. We analyze the solutions of the FP and the corresponding Langevin equations and connect it to the conformal field theory (CFT) and present some exact results. We find the perturbative FP equation of the SLE(κ,ρc) traces and show that it is related to the higher-order correlation functions. Using the Langevin equation we find the long-time behaviors in this case. The CFT correspondence of this case is established and some exact results are presented. PMID:26382350

  6. Variance Reduction Using Nonreversible Langevin Samplers

    NASA Astrophysics Data System (ADS)

    Duncan, A. B.; Lelièvre, T.; Pavliotis, G. A.

    2016-05-01

    A standard approach to computing expectations with respect to a given target measure is to introduce an overdamped Langevin equation which is reversible with respect to the target distribution, and to approximate the expectation by a time-averaging estimator. As has been noted in recent papers [30, 37, 61, 72], introducing an appropriately chosen nonreversible component to the dynamics is beneficial, both in terms of reducing the asymptotic variance and of speeding up convergence to the target distribution. In this paper we present a detailed study of the dependence of the asymptotic variance on the deviation from reversibility. Our theoretical findings are supported by numerical simulations.

  7. Classical field theories from Hamiltonian constraint: Canonical equations of motion and local Hamilton-Jacobi theory

    NASA Astrophysics Data System (ADS)

    Zatloukal, Václav

    2016-04-01

    Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics is defined by a (Hamiltonian) constraint between multivector-valued generalized momenta, and points in the configuration space. Starting from a variational principle, we derive local equations of motion, that is, differential equations that determine classical surfaces and momenta. A local Hamilton-Jacobi equation applicable in the field theory then follows readily. The general method is illustrated with three examples: non-relativistic Hamiltonian mechanics, De Donder-Weyl scalar field theory, and string theory.

  8. Theory of relativistic Brownian motion: the (1+1)-dimensional case.

    PubMed

    Dunkel, Jörn; Hänggi, Peter

    2005-01-01

    We construct a theory for the (1+1)-dimensional Brownian motion in a viscous medium, which is (i) consistent with Einstein's theory of special relativity and (ii) reduces to the standard Brownian motion in the Newtonian limit case. In the first part of this work the classical Langevin equations of motion, governing the nonrelativistic dynamics of a free Brownian particle in the presence of a heat bath (white noise), are generalized in the framework of special relativity. Subsequently, the corresponding relativistic Langevin equations are discussed in the context of the generalized Ito (prepoint discretization rule) versus the Stratonovich (midpoint discretization rule) dilemma: It is found that the relativistic Langevin equation in the Hänggi-Klimontovich interpretation (with the postpoint discretization rule) is the only one that yields agreement with the relativistic Maxwell distribution. Numerical results for the relativistic Langevin equation of a free Brownian particle are presented. PMID:15697675

  9. Filtration theory using computer simulations

    SciTech Connect

    Bergman, W.; Corey, I.

    1997-08-01

    We have used commercially available fluid dynamics codes based on Navier-Stokes theory and the Langevin particle equation of motion to compute the particle capture efficiency and pressure drop through selected two- and three-dimensional fiber arrays. The approach we used was to first compute the air velocity vector field throughout a defined region containing the fiber matrix. The particle capture in the fiber matrix is then computed by superimposing the Langevin particle equation of motion over the flow velocity field. Using the Langevin equation combines the particle Brownian motion, inertia and interception mechanisms in a single equation. In contrast, most previous investigations treat the different capture mechanisms separately. We have computed the particle capture efficiency and the pressure drop through one, 2-D and two, 3-D fiber matrix elements. 5 refs., 11 figs.

  10. Velocity-Field Theory, Boltzmann's Transport Equation and Geometry

    NASA Astrophysics Data System (ADS)

    Ichinose, Shoichi

    Boltzmann equation describes the time development of the velocity distribution in the continuum fluid matter. We formulate the equation using the field theory where the velocity-field plays the central role. The matter (constituent particles) fields appear as the density and the viscosity. Fluctuation is examined, and is clearly discriminated from the quantum effect. The time variable is emergently introduced through the computational process step. The collision term, for the (velocity)**4 potential (4-body interaction), is explicitly obtained and the (statistical) fluctuation is closely explained. The present field theory model does not conserve energy and is an open-system model. (One dimensional) Navier-Stokes equation or Burger's equation, appears. In the latter part, we present a way to directly define the distribution function by use of the geometry, appearing in the mechanical dynamics, and Feynman's path-integral.

  11. Einstein equations and MOND theory from Debye entropic gravity

    SciTech Connect

    Sheykhi, A.; Sarab, K. Rezazadeh E-mail: kazem.rezazadeh.sarab@gmail.com

    2012-10-01

    Verlinde's proposal on the entropic origin of gravity is based strongly on the assumption that the equipartition law of energy holds on the holographic screen induced by the mass distribution of the system. However, from the theory of statistical mechanics we know that the equipartition law of energy does not hold in the limit of very low temperature. Inspired by the Debye model for the equipartition law of energy in statistical thermodynamics and adopting the viewpoint that gravitational systems can be regarded as a thermodynamical system, we modify Einstein field equations. We also perform the study for Poisson equation and modified Newtonian dynamics (MOND). Interestingly enough, we find that the origin of the MOND theory can be understood from Debye entropic gravity perspective. Thus our study may fill in the gap existing in the literature understanding the theoretical origin of MOND theory. In the limit of high temperature our results reduce to their respective standard gravitational equations.

  12. Semigroup theory and numerical approximation for equations in linear viscoelasticity

    NASA Technical Reports Server (NTRS)

    Fabiano, R. H.; Ito, K.

    1990-01-01

    A class of abstract integrodifferential equations used to model linear viscoelastic beams is investigated analytically, applying a Hilbert-space approach. The basic equation is rewritten as a Cauchy problem, and its well-posedness is demonstrated. Finite-dimensional subspaces of the state space and an estimate of the state operator are obtained; approximation schemes for the equations are constructed; and the convergence is proved using the Trotter-Kato theorem of linear semigroup theory. The actual convergence behavior of different approximations is demonstrated in numerical computations, and the results are presented in tables.

  13. Accurate Langevin approaches to simulate Markovian channel dynamics

    NASA Astrophysics Data System (ADS)

    Huang, Yandong; Rüdiger, Sten; Shuai, Jianwei

    2015-12-01

    The stochasticity of ion-channels dynamic is significant for physiological processes on neuronal cell membranes. Microscopic simulations of the ion-channel gating with Markov chains can be considered to be an accurate standard. However, such Markovian simulations are computationally demanding for membrane areas of physiologically relevant sizes, which makes the noise-approximating or Langevin equation methods advantageous in many cases. In this review, we discuss the Langevin-like approaches, including the channel-based and simplified subunit-based stochastic differential equations proposed by Fox and Lu, and the effective Langevin approaches in which colored noise is added to deterministic differential equations. In the framework of Fox and Lu’s classical models, several variants of numerical algorithms, which have been recently developed to improve accuracy as well as efficiency, are also discussed. Through the comparison of different simulation algorithms of ion-channel noise with the standard Markovian simulation, we aim to reveal the extent to which the existing Langevin-like methods approximate results using Markovian methods. Open questions for future studies are also discussed.

  14. Experimenting with Langevin lattice QCD

    SciTech Connect

    Gavai, R.V.; Potvin, J.; Sanielevici, S.

    1987-05-01

    We report on the status of our investigations of the effects of systematic errors upon the practical merits of Langevin updating in full lattice QCD. We formulate some rules for the safe use of this updating procedure and some observations on problems which may be common to all approximate fermion algorithms.

  15. Control theory based airfoil design using the Euler equations

    NASA Technical Reports Server (NTRS)

    Jameson, Antony; Reuther, James

    1994-01-01

    This paper describes the implementation of optimization techniques based on control theory for airfoil design. In our previous work it was shown that control theory could be employed to devise effective optimization procedures for two-dimensional profiles by using the potential flow equation with either a conformal mapping or a general coordinate system. The goal of our present work is to extend the development to treat the Euler equations in two-dimensions by procedures that can readily be generalized to treat complex shapes in three-dimensions. Therefore, we have developed methods which can address airfoil design through either an analytic mapping or an arbitrary grid perturbation method applied to a finite volume discretization of the Euler equations. Here the control law serves to provide computationally inexpensive gradient information to a standard numerical optimization method. Results are presented for both the inverse problem and drag minimization problem.

  16. Driven Langevin systems: fluctuation theorems and faithful dynamics

    NASA Astrophysics Data System (ADS)

    Sivak, David; Chodera, John; Crooks, Gavin

    2014-03-01

    Stochastic differential equations of motion (e.g., Langevin dynamics) provide a popular framework for simulating molecular systems. Any computational algorithm must discretize these equations, yet the resulting finite time step integration schemes suffer from several practical shortcomings. We show how any finite time step Langevin integrator can be thought of as a driven, nonequilibrium physical process. Amended by an appropriate work-like quantity (the shadow work), nonequilibrium fluctuation theorems can characterize or correct for the errors introduced by the use of finite time steps. We also quantify, for the first time, the magnitude of deviations between the sampled stationary distribution and the desired equilibrium distribution for equilibrium Langevin simulations of solvated systems of varying size. We further show that the incorporation of a novel time step rescaling in the deterministic updates of position and velocity can correct a number of dynamical defects in these integrators. Finally, we identify a particular splitting that has essentially universally appropriate properties for the simulation of Langevin dynamics for molecular systems in equilibrium, nonequilibrium, and path sampling contexts.

  17. The Kelvin equation and self-consistent nucleation theory

    SciTech Connect

    Wilemski, G. |

    1995-07-15

    Issues of self-consistency are reviewed for several unary equilibrium size distributions based on the capillarity approximation. Some apparent difficulties of interpretation are resolved. In terms of the kinetic approach to nucleation theory, the influence of self-consistency on the nucleation rate is shown to arise entirely from differences in the dimer evaporation rates for nearly all versions of classical theory. The nucleation rate behavior of the Kelvin model is explored. In this model, the Kelvin equation is used to prescribe all cluster evaporation rates. Nucleation rates predicted by the Kelvin model are quantitatively similar to those of the self-consistent classical (SCC) theory, but not to other simple versions of the classical theory. This behavior arises entirely from the relatively close coincidence of the SCC and Kelvin dimer evaporation rates. This means that, for the distribution-based versions of classical theory, the SCC model is the closest analogue of the Kelvin model. Because the Kelvin equation is fundamentally inadequate for very small clusters, the close relationship between the Kelvin and SCC formulations indicates that both are equally lacking in fundamental justification. The Kelvin model may, however, have some pragmatic utility, and a simple analytical rate expression is also derived for it to simplify the calculation of nucleation rates for this model. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.

  18. Master equation based steady-state cluster perturbation theory

    NASA Astrophysics Data System (ADS)

    Nuss, Martin; Dorn, Gerhard; Dorda, Antonius; von der Linden, Wolfgang; Arrigoni, Enrico

    2015-09-01

    A simple and efficient approximation scheme to study electronic transport characteristics of strongly correlated nanodevices, molecular junctions, or heterostructures out of equilibrium is provided by steady-state cluster perturbation theory. In this work, we improve the starting point of this perturbative, nonequilibrium Green's function based method. Specifically, we employ an improved unperturbed (so-called reference) state ρ̂S, constructed as the steady state of a quantum master equation within the Born-Markov approximation. This resulting hybrid method inherits beneficial aspects of both the quantum master equation as well as the nonequilibrium Green's function technique. We benchmark this scheme on two experimentally relevant systems in the single-electron transistor regime: an electron-electron interaction based quantum diode and a triple quantum dot ring junction, which both feature negative differential conductance. The results of this method improve significantly with respect to the plain quantum master equation treatment at modest additional computational cost.

  19. Theory of a ring laser. [electromagnetic field and wave equations

    NASA Technical Reports Server (NTRS)

    Menegozzi, L. N.; Lamb, W. E., Jr.

    1973-01-01

    Development of a systematic formulation of the theory of a ring laser which is based on first principles and uses a well-known model for laser operation. A simple physical derivation of the electromagnetic field equations for a noninertial reference frame in uniform rotation is presented, and an attempt is made to clarify the nature of the Fox-Li modes for an open polygonal resonator. The polarization of the active medium is obtained by using a Fourier-series method which permits the formulation of a strong-signal theory, and solutions are given in terms of continued fractions. It is shown that when such a continued fraction is expanded to third order in the fields, the familiar small-signal ring-laser theory is obtained.

  20. Langevin dynamics neglecting detailed balance condition.

    PubMed

    Ohzeki, Masayuki; Ichiki, Akihisa

    2015-07-01

    An improved method for driving a system into a desired distribution, for example, the Gibbs-Boltzmann distribution, is proposed, which makes use of an artificial relaxation process. The standard techniques for achieving the Gibbs-Boltzmann distribution involve numerical simulations under the detailed balance condition. In contrast, in the present study we formulate the Langevin dynamics, for which the corresponding Fokker-Planck operator includes an asymmetric component violating the detailed balance condition. This leads to shifts in the eigenvalues and results in the acceleration of the relaxation toward the steady state. The numerical implementation demonstrates faster convergence and shorter correlation time, and the technique of biased event sampling, Nemoto-Sasa theory, further highlights the efficacy of our method. PMID:26274123

  1. Integrals and integral equations in linearized wing theory

    NASA Technical Reports Server (NTRS)

    Lomax, Harvard; Heaslet, Max A; Fuller, Franklyn B

    1951-01-01

    The formulas of subsonic and supersonic wing theory for source, doublet, and vortex distributions are reviewed and a systematic presentation is provided which relates these distributions to the pressure and to the vertical induced velocity in the plane of the wing. It is shown that care must be used in treating the singularities involved in the analysis and that the order of integration is not always reversible. Concepts suggested by the irreversibility of order of integration are shown to be useful in the inversion of singular integral equations when operational techniques are used. A number of examples are given to illustrate the methods presented, attention being directed to supersonic flight speed.

  2. Classical irregular block, = 2 pure gauge theory and Mathieu equation

    NASA Astrophysics Data System (ADS)

    Piątek, Marcin; Pietrykowski, Artur R.

    2014-12-01

    Combining the semiclassical/Nekrasov-Shatashvili limit of the AGT conjecture and the Bethe/gauge correspondence results in a triple correspondence which identifies classical conformal blocks with twisted superpotentials and then with Yang-Yang functions. In this paper the triple correspondence is studied in the simplest, yet not completely understood case of pure SU(2) super-Yang-Mills gauge theory. A missing element of that correspondence is identified with the classical irregular block. Explicit tests provide a convincing evidence that such a function exists. In particular, it has been shown that the classical irregular block can be recovered from classical blocks on the torus and sphere in suitably defined decoupling limits of classical external conformal weights. These limits are "classical analogues" of known decoupling limits for corresponding quantum blocks. An exact correspondence between the classical irregular block and the SU(2) gauge theory twisted superpotential has been obtained as a result of another consistency check. The latter determines the spectrum of the 2-particle periodic Toda (sin-Gordon) Hamiltonian in accord with the Bethe/gauge correspondence. An analogue of this statement is found entirely within 2 d CFT. Namely, considering the classical limit of the null vector decoupling equation for the degenerate irregular block a celebrated Mathieu's equation is obtained with an eigenvalue determined by the classical irregular block. As it has been checked this result reproduces a well known weak coupling expansion of Mathieu's eigenvalue. Finally, yet another new formulae for Mathieu's eigenvalue relating the latter to a solution of certain Bethe-like equation are found.

  3. Heavy quark diffusion with relativistic Langevin dynamics in the quark-gluon fluid

    SciTech Connect

    Akamatsu, Yukinao; Hatsuda, Tetsuo; Hirano, Tetsufumi

    2009-05-15

    The relativistic diffusion process of heavy quarks is formulated on the basis of the relativistic Langevin equation in Ito discretization scheme. The drag force inside the quark-gluon plasma (QGP) is parametrized according to the formula for the strongly coupled plasma obtained by the anti-de-Sitter space/conformal field theory (AdS/CFT) correspondence. The diffusion dynamics of charm and bottom quarks in QGP is described by combining the Langevin simulation under the background matter described by the relativistic hydrodynamics. Theoretical calculations of the nuclear modification factor R{sub AA} and the elliptic flow v{sub 2} for the single electrons from the charm and bottom decays are compared with the experimental data from the relativistic heavy-ion collisions. The R{sub AA} for electrons with large transverse momentum (p{sub T}>3 GeV) indicates that the drag force from the QGP is as strong as the AdS/CFT prediction.

  4. Multiphoton-scattering theory and generalized master equations

    NASA Astrophysics Data System (ADS)

    Shi, Tao; Chang, Darrick E.; Cirac, J. Ignacio

    2015-11-01

    We develop a scattering theory to investigate the multiphoton transmission in a one-dimensional waveguide in the presence of quantum emitters. It is based on a path integral formalism, uses displacement transformations, and does not require the Markov approximation. We obtain the full time evolution of the global system, including the emitters and the photonic field. Our theory allows us to compute the transition amplitude between arbitrary initial and final states, as well as the S matrix of the asymptotic in and out states. For the case of few incident photons in the waveguide, we also rederive a generalized master equation in the Markov limit. We compare the predictions of the developed scattering theory and that with the Markov approximation. We illustrate our methods with five examples of few-photon scattering: (i) by a two-level emitter, (ii) in the Jaynes-Cummings model; (iii) by an array of two-level emitters; (iv) by a two-level emitter in the half-end waveguide; and (v) by an array of atoms coupled to Rydberg levels. In the first two, we show the application of the scattering theory in the photon scattering by a single emitter, and examine the correctness of our theory with the well-known results. In the third example, we analyze the condition of the Markov approximation for the photon scattering in the array of emitters. In the fourth one, we show how a quantum emitter can generate entanglement of outgoing photons. Finally, we highlight the interplay between the phenomenon of electromagnetic-induced transparency and the Rydberg interaction, and show how this results in a rich variety of possibilities in the quantum statistics of the scattering photons.

  5. Langevin dynamics for vector variables driven by multiplicative white noise: A functional formalism.

    PubMed

    Moreno, Miguel Vera; Arenas, Zochil González; Barci, Daniel G

    2015-04-01

    We discuss general multidimensional stochastic processes driven by a system of Langevin equations with multiplicative white noise. In particular, we address the problem of how time reversal diffusion processes are affected by the variety of conventions available to deal with stochastic integrals. We present a functional formalism to build up the generating functional of correlation functions without any type of discretization of the Langevin equations at any intermediate step. The generating functional is characterized by a functional integration over two sets of commuting variables, as well as Grassmann variables. In this representation, time reversal transformation became a linear transformation in the extended variables, simplifying in this way the complexity introduced by the mixture of prescriptions and the associated calculus rules. The stochastic calculus is codified in our formalism in the structure of the Grassmann algebra. We study some examples such as higher order derivative Langevin equations and the functional representation of the micromagnetic stochastic Landau-Lifshitz-Gilbert equation. PMID:25974436

  6. Langevin dynamics for vector variables driven by multiplicative white noise: A functional formalism

    NASA Astrophysics Data System (ADS)

    Moreno, Miguel Vera; Arenas, Zochil González; Barci, Daniel G.

    2015-04-01

    We discuss general multidimensional stochastic processes driven by a system of Langevin equations with multiplicative white noise. In particular, we address the problem of how time reversal diffusion processes are affected by the variety of conventions available to deal with stochastic integrals. We present a functional formalism to build up the generating functional of correlation functions without any type of discretization of the Langevin equations at any intermediate step. The generating functional is characterized by a functional integration over two sets of commuting variables, as well as Grassmann variables. In this representation, time reversal transformation became a linear transformation in the extended variables, simplifying in this way the complexity introduced by the mixture of prescriptions and the associated calculus rules. The stochastic calculus is codified in our formalism in the structure of the Grassmann algebra. We study some examples such as higher order derivative Langevin equations and the functional representation of the micromagnetic stochastic Landau-Lifshitz-Gilbert equation.

  7. Integral Equation Theory for the Conformation of Polyelectrolytes

    NASA Astrophysics Data System (ADS)

    Shew, C.-Y.; Yethiraj, A.

    1996-03-01

    The equilibrium conformation properties of polyelectrolyes are explored using the integral equation theory. The polymer molecules are modeled as freely-jointed beads that interact via a hard sphere plus screened Coulomb potential. To obtain the intramolecuar correlation function ( and hence the chain conformations) the many chain system is replaced by a single chain whose beads interact via the bare interaction plus a solvent-induced potential, which approximately accounts for the presence of the other molecules. Since this solvent induced potential is a functional of the intramolecular correlations it is obtained iteratively in a self-consistent fashion. The intramolecular correlation functions for a given solvation potential are obtained via Monte Carlo simulation of a single chain. A thread model of the polymer molecules is also investigated, in which case the single chain conformations are obtained using a variational method. The predictions of the theory for these two models are similar. For single chains ~ N^2 ( is the mean square end-to-end distance and N is the degree of polymerization) in salt free solutions, and ~ N^1.2 in high salt solutions. At high polymer concentration ~ N. The theory provides a means of interpolating between these limiting cases. An interesting feature is that there is a very sharp drop in polymer size at very low concentrations which happens because the overlap threshold concentration in polyelectrolytes solutions is very small.

  8. The Small-Mass Limit for Langevin Dynamics with Unbounded Coefficients and Positive Friction

    NASA Astrophysics Data System (ADS)

    Herzog, David P.; Hottovy, Scott; Volpe, Giovanni

    2016-05-01

    A class of Langevin stochastic differential equations is shown to converge in the small-mass limit under very weak assumptions on the coefficients defining the equation. The convergence result is applied to three physically realizable examples where the coefficients defining the Langevin equation for these examples grow unboundedly either at a boundary, such as a wall, and/or at the point at infinity. This unboundedness violates the assumptions of previous limit theorems in the literature. The main result of this paper proves convergence for such examples.

  9. Combined Néel and Brown rotational Langevin dynamics in magnetic particle imaging, sensing, and therapy

    SciTech Connect

    Reeves, Daniel B.; Weaver, John B.

    2015-11-30

    Magnetic nanoparticles have been studied intensely because of their possible uses in biomedical applications. Biosensing using the rotational freedom of particles has been used to detect biomarkers for cancer, hyperthermia therapy has been used to treat tumors, and magnetic particle imaging is a promising new imaging modality that can spatially resolve the concentration of nanoparticles. There are two mechanisms by which the magnetization of a nanoparticle can rotate, a fact that poses a challenge for applications that rely on precisely one mechanism. The challenge is exacerbated by the high sensitivity of the dominant mechanism to applied fields. Here, we demonstrate stochastic Langevin equation simulations for the combined rotation in magnetic nanoparticles exposed to oscillating applied fields typical to these applications to both highlight the existing relevant theory and quantify which mechanism should occur in various parameter ranges.

  10. Fluctuation theory of starlight polarization

    SciTech Connect

    Nee, S.F.

    1980-04-15

    The average and the variance of absolute polarization of starlight are calculated as a function of distance based on the fluctuation theory of Langevin's scheme. The computed curves from the theory agree with the sample observational data. It estimates a correlation length of 225 pc and a fluctuating angle of 22./sup 0/5 for the fluctuation of interstellar magnetic field for the observation direction within 60/sup 0/equator.

  11. Random matrix theory and the sixth Painlevé equation

    NASA Astrophysics Data System (ADS)

    Forrester, P. J.; Witte, N. S.

    2006-09-01

    A feature of certain ensembles of random matrices is that the corresponding measure is invariant under conjugation by unitary matrices. Study of such ensembles realized by matrices with Gaussian entries leads to statistical quantities related to the eigenspectrum, such as the distribution of the largest eigenvalue, which can be expressed as multidimensional integrals or equivalently as determinants. These distributions are well known to be τ-functions for Painlevé systems, allowing for the former to be characterized as the solution of certain nonlinear equations. We consider the random matrix ensembles for which the nonlinear equation is the σ form of PVI. Known results are reviewed, as is their implication by way of series expansions for the distributions. New results are given for the boundary conditions in the neighbourhood of the fixed singularities at t = 0, 1, ∞ of σPVI displayed by a generalization of the generating function for the distributions. The structure of these expansions is related to Jimbo's general expansions for the τ-function of σPVI in the neighbourhood of its fixed singularities, and this theory is itself put in its context of the linear isomonodromy problem relating to PVI.

  12. A simple and accurate algorithm for path integral molecular dynamics with the Langevin thermostat.

    PubMed

    Liu, Jian; Li, Dezhang; Liu, Xinzijian

    2016-07-14

    We introduce a novel simple algorithm for thermostatting path integral molecular dynamics (PIMD) with the Langevin equation. The staging transformation of path integral beads is employed for demonstration. The optimum friction coefficients for the staging modes in the free particle limit are used for all systems. In comparison to the path integral Langevin equation thermostat, the new algorithm exploits a different order of splitting for the phase space propagator associated to the Langevin equation. While the error analysis is made for both algorithms, they are also employed in the PIMD simulations of three realistic systems (the H2O molecule, liquid para-hydrogen, and liquid water) for comparison. It is shown that the new thermostat increases the time interval of PIMD by a factor of 4-6 or more for achieving the same accuracy. In addition, the supplementary material shows the error analysis made for the algorithms when the normal-mode transformation of path integral beads is used. PMID:27421393

  13. A simple and accurate algorithm for path integral molecular dynamics with the Langevin thermostat

    NASA Astrophysics Data System (ADS)

    Liu, Jian; Li, Dezhang; Liu, Xinzijian

    2016-07-01

    We introduce a novel simple algorithm for thermostatting path integral molecular dynamics (PIMD) with the Langevin equation. The staging transformation of path integral beads is employed for demonstration. The optimum friction coefficients for the staging modes in the free particle limit are used for all systems. In comparison to the path integral Langevin equation thermostat, the new algorithm exploits a different order of splitting for the phase space propagator associated to the Langevin equation. While the error analysis is made for both algorithms, they are also employed in the PIMD simulations of three realistic systems (the H2O molecule, liquid para-hydrogen, and liquid water) for comparison. It is shown that the new thermostat increases the time interval of PIMD by a factor of 4-6 or more for achieving the same accuracy. In addition, the supplementary material shows the error analysis made for the algorithms when the normal-mode transformation of path integral beads is used.

  14. Langevin Dynamics with Space-Time Periodic Nonequilibrium Forcing

    NASA Astrophysics Data System (ADS)

    Joubaud, R.; Pavliotis, G. A.; Stoltz, G.

    2015-01-01

    We present results on the ballistic and diffusive behavior of the Langevin dynamics in a periodic potential that is driven away from equilibrium by a space-time periodic driving force, extending some of the results obtained by Collet and Martinez in (J Math Biol, 56(6):765-792 2008). In the hyperbolic scaling, a nontrivial average velocity can be observed even if the external forcing vanishes in average. More surprisingly, an average velocity in the direction opposite to the forcing may develop at the linear response level—a phenomenon called negative mobility. The diffusive limit of the non-equilibrium Langevin dynamics is also studied using the general methodology of central limit theorems for additive functionals of Markov processes. To apply this methodology, which is based on the study of appropriate Poisson equations, we extend recent results on pointwise estimates of the resolvent of the generator associated with the Langevin dynamics. Our theoretical results are illustrated by numerical simulations of a two-dimensional system.

  15. The Lorentz-Dirac and Landau-Lifshitz equations from the perspective of modern renormalization theory

    NASA Astrophysics Data System (ADS)

    Nakhleh, Charles W.

    2013-03-01

    This paper uses elementary techniques drawn from renormalization theory to derive the Lorentz-Dirac equation for the relativistic classical electron from the Maxwell-Lorentz equations for a classical charged particle coupled to the electromagnetic field. I show that the resulting effective theory, valid for electron motions that change over distances large compared to the classical electron radius, reduces naturally to the Landau-Lifshitz equation. No familiarity with renormalization or quantum field theory is assumed.

  16. Modern integral equation techniques for quantum reactive scattering theory

    SciTech Connect

    Auerbach, S.M.

    1993-11-01

    Rigorous calculations of cross sections and rate constants for elementary gas phase chemical reactions are performed for comparison with experiment, to ensure that our picture of the chemical reaction is complete. We focus on the H/D+H{sub 2} {yields} H{sub 2}/DH + H reaction, and use the time independent integral equation technique in quantum reactive scattering theory. We examine the sensitivity of H+H{sub 2} state resolved integral cross sections {sigma}{sub v{prime}j{prime},vj}(E) for the transitions (v = 0,j = 0) to (v{prime} = 1,j{prime} = 1,3), to the difference between the Liu-Siegbahn-Truhlar-Horowitz (LSTH) and double many body expansion (DMBE) ab initio potential energy surfaces (PES). This sensitivity analysis is performed to determine the origin of a large discrepancy between experimental cross sections with sharply peaked energy dependence and theoretical ones with smooth energy dependence. We find that the LSTH and DMBE PESs give virtually identical cross sections, which lends credence to the theoretical energy dependence.

  17. The theory of relaxation oscillations for Hutchinson's equation

    SciTech Connect

    Kolesov, Andrei Yu; Rozov, Nikolai Kh

    2011-06-30

    Hutchinson's equation is a scalar equation with time delay which is well known in ecology. In this paper a complete asymptotic representation is constructed for a stable relaxation cycle of this equation, in the form of series in integer powers of a certain small parameter. The techniques of asymptotic integration developed on the way are then applied to analyse the question of attractors for a system of circularly interrelated Hutchinson equations. Bibliography: 8 titles.

  18. Langevin description of gauged scalar fields in a thermal bath

    NASA Astrophysics Data System (ADS)

    Miyamoto, Yuhei; Motohashi, Hayato; Suyama, Teruaki; Yokoyama, Jun'ichi

    2014-04-01

    We study the dynamics of the oscillating gauged scalar field in a thermal bath. A Langevin-type equation of motion of the scalar field, which contains both dissipation and fluctuation terms, is derived by using the real-time finite-temperature effective action approach. The existence of the quantum fluctuation-dissipation relation between the nonlocal dissipation term and the Gaussian stochastic noise terms is verified. We find that the noise variables are anticorrelated at equal time. The dissipation rate for each mode is also studied, which turns out to depend on the wave number.

  19. Fractional Diffusion Equation, Quantum Subdynamics and EINSTEIN'S Theory of Brownian Motion

    NASA Astrophysics Data System (ADS)

    Abe, Sumiyoshi

    The fractional diffusion equation for describing the anomalous diffusion phenomenon is derived in the spirit of Einstein's 1905 theory of Brownian motion. It is shown how naturally fractional calculus appears in the theory. Then, Einstein's theory is examined in view of quantum theory. An isolated quantum system composed of the objective system and the environment is considered, and then subdynamics of the objective system is formulated. The resulting quantum master equation is found to be of the Lindblad type.

  20. Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation

    SciTech Connect

    He, Xiaoyi; Lou, Li-Shi Lou, Li-Shi

    1997-12-01

    In this paper, the lattice Boltzmann equation is directly derived from the Boltzmann equation. It is shown that the lattice Boltzmann equation is a special discretized form of the Boltzmann equation. Various approximations for the discretization of the Boltzmann equation in both time and phase space are discussed in detail. A general procedure to derive the lattice Boltzmann model from the continuous Boltzmann equation is demonstrated explicitly. The lattice Boltzmann models derived include the two-dimensional 6-bit, 7-bit, and 9-bit, and three-dimensional 27-bit models. {copyright} {ital 1997} {ital The American Physical Society}

  1. Relation between the Rayleigh equation in diffraction theory and the equation based on Green's formula

    NASA Astrophysics Data System (ADS)

    Tatarskii, V. I.

    1995-06-01

    The steps necessary to produce the Rayleigh equation that is based on the Rayleigh hypothesis from the equation that is based on the Green's formula are shown. First a definition is given for the scattering amplitude that is true not only in the far zone of diffraction but also near the scattering surface. With this definition the Rayleigh equation coincides with the rigorous equation for the surface secondary sources that is based on Green's formula. The Rayleigh hypothesis is equivalent to substituting the far-zone expression of the scattering amplitude into this rigorous equation. In this case it turns out to be the equation not for the sources but directly for the scattering amplitude, which is the main advantage of this method. For comparing the Rayleigh equation with the initial rigorous equation, the Rayleigh equation is represented in terms of secondary sources. The kernel of this equation contains an integral that converges for positive and diverges for negative values of some parameter. It is shown that if we regularize this integral, defining it for the negative values of this parameter as an analytical continuation from the domain of positive values, this kernel becomes equal to the kernel of the initial rigorous equation. It follows that the formal perturbation series for the scattering amplitude obtained from the Rayleigh equation and from Green's equation always coincide. This means that convergence of the perturbation series is a sufficient condition

  2. A novel Generalized Langevin approach to bridge different timescales of relaxation in Protein Dynamics

    NASA Astrophysics Data System (ADS)

    Caballero Manrique, Esther; Bray, Jenelle; Guenza, Marina

    2006-03-01

    The derivation of a Generalized Langevin Equation (GLE) for the long-time dynamics of biological systems presents several challenges as hydrogen bonding, secondary and tertiary structure, Coulombic interactions, and hydrophobic effects come into play. Here we propose a novel GLE approach where the internal friction is explicitly included in the protein dynamics, allowing the distinction between hydrophobic and hydrophilic effects. The protein is described as a linear chain of beads (centered at the alpha carbons) that are connected by harmonic springs. Input for our theory is short time (ns) molecular dynamics simulations of a single protein (or complex) in solution, in this case the bacterial signal transduction protein CheY. Effective inter-bead potentials and local friction coefficients are obtained from the simulations. A comparison of the bond autocorrelation function predicted from the theory and calculated directly from the simulation affords the test of the theory in the short timescales (ns). In the long timescales (ms), the theory is tested against experimental NMR T1 relaxation values. Our results show a remarkable agreement in both cases, indicating that our GLE correctly bridges from the short- to the long-time scale of protein dynamics.

  3. Scaling theory for homogenization of the Maxwell equations

    NASA Astrophysics Data System (ADS)

    Vinogradov, Alexei P.

    1997-11-01

    The wide application of composite materials is a distinctive feature of modern technologies. This encourages scientists dealing with radio physics and optics, to search for new type of artificial materials. Recently such investigations have shifted in the field of materials with weak spatial dispersion: chiral, omega materials, artificial magnets, etc. By weak spatial dispersion we mean that the constitutive relations are still local but constitutive parameters depend upon a wavenumber k. It is the dependence that is responsible for non-encountered-in-nature properties of the materials such as chirality [a first order in (ka) effect] or artificial magnetism [a second order in (ka effect)]. Here a is a typical size of an inclusion. Certainly, all these effects are small enough unless there is a resonance interaction of electromagnetic wave with an inclusion. Near the resonance frequency the effects are significant and perturbation theory in (ka) fails. Nevertheless it is convenient to describe the effects in terms of orders in (ka), understanding this as a matter of classification. In spite of physical clarity of the classification the constitutive relations are treated in terms of multipole expansion. The multipoles naturally appear at field expansion in (d/R) where d is the source size and R is the distance between the source and recorder. Such an expansion is useful in 'molecular optics' approximation where d very much less than r, with r to be a mean distance between the 'molecules.' Though the 'molecular optics' ceases to be a good approximation if we deal with composites where d approximately equals r, the mean current in the right hand side of the Maxwell equations is still expressed through multipoles (see Fig. 1). Below we consider the reasons justifying this sight on things even if we are working beyond the 'molecular optics' approximation. To repel an accusation in abstract contemplation let us consider examples of the 'multipole' media. Permeable

  4. Complex Langevin simulation of chiral symmetry restoration at finite baryonic density

    NASA Astrophysics Data System (ADS)

    Ilgenfritz, Ernst-Michael

    1986-12-01

    A recently proposed effective SU(3) spin model with chiral order parameter is studied by means of the complex Langevin equation. A first-order chiral symmetry restoring and deconfining transition is observed at sufficiently low temperature at finite baryonic density. Permanent address: Sektion Physik, Karl-Marx Universität, DDR-7010 Leipzig, German Democratic Republic.

  5. Solution to the nonlinear field equations of ten dimensional supersymmetric Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Mafra, Carlos R.; Schlotterer, Oliver

    2015-09-01

    In this paper, we present a formal solution to the nonlinear field equations of ten-dimensional super Yang-Mills theory. It is assembled from products of linearized superfields which have been introduced as multiparticle superfields in the context of superstring perturbation theory. Their explicit form follows recursively from the conformal field theory description of the gluon multiplet in the pure spinor superstring. Furthermore, superfields of higher-mass dimensions are defined and their equations of motion are spelled out.

  6. Existence of a solution to an equation arising from the theory of Mean Field Games

    NASA Astrophysics Data System (ADS)

    Gangbo, Wilfrid; Święch, Andrzej

    2015-12-01

    We construct a small time strong solution to a nonlocal Hamilton-Jacobi equation (1.1) introduced in [48], the so-called master equation, originating from the theory of Mean Field Games. We discover a link between metric viscosity solutions to local Hamilton-Jacobi equations studied in [2,19,20] and solutions to (1.1). As a consequence we recover the existence of solutions to the First Order Mean Field Games equations (1.2), first proved in [48], and make a more rigorous connection between the master equation (1.1) and the Mean Field Games equations (1.2).

  7. Distribution theory for Schrödinger’s integral equation

    SciTech Connect

    Lange, Rutger-Jan

    2015-12-15

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

  8. Distribution theory for Schrödinger's integral equation

    NASA Astrophysics Data System (ADS)

    Lange, Rutger-Jan

    2015-12-01

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

  9. Quantum theory of rotational isomerism and Hill equation

    SciTech Connect

    Ugulava, A.; Toklikishvili, Z.; Chkhaidze, S.; Abramishvili, R.; Chotorlishvili, L.

    2012-06-15

    The process of rotational isomerism of linear triatomic molecules is described by the potential with two different-depth minima and one barrier between them. The corresponding quantum-mechanical equation is represented in the form that is a special case of the Hill equation. It is shown that the Hill-Schroedinger equation has a Klein's quadratic group symmetry which, in its turn, contains three invariant subgroups. The presence of these subgroups makes it possible to create a picture of energy spectrum which depends on a parameter and has many merging and branch points. The parameter-dependent energy spectrum of the Hill-Schroedinger equation, like Mathieu-characteristics, contains branch points from the left and from the right of the demarcation line. However, compared to the Mathieu-characteristics, in the Hill-Schroedinger equation spectrum the 'right' points are moved away even further for some distance that is the bigger, the bigger is the less deep well. The asymptotic wave functions of the Hill-Schroedinger equation for the energy values near the potential minimum contain two isolated sharp peaks indicating a possibility of the presence of two stable isomers. At high energy values near the potential maximum, the height of two peaks decreases, and between them there appear chaotic oscillations. This form of the wave functions corresponds to the process of isomerization.

  10. Dynamic field theory and equations of motion in cosmology

    NASA Astrophysics Data System (ADS)

    Kopeikin, Sergei M.; Petrov, Alexander N.

    2014-11-01

    We discuss a field-theoretical approach based on general-relativistic variational principle to derive the covariant field equations and hydrodynamic equations of motion of baryonic matter governed by cosmological perturbations of dark matter and dark energy. The action depends on the gravitational and matter Lagrangian. The gravitational Lagrangian depends on the metric tensor and its first and second derivatives. The matter Lagrangian includes dark matter, dark energy and the ordinary baryonic matter which plays the role of a bare perturbation. The total Lagrangian is expanded in an asymptotic Taylor series around the background cosmological manifold defined as a solution of Einstein's equations in the form of the Friedmann-Lemaître-Robertson-Walker (FLRW) metric tensor. The small parameter of the decomposition is the magnitude of the metric tensor perturbation. Each term of the series expansion is gauge-invariant and all of them together form a basis for the successive post-Friedmannian approximations around the background metric. The approximation scheme is covariant and the asymptotic nature of the Lagrangian decomposition does not require the post-Friedmannian perturbations to be small though computationally it works the most effectively when the perturbed metric is close enough to the background FLRW metric. The temporal evolution of the background metric is governed by dark matter and dark energy and we associate the large scale inhomogeneities in these two components as those generated by the primordial cosmological perturbations with an effective matter density contrast δρ / ρ ≤ 1. The small scale inhomogeneities are generated by the condensations of baryonic matter considered as the bare perturbations of the background manifold that admits δρ / ρ ≫ 1. Mathematically, the large scale perturbations are given by the homogeneous solution of the linearized field equations while the small scale perturbations are described by a particular solution of

  11. Dynamic field theory and equations of motion in cosmology

    SciTech Connect

    Kopeikin, Sergei M.; Petrov, Alexander N.

    2014-11-15

    We discuss a field-theoretical approach based on general-relativistic variational principle to derive the covariant field equations and hydrodynamic equations of motion of baryonic matter governed by cosmological perturbations of dark matter and dark energy. The action depends on the gravitational and matter Lagrangian. The gravitational Lagrangian depends on the metric tensor and its first and second derivatives. The matter Lagrangian includes dark matter, dark energy and the ordinary baryonic matter which plays the role of a bare perturbation. The total Lagrangian is expanded in an asymptotic Taylor series around the background cosmological manifold defined as a solution of Einstein’s equations in the form of the Friedmann–Lemaître–Robertson–Walker (FLRW) metric tensor. The small parameter of the decomposition is the magnitude of the metric tensor perturbation. Each term of the series expansion is gauge-invariant and all of them together form a basis for the successive post-Friedmannian approximations around the background metric. The approximation scheme is covariant and the asymptotic nature of the Lagrangian decomposition does not require the post-Friedmannian perturbations to be small though computationally it works the most effectively when the perturbed metric is close enough to the background FLRW metric. The temporal evolution of the background metric is governed by dark matter and dark energy and we associate the large scale inhomogeneities in these two components as those generated by the primordial cosmological perturbations with an effective matter density contrast δρ/ρ≤1. The small scale inhomogeneities are generated by the condensations of baryonic matter considered as the bare perturbations of the background manifold that admits δρ/ρ≫1. Mathematically, the large scale perturbations are given by the homogeneous solution of the linearized field equations while the small scale perturbations are described by a particular solution of

  12. Approximating electronically excited states with equation-of-motion linear coupled-cluster theory

    SciTech Connect

    Byrd, Jason N. Rishi, Varun; Perera, Ajith; Bartlett, Rodney J.

    2015-10-28

    A new perturbative approach to canonical equation-of-motion coupled-cluster theory is presented using coupled-cluster perturbation theory. A second-order Møller-Plesset partitioning of the Hamiltonian is used to obtain the well known equation-of-motion many-body perturbation theory equations and two new equation-of-motion methods based on the linear coupled-cluster doubles and linear coupled-cluster singles and doubles wavefunctions. These new methods are benchmarked against very accurate theoretical and experimental spectra from 25 small organic molecules. It is found that the proposed methods have excellent agreement with canonical equation-of-motion coupled-cluster singles and doubles state for state orderings and relative excited state energies as well as acceptable quantitative agreement for absolute excitation energies compared with the best estimate theory and experimental spectra.

  13. Modern Integral Equation Techniques for Quantum Reactive Scattering Theory.

    NASA Astrophysics Data System (ADS)

    Auerbach, Scott Michael

    Rigorous calculations of cross sections and rate constants for elementary gas phase chemical reactions are performed for comparison with experiment, to ensure that our picture of the chemical reaction is complete. We focus on the H/D + H_2 to H _2/DH + H reaction, and use the time independent integral equation technique in quantum reactive scattering theory. We examine the sensitivity of H + H_2 state resolved integral cross sections sigma_{v^' j^ ',vj}(E) for the transitions (v = 0, j = 0) to (v^' = 1,j^ ' = 1,3), to the difference between the Liu-Siegbahn-Truhlar-Horowitz (LSTH) and double many body expansion (DMBE) ab initio potential energy surfaces (PES). This sensitivity analysis is performed to determine the origin of a large discrepancy between experimental cross sections with sharply peaked energy dependence and theoretical ones with smooth energy dependence. We find that the LSTH and DMBE PESs give virtually identical cross sections, which lends credence to the theoretical energy dependence. To facilitate quantum calculations on more complex reactive systems, we develop a new method to compute the energy Green's function with absorbing boundary conditions (ABC), for use in calculating the cumulative reaction probability. The method is an iterative technique to compute the inverse of a non-Hermitian matrix which is based on Fourier transforming time dependent dynamics, and which requires very little core memory. The Hamiltonian is evaluated in a sinc-function based discrete variable representation (DVR) which we argue may often be superior to the fast Fourier transform method for reactive scattering. We apply the resulting power series Green's function to the benchmark collinear H + H_2 system over the energy range 3.37 to 1.27 eV. The convergence of the power series is stable at all energies, and is accelerated by the use of a stronger absorbing potential. The practicality of computing the ABC-DVR Green's function in a polynomial of the Hamiltonian is

  14. Effective equations and the inverse cascade theory for Kolmogorov flows

    NASA Technical Reports Server (NTRS)

    Weinan, E.; Shu, Chi-Wang

    1993-01-01

    We study the two-dimensional Kolmogorov flows in the limit as the forcing frequency goes to infinity. Direct numerical simulation indicates that the low frequency energy spectrum evolves to a universal kappa (exp -4) decay law. We derive effective equations governing the behavior of the large scale flow quantities. We then present numerical evidence that with smooth initial data, the solution to the effective equation develops a kappa (exp -4) type singularity at a finite time. This gives a convenient explanation for the kappa (exp -4) decay law exhibited by the original Kolmogorov flows.

  15. Effective equations and the inverse cascade theory for Kolmogorov flows

    NASA Technical Reports Server (NTRS)

    Weinan, E.; Shu, Chi-Wang

    1992-01-01

    We study the two dimensional Kolmogorov flows in the limit as the forcing frequency goes to infinity. Direct numerical simulation indicates that the low frequency energy spectrum evolves to a universal kappa (exp -4) decay law. We derive effective equations governing the behavior of the large scale flow quantities. We then present numerical evidence that with smooth initial data, the solution to the effective equation develops a kappa (exp -4) type singularity at a finite time. This gives a convenient explanation for the kappa (exp -4) decay law exhibited by the original Kolmogorov flows.

  16. Isothermal Langevin dynamics in systems with power-law spatially dependent friction

    NASA Astrophysics Data System (ADS)

    Regev, Shaked; Grønbech-Jensen, Niels; Farago, Oded

    2016-07-01

    We study the dynamics of Brownian particles in a heterogeneous one-dimensional medium with a spatially dependent diffusion coefficient of the form D (x ) ˜|x| c , at constant temperature. The particle's probability distribution function (PDF) is calculated both analytically, by solving Fick's diffusion equation, and from numerical simulations of the underdamped Langevin equation. At long times, the PDFs calculated by both approaches yield identical results, corresponding to subdiffusion for c <0 and superdiffusion for 0 1 , the diffusion equation predicts that the particles accelerate. Here we show that this phenomenon, previously considered in several works as an illustration for the possible dramatic effects of spatially dependent thermal noise, is unphysical. We argue that in an isothermal medium, the motion cannot exceed the ballistic limit (˜t2 ). The ballistic limit is reached when the friction coefficient drops sufficiently fast at large distances from the origin and is correctly captured by Langevin's equation.

  17. The quantum probability equation: I. Bound state perturbation theory

    NASA Astrophysics Data System (ADS)

    Milward, Geoffrey C.; Wilkin, Colin

    2000-10-01

    The partial-wave Schrödinger equation with real boundary conditions is recast as an equation for the probability density. When a small additional potential is included, the changes in the bound-state energy eigenvalues are obtained, up to third order in the perturbation, purely in terms of the perturbing potential and the unperturbed probability density. Although the approach is different, our results are equivalent to those derived by Bender (Bender C M 1978 Advanced Mathematical Methods for Scientists and Engineers (New York: McGraw-Hill) p 330). Knowledge of neither the unperturbed energy spectrum nor the wavefunctions of excited states is required. Evaluations of the second-order energy shift are given for some soluble S-wave problems.

  18. Equation-of-motion coupled cluster perturbation theory revisited

    SciTech Connect

    Eriksen, Janus J. Jørgensen, Poul; Olsen, Jeppe; Gauss, Jürgen

    2014-05-07

    The equation-of-motion coupled cluster (EOM-CC) framework has been used for deriving a novel series of perturbative corrections to the coupled cluster singles and doubles energy that formally converges towards the full configuration interaction energy limit. The series is based on a Møller-Plesset partitioning of the Hamiltonian and thus size extensive at any order in the perturbation, thereby remedying the major deficiency inherent to previous perturbation series based on the EOM-CC ansatz.

  19. Application of integral equation theory to polyolefin liquids and blends

    SciTech Connect

    Curro, J.G.; Weinhold, J.D.

    1997-11-01

    The ability to model the packing of polymers in melts and blends is important in many polymer applications. One significant application is the development of new polymer blends. It would be exceedingly helpful to the materials chemist if molecular modeling could be employed to predict the thermodynamics and phase behavior of hypothetical polymer alloys before embarking on a time consuming and expensive synthesis program. The well known Flory-Huggins theory has been remarkably successful in describing many aspects of polymer mixing from a qualitative point of view. This theory is known, however, to suffer from several deficiencies which can be traceable to the fact that: (1) it is a lattice model requiring both monomer components to have the same volume; and (2) a mean field or random mixing approximation is made which effectively ignores chain connectivity. Because of these limitations the Flory-Huggins theory does not include packing effects and cannot be used to make quantitative molecular engineering calculations. Recently Curro and Schweizer developed a new approach for treating polymer liquids and mixtures which the authors call PRISM theory. This is an extension to polymers of the Reference Interaction Site Model (RISM Theory) developed by Chandler and Andersen to describe the statistical mechanics of small molecule liquids. The PRISM theory is a continuous space description of a polymer liquid, which includes chain connectivity and nonrandom mixing effects in a computationally tractable manner. The primary output from PRISM calculations is the average structure or packing of the amorphous liquid given by the radial distribution function denoted as g(r). This radial distribution function is employed to deduce thermodynamic or structural properties of interest. Here, the authors describe the theoretical approach and demonstrate its application to polyethylene, isotactic polypropylene, syndiotactic polypropylene, and polyisobutylene liquids and blends.

  20. The application of the integral equation theory to study the hydrophobic interaction

    PubMed Central

    Mohorič, Tomaž; Urbic, Tomaz; Hribar-Lee, Barbara

    2014-01-01

    The Wertheim's integral equation theory was tested against newly obtained Monte Carlo computer simulations to describe the potential of mean force between two hydrophobic particles. An excellent agreement was obtained between the theoretical and simulation results. Further, the Wertheim's integral equation theory with polymer Percus-Yevick closure qualitatively correctly (with respect to the experimental data) describes the solvation structure under conditions where the simulation results are difficult to obtain with good enough accuracy. PMID:24437891

  1. Fundamental equations of a mixture of gas and small spherical solid particles from simple kinetic theory.

    NASA Technical Reports Server (NTRS)

    Pai, S. I.

    1973-01-01

    The fundamental equations of a mixture of a gas and pseudofluid of small spherical solid particles are derived from the Boltzmann equation of two-fluid theory. The distribution function of the gas molecules is defined in the same manner as in the ordinary kinetic theory of gases, but the distribution function for the solid particles is different from that of the gas molecules, because it is necessary to take into account the different size and physical properties of solid particles. In the proposed simple kinetic theory, two additional parameters are introduced: one is the radius of the spheres and the other is the instantaneous temperature of the solid particles in the distribution of the solid particles. The Boltzmann equation for each species of the mixture is formally written, and the transfer equations of these Boltzmann equations are derived and compared to the well-known fundamental equations of the mixture of a gas and small solid particles from continuum theory. The equations obtained reveal some insight into various terms in the fundamental equations. For instance, the partial pressure of the pseudofluid of solid particles is not negligible if the volume fraction of solid particles is not negligible as in the case of lunar ash flow.

  2. LOGTRUE: A Computer Program for Test Equating with Item Response Theory.

    ERIC Educational Resources Information Center

    Phillips, S. E.; Anderson, A. E.

    The LOGTRUE program can be used to obtain a scale of equated raw scores for two tests with parameter estimates on a common item response theory scale. The program derives its name from the method of logistic true score equating described by Lord (1980). The method can be applied to two tests with overlapping items administered to different groups…

  3. Mapping the Monte Carlo scheme to Langevin dynamics: a Fokker-Planck approach.

    PubMed

    Cheng, X Z; Jalil, M B A; Lee, Hwee Kuan; Okabe, Yutaka

    2006-02-17

    We propose a general method of using the Fokker-Planck equation (FPE) to link the Monte Carlo (MC) and the Langevin micromagnetic schemes. We derive the drift and diffusion FPE terms corresponding to the MC method and show that it is analytically equivalent to the stochastic Landau-Lifshitz-Gilbert (LLG) equation of Langevin-based micromagnetics. Subsequent results such as the time-quantification factor for the Metropolis MC method can be rigorously derived from this mapping equivalence. The validity of the mapping is shown by the close numerical convergence between the MC method and the LLG equation for the case of a single magnetic particle as well as interacting arrays of particles. We also find that our Metropolis MC method is accurate for a large range of damping factors alpha, unlike previous time-quantified MC methods which break down at low alpha, where precessional motion dominates. PMID:16606044

  4. Mapping the Monte Carlo Scheme to Langevin Dynamics: A Fokker-Planck Approach

    NASA Astrophysics Data System (ADS)

    Cheng, X. Z.; Jalil, M. B.; Lee, Hwee Kuan; Okabe, Yutaka

    2006-02-01

    We propose a general method of using the Fokker-Planck equation (FPE) to link the Monte Carlo (MC) and the Langevin micromagnetic schemes. We derive the drift and diffusion FPE terms corresponding to the MC method and show that it is analytically equivalent to the stochastic Landau-Lifshitz-Gilbert (LLG) equation of Langevin-based micromagnetics. Subsequent results such as the time-quantification factor for the Metropolis MC method can be rigorously derived from this mapping equivalence. The validity of the mapping is shown by the close numerical convergence between the MC method and the LLG equation for the case of a single magnetic particle as well as interacting arrays of particles. We also find that our Metropolis MC method is accurate for a large range of damping factors α, unlike previous time-quantified MC methods which break down at low α, where precessional motion dominates.

  5. Formulation and closure of compressible turbulence equations in the light of kinetic theory

    NASA Technical Reports Server (NTRS)

    Tsuge, S.; Sagara, K.

    1976-01-01

    Fluid-dynamic moment equations, based on a kinetic hierarchy system, are derived governing the interaction between turbulent and thermal fluctuations. The kinetic theory is shown to reduce the inherent complexity of the conventional formalism of compressible turbulence theory and to minimize arbitrariness in formulating the closure condition.

  6. Theory of Perturbed Equilibria for Solving the Grad-Shafranov Equation

    SciTech Connect

    A. Pletzer; L.E. Zakharov

    1999-07-01

    The theory of perturbed magnetohydrodynamic equilibria is presented for different formulations of the tokamak equilibrium problem. For numerical codes, it gives an explicit Newton scheme for solving the Grad-Shafranov equation subject to different constraints. The problem of stability of axisymmetric modes is shown to be a particular case of the equilibrium perturbation theory.

  7. An Extension of IRT-Based Equating to the Dichotomous Testlet Response Theory Model

    ERIC Educational Resources Information Center

    Tao, Wei; Cao, Yi

    2016-01-01

    Current procedures for equating number-correct scores using traditional item response theory (IRT) methods assume local independence. However, when tests are constructed using testlets, one concern is the violation of the local item independence assumption. The testlet response theory (TRT) model is one way to accommodate local item dependence.…

  8. On p -form theories with gauge invariant second order field equations

    NASA Astrophysics Data System (ADS)

    Deffayet, Cédric; Mukohyama, Shinji; Sivanesan, Vishagan

    2016-04-01

    We explore field theories of a single p -form with equations of motions of order strictly equal to 2 and gauge invariance. We give a general method for the classification of such theories which are extensions to the p -forms of the Galileon models for scalars. Our classification scheme allows us to compute an upper bound on the number of different such theories depending on p and on the space-time dimension. We are also able to build a nontrivial Galileon-like theory for a 3-form with gauge invariance and an action which is polynomial into the derivatives of the form. This theory has gauge invariant field equations but an action which is not, like a Chern-Simons theory. Hence the recently discovered no-go theorem stating that there are no nontrivial gauge invariant vector Galileons (which we are also able here to confirm with our method) does not extend to other odd-p cases.

  9. Error Analysis of Modified Langevin Dynamics

    NASA Astrophysics Data System (ADS)

    Redon, Stephane; Stoltz, Gabriel; Trstanova, Zofia

    2016-06-01

    We consider Langevin dynamics associated with a modified kinetic energy vanishing for small momenta. This allows us to freeze slow particles, and hence avoid the re-computation of inter-particle forces, which leads to computational gains. On the other hand, the statistical error may increase since there are a priori more correlations in time. The aim of this work is first to prove the ergodicity of the modified Langevin dynamics (which fails to be hypoelliptic), and next to analyze how the asymptotic variance on ergodic averages depends on the parameters of the modified kinetic energy. Numerical results illustrate the approach, both for low-dimensional systems where we resort to a Galerkin approximation of the generator, and for more realistic systems using Monte Carlo simulations.

  10. Multidimensional Langevin Modeling of Nonoverdamped Dynamics

    NASA Astrophysics Data System (ADS)

    Schaudinnus, Norbert; Bastian, Björn; Hegger, Rainer; Stock, Gerhard

    2015-07-01

    Based on a given time series, data-driven Langevin modeling aims to construct a low-dimensional dynamical model of the underlying system. When dealing with physical data as provided by, e.g., all-atom molecular dynamics simulations, effects due to small damping may be important to correctly describe the statistics (e.g., the energy landscape) and the dynamics (e.g., transition times). To include these effects in a dynamical model, an algorithm that propagates a second-order Langevin scheme is derived, which facilitates the treatment of multidimensional data. Adopting extensive molecular dynamics simulations of a peptide helix, a five-dimensional model is constructed that successfully forecasts the complex structural dynamics of the system. Neglect of small damping effects, on the other hand, is shown to lead to significant errors and inconsistencies.

  11. Error Analysis of Modified Langevin Dynamics

    NASA Astrophysics Data System (ADS)

    Redon, Stephane; Stoltz, Gabriel; Trstanova, Zofia

    2016-08-01

    We consider Langevin dynamics associated with a modified kinetic energy vanishing for small momenta. This allows us to freeze slow particles, and hence avoid the re-computation of inter-particle forces, which leads to computational gains. On the other hand, the statistical error may increase since there are a priori more correlations in time. The aim of this work is first to prove the ergodicity of the modified Langevin dynamics (which fails to be hypoelliptic), and next to analyze how the asymptotic variance on ergodic averages depends on the parameters of the modified kinetic energy. Numerical results illustrate the approach, both for low-dimensional systems where we resort to a Galerkin approximation of the generator, and for more realistic systems using Monte Carlo simulations.

  12. Pure gauge configurations and solutions to fermionic superstring field theory equations of motion

    NASA Astrophysics Data System (ADS)

    Aref'eva, I. Ya; Gorbachev, R. V.; Medvedev, P. B.

    2009-07-01

    Recent results on solutions to the equation of motion of the cubic fermionic string field theory and an equivalence of nonpolynomial and cubic string field theory are discussed. To have the possibility of dealing with both GSO(+) and GSO(-) sectors in the uniform way, a matrix formulation for the NS fermionic SFT is used. In constructions of analytical solutions to open-string field theories truncated pure gauge configurations parametrized by wedge states play an essential role. The matrix form of this parametrization for NS fermionic SFT is presented. Using the cubic open superstring field theory as an example we demonstrate explicitly that for the large parameter of the perturbation expansion these truncated pure gauge configurations give divergent contributions to the equations of motion on the subspace of the wedge states. The perturbation expansion is corrected by adding extra terms that are just those necessary for the equation of motion contracted with the solution itself to be satisfied.

  13. Sampling the isothermal-isobaric ensemble by Langevin dynamics

    NASA Astrophysics Data System (ADS)

    Gao, Xingyu; Fang, Jun; Wang, Han

    2016-03-01

    We present a new method of conducting fully flexible-cell molecular dynamics simulation in isothermal-isobaric ensemble based on Langevin equations of motion. The stochastic coupling to all particle and cell degrees of freedoms is introduced in a correct way, in the sense that the stationary configurational distribution is proved to be consistent with that of the isothermal-isobaric ensemble. In order to apply the proposed method in computer simulations, a second order symmetric numerical integration scheme is developed by Trotter's splitting of the single-step propagator. Moreover, a practical guide of choosing working parameters is suggested for user specified thermo- and baro-coupling time scales. The method and software implementation are carefully validated by a numerical example.

  14. Langevin Dynamics Deciphers the Motility Pattern of Swimming Parasites

    NASA Astrophysics Data System (ADS)

    Zaburdaev, Vasily; Uppaluri, Sravanti; Pfohl, Thomas; Engstler, Markus; Friedrich, Rudolf; Stark, Holger

    2011-05-01

    The parasite African trypanosome swims in the bloodstream of mammals and causes the highly dangerous human sleeping sickness. Cell motility is essential for the parasite’s survival within the mammalian host. We present an analysis of the random-walk pattern of a swimming trypanosome. From experimental time-autocorrelation functions for the direction of motion we identify two relaxation times that differ by an order of magnitude. They originate from the rapid deformations of the cell body and a slower rotational diffusion of the average swimming direction. Velocity fluctuations are athermal and increase for faster cells whose trajectories are also straighter. We demonstrate that such a complex dynamics is captured by two decoupled Langevin equations that decipher the complex trajectory pattern by referring it to the microscopic details of cell behavior.

  15. The most general second-order field equations of bi-scalar-tensor theory in four dimensions

    NASA Astrophysics Data System (ADS)

    Ohashi, Seiju; Tanahashi, Norihiro; Kobayashi, Tsutomu; Yamaguchi, Masahide

    2015-07-01

    The Horndeski theory is known as the most general scalar-tensor theory with second-order field equations. In this paper, we explore the bi-scalar extension of the Horndeski theory. Following Horndeski's approach, we determine all the possible terms appearing in the second-order field equations of the bi-scalar-tensor theory. We compare the field equations with those of the generalized multi-Galileons, and confirm that our theory contains new terms that are not included in the latter theory. We also discuss the construction of the Lagrangian leading to our most general field equations.

  16. Gauge theories on noncommutative ℂPN and Bogomol'nyi-Prasad-Sommerfield-like equations

    NASA Astrophysics Data System (ADS)

    Sako, Akifumi; Suzuki, Toshiya; Umetsu, Hiroshi

    2015-11-01

    We give the Fock representation of a noncommutative ℂPN and gauge theories on it. The Fock representation is constructed based on star products given by deformation quantization with separation of variables and operators which act on states in the Fock space are explicitly described by functions of inhomogeneous coordinates on ℂPN. Using the Fock representation, we are able to discuss the positivity of Yang-Mills type actions and the minimal action principle. Bogomol'nyi-Prasad-Sommerfield (BPS)-like equations on noncommutative ℂP1 and ℂP2 are derived from these actions. There are analogies between BPS-like equations on ℂP1 and monopole equations on ℝ3 and BPS-like equations on ℂP2 and instanton equations on ℝ8. We discuss solutions of these BPS-like equations.

  17. Consistency of Equations in the Second-Order Gauge-Invariant Cosmological Perturbation Theory

    NASA Astrophysics Data System (ADS)

    Nakamura, K.

    2009-06-01

    Along the general framework of the gauge-invariant perturbation theory developed in the papers [K.~Nakamura, Prog.~Theor.~Phys. 110 (2003), 723; Prog.~Theor.~Phys. 113 (2005), 481], we rederive the second-order Einstein equation on four-dimensional homogeneous isotropic background universe in a gauge-invariant manner without ignoring any mode of perturbations. We consider the perturbations both in the universe dominated by the single perfect fluid and in that dominated by the single scalar field. We also confirmed the consistency of all the equations of the second-order Einstein equation and the equations of motion for matter fields, which are derived in the paper [K.~Nakamura, arXiv:0804.3840]. This confirmation implies that all the derived equations of the second order are self-consistent and these equations are correct in this sense.

  18. Predictive equation of state method for heavy materials based on the Dirac equation and density functional theory

    NASA Astrophysics Data System (ADS)

    Wills, John M.; Mattsson, Ann E.

    2012-02-01

    Density functional theory (DFT) provides a formally predictive base for equation of state properties. Available approximations to the exchange/correlation functional provide accurate predictions for many materials in the periodic table. For heavy materials however, DFT calculations, using available functionals, fail to provide quantitative predictions, and often fail to be even qualitative. This deficiency is due both to the lack of the appropriate confinement physics in the exchange/correlation functional and to approximations used to evaluate the underlying equations. In order to assess and develop accurate functionals, it is essential to eliminate all other sources of error. In this talk we describe an efficient first-principles electronic structure method based on the Dirac equation and compare the results obtained with this method with other methods generally used. Implications for high-pressure equation of state of relativistic materials are demonstrated in application to Ce and the light actinides. Sandia National Laboratories is a multi-program laboratory managed andoperated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

  19. Zwanzig-Mori projection operators and EEG dynamics: deriving a simple equation of motion

    PubMed Central

    Hsu, David; Hsu, Murielle

    2009-01-01

    We present a macroscopic theory of electroencephalogram (EEG) dynamics based on the laws of motion that govern atomic and molecular motion. The theory is an application of Zwanzig-Mori projection operators. The result is a simple equation of motion that has the form of a generalized Langevin equation (GLE), which requires knowledge only of macroscopic properties. The macroscopic properties can be extracted from experimental data by one of two possible variational principles. These variational principles are our principal contribution to the formalism. Potential applications are discussed, including applications to the theory of critical phenomena in the brain, Granger causality and Kalman filters. PACS code: 87.19.lj PMID:19594920

  20. A theory of post-stall transients in axial compression systems. I - Development of equations

    NASA Technical Reports Server (NTRS)

    Moore, F. K.; Greitzer, E. M.

    1985-01-01

    An approximate theory is presented for post-stall transients in multistage axial compression systems. The theory leads to a set of three simultaneous nonlinear third-order partial differential equations for pressure rise, and average and disturbed values of flow coefficient, as functions of time and angle around the compressor. By a Galerkin procedure, angular dependence is averaged, and the equations become first order in time. These final equations are capable of describing the growth and possible decay of a rotating-stall cell during a compressor mass-flow transient. It is shown how rotating-stall-like and surgelike motions are coupled through these equations, and also how the instantaneous compressor pumping characteristic changes during the transient stall process.

  1. Thermodynamics and structure of a two-dimensional electrolyte by integral equation theory.

    PubMed

    Aupic, Jana; Urbic, Tomaz

    2014-05-14

    Monte Carlo simulations and integral equation theory were used to predict the thermodynamics and structure of a two-dimensional Coulomb fluid. We checked the possibility that integral equations reproduce Kosterlitz-Thouless and vapor-liquid phase transitions of the electrolyte and critical points. Integral equation theory results were compared to Monte Carlo data and the correctness of selected closure relations was assessed. Among selected closures hypernetted-chain approximation results matched computer simulation data best, but these equations unfortunately break down at temperatures well above the Kosterlitz-Thouless transition. The Kovalenko-Hirata closure produces results even at very low temperatures and densities, but no sign of phase transition was detected. PMID:24832290

  2. Thermodynamics and structure of a two-dimensional electrolyte by integral equation theory

    SciTech Connect

    Aupic, Jana; Urbic, Tomaz

    2014-05-14

    Monte Carlo simulations and integral equation theory were used to predict the thermodynamics and structure of a two-dimensional Coulomb fluid. We checked the possibility that integral equations reproduce Kosterlitz-Thouless and vapor-liquid phase transitions of the electrolyte and critical points. Integral equation theory results were compared to Monte Carlo data and the correctness of selected closure relations was assessed. Among selected closures hypernetted-chain approximation results matched computer simulation data best, but these equations unfortunately break down at temperatures well above the Kosterlitz-Thouless transition. The Kovalenko-Hirata closure produces results even at very low temperatures and densities, but no sign of phase transition was detected.

  3. Dual chain perturbation theory: A new equation of state for polyatomic molecules

    NASA Astrophysics Data System (ADS)

    Marshall, Bennett D.

    2016-04-01

    In the development of equations of state for polyatomic molecules, thermodynamic perturbation theory (TPT) is widely used to calculate the change in free energy due to chain formation. TPT is a simplification of a more general and exact multi-density cluster expansion for associating fluids. In TPT, all contributions to the cluster expansion which contain chain-chain interactions are neglected. That is, all inter-chain interactions are treated at the reference fluid level. This allows for the summation of the cluster theory in terms of reference system correlation functions only. The resulting theory has been shown to be accurate and has been widely employed as the basis of many engineering equations of state. While highly successful, TPT has many handicaps which result from the neglect of chain-chain contributions. The subject of this document is to move beyond the limitations of TPT and include chain-chain contributions to the equation of state.

  4. Toward a gauge theory for evolution equations on vector-valued spaces

    SciTech Connect

    Cardanobile, Stefano; Mugnolo, Delio

    2009-10-15

    We investigate symmetry properties of vector-valued diffusion and Schroedinger equations. For a separable Hilbert space H we characterize the subspaces of L{sup 2}(R{sup 3};H) that are local (i.e., defined pointwise) and discuss the issue of their invariance under the time evolution of the differential equation. In this context, the possibility of a connection between our results and the theory of gauge symmetries in mathematical physics is explored.

  5. Polynomial elimination theory and non-linear stability analysis for the Euler equations

    NASA Technical Reports Server (NTRS)

    Kennon, S. R.; Dulikravich, G. S.; Jespersen, D. C.

    1986-01-01

    Numerical methods are presented that exploit the polynomial properties of discretizations of the Euler equations. It is noted that most finite difference or finite volume discretizations of the steady-state Euler equations produce a polynomial system of equations to be solved. These equations are solved using classical polynomial elimination theory, with some innovative modifications. This paper also presents some preliminary results of a new non-linear stability analysis technique. This technique is applicable to determining the stability of polynomial iterative schemes. Results are presented for applying the elimination technique to a one-dimensional test case. For this test case, the exact solution is computed in three iterations. The non-linear stability analysis is applied to determine the optimal time step for solving Burgers' equation using the MacCormack scheme. The estimated optimal time step is very close to the time step that arises from a linear stability analysis.

  6. Equilibrium dynamics of the Dean-Kawasaki equation: Mode-coupling theory and its extension

    NASA Astrophysics Data System (ADS)

    Kim, Bongsoo; Kawasaki, Kyozi; Jacquin, Hugo; van Wijland, Frédéric

    2014-01-01

    We extend a previously proposed field-theoretic self-consistent perturbation approach for the equilibrium dynamics of the Dean-Kawasaki equation presented in [Kim and Kawasaki, J. Stat. Mech. (2008) P02004, 10.1088/1742-5468/2008/02/P02004]. By taking terms missing in the latter analysis into account we arrive at a set of three new equations for correlation functions of the system. These correlations involve the density and its logarithm as local observables. Our new one-loop equations, which must carefully deal with the noninteracting Brownian gas theory, are more general than the historic mode-coupling one in that a further approximation corresponding to Gaussian density fluctuations leads back to the original mode-coupling equation for the density correlations alone. However, without performing any further approximation step, our set of three equations does not feature any ergodic-nonergodic transition, as opposed to the historical mode-coupling approach.

  7. Numerical methods for solving moment equations in kinetic theory of neuronal network dynamics

    NASA Astrophysics Data System (ADS)

    Rangan, Aaditya V.; Cai, David; Tao, Louis

    2007-02-01

    Recently developed kinetic theory and related closures for neuronal network dynamics have been demonstrated to be a powerful theoretical framework for investigating coarse-grained dynamical properties of neuronal networks. The moment equations arising from the kinetic theory are a system of (1 + 1)-dimensional nonlinear partial differential equations (PDE) on a bounded domain with nonlinear boundary conditions. The PDEs themselves are self-consistently specified by parameters which are functions of the boundary values of the solution. The moment equations can be stiff in space and time. Numerical methods are presented here for efficiently and accurately solving these moment equations. The essential ingredients in our numerical methods include: (i) the system is discretized in time with an implicit Euler method within a spectral deferred correction framework, therefore, the PDEs of the kinetic theory are reduced to a sequence, in time, of boundary value problems (BVPs) with nonlinear boundary conditions; (ii) a set of auxiliary parameters is introduced to recast the original BVP with nonlinear boundary conditions as BVPs with linear boundary conditions - with additional algebraic constraints on the auxiliary parameters; (iii) a careful combination of two Newton's iterates for the nonlinear BVP with linear boundary condition, interlaced with a Newton's iterate for solving the associated algebraic constraints is constructed to achieve quadratic convergence for obtaining the solutions with self-consistent parameters. It is shown that a simple fixed-point iteration can only achieve a linear convergence for the self-consistent parameters. The practicability and efficiency of our numerical methods for solving the moment equations of the kinetic theory are illustrated with numerical examples. It is further demonstrated that the moment equations derived from the kinetic theory of neuronal network dynamics can very well capture the coarse-grained dynamical properties of

  8. On the reduction of the multidimensional stationary Schrödinger equation to a first-order equation and its relation to the pseudoanalytic function theory

    NASA Astrophysics Data System (ADS)

    Kravchenko, Vladislav V.

    2005-01-01

    Given a particular solution of a one-dimensional stationary Schrödinger equation this equation of second order can be reduced to a first-order linear ordinary differential equation. This is done with the aid of an auxiliary Riccati differential equation. In the present work we show that the same fact is true in a multidimensional situation also. For simplicity we consider the case of two or three independent variables. One particular solution of the stationary Schrödinger equation allows us to reduce this second-order equation to a linear first-order quaternionic differential equation. As in the one-dimensional case this is done with the aid of an auxiliary quaternionic Riccati equation. The resulting first-order quaternionic equation is equivalent to the static Maxwell system and is closely related to the Dirac equation. In the case of two independent variables it is the well-known Vekua equation from theory of pseudoanalytic (or generalized analytic) functions. Nevertheless, we show that even in this case it is very useful to consider not only complex valued functions, solutions of the Vekua equation, but complete quaternionic functions. In this way the first-order quaternionic equation represents two separate Vekua equations, one of which gives us solutions of the Schrödinger equation and the other one can be considered as an auxiliary equation of a simpler structure. Moreover for the auxiliary equation we always have the corresponding Bers generating pair (F, G), the base of the Bers theory of pseudoanalytic functions, and what is very important, the Bers derivatives of solutions of the auxiliary equation give us solutions of the main Vekua equation and as a consequence of the Schrödinger equation. Based on this fact we obtain an analogue of the Cauchy integral theorem for solutions of the stationary Schrödinger equation. Other results from theory of pseudoanalytic functions can be written for solutions of the Schrödinger equation. Moreover, for an ample

  9. The Scherrer equation and the dynamical theory of X-ray diffraction.

    PubMed

    Muniz, Francisco Tiago Leitão; Miranda, Marcus Aurélio Ribeiro; Morilla Dos Santos, Cássio; Sasaki, José Marcos

    2016-05-01

    The Scherrer equation is a widely used tool to determine the crystallite size of polycrystalline samples. However, it is not clear if one can apply it to large crystallite sizes because its derivation is based on the kinematical theory of X-ray diffraction. For large and perfect crystals, it is more appropriate to use the dynamical theory of X-ray diffraction. Because of the appearance of polycrystalline materials with a high degree of crystalline perfection and large sizes, it is the authors' belief that it is important to establish the crystallite size limit for which the Scherrer equation can be applied. In this work, the diffraction peak profiles are calculated using the dynamical theory of X-ray diffraction for several Bragg reflections and crystallite sizes for Si, LaB6 and CeO2. The full width at half-maximum is then extracted and the crystallite size is computed using the Scherrer equation. It is shown that for crystals with linear absorption coefficients below 2117.3 cm(-1) the Scherrer equation is valid for crystallites with sizes up to 600 nm. It is also shown that as the size increases only the peaks at higher 2θ angles give good results, and if one uses peaks with 2θ > 60° the limit for use of the Scherrer equation would go up to 1 µm. PMID:27126115

  10. Many-body-QED perturbation theory: Connection to the two-electron Bethe-Salpeter equation

    NASA Astrophysics Data System (ADS)

    Lindgren, I.; Salomonson, S.; Hedendahl, D.

    2005-03-01

    The connection between many-body perturbation theory (MBPT) and quantum electrodynamics (QED) is reviewed for systems of two fermions in an external field. The treatment is mainly based on the recently developed covariant-evolution-operator method for QED calculations (I. Lindgren, S. Salomonson, and B. Asen. Phys. Rep. 389, 161 (2004)), which is quite similar in structure to MBPT. At the same time, this procedure is closely related to the S-matrix and Green's-function formalisms and can therefore serve as a bridge connecting various approaches. It is demonstrated that the MBPT-QED scheme, when carried to all orders, leads to a Schrodinger-like equation, equivalent to the Bethe-Salpeter (BS) equation. A Bloch equation in commutator form that can be used for an "extended" or quasi-degenerate model space is derived. This is a multi-state equation that has the same relation to the single-state BS equation as the standard Bloch equation has to the ordinary Schrodinger equation. It can be used to generate a perturbation expansion compatible with the BS equation even in the case of a quasi-degenerate model space.

  11. Hamiltonian Dyson-Schwinger and FRG Flow Equations of Yang-Mills Theory in Coulomb Gauge

    SciTech Connect

    Reinhardt, Hugo; Leder, Markus; Pawlowski, Jan M.; Weber, Axel

    2011-05-23

    A new functional renormalization group equation for Hamiltonian Yang-Mills theory in Coulomb gauge is presented and solved for the static gluon and ghost propagators under the assumption of ghost dominance. The results are compared to those obtained in the variational approach.

  12. The Layzer-Irvine equation in theories with non-minimal coupling between matter and curvature

    SciTech Connect

    Bertolami, O.; Gomes, C. E-mail: claudio.gomes@fc.up.pt

    2014-09-01

    We derive the Layzer-Irvine equation for alternative gravitational theories with non-minimal coupling between curvature and matter for an homogeneous and isotropic Universe. As an application, we study the case of Abell 586, a relaxed and spherically symmetric galaxy cluster, assuming some matter density profiles.

  13. Bayesian Structural Equation Modeling: A More Flexible Representation of Substantive Theory

    ERIC Educational Resources Information Center

    Muthen, Bengt; Asparouhov, Tihomir

    2012-01-01

    This article proposes a new approach to factor analysis and structural equation modeling using Bayesian analysis. The new approach replaces parameter specifications of exact zeros with approximate zeros based on informative, small-variance priors. It is argued that this produces an analysis that better reflects substantive theories. The proposed…

  14. Dirac equation and optical scalars in the Einstein-Cartan theory

    NASA Astrophysics Data System (ADS)

    Timofeev, Vladimir

    2016-03-01

    The article deals with the Dirac equation in the Newman-Penrose formalism within the framework of Einstein-Cartan theory and behavior of isotropic congruence of autoparallels, i. e. a congruence of the curves along which tangent null vector transferred in parallel.

  15. IRTEQ: Windows Application that Implements Item Response Theory Scaling and Equating

    ERIC Educational Resources Information Center

    Han, Kyung T.

    2009-01-01

    This article provides a brief description of a Windows application called IRTEQ. IRTEQ employs an intuitive, user-friendly graphic user interface that can rescale one test form to another by using various item response theory (IRT) scaling methods. It supports various IRT models for test forms. It can also equate test scores on the scale of one…

  16. The general class of the vacuum spherically symmetric equations of the general relativity theory

    SciTech Connect

    Karbanovski, V. V. Sorokin, O. M.; Nesterova, M. I.; Bolotnyaya, V. A.; Markov, V. N. Kairov, T. V.; Lyash, A. A.; Tarasyuk, O. R.

    2012-08-15

    The system of the spherical-symmetric vacuum equations of the General Relativity Theory is considered. The general solution to a problem representing two classes of line elements with arbitrary functions g{sub 00} and g{sub 22} is obtained. The properties of the found solutions are analyzed.

  17. Scattering theory for the Klein-Gordon equation with nondecreasing potentials

    SciTech Connect

    Cruz, Maximino; Arredondo R, Juan H.

    2008-11-15

    The Klein-Gordon equation is considered in the case of nondecreasing potentials. The energy inner product is nonpositive on a subspace of infinite dimension, not consisting entirely of eigenvectors of the associated operator. A scattering theory for this case is developed and asymptotic completeness for generalized Moeller operators is proven.

  18. Observed Score and True Score Equating Procedures for Multidimensional Item Response Theory

    ERIC Educational Resources Information Center

    Brossman, Bradley Grant

    2010-01-01

    The purpose of this research was to develop observed score and true score equating procedures to be used in conjunction with the Multidimensional Item Response Theory (MIRT) framework. Currently, MIRT scale linking procedures exist to place item parameter estimates and ability estimates on the same scale after separate calibrations are conducted.…

  19. Asymptotic Standard Errors for Item Response Theory True Score Equating of Polytomous Items

    ERIC Educational Resources Information Center

    Cher Wong, Cheow

    2015-01-01

    Building on previous works by Lord and Ogasawara for dichotomous items, this article proposes an approach to derive the asymptotic standard errors of item response theory true score equating involving polytomous items, for equivalent and nonequivalent groups of examinees. This analytical approach could be used in place of empirical methods like…

  20. An approximation theory for nonlinear partial differential equations with applications to identification and control

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Kunisch, K.

    1982-01-01

    Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.

  1. Second-Order Gauge Invariant Cosmological Perturbation Theory --- Einstein Equations in Terms of Gauge Invariant Variables ---

    NASA Astrophysics Data System (ADS)

    Nakamura, K.

    2007-01-01

    Following the general framework of the gauge invariant perturbation theory developed in the papers [K. Nakamura, Prog. Theor. Phys. 110 (2003), 723; ibid. 113 (2005), 481], we formulate second-order gauge invariant cosmological perturbation theory in a four-dimensional homogeneous isotropic universe. We consider perturbations both in the universe dominated by a single perfect fluid and in that dominated by a single scalar field. We derive all the components of the Einstein equations in the case that the first-order vector and tensor modes are negligible. All equations are derived in terms of gauge invariant variables without any gauge fixing. These equations imply that second-order vector and tensor modes may be generated due to the mode-mode coupling of the linear-order scalar perturbations. We also briefly discuss the main progress of this work through comparison with previous works.

  2. Role of secondary instability theory and parabolized stability equations in transition modeling

    NASA Technical Reports Server (NTRS)

    El-Hady, Nabil M.; Dinavahi, Surya P.; Chang, Chau-Lyan; Zang, Thomas A.

    1993-01-01

    In modeling the laminar-turbulent transition region, the designer depends largely on benchmark data from experiments and/or direct numerical simulations that are usually extremely expensive. An understanding of the evolution of the Reynolds stresses, turbulent kinetic energy, and quantifies in the transport equations like the dissipation and production is essential in the modeling process. The secondary instability theory and the parabolized stability equations method are used to calculate these quantities, which are then compared with corresponding quantities calculated from available direct numerical simulation data for the incompressible boundary-layer flow of laminar-turbulent transition conditions. The potential of the secondary instability theory and the parabolized stability equations approach in predicting these quantities is discussed; results indicate that inexpensive data that are useful for transition modeling in the early stages of the transition region can be provided by these tools.

  3. Initial states in integrable quantum field theory quenches from an integral equation hierarchy

    NASA Astrophysics Data System (ADS)

    Horváth, D. X.; Sotiriadis, S.; Takács, G.

    2016-01-01

    We consider the problem of determining the initial state of integrable quantum field theory quenches in terms of the post-quench eigenstates. The corresponding overlaps are a fundamental input to most exact methods to treat integrable quantum quenches. We construct and examine an infinite integral equation hierarchy based on the form factor bootstrap, proposed earlier as a set of conditions determining the overlaps. Using quenches of the mass and interaction in Sinh-Gordon theory as a concrete example, we present theoretical arguments that the state has the squeezed coherent form expected for integrable quenches, and supporting an Ansatz for the solution of the hierarchy. Moreover we also develop an iterative method to solve numerically the lowest equation of the hierarchy. The iterative solution along with extensive numerical checks performed using the next equation of the hierarchy provides a strong numerical evidence that the proposed Ansatz gives a very good approximation for the solution.

  4. Langevin processes, agent models and socio-economic systems

    NASA Astrophysics Data System (ADS)

    Richmond, Peter; Sabatelli, Lorenzo

    2004-05-01

    We review some approaches to the understanding of fluctuations of financial asset prices. Our approach builds on the development of a simple Langevin equation that characterises stochastic processes. This provides a unifying approach that allows first a straightforward description of the early approaches of Bachelier. We generalize the approach to stochastic equations that model interacting agents. The agent models recently advocated by Marsilli and Solomon are motivated. Using a simple change of variable, we show that the peer pressure model of Marsilli and the wealth dynamics model of Solomon are essentially equivalent. The methods are further shown to be consistent with a global free energy functional that invokes an entropy term based on the Boltzmann formula. There follows a brief digression on the Heston model that extends the simple model to one that, in the language of physics, exhibits a temperature this is subject to stochastic fluctuations. Mathematically the model corresponds to a Feller process. Dragulescu and Yakovenko have shown how the model yields some of the stylised features of asset prices. A more recent approach by Michael and Johnson maximised a Tsallis entropy function subject to simple constraints. They obtain a distribution function for financial returns that exhibits power law tails and which can describe the distribution of returns not only over low but also high frequencies (minute by minute) data for the Dow Jones index. We show how this approach can be developed from an agent model, where the simple Langevin process is now conditioned by local rather than global noise. Such local noise may of course be the origin of speculative frenzy or herding in the market place. The approach yields a BBGKY type hierarchy of equations for the system correlation functions. Of especial interest is that the results can be obtained from a new free energy functional similar to that mentioned above except that a Tsallis like entropy term replaces the

  5. Langevin power curve analysis for numerical wind energy converter models with new insights on high frequency power performance

    NASA Astrophysics Data System (ADS)

    Mücke, Tanja A.; Wächter, Matthias; Milan, Patrick; Peinke, Joachim

    2015-11-01

    Based on the Langevin equation it has been proposed to obtain power curves for wind turbines from high frequency data of wind speed measurements u(t) and power output P (t). The two parts of the Langevin approach, power curve and drift field, give a comprehensive description of the conversion dynamic over the whole operating range of the wind turbine. The method deals with high frequent data instead of 10 min means. It is therefore possible to gain a reliable power curve already from a small amount of data per wind speed. Furthermore, the method is able to visualize multiple fixed points, which is e.g. characteristic for the transition from partial to full load or in case the conversion process deviates from the standard procedures. In order to gain a deeper knowledge it is essential that the method works not only for measured data but also for numerical wind turbine models and synthetic wind fields. Here, we characterize the dynamics of a detailed numerical wind turbine model and calculate the Langevin power curve for different data samplings. We show, how to get reliable results from synthetic data and verify the applicability of the method for field measurements with ultra-sonic, cup and Lidar measurements. The independence of the fixed points on site specific turbulence effects is also confirmed with the numerical model. Furthermore, we demonstrate the potential of the Langevin approach to detect failures in the conversion process and thus show the potential of the Langevin approach for a condition monitoring system.

  6. On a derivation of the Boltzmann equation in Quantum Field Theory

    NASA Astrophysics Data System (ADS)

    Leiler, Gregor

    The Boltzmann equation (BE) is a commonly used tool for the study of non-equilibrium many particle systems. It has been introduced in 1872 by Ludwig Boltzmann and has been widely generalized throughout the years. Today it is commonly used in physical applications, from the study of ordinary fluids to problems in particle Cosmology where Quantum Field Theoretical techniques are essential. Despite its numerous experimental successes, the conceptual basis of the BE is not entirely clear. For instance, it is well known that it is not a fundamental equation of physics like, say, the Heisenberg equation (HE). A natural question then arises whether it is possible to derive the BE from physical first principles, i.e. the Heisenberg equation in Quantum Field Theory. In this work we attempted to answer this question and succeeded in deriving the BE from the HE, thus further clarifying its conceptual status. In particular, the results we have obtained are as follows. Firstly, we establish the non-perturbative validity of what we call the "pre-Boltzmann equation". The crucial point here is that this latter equation is equivalent to the Heisenberg equation. Secondly, we proceed to consider various limits of the pre-Boltzmann equation, namly the "low density" and the "weak coupling" limits, to obtain two equations that can be considered as generalizations of the BE. These limits are always taken together with the "long time" limit, which allows us to interpret the BE as an appropriate long time limit of the HE. The generalization we obtain consists in additional "correction" terms to the usual Boltzmann collision factor, and can be associated to multiple particle scattering. Unlike the pre-Boltzmann equation, these latter results are only valid pertubatively. Finally, we briefly consider the possibility to extend these results beyond said limits and outline some important aspects in this case.

  7. Irreversible Langevin samplers and variance reduction: a large deviations approach

    NASA Astrophysics Data System (ADS)

    Rey-Bellet, Luc; Spiliopoulos, Konstantinos

    2015-07-01

    In order to sample from a given target distribution (often of Gibbs type), the Monte Carlo Markov chain method consists of constructing an ergodic Markov process whose invariant measure is the target distribution. By sampling the Markov process one can then compute, approximately, expectations of observables with respect to the target distribution. Often the Markov processes used in practice are time-reversible (i.e. they satisfy detailed balance), but our main goal here is to assess and quantify how the addition of a non-reversible part to the process can be used to improve the sampling properties. We focus on the diffusion setting (overdamped Langevin equations) where the drift consists of a gradient vector field as well as another drift which breaks the reversibility of the process but is chosen to preserve the Gibbs measure. In this paper we use the large deviation rate function for the empirical measure as a tool to analyze the speed of convergence to the invariant measure. We show that the addition of an irreversible drift leads to a larger rate function and it strictly improves the speed of convergence of ergodic average for (generic smooth) observables. We also deduce from this result that the asymptotic variance decreases under the addition of the irreversible drift and we give an explicit characterization of the observables whose variance is not reduced reduced, in terms of a nonlinear Poisson equation. Our theoretical results are illustrated and supplemented by numerical simulations.

  8. Time Step Rescaling Recovers Continuous-Time Dynamical Properties for Discrete-Time Langevin Integration of Nonequilibrium Systems

    PubMed Central

    2015-01-01

    When simulating molecular systems using deterministic equations of motion (e.g., Newtonian dynamics), such equations are generally numerically integrated according to a well-developed set of algorithms that share commonly agreed-upon desirable properties. However, for stochastic equations of motion (e.g., Langevin dynamics), there is still broad disagreement over which integration algorithms are most appropriate. While multiple desiderata have been proposed throughout the literature, consensus on which criteria are important is absent, and no published integration scheme satisfies all desiderata simultaneously. Additional nontrivial complications stem from simulating systems driven out of equilibrium using existing stochastic integration schemes in conjunction with recently developed nonequilibrium fluctuation theorems. Here, we examine a family of discrete time integration schemes for Langevin dynamics, assessing how each member satisfies a variety of desiderata that have been enumerated in prior efforts to construct suitable Langevin integrators. We show that the incorporation of a novel time step rescaling in the deterministic updates of position and velocity can correct a number of dynamical defects in these integrators. Finally, we identify a particular splitting (related to the velocity Verlet discretization) that has essentially universally appropriate properties for the simulation of Langevin dynamics for molecular systems in equilibrium, nonequilibrium, and path sampling contexts. PMID:24555448

  9. Propagation equations for deformable test bodies with microstructure in extended theories of gravity

    SciTech Connect

    Puetzfeld, Dirk; Obukhov, Yuri N.

    2007-10-15

    We derive the equations of motion in metric-affine gravity by making use of the conservation laws obtained from Noether's theorem. The results are given in the form of propagation equations for the multipole decomposition of the matter sources in metric-affine gravity, i.e., the canonical energy-momentum current and the hypermomentum current. In particular, the propagation equations allow for a derivation of the equations of motion of test particles in this generalized gravity theory, and allow for direct identification of the couplings between the matter currents and the gauge gravitational field strengths of the theory, namely, the curvature, the torsion, and the nonmetricity. We demonstrate that the possible non-Riemannian spacetime geometry can only be detected with the help of the test bodies that are formed of matter with microstructure. Ordinary gravitating matter, i.e., matter without microscopic internal degrees of freedom, can probe only the Riemannian spacetime geometry. Thereby, we generalize previous results of general relativity and Poincare gauge theory.

  10. A Matter of Principle: The Principles of Quantum Theory, Dirac's Equation, and Quantum Information

    NASA Astrophysics Data System (ADS)

    Plotnitsky, Arkady

    2015-10-01

    This article is concerned with the role of fundamental principles in theoretical physics, especially quantum theory. The fundamental principles of relativity will be addressed as well, in view of their role in quantum electrodynamics and quantum field theory, specifically Dirac's work, which, in particular Dirac's derivation of his relativistic equation of the electron from the principles of relativity and quantum theory, is the main focus of this article. I shall also consider Heisenberg's earlier work leading him to the discovery of quantum mechanics, which inspired Dirac's work. I argue that Heisenberg's and Dirac's work was guided by their adherence to and their confidence in the fundamental principles of quantum theory. The final section of the article discusses the recent work by D'Ariano and coworkers on the principles of quantum information theory, which extend quantum theory and its principles in a new direction. This extension enabled them to offer a new derivation of Dirac's equations from these principles alone, without using the principles of relativity.

  11. Theory of magnetohydrodynamic accretion of matter with an ultrahard equation of state onto a black hole

    SciTech Connect

    Chernov, S. V.

    2015-06-15

    We consider the magnetohydrodynamic theory of spherically symmetric accretion of a perfect fluid onto a Schwarzschild black hole with an ultrahard equation of state, p = μ ∼ ρ{sup 2}, where p is the pressure, μ is the total energy density, and ρ is the fluid density. An approximate analytical solution is written out. We show that one critical sonic surface that coincides with the black hole event horizon is formed instead of two critical surfaces (fast and slow magnetosonic surfaces) for a degenerate ultrahard equation of state of matter.

  12. Game theory to characterize solutions of a discrete-time Hamilton-Jacobi equation

    NASA Astrophysics Data System (ADS)

    Toledo, Porfirio

    2013-12-01

    We study the behavior of solutions of a discrete-time Hamilton-Jacobi equation in a minimax framework of game theory. The solutions of this problem represent the optimal payoff of a zero-sum game of two players, where the number of moves between the players converges to infinity. A real number, called the critical value, plays a central role in this work; this number is the asymptotic average action of optimal trajectories. The aim of this paper is to show the existence and characterization of solutions of a Hamilton-Jacobi equation for this kind of games.

  13. Hierarchy of equations for the energy functional of the density-functional theory

    NASA Astrophysics Data System (ADS)

    Nagy, Á.

    1993-04-01

    A hierarchy of equations has been derived for the energy functionals of the density-functional theory using the virial theorem and the Levy-Perdew relation. In the local-density approximation, the solution of the equations of hierarchy for the kinetic and exchange energies provides the well-known Thomas-Fermi expression for the kinetic energy and the Slater-Gáspár-Kohn-Sham expression for the exchange. The truncation of the hierarchies of the kinetic and exchange energies results in rigorous lower bounds to the kinetic energy and upper bounds to the exchange energy in the plane-wave approximation.

  14. Number-conserving master equation theory for a dilute Bose-Einstein condensate

    SciTech Connect

    Schelle, Alexej; Wellens, Thomas; Buchleitner, Andreas; Delande, Dominique

    2011-01-15

    We describe the transition of N weakly interacting atoms into a Bose-Einstein condensate within a number-conserving quantum master equation theory. Based on the separation of time scales for condensate formation and noncondensate thermalization, we derive a master equation for the condensate subsystem in the presence of the noncondensate environment under the inclusion of all two-body interaction processes. We numerically monitor the condensate particle number distribution during condensate formation, and derive a condition under which the unique equilibrium steady state of a dilute, weakly interacting Bose-Einstein condensate is given by a Gibbs-Boltzmann thermal state of N noninteracting atoms.

  15. Seismic wavefield propagation in 2D anisotropic media: Ray theory versus wave-equation simulation

    NASA Astrophysics Data System (ADS)

    Bai, Chao-ying; Hu, Guang-yi; Zhang, Yan-teng; Li, Zhong-sheng

    2014-05-01

    Despite the ray theory that is based on the high frequency assumption of the elastic wave-equation, the ray theory and the wave-equation simulation methods should be mutually proof of each other and hence jointly developed, but in fact parallel independent progressively. For this reason, in this paper we try an alternative way to mutually verify and test the computational accuracy and the solution correctness of both the ray theory (the multistage irregular shortest-path method) and the wave-equation simulation method (both the staggered finite difference method and the pseudo-spectral method) in anisotropic VTI and TTI media. Through the analysis and comparison of wavefield snapshot, common source gather profile and synthetic seismogram, it is able not only to verify the accuracy and correctness of each of the methods at least for kinematic features, but also to thoroughly understand the kinematic and dynamic features of the wave propagation in anisotropic media. The results show that both the staggered finite difference method and the pseudo-spectral method are able to yield the same results even for complex anisotropic media (such as a fault model); the multistage irregular shortest-path method is capable of predicting similar kinematic features as the wave-equation simulation method does, which can be used to mutually test each other for methodology accuracy and solution correctness. In addition, with the aid of the ray tracing results, it is easy to identify the multi-phases (or multiples) in the wavefield snapshot, common source point gather seismic section and synthetic seismogram predicted by the wave-equation simulation method, which is a key issue for later seismic application.

  16. Transcendental equations in the Schwinger-Keldysh nonequilibrium theory and nonvanishing correlations

    SciTech Connect

    Giraldi, Filippo

    2015-09-15

    The Schwinger-Keldysh nonequilibrium theory allows the description of various transport phenomena involving bosons (fermions) embedded in bosonic (fermionic) environments. The retarded Green’s function obeys the Dyson equation and determines via its non-vanishing asymptotic behavior the dissipationless open dynamics. The appearance of this regime is conditioned by the existence of the solution of a general class of transcendental equations in complex domain that we study. Particular cases consist in transcendental equations containing exponential, hyperbolic, power law, logarithmic, and special functions. The present analysis provides an analytical description of the thermal and temporal correlation function of two general observables of a quantum system in terms of the corresponding spectral function. Special integral properties of the spectral function guarantee non-vanishing asymptotic behavior of the correlation function.

  17. Evolutionary game theory for physical and biological scientists. I. Training and validating population dynamics equations

    PubMed Central

    Liao, David; Tlsty, Thea D.

    2014-01-01

    Failure to understand evolutionary dynamics has been hypothesized as limiting our ability to control biological systems. An increasing awareness of similarities between macroscopic ecosystems and cellular tissues has inspired optimism that game theory will provide insights into the progression and control of cancer. To realize this potential, the ability to compare game theoretic models and experimental measurements of population dynamics should be broadly disseminated. In this tutorial, we present an analysis method that can be used to train parameters in game theoretic dynamics equations, used to validate the resulting equations, and used to make predictions to challenge these equations and to design treatment strategies. The data analysis techniques in this tutorial are adapted from the analysis of reaction kinetics using the method of initial rates taught in undergraduate general chemistry courses. Reliance on computer programming is avoided to encourage the adoption of these methods as routine bench activities. PMID:25097751

  18. Physical theories in Galilean space-time and the origin of Schroedinger-like equations

    SciTech Connect

    Musielak, Z.E. Fry, J.L.

    2009-02-15

    A method to develop physical theories of free particles in space-time with the Galilean metric is presented. The method is based on a Principle of Analyticity and a Principle of Relativity, and uses the Galilei group of the metric. The first principle requires that state functions describing the particles are analytic and the second principle demands that dynamical equations for these functions are Galilean invariant. It is shown that the method can be used to formally derive Schroedinger-like equations and to determine modifications of the Galilei group of the metric that are necessary to fullfil the requirements of analyticity and Galilean invariance. The obtained results shed a new light on the origin of Schroedinger's equation of non-relativistic quantum mechanics.

  19. Correlation functions of three-dimensional Yang-Mills theory from Dyson-Schwinger equations

    NASA Astrophysics Data System (ADS)

    Huber, Markus Q.

    2016-04-01

    The two- and three-point functions and the four-gluon vertex of three-dimensional Yang-Mills theory are calculated from their Dyson-Schwinger equations and the three-particle irreducible effective action. Within a self-contained truncation, various effects of truncating Dyson-Schwinger equations are studied. Estimates for the errors induced by truncations are derived from comparisons between results from different equations, comparisons with lattice results, and varying higher Green functions. The results indicate that the two-loop diagrams are important in the gluon propagator, where they are explicitly calculated, but not for the vertices. Furthermore, the influence of the four-gluon vertex on lower Green functions is found to be small.

  20. A Revisiting of the -Stability Theory of the Boltzmann Equation Near Global Maxwellians

    NASA Astrophysics Data System (ADS)

    Ha, Seung-Yeal; Xiao, Qinghua

    2015-07-01

    We study the -stability theory of the Boltzmann equation near a global Maxwellian. When an initial datum is a perturbation of a global Maxwellian, we show that the -distance between two classical solutions can be controlled by the initial data in a Lipschitz manner, which illustrates the Lipschitz continuity of the solution operator for the Boltzmann equation in -topology. Our local-in-time -stability results cover cutoff very soft potentials as well as non-cutoff hard and soft potentials. These cases were not treated in the previous work (Ha et al. in Arch Ration Mech Anal 197:657-688, 2010). Thus, our results together with the results in Ha et al. (2010) complete the -stability theory for the Boltzmann equation near a global Maxwellian. For this -stability estimate, we use the coercivity estimate of the linearized collision operator, the smallness of perturbation in a mixed Lebesgue norm, and Strichartz-type estimates of perturbation. We also show that for all classical solutions available in the literature, the Lipschitz constant can be chosen as independent of time to obtain the uniform -stability of the Boltzmann equation.

  1. Orientation-dependent integral equation theory for a two-dimensional model of water

    NASA Astrophysics Data System (ADS)

    Urbič, T.; Vlachy, V.; Kalyuzhnyi, Yu. V.; Dill, K. A.

    2003-03-01

    We develop an integral equation theory that applies to strongly associating orientation-dependent liquids, such as water. In an earlier treatment, we developed a Wertheim integral equation theory (IET) that we tested against NPT Monte Carlo simulations of the two-dimensional Mercedes Benz model of water. The main approximation in the earlier calculation was an orientational averaging in the multidensity Ornstein-Zernike equation. Here we improve the theory by explicit introduction of an orientation dependence in the IET, based upon expanding the two-particle angular correlation function in orthogonal basis functions. We find that the new orientation-dependent IET (ODIET) yields a considerable improvement of the predicted structure of water, when compared to the Monte Carlo simulations. In particular, ODIET predicts more long-range order than the original IET, with hexagonal symmetry, as expected for the hydrogen bonded ice in this model. The new theoretical approximation still errs in some subtle properties; for example, it does not predict liquid water's density maximum with temperature or the negative thermal expansion coefficient.

  2. Unification of classical nucleation theories via a unified Itô-Stratonovich stochastic equation.

    PubMed

    Durán-Olivencia, Miguel A; Lutsko, James F

    2015-09-01

    Classical nucleation theory (CNT) is the most widely used framework to describe the early stage of first-order phase transitions. Unfortunately, the different points of view adopted to derive it yield different kinetic equations for the probability density function, e.g., Zeldovich-Frenkel or Becker-Döring-Tunitskii equations. Starting from a phenomenological stochastic differential equation, a unified equation is obtained in this work. In other words, CNT expressions are recovered by selecting one or another stochastic calculus. Moreover, it is shown that the unified CNT thus obtained produces the same Fokker-Planck equation as that from a recent update of CNT [J. F. Lutsko and M. A. Durán-Olivencia, J. Chem. Phys. 138, 244908 (2013)10.1063/1.4811490] when mass transport is governed by diffusion. Finally, we derive a general induction-time expression along with specific approximations of it to be used under different scenarios, in particular, when the mass-transport mechanism is governed by direct impingement, volume diffusion, surface diffusion, or interface transfer. PMID:26465482

  3. Parametrizing linear generalized Langevin dynamics from explicit molecular dynamics simulations

    SciTech Connect

    Gottwald, Fabian; Karsten, Sven; Ivanov, Sergei D. Kühn, Oliver

    2015-06-28

    Fundamental understanding of complex dynamics in many-particle systems on the atomistic level is of utmost importance. Often the systems of interest are of macroscopic size but can be partitioned into a few important degrees of freedom which are treated most accurately and others which constitute a thermal bath. Particular attention in this respect attracts the linear generalized Langevin equation, which can be rigorously derived by means of a linear projection technique. Within this framework, a complicated interaction with the bath can be reduced to a single memory kernel. This memory kernel in turn is parametrized for a particular system studied, usually by means of time-domain methods based on explicit molecular dynamics data. Here, we discuss that this task is more naturally achieved in frequency domain and develop a Fourier-based parametrization method that outperforms its time-domain analogues. Very surprisingly, the widely used rigid bond method turns out to be inappropriate in general. Importantly, we show that the rigid bond approach leads to a systematic overestimation of relaxation times, unless the system under study consists of a harmonic bath bi-linearly coupled to the relevant degrees of freedom.

  4. A Langevin model for low density pedestrian dynamics

    NASA Astrophysics Data System (ADS)

    Corbetta, Alessandro; Lee, Chung-Min; Benzi, Roberto; Muntean, Adrian; Toschi, Federico

    The dynamics of pedestrian crowds shares deep connections with statistical physics and fluid dynamics. Reaching a quantitative understanding, not only of the average behaviours but also of the statistics of (rare) fluctuations would have major impact, for instance, on the design and safety of civil infrastructures. A key feature of pedestrian dynamics is its strong intrinsic variability, that we can already observe at the single individual level. In this work we aim at a quantitative characterisation of this statistical variability by studying individual fluctuations. We consider experimental observations of low-density pedestrian flows in a corridor within a building at Eindhoven University of Technology. Few hundreds of thousands of pedestrian trajectories with high space and time resolutions have been collected via a Microsoft Kinect 3D-range sensor and automatic head tracking techniques. From these observations we model pedestrians as active Brownian particles by means of a generalised Langevin equation. With this model we can quantitatively reproduce the observed dynamics including the statistics of ordinary pedestrian fluctuations and of rarer U-turn events. Low density, pair-wise interactions between pedestrians are also discussed.

  5. Theory of the Lattice Boltzmann Equation: Symmetry properties of Discrete Velocity Sets

    NASA Technical Reports Server (NTRS)

    Rubinstein, Robert; Luo, Li-Shi

    2007-01-01

    In the lattice Boltzmann equation, continuous particle velocity space is replaced by a finite dimensional discrete set. The number of linearly independent velocity moments in a lattice Boltzmann model cannot exceed the number of discrete velocities. Thus, finite dimensionality introduces linear dependencies among the moments that do not exist in the exact continuous theory. Given a discrete velocity set, it is important to know to exactly what order moments are free of these dependencies. Elementary group theory is applied to the solution of this problem. It is found that by decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group, it becomes relatively straightforward to assess the behavior of moments in the theory. The construction of some standard two- and three-dimensional models is reviewed from this viewpoint, and procedures for constructing some new higher dimensional models are suggested.

  6. An analytical theory of radio-wave scattering from meteoric ionization - I. Basic equation

    NASA Astrophysics Data System (ADS)

    Pecina, P.

    2016-01-01

    We have developed an analytical theory of radio-wave scattering from ionization of meteoric origin. It is based on an integro-differential equation for the polarization vector, P, inside the meteor trail, representing an analytical solution of the set of Maxwell equations, in combination with a generalized radar equation involving an integral of the trail volume electron density, Ne, and P represented by an auxiliary vector, Q, taken over the whole trail volume. During the derivation of the final formulae, the following assumptions were applied: transversal as well as longitudinal dimensions of the meteor trail are small compared with the distances of the relevant trail point to both the transmitter and receiver and the ratio of these distances to the wavelength of the wave emitted by the radar is very large, so that the stationary-phase method can be employed for evaluation of the relevant integrals. Further, it is shown that in the case of sufficiently low electron density, Ne, corresponding to the case of underdense trails, the classical McKinley's radar equation results as a special case of the general theory. The same also applies regarding the Fresnel characteristics. Our approach is also capable of yielding solutions to the problems of the formation of Fresnel characteristics on trails having any electron density, forward scattering and scattering on trails immersed in the magnetic field. However, we have also shown that the geomagnetic field can be removed from consideration, due to its low strength. The full solution of the above integro-differential equation, valid for any electron volume densities, has been left to subsequent works dealing with this particular problem, due to its complexity.

  7. Two dimensional Langevin recombination in regioregular poly(3-hexylthiophene)

    NASA Astrophysics Data System (ADS)

    Juška, Gytis; Genevičius, Kristijonas; Nekrašas, Nerijus; Sliaužys, Gytis; Österbacka, Ronald

    2009-07-01

    In this work, it is shown that recombination in regioregular poly(3-hexylthiophene):[6,6]-phenyl-C61-butyric acid methyl ester (RRP3HT:PCBM) bulk-heterojunction solar cells is caused by the two dimensional (2D) Langevin recombination in the lamellar structures of RRP3HT, which are formed after annealing process. Due to 2D Langevin process, bimolecular recombination coefficient is reduced in comparison with three dimensional Langevin case, and bimolecular recombination coefficient depends on the density of charge carriers n1/2. Data obtained from the different experimental techniques (charge extraction with linearly increasing voltage, integral time of flight, double injection current transients and transient absorption spectroscopy) confirms 2D Langevin recombination in RR3PHT.

  8. Isothermal Langevin dynamics in systems with power-law spatially dependent friction.

    PubMed

    Regev, Shaked; Grønbech-Jensen, Niels; Farago, Oded

    2016-07-01

    We study the dynamics of Brownian particles in a heterogeneous one-dimensional medium with a spatially dependent diffusion coefficient of the form D(x)∼|x|^{c}, at constant temperature. The particle's probability distribution function (PDF) is calculated both analytically, by solving Fick's diffusion equation, and from numerical simulations of the underdamped Langevin equation. At long times, the PDFs calculated by both approaches yield identical results, corresponding to subdiffusion for c<0 and superdiffusion for 01, the diffusion equation predicts that the particles accelerate. Here we show that this phenomenon, previously considered in several works as an illustration for the possible dramatic effects of spatially dependent thermal noise, is unphysical. We argue that in an isothermal medium, the motion cannot exceed the ballistic limit (〈x^{2}〉∼t^{2}). The ballistic limit is reached when the friction coefficient drops sufficiently fast at large distances from the origin and is correctly captured by Langevin's equation. PMID:27575086

  9. Langevin analysis for time-nonlocal Brownian motion with algebraic memories and delay interactions

    NASA Astrophysics Data System (ADS)

    Chase, Matthew; McKetterick, Tom J.; Giuggioli, Luca; Kenkre, V. M.

    2016-04-01

    Starting from a Langevin equation with memory describing the attraction of a particle to a center, we investigate its transport and response properties corresponding to two special forms of the memory: one is algebraic, i.e., power-law, and the other involves a delay. We examine the properties of the Green function of the Langevin equation and encounter Mittag-Leffler and Lambert W-functions well-known in the literature. In the presence of white noise, we study two experimental situations, one involving the motional narrowing of spectral lines and the other the steady-state size of the particle under consideration. By comparing the results to counterparts for a simple exponential memory, we uncover instructive similarities and differences. Perhaps surprisingly, we find that the Balescu-Swenson theorem that states that non-Markoffian equations do not add anything new to the description of steady-state or equilibrium observables is violated for our system in that the saturation size of the particle in the steady-state depends on the memory function utilized. A natural generalization of the Smoluchowski equation for the time-local case is examined and found to satisfy the Balescu-Swenson theorem and describe accurately the first moment but not the second and higher moments. We also calculate two-time correlation functions for all three cases of the memory, and show how they differ from (tend to) their Markoffian counterparts at small (large) values of the difference between the two times.

  10. PyR@TE. Renormalization group equations for general gauge theories

    NASA Astrophysics Data System (ADS)

    Lyonnet, F.; Schienbein, I.; Staub, F.; Wingerter, A.

    2014-03-01

    Although the two-loop renormalization group equations for a general gauge field theory have been known for quite some time, deriving them for specific models has often been difficult in practice. This is mainly due to the fact that, albeit straightforward, the involved calculations are quite long, tedious and prone to error. The present work is an attempt to facilitate the practical use of the renormalization group equations in model building. To that end, we have developed two completely independent sets of programs written in Python and Mathematica, respectively. The Mathematica scripts will be part of an upcoming release of SARAH 4. The present article describes the collection of Python routines that we dubbed PyR@TE which is an acronym for “Python Renormalization group equations At Two-loop for Everyone”. In PyR@TE, once the user specifies the gauge group and the particle content of the model, the routines automatically generate the full two-loop renormalization group equations for all (dimensionless and dimensionful) parameters. The results can optionally be exported to LaTeX and Mathematica, or stored in a Python data structure for further processing by other programs. For ease of use, we have implemented an interactive mode for PyR@TE in form of an IPython Notebook. As a first application, we have generated with PyR@TE the renormalization group equations for several non-supersymmetric extensions of the Standard Model and found some discrepancies with the existing literature. Catalogue identifier: AERV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERV_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 924959 No. of bytes in distributed program, including test data, etc.: 495197 Distribution format: tar.gz Programming language: Python. Computer

  11. Application and development of the Schwinger multichannel scattering theory and the partial differential equation theory of electron-molecule scattering

    NASA Technical Reports Server (NTRS)

    Weatherford, Charles A.

    1993-01-01

    One version of the multichannel theory for electron-target scattering based on the Schwinger variational principle, the SMC method, requires the introduction of a projection parameter. The role of the projection parameter a is investigated and it is shown that the principal-value operator in the SMC equation is Hermitian regardless of the value of a as long as it is real and nonzero. In a basis that is properly orthonormalizable, the matrix representation of this operator is also Hermitian. The use of such basis is consistent with the Schwinger variational principle because the Lippmann-Schwinger equation automatically builds in the correct boundary conditions. Otherwise, an auxiliary condition needs to be introduced, and Takatsuka and McKoy's original value of a is one of the three possible ways to achieve Hermiticity. In all cases but one, a can be uncoupled from the Hermiticity condition and becomes a free parameter. An equation for a based on the variational stability of the scattering amplitude is derived; its solution has an interesting property that the scattering amplitude from a converged SMC calculation is independent of the choice of a even though the SMC operator itself is a-dependent. This property provides a sensitive test of the convergence of the calculation. For a static-exchange calculation, the convergence requirement only depends on the completeness of the one-electron basis, but for a general multichannel case, the a-invariance in the scattering amplitude requires both the one-electron basis and the N plus 1-electron basis to be complete. The role of a in the SMC equation and the convergence property are illustrated using two examples: e-CO elastic scattering in the static-exchange approximation, and a two-state treatment of the e-H2 Chi(sup 1)Sigma(sub g)(+) yields b(sup 3)Sigma(sub u)(+) excitation.

  12. Quantum theory as a description of robust experiments: Derivation of the Pauli equation

    SciTech Connect

    De Raedt, Hans; Katsnelson, Mikhail I.; Donker, Hylke C.; Michielsen, Kristel

    2015-08-15

    It is shown that the Pauli equation and the concept of spin naturally emerge from logical inference applied to experiments on a charged particle under the conditions that (i) space is homogeneous (ii) the observed events are logically independent, and (iii) the observed frequency distributions are robust with respect to small changes in the conditions under which the experiment is carried out. The derivation does not take recourse to concepts of quantum theory and is based on the same principles which have already been shown to lead to e.g. the Schrödinger equation and the probability distributions of pairs of particles in the singlet or triplet state. Application to Stern–Gerlach experiments with chargeless, magnetic particles, provides additional support for the thesis that quantum theory follows from logical inference applied to a well-defined class of experiments. - Highlights: • The Pauli equation is obtained through logical inference applied to robust experiments on a charged particle. • The concept of spin appears as an inference resulting from the treatment of two-valued data. • The same reasoning yields the quantum theoretical description of neutral magnetic particles. • Logical inference provides a framework to establish a bridge between objective knowledge gathered through experiments and their description in terms of concepts.

  13. Chiral transport equation from the quantum Dirac Hamiltonian and the on-shell effective field theory

    NASA Astrophysics Data System (ADS)

    Manuel, Cristina; Torres-Rincon, Juan M.

    2014-10-01

    We derive the relativistic chiral transport equation for massless fermions and antifermions by performing a semiclassical Foldy-Wouthuysen diagonalization of the quantum Dirac Hamiltonian. The Berry connection naturally emerges in the diagonalization process to modify the classical equations of motion of a fermion in an electromagnetic field. We also see that the fermion and antifermion dispersion relations are corrected at first order in the Planck constant by the Berry curvature, as previously derived by Son and Yamamoto for the particular case of vanishing temperature. Our approach does not require knowledge of the state of the system, and thus it can also be applied at high temperature. We provide support for our result by an alternative computation using an effective field theory for fermions and antifermions: the on-shell effective field theory. In this formalism, the off-shell fermionic modes are integrated out to generate an effective Lagrangian for the quasi-on-shell fermions/antifermions. The dispersion relation at leading order exactly matches the result from the semiclassical diagonalization. From the transport equation, we explicitly show how the axial and gauge anomalies are not modified at finite temperature and density despite the incorporation of the new dispersion relation into the distribution function.

  14. PSPICE controlled-source models of analogous circuit for Langevin type piezoelectric transducer

    NASA Astrophysics Data System (ADS)

    Chen, Yeongchin; Wu, Menqjiun; Liu, Weikuo

    2007-02-01

    The design and construction of wide-band and high efficiency acoustical projector has long been considered an art beyond the capabilities of many smaller groups. Langevin type piezoelectric transducers have been the most candidate of sonar array system applied in underwater communication. The transducers are fabricated, by bolting head mass and tail mass on both ends of stacked piezoelectric ceramic, to satisfy the multiple, conflicting design for high power transmitting capability. The aim of this research is to study the characteristics of Langevin type piezoelectric transducer that depend on different metal loading. First, the Mason equivalent circuit is used to model the segmented piezoelectric ceramic, then, the impedance network of tail and head masses is deduced by the Newton’s theory. To obtain the optimal solution to a specific design formulation, PSPICE controlled-source programming techniques can be applied. A valid example of the application of PSPICE models for Langevin type transducer analysis is presented and the simulation results are in good agreement with the experimental measurements.

  15. Equation of state of detonation products based on statistical mechanical theory

    NASA Astrophysics Data System (ADS)

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

    2015-06-01

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

  16. Cosmology in generalized Horndeski theories with second-order equations of motion

    NASA Astrophysics Data System (ADS)

    Kase, Ryotaro; Tsujikawa, Shinji

    2014-08-01

    We study the cosmology of an extended version of Horndeski theories with second-order equations of motion on the flat Friedmann-Lemaître-Robertson-Walker background. In addition to a dark energy field χ associated with the gravitational sector, we take into account multiple scalar fields ϕI (I =1,2,…,N-1) characterized by the Lagrangians P(I)(XI) with XI=∂μϕI∂μϕI. These additional scalar fields can model the perfect fluids of radiation and nonrelativistic matter. We derive propagation speeds of scalar and tensor perturbations as well as conditions for the absence of ghosts. The theories beyond Horndeski induce nontrivial modifications to all the propagation speeds of N scalar fields, but the modifications to those for the matter fields ϕI are generally suppressed relative to that for the dark energy field χ. We apply our results to the covariantized Galileon with an Einstein-Hilbert term in which partial derivatives of the Minkowski Galileon are replaced by covariant derivatives. Unlike the covariant Galileon with second-order equations of motion in general space-time, the scalar propagation speed square cs12 associated with the field χ becomes negative during the matter era for late-time tracking solutions, so the two Galileon theories can be clearly distinguished at the level of linear cosmological perturbations.

  17. Magic bases, metric ansaetze and generalized graph theories in the Virasoro master equation

    SciTech Connect

    Halpern, M.B.; Obers, N.A. )

    1991-11-15

    The authors define a class of magic Lie group bases in which the Virasoro master equation admits a class of simple metric ansaetze (g{sub metric}), whose structure is visible in the high-level expansion. When a magic basis is real on compact g, the corresponding g{sub metric} is a large system of unitary, generically irrational conformal field theories. Examples in this class include the graph-theory ansatz SO(n){sub diag} in the Cartesian basis of So(n) and the ansatz SU(n){sub metric} in the Pauli-like basis of SU(n). A new phenomenon is observed in the high-level comparison of SU(n){sub metric}: Due to the trigonometric structure constants of the Pauli-like basis, irrational central charge is clearly visible at finite order of the expansion. They also define the sine-area graphs of SU(n), which label the conformal field theories of SU(n){sub metric} and note that, in a similar fashion, each magic basis of g defines a generalize graph theory on g which labels the conformal field theories of g{sub metric}.

  18. Einstein-Cartan Theory of Gravitation: Kinematical Parameters and Maxwell Equations

    NASA Astrophysics Data System (ADS)

    Katkar, L. N.

    2015-03-01

    In the space-time manifold of Einstein-Cartan Theory (ECT) of gravitation, the expressions for the time-like kinematical parameters are derived and the propagation equation for expansion is obtained.It has been observed that when the spin tensor is u-orthogonal the spin of the gravitating matter has no influence on the propagation equation of expansion while it has influence when it is not u-orthogonal. The usual formula for the curl of gradient of a scalar function is not zero in ECT. So is the case with the divergence of the curl of a vector.Their expressions on the space-time manifold of ECT are derived. A new derivative operator d ∗ is introduced to develop the calculus on space-time manifold of ECT. It is obtained by taking the covariant derivative of an associated tensor of a form with respect to an asymmetric connections. We have used this differential operator to obtain the form of the Maxwell's equations in the ECT of gravitation. Cartan's equations of structure are also derived through the new derivative operator. It has been shown that unlike the consequences of exterior derivative in Einstein space-time, the repetition of d ∗ on a form of any degree is not zero.

  19. Kinematic assumptions and their consequences on the structure of field equations in continuum dislocation theory

    NASA Astrophysics Data System (ADS)

    Silbermann, C. B.; Ihlemann, J.

    2016-03-01

    Continuum Dislocation Theory (CDT) relates gradients of plastic deformation in crystals with the presence of geometrically necessary dislocations. Therefore, the dislocation tensor is introduced as an additional thermodynamic state variable which reflects tensorial properties of dislocation ensembles. Moreover, the CDT captures both the strain energy from the macroscopic deformation of the crystal and the elastic energy of the dislocation network, as well as the dissipation of energy due to dislocation motion. The present contribution deals with the geometrically linear CDT. More precise, the focus is on the role of dislocation kinematics for single and multi-slip and its consequences on the field equations. Thereby, the number of active slip systems plays a crucial role since it restricts the degrees of freedom of plastic deformation. Special attention is put on the definition of proper, well-defined invariants of the dislocation tensor in order to avoid any spurious dependence of the resulting field equations on the coordinate system. It is shown how a slip system based approach can be in accordance with the tensor nature of the involved quantities. At first, only dislocation glide in one active slip system of the crystal is allowed. Then, the special case of two orthogonal (interacting) slip systems is considered and the governing field equations are presented. In addition, the structure and symmetry of the backstress tensor is investigated from the viewpoint of thermodynamical consistency. The results will again be used in order to facilitate the set of field equations and to prepare for a robust numerical implementation.

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

    NASA Astrophysics Data System (ADS)

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

    2015-02-01

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

  1. Pure gauge configurations and tachyon solutions to string field theories equations of motion

    NASA Astrophysics Data System (ADS)

    Aref'eva, Irina Ya.; Gorbachev, Roman V.; Grigoryev, Dmitry A.; Khromov, Pavel N.; Maltsev, Maxim V.; Medvedev, Peter B.

    2009-05-01

    In construction of analytical solutions to open string field theories pure gauge configurations parameterized by wedge states play an essential role. These pure gauge configurations are constructed as perturbation expansions and to guaranty that these configurations are asymptotical solutions to equations of motion one needs to study convergence of the perturbation expansions. We demonstrate that for the large parameter of the perturbation expansion these pure gauge truncated configurations give divergent contributions to the equation of motion on the subspace of the wedge states. We perform this demonstration numerically for the pure gauge configurations related to tachyon solutions for the bosonic and NS fermionic SFT. By the numerical calculations we also show that the perturbation expansions are cured by adding extra terms. These terms are nothing but the terms necessary to make valued the Sen conjectures.

  2. On loop equations in KdV exactly solvable string theory

    SciTech Connect

    Dalley, S. . Joseph Henry Labs.)

    1992-05-10

    In this paper, the non-perturbative behavior of macroscopic loop amplitudes in the exactly solvable string theories based on the KdV hierarchies is considered. Loop equations are presented for the real non-perturbative solutions living on the spectral half-line, allowed by the most general string equation ({bar P}, Q) = Q, where {bar P} generates scale transformations. In general the end of the half-line (the wall) is a non-perturbative parameter whose role is that of boundary cosmological constant. The properties are compared with the perturbative behavior and solutions of (P,Q) = 1. Detailed arguments are given for the (2,2m {minus} 1) models while generalization to the other (p,q) minimal models and c = 1 is briefly addressed.

  3. Elasticity theory equations and fracture condition for materials of varying moduli

    SciTech Connect

    Oleinikov, A.I.

    1986-11-01

    Many massive rocks and composite materials belong to the class of materials of varying moduli with definite distinct deformation and strength properties under tension and compression. The results of experiments indicate that the difference between the properties of materials of different moduli is not limited to tension and compression cases but can also appear clearly for any change in the form of the state of stress. Elasticity theory equations are constructed here to describe the strain of materials of varying moduli as well as the dependence of the strength properties on the form of the state of strain. Tests were done on coal, limestone, diabase and cement and results are shown. Using the dependencies obtained, Poisson's ratio and the elastic modulus can be calculated for these rocks. The equations and conditions of fracture proposed, are written in a simple invariant form.

  4. Raychaudhuri equation in the self-consistent Einstein-Cartan theory with spin-density

    NASA Technical Reports Server (NTRS)

    Fennelly, A. J.; Krisch, Jean P.; Ray, John R.; Smalley, Larry L.

    1988-01-01

    The physical implications of the Raychaudhuri equation for a spinning fluid in a Riemann-Cartan spacetime is developed and discussed using the self-consistent Lagrangian based formulation for the Einstein-Cartan theory. It was found that the spin-squared terms contribute to expansion (inflation) at early times and may lead to a bounce in the final collapse. The relationship between the fluid's vorticity and spin angular velocity is clarified and the effect of the interaction terms between the spin angular velocity and the spin in the Raychaudhuri equation investigated. These results should prove useful for studies of systems with an intrinsic spin angular momentum in extreme astrophysical or cosmological problems.

  5. Numerical methods for the weakly compressible Generalized Langevin Model in Eulerian reference frame

    NASA Astrophysics Data System (ADS)

    Azarnykh, Dmitrii; Litvinov, Sergey; Adams, Nikolaus A.

    2016-06-01

    A well established approach for the computation of turbulent flow without resolving all turbulent flow scales is to solve a filtered or averaged set of equations, and to model non-resolved scales by closures derived from transported probability density functions (PDF) for velocity fluctuations. Effective numerical methods for PDF transport employ the equivalence between the Fokker-Planck equation for the PDF and a Generalized Langevin Model (GLM), and compute the PDF by transporting a set of sampling particles by GLM (Pope (1985) [1]). The natural representation of GLM is a system of stochastic differential equations in a Lagrangian reference frame, typically solved by particle methods. A representation in a Eulerian reference frame, however, has the potential to significantly reduce computational effort and to allow for the seamless integration into a Eulerian-frame numerical flow solver. GLM in a Eulerian frame (GLMEF) formally corresponds to the nonlinear fluctuating hydrodynamic equations derived by Nakamura and Yoshimori (2009) [12]. Unlike the more common Landau-Lifshitz Navier-Stokes (LLNS) equations these equations are derived from the underdamped Langevin equation and are not based on a local equilibrium assumption. Similarly to LLNS equations the numerical solution of GLMEF requires special considerations. In this paper we investigate different numerical approaches to solving GLMEF with respect to the correct representation of stochastic properties of the solution. We find that a discretely conservative staggered finite-difference scheme, adapted from a scheme originally proposed for turbulent incompressible flow, in conjunction with a strongly stable (for non-stochastic PDE) Runge-Kutta method performs better for GLMEF than schemes adopted from those proposed previously for the LLNS. We show that equilibrium stochastic fluctuations are correctly reproduced.

  6. Phase Behavior of Active Swimmers in Depletants: Molecular Dynamics and Integral Equation Theory

    NASA Astrophysics Data System (ADS)

    Das, Subir K.; Egorov, Sergei A.; Trefz, Benjamin; Virnau, Peter; Binder, Kurt

    2014-05-01

    We study the structure and phase behavior of a binary mixture where one of the components is self-propelling in nature. The interparticle interactions in the system are taken from the Asakura-Oosawa model for colloid-polymer mixtures for which the phase diagram is known. In the current model version, the colloid particles are made active using the Vicsek model for self-propelling particles. The resultant active system is studied by molecular dynamics methods and integral equation theory. Both methods produce results consistent with each other and demonstrate that the Vicsek model-based activity facilitates phase separation, thus, broadening the coexistence region.

  7. Phase behavior of active swimmers in depletants: molecular dynamics and integral equation theory.

    PubMed

    Das, Subir K; Egorov, Sergei A; Trefz, Benjamin; Virnau, Peter; Binder, Kurt

    2014-05-16

    We study the structure and phase behavior of a binary mixture where one of the components is self-propelling in nature. The interparticle interactions in the system are taken from the Asakura-Oosawa model for colloid-polymer mixtures for which the phase diagram is known. In the current model version, the colloid particles are made active using the Vicsek model for self-propelling particles. The resultant active system is studied by molecular dynamics methods and integral equation theory. Both methods produce results consistent with each other and demonstrate that the Vicsek model-based activity facilitates phase separation, thus, broadening the coexistence region. PMID:24877969

  8. Current noise spectra and mechanisms with dissipaton equation of motion theory

    SciTech Connect

    Jin, Jinshuang; Wang, Shikuan; Zheng, Xiao; Yan, YiJing

    2015-06-21

    Based on the Yan’s dissipaton equation of motion (DEOM) theory [J. Chem. Phys. 140, 054105 (2014)], we investigate the characteristic features of current noise spectrum in several typical transport regimes of a single-impurity Anderson model. Many well-known features such as Kondo features are correctly recovered by our DEOM calculations. More importantly, it is revealed that the intrinsic electron cotunneling process is responsible for the characteristic signature of current noise at anti-Stokes frequency. We also identify completely destructive interference in the noise spectra of noninteracting systems with two degenerate transport channels.

  9. Poisson equation for the Mercedes diagram in string theory at genus one

    NASA Astrophysics Data System (ADS)

    Basu, Anirban

    2016-03-01

    The Mercedes diagram has four trivalent vertices which are connected by six links such that they form the edges of a tetrahedron. This three-loop Feynman diagram contributes to the {D}12{{ R }}4 amplitude at genus one in type II string theory, where the vertices are the points of insertion of the graviton vertex operators, and the links are the scalar propagators on the toroidal worldsheet. We obtain a modular invariant Poisson equation satisfied by the Mercedes diagram, where the source terms involve one- and two-loop Feynman diagrams. We calculate its contribution to the {D}12{{ R }}4 amplitude.

  10. Current noise spectra and mechanisms with dissipaton equation of motion theory.

    PubMed

    Jin, Jinshuang; Wang, Shikuan; Zheng, Xiao; Yan, YiJing

    2015-06-21

    Based on the Yan's dissipaton equation of motion (DEOM) theory [J. Chem. Phys. 140, 054105 (2014)], we investigate the characteristic features of current noise spectrum in several typical transport regimes of a single-impurity Anderson model. Many well-known features such as Kondo features are correctly recovered by our DEOM calculations. More importantly, it is revealed that the intrinsic electron cotunneling process is responsible for the characteristic signature of current noise at anti-Stokes frequency. We also identify completely destructive interference in the noise spectra of noninteracting systems with two degenerate transport channels. PMID:26093551

  11. Thin airfoil theory based on approximate solution of the transonic flow equation

    NASA Technical Reports Server (NTRS)

    Spreiter, John R; Alksne, Alberta Y

    1957-01-01

    A method is presented for the approximate solution of the nonlinear equations transonic flow theory. Solutions are found for two-dimensional flows at a Mach number of 1 and for purely subsonic and purely supersonic flows. Results are obtained in closed analytic form for a large and significant class of nonlifting airfoils. At a Mach number of 1 general expressions are given for the pressure distribution on an airfoil of specified geometry and for the shape of an airfoil having a prescribed pressure distribution. Extensive comparisons are made with available data, particularly for a Mach number of 1, and with existing solutions.

  12. Thin airfoil theory based on approximate solution of the transonic flow equation

    NASA Technical Reports Server (NTRS)

    Spreiter, John R; Alksne, Alberta Y

    1958-01-01

    A method is presented for the approximate solution of the nonlinear equations of transonic flow theory. Solutions are found for two-dimensional flows at a Mach number of 1 and for purely subsonic and purely supersonic flows. Results are obtained in closed analytic form for a large and significant class of nonlifting airfoils. At a Mach number of 1 general expressions are given for the pressure distribution on an airfoil of specified geometry and for the shape of an airfoil having a prescribed pressure distribution. Extensive comparisons are made with available data, particularly for a Mach number of 1, and with existing solutions.

  13. Coupled wave equations theory of surface-enhanced femtosecond stimulated Raman scattering.

    PubMed

    McAnally, Michael O; McMahon, Jeffrey M; Van Duyne, Richard P; Schatz, George C

    2016-09-01

    We present a coupled wave semiclassical theory to describe plasmonic enhancement effects in surface-enhanced femtosecond stimulated Raman scattering (SE-FSRS). A key result is that the plasmon enhanced fields which drive the vibrational equation of motion for each normal mode results in dispersive lineshapes in the SE-FSRS spectrum. This result, which reproduces experimental lineshapes, demonstrates that plasmon-enhanced stimulated Raman methods provide unique sensitivity to a plasmonic response. Our derived SE-FSRS theory shows a plasmonic enhancement of |gpu|(2)ImχR(ω)gst (2)/ImχR(ω), where |gpu|(2) is the absolute square of the plasmonic enhancement from the Raman pump, χR(ω) is the Raman susceptibility, and gst is the plasmonic enhancement of the Stokes field in SE-FSRS. We conclude with a discussion on potential future experimental and theoretical directions for the field of plasmonically enhanced coherent Raman scattering. PMID:27608988

  14. Slender-Body Theory Based On Approximate Solution of the Transonic Flow Equation

    NASA Technical Reports Server (NTRS)

    Spreiter, John R.; Alksne, Alberta Y.

    1959-01-01

    Approximate solution of the nonlinear equations of the small disturbance theory of transonic flow are found for the pressure distribution on pointed slender bodies of revolution for flows with free-stream, Mach number 1, and for flows that are either purely subsonic or purely supersonic. These results are obtained by application of a method based on local linearization that was introduced recently in the analysis of similar problems in two-dimensional flows. The theory is developed for bodies of arbitrary shape, and specific results are given for cone-cylinders and for parabolic-arc bodies at zero angle of attack. All results are compared either with existing theoretical results or with experimental data.

  15. Precise determination of critical exponents and equation of state by field theory methods

    NASA Astrophysics Data System (ADS)

    Zinn-Justin, J. Z.

    2001-04-01

    Renormalization group, and in particular its quantum field theory implementation has provided us with essential tools for the description of the phase transitions and critical phenomena beyond mean field theory. We therefore review the methods, based on renormalized φ34 quantum field theory and renormalization group, which have led to a precise determination of critical exponents of the N-vector model (Le Guillou and Zinn-Justin, Phys. Rev. Lett. 39 (1977) 95; Phys. Rev. B 21 (1980) 3976; Guida and Zinn-Justin, J. Phys. A 31 (1998) 8103; cond-mat/9803240) and of the equation of state of the 3D Ising model (Guida and Zinn-Justin, Nucl. Phys. B 489 [FS] (1997) 626, hep-th/9610223). These results are among the most precise available probing field theory in a non-perturbative regime. Precise calculations first require enough terms of the perturbative expansion. However perturbation series are known to be divergent. The divergence has been characterized by relating it to instanton contributions. The information about large-order behaviour of perturbation series has then allowed to develop efficient “summation” techniques, based on Borel transformation and conformal mapping (Le Guillou and Zinn-Justin (Eds.), Large Order Behaviour of Perturbation Theory, Current Physics, vol. 7, North-Holland, Amsterdam, 1990). We first discuss exponents and describe our recent results (Guida and Zinn-Justin, 1998). Compared to exponents, the determination of the scaling equation of state of the 3D Ising model involves a few additional (non-trivial) technical steps, like the use of the parametric representation, and the order dependent mapping method. From the knowledge of the equation of state a number of ratio of critical amplitudes can also be derived. Finally we emphasize that few physical quantities which are predicted by renormalization group to be universal have been determined precisely, and much work remains to be done. Considering the steady increase in the available

  16. Spectral methods for the equations of classical density-functional theory: relaxation dynamics of microscopic films.

    PubMed

    Yatsyshin, Petr; Savva, Nikos; Kalliadasis, Serafim

    2012-03-28

    We propose a numerical scheme based on the Chebyshev pseudo-spectral collocation method for solving the integral and integro-differential equations of the density-functional theory and its dynamic extension. We demonstrate the exponential convergence of our scheme, which typically requires much fewer discretization points to achieve the same accuracy compared to conventional methods. This discretization scheme can also incorporate the asymptotic behavior of the density, which can be of interest in the investigation of open systems. Our scheme is complemented with a numerical continuation algorithm and an appropriate time stepping algorithm, thus constituting a complete tool for an efficient and accurate calculation of phase diagrams and dynamic phenomena. To illustrate the numerical methodology, we consider an argon-like fluid adsorbed on a Lennard-Jones planar wall. First, we obtain a set of phase diagrams corresponding to the equilibrium adsorption and compare our results obtained from different approximations to the hard sphere part of the free energy functional. Using principles from the theory of sub-critical dynamic phase field models, we formulate the time-dependent equations which describe the evolution of the adsorbed film. Through dynamic considerations we interpret the phase diagrams in terms of their stability. Simulations of various wetting and drying scenarios allow us to rationalize the dynamic behavior of the system and its relation to the equilibrium properties of wetting and drying. PMID:22462841

  17. Non-viscous regularization of the Davey-Stewartson equations: Analysis and modulation theory

    NASA Astrophysics Data System (ADS)

    Guo, Yanqiu; Hacinliyan, Irma; Titi, Edriss S.

    2016-08-01

    In the present study, we are interested in the Davey-Stewartson equations (DSE) that model packets of surface and capillary-gravity waves. We focus on the elliptic-elliptic case, for which it is known that DSE may develop a finite-time singularity. We propose three systems of non-viscous regularization to the DSE in a variety of parameter regimes under which the finite-time blow-up of solutions to the DSE occurs. We establish the global well-posedness of the regularized systems for all initial data. The regularized systems, which are inspired by the α-models of turbulence and therefore are called the α-regularized DSE, are also viewed as unbounded, singularly perturbed DSE. Therefore, we also derive reduced systems of ordinary differential equations for the α-regularized DSE by using the modulation theory to investigate the mechanism with which the proposed non-viscous regularization prevents the formation of the singularities in the regularized DSE. This is a follow-up of the work [Cao et al., Nonlinearity 21, 879-898 (2008); Cao et al., Numer. Funct. Anal. Optim. 30, 46-69 (2009)] on the non-viscous α-regularization of the nonlinear Schrödinger equation.

  18. Bayesian structural equation modeling: a more flexible representation of substantive theory.

    PubMed

    Muthén, Bengt; Asparouhov, Tihomir

    2012-09-01

    This article proposes a new approach to factor analysis and structural equation modeling using Bayesian analysis. The new approach replaces parameter specifications of exact zeros with approximate zeros based on informative, small-variance priors. It is argued that this produces an analysis that better reflects substantive theories. The proposed Bayesian approach is particularly beneficial in applications where parameters are added to a conventional model such that a nonidentified model is obtained if maximum-likelihood estimation is applied. This approach is useful for measurement aspects of latent variable modeling, such as with confirmatory factor analysis, and the measurement part of structural equation modeling. Two application areas are studied, cross-loadings and residual correlations in confirmatory factor analysis. An example using a full structural equation model is also presented, showing an efficient way to find model misspecification. The approach encompasses 3 elements: model testing using posterior predictive checking, model estimation, and model modification. Monte Carlo simulations and real data are analyzed using Mplus. The real-data analyses use data from Holzinger and Swineford's (1939) classic mental abilities study, Big Five personality factor data from a British survey, and science achievement data from the National Educational Longitudinal Study of 1988. PMID:22962886

  19. Requirements for Predictive Density Functional Theory Methods for Heavy Materials Equation of State

    NASA Astrophysics Data System (ADS)

    Mattsson, Ann E.; Wills, John M.

    2012-02-01

    The difficulties in experimentally determining the Equation of State of actinide and lanthanide materials has driven the development of many computational approaches with varying degree of empiricism and predictive power. While Density Functional Theory (DFT) based on the Schr"odinger Equation (possibly with relativistic corrections including the scalar relativistic approach) combined with local and semi-local functionals has proven to be a successful and predictive approach for many materials, it is not giving enough accuracy, or even is a complete failure, for the actinides. To remedy this failure both an improved fundamental description based on the Dirac Equation (DE) and improved functionals are needed. Based on results obtained using the appropriate fundamental approach of DFT based on the DE we discuss the performance of available semi-local functionals, the requirements for improved functionals for actinide/lanthanide materials, and the similarities in how functionals behave in transition metal oxides. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

  20. Field transformations and the classical equation of motion in chiral perturbation theory

    SciTech Connect

    Scherer, S.; Fearing, H.W.

    1995-12-01

    The construction of effective Lagrangians commonly involves the application of the ``classical equation of motion`` to eliminate redundant structures and thus generate the minimal number of independent terms. We investigate this procedure in the framework of chiral perturbation theory with particular emphasis on the new features which appear at {ital O}({ital p}{sup 6}). The use of the ``classical equation of motion`` is interpreted in terms of field transformations. Such an interpretation is crucial if one wants to bring a given Lagrangian into a canonical form with a minimal number of terms. We emphasize that the application of field transformations leads to a modification of the coefficients of higher-order terms as well as eliminating structures, or what is equivalent, expressing certain structures in terms of already known different structures. This will become relevant once one considers the problem of expressing in canonical form a model effective interaction containing terms beyond next-to-leading order, i.e., beyond {ital O}({ital p}{sup 4}). In such circumstances the naive application of the clasical equation of motion to simply drop terms, as is commonly done at lowest order, leads to subtle errors, which we discuss.

  1. Stochastic differential equations and turbulent dispersion

    NASA Technical Reports Server (NTRS)

    Durbin, P. A.

    1983-01-01

    Aspects of the theory of continuous stochastic processes that seem to contribute to an understanding of turbulent dispersion are introduced and the theory and philosophy of modelling turbulent transport is emphasized. Examples of eddy diffusion examined include shear dispersion, the surface layer, and channel flow. Modeling dispersion with finite-time scale is considered including the Langevin model for homogeneous turbulence, dispersion in nonhomogeneous turbulence, and the asymptotic behavior of the Langevin model for nonhomogeneous turbulence.

  2. Equations of state of freely jointed hard-sphere chain fluids: Theory

    SciTech Connect

    Stell, G.; Lin, C.; Kalyuzhnyi, Y.V.

    1999-03-01

    Using the analytical solution of a multidensity integral equation solved in our previous papers [J. Chem. Phys. {bold 108}, 6513, 6525 (1998)], we derive two compressibility and two virial equations of state (EOS) for freely jointed hard-sphere chain fluids on the basis of the approximations defined by the polymer Percus{endash}Yevick (PPY) closure and of the PPY ideal-chain closure for the integral equations. We also extend a version of first-order thermodynamic perturbation theory to polymers, using a dimer fluid as the reference system, to treat mixtures of heteronuclear chain fluids and polymer solutions; the structural information of the dimer fluid is obtained from the PPY ideal-chain approximation in the complete-association limit. The attractive forces between monomers of chain molecules are treated using simple perturbation theory. We find that the compressibility EOS derived on the basis of the PPY approximation subject to the chain-connectivity condition reduces to the compressibility EOS based upon the PPY ideal-chain approximation in the complete-association limit, which is also equivalent to the EOS derived by Chiew [Mol. Phys. {bold 70}, 129 (1990)] and to the EOS derived by Kalyuzhnyi and Cummings [J. Chem. Phys. {bold 105}, 2011 (1996)]. On the other hand, the virial EOS derived on the basis of the PPY ideal-chain approximation coincides with Attard{close_quote}s virial EOS [J. Chem. Phys. {bold 102}, 5411 (1995)] only in the zero-density limit. The advantages in numerical implementation of the EOS presented in this work are also discussed, but a full quantitative assessment of our results and a detailed numerical comparison among them are made in a companion paper, as is comparison with available simulation results. {copyright} {ital 1999 American Institute of Physics.}

  3. Toward a General Theory for Multiphase Turbulence Part I: Development and Gauging of the Model Equations

    SciTech Connect

    B. A. Kashiwa; W. B. VanderHeyden

    2000-12-01

    A formalism for developing multiphase turbulence models is introduced by analogy to the phenomenological method used for single-phase turbulence. A sample model developed using the formalism is given in detail. The procedure begins with ensemble averaging of the exact conservation equations, with closure accomplished by using a combination of analytical and experimental results from the literature. The resulting model is applicable to a wide range of common multiphase flows including gas-solid, liquid-solid and gas-liquid (bubbly) flows. The model is positioned for ready extension to three-phase turbulence, or for use in two-phase turbulence in which one phase is accounted for in multiple size classes, representing polydispersivity. The formalism is expected to suggest directions toward a more fundamentally based theory, similar to the way that early work in single-phase turbulence has led to the spectral theory. The approach is unique in that a portion of the total energy decay rate is ascribed to each phase, as is dictated by the exact averaged equations, and results in a transport equation for energy decay rate associated with each phase. What follows is a straightforward definition of a turbulent viscosity for each phase, and accounts for the effect of exchange of fluctuational energy among phases on the turbulent shear viscosity. The model also accounts for the effect of slip momentum transfer among the phases on the production of turbulence kinetic energy and on the tensor character of the Reynolds stress. Collisional effects, when appropriate, are included by superposition. The model reduces to a standard form in limit of a single, pure material, and is expected to do a credible job of describing multiphase turbulent flows in a wide variety of regimes using a single set of coefficients.

  4. Inertial stochastic dynamics. I. Long-time-step methods for Langevin dynamics

    NASA Astrophysics Data System (ADS)

    Beard, Daniel A.; Schlick, Tamar

    2000-05-01

    Two algorithms are presented for integrating the Langevin dynamics equation with long numerical time steps while treating the mass terms as finite. The development of these methods is motivated by the need for accurate methods for simulating slow processes in polymer systems such as two-site intermolecular distances in supercoiled DNA, which evolve over the time scale of milliseconds. Our new approaches refine the common Brownian dynamics (BD) scheme, which approximates the Langevin equation in the highly damped diffusive limit. Our LTID ("long-time-step inertial dynamics") method is based on an eigenmode decomposition of the friction tensor. The less costly integrator IBD ("inertial Brownian dynamics") modifies the usual BD algorithm by the addition of a mass-dependent correction term. To validate the methods, we evaluate the accuracy of LTID and IBD and compare their behavior to that of BD for the simple example of a harmonic oscillator. We find that the LTID method produces the expected correlation structure for Langevin dynamics regardless of the level of damping. In fact, LTID is the only consistent method among the three, with error vanishing as the time step approaches zero. In contrast, BD is accurate only for highly overdamped systems. For cases of moderate overdamping, and for the appropriate choice of time step, IBD is significantly more accurate than BD. IBD is also less computationally expensive than LTID (though both are the same order of complexity as BD), and thus can be applied to simulate systems of size and time scale ranges previously accessible to only the usual BD approach. Such simulations are discussed in our companion paper, for long DNA molecules modeled as wormlike chains.

  5. Integral equation theory of the structure and thermodynamics of polymer blends

    NASA Astrophysics Data System (ADS)

    Schweizer, Kenneth S.; Curro, John G.

    1989-10-01

    Our recently developed RISM integral equation theory of the structure and thermodynamics of homopolymer melts is generalized to polymer mixtures. The mean spherical approximation (MSA) closure to the generalized Ornstein-Zernike equations is employed, in conjunction with the neglect of explicit chain end effects and the assumption of ideality of intramolecular structure. The theory is developed in detail for binary blends, and the random phase approximation (RPA) form for concentration fluctuation scattering is rigorously obtained by enforcing incompressibility. A microscopic, wave vector-dependent expression for the effective chi parameter measured in small angle neutron scattering (SANS) experiments is derived in terms of the species-dependent direct correlation functions of the blend. The effective chi parameter is found to depend, in general, on thermodynamic state, intermolecular forces, intramolecular structure, degree of polymerization, and global architecture. The relationship between the mean field Flory-Huggins expression for the free energy of mixing and our RISM-MSA theory is determined, along with general analytical connections between the chi parameter and intermolecular pair correlations in the liquid. Detailed numerical applications to athermal and isotopic chain polymer blend models are presented for both the chi parameter and the structure. For athermal blends a negative, concentration-dependent chi parameter is found which decreases with density, structural asymmetry, and increases with molecular weight. For isotopic blends, the effective (positive) chi parameter is found to be strongly renormalized downward from its mean field enthalpic value by long range fluctuations in monomer concentration induced by polymeric connectivity and excluded volume. Both the renormalization and composition dependence of the chi parameter increase with chain length and proximity to the spinodal instability. The critical temperature is found to be proportional to

  6. Padé Approximants for the Equation of State for Relativistic Hydrodynamics by Kinetic Theory

    NASA Astrophysics Data System (ADS)

    Tsai, Shang-Hsi; Yang, Jaw-Yen

    2015-07-01

    A two-point Padé approximant (TPPA) algorithm is developed for the equation of state (EOS) for relativistic hydrodynamic systems, which are described by the classical Maxwell-Boltzmann statistics and the semiclassical Fermi-Dirac statistics with complete degeneracy. The underlying rational function is determined by the ratios of the macroscopic state variables with various orders of accuracy taken at the extreme relativistic limits. The nonunique TPPAs are validated by Taub's inequality for the consistency of the kinetic theory and the special theory of relativity. The proposed TPPA is utilized in deriving the EOS of the dilute gas and in calculating the specific heat capacity, the adiabatic index function, and the isentropic sound speed of the ideal gas. Some general guidelines are provided for the application of an arbitrary accuracy requirement. The superiority of the proposed TPPA is manifested in manipulating the constituent polynomials of the approximants, which avoids the arithmetic complexity of struggling with the modified Bessel functions and the hyperbolic trigonometric functions arising from the relativistic kinetic theory.

  7. A nonparametric scaling equation of state, developed on the basis of the Migdal's phenomenological theory and Benedek's hypothesis

    NASA Astrophysics Data System (ADS)

    Kudryavtseva, I. V.; Rykov, S. V.

    2016-07-01

    A new nonparametric scaling equation with density and temperature as variables is proposed using the phenomenological theory of critical phenomena and the experimentally confirmed Benedek's hypothesis, on the basis of which we assume that the behavior of a number of thermodynamic functions for the critical and near-critical isochores in the neighborhood of an asymptotic critical point is similar. In comparison to Scofield's linear model (LM), the proposed scale equation is not inferior to known nonparametric equations of the same type; in contrast to the latter, however, its physical grounds are just as valid as the LM equation.

  8. Quantum theory of multiwave mixing - Squeezed-vacuum model

    NASA Astrophysics Data System (ADS)

    An, Sunghyuck; Sargent, Murray, III

    1989-12-01

    The present paper combines a Langevin quantum-regression method with a denisty-operator approach to derive the master equation for the quantum theory of multiwave mixing in a very efficient way. The approach is quite general and is particularly valuable for analyzing complicated media such as semiconductors. It is used in the present paper to derive the quantum multiwave-mixing equations in a squeezed vacuum. Improved formulas are found for resonance fluorescence in a squeezed vacuum as well as the squeezing coefficients in a squeezed vacuum. Comparing squeezing spectra in squeezed and ordinary vacuums, significantly enhanced squeezing for the appropriate pump-vacuum relative phase is found.

  9. Two-dimensional Langevin modeling of fission dynamics of the excited compound nuclei 188Pt, 227Pa and 251Es

    NASA Astrophysics Data System (ADS)

    Eslamizadeh, H.

    2016-02-01

    A stochastic approach based on one- and two-dimensional Langevin equations is applied to calculate the pre-scission neutron multiplicity, fission probability, anisotropy of fission fragment angular distribution, fission cross section and the evaporation cross section for the compound nuclei 188Pt, 227Pa and 251Es in an intermediate range of excitation energies. The chaos weighted wall and window friction formula are used in the Langevin equations. The elongation parameter, c, is used as the first dimension and projection of the total spin of the compound nucleus onto the symmetry axis, K, considered as the second dimension in Langevin dynamical calculations. A constant dissipation coefficient of K, γK = 0.077(MeV zs)-1/2, is used in two-dimensional calculations to reproduce the above mentioned experimental data. Comparison of the theoretical results of the pre-scission neutron multiplicity, fission probability, fission cross section and the evaporation cross section with the experimental data shows that the results of two-dimensional calculations are in better agreement with the experimental data. Furthermore, it is shown that the two-dimensional Langevin equations together with a dissipation coefficient of K, γK = 0.077(MeV zs)-1/2, can satisfactorily reproduce the anisotropy of fission fragment angular distribution for the heavy compound nucleus 251Es. However, a larger value of γK = 0.250(MeV zs)-1/2 is needed to reproduce the anisotropy of fission fragment angular distribution for the lighter compound nucleus 227Pa.

  10. Molecular response properties in equation of motion coupled cluster theory: A time-dependent perspective

    NASA Astrophysics Data System (ADS)

    Coriani, Sonia; Pawłowski, Filip; Olsen, Jeppe; Jørgensen, Poul

    2016-01-01

    Molecular response properties for ground and excited states and for transitions between these states are defined by solving the time-dependent Schrödinger equation for a molecular system in a field of a time-periodic perturbation. In equation of motion coupled cluster (EOM-CC) theory, molecular response properties are commonly obtained by replacing, in configuration interaction (CI) molecular response property expressions, the energies and eigenstates of the CI eigenvalue equation with the energies and eigenstates of the EOM-CC eigenvalue equation. We show here that EOM-CC molecular response properties are identical to the molecular response properties that are obtained in the coupled cluster-configuration interaction (CC-CI) model, where the time-dependent Schrödinger equation is solved using an exponential (coupled cluster) parametrization to describe the unperturbed system and a linear (configuration interaction) parametrization to describe the time evolution of the unperturbed system. The equivalence between EOM-CC and CC-CI molecular response properties only holds when the CI molecular response property expressions—from which the EOM-CC expressions are derived—are determined using projection and not using the variational principle. In a previous article [F. Pawłowski, J. Olsen, and P. Jørgensen, J. Chem. Phys. 142, 114109 (2015)], it was stated that the equivalence between EOM-CC and CC-CI molecular response properties only held for a linear response function, whereas quadratic and higher order response functions were mistakenly said to differ in the two approaches. Proving the general equivalence between EOM-CC and CC-CI molecular response properties is a challenging task, that is undertaken in this article. Proving this equivalence not only corrects the previous incorrect statement but also first and foremost leads to a new, time-dependent, perspective for understanding the basic assumptions on which the EOM-CC molecular response property expressions

  11. Molecular response properties in equation of motion coupled cluster theory: A time-dependent perspective.

    PubMed

    Coriani, Sonia; Pawłowski, Filip; Olsen, Jeppe; Jørgensen, Poul

    2016-01-14

    Molecular response properties for ground and excited states and for transitions between these states are defined by solving the time-dependent Schrödinger equation for a molecular system in a field of a time-periodic perturbation. In equation of motion coupled cluster (EOM-CC) theory, molecular response properties are commonly obtained by replacing, in configuration interaction (CI) molecular response property expressions, the energies and eigenstates of the CI eigenvalue equation with the energies and eigenstates of the EOM-CC eigenvalue equation. We show here that EOM-CC molecular response properties are identical to the molecular response properties that are obtained in the coupled cluster-configuration interaction (CC-CI) model, where the time-dependent Schrödinger equation is solved using an exponential (coupled cluster) parametrization to describe the unperturbed system and a linear (configuration interaction) parametrization to describe the time evolution of the unperturbed system. The equivalence between EOM-CC and CC-CI molecular response properties only holds when the CI molecular response property expressions-from which the EOM-CC expressions are derived-are determined using projection and not using the variational principle. In a previous article [F. Pawłowski, J. Olsen, and P. Jørgensen, J. Chem. Phys. 142, 114109 (2015)], it was stated that the equivalence between EOM-CC and CC-CI molecular response properties only held for a linear response function, whereas quadratic and higher order response functions were mistakenly said to differ in the two approaches. Proving the general equivalence between EOM-CC and CC-CI molecular response properties is a challenging task, that is undertaken in this article. Proving this equivalence not only corrects the previous incorrect statement but also first and foremost leads to a new, time-dependent, perspective for understanding the basic assumptions on which the EOM-CC molecular response property expressions are

  12. Advances in numerical solutions to integral equations in liquid state theory

    NASA Astrophysics Data System (ADS)

    Howard, Jesse J.

    Solvent effects play a vital role in the accurate description of the free energy profile for solution phase chemical and structural processes. The inclusion of solvent effects in any meaningful theoretical model however, has proven to be a formidable task. Generally, methods involving Poisson-Boltzmann (PB) theory and molecular dynamic (MD) simulations are used, but they either fail to accurately describe the solvent effects or require an exhaustive computation effort to overcome sampling problems. An alternative to these methods are the integral equations (IEs) of liquid state theory which have become more widely applicable due to recent advancements in the theory of interaction site fluids and the numerical methods to solve the equations. In this work a new numerical method is developed based on a Newton-type scheme coupled with Picard/MDIIS routines. To extend the range of these numerical methods to large-scale data systems, the size of the Jacobian is reduced using basis functions, and the Newton steps are calculated using a GMRes solver. The method is then applied to calculate solutions to the 3D reference interaction site model (RISM) IEs of statistical mechanics, which are derived from first principles, for a solute model of a pair of parallel graphene plates at various separations in pure water. The 3D IEs are then extended to electrostatic models using an exact treatment of the long-range Coulomb interactions for negatively charged walls and DNA duplexes in aqueous electrolyte solutions to calculate the density profiles and solution thermodynamics. It is found that the 3D-IEs provide a qualitative description of the density distributions of the solvent species when compared to MD results, but at a much reduced computational effort in comparison to MD simulations. The thermodynamics of the solvated systems are also qualitatively reproduced by the IE results. The findings of this work show the IEs to be a valuable tool for the study and prediction of

  13. Fierz-Pauli equation for massive gravitons from Induced Matter theory of gravity

    NASA Astrophysics Data System (ADS)

    Bellini, Mauricio

    2011-01-01

    Starting with a 5D physical vacuum described by a 5D Ricci-flat background metric, we study the emergence of gravitational waves (GW) from the Induce Matter (IM) theory of gravity. We obtain the equation of motion for GW on a 4D curved spacetime which has the form of a Fierz-Pauli one. In our model the mass of gravitons mg is induced by a static foliation on the noncompact space-like extra dimension and the source-term is originated in the interaction of the GW with the induced connections of the background 5D metric. Here, relies the main difference of this formalism with the original Fierz-Pauli one.

  14. Periodic solutions of Lienard differential equations via averaging theory of order two.

    PubMed

    Llibre, Jaume; Novaes, Douglas D; Teixeira, Marco A

    2015-01-01

    For ε ≠ 0 sufficiently small we provide sufficient conditions for the existence of periodic solutions for the Lienard differential equations of the form x'' + f ⁢(x)⁢ x' + n2⁢x + g (x) = ε2p1 ⁢(t) + ε3 ⁢p2(t), where n is a positive integer, f : ℝ → ℝ is a C 3 function, g : ℝ → ℝ is a C 4 function, and p i : ℝ → ℝ for i = 1, 2 are continuous 2π-periodic function. The main tool used in this paper is the averaging theory of second order. We also provide one application of the main result obtained. PMID:26648545

  15. Integral-equation approach to the weak-field asymptotic theory of tunneling ionization

    NASA Astrophysics Data System (ADS)

    Dnestryan, Andrey I.; Tolstikhin, Oleg I.

    2016-03-01

    An integral equation approach to the weak-field asymptotic theory (WFAT) of tunneling ionization is developed. An integral representation for the exact partial amplitudes of ionization into parabolic channels is derived. The WFAT expansion for the ionization rate follows immediately from this relation. Integral representations for the coefficients in the expansion are obtained. The integrals accumulate where the ionizing orbital has large amplitude and are not sensitive to its behavior in the asymptotic region. Hence, these formulas enable one to reliably calculate the WFAT coefficients even if the orbital is represented by an expansion in Gaussian basis, as is usually the case in standard software packages for electronic structure calculations. This development is expected to greatly simplify the implementation of the WFAT for polyatomic molecules, and thus facilitate its growing applications in strong-field physics.

  16. Elementary solutions of coupled model equations in the kinetic theory of gases

    NASA Technical Reports Server (NTRS)

    Kriese, J. T.; Siewert, C. E.; Chang, T. S.

    1974-01-01

    The method of elementary solutions is employed to solve two coupled integrodifferential equations sufficient for determining temperature-density effects in a linearized BGK model in the kinetic theory of gases. Full-range completeness and orthogonality theorems are proved for the developed normal modes and the infinite-medium Green's function is constructed as an illustration of the full-range formalism. The appropriate homogeneous matrix Riemann problem is discussed, and half-range completeness and orthogonality theorems are proved for a certain subset of the normal modes. The required existence and uniqueness theorems relevant to the H matrix, basic to the half-range analysis, are proved, and an accurate and efficient computational method is discussed. The half-space temperature-slip problem is solved analytically, and a highly accurate value of the temperature-slip coefficient is reported.

  17. Solution of the one-dimensional consolidation theory equation with a pseudospectral method

    USGS Publications Warehouse

    Sepulveda, N.

    1991-01-01

    The one-dimensional consolidation theory equation is solved for an aquifer system using a pseudospectral method. The spatial derivatives are computed using Fast Fourier Transforms and the time derivative is solved using a fourth-order Runge-Kutta scheme. The computer model calculates compaction based on the void ratio changes accumulated during the simulated periods of time. Compactions and expansions resulting from groundwater withdrawals and recharges are simulated for two observation wells in Santa Clara Valley and two in San Joaquin Valley, California. Field data previously published are used to obtain mean values for the soil grain density and the compression index and to generate depth-dependent profiles for hydraulic conductivity and initial void ratio. The water-level plots for the wells studied were digitized and used to obtain the time dependent profiles of effective stress.

  18. Didactic derivation of the special theory of relativity from the Klein-Gordon equation

    NASA Astrophysics Data System (ADS)

    Arodź, H.

    2014-09-01

    We present a didactic derivation of the special theory of relativity in which Lorentz transformations are ‘discovered’ as symmetry transformations of the Klein-Gordon equation. The interpretation of Lorentz boosts as transformations to moving inertial reference frames is not assumed at the start, but it naturally appears at a later stage. The relative velocity v of two inertial reference frames is defined in terms of the elements of the pertinent Lorentz matrix, and the bound |{\\bf v}| is presented as a simple theorem that follows from the structure of the Lorentz group. The polar decomposition of Lorentz matrices is used to explain noncommutativity and nonassociativity of the relativistic composition (‘addition’) of velocities.

  19. Mixing of equations of state for xenon-deuterium using density functional theory

    SciTech Connect

    Magyar, Rudolph J.; Mattsson, Thomas R.

    2013-03-15

    We report on a theoretical study of equation of state (EOS) properties of fluid and dense plasma mixtures of xenon and deuterium to explore and illustrate the basic physics of the mixing of a light element with a heavy element. Accurate EOS models are crucial to achieve high-fidelity hydrodynamics simulations of many high-energy-density phenomena, for example inertial confinement fusion and strong shock waves. While the EOS is often tabulated for separate species, the equation of state for arbitrary mixtures is generally not available, requiring properties of the mixture to be approximated by combining physical properties of the pure systems. Density functional theory (DFT) at elevated-temperature is used to assess the thermodynamics of the xenon-deuterium mixture at different mass ratios. The DFT simulations are unbiased as to elemental species and therefore provide comparable accuracy when describing total energies, pressures, and other physical properties of mixtures as they do for pure systems. The study focuses on addressing the accuracy of different mixing rules in the temperature range 1000-40 000 K for pressures between 100 and 600 GPa (1-6 Mbar), thus, including the challenging warm dense matter regime of the phase diagram. We find that a mix rule taking into account pressure equilibration between the two species performs very well over the investigated range.

  20. Tensor decomposition techniques in the solution of vibrational coupled cluster response theory eigenvalue equations

    NASA Astrophysics Data System (ADS)

    Godtliebsen, Ian H.; Hansen, Mads Bøttger; Christiansen, Ove

    2015-01-01

    We show how the eigenvalue equations of vibrational coupled cluster response theory can be solved using a subspace projection method with Davidson update, where basis vectors are stacked tensors decomposed into canonical (CP, Candecomp/Parafac) form. In each update step, new vectors are first orthogonalized to old vectors, followed by a tensor decomposition to a prescribed threshold TCP. The algorithm can provide excitation energies and eigenvectors of similar accuracy as a full vector approach and with only a very modest increase in the number of vectors required for convergence. The algorithm is illustrated with sample calculations for formaldehyde, 1,2,5-thiadiazole, and water. Analysis of the formaldehyde and thiadiazole calculations illustrate a number of interesting features of the algorithm. For example, the tensor decomposition threshold is optimally put to rather loose values, such as TCP = 10-2. With such thresholds for the tensor decompositions, the original eigenvalue equations can still be solved accurately. It is thus possible to directly calculate vibrational wave functions in tensor decomposed format.

  1. On the question of current conservation for the two-body Dirac equations of constraint theory

    NASA Astrophysics Data System (ADS)

    Lienert, Matthias

    2015-08-01

    The two-body Dirac (2BD) equations of constraint theory are of special interest not only in view of applications for phenomenological calculations of mesonic spectra but also because they avoid no-go theorems about relativistic interactions. Furthermore, they provide a quantum mechanical description in a manifestly Lorentz invariant way using the concept of a multi-time wave function. In this paper, we place them into the context of the multi-time formalism of Dirac, Tomonaga and Schwinger for the first time. A general physical and mathematical framework is outlined and the mechanism which permits relativistic interaction is identified. The main requirement derived from the general framework is the existence of conserved tensor currents with a positive component which can play the role of a probability density. We analyze this question for a general class of 2BD equations thoroughly and comprehensively. While the free Dirac current is not conserved, it is possible to find replacements. Improving on previous research, we achieve definite conclusions whether restrictions of the function space or of the interaction terms can guarantee the positive definiteness of the currents—and whether such restrictions are physically adequate. The consequences of the results are drawn, with respect to both applied and foundational perspectives.

  2. A dispersion minimizing scheme for the 3-D Helmholtz equation based on ray theory

    NASA Astrophysics Data System (ADS)

    Stolk, Christiaan C.

    2016-06-01

    We develop a new dispersion minimizing compact finite difference scheme for the Helmholtz equation in 2 and 3 dimensions. The scheme is based on a newly developed ray theory for difference equations. A discrete Helmholtz operator and a discrete operator to be applied to the source and the wavefields are constructed. Their coefficients are piecewise polynomial functions of hk, chosen such that phase and amplitude errors are minimal. The phase errors of the scheme are very small, approximately as small as those of the 2-D quasi-stabilized FEM method and substantially smaller than those of alternatives in 3-D, assuming the same number of gridpoints per wavelength is used. In numerical experiments, accurate solutions are obtained in constant and smoothly varying media using meshes with only five to six points per wavelength and wave propagation over hundreds of wavelengths. When used as a coarse level discretization in a multigrid method the scheme can even be used with down to three points per wavelength. Tests on 3-D examples with up to 108 degrees of freedom show that with a recently developed hybrid solver, the use of coarser meshes can lead to corresponding savings in computation time, resulting in good simulation times compared to the literature.

  3. Actinide electronic structure based on the Dirac equation and density functional theory

    NASA Astrophysics Data System (ADS)

    Wills, John M.; Mattsson, Ann E.

    2013-03-01

    Density functional theory (DFT) provides a formally predictive basis for predicting the structural properties of actinides. Although available approximations to the exchange/correlation functional provide accurate predictions for many materials, they fail qualitatively and sometimes quantitatively when applied to actinides. Major contributors to this deficiency are an inadequate treatment of confinement physics and an incomplete treatment of relativity in the underlying equations. The development of a functional correctly incorporating confinement physics with a proper treatment of relativity would provide definitive, internally consistent predictions of actinide properties. To enable the development of such a functional and quantify the predictions of currently available functionals, we have developed an efficient first-principles electronic structure method based on the Dirac equation. Results are compared with current methods, and the implications for relativistic density functionals discussed. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

  4. Theory of runaway electrons in ITER: Equations, important parameters, and implications for mitigation

    SciTech Connect

    Boozer, Allen H.

    2015-03-15

    The plasma current in ITER cannot be allowed to transfer from thermal to relativistic electron carriers. The potential for damage is too great. Before the final design is chosen for the mitigation system to prevent such a transfer, it is important that the parameters that control the physics be understood. Equations that determine these parameters and their characteristic values are derived. The mitigation benefits of the injection of impurities with the highest possible atomic number Z and the slowing plasma cooling during halo current mitigation to ≳40 ms in ITER are discussed. The highest possible Z increases the poloidal flux consumption required for each e-fold in the number of relativistic electrons and reduces the number of high energy seed electrons from which exponentiation builds. Slow cooling of the plasma during halo current mitigation also reduces the electron seed. Existing experiments could test physics elements required for mitigation but cannot carry out an integrated demonstration. ITER itself cannot carry out an integrated demonstration without excessive danger of damage unless the probability of successful mitigation is extremely high. The probability of success depends on the reliability of the theory. Equations required for a reliable Monte Carlo simulation are derived.

  5. Continuum regularization of gauge theory with fermions

    SciTech Connect

    Chan, H.S.

    1987-03-01

    The continuum regularization program is discussed in the case of d-dimensional gauge theory coupled to fermions in an arbitrary representation. Two physically equivalent formulations are given. First, a Grassmann formulation is presented, which is based on the two-noise Langevin equations of Sakita, Ishikawa and Alfaro and Gavela. Second, a non-Grassmann formulation is obtained by regularized integration of the matter fields within the regularized Grassmann system. Explicit perturbation expansions are studied in both formulations, and considerable simplification is found in the integrated non-Grassmann formalism.

  6. Diffusion in the special theory of relativity.

    PubMed

    Herrmann, Joachim

    2009-11-01

    The Markovian diffusion theory is generalized within the framework of the special theory of relativity. Since the velocity space in relativity is a hyperboloid, the mathematical stochastic calculus on Riemanian manifolds can be applied but adopted here to the velocity space. A generalized Langevin equation in the fiber space of position, velocity, and orthonormal velocity frames is defined from which the generalized relativistic Kramers equation in the phase space in external force fields is derived. The obtained diffusion equation is invariant under Lorentz transformations and its stationary solution is given by the Jüttner distribution. Besides, a nonstationary analytical solution is derived for the example of force-free relativistic diffusion. PMID:20364950

  7. Generalized Langevin dynamics of a nanoparticle using a finite element approach: Thermostating with correlated noise

    NASA Astrophysics Data System (ADS)

    Uma, B.; Swaminathan, T. N.; Ayyaswamy, P. S.; Eckmann, D. M.; Radhakrishnan, R.

    2011-09-01

    A direct numerical simulation (DNS) procedure is employed to study the thermal motion of a nanoparticle in an incompressible Newtonian stationary fluid medium with the generalized Langevin approach. We consider both the Markovian (white noise) and non-Markovian (Ornstein-Uhlenbeck noise and Mittag-Leffler noise) processes. Initial locations of the particle are at various distances from the bounding wall to delineate wall effects. At thermal equilibrium, the numerical results are validated by comparing the calculated translational and rotational temperatures of the particle with those obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation functions and mean square displacements with analytical results. Numerical predictions of wall interactions with the particle in terms of mean square displacements are compared with analytical results. In the non-Markovian Langevin approach, an appropriate choice of colored noise is required to satisfy the power-law decay in the velocity autocorrelation function at long times. The results obtained by using non-Markovian Mittag-Leffler noise simultaneously satisfy the equipartition theorem and the long-time behavior of the hydrodynamic correlations for a range of memory correlation times. The Ornstein-Uhlenbeck process does not provide the appropriate hydrodynamic correlations. Comparing our DNS results to the solution of an one-dimensional generalized Langevin equation, it is observed that where the thermostat adheres to the equipartition theorem, the characteristic memory time in the noise is consistent with the inherent time scale of the memory kernel. The performance of the thermostat with respect to equilibrium and dynamic properties for various noise schemes is discussed.

  8. Hybrid two-chain simulation and integral equation theory : application to polyethylene liquids.

    SciTech Connect

    Huimin Li, David T. Wu; Curro, John G.; McCoy, John Dwane

    2006-02-01

    We present results from a hybrid simulation and integral equation approach to the calculation of polymer melt properties. The simulation consists of explicit Monte Carlo (MC) sampling of two polymer molecules, where the effect of the surrounding chains is accounted for by an HNC solvation potential. The solvation potential is determined from the Polymer Reference Interaction Site Model (PRISM) as a functional of the pair correlation function from simulation. This hybrid two-chain MC-PRISM approach was carried out on liquids of polyethylene chains of 24 and 66 CH{sub 2} units. The results are compared with MD simulation and self-consistent PRISM-PY theory under the same conditions, revealing that the two-chain calculation is close to MD, and able to overcome the defects of the PRISM-PY closure and predict more accurate structures of the liquid at both short and long range. The direct correlation function, for instance, has a tail at longer range which is consistent with MD simulation and avoids the short-range assumptions in PRISM-PY theory. As a result, the self-consistent two-chain MC-PRISM calculation predicts an isothermal compressibility closer to the MD results.

  9. Solvation effects on chemical shifts by embedded cluster integral equation theory.

    PubMed

    Frach, Roland; Kast, Stefan M

    2014-12-11

    The accurate computational prediction of nuclear magnetic resonance (NMR) parameters like chemical shifts represents a challenge if the species studied is immersed in strongly polarizing environments such as water. Common approaches to treating a solvent in the form of, e.g., the polarizable continuum model (PCM) ignore strong directional interactions such as H-bonds to the solvent which can have substantial impact on magnetic shieldings. We here present a computational methodology that accounts for atomic-level solvent effects on NMR parameters by extending the embedded cluster reference interaction site model (EC-RISM) integral equation theory to the prediction of chemical shifts of N-methylacetamide (NMA) in aqueous solution. We examine the influence of various so-called closure approximations of the underlying three-dimensional RISM theory as well as the impact of basis set size and different treatment of electrostatic solute-solvent interactions. We find considerable and systematic improvement over reference PCM and gas phase calculations. A smaller basis set in combination with a simple point charge model already yields good performance which can be further improved by employing exact electrostatic quantum-mechanical solute-solvent interaction energies. A larger basis set benefits more significantly from exact over point charge electrostatics, which can be related to differences of the solvent's charge distribution. PMID:25377116

  10. Unified field theory from the classical wave equation: Preliminary application to atomic and nuclear structure

    NASA Astrophysics Data System (ADS)

    Múnera, Héctor A.

    2016-07-01

    It is postulated that there exists a fundamental energy-like fluid, which occupies the flat three-dimensional Euclidean space that contains our universe, and obeys the two basic laws of classical physics: conservation of linear momentum, and conservation of total energy; the fluid is described by the classical wave equation (CWE), which was Schrödinger's first candidate to develop his quantum theory. Novel solutions for the CWE discovered twenty years ago are nonharmonic, inherently quantized, and universal in the sense of scale invariance, thus leading to quantization at all scales of the universe, from galactic clusters to the sub-quark world, and yielding a unified Lorentz-invariant quantum theory ab initio. Quingal solutions are isomorphic under both neo-Galilean and Lorentz transformations, and exhibit nother remarkable property: intrinsic unstability for large values of ℓ (a quantum number), thus limiting the size of each system at a given scale. Unstability and scale-invariance together lead to nested structures observed in our solar system; unstability may explain the small number of rows in the chemical periodic table, and nuclear unstability of nuclides beyond lead and bismuth. Quingal functions lend mathematical basis for Boscovich's unified force (which is compatible with many pieces of evidence collected over the past century), and also yield a simple geometrical solution for the classical three-body problem, which is a useful model for electronic orbits in simple diatomic molecules. A testable prediction for the helicoidal-type force is suggested.

  11. A new theory for multistep discretizations of stiff ordinary differential equations: Stability with large step sizes

    NASA Technical Reports Server (NTRS)

    Majda, G.

    1985-01-01

    A large set of variable coefficient linear systems of ordinary differential equations which possess two different time scales, a slow one and a fast one is considered. A small parameter epsilon characterizes the stiffness of these systems. A system of o.d.e.s. in this set is approximated by a general class of multistep discretizations which includes both one-leg and linear multistep methods. Sufficient conditions are determined under which each solution of a multistep method is uniformly bounded, with a bound which is independent of the stiffness of the system of o.d.e.s., when the step size resolves the slow time scale, but not the fast one. This property is called stability with large step sizes. The theory presented lets one compare properties of one-leg methods and linear multistep methods when they approximate variable coefficient systems of stiff o.d.e.s. In particular, it is shown that one-leg methods have better stability properties with large step sizes than their linear multistep counter parts. The theory also allows one to relate the concept of D-stability to the usual notions of stability and stability domains and to the propagation of errors for multistep methods which use large step sizes.

  12. Primer vector theory applied to the linear relative-motion equations. [for N-impulse space trajectory optimization

    NASA Technical Reports Server (NTRS)

    Jezewski, D.

    1980-01-01

    Prime vector theory is used in analyzing a set of linear relative-motion equations - the Clohessy-Wiltshire (C/W) equations - to determine the criteria and necessary conditions for an optimal N-impulse trajectory. The analysis develops the analytical criteria for improving a solution by: (1) moving any dependent or independent variable in the initial and/or final orbit, and (2) adding intermediate impulses. If these criteria are violated, the theory establishes a sufficient number of analytical equations. The subsequent satisfaction of these equations will result in the optimal position vectors and times of an N-impulse trajectory. The solution is examined for the specific boundary conditions of: (1) fixed-end conditions, two impulse, and time-open transfer; (2) an orbit-to-orbit transfer; and (3) a generalized renezvous problem.

  13. Designing molecular complexes using free-energy derivatives from liquid-state integral equation theory.

    PubMed

    Mrugalla, Florian; Kast, Stefan M

    2016-09-01

    Complex formation between molecules in solution is the key process by which molecular interactions are translated into functional systems. These processes are governed by the binding or free energy of association which depends on both direct molecular interactions and the solvation contribution. A design goal frequently addressed in pharmaceutical sciences is the optimization of chemical properties of the complex partners in the sense of minimizing their binding free energy with respect to a change in chemical structure. Here, we demonstrate that liquid-state theory in the form of the solute-solute equation of the reference interaction site model provides all necessary information for such a task with high efficiency. In particular, computing derivatives of the potential of mean force (PMF), which defines the free-energy surface of complex formation, with respect to potential parameters can be viewed as a means to define a direction in chemical space toward better binders. We illustrate the methodology in the benchmark case of alkali ion binding to the crown ether 18-crown-6 in aqueous solution. In order to examine the validity of the underlying solute-solute theory, we first compare PMFs computed by different approaches, including explicit free-energy molecular dynamics simulations as a reference. Predictions of an optimally binding ion radius based on free-energy derivatives are then shown to yield consistent results for different ion parameter sets and to compare well with earlier, orders-of-magnitude more costly explicit simulation results. This proof-of-principle study, therefore, demonstrates the potential of liquid-state theory for molecular design problems. PMID:27366935

  14. Designing molecular complexes using free-energy derivatives from liquid-state integral equation theory

    NASA Astrophysics Data System (ADS)

    Mrugalla, Florian; Kast, Stefan M.

    2016-09-01

    Complex formation between molecules in solution is the key process by which molecular interactions are translated into functional systems. These processes are governed by the binding or free energy of association which depends on both direct molecular interactions and the solvation contribution. A design goal frequently addressed in pharmaceutical sciences is the optimization of chemical properties of the complex partners in the sense of minimizing their binding free energy with respect to a change in chemical structure. Here, we demonstrate that liquid-state theory in the form of the solute–solute equation of the reference interaction site model provides all necessary information for such a task with high efficiency. In particular, computing derivatives of the potential of mean force (PMF), which defines the free-energy surface of complex formation, with respect to potential parameters can be viewed as a means to define a direction in chemical space toward better binders. We illustrate the methodology in the benchmark case of alkali ion binding to the crown ether 18-crown-6 in aqueous solution. In order to examine the validity of the underlying solute–solute theory, we first compare PMFs computed by different approaches, including explicit free-energy molecular dynamics simulations as a reference. Predictions of an optimally binding ion radius based on free-energy derivatives are then shown to yield consistent results for different ion parameter sets and to compare well with earlier, orders-of-magnitude more costly explicit simulation results. This proof-of-principle study, therefore, demonstrates the potential of liquid-state theory for molecular design problems.

  15. The molecular quantum rotor in cold reactions at the Langevin universal limit

    NASA Astrophysics Data System (ADS)

    Shagam, Yuval; Klein, Ayelet; Skomorowski, Wojciech; Yun, Renjie; Averbukh, Vitali; Koch, Christiane; Narevicius, Edvardas

    2015-05-01

    Fast chemical reactions have been predicted to be solely governed by long-range interactions as was established by Langevin in 1905. The theory has become central to astrochemistry, where fast chemical processes dominate, giving rise to collision energy scaling laws of reaction rates, such as E1/6 for the van der Waals interaction. Importantly, for molecular reactants, the presence of additional anisotropic long-range interactions, such as quadrupole-quadrupole, is predicted to surface only when the molecule is rotationally excited, changing the scaling law to E1/10. Although molecular reactions with near unit probability have been observed at ultra-cold temperatures, these scaling laws and the role of the rotational state remain unconfirmed experimentally. We report the direct observation of universal scaling laws in chemi-ionization reactions of H2 and HD by He(23P2) extending over three orders of magnitude in collision energies. For rotationally ground-state HD molecules the rate follows the E1/6 scaling, while for H2, where the majority of the molecules are rotationally excited, the scaling changes to E1/10 at low collision energies only. At the lowest collision energies the Wigner threshold laws start governing the reactions as the classical Langevin theory breaks down.

  16. Complex Langevin method: When can it be trusted?

    SciTech Connect

    Aarts, Gert; Seiler, Erhard; Stamatescu, Ion-Olimpiu

    2010-03-01

    We analyze to what extent the complex Langevin method, which is in principle capable of solving the so-called sign problems, can be considered as reliable. We give a formal derivation of the correctness and then point out various mathematical loopholes. The detailed study of some simple examples leads to practical suggestions about the application of the method.

  17. Performance assessment of several equations of state and second virial coefficients in modified Enskog theory: Results for transport properties

    NASA Astrophysics Data System (ADS)

    Kiani, M.; Alavianmehr, M. M.; Otoofat, M.; Mohsenipour, A. A.; Ghatee, A.

    2015-11-01

    In this work, we identify a simple method for predicting transport properties of fluids over wide ranges of temperatures and pressure. In this respect, the capability of several equations of state (EOS) and second virial coefficient correlations to predict transport properties of fluids including carbon dioxide, methane and argon using modified Enskog theory (MET) is investigated. The transport properties in question are viscosity and thermal conductivity. The results indicate that the SRK EOS employed in the modified Enskog theory outperforms other equations of state. The average absolute deviation was found to be 12.2 and 18.5% for, respectively, the calculated thermal conductivity and viscosity using the MET.

  18. To the theory of volterra integral equations of the first kind with discontinuous kernels

    NASA Astrophysics Data System (ADS)

    Apartsin, A. S.

    2016-05-01

    A nonclassical Volterra linear integral equation of the first kind describing the dynamics of an developing system with allowance for its age structure is considered. The connection of this equation with the classical Volterra linear integral equation of the first kind with a piecewise-smooth kernel is studied. For solving such equations, the quadrature method is applied.

  19. Einstein equations for generalized theories of gravity and the thermodynamic relation deltaQ=TdeltaS are equivalent.

    PubMed

    Brustein, Ram; Hadad, Merav

    2009-09-01

    We show that the equations of motion of generalized theories of gravity are equivalent to the thermodynamic relation deltaQ=TdeltaS. Our proof relies on extending previous arguments by using a more general definition of the Noether charge entropy. We have thus completed the implementation of Jacobson's proposal to express Einstein's equations as a thermodynamic equation of state. Additionally, we find that the Noether charge entropy obeys the second law of thermodynamics if the energy-momentum tensor obeys the null energy condition. Our results support the idea that gravitation on a macroscopic scale is a manifestation of the thermodynamics of the vacuum. PMID:19792292

  20. Continuum regularization of quantum field theory

    SciTech Connect

    Bern, Z.

    1986-04-01

    Possible nonperturbative continuum regularization schemes for quantum field theory are discussed which are based upon the Langevin equation of Parisi and Wu. Breit, Gupta and Zaks made the first proposal for new gauge invariant nonperturbative regularization. The scheme is based on smearing in the ''fifth-time'' of the Langevin equation. An analysis of their stochastic regularization scheme for the case of scalar electrodynamics with the standard covariant gauge fixing is given. Their scheme is shown to preserve the masslessness of the photon and the tensor structure of the photon vacuum polarization at the one-loop level. Although stochastic regularization is viable in one-loop electrodynamics, two difficulties arise which, in general, ruins the scheme. One problem is that the superficial quadratic divergences force a bottomless action for the noise. Another difficulty is that stochastic regularization by fifth-time smearing is incompatible with Zwanziger's gauge fixing, which is the only known nonperturbaive covariant gauge fixing for nonabelian gauge theories. Finally, a successful covariant derivative scheme is discussed which avoids the difficulties encountered with the earlier stochastic regularization by fifth-time smearing. For QCD the regularized formulation is manifestly Lorentz invariant, gauge invariant, ghost free and finite to all orders. A vanishing gluon mass is explicitly verified at one loop. The method is designed to respect relevant symmetries, and is expected to provide suitable regularization for any theory of interest. Hopefully, the scheme will lend itself to nonperturbative analysis. 44 refs., 16 figs.

  1. Effective particle methods for Fisher-Kolmogorov equations: Theory and applications to brain tumor dynamics

    NASA Astrophysics Data System (ADS)

    Belmonte-Beitia, Juan; Calvo, Gabriel F.; Pérez-García, Víctor M.

    2014-09-01

    Extended systems governed by partial differential equations can, under suitable conditions, be approximated by means of sets of ordinary differential equations for global quantities capturing the essential features of the systems dynamics. Here we obtain a small number of effective equations describing the dynamics of single-front and localized solutions of Fisher-Kolmogorov type equations. These solutions are parametrized by means of a minimal set of time-dependent quantities for which ordinary differential equations ruling their dynamics are found. A comparison of the finite dimensional equations and the dynamics of the full partial differential equation is made showing a very good quantitative agreement with the dynamics of the partial differential equation. We also discuss some implications of our findings for the understanding of the growth progression of certain types of primary brain tumors and discuss possible extensions of our results to related equations arising in different modeling scenarios.

  2. Minding one's P's and Q's: From the one loop effective action in quantum field theory to classical transport theory

    SciTech Connect

    Jalilian-Marian, Jamal; Jeon, Sangyong; Venugopalan, Raju; Wirstam, Jens

    2000-08-15

    The one loop effective action in quantum field theory can be expressed as a quantum mechanical path integral over world lines, with internal symmetries represented by Grassmanian variables. In this paper, we develop a real time, many body, world line formalism for the one loop effective action. In particular, we study hot QCD and obtain the classical transport equations which, as Litim and Manuel have shown, reduce in the appropriate limit to the non-Abelian Boltzmann-Langevin equation first obtained by Boedeker. In the Vlasov limit, the classical kinetic equations are those that correspond to the hard thermal loop effective action. We also discuss the imaginary time world line formalism for a hot {phi}{sup 4} theory, and elucidate its relation to classical transport theory. (c) 2000 The American Physical Society.

  3. A Practitioner's Introduction to Equating with Primers on Classical Test Theory and Item Response Theory

    ERIC Educational Resources Information Center

    Ryan, Joseph; Brockmann, Frank

    2009-01-01

    Equating is an essential tool in educational assessment due the critical role it plays in several key areas: establishing validity across forms and years; fairness; test security; and, increasingly, continuity in programs that release items or require ongoing development. Although the practice of equating is rooted in long standing practices that…

  4. Perturbation theory of relativistic corrections. 1. The non-relativistic limit of the Dirac equation and a direct perturbation expansion

    NASA Astrophysics Data System (ADS)

    Kutzelnigg, W.

    1989-03-01

    After a discussion of the problems associated with the non-relativistic limit of the Dirac equation and of the expansion of the exact eigenvalues and eigenfunctions of the H atom in powers of c -2 the traditional approaches for a perturbation theory of relativistic effects are critically reviewed. Then a direct perturbation theory is presented, that is characterized by a change of the metric in 4-component spinor space such that the Lévy-Leblond equation appears as the straightforward non-relativistic limit of the Dirac equation. The various orders in perturbation theory of the energy and the wave function are derived first in a direct way, then in a resolvent formalism. The formulas are very compact and easily generalizeable to arbitrary order. All integrals that arise to any order exist, and no controlled cancellation of divergent terms (as in other approaches) is necessary. In the same philosophy an iterative approach towards the solution of the Dirac equation is derived, in which the solution of the Schrödinger equation is the first iteration step.

  5. A tentative of interpreting Richards' Equation in media with high heterogeneity by Filippov theory

    NASA Astrophysics Data System (ADS)

    Berardi, Marco; Difonzo, Fabio; Clementina Caputo, Maria; De Carlo, Lorenzo; Vurro, Michele

    2016-04-01

    The numerical solution of Richards' equation is accomplished by means of method of lines, that typically allows the spatial derivative to be approximated by some finite element scheme, in such a way that any solver for ODEs can be used. The ψ-based form is used, i.e. [ ( )] ∂ψ- ∂-- ∂ψ- C(ψ) ∂t = ∂z K (ψ) ∂z ‑ 1 , (1) for suitable choices of hydraulic capacity function C and hydraulic conductivity function K. The real challenge is modelling the infiltration at the interface between two media with high heterogeneity. The interface between two layered media with very different characteristics can be handled as a discontinuity surface. The effort is to review this case as a differential system with discontinuous right-hand side and to clarify the meaning of crossing and sliding in this context, according to Filippov theory. For our scopes, the temporal derivative has been approximated by means of a finite difference method in such a way that the numerical integration is accomplished with respect to the spatial variable z in (1): this choice is particularly convenient since it allows to have a Filippov system, with a state-dependent threshold, and to have a possible sliding behavior.

  6. Equation of state of imbalanced cold matter from chiral perturbation theory

    NASA Astrophysics Data System (ADS)

    Carignano, Stefano; Mammarella, Andrea; Mannarelli, Massimo

    2016-03-01

    We study the thermodynamic properties of matter at vanishing temperature for nonextreme values of the isospin chemical potential and of the strange quark chemical potential. From the leading-order pressure obtained by maximizing the static chiral Lagrangian density, we derive a simple expression for the equation of state in the pion condensed phase and in the kaon condensed phase. We find an analytical expression for the maximum of the ratio between the energy density and the Stefan-Boltzmann energy density and for the isospin chemical potential at the peak, both in good agreement with lattice simulations of quantum chromodynamics. We speculate on the location of the crossover from the Bose-Einstein condensate state to the Bardeen-Cooper-Schrieffer state by a simple analysis of the thermodynamic properties of the system. For μI≳2 mπ, the leading-order chiral perturbation theory breaks down; for example, it underestimates the energy density of the system and leads to a wrong asymptotic behavior.

  7. Sp(8) invariant higher spin theory, twistors and geometric BRST formulation of unfolded field equations

    NASA Astrophysics Data System (ADS)

    Gelfond, O. A.; Vasiliev, M. A.

    2009-12-01

    We discuss twistor-like interpretation of the Sp(8) invariant formulation of 4d massless fields in ten dimensional Lagrangian Grassmannian Sp(8)/P which is the generalized space-time in this framework. The correspondence space C is SpH(8)/PH where SpH(8) is the semidirect product of Sp(8) with Heisenberg group SpHM and PH is some quasiparabolic subgroup of SpH(8). Spaces of functions on Sp(8)/P and SpH(8)/PH consist of QP closed functions on Sp(8) and QPH closed functions on SpH(8), where QP and QPH are canonical BRST operators of P and PH. The space of functions on the generalized twistor space T identifies with the SpH(8) Fock module. Although T cannot be realized as a homogeneous space, we find a nonstandard SpH(8) invariant BRST operator Q (Q2 = 0) that gives rise to an appropriate class of functions via the condition Qf = 0 equivalent to the unfolded higher-spin equations. The proposed construction is manifestly Sp(8) invariant, globally defined and coordinate independent. Its Minkowski analogue gives a version of twistor theory with both types of chiral spinors treated on equal footing. The extensions to the higher rank case with several Heisenberg groups and to the complex case are considered. A relation with Riemann theta functions, that are Q-closed, is discussed.

  8. Entanglement entropy of excited states in conformal perturbation theory and the Einstein equation

    NASA Astrophysics Data System (ADS)

    Speranza, Antony J.

    2016-04-01

    For a conformal field theory (CFT) deformed by a relevant operator, the entanglement entropy of a ball-shaped region may be computed as a perturbative expansion in the coupling. A similar perturbative expansion exists for excited states near the vacuum. Using these expansions, this work investigates the behavior of excited state entanglement entropies of small, ball-shaped regions. The motivation for these calculations is Jacobson's recent work on the equivalence of the Einstein equation and the hypothesis of maximal vacuum entropy [arXiv:1505.04753], which relies on a conjecture stating that the behavior of these entropies is sufficiently similar to a CFT. In addition to the expected type of terms which scale with the ball radius as R d , the entanglement entropy calculation gives rise to terms scaling as R 2Δ, where Δ is the dimension of the deforming operator. When \\varDelta ≤ d/2 , the latter terms dominate the former, and suggest that a modification to the conjecture is needed.

  9. Calculating cold curves for Equation of State using different types of Density Functional Theory codes

    NASA Astrophysics Data System (ADS)

    Mattsson, Ann E.; Cochrane, Kyle R.; Carpenter, John H.; Desjarlais, Michael P.

    2008-03-01

    With fast computers and improved radiation-hydrodynamics simulation techniques, increasingly complex high energy-density physics systems are investigated by modeling and simulation efforts, putting unprecedented strain on the underlying Equation of State (EOS) modeling. EOS models that have been adequate in the past can fail in unexpected ways. With the aim of improving the EOS, models are often fitted to calculated data in parts of the parameter space where little or no experimental data is available. One example is the compression part of the cold curve. We show that care needs to be taken in using Density Functional Theory (DFT) codes. While being perfectly adequate for calculations in many parts of the parameter space, approximations inherent to pseudo-potential codes can limit their applicability for large compressions. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

  10. Testing a theory of aircraft noise annoyance: a structural equation analysis.

    PubMed

    Kroesen, Maarten; Molin, Eric J E; van Wee, Bert

    2008-06-01

    Previous research has stressed the relevance of nonacoustical factors in the perception of aircraft noise. However, it is largely empirically driven and lacks a sound theoretical basis. In this paper, a theoretical model which explains noise annoyance based on the psychological stress theory is empirically tested. The model is estimated by applying structural equation modeling based on data from residents living in the vicinity of Amsterdam Airport Schiphol in The Netherlands. The model provides a good model fit and indicates that concern about the negative health effects of noise and pollution, perceived disturbance, and perceived control and coping capacity are the most important variables that explain noise annoyance. Furthermore, the model provides evidence for the existence of two reciprocal relationships between (1) perceived disturbance and noise annoyance and (2) perceived control and coping capacity and noise annoyance. Lastly, the model yielded two unexpected results. Firstly, the variables noise sensitivity and fear related to the noise source were unable to explain additional variance in the endogenous variables of the model and were therefore excluded from the model. And secondly, the size of the total effect of noise exposure on noise annoyance was relatively small. The paper concludes with some recommended directions for further research. PMID:18537376

  11. The transversely isotropic poroelastic wave equation including the Biot and the squirt mechanisms: Theory and application

    SciTech Connect

    Parra, J.O.

    1997-01-01

    The transversely isotropic poroelastic wave equation can be formulated to include the Biot and the squirt-flow mechanisms to yield a new analytical solution in terms of the elements of the squirt-flow tensor. The new model gives estimates of the vertical and the horizontal permeabilities, as well as other measurable rock and fluid properties. Modeling suggests that the attenuation of both the quasi P-wave and quasi SV-wave depend on the direction of permeability. To test the theory, interwell seismic waveforms, well logs, and hydraulic conductivity measurements (recorded in the fluvial Gypsy sandstone reservoir, Oklahoma) provide the material and fluid property parameters. This analysis with the new analytical solution is the first step toward a quantitative evaluation of the preferential directions of fluid flow in reservoir formation containing hydrocarbons. The results of the present work may lead to the development of algorithms to extract the permeability anisotropy from attenuation and dispersion data (derived from sonic logs and crosswell seismics) to map the fluid flow distribution in a reservoir.

  12. The Best of Both Worlds: Factor Analysis of Dichotomous Data Using Item Response Theory and Structural Equation Modeling

    ERIC Educational Resources Information Center

    Glockner-Rist, Angelika; Hoijtink, Herbert

    2003-01-01

    Both structural equation modeling (SEM) and item response theory (IRT) can be used for factor analysis of dichotomous item responses. In this case, the measurement models of both approaches are formally equivalent. They were refined within and across different disciplines, and make complementary contributions to central measurement problems…

  13. Multinomial diffusion equation

    NASA Astrophysics Data System (ADS)

    Balter, Ariel; Tartakovsky, Alexandre M.

    2011-06-01

    We describe a new, microscopic model for diffusion that captures diffusion induced fluctuations at scales where the concept of concentration gives way to discrete particles. We show that in the limit as the number of particles N→∞, our model is equivalent to the classical stochastic diffusion equation (SDE). We test our new model and the SDE against Langevin dynamics in numerical simulations, and show that our model successfully reproduces the correct ensemble statistics, while the classical model fails.

  14. Multinomial diffusion equation

    SciTech Connect

    Balter, Ariel I.; Tartakovsky, Alexandre M.

    2011-06-24

    We describe a new, microscopic model for diffusion that captures diffusion induced uctuations at scales where the concept of concentration gives way to discrete par- ticles. We show that in the limit as the number of particles N ! 1, our model is equivalent to the classical stochastic diffusion equation (SDE). We test our new model and the SDE against Langevin dynamics in numerical simulations, and show that our model successfully reproduces the correct ensemble statistics, while the classical model fails.

  15. Unpacking the Complexity of Linear Equations from a Cognitive Load Theory Perspective

    ERIC Educational Resources Information Center

    Ngu, Bing Hiong; Phan, Huy P.

    2016-01-01

    The degree of element interactivity determines the complexity and therefore the intrinsic cognitive load of linear equations. The unpacking of linear equations at the level of operational and relational lines allows the classification of linear equations in a hierarchical level of complexity. Mapping similar operational and relational lines across…

  16. An Integral Equation Approach to Orientational Phase Transitions in Quadrupolar Gay-Berne Fluid Using Density-Functional Theory

    NASA Astrophysics Data System (ADS)

    Singh, R. C.

    2009-07-01

    The effects of quadrupole moments on the phase behaviour of isotropic-nematic transition are studied by using density functional theory for a system of molecules which interact via the Gay-Berne pair potential. The pair correlation functions of isotropic phase, which enter in the theory as input information, are found from the Percus-Yevick integral equation theory. The method used involves an expansion of angle-dependent functions appearing in the integral equations in terms of spherical harmonics and the harmonic coefficients are obtained by an iterative algorithm. All the terms of harmonic coefficients which involve l indices up to less than or equal to six have been considered. The dependence of the accuracy of the results on the number of terms taken in the basis set is explored for both fluids at different densities, temperatures and quadrupole moments. The results have been compared with the available computer simulation results.

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

    NASA Astrophysics Data System (ADS)

    Ausloos, M.

    2000-09-01

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

  18. Protein displacements under external forces: An atomistic Langevin dynamics approach

    NASA Astrophysics Data System (ADS)

    Gnandt, David; Utz, Nadine; Blumen, Alexander; Koslowski, Thorsten

    2009-02-01

    We present a fully atomistic Langevin dynamics approach as a method to simulate biopolymers under external forces. In the harmonic regime, this approach permits the computation of the long-term dynamics using only the eigenvalues and eigenvectors of the Hessian matrix of second derivatives. We apply this scheme to identify polymorphs of model proteins by their mechanical response fingerprint, and we relate the averaged dynamics of proteins to their biological functionality, with the ion channel gramicidin A, a phosphorylase, and neuropeptide Y as examples. In an environment akin to dilute solutions, even small proteins show relaxation times up to 50 ns. Atomically resolved Langevin dynamics computations have been performed for the stretched gramicidin A ion channel.

  19. Free-complement local-Schrödinger-equation method for solving the Schrödinger equation of atoms and molecules: basic theories and features.

    PubMed

    Nakatsuji, Hiroshi; Nakashima, Hiroyuki

    2015-02-28

    The free-complement (FC) method is a general method for solving the Schrödinger equation (SE): The produced wave function has the potentially exact structure as the solution of the Schrödinger equation. The variables included are determined either by using the variational principle (FC-VP) or by imposing the local Schrödinger equations (FC-LSE) at the chosen set of the sampling points. The latter method, referred to as the local Schrödinger equation (LSE) method, is integral-free and therefore applicable to any atom and molecule. The purpose of this paper is to formulate the basic theories of the LSE method and explain their basic features. First, we formulate three variants of the LSE method, the AB, HS, and H(T)Q methods, and explain their properties. Then, the natures of the LSE methods are clarified in some detail using the simple examples of the hydrogen atom and the Hooke's atom. Finally, the ideas obtained in this study are applied to solving the SE of the helium atom highly accurately with the FC-LSE method. The results are very encouraging: we could get the world's most accurate energy of the helium atom within the sampling-type methodologies, which is comparable to those obtained with the FC-VP method. Thus, the FC-LSE method is an easy and yet a powerful integral-free method for solving the Schrödinger equation of general atoms and molecules. PMID:25725722

  20. Free-complement local-Schrödinger-equation method for solving the Schrödinger equation of atoms and molecules: Basic theories and features

    SciTech Connect

    Nakatsuji, Hiroshi Nakashima, Hiroyuki

    2015-02-28

    The free-complement (FC) method is a general method for solving the Schrödinger equation (SE): The produced wave function has the potentially exact structure as the solution of the Schrödinger equation. The variables included are determined either by using the variational principle (FC-VP) or by imposing the local Schrödinger equations (FC-LSE) at the chosen set of the sampling points. The latter method, referred to as the local Schrödinger equation (LSE) method, is integral-free and therefore applicable to any atom and molecule. The purpose of this paper is to formulate the basic theories of the LSE method and explain their basic features. First, we formulate three variants of the LSE method, the AB, HS, and H{sup T}Q methods, and explain their properties. Then, the natures of the LSE methods are clarified in some detail using the simple examples of the hydrogen atom and the Hooke’s atom. Finally, the ideas obtained in this study are applied to solving the SE of the helium atom highly accurately with the FC-LSE method. The results are very encouraging: we could get the world’s most accurate energy of the helium atom within the sampling-type methodologies, which is comparable to those obtained with the FC-VP method. Thus, the FC-LSE method is an easy and yet a powerful integral-free method for solving the Schrödinger equation of general atoms and molecules.

  1. SELF-CONSISTENT LANGEVIN SIMULATION OF COULOMB COLLISIONS IN CHARGED-PARTICLE BEAMS

    SciTech Connect

    J. QIANG; R. RYNE; S. HABIB

    2000-05-01

    In many plasma physics and charged-particle beam dynamics problems, Coulomb collisions are modeled by a Fokker-Planck equation. In order to incorporate these collisions, we present a three-dimensional parallel Langevin simulation method using a Particle-In-Cell (PIC) approach implemented on high-performance parallel computers. We perform, for the first time, a fully self-consistent simulation, in which the friction and diffusion coefficients are computed from first principles. We employ a two-dimensional domain decomposition approach within a message passing programming paradigm along with dynamic load balancing. Object oriented programming is used to encapsulate details of the communication syntax as well as to enhance reusability and extensibility. Performance tests on the SGI Origin 2000 and the Cray T3E-900 have demonstrated good scalability. Work is in progress to apply our technique to intrabeam scattering in accelerators.

  2. Study on the Langevin piezoelectric ceramic ultrasonic transducer of longitudinal-flexural composite vibrational mode.

    PubMed

    Lin, Shuyu

    2006-01-01

    In this paper, the Langevin longitudinal-flexural composite mode piezoelectric ultrasonic transducer is studied. This type of transducers consists of slender metal rods and longitudinally polarized piezoelectric ceramic rings. The resonance frequency equations for the longitudinal and flexural vibrations in the transducer are derived. By correcting the length of the metal slender rods, the simultaneous resonance of the longitudinal and flexural vibrations in the transducer is acquired. The experimental results show that the measured resonance frequencies of the transducers are in good agreement with the computed ones, and the measured resonance frequencies of the longitudinal and the flexural vibrations in the composite transducers are also in good agreement with each other. PMID:16289195

  3. Quantum non-Markovian Langevin formalism for heavy ion reactions near the Coulomb barrier

    SciTech Connect

    Sargsyan, V. V.; Antonenko, N. V.; Kanokov, Z.; Adamian, G. G.

    2008-02-15

    The generalized Langevin approach is suggested to describe the capture inside of the Coulomb barrier of two heavy nuclei at bombarding energies near the barrier. The equations of motion for the relative distance (collective coordinate) between two interacting nuclei are consistent with the generalized quantum fluctuation-dissipation relations. The analytical expressions are derived for the time-dependent non-Markovian microscopic transport coefficients for the stable and unstable collective modes. The calculated results show that the quantum effects in the diffusion process increase with increasing friction or/and decreasing temperature. The capture probability inside of the Coulomb barrier is enhanced by the quantum noise at low energies near the barrier. An increase of the passing probability with dissipation is found at sub-barrier energies.

  4. Accurate nonadiabatic quantum dynamics on the cheap: Making the most of mean field theory with master equations

    SciTech Connect

    Kelly, Aaron; Markland, Thomas E.; Brackbill, Nora

    2015-03-07

    In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.

  5. Kinetic theory of transport processes in partially ionized reactive plasma, I: General transport equations

    NASA Astrophysics Data System (ADS)

    Zhdanov, V. M.; Stepanenko, A. A.

    2016-03-01

    In this paper we derive the set of general transport equations for multicomponent partially ionized reactive plasma in the presence of electric and magnetic fields taking into account the internal degrees of freedom and electronic excitation of plasma particles. Our starting point is a generalized Boltzmann equation with the collision integral in the Wang-Chang and Uhlenbeck form and a reactive collision integral. We obtain a set of conservation equations for such plasma and employ a linearized variant of Grad's moment method to derive the system of moment (or transport) equations for the plasma species nonequilibrium parameters. Full and reduced transport equations, resulting from the linearized system of moment equations, are presented, which can be used to obtain transport relations and expressions for transport coefficients of electrons and heavy plasma particles (molecules, atoms and ions) in partially ionized reactive plasma.

  6. 2D/1D approximations to the 3D neutron transport equation. I: Theory

    SciTech Connect

    Kelley, B. W.; Larsen, E. W.

    2013-07-01

    A new class of '2D/1D' approximations is proposed for the 3D linear Boltzmann equation. These approximate equations preserve the exact transport physics in the radial directions x and y and diffusion physics in the axial direction z. Thus, the 2D/1D equations are more accurate approximations of the 3D Boltzmann equation than the conventional 3D diffusion equation. The 2D/1D equations can be systematically discretized, to yield accurate simulation methods for 3D reactor core problems. The resulting solutions will be more accurate than 3D diffusion solutions, and less expensive to generate than standard 3D transport solutions. In this paper, we (i) show that the simplest 2D/1D equation has certain desirable properties, (ii) systematically discretize this equation, and (iii) derive a stable iteration scheme for solving the discrete system of equations. In a companion paper [1], we give numerical results that confirm the theoretical predictions of accuracy and iterative stability. (authors)

  7. From square-well to Janus: Improved algorithm for integral equation theory and comparison with thermodynamic perturbation theory within the Kern-Frenkel model

    SciTech Connect

    Giacometti, Achille; Gögelein, Christoph; Lado, Fred; Sciortino, Francesco; Ferrari, Silvano

    2014-03-07

    Building upon past work on the phase diagram of Janus fluids [F. Sciortino, A. Giacometti, and G. Pastore, Phys. Rev. Lett. 103, 237801 (2009)], we perform a detailed study of integral equation theory of the Kern-Frenkel potential with coverage that is tuned from the isotropic square-well fluid to the Janus limit. An improved algorithm for the reference hypernetted-chain (RHNC) equation for this problem is implemented that significantly extends the range of applicability of RHNC. Results for both structure and thermodynamics are presented and compared with numerical simulations. Unlike previous attempts, this algorithm is shown to be stable down to the Janus limit, thus paving the way for analyzing the frustration mechanism characteristic of the gas-liquid transition in the Janus system. The results are also compared with Barker-Henderson thermodynamic perturbation theory on the same model. We then discuss the pros and cons of both approaches within a unified treatment. On balance, RHNC integral equation theory, even with an isotropic hard-sphere reference system, is found to be a good compromise between accuracy of the results, computational effort, and uniform quality to tackle self-assembly processes in patchy colloids of complex nature. Further improvement in RHNC however clearly requires an anisotropic reference bridge function.

  8. From square-well to Janus: improved algorithm for integral equation theory and comparison with thermodynamic perturbation theory within the Kern-Frenkel model.

    PubMed

    Giacometti, Achille; Gögelein, Christoph; Lado, Fred; Sciortino, Francesco; Ferrari, Silvano; Pastore, Giorgio

    2014-03-01

    Building upon past work on the phase diagram of Janus fluids [F. Sciortino, A. Giacometti, and G. Pastore, Phys. Rev. Lett. 103, 237801 (2009)], we perform a detailed study of integral equation theory of the Kern-Frenkel potential with coverage that is tuned from the isotropic square-well fluid to the Janus limit. An improved algorithm for the reference hypernetted-chain (RHNC) equation for this problem is implemented that significantly extends the range of applicability of RHNC. Results for both structure and thermodynamics are presented and compared with numerical simulations. Unlike previous attempts, this algorithm is shown to be stable down to the Janus limit, thus paving the way for analyzing the frustration mechanism characteristic of the gas-liquid transition in the Janus system. The results are also compared with Barker-Henderson thermodynamic perturbation theory on the same model. We then discuss the pros and cons of both approaches within a unified treatment. On balance, RHNC integral equation theory, even with an isotropic hard-sphere reference system, is found to be a good compromise between accuracy of the results, computational effort, and uniform quality to tackle self-assembly processes in patchy colloids of complex nature. Further improvement in RHNC however clearly requires an anisotropic reference bridge function. PMID:24606350

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

    ERIC Educational Resources Information Center

    Koutsoyiannis, Demetris

    2012-01-01

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

  10. Impact of Accumulated Error on Item Response Theory Pre-Equating with Mixed Format Tests

    ERIC Educational Resources Information Center

    Keller, Lisa A.; Keller, Robert; Cook, Robert J.; Colvin, Kimberly F.

    2016-01-01

    The equating of tests is an essential process in high-stakes, large-scale testing conducted over multiple forms or administrations. By adjusting for differences in difficulty and placing scores from different administrations of a test on a common scale, equating allows scores from these different forms and administrations to be directly compared…

  11. A New Approach to Test Score Equating Using Item Response Theory with Fixed C-Parameters

    ERIC Educational Resources Information Center

    Lee, Guemin; Fitzpatrick, Anne R.

    2008-01-01

    Because parameter estimates from different calibration runs under the IRT model are linearly related, a linear equation can convert IRT parameter estimates onto another scale metric without changing the probability of a correct response (Kolen & Brennan, 1995, 2004). This study was designed to explore a new approach to finding a linear equation by…

  12. An electric-analog simulation of elliptic partial differential equations using finite element theory

    USGS Publications Warehouse

    Franke, O.L.; Pinder, G.F.; Patten, E.P.

    1982-01-01

    Elliptic partial differential equations can be solved using the Galerkin-finite element method to generate the approximating algebraic equations, and an electrical network to solve the resulting matrices. Some element configurations require the use of networks containing negative resistances which, while physically realizable, are more expensive and time-consuming to construct. ?? 1982.

  13. Hamiltonian structure of Dubrovin{close_quote}s equation of associativity in 2-d topological field theory

    SciTech Connect

    Galvao, C.A.; Nutku, Y.

    1996-12-01

    mA third order Monge-Amp{grave e}re type equation of associativity that Dubrovin has obtained in 2-d topological field theory is formulated in terms of a variational principle subject to second class constraints. Using Dirac{close_quote}s theory of constraints this degenerate Lagrangian system is cast into Hamiltonian form and the Hamiltonian operator is obtained from the Dirac bracket. There is a new type of Kac-Moody algebra that corresponds to this Hamiltonian operator. In particular, it is not a W-algebra. {copyright} {ital 1996 American Institute of Physics.}

  14. The study of Renner-Teller excited states with equation of motion coupled-cluster theory

    NASA Astrophysics Data System (ADS)

    Brown, Shawn Thomas

    The Renner-Teller (R-T) effect causes splitting in the bending potential of linear molecules with degenerate electronic states and greatly complicates experimental spectra. Traditional SCF procedures fail to describe most of these R-T electronic excited states because they suffer from the so-called variational collapse. To avoid the difficulty involved in applying multi-reference methods to these systems, we make use of the equation of motion coupled cluster method (EOM-CC). The EOM-CC method utilizes the ground state CC wave function to obtain electronic excited state energies, therefore it does not suffer from variational collapse. So in an effort to find a straightforward and accurate method for application to these special cases, we employed EOM-CC in the examination of several triatomic electronic excited states. In the first work included, EOM-CCSD was used to produce the bending potentials of the first seven electronic excited states of CS2 in order to resolve definitively some discrepancies between experiment and theory. The geometry of the B~1 B2 state was found to be severely bent and to be the lower R-T component of the 1Δu state. The second work involves determining the energetics, harmonic vibrational frequencies, equilibrium geometries and dipole moments of the ground and first triplet excited state of CCO. In order to compute the antisymmetric bending frequency, EOM-CCSD was needed. The Renner parameter, ɛ, and average harmonic bending frequency, ω2, were computed via EOM- CCSD and agreed well with experiment. Based on this agreement, similar analysis was performed on the SiSiO molecule in the third work presented. Comparison of a number of properties amongst CCO, SiCO, CSiO, SiSiO were discussed. CSiO was found to have an aberrantly large ɛ value. Since the trend in the bending frequency appears to follow expectation, ɛ seems to be a value dependent on the electronic structure. It is shown through these three examples that EOM-CCSD is indeed a

  15. L{sup p} Theory for Super-Parabolic Backward Stochastic Partial Differential Equations in the Whole Space

    SciTech Connect

    Du Kai Qiu, Jinniao Tang Shanjian

    2012-04-15

    This paper is concerned with semi-linear backward stochastic partial differential equations (BSPDEs for short) of super-parabolic type. An L{sup p}-theory is given for the Cauchy problem of BSPDEs, separately for the case of p Element-Of (1,2] and for the case of p Element-Of (2,{infinity}). A comparison theorem is also addressed.

  16. Test for a universal behavior of Dirac eigenvalues in the complex Langevin method

    NASA Astrophysics Data System (ADS)

    Ichihara, Terukazu; Nagata, Keitaro; Kashiwa, Kouji

    2016-05-01

    We apply the complex Langevin (CL) method to a chiral random matrix theory (ChRMT) at nonzero chemical potential and study the nearest neighbor spacing (NNS) distribution of the Dirac eigenvalues. The NNS distribution is extracted using an unfolding procedure for the Dirac eigenvalues obtained in the CL method. For large quark mass, we find that the NNS distribution obeys the Ginibre ensemble as expected. For small quark mass, the NNS distribution follows the Wigner surmise for the correct convergence case, while it follows the Ginibre ensemble for the wrong convergence case. The Wigner surmise is physically reasonable from the chemical potential independence of the ChRMT. The Ginibre ensemble is known to be favored in a phase-quenched QCD at finite chemical potential. Our result suggests a possibility that the originally universal behavior of the NNS distribution is preserved even in the CL method for the correct convergence case.

  17. Analytical Theory of the Destruction Terms in Dissipation Rate Transport Equations

    NASA Technical Reports Server (NTRS)

    Rubinstein, Robert; Zhou, Ye

    1996-01-01

    Modeled dissipation rate transport equations are often derived by invoking various hypotheses to close correlations in the corresponding exact equations. D. C. Leslie suggested that these models might be derived instead from Kraichnan's wavenumber space integrals for inertial range transport power. This suggestion is applied to the destruction terms in the dissipation rate equations for incompressible turbulence, buoyant turbulence, rotating incompressible turbulence, and rotating buoyant turbulence. Model constants like C(epsilon 2) are expressed as integrals; convergence of these integrals implies the absence of Reynolds number dependence in the corresponding destruction term. The dependence of C(epsilon 2) on rotation rate emerges naturally; sensitization of the modeled dissipation rate equation to rotation is not required. A buoyancy related effect which is absent in the exact transport equation for temperature variance dissipation, but which sometimes improves computational predictions, also arises naturally. Both the presence of this effect and the appropriate time scale in the modeled transport equation depend on whether Bolgiano or Kolmogorov inertial range scaling applies. A simple application of these methods leads to a preliminary, dissipation rate equation for rotating buoyant turbulence.

  18. Self-consistent field theory of collisions: Orbital equations with asymptotic sources and self-averaged potentials

    NASA Astrophysics Data System (ADS)

    Hahn, Y. K.

    2014-12-01

    The self-consistent field theory of collisions is formulated, incorporating the unique dynamics generated by the self-averaged potentials. The bound state Hartree-Fock approach is extended for the first time to scattering states, by properly resolving the principal difficulties of non-integrable continuum orbitals and imposing complex asymptotic conditions. The recently developed asymptotic source theory provides the natural theoretical basis, as the asymptotic conditions are completely transferred to the source terms and the new scattering function is made fullyintegrable. The scattering solutions can then be directly expressed in terms of bound state HF configurations, establishing the relationship between the bound and scattering state solutions. Alternatively, the integrable spin orbitals are generated by constructing the individual orbital equations that contain asymptotic sources and self-averaged potentials. However, the orbital energies are not determined by the equations, and a special channel energy fixing procedure is developed to secure the solutions. It is also shown that the variational construction of the orbital equations has intrinsic ambiguities that are generally associated with the self-consistent approach. On the other hand, when a small subset of open channels is included in the source term, the solutions are only partiallyintegrable, but the individual open channels can then be treated more simply by properly selecting the orbital energies. The configuration mixing and channel coupling are then necessary to complete the solution. The new theory improves the earlier continuum HF model.

  19. Deformed SW curve and the null vector decoupling equation in Toda field theory

    NASA Astrophysics Data System (ADS)

    Poghossian, Rubik

    2016-04-01

    It is shown that the deformed Seiberg-Witten curve equation after Fourier transform is mapped into a differential equation for the AGT dual 2d CFT cnformal block containing an extra completely degenerate field. We carefully match parameters in two sides of duality thus providing not only a simple independent prove of the AGT correspondence in Nekrasov-Shatashvili limit, but also an extension of AGT to the case when a secondary field is included in the CFT conformal block. Implications of our results in the study of monodromy problems for a large class of n'th order Fuchsian differential equations are discussed.

  20. Thermodynamically self-consistent integral equation theory for pair-correlation functions of molecular fluids-II

    NASA Astrophysics Data System (ADS)

    Singh, Ram Chandra; Ram, Jokhan

    2006-09-01

    A closure for the pair-correlation functions of molecular fluids is described in which the hypernetted-chain and the Percus-Yevick approximations are “mixed” as a function of interparticle separation. An adjustable parameter α in the mixing function is used to enforce thermodynamic consistency, by which it is meant that identical results are obtained when the equations of state are calculated via the virial and compressibility routes, respectively. The mixed integral equation for the pair-correlation functions has been solved for two model fluids: (i) a fluid of the hard Gaussian overlap model, and (ii) a fluid the molecules of which interact via a modified Gay-Berne model potential. For the modified Gay-Berne fluid we have slightly modified the original Gay-Berne potential to study the effect of attraction on hard core systems. The pair-correlation functions of the isotropic phase which enter in the density-functional theory as input informations have been calculated from the integral equation theories for these model fluids. We have used two different versions of the density-functional theory known as the second order and modified weighted-density-functional theory to locate the isotropic-nematic (I-N) transitions and calculate the values of transition parameters for the hard Gaussian overlap and modified Gay-Berne model fluids. We have compared our results with those of computer simulations wherever they are available. We find that the density-functional theory is good to study the I-N transition in molecular fluids if the values of the pair-correlation functions in the isotropic phase are accurately known.

  1. A kinetic-theory approach to turbulent chemically reacting flows

    NASA Technical Reports Server (NTRS)

    Chung, P. M.

    1976-01-01

    The paper examines the mathematical and physical foundations for the kinetic theory of reactive turbulent flows, discussing the differences and relation between the kinetic and averaged equations, and comparing some solutions of the kinetic equations obtained by the Green's function method with those obtained by the approximate bimodal method. The kinetic method described consists essentially in constructing the probability density functions of the chemical species on the basis of solutions of the Langevin stochastic equation for the influence of eddies on the behavior of fluid elements. When the kinetic equations are solved for the structure of the diffusion flame established in a shear layer by the bimodal method, discontinuities in gradients of the mean concentrations at the two flame edges appear. This is a consequence of the bimodal approximation of all distribution functions by two dissimilar half-Maxwellian functions, which is a very crude approximation. These discontinuities do not appear when the solutions are constructed by the Green's function method described here.

  2. Self-affine polytopes. Applications to functional equations and matrix theory

    SciTech Connect

    Voynov, Andrey S

    2011-10-31

    A special kind of functional equation with compression of the argument--the affine self-similarity equation--is studied. The earlier known one-dimensional self-similarity equations are generalized to the multidimensional case of functions of several variables. A criterion for the existence and uniqueness of an L{sub p}-solution is established. Description of such equations involves classification of finite-dimensional convex self-affine compact sets. In this work properties of such objects are thoroughly analysed; in particular, a counterexample to the well-known conjecture about the structure of such bodies, which was put forward in 1991, is given. Applications of the results obtained include some facts about the convergence of products of stochastic matrices; also, criteria for the convergence of some subdivision algorithms are suggested. Bibliography: 39 titles.

  3. A covariant Fokker-Planck equation for a simple gas from relativistic kinetic theory

    SciTech Connect

    Chacon-Acosta, Guillermo; Dagdug, Leonardo; Morales-Tecotl, Hugo A.

    2010-12-14

    A manifestly covariant Fokker-Planck differential equation is derived for the case of a relativistic simple gas by taking a small momentum transfer approximation within the collision integral of the relativistic Boltzmann equation. We follow closely previous work, with the main difference that we keep manifest covariance at every stage of the analysis. In addition, we use the covariant Juettner distribution function to find a relativistic generalization of the Einstein's fluctuation-dissipation relation.

  4. The equation of state of pure iron-theory and simulation

    NASA Astrophysics Data System (ADS)

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

    2015-06-01

    We calculate the equation of state of pure iron in wide pressure and temperature regime with several models, such as two-body potential, TF and TFC models, and considering electron excite and nucleus anharmonic. In order to address how accuracy of our iron EOS, we simulate EOS by QMD, isentropic compression by fluid dynamic and compare results with expertiment. Our research brings new insights for how to comment the accuracy of equation of state.

  5. Application of the integral equation theory of polymers: Distribution function, chemical potential, and mean expansion coefficient

    NASA Astrophysics Data System (ADS)

    Gan, Hin Hark; Eu, Byung Chan

    1993-09-01

    A recursive integral equation for the intramolecular correlation function of an isolated linear polymer of N bonds is derived from the integral equations presented in the preceding paper. The derivation basically involves limiting the density of the polymer to zero so that polymers do not interact with each other, and thus taking into account the intramolecular part only. The integral equation still has the form of a generalized Percus-Yevick integral equation. The intramolecular correlation function of a polymer of N bonds is recursively generated by means of it from those of polymers of 2, 3,..., (N-1) bonds. The end-to-end distance distribution functions are computed by using the integral equation for various chain lengths, temperatures, and bond lengths in the case of a repulsive soft-sphere potential. Numerical solutions of the recursive integral equation yield universal exponents for the mean square end-to-end distance in two and three dimensions with values which are close to the Flory results: 0.77 and 0.64 vs Flory's values 0.75 and 0.6 for two and three dimensions, respectively. The intramolecular correlation functions computed can be fitted with displaced Gaussian forms. The N dependence of the internal chemical potential is found to saturate after some value of N depending on the ratio of the bond length to the bead radius.

  6. Analytic evaluation of the nonadiabatic coupling vector between excited states using equation-of-motion coupled-cluster theory

    NASA Astrophysics Data System (ADS)

    Tajti, Attila; Szalay, Péter G.

    2009-09-01

    Theory and implementation for evaluation of the nonadiabatic coupling vector between excited electronic states described by equation-of-motion excitation energy coupled-cluster singles and doubles (EOMEE-CCSD) method is presented. Problems arising from the non-Hermitian nature of the theory are discussed in detail. The performance of the new approach is demonstrated by the nice agreement of the nonadiabatic coupling curves for LiH obtained at the EOMEE-CCSD and MR-CISD levels. Using the tools developed we also present a computational procedure to evaluate the interstate coupling constants used in vibronic coupling theories. As an application of this part of the implementation we present simulation of the electronic absorption spectrum of the pyrazine molecule within the linear vibronic coupling model.

  7. Solving the Schrödinger equation of molecules by relaxing the antisymmetry rule: Inter-exchange theory.

    PubMed

    Nakatsuji, Hiroshi; Nakashima, Hiroyuki

    2015-05-21

    The Schrödinger equation (SE) and the antisymmetry principle constitute the governing principle of chemistry. A general method of solving the SE was presented before as the free complement (FC) theory, which gave highly accurate solutions for small atoms and molecules. We assume here to use the FC theory starting from the local valence bond wave function. When this theory is applied to larger molecules, antisymmetrizations of electronic wave functions become time-consuming and therefore, an additional breakthrough is necessary concerning the antisymmetry principle. Usually, in molecular calculations, we first construct the wave function to satisfy the antisymmetry rule, "electronic wave functions must be prescribed to be antisymmetric for all exchanges of electrons, otherwise bosonic interference may disturb the basis of the science." Starting from determinantal wave functions is typical. Here, we give an antisymmetrization theory, called inter-exchange (iExg) theory, by dividing molecular antisymmetrizations to those within atoms and between atoms. For the electrons belonging to distant atoms in a molecule, only partial antisymmetrizations or even no antisymmetrizations are necessary, depending on the distance between the atoms. So, the above antisymmetry rule is not necessarily followed strictly to get the results of a desired accuracy. For this and other reasons, the necessary parts of the antisymmetrization operations become very small as molecules become larger, leading finally to the operation counts of lower orders of N, the number of electrons. This theory creates a natural antisymmetrization method that is useful for large molecules. PMID:26001441

  8. Solving the Schrödinger equation of molecules by relaxing the antisymmetry rule: Inter-exchange theory

    SciTech Connect

    Nakatsuji, Hiroshi Nakashima, Hiroyuki

    2015-05-21

    The Schrödinger equation (SE) and the antisymmetry principle constitute the governing principle of chemistry. A general method of solving the SE was presented before as the free complement (FC) theory, which gave highly accurate solutions for small atoms and molecules. We assume here to use the FC theory starting from the local valence bond wave function. When this theory is applied to larger molecules, antisymmetrizations of electronic wave functions become time-consuming and therefore, an additional breakthrough is necessary concerning the antisymmetry principle. Usually, in molecular calculations, we first construct the wave function to satisfy the antisymmetry rule, “electronic wave functions must be prescribed to be antisymmetric for all exchanges of electrons, otherwise bosonic interference may disturb the basis of the science.” Starting from determinantal wave functions is typical. Here, we give an antisymmetrization theory, called inter-exchange (iExg) theory, by dividing molecular antisymmetrizations to those within atoms and between atoms. For the electrons belonging to distant atoms in a molecule, only partial antisymmetrizations or even no antisymmetrizations are necessary, depending on the distance between the atoms. So, the above antisymmetry rule is not necessarily followed strictly to get the results of a desired accuracy. For this and other reasons, the necessary parts of the antisymmetrization operations become very small as molecules become larger, leading finally to the operation counts of lower orders of N, the number of electrons. This theory creates a natural antisymmetrization method that is useful for large molecules.

  9. Harmonically bound Brownian motion in fluids under shear: Fokker-Planck and generalized Langevin descriptions.

    PubMed

    Híjar, Humberto

    2015-02-01

    We study the Brownian motion of a particle bound by a harmonic potential and immersed in a fluid with a uniform shear flow. We describe this problem first in terms of a linear Fokker-Planck equation which is solved to obtain the probability distribution function for finding the particle in a volume element of its associated phase space. We find the explicit form of this distribution in the stationary limit and use this result to show that both the equipartition law and the equation of state of the trapped particle are modified from their equilibrium form by terms increasing as the square of the imposed shear rate. Subsequently, we propose an alternative description of this problem in terms of a generalized Langevin equation that takes into account the effects of hydrodynamic correlations and sound propagation on the dynamics of the trapped particle. We show that these effects produce significant changes, manifested as long-time tails and resonant peaks, in the equilibrium and nonequilibrium correlation functions for the velocity of the Brownian particle. We implement numerical simulations based on molecular dynamics and multiparticle collision dynamics, and observe a very good quantitative agreement between the predictions of the model and the numerical results, thus suggesting that this kind of numerical simulations could be used as complement of current experimental techniques. PMID:25768490

  10. Self-consistent field theory of collisions: Orbital equations with asymptotic sources and self-averaged potentials

    SciTech Connect

    Hahn, Y.K.

    2014-12-15

    The self-consistent field theory of collisions is formulated, incorporating the unique dynamics generated by the self-averaged potentials. The bound state Hartree–Fock approach is extended for the first time to scattering states, by properly resolving the principal difficulties of non-integrable continuum orbitals and imposing complex asymptotic conditions. The recently developed asymptotic source theory provides the natural theoretical basis, as the asymptotic conditions are completely transferred to the source terms and the new scattering function is made fullyintegrable. The scattering solutions can then be directly expressed in terms of bound state HF configurations, establishing the relationship between the bound and scattering state solutions. Alternatively, the integrable spin orbitals are generated by constructing the individual orbital equations that contain asymptotic sources and self-averaged potentials. However, the orbital energies are not determined by the equations, and a special channel energy fixing procedure is developed to secure the solutions. It is also shown that the variational construction of the orbital equations has intrinsic ambiguities that are generally associated with the self-consistent approach. On the other hand, when a small subset of open channels is included in the source term, the solutions are only partiallyintegrable, but the individual open channels can then be treated more simply by properly selecting the orbital energies. The configuration mixing and channel coupling are then necessary to complete the solution. The new theory improves the earlier continuum HF model. - Highlights: • First extension of HF to scattering states, with proper asymptotic conditions. • Orbital equations with asymptotic sources and integrable orbital solutions. • Construction of self-averaged potentials, and orbital energy fixing. • Channel coupling and configuration mixing, involving the new orbitals. • Critical evaluation of the

  11. Dynamics of essential collective motions in proteins: Theory

    NASA Astrophysics Data System (ADS)

    Stepanova, Maria

    2007-11-01

    A general theoretical background is introduced for characterization of conformational motions in protein molecules, and for building reduced coarse-grained models of proteins, based on the statistical analysis of their phase trajectories. Using the projection operator technique, a system of coupled generalized Langevin equations is derived for essential collective coordinates, which are generated by principal component analysis of molecular dynamic trajectories. The number of essential degrees of freedom is not limited in the theory. An explicit analytic relation is established between the generalized Langevin equation for essential collective coordinates and that for the all-atom phase trajectory projected onto the subspace of essential collective degrees of freedom. The theory introduced is applied to identify correlated dynamic domains in a macromolecule and to construct coarse-grained models representing the conformational motions in a protein through a few interacting domains embedded in a dissipative medium. A rigorous theoretical background is provided for identification of dynamic correlated domains in a macromolecule. Examples of domain identification in protein G are given and employed to interpret NMR experiments. Challenges and potential outcomes of the theory are discussed.

  12. Equation-of-state spinning fluids in the Einstein-Cartan theory

    NASA Technical Reports Server (NTRS)

    Ray, John R.; Smalley, Larry L.

    1987-01-01

    The relativistic fluid equations may be completed in two physically distinct methods. One method assumes the mass, rho, (or particle number) is conserved, while the other method assumes an equation of state of the form P = P(rho). A variational principle for the mass conservation method both with and without an intrinsic spin for the fluid was constructed earlier (Ray and Smalley, 1982 and 1983). A variational principle for the fluid described by an equation of state both with and without spin is formulated. In all cases the variational principle is set in the Einstein-Cartan metric-torsion U4 geometry. The results for general relativity follow as a special case.

  13. Equations of motion and conservation laws in a theory of stably stratified turbulence

    NASA Astrophysics Data System (ADS)

    L'vov, Victor S.; Rudenko, Oleksii

    2008-12-01

    This paper is part of an invited talk given at the international conference 'Turbulent Mixing and Beyond'. We consider non-isothermal fluid flows and revise simplifications of basic hydrodynamic equations for such flows, arriving eventually at a generalization of the Oberbeck-Boussinesq approximation valid for arbitrary equation of state including both non-ideal gases as well as liquids. The proposed approach is based on a suggested general definition of potential temperature. Special attention is paid to the energy conservation principle: the proposed approximation exactly preserves the total mechanical energy by approximate equations of motion. It is emphasized explicitly the importance for any turbulent boundary layer model to respect the conservation laws.

  14. One-dimensional transport equation models for sound energy propagation in long spaces: theory.

    PubMed

    Jing, Yun; Larsen, Edward W; Xiang, Ning

    2010-04-01

    In this paper, a three-dimensional transport equation model is developed to describe the sound energy propagation in a long space. Then this model is reduced to a one-dimensional model by approximating the solution using the method of weighted residuals. The one-dimensional transport equation model directly describes the sound energy propagation in the "long" dimension and deals with the sound energy in the "short" dimensions by prescribed functions. Also, the one-dimensional model consists of a coupled set of N transport equations. Only N=1 and N=2 are discussed in this paper. For larger N, although the accuracy could be improved, the calculation time is expected to significantly increase, which diminishes the advantage of the model in terms of its computational efficiency. PMID:20370013

  15. The statistical theory of the fracture of fragile bodies. Part 2: The integral equation method

    NASA Technical Reports Server (NTRS)

    Kittl, P.

    1984-01-01

    It is demonstrated how with the aid of a bending test, the Weibull fracture risk function can be determined - without postulating its analytical form - by resolving an integral equation. The respective solutions for rectangular and circular section beams are given. In the first case the function is expressed as an algorithm and in the second, in the form of series. Taking into account that the cumulative fracture probability appearing in the solution to the integral equation must be continuous and monotonically increasing, any case of fabrication or selection of samples can be treated.

  16. Solving the transport equation with quadratic finite elements: Theory and applications

    SciTech Connect

    Ferguson, J.M.

    1997-12-31

    At the 4th Joint Conference on Computational Mathematics, the author presented a paper introducing a new quadratic finite element scheme (QFEM) for solving the transport equation. In the ensuing year the author has obtained considerable experience in the application of this method, including solution of eigenvalue problems, transmission problems, and solution of the adjoint form of the equation as well as the usual forward solution. He will present detailed results, and will also discuss other refinements of his transport codes, particularly for 3-dimensional problems on rectilinear and non-rectilinear grids.

  17. AdS/CFT connection between Boltzmann and Einstein equations: Kinetic theory and pure gravity in AdS space

    SciTech Connect

    Iyer, Ramakrishnan; Mukhopadhyay, Ayan

    2010-04-15

    The AdS/CFT correspondence defines a sector with universal strongly coupled dynamics in the field theory as the dual of pure gravity in AdS described by Einstein's equation with a negative cosmological constant. We explain here, from the field-theoretic viewpoint how the dynamics in this sector gets determined by the expectation value of the energy-momentum tensor alone. We first show that the Boltzmann equation has very special solutions which could be functionally completely determined in terms of the energy-momentum tensor alone. We call these solutions conservative solutions. We indicate why conservative solutions should also exist when we refine this kinetic description to go closer to the exact microscopic theory or even move away from the regime of weak coupling so that no kinetic description could be employed. We argue that these conservative solutions form the universal sector dual to pure gravity at strong coupling and large N. Based on this observation, we propose a regularity condition on the energy-momentum tensor so that the dual solution in pure gravity has a smooth future horizon. We also study if irreversibility emerges only at long time scales of observation, unlike the case of the Boltzmann equation.

  18. Soliton Theory of Two-Dimensional Lattices: The Discrete Nonlinear Schroedinger Equation

    SciTech Connect

    Arevalo, Edward

    2009-06-05

    We theoretically investigate the motion of collective excitations in the two-dimensional nonlinear Schroedinger equation with cubic nonlinearity. The form of these excitations for a broad range of parameters is derived. Their evolution and interaction is numerically studied and the modulation instability is discussed. The case of saturable nonlinearity is revisited.

  19. Equations of State of Elements Based on the Generalized Fermi-Thomas Theory

    DOE R&D Accomplishments Database

    Feynman, R. P.; Metropolis, N.; Teller, E.

    1947-04-28

    The Fermi-Thomas model has been used to derive the equation of state of matter at high pressures and at various temperatures. Calculations have been carried out both without and with the exchange terms. Discussion of similarity transformations lead to the virial theorem and to correlation of solutions for different Z-values.

  20. The method of local linear approximation in the theory of nonlinear functional-differential equations

    SciTech Connect

    Slyusarchuk, Vasilii E

    2010-10-06

    Conditions for the existence of solutions to the nonlinear functional-differential equation (d{sup m}x(t))/dt{sup m} + (fx)(t)=h(t), t element of R in the space of functions bounded on the axes are obtained by using local linear approximation to the operator F. Bibliography: 21 items.

  1. Accurate integral equation theory for the central force model of liquid water and ionic solutions

    NASA Astrophysics Data System (ADS)

    Ichiye, Toshiko; Haymet, A. D. J.

    1988-10-01

    The atom-atom pair correlation functions and thermodynamics of the central force model of water, introduced by Lemberg, Stillinger, and Rahman, have been calculated accurately by an integral equation method which incorporates two new developments. First, a rapid new scheme has been used to solve the Ornstein-Zernike equation. This scheme combines the renormalization methods of Allnatt, and Rossky and Friedman with an extension of the trigonometric basis-set solution of Labik and co-workers. Second, by adding approximate ``bridge'' functions to the hypernetted-chain (HNC) integral equation, we have obtained predictions for liquid water in which the hydrogen bond length and number are in good agreement with ``exact'' computer simulations of the same model force laws. In addition, for dilute ionic solutions, the ion-oxygen and ion-hydrogen coordination numbers display both the physically correct stoichiometry and good agreement with earlier simulations. These results represent a measurable improvement over both a previous HNC solution of the central force model and the ex-RISM integral equation solutions for the TIPS and other rigid molecule models of water.

  2. Theory of the Lattice Boltzmann method: Derivation of macroscopic equations via the Maxwell iteration.

    PubMed

    Yong, Wen-An; Zhao, Weifeng; Luo, Li-Shi

    2016-03-01

    We propose using the Maxwell iteration to derive the hydrodynamic equations from the lattice Boltzmann equation (LBE) with an external forcing term. The proposed methodology differs from existing approaches in several aspects. First, it need not explicitly introduce multiple-timescales or the Knudsen number, both of which are required in the Chapman-Enskog analysis. Second, it need not use the Hilbert expansion of the hydrodynamic variables, which is necessary in the asymptotic analysis of the LBE. The proposed methodology assumes the acoustic scaling (or the convective scaling) δ_{t}∼δ_{x}, thus δ_{t} is the only expansion parameter in the analysis of the LBE system, and it leads to the Navier-Stokes equations in compressible form. The forcing density derived in this work can reproduce existing forcing schemes by adjusting appropriate parameters. The proposed methodology also analyzes the numerical accuracy of the LBE. In particular, it shows the Mach number Ma should scale as O(δ_{t}^{1/3}) to maintain the truncation errors due to Ma and δ_{t} in balance when δ_{t}→0, so that the LBE can converge to the expected hydrodynamic equations effectively and efficiently. PMID:27078487

  3. Theory of the Lattice Boltzmann method: Derivation of macroscopic equations via the Maxwell iteration

    NASA Astrophysics Data System (ADS)

    Yong, Wen-An; Zhao, Weifeng; Luo, Li-Shi

    2016-03-01

    We propose using the Maxwell iteration to derive the hydrodynamic equations from the lattice Boltzmann equation (LBE) with an external forcing term. The proposed methodology differs from existing approaches in several aspects. First, it need not explicitly introduce multiple-timescales or the Knudsen number, both of which are required in the Chapman-Enskog analysis. Second, it need not use the Hilbert expansion of the hydrodynamic variables, which is necessary in the asymptotic analysis of the LBE. The proposed methodology assumes the acoustic scaling (or the convective scaling) δt˜δx , thus δt is the only expansion parameter in the analysis of the LBE system, and it leads to the Navier-Stokes equations in compressible form. The forcing density derived in this work can reproduce existing forcing schemes by adjusting appropriate parameters. The proposed methodology also analyzes the numerical accuracy of the LBE. In particular, it shows the Mach number Ma should scale as O (δt1 /3) to maintain the truncation errors due to Ma and δt in balance when δt→0 , so that the LBE can converge to the expected hydrodynamic equations effectively and efficiently.

  4. Separability of a modified Dirac equation in a five-dimensional rotating, charged black hole in string theory

    NASA Astrophysics Data System (ADS)

    Wu, Shuang-Qing

    2009-08-01

    The aim of this paper is to investigate the separability of a spin-1/2 spinor field in a five-dimensional rotating, charged black hole constructed by Cvetič and Youm in string theory, in the case when three U(1) charges are set equal. This black hole solution represents a natural generalization of the famous four-dimensional Kerr-Newman solution to five dimensions with the inclusion of a Chern-Simons term to the Maxwell equation. It is shown that the usual Dirac equation cannot be separated by variables in this general spacetime with two independent angular momenta. However if one supplements an additional counterterm into the usual Dirac operator, then the modified Dirac equation for the spin-1/2 spinor particles is separable in this rotating, charged Einstein-Maxwell-Chern-Simons black hole background geometry. A first-order symmetry operator that commutes with the modified Dirac operator has exactly the same form as that previously found in the uncharged Myers-Perry black hole case. It is expressed in terms of a rank-three totally antisymmetric tensor and its covariant derivative. This tensor obeys a generalized Killing-Yano equation and its square is a second-order symmetric Stäckel-Killing tensor admitted by the five-dimensional rotating, charged black hole spacetime.

  5. Separability of a modified Dirac equation in a five-dimensional rotating, charged black hole in string theory

    SciTech Connect

    Wu Shuangqing

    2009-08-15

    The aim of this paper is to investigate the separability of a spin-1/2 spinor field in a five-dimensional rotating, charged black hole constructed by Cvetic and Youm in string theory, in the case when three U(1) charges are set equal. This black hole solution represents a natural generalization of the famous four-dimensional Kerr-Newman solution to five dimensions with the inclusion of a Chern-Simons term to the Maxwell equation. It is shown that the usual Dirac equation cannot be separated by variables in this general spacetime with two independent angular momenta. However if one supplements an additional counterterm into the usual Dirac operator, then the modified Dirac equation for the spin-1/2 spinor particles is separable in this rotating, charged Einstein-Maxwell-Chern-Simons black hole background geometry. A first-order symmetry operator that commutes with the modified Dirac operator has exactly the same form as that previously found in the uncharged Myers-Perry black hole case. It is expressed in terms of a rank-three totally antisymmetric tensor and its covariant derivative. This tensor obeys a generalized Killing-Yano equation and its square is a second-order symmetric Staeckel-Killing tensor admitted by the five-dimensional rotating, charged black hole spacetime.

  6. Tap density equations of granular powders based on the rate process theory and the free volume concept.

    PubMed

    Hao, Tian

    2015-02-28

    The tap density of a granular powder is often linked to the flowability via the Carr index that measures how tight a powder can be packed, under an assumption that more easily packed powders usually flow poorly. Understanding how particles are packed is important for revealing why a powder flows better than others. There are two types of empirical equations that were proposed to fit the experimental data of packing fractions vs. numbers of taps in the literature: the inverse logarithmic and the stretched exponential. Using the rate process theory and the free volume concept under the assumption that particles will obey similar thermodynamic laws during the tapping process if the "granular temperature" is defined in a different way, we obtain the tap density equations, and they are reducible to the two empirical equations currently widely used in literature. Our equations could potentially fit experimental data better with an additional adjustable parameter. The tapping amplitude and frequency, the weight of the granular materials, and the environmental temperature are grouped into this parameter that weighs the pace of the packing process. The current results, in conjunction with our previous findings, may imply that both "dry" (granular) and "wet" (colloidal and polymeric) particle systems are governed by the same physical mechanisms in term of the role of the free volume and how particles behave (a rate controlled process). PMID:25589375

  7. The theory of semipermeable vesicles and membranes: An integral-equation approach. II. Donnan equilibrium

    NASA Astrophysics Data System (ADS)

    Zhou, Yaoqi; Stell, George

    1988-12-01

    Integral equations that yield the charge and density profiles are derived for a Donnan system, in which an ionic solution is separated into two regions by a semipermeable membrane (SPM) or a spherical semipermeable vesicle (SPV). These equations are obtained from the Ornstein-Zernike (OZ) equation. We show how quantitative results can be obtained from either the mean spherical approximation (MSA) closure or the hypernetted-chain (HNC) closure for profiles. Use is made of bulk-correlation input obtained by means of the Debye-Hückel approximation, the MSA approximation, or the HNC approximation. The resulting approximations will be referred as MSA/DH, HNC/DH, MSA/MSA, etc. The system on which we focus contains three charged hard-sphere species: cation, anion, and a large ion (a protein or polymer ion) separated by a plane SPM, through which the large ion cannot pass, and to one side of which all large ions are confined, or a spherical SPV, outside of which the large ions are confined. Analytical expressions for the bulk density ratio between the two sides of a plane membrane as well as the membrane potential in various approximations are obtained. Results obtained from these expresssions are compared with the results obtained by equating electrochemical potentials. A new contact-value theorem is provided for the plane SPM system. Analytical solutions for the charge profile and the potential profile in the MSA/DH approximation are obtained. It turns out that results obtained in the HNC/DH approximation are exactly the same as those obtained by using 1D nonlinear Poisson-Boltzmann equations if the repulsive cores of the macroions are neglected.

  8. Orbital-free extension to Kohn-Sham density functional theory equation of state calculations: Application to silicon dioxide

    SciTech Connect

    Sjostrom, Travis; Crockett, Scott

    2015-09-02

    The liquid regime equation of state of silicon dioxide SiO2 is calculated via quantum molecular dynamics in the density range of 5 to 15 g/cc and with temperatures from 0.5 to 100 eV, including the α-quartz and stishovite phase Hugoniot curves. Below 8 eV calculations are based on Kohn-Sham density functional theory (DFT), and above 8 eV a new orbital-free DFT formulation, presented here, based on matching Kohn-Sham DFT calculations is employed. Recent experimental shock data are found to be in very good agreement with the current results. Finally both experimental and simulation data are used in constructing a new liquid regime equation of state table for SiO2.

  9. Orbital-free extension to Kohn-Sham density functional theory equation of state calculations: Application to silicon dioxide

    DOE PAGESBeta

    Sjostrom, Travis; Crockett, Scott

    2015-09-02

    The liquid regime equation of state of silicon dioxide SiO2 is calculated via quantum molecular dynamics in the density range of 5 to 15 g/cc and with temperatures from 0.5 to 100 eV, including the α-quartz and stishovite phase Hugoniot curves. Below 8 eV calculations are based on Kohn-Sham density functional theory (DFT), and above 8 eV a new orbital-free DFT formulation, presented here, based on matching Kohn-Sham DFT calculations is employed. Recent experimental shock data are found to be in very good agreement with the current results. Finally both experimental and simulation data are used in constructing a newmore » liquid regime equation of state table for SiO2.« less

  10. Configurational entropy of protein: A combined approach based on molecular simulation and integral-equation theory of liquids

    NASA Astrophysics Data System (ADS)

    Chong, Song-Ho; Ham, Sihyun

    2011-03-01

    We report the recent development of a theoretical method to calculate the protein configurational entropy in explicit solvent from statistical properties of the solvent-averaged protein potential energy surface. This method can be implemented by combining molecular simulation and integral-equation theory of liquids. Our method does not assume Gaussian distribution of protein configurations, and can be applied to unfolded or misfolded states of protein in which an average protein structure is not well defined. An illustrative application is made to misfolded state of 42-residue amyloid beta protein in water.

  11. General theory of multistage geminate reactions of isolated pairs of reactants. I. Kinetic equations

    SciTech Connect

    Doktorov, Alexander B.; Kipriyanov, Alexey A.

    2014-05-14

    General matrix approach to the consideration of multistage geminate reactions of isolated pairs of reactants depending on reactant mobility is formulated on the basis of the concept of “effective” particles. Various elementary reactions (stages of multistage reaction including physicochemical processes of internal quantum state changes) proceeding with the participation of isolated pairs of reactants (or isolated reactants) are taken into account. Investigation has been made in terms of kinetic approach implying the derivation of general (matrix) kinetic equations for local and mean probabilities of finding any of the reaction species in the sample under study (or for local and mean concentrations). The recipes for the calculation of kinetic coefficients of the equations for mean quantities in terms of relative coordinates of reactants have been formulated in the general case of inhomogeneous reacting systems. Important specific case of homogeneous reacting systems is considered.

  12. Patched-grid calculations with the Euler and Navier-Stokes equations: Theory and application

    NASA Technical Reports Server (NTRS)

    Rai, M. M.

    1986-01-01

    The Rai (1984,85) patch-boundary scheme for the Euler equations is described. The integration methods used to update the interior grid points are are discussed. Stability of patch-boundary schemes and the use of these schemes in Navier-Stokes calculations are mentioned. Results for inviscid, supersonic flow over a cylinder, blast wave diffraction by ramp, and the motion of a vortex in a freestream are presented. These test cases demonstrate the quality of solutions possible with the scheme.

  13. Integration of the Equations of Classical Electrode-Effect Theory with Aerosols

    NASA Astrophysics Data System (ADS)

    Kalinin, A. V.; Leont'ev, N. V.; Terent'ev, A. M.; Umnikov, E. D.

    2016-04-01

    This paper is devoted to an analytical study of the one-dimensional stationary system of equations for modeling of the electrode effect in the Earth's atmospheric layer with aerosols. New integrals of the system are derived. Using these integrals, the expressions for solutions of the system and estimates of the electrode layer's thickness as a function of the aerosol concentration are obtained for numerical parameters close to real.

  14. Scattering theory for the fourth-order Schrödinger equation in low dimensions

    NASA Astrophysics Data System (ADS)

    Pausader, Benoit; Xia, Suxia

    2013-08-01

    We prove scattering for the defocusing fourth-order Schrödinger equation in low spatial dimensions (1 ⩽ n ⩽ 4). Inspired by the method in (Pausader 2010 Indiana Univ. Math. J. 59 791-822), we utilize a strategy from Kenig and Merle (2006 Invent. Math. 166 645-75) to compensate for the absence of a Morawetz-type estimate, then we use a new virial-type ingredient to finish the proof.

  15. Integration of the Equations of Classical Electrode-Effect Theory with Aerosols

    NASA Astrophysics Data System (ADS)

    Kalinin, A. V.; Leont'ev, N. V.; Terent'ev, A. M.; Umnikov, E. D.

    2016-05-01

    This paper is devoted to an analytical study of the one-dimensional stationary system of equations for modeling of the electrode effect in the Earth's atmospheric layer with aerosols. New integrals of the system are derived. Using these integrals, the expressions for solutions of the system and estimates of the electrode layer's thickness as a function of the aerosol concentration are obtained for numerical parameters close to real.

  16. Properties of a soft-core model of methanol: An integral equation theory and computer simulation study

    SciTech Connect

    Huš, Matej; Urbic, Tomaz; Munaò, Gianmarco

    2014-10-28

    Thermodynamic and structural properties of a coarse-grained model of methanol are examined by Monte Carlo simulations and reference interaction site model (RISM) integral equation theory. Methanol particles are described as dimers formed from an apolar Lennard-Jones sphere, mimicking the methyl group, and a sphere with a core-softened potential as the hydroxyl group. Different closure approximations of the RISM theory are compared and discussed. The liquid structure of methanol is investigated by calculating site-site radial distribution functions and static structure factors for a wide range of temperatures and densities. Results obtained show a good agreement between RISM and Monte Carlo simulations. The phase behavior of methanol is investigated by employing different thermodynamic routes for the calculation of the RISM free energy, drawing gas-liquid coexistence curves that match the simulation data. Preliminary indications for a putative second critical point between two different liquid phases of methanol are also discussed.

  17. Automatic Generation of Analytic Equations for Vibrational and Rovibrational Constants from Fourth-Order Vibrational Perturbation Theory

    NASA Astrophysics Data System (ADS)

    Matthews, Devin A.; Gong, Justin Z.; Stanton, John F.

    2014-06-01

    The derivation of analytic expressions for vibrational and rovibrational constants, for example the anharmonicity constants χij and the vibration-rotation interaction constants α^B_r, from second-order vibrational perturbation theory (VPT2) can be accomplished with pen and paper and some practice. However, the corresponding quantities from fourth-order perturbation theory (VPT4) are considerably more complex, with the only known derivations by hand extensively using many layers of complicated intermediates and for rotational quantities requiring specialization to orthorhombic cases or the form of Watson's reduced Hamiltonian. We present an automatic computer program for generating these expressions with full generality based on the adaptation of an existing numerical program based on the sum-over-states representation of the energy to a computer algebra context. The measures taken to produce well-simplified and factored expressions in an efficient manner are discussed, as well as the framework for automatically checking the correctness of the generated equations.

  18. Properties of a soft-core model of methanol: An integral equation theory and computer simulation study

    PubMed Central

    Huš, Matej; Munaò, Gianmarco; Urbic, Tomaz

    2014-01-01

    Thermodynamic and structural properties of a coarse-grained model of methanol are examined by Monte Carlo simulations and reference interaction site model (RISM) integral equation theory. Methanol particles are described as dimers formed from an apolar Lennard-Jones sphere, mimicking the methyl group, and a sphere with a core-softened potential as the hydroxyl group. Different closure approximations of the RISM theory are compared and discussed. The liquid structure of methanol is investigated by calculating site-site radial distribution functions and static structure factors for a wide range of temperatures and densities. Results obtained show a good agreement between RISM and Monte Carlo simulations. The phase behavior of methanol is investigated by employing different thermodynamic routes for the calculation of the RISM free energy, drawing gas-liquid coexistence curves that match the simulation data. Preliminary indications for a putative second critical point between two different liquid phases of methanol are also discussed. PMID:25362323

  19. Development of metal-bonded Langevin transducer using LiNbO3

    NASA Astrophysics Data System (ADS)

    Ito, Hiroshi; Jimbo, Hikaru; Shiotani, Koichi; Sakai, Nagahide

    2016-07-01

    We newly developed a metal-bonded Langevin transducer using LiNbO3 in order to realize a practical high-power LiNbO3 Langevin transducer. It utilizes metal bonding with a lead-free solder as an assembly method for a Langevin transducer, instead of a bolt as used in a conventional bolt-clamped Langevin transducer. The newly developed metal-bonded LiNbO3 Langevin transducer achieved a high vibration velocity of over 1.5 m/s and stable operation. Because of rigid metal bonding, it does not show nonlinear phenomena such as a jump phenomenon and/or a resonant frequency shift.

  20. Expectation-maximization of the potential of mean force and diffusion coefficient in Langevin dynamics from single molecule FRET data photon by photon.

    PubMed

    Haas, Kevin R; Yang, Haw; Chu, Jhih-Wei

    2013-12-12

    The dynamics of a protein along a well-defined coordinate can be formally projected onto the form of an overdamped Lagevin equation. Here, we present a comprehensive statistical-learning framework for simultaneously quantifying the deterministic force (the potential of mean force, PMF) and the stochastic force (characterized by the diffusion coefficient, D) from single-molecule Förster-type resonance energy transfer (smFRET) experiments. The likelihood functional of the Langevin parameters, PMF and D, is expressed by a path integral of the latent smFRET distance that follows Langevin dynamics and realized by the donor and the acceptor photon emissions. The solution is made possible by an eigen decomposition of the time-symmetrized form of the corresponding Fokker-Planck equation coupled with photon statistics. To extract the Langevin parameters from photon arrival time data, we advance the expectation-maximization algorithm in statistical learning, originally developed for and mostly used in discrete-state systems, to a general form in the continuous space that allows for a variational calculus on the continuous PMF function. We also introduce the regularization of the solution space in this Bayesian inference based on a maximum trajectory-entropy principle. We use a highly nontrivial example with realistically simulated smFRET data to illustrate the application of this new method. PMID:23937300

  1. Langevin Bimolecular Recombination Kinetics of a Layered Exciton-Trion Gas

    NASA Astrophysics Data System (ADS)

    Crowne, Frank; Birdwell, Anthony

    The use of rate equations to describe various many-body kinetic processes in highly photoexcited layered semiconductors is discussed. In these systems, pairs of electrons and holes generated by photons from an external laser combine to form a multicomponent plasma whose time evolution is governed by gas dynamics and various recombination processes. At high levels of illumination this leads to a variety of secondary components in addition to neutral excitons, notably the so-called trions, which consist of exciton-electron and exciton-hole bound states. Although the recombination is modeled as bimolecular for all pairs of carrier species, the structure of the rate terms is sensitive to the dimensionality of the system due to the Langevin nature of encounters between carriers. It is demonstrated that charge neutrality does not apply to individual carrier species, e.g., electron and hole densities need not be equal in the presence of trions. In order to track the full time evolution from laser initiation to steady state, the system of rate equations is simulated numerically.

  2. Structural Equation Model of the Consumer-Directed Theory of Empowerment in a Vocational Rehabilitation Context

    ERIC Educational Resources Information Center

    Kosciulek, John F.

    2005-01-01

    One model that is potentially useful in the rehabilitation field is the Consumer-Directed Theory of Empowerment (CDTE; Kosciulek, 1999a). However, additional empirical data are needed to further develop and critically evaluate the CDTE. To accomplish this task, the purpose of this study was to test the hypothesized structural model CDTE in a…

  3. Investigating the Population Sensitivity Assumption of Item Response Theory True-Score Equating across Two Subgroups of Examinees and Two Test Formats

    ERIC Educational Resources Information Center

    von Davier, Alina A.; Wilson, Christine

    2008-01-01

    Dorans and Holland (2000) and von Davier, Holland, and Thayer (2003) introduced measures of the degree to which an observed-score equating function is sensitive to the population on which it is computed. This article extends the findings of Dorans and Holland and of von Davier et al. to item response theory (IRT) true-score equating methods that…

  4. Speeding up equation of motion coupled cluster theory with the chain of spheres approximation

    NASA Astrophysics Data System (ADS)

    Dutta, Achintya Kumar; Neese, Frank; Izsák, Róbert

    2016-01-01

    In the present paper, the chain of spheres exchange (COSX) approximation is applied to the highest scaling terms in the equation of motion (EOM) coupled cluster equations with single and double excitations, in particular, the terms involving integrals with four virtual labels. It is found that even the acceleration of this single term yields significant computational gains without compromising the desired accuracy of the method. For an excitation energy calculation on a cluster of five water molecules using 585 basis functions, the four virtual term is 9.4 times faster using COSX with a loose grid than using the canonical implementation, which yields a 2.6 fold acceleration for the whole of the EOM calculation. For electron attachment calculations, the four virtual term is 15 times and the total EOM calculation is 10 times faster than the canonical calculation for the same system. The accuracy of the new method was tested using Thiel's test set for excited states using the same settings and the maximum absolute deviation over the whole test set was found to be 12.945 cm-1 (59 μHartree) for excitation energies and 6.799 cm-1 (31 μHartree) for electron attachments. Using MP2 amplitudes for the ground state in combination with the parallel evaluation of the full EOM equations in the manner discussed in this paper enabled us to perform calculations for large systems. Electron affinity values for the two lowest states of a Zn protoporphyrine model compound (224 correlated electrons and 1120 basis functions) were obtained in 3 days 19 h using 4 cores of a Xeon E5-2670 processor allocating 10 GB memory per core. Calculating the lowest two excitation energies for trans-retinal (114 correlated electrons and 539 basis functions) took 1 day 21 h using eight cores of the same processor and identical memory allocation per core.

  5. Speeding up equation of motion coupled cluster theory with the chain of spheres approximation.

    PubMed

    Dutta, Achintya Kumar; Neese, Frank; Izsák, Róbert

    2016-01-21

    In the present paper, the chain of spheres exchange (COSX) approximation is applied to the highest scaling terms in the equation of motion (EOM) coupled cluster equations with single and double excitations, in particular, the terms involving integrals with four virtual labels. It is found that even the acceleration of this single term yields significant computational gains without compromising the desired accuracy of the method. For an excitation energy calculation on a cluster of five water molecules using 585 basis functions, the four virtual term is 9.4 times faster using COSX with a loose grid than using the canonical implementation, which yields a 2.6 fold acceleration for the whole of the EOM calculation. For electron attachment calculations, the four virtual term is 15 times and the total EOM calculation is 10 times faster than the canonical calculation for the same system. The accuracy of the new method was tested using Thiel's test set for excited states using the same settings and the maximum absolute deviation over the whole test set was found to be 12.945 cm(-1) (59 μHartree) for excitation energies and 6.799 cm(-1) (31 μHartree) for electron attachments. Using MP2 amplitudes for the ground state in combination with the parallel evaluation of the full EOM equations in the manner discussed in this paper enabled us to perform calculations for large systems. Electron affinity values for the two lowest states of a Zn protoporphyrine model compound (224 correlated electrons and 1120 basis functions) were obtained in 3 days 19 h using 4 cores of a Xeon E5-2670 processor allocating 10 GB memory per core. Calculating the lowest two excitation energies for trans-retinal (114 correlated electrons and 539 basis functions) took 1 day 21 h using eight cores of the same processor and identical memory allocation per core. PMID:26801015

  6. Theory of warm ionized gases: equation of state and kinetic Schottky anomaly.

    PubMed

    Capolupo, A; Giampaolo, S M; Illuminati, F

    2013-10-01

    Based on accurate Lennard-Jones-type interaction potentials, we derive a closed set of state equations for the description of warm atomic gases in the presence of ionization processes. The specific heat is predicted to exhibit peaks in correspondence to single and multiple ionizations. Such kinetic analog in atomic gases of the Schottky anomaly in solids is enhanced at intermediate and low atomic densities. The case of adiabatic compression of noble gases is analyzed in detail and the implications on sonoluminescence are discussed. In particular, the predicted plasma electron density in a sonoluminescent bubble turns out to be in good agreement with the value measured in recent experiments. PMID:24229140

  7. Field theory and weak Euler-Lagrange equation for classical particle-field systems

    SciTech Connect

    Qin, Hong; Burby, Joshua W; Davidson, Ronald C

    2014-10-01

    It is commonly believed that energy-momentum conservation is the result of space-time symmetry. However, for classical particle-field systems, e.g., Klimontovich-Maxwell and Klimontovich- Poisson systems, such a connection hasn't been formally established. The difficulty is due to the fact that particles and the electromagnetic fields reside on different manifolds. To establish the connection, the standard Euler-Lagrange equation needs to be generalized to a weak form. Using this technique, energy-momentum conservation laws that are difficult to find otherwise can be systematically derived.

  8. Spectra and dynamics in the B800 antenna: comparing hierarchical equations, Redfield and Förster theories.

    PubMed

    Novoderezhkin, Vladimir; van Grondelle, Rienk

    2013-09-26

    We model the spectra (absorption and circular dichroism) and excitation dynamics in the B800 ring of the LH2 antenna complex from Rs. molischianum using different theoretical approaches, i.e., Förster theory, standard and modified versions of the Redfield theory, and the more versatile nonperturbative approach based on hierarchically coupled equations for the reduced density operator. We demonstrate that, although excitations in the B800 ring are localized due to disorder, thermal effects, and phonons, there are still sizable excitonic effects producing shift, narrowing, and asymmetry of the spectra. Moreover, the excitation dynamics reveals the presence of long-lived (up to 1 ps) non-oscillatory coherences between the exciton states maintained due to nonsecular population-to-coherence transfers. The sub-ps decay of the coherences is followed by slow motion of the excitation around the ring, producing equilibration of the site populations with a time constant of about 3-4 ps, which is slower than the B800 → B850 transfer. The exact solution obtained with the hierarchical equations is compared with other approaches, thus illustrating limitations of the Förster and Redfield pictures. PMID:23531197

  9. Comments on the symmetry of AdS6 solutions in string/M-theory and Killing spinor equations

    NASA Astrophysics Data System (ADS)

    Kim, Hyojoong; Kim, Nakwoo

    2016-09-01

    It was recently pointed out in [1] that AdS6 solutions in IIB theory enjoy an extended symmetry structure and the consistent truncation to D = 4 internal space leads to a nonlinear sigma model with target SL (3 , R) / SO (2 , 1). We continue to study the purely bosonic D = 4 effective action, and elucidate how the addition of scalar potential term still allows Killing spinor equations in the absence of gauge fields. In particular, the potential turns out to be a single diagonal component of the coset representative. Furthermore, we perform a general analysis of the integrability conditions of Killing spinor equations and establish that the effective action can be in fact generalized to arbitrary sizes and signatures, e.g. with target SL (n , R) / SO (p , n - p) and the scalar potential expressible by a single diagonal component of the coset representative. We also comment on a similar construction and its generalizations of effective D = 5 purely bosonic non-linear sigma model action related to AdS6 in M-theory.

  10. Time-optimal path planning in dynamic flows using level set equations: theory and schemes

    NASA Astrophysics Data System (ADS)

    Lolla, Tapovan; Lermusiaux, Pierre F. J.; Ueckermann, Mattheus P.; Haley, Patrick J.

    2014-09-01

    We develop an accurate partial differential equation-based methodology that predicts the time-optimal paths of autonomous vehicles navigating in any continuous, strong, and dynamic ocean currents, obviating the need for heuristics. The goal is to predict a sequence of steering directions so that vehicles can best utilize or avoid currents to minimize their travel time. Inspired by the level set method, we derive and demonstrate that a modified level set equation governs the time-optimal path in any continuous flow. We show that our algorithm is computationally efficient and apply it to a number of experiments. First, we validate our approach through a simple benchmark application in a Rankine vortex flow for which an analytical solution is available. Next, we apply our methodology to more complex, simulated flow fields such as unsteady double-gyre flows driven by wind stress and flows behind a circular island. These examples show that time-optimal paths for multiple vehicles can be planned even in the presence of complex flows in domains with obstacles. Finally, we present and support through illustrations several remarks that describe specific features of our methodology.

  11. Time-optimal path planning in dynamic flows using level set equations: theory and schemes

    NASA Astrophysics Data System (ADS)

    Lolla, Tapovan; Lermusiaux, Pierre F. J.; Ueckermann, Mattheus P.; Haley, Patrick J.

    2014-10-01

    We develop an accurate partial differential equation-based methodology that predicts the time-optimal paths of autonomous vehicles navigating in any continuous, strong, and dynamic ocean currents, obviating the need for heuristics. The goal is to predict a sequence of steering directions so that vehicles can best utilize or avoid currents to minimize their travel time. Inspired by the level set method, we derive and demonstrate that a modified level set equation governs the time-optimal path in any continuous flow. We show that our algorithm is computationally efficient and apply it to a number of experiments. First, we validate our approach through a simple benchmark application in a Rankine vortex flow for which an analytical solution is available. Next, we apply our methodology to more complex, simulated flow fields such as unsteady double-gyre flows driven by wind stress and flows behind a circular island. These examples show that time-optimal paths for multiple vehicles can be planned even in the presence of complex flows in domains with obstacles. Finally, we present and support through illustrations several remarks that describe specific features of our methodology.

  12. On boundary conditions for the diffusion equation in room-acoustic prediction: Theory, simulations, and experiments.

    PubMed

    Jing, Yun; Xiang, Ning

    2008-01-01

    This paper proposes a modified boundary condition to improve the room-acoustic prediction accuracy of a diffusion equation model. Previous boundary conditions for the diffusion equation model have certain limitations which restrict its application to a certain number of room types. The boundary condition employing the Sabine absorption coefficient [V. Valeau et al., J. Acoust. Soc. Am. 119, 1504-1513 (2006)] cannot predict the sound field well when the absorption coefficient is high, while the boundary condition employing the Eyring absorption coefficient [Y. Jing and N. Xiang, J. Acoust. Soc. Am. 121, 3284-3287 (2007); A. Billon et al., Appl. Acoust. 69, (2008)] has a singularity whenever any surface material has an absorption coefficient of 1.0. The modified boundary condition is derived based on an analogy between sound propagation and light propagation. Simulated and experimental data are compared to verify the modified boundary condition in terms of room-acoustic parameter prediction. The results of this comparison suggest that the modified boundary condition is valid for a range of absorption coefficient values and successfully eliminates the singularity problem. PMID:18177146

  13. Application of functional analysis to perturbation theory of differential equations. [nonlinear perturbation of the harmonic oscillator

    NASA Technical Reports Server (NTRS)

    Bogdan, V. M.; Bond, V. B.

    1980-01-01

    The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.

  14. On the equation-of-motion versus in-in approach in cosmological perturbation theory

    NASA Astrophysics Data System (ADS)

    Chen, Xingang; Namjoo, Mohammad Hossein; Wang, Yi

    2016-01-01

    In this paper, we study several issues in the linear equation-of-motion (EoM) and in-in approaches of computing the two-point correlation functions in multi-field inflation. We prove the equivalence between this EoM approach and the first-principle in-in formalism. We check this equivalence using several explicit examples, including cases with scale-invariant corrections and scale-dependent features. Motivated by the explicit proof, we show that the usual procedures in these approaches can be extended and applied to some interesting model categories beyond what has been studied in the literature so far. These include the density perturbations with strong couplings and correlated multi-field initial states.

  15. A theory of solving TAP equations for Ising models with general invariant random matrices

    NASA Astrophysics Data System (ADS)

    Opper, Manfred; Çakmak, Burak; Winther, Ole

    2016-03-01

    We consider the problem of solving TAP mean field equations by iteration for Ising models with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical functional approach that in the thermodynamic limit yields an effective dynamics of a single variable trajectory. Our main novel contribution is the expression for the implicit memory term of the dynamics for general invariant ensembles. By subtracting these terms, that depend on magnetizations at previous time steps, the implicit memory terms cancel making the iteration dependent on a Gaussian distributed field only. The TAP magnetizations are stable fixed points if a de Almeida-Thouless stability criterion is fulfilled. We illustrate our method explicitly for coupling matrices drawn from the random orthogonal ensemble.

  16. Patched-grid calculations with the Euler and Navier-Stokes equations: Theory and applications

    NASA Technical Reports Server (NTRS)

    Rai, M. M.

    1986-01-01

    A patched-grid approach is one in which the flow region of interest is divided into subregions which are then discretized independently using existing grid generator. The equations of motion are integrated in each subregion in conjunction with patch-boundary schemes which allow proper information transfer across interfaces that separate subregions. The patched-grid approach greatly simplifies the treatment of complex geometries and also the addition of grid points to selected regions of the flow. A conservative patch-boundary condition that can be used with explicit, implicit factored and implicit relaxation schemes is described. Several example calculations that demonstrate the capabilities of the patched-grid scheme are also included.

  17. COMPARISON OF NUMERICAL METHODS FOR SOLVING THE SECOND-ORDER DIFFERENTIAL EQUATIONS OF MOLECULAR SCATTERING THEORY

    SciTech Connect

    Thomas, L.D.; Alexander, M.H.; Johnson, B.R.; Lester Jr., W. A.; Light, J.C.; McLenithan, K.D.; Parker, G.A.; Redmon, M.J.; Schmalz, T.G.; Secrest, D.; Walker, R.B.

    1980-07-01

    The numerical solution of coupled, second-order differential equations is a fundamental problem in theoretical physics and chemistry. There are presently over 20 commonly used methods. Unbiased comparisons of the methods are difficult to make and few have been attempted. Here we report a comparison of 11 different methods applied to 3 different test problems. The test problems have been constructed to approximate chemical systems of current research interest and to be representative of the state of the art in inelastic molecular collisions. All calculations were done on the same computer and the attempt was made to do all calculations to the same level of accuracy. The results of the initial tests indicated that an improved method might be obtained by using different methods in different integration regions. Such a hybrid program was developed and found to be at least 1.5 to 2.0 times faster than any individual method.

  18. The Solution of Fully Fuzzy Quadratic Equation Based on Optimization Theory

    PubMed Central

    Allahviranloo, T.; Gerami Moazam, L.

    2014-01-01

    Firstly in this paper we introduce a new concept of the 2nd power of a fuzzy number. It is exponent to production (EP) method that provides an analytical and approximate solution for fully fuzzy quadratic equation (FFQE) : F(X˜)=D˜, where F(X˜)=A˜X˜2+B˜X˜+C˜. To use the mentioned EP method, at first the 1-cut solution of FFQE as a real root is obtained and then unknown manipulated unsymmetrical spreads are allocated to the core point. To this purpose we find λ and μ as optimum values which construct the best spreads. Finally to illustrate easy application and rich behavior of EP method, several examples are given. PMID:25009826

  19. Third order wave equation in Duffin-Kemmer-Petiau theory: Massive case

    NASA Astrophysics Data System (ADS)

    Markov, Yu. A.; Markova, M. A.; Bondarenko, A. I.

    2015-11-01

    Within the framework of the Duffin-Kemmer-Petiau (DKP) formalism a more consistent approach to the derivation of the third order wave equation obtained earlier by M. Nowakowski [1] on the basis of heuristic considerations is suggested. For this purpose an additional algebraic object, the so-called q -commutator (q is a primitive cubic root of unity) and a new set of matrices ημ instead of the original matrices βμ of the DKP algebra are introduced. It is shown that in terms of these ημ matrices we have succeeded in reducing a procedure of the construction of cubic root of the third order wave operator to a few simple algebraic transformations and to a certain operation of the passage to the limit z →q , where z is some complex deformation parameter entering into the definition of the η -matrices. A corresponding generalization of the result obtained to the case of the interaction with an external electromagnetic field introduced through the minimal coupling scheme is carried out and a comparison with M. Nowakowski's result is performed. A detailed analysis of the general structure for a solution of the first order differential equation for the wave function ψ (x ;z ) is performed and it is shown that the solution is singular in the z →q limit. The application to the problem of construction within the DKP approach of the path integral representation in parasuperspace for the propagator of a massive vector particle in a background gauge field is discussed.

  20. Mercedes–Benz water molecules near hydrophobic wall: Integral equation theories vs Monte Carlo simulations

    PubMed Central

    Urbic, T.; Holovko, M. F.

    2011-01-01

    Associative version of Henderson-Abraham-Barker theory is applied for the study of Mercedes–Benz model of water near hydrophobic surface. We calculated density profiles and adsorption coefficients using Percus-Yevick and soft mean spherical associative approximations. The results are compared with Monte Carlo simulation data. It is shown that at higher temperatures both approximations satisfactory reproduce the simulation data. For lower temperatures, soft mean spherical approximation gives good agreement at low and at high densities while in at mid range densities, the prediction is only qualitative. The formation of a depletion layer between water and hydrophobic surface was also demonstrated and studied. PMID:21992334

  1. Mercedes-Benz water molecules near hydrophobic wall: Integral equation theories vs Monte Carlo simulations

    NASA Astrophysics Data System (ADS)

    Urbic, T.; Holovko, M. F.

    2011-10-01

    Associative version of Henderson-Abraham-Barker theory is applied for the study of Mercedes-Benz model of water near hydrophobic surface. We calculated density profiles and adsorption coefficients using Percus-Yevick and soft mean spherical associative approximations. The results are compared with Monte Carlo simulation data. It is shown that at higher temperatures both approximations satisfactory reproduce the simulation data. For lower temperatures, soft mean spherical approximation gives good agreement at low and at high densities while in at mid range densities, the prediction is only qualitative. The formation of a depletion layer between water and hydrophobic surface was also demonstrated and studied.

  2. Mercedes-Benz water molecules near hydrophobic wall: integral equation theories vs Monte Carlo simulations.

    PubMed

    Urbic, T; Holovko, M F

    2011-10-01

    Associative version of Henderson-Abraham-Barker theory is applied for the study of Mercedes-Benz model of water near hydrophobic surface. We calculated density profiles and adsorption coefficients using Percus-Yevick and soft mean spherical associative approximations. The results are compared with Monte Carlo simulation data. It is shown that at higher temperatures both approximations satisfactory reproduce the simulation data. For lower temperatures, soft mean spherical approximation gives good agreement at low and at high densities while in at mid range densities, the prediction is only qualitative. The formation of a depletion layer between water and hydrophobic surface was also demonstrated and studied. PMID:21992334

  3. Langevin dynamics simulation of polymer-assisted virus-like assembly

    NASA Astrophysics Data System (ADS)

    Mahalik, J. P.; Muthukumar, M.

    2012-04-01

    Starting from a coarse grained representation of the building units of the minute virus of mice and a flexible polyelectrolyte molecule, we have explored the mechanism of assembly into icosahedral structures with the help of Langevin dynamics simulations and the parallel tempering technique. Regular icosahedra with appropriate symmetry form only in a narrow range of temperature and polymer length. Within this region of parameters where successful assembly would proceed, we have systematically investigated the growth kinetics. The assembly of icosahedra is found to follow the classical nucleation and growth mechanism in the absence of the polymer, with the three regimes of nucleation, linear growth, and slowing down in the later stage. The calculated average nucleation time obeys the laws expected from the classical nucleation theory. The linear growth rate is found to obey the laws of secondary nucleation as in the case of lamellar growth in polymer crystallization. The same mechanism is seen in the simulations of the assembly of icosahedra in the presence of the polymer as well. The polymer reduces the nucleation barrier significantly by enhancing the local concentration of subunits via adsorbing them on their backbone. The details of growth in the presence of the polymer are also found to be consistent with the classical nucleation theory, despite the smallness of the assembled structures.

  4. Perturbative treatment of anharmonic vibrational effects on bond distances: an extended Langevin dynamics method.

    PubMed

    Shen, Tonghao; Su, Neil Qiang; Wu, Anan; Xu, Xin

    2014-03-01

    In this work, we first review the perturbative treatment of an oscillator with cubic anharmonicity. It is shown that there is a quantum-classical correspondence in terms of mean displacement, mean-squared displacement, and the corresponding variance in the first-order perturbation theory, provided that the amplitude of the classical oscillator is fixed at the zeroth-order energy of quantum mechanics EQM (0). This correspondence condition is realized by proposing the extended Langevin dynamics (XLD), where the key is to construct a proper driving force. It is assumed that the driving force adopts a simple harmonic form with its amplitude chosen according to EQM (0), while the driving frequency chosen as the harmonic frequency. The latter can be improved by using the natural frequency of the system in response to the potential if its anharmonicity is strong. By comparing to the accurate numeric results from discrete variable representation calculations for a set of diatomic species, it is shown that the present method is able to capture the large part of anharmonicity, being competitive with the wave function-based vibrational second-order perturbation theory, for the whole frequency range from ∼4400 cm(-1) (H2 ) to ∼160 cm(-1) (Na2 ). XLD shows a substantial improvement over the classical molecular dynamics which ceases to work for hard mode when zero-point energy effects are significant. PMID:24375394

  5. Homogeneous droplet nucleation modeled using the gradient theory combined with the PC-SAFT equation of state

    NASA Astrophysics Data System (ADS)

    Planková, Barbora; Hrubý, Jan; Vinš, Václav

    2013-04-01

    In this work, we used the density gradient theory (DGT) combined with the cubic equation of state (EoS) by Peng and Robinson (PR) and the perturbed chain (PC) modification of the SAFT EoS developed by Gross and Sadowski [1]. The PR EoS is based on very simplified physical foundations, it has significant limitations in the accuracy of the predicted thermodynamic properties. On the other hand, the PC-SAFT EoS combines different intermolecular forces, e.g., hydrogen bonding, covalent bonding, Coulombic forces which makes it more accurate in predicting of the physical variables. We continued in our previous works [2,3] by solving the boundary value problem which arose by mathematical solution of the DGT formulation and including the boundary conditions. Achieving the numerical solution was rather tricky; this study describes some of the crucial developments that helped us to overcome the partial problems. The most troublesome were computations for low temperatures where we achieved great improvements compared to [3]. We applied the GT for the n-alkanes: nheptane, n-octane, n-nonane, and n-decane because of the availability of the experimental data. Comparing them with our numerical results, we observed great differences between the theories; the best results gave the combination of the GT and the PC-SAFT. However, a certain temperature drift was observed that is not satisfactorily explained by the present theories.

  6. Effective field theory out of equilibrium: Brownian quantum fields

    NASA Astrophysics Data System (ADS)

    Boyanovsky, D.

    2015-06-01

    The emergence of an effective field theory out of equilibrium is studied in the case in which a light field—the system—interacts with very heavy fields in a finite temperature bath. We obtain the reduced density matrix for the light field, its time evolution is determined by an effective action that includes the influence action from correlations of the heavy degrees of freedom. The non-equilibrium effective field theory yields a Langevin equation of motion for the light field in terms of dissipative and noise kernels that obey a generalized fluctuation dissipation relation. These are completely determined by the spectral density of the bath which is analyzed in detail for several cases. At T = 0 we elucidate the effect of thresholds in the renormalization aspects and the asymptotic emergence of a local effective field theory with unitary time evolution. At T\

  7. Solvent exchange in liquid methanol and rate theory

    NASA Astrophysics Data System (ADS)

    Dang, Liem X.; Schenter, Gregory K.

    2016-01-01

    To enhance our understanding of the solvent exchange mechanism in liquid methanol, we report a systematic study using molecular dynamics simulations. We use transition state theory, the Impey-Madden-McDonald method, the reactive flux method, and Grote-Hynes theory to compute the rate constants for this process. Solvent coupling was found to dominate, resulting in a significantly small transmission coefficient. We predict a positive activation volume for methanol exchange. The essential features of the dynamics as well as the pressure dependence are recovered from a Generalized Langevin Equation description of the dynamics. We find that the response to anharmonicity can be decomposed into two time regimes, one corresponding to short time response (<0.1 ps) and long time response (>5 ps). An effective characterization of the process is obtained from launching dynamics from the planar hypersurface corresponding to Grote-Hynes theory, resulting in improved numerical convergence of correlation functions.

  8. Control Theory based Shape Design for the Incompressible Navier-Stokes Equations

    NASA Astrophysics Data System (ADS)

    Cowles, G.; Martinelli, L.

    2003-12-01

    A design method for shape optimization in incompressible turbulent viscous flow has been developed and validated for inverse design. The gradient information is determined using a control theory based algorithm. With such an approach, the cost of computing the gradient is negligible. An additional adjoint system must be solved which requires the cost of a single steady state flow solution. Thus, this method has an enormous advantage over traditional finite-difference based algorithms. The method of artificial compressibility is utilized to solve both the flow and adjoint systems. An algebraic turbulence model is used to compute the eddy viscosity. The method is validated using several inverse wing design test cases. In each case, the program must modify the shape of the initial wing such that its pressure distribution matches that of the target wing. Results are shown for the inversion of both finite thickness wings as well as zero thickness wings which can be considered a model of yacht sails.

  9. Second order classical perturbation theory for the sticking probability of heavy atoms scattered on surfaces

    SciTech Connect

    Sahoo, Tapas; Pollak, Eli

    2015-08-14

    A second order classical perturbation theory is developed to calculate the sticking probability of a particle scattered from an uncorrugated thermal surface. An analytic expression for the temperature dependent energy loss of the particle to the surface is derived by employing a one-dimensional generalized Langevin equation. The surface temperature reduces the energy loss, since the thermal surface transfers energy to the particle. Using a Gaussian energy loss kernel and the multiple collision theory of Fan and Manson [J. Chem. Phys. 130, 064703 (2009)], enables the determination of the fraction of particles trapped on the surface after subsequent momentum reversals of the colliding particle. This then leads to an estimate of the trapping probability. The theory is tested for the model scattering of Ar on a LiF(100) surface. Comparison with numerical simulations shows excellent agreement of the analytical theory with simulations, provided that the energy loss is determined by the second order perturbation theory.

  10. Scattering theory for the radial H˙1/2-critical wave equation with a cubic convolution

    NASA Astrophysics Data System (ADS)

    Miao, Changxing; Zhang, Junyong; Zheng, Jiqiang

    2015-12-01

    In this paper, we study the global well-posedness and scattering for the wave equation with a cubic convolution ∂t2 u - Δu = ± (| x | - 3 *| u | 2) u in dimensions d ≥ 4. We prove that if the radial solution u with life-span I obeys (u, ut) ∈ Lt∞ (I ; H˙x 1 / 2 (Rd) × H˙x - 1 / 2 (Rd)), then u is global and scatters. By the strategy derived from concentration compactness, we show that the proof of the global well-posedness and scattering is reduced to disprove the existence of two scenarios: soliton-like solution and high to low frequency cascade. Making use of the No-waste Duhamel formula and double Duhamel trick, we deduce that these two scenarios enjoy the additional regularity by the bootstrap argument of [7]. This together with virial analysis implies the energy of such two scenarios is zero and so we get a contradiction.

  11. On Self-Similar Solutions to a Kinetic Equation Arising in Weak Turbulence Theory for the Nonlinear Schrödinger Equation

    NASA Astrophysics Data System (ADS)

    Kierkels, A. H. M.; Velázquez, J. J. L.

    2016-06-01

    We construct a family of self-similar solutions with fat tails to a quadratic kinetic equation. This equation describes the long time behaviour of weak solutions with finite mass to the weak turbulence equation associated to the nonlinear Schrödinger equation. The solutions that we construct have finite mass, but infinite energy. In Kierkels and Velázquez (J Stat Phys 159:668-712, 2015) self-similar solutions with finite mass and energy were constructed. Here we prove upper and lower exponential bounds on the tails of these solutions.

  12. On Self-Similar Solutions to a Kinetic Equation Arising in Weak Turbulence Theory for the Nonlinear Schrödinger Equation

    NASA Astrophysics Data System (ADS)

    Kierkels, A. H. M.; Velázquez, J. J. L.

    2016-04-01

    We construct a family of self-similar solutions with fat tails to a quadratic kinetic equation. This equation describes the long time behaviour of weak solutions with finite mass to the weak turbulence equation associated to the nonlinear Schrödinger equation. The solutions that we construct have finite mass, but infinite energy. In Kierkels and Velázquez (J Stat Phys 159:668-712, 2015) self-similar solutions with finite mass and energy were constructed. Here we prove upper and lower exponential bounds on the tails of these solutions.

  13. Generalized Langevin models of molecular dynamics simulations with applications to ion channels

    NASA Astrophysics Data System (ADS)

    Gordon, Dan; Krishnamurthy, Vikram; Chung, Shin-Ho

    2009-10-01

    We present a new methodology, which combines molecular dynamics and stochastic dynamics, for modeling the permeation of ions across biological ion channels. Using molecular dynamics, a free energy profile is determined for the ion(s) in the channel, and the distribution of random and frictional forces is measured over discrete segments of the ion channel. The parameters thus determined are used in stochastic dynamics simulations based on the nonlinear generalized Langevin equation. We first provide the theoretical basis of this procedure, which we refer to as "distributional molecular dynamics," and detail the methods for estimating the parameters from molecular dynamics to be used in stochastic dynamics. We test the technique by applying it to study the dynamics of ion permeation across the gramicidin pore. Given the known difficulty in modeling the conduction of ions in gramicidin using classical molecular dynamics, there is a degree of uncertainty regarding the validity of the MD-derived potential of mean force (PMF) for gramicidin. Using our techniques and systematically changing the PMF, we are able to reverse engineer a modified PMF which gives a current-voltage curve closely matching experimental results.

  14. Stochastic thermodynamics of Langevin systems under time-delayed feedback control: Second-law-like inequalities.

    PubMed

    Rosinberg, M L; Munakata, T; Tarjus, G

    2015-04-01

    Response lags are generic to almost any physical system and often play a crucial role in the feedback loops present in artificial nanodevices and biological molecular machines. In this paper, we perform a comprehensive study of small stochastic systems governed by an underdamped Langevin equation and driven out of equilibrium by a time-delayed continuous feedback control. In their normal operating regime, these systems settle in a nonequilibrium steady state in which work is permanently extracted from the surrounding heat bath. By using the Fokker-Planck representation of the dynamics, we derive a set of second-law-like inequalities that provide bounds to the rate of extracted work. These inequalities involve additional contributions characterizing the reduction of entropy production due to the continuous measurement process. We also show that the non-Markovian nature of the dynamics requires a modification of the basic relation linking dissipation to the breaking of time-reversal symmetry at the level of trajectories. The modified relation includes a contribution arising from the acausal character of the reverse process. This, in turn, leads to another second-law-like inequality. We illustrate the general formalism with a detailed analytical and numerical study of a harmonic oscillator driven by a linear feedback, which describes actual experimental setups. PMID:25974446

  15. Stochastic thermodynamics of Langevin systems under time-delayed feedback control: Second-law-like inequalities

    NASA Astrophysics Data System (ADS)

    Rosinberg, M. L.; Munakata, T.; Tarjus, G.

    2015-04-01

    Response lags are generic to almost any physical system and often play a crucial role in the feedback loops present in artificial nanodevices and biological molecular machines. In this paper, we perform a comprehensive study of small stochastic systems governed by an underdamped Langevin equation and driven out of equilibrium by a time-delayed continuous feedback control. In their normal operating regime, these systems settle in a nonequilibrium steady state in which work is permanently extracted from the surrounding heat bath. By using the Fokker-Planck representation of the dynamics, we derive a set of second-law-like inequalities that provide bounds to the rate of extracted work. These inequalities involve additional contributions characterizing the reduction of entropy production due to the continuous measurement process. We also show that the non-Markovian nature of the dynamics requires a modification of the basic relation linking dissipation to the breaking of time-reversal symmetry at the level of trajectories. The modified relation includes a contribution arising from the acausal character of the reverse process. This, in turn, leads to another second-law-like inequality. We illustrate the general formalism with a detailed analytical and numerical study of a harmonic oscillator driven by a linear feedback, which describes actual experimental setups.

  16. Lattice model theory of the equation of state covering the gas, liquid, and solid phases

    NASA Technical Reports Server (NTRS)

    Bonavito, N. L.; Tanaka, T.; Chan, E. M.; Horiguchi, T.; Foreman, J. C.

    1975-01-01

    The three stable states of matter and the corresponding phase transitions were obtained with a single model. Patterned after Lennard-Jones and Devonshires's theory, a simple cubic lattice model containing two fcc sublattices (alpha and beta) is adopted. The interatomic potential is taken to be the Lennard-Jones (6-12) potential. Employing the cluster variation method, the Weiss and the pair approximations on the lattice gas failed to give the correct phase diagrams. Hybrid approximations were devised to describe the lattice term in the free energy. A lattice vibration term corresponding to a free volume correction is included semi-phenomenologically. The combinations of the lattice part and the free volume part yield the three states and the proper phase diagrams. To determine the coexistence regions, the equalities of the pressure and Gibbs free energy per molecule of the coexisting phases were utilized. The ordered branch of the free energy gives rise to the solid phase while the disordered branch yields the gas and liquid phases. It is observed that the triple point and the critical point quantities, the phase diagrams and the coexistence regions plotted are in good agreement with the experimental values and graphs for argon.

  17. Use of variational equations and optimal control theory in the description of the satellites desorbitation

    NASA Astrophysics Data System (ADS)

    Gobinddass, Marie-Line; Omrane, Abdennebi

    Among scientific challenges in space science we find the understanding and the managing of relativity and acceleration's effects on space satellites. Due to the high number of satellite launch every year, the question of recycling addressed by several countries in the world. Some projects focus on the rejection of satellites out of the gravity field of the earth for avoiding a sudden fall in a populated area, but other environmentally friendly projects involve trying to get these satellites for recycling purposes. We will focus on the second recycling point. The good knowledge of these effects can allow the control of all satellites orbit during their lifetime and also after. A mathematical analysis together with the optimal control point of view are here used. We will develop an existence method based on a variational formulation. Then we will use the optimal control theory for the trajectory optimal control under pollution (recycling satellites). Finally, we will focus on the possible generalization of the method with different fixed parameters.

  18. Beyond the Gross-Pitaevskii Equation, Quantum Many-Body Perturbation Theory for Bose-Einstein Condensates

    NASA Astrophysics Data System (ADS)

    McKinney, Brett; Watson, Deborah

    2000-06-01

    We apply low-order dimensional perturbation theory to both the Gross-Pitaevskii equation and to the full many-body Hamiltonian. The perturbation parameter is 1/D, where D is the condensate dimensionality. Unlike the Thomas-Fermi approximation, the zeroth-order DPT solution (Darrow ∞) of the GPE retains a centrifugal term of the kinetic energy. This results in an analytic approximation that is more accurate than TF except for extremely large N where the two approximations agree. The low-order DPT approximation of the full many-body Schrödinger equation for N trapped condensate atoms is an analytic semiclassical approximation that becomes more accurate as the condensate enters a denser regime; precisely the regime where the delta-function potential (pseudopotential) and the GPE should break down. We compare the low-order many-body results for the ground state using the delta-function approximation, which breaks down for high density, with a more realistic interaction potential that reproduces the correct s-wave scattering length.

  19. Divergence of the isospin-asymmetry expansion of the nuclear equation of state in many-body perturbation theory

    NASA Astrophysics Data System (ADS)

    Wellenhofer, Corbinian; Holt, Jeremy W.; Kaiser, Norbert

    2016-05-01

    The isospin-asymmetry dependence of the nuclear-matter equation of state obtained from microscopic chiral two- and three-body interactions in second-order many-body perturbation theory is examined in detail. The quadratic, quartic, and sextic coefficients in the Maclaurin expansion of the free energy per particle of infinite homogeneous nuclear matter with respect to the isospin asymmetry are extracted numerically using finite differences, and the resulting polynomial isospin-asymmetry parametrizations are compared to the full isospin-asymmetry dependence of the free energy. It is found that in the low-temperature and high-density regime where the radius of convergence of the expansion is generically zero, the inclusion of higher-order terms beyond the leading quadratic approximation leads overall to a significantly poorer description of the isospin-asymmetry dependence. In contrast, at high temperatures and densities well below nuclear saturation density, the interaction contributions to the higher-order coefficients are negligible and the deviations from the quadratic approximation are predominantly from the noninteracting term in the many-body perturbation series. Furthermore, we extract the leading logarithmic term in the isospin-asymmetry expansion of the equation of state at zero temperature from the analysis of linear combinations of finite differences. It is shown that the logarithmic term leads to a considerably improved description of the isospin-asymmetry dependence at zero temperature.

  20. Lanczos-based Low-Rank Correction Method for Solving the Dyson Equation in Inhomogenous Dynamical Mean-Field Theory

    NASA Astrophysics Data System (ADS)

    Carrier, Pierre; Tang, Jok M.; Saad, Yousef; Freericks, James K.

    Inhomogeneous dynamical mean-field theory has been employed to solve many interesting strongly interacting problems from transport in multilayered devices to the properties of ultracold atoms in a trap. The main computational step, especially for large systems, is the problem of calculating the inverse of a large sparse matrix to solve Dyson's equation and determine the local Green's function at each lattice site from the corresponding local self-energy. We present a new e_cient algorithm, the Lanczos-based low-rank algorithm, for the calculation of the inverse of a large sparse matrix which yields this local (imaginary time) Green's function. The Lanczos-based low-rank algorithm is based on a domain decomposition viewpoint, but avoids explicit calculation of Schur complements and relies instead on low-rank matrix approximations derived from the Lanczos algorithm, for solving the Dyson equation. We report at least a 25-fold improvement of performance compared to explicit decomposition (such as sparse LU) of the matrix inverse. We also report that scaling relative to matrix sizes, of the low-rank correction method on the one hand and domain decomposition methods on the other, are comparable.

  1. Equation of state of warm dense deuterium and its isotopes from density-functional theory molecular dynamics

    NASA Astrophysics Data System (ADS)

    Danel, J.-F.; Kazandjian, L.; Piron, R.

    2016-04-01

    Of the two approaches of density-functional theory molecular dynamics, quantum molecular dynamics is limited at high temperature by computational cost whereas orbital-free molecular dynamics, based on an approximation of the kinetic electronic free energy, can be implemented in this domain. In the case of deuterium, it is shown how orbital-free molecular dynamics can be regarded as the limit of quantum molecular dynamics at high temperature for the calculation of the equation of state. To this end, accurate quantum molecular dynamics calculations are performed up to 20 eV at mass densities as low as 0.5 g /cm3 and up to 10 eV at mass densities as low as 0.2 g /cm3 . As a result, the limitation in temperature so far attributed to quantum molecular dynamics is overcome and an approach combining quantum and orbital-free molecular dynamics is used to construct an equation of state of deuterium. The thermodynamic domain addressed is that of the fluid phase above 1 eV and 0.2 g /cm3 . Both pressure and internal energy are calculated as functions of temperature and mass density, and various exchange-correlation contributions are compared. The generalized gradient approximation of the exchange-correlation functional, corrected to approximately include the influence of temperature, is retained and the results obtained are compared to other approaches and to experimental shock data; in parts of the thermodynamic domain addressed, these results significantly differ from those obtained in other first-principles investigations which themselves disagree. The equations of state of hydrogen and tritium above 1 eV and above, respectively, 0.1 g /cm3 and 0.3 g /cm3 , can be simply obtained by mass density scaling from the results found for deuterium. This ab initio approach allows one to consistently cover a very large domain of temperature on the domain of mass density outlined above.

  2. Theory of damped quantum rotation in nuclear magnetic resonance spectra. III. Nuclear permutation symmetry of the line shape equation.

    PubMed

    Szymański, S

    2009-12-28

    The damped quantum rotation (DQR) theory describes manifestations in nuclear magnetic resonance spectra of the coherent and stochastic dynamics of N-fold molecular rotors composed of indistinguishable particles. The standard jump model is only a limiting case of the DQR approach; outside this limit, the stochastic motions of such rotors have no kinematic description. In this paper, completing the previous two of this series, consequences of nuclear permutation symmetry for the properties of the DQR line shape equation are considered. The systems addressed are planar rotors, such as aromatic hydrocarbons' rings, occurring inside of molecular crystals oriented in the magnetic field. Under such conditions, oddfold rotors can have nontrivial permutation symmetries only for peculiar orientations while evenfold ones always retain their intrinsic symmetry element, which is rotation by 180 degrees about the N-fold axis; in specific orientations the latter can gain two additional symmetry elements. It is shown that the symmetry selection rules applicable to the classical rate processes in fluids, once recognized as having two diverse aspects, macroscopic and microscopic, are also rigorously valid for the DQR processes in the solid state. However, formal justification of these rules is different because the DQR equation is based on the Pauli principle, which is ignored in the jump model. For objects like the benzene ring, exploitation of these rules in simulations of spectra using the DQR equation can be of critical significance for the feasibility of the calculations. Examples of such calculations for the proton system of the benzene ring in a general orientation are provided. It is also shown that, because of the intrinsic symmetries of the evenfold rotors, many of the DQR processes, which such rotors can undergo, are unobservable in NMR spectra. PMID:20059076

  3. Masking Resonance Artifacts in Force-Splitting Methods for Biomolecular Simulations by Extrapolative Langevin Dynamics

    NASA Astrophysics Data System (ADS)

    Sandu, Adrian; Schlick, Tamar

    1999-05-01

    Numerical resonance artifacts have become recognized recently as a limiting factor to increasing the timestep in multiple-timestep (MTS) biomolecular dynamics simulations. At certain timesteps correlated to internal motions (e.g., 5 fs, around half the period of the fastest bond stretch, Tmin), visible inaccuracies or instabilities can occur. Impulse-MTS schemes are vulnerable to these resonance errors since large energy pulses are introduced to the governing dynamics equations when the slow forces are evaluated. We recently showed that such resonance artifacts can be masked significantly by applying extrapolative splitting to stochastic dynamics. Theoretical and numerical analyses of force-splitting integrators based on the Verlet discretization are reported here for linear models to explain these observations and to suggest how to construct effective integrators for biomolecular dynamics that balance stability with accuracy. Analyses for Newtonian dynamics demonstrate the severe resonance patterns of the Impulse splitting, with this severity worsening with the outer timestep, Δ t; Constant Extrapolation is generally unstable, but the disturbances do not grow with Δ t. Thus, the stochastic extrapolative combination can counteract generic instabilities and largely alleviate resonances with a sufficiently strong Langevin heat-bath coupling (γ), estimates for which are derived here based on the fastest and slowest motion periods. These resonance results generally hold for nonlinear test systems: a water tetramer and solvated protein. Proposed related approaches such as Extrapolation/Correction and Midpoint Extrapolation work better than Constant Extrapolation only for timesteps less than Tmin/2. An effective extrapolative stochastic approach for biomolecules that balances long-timestep stability with good accuracy for the fast subsystem is then applied to a biomolecule using a three-class partitioning: the medium forces are treated by Midpoint Extrapolationvia

  4. Evaluation of minor hysteresis loops using Langevin transforms in modified inverse Jiles-Atherton model

    NASA Astrophysics Data System (ADS)

    Hamimid, M.; Mimoune, S. M.; Feliachi, M.

    2013-11-01

    In this paper, we present a Langevin transforms model which evaluates accurately minor hysteresis loops for the modified inverse Jiles-Atherton model by using appropriate expressions in order to improve minor hysteresis loops characteristics. The parameters of minor hysteresis loops are then related to the parameters of the major hysteresis loop according to each level of maximal induction by using Langevin transforms expressions. The stochastic optimization method “simulated annealing” is used for the determination of the Langevin transforms coefficients. This model needs only two experimental tests to generate all hysteresis loops. The validity of the Langevin transforms model is justified by comparison of calculated minor hysteresis loops to measured ones and good agreements are obtained with better results than the exponential transforms model (Hamimid et al., 2011 [4]).

  5. An extension of the theory of planned behavior to predict pedestrians' violating crossing behavior using structural equation modeling.

    PubMed

    Zhou, Hongmei; Romero, Stephanie Ballon; Qin, Xiao

    2016-10-01

    This paper aimed to examine pedestrians' self-reported violating crossing behavior intentions by applying the theory of planned behavior (TPB). We studied the behavior intentions regarding instrumental attitude, subjective norm, perceived behavioral control, the three basic components of TPB, and extended the theory by adding new factors including descriptive norm, perceived risk and conformity tendency to evaluate their respective impacts on pedestrians' behavior intentions. A questionnaire presented with a scenario that pedestrians crossed the road violating the pedestrian lights at an intersection was designed, and the survey was conducted in Dalian, China. Based on the 260 complete and valid responses, reliability and validity of the data for each question was evaluated. The data were then analyzed by using the structural equation modeling (SEM). The results showed that people had a negative attitude toward the behavior of violating road-crossing rules; they perceived social influences from their family and friends; and they believed that this kind of risky behavior would potentially harm them in a traffic accident. The results also showed that instrumental attitude and subjective norm were significant in the basic TPB model. After adding descriptive norm, subjective norm was no more significant. Other models showed that conformity tendency was a strong predictor, indicating that the presence of other pedestrians would influence behavioral intention. The findings could help to design more effective interventions and safety campaigns, such as changing people's attitude toward this violation behavior, correcting the social norms, increasing their safety awareness, etc. in order to reduce pedestrians' road crossing violations. PMID:26433568

  6. Using Structural Equation Modeling to Understand Prescription Stimulant Misuse: A Test of the Theory of Triadic Influence

    PubMed Central

    Bavarian, Niloofar; Flay, Brian R.; Ketcham, Patricia L.; Smit, Ellen; Kodama, Cathy; Martin, Melissa; Saltz, Robert F.

    2014-01-01

    Objective To test a theory-driven model of health behavior to predict the illicit use of prescription stimulants (IUPS) among college students. Participants A probability sample of 554 students from one university located in California (response rate = 90.52%). Methods Students completed a paper-based survey developed with guidance from the Theory of Triadic Influence. We first assessed normality of measures and checked for multicollinearity. A single structural equation model of frequency of IUPS in college was then tested using constructs from the theory’s three streams of influence (i.e., intrapersonal, social situation/context, and sociocultural environment) and four levels of causation (i.e., ultimate causes, distal influences, proximal predictors, and immediate precursors). Results Approximately 18% of students reported engaging in IUPS during college, with frequency of use ranging from never to 40 or more times per academic term. The model tested had strong fit and the majority of paths specified within and across streams were significant at the p<.01 level. Additionally, 46% of the variance in IUPS frequency was explained by the tested model. Conclusions Results suggest the utility of the TTI as an integrative model of health behavior, specifically in predicting IUPS, and provide insight on the need for multifaceted prevention and intervention efforts. PMID:24647369

  7. Calibrated Langevin-dynamics simulations of intrinsically disordered proteins

    NASA Astrophysics Data System (ADS)

    Smith, W. Wendell; Ho, Po-Yi; O'Hern, Corey S.

    2014-10-01

    We perform extensive coarse-grained (CG) Langevin dynamics simulations of intrinsically disordered proteins (IDPs), which possess fluctuating conformational statistics between that for excluded volume random walks and collapsed globules. Our CG model includes repulsive steric, attractive hydrophobic, and electrostatic interactions between residues and is calibrated to a large collection of single-molecule fluorescence resonance energy transfer data on the interresidue separations for 36 pairs of residues in five IDPs: α-, β-, and γ-synuclein, the microtubule-associated protein τ, and prothymosin α. We find that our CG model is able to recapitulate the average interresidue separations regardless of the choice of the hydrophobicity scale, which shows that our calibrated model can robustly capture the conformational dynamics of IDPs. We then employ our model to study the scaling of the radius of gyration with chemical distance in 11 known IDPs. We identify a strong correlation between the distance to the dividing line between folded proteins and IDPs in the mean charge and hydrophobicity space and the scaling exponent of the radius of gyration with chemical distance along the protein.

  8. Calibrated Langevin-dynamics simulations of intrinsically disordered proteins.

    PubMed

    Smith, W Wendell; Ho, Po-Yi; O'Hern, Corey S

    2014-10-01

    We perform extensive coarse-grained (CG) Langevin dynamics simulations of intrinsically disordered proteins (IDPs), which possess fluctuating conformational statistics between that for excluded volume random walks and collapsed globules. Our CG model includes repulsive steric, attractive hydrophobic, and electrostatic interactions between residues and is calibrated to a large collection of single-molecule fluorescence resonance energy transfer data on the interresidue separations for 36 pairs of residues in five IDPs: α-, β-, and γ-synuclein, the microtubule-associated protein τ, and prothymosin α. We find that our CG model is able to recapitulate the average interresidue separations regardless of the choice of the hydrophobicity scale, which shows that our calibrated model can robustly capture the conformational dynamics of IDPs. We then employ our model to study the scaling of the radius of gyration with chemical distance in 11 known IDPs. We identify a strong correlation between the distance to the dividing line between folded proteins and IDPs in the mean charge and hydrophobicity space and the scaling exponent of the radius of gyration with chemical distance along the protein. PMID:25375525

  9. Schwinger-Keldysh theory for Bose-Einstein condensation of photons in a dye-filled optical microcavity

    NASA Astrophysics Data System (ADS)

    de Leeuw, A.-W.; Stoof, H. T. C.; Duine, R. A.

    2013-09-01

    We consider Bose-Einstein condensation of photons in an optical cavity filled with dye molecules that are excited by laser light. By using the Schwinger-Keldysh formalism we derive a Langevin field equation that describes the dynamics of the photon gas and, in particular, its equilibrium properties and relaxation towards equilibrium. Furthermore we show that the finite lifetime effects of the photons are captured in a single dimensionless damping parameter that depends on the power of the external laser pumping the dye. Finally, as applications of our theory we determine spectral functions and collective modes of the photon gas in both the normal and the Bose-Einstein condensed phases.

  10. Unification of dynamic density functional theory for colloidal fluids to include inertia and hydrodynamic interactions: derivation and numerical experiments.

    PubMed

    Goddard, B D; Nold, A; Savva, N; Yatsyshin, P; Kalliadasis, S

    2013-01-23

    Starting from the Kramers equation for the phase-space dynamics of the N-body probability distribution, we derive a dynamical density functional theory (DDFT) for colloidal fluids including the effects of inertia and hydrodynamic interactions (HI). We compare the resulting theory to extensive Langevin dynamics simulations for both hard rod systems and three-dimensional hard sphere systems with radially symmetric external potentials. As well as demonstrating the accuracy of the new DDFT, by comparing with previous DDFTs which neglect inertia, HI, or both, we also scrutinize the significance of including these effects. Close to local equilibrium we derive a continuum equation from the microscopic dynamics which is a generalized Navier-Stokes-like equation with additional non-local terms governing the effects of HI. For the overdamped limit we recover analogues of existing configuration-space DDFTs but with a novel diffusion tensor. PMID:23220969

  11. Thermal balance and quantum heat transport in nanostructures thermalized by local Langevin heat baths

    NASA Astrophysics Data System (ADS)

    Sääskilahti, K.; Oksanen, J.; Tulkki, J.

    2013-07-01

    Modeling of thermal transport in practical nanostructures requires making tradeoffs between the size of the system and the completeness of the model. We study quantum heat transfer in a self-consistent thermal bath setup consisting of two lead regions connected by a center region. Atoms both in the leads and in the center region are coupled to quantum Langevin heat baths that mimic the damping and dephasing of phonon waves by anharmonic scattering. This approach treats the leads and the center region on the same footing and thereby allows for a simple and physically transparent thermalization of the system, enabling also perfect acoustic matching between the leads and the center region. Increasing the strength of the coupling reduces the mean-free path of phonons and gradually shifts phonon transport from ballistic regime to diffusive regime. In the center region, the bath temperatures are determined self-consistently from the requirement of zero net energy exchange between the local heat bath and each atom. By solving the stochastic equations of motion in frequency space and averaging over noise using the general fluctuation-dissipation relation derived by Dhar and Roy [J. Stat. Phys.JSTPBS0022-471510.1007/s10955-006-9235-3 125, 801 (2006)], we derive the formula for thermal current, which contains the Caroli formula for phonon transmission function and reduces to the Landauer-Büttiker formula in the limit of vanishing coupling to local heat baths. We prove that the bath temperatures measure local kinetic energy and can, therefore, be interpreted as true atomic temperatures. In a setup where phonon reflections are eliminated, the Boltzmann transport equation under gray approximation with full phonon dispersion is shown to be equivalent to the self-consistent heat bath model. We also study thermal transport through two-dimensional constrictions in square lattice and graphene and discuss the differences between the exact solution and linear approximations.

  12. Finite-Temperature Non-equilibrium Quasicontinuum Method based on Langevin Dynamics

    SciTech Connect

    Marian, J; Venturini, G; Hansen, B; Knap, J; Ortiz, M; Campbell, G

    2009-05-08

    The concurrent bridging of molecular dynamics and continuum thermodynamics presents a number of challenges, mostly associated with energy transmission and changes in the constitutive description of a material across domain boundaries. In this paper, we propose a framework for simulating coarse dynamic systems in the canonical ensemble using the Quasicontinuum method (QC). The equations of motion are expressed in reduced QC coordinates and are strictly derived from dissipative Lagrangian mechanics. The derivation naturally leads to a classical Langevin implementation where the timescale is governed by vibrations emanating from the finest length scale occurring in the computational cell. The equations of motion are integrated explicitly via Newmark's ({beta} = 0; {gamma} = 1/2) method, leading to a robust numerical behavior and energy conservation. In its current form, the method only allows for wave propagations supported by the less compliant of the two meshes across a heterogeneous boundary, which requires the use of overdamped dynamics to avoid spurious heating due to reflected vibrations. We have applied the method to two independent crystallographic systems characterized by different interatomic potentials (Al and Ta) and have measured thermal expansion in order to quantify the vibrational entropy loss due to homogenization. We rationalize the results in terms of system size, mesh coarseness, and nodal cluster diameter within the framework of the quasiharmonic approximation. For Al, we find that the entropy loss introduced by mesh coarsening varies linearly with the element size, and that volumetric effects are not critical in driving the anharmonic behavior of the simulated systems. In Ta, the anomalies of the interatomic potential employed result in negative and zero thermal expansion at low and high temperatures, respectively.

  13. Theory of dynamic arrest in colloidal mixtures

    NASA Astrophysics Data System (ADS)

    Juárez-Maldonado, R.; Medina-Noyola, M.

    2008-05-01

    We present a first-principles theory of dynamic arrest in colloidal mixtures based on the multicomponent self-consistent generalized Langevin equation theory of colloid dynamics [M. A. Chávez-Rojo and M. Medina-Noyola, Phys. Rev. E 72, 031107 (2005); M. A. Chávez-Rojo and M. Medina-Noyola, Phys. Rev. E76, 039902 (2007)]. We illustrate its application with a description of dynamic arrest in two simple model colloidal mixtures: namely, hard-sphere and repulsive Yukawa binary mixtures. Our results include observation of the two patterns of dynamic arrest, one in which both species become simultaneously arrested and the other involving the sequential arrest of the two species. The latter case gives rise to mixed states in which one species is arrested while the other species remains mobile. We also derive the (”bifurcation” or fixed-point”) equations for the nonergodic parameters of the system, which takes the surprisingly simple form of a system of coupled equations for the localization length of the particles of each species. The solution of this system of equations indicates unambiguously which species is arrested (finite localization length) and which species remains ergodic (infinite localization length). As a result, we are able to draw the entire ergodic-nonergodic phase diagram of the binary hard-sphere mixture.

  14. Evolution equation for the B-meson distribution amplitude in the heavy-quark effective theory in coordinate space

    SciTech Connect

    Kawamura, Hiroyuki; Tanaka, Kazuhiro

    2010-06-01

    The B-meson distribution amplitude (DA) is defined as the matrix element of a quark-antiquark bilocal light-cone operator in the heavy-quark effective theory, corresponding to a long-distance component in the factorization formula for exclusive B-meson decays. The evolution equation for the B-meson DA is governed by the cusp anomalous dimension as well as the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi-type anomalous dimension, and these anomalous dimensions give the ''quasilocal'' kernel in the coordinate-space representation. We show that this evolution equation can be solved analytically in the coordinate space, accomplishing the relevant Sudakov resummation at the next-to-leading logarithmic accuracy. The quasilocal nature leads to a quite simple form of our solution which determines the B-meson DA with a quark-antiquark light-cone separation t in terms of the DA at a lower renormalization scale {mu} with smaller interquark separations zt (z{<=}1). This formula allows us to present rigorous calculation of the B-meson DA at the factorization scale {approx}{radical}(m{sub b{Lambda}QCD}) for t less than {approx}1 GeV{sup -1}, using the recently obtained operator product expansion of the DA as the input at {mu}{approx}1 GeV. We also derive the master formula, which reexpresses the integrals of the DA at {mu}{approx}{radical}(m{sub b{Lambda}QCD}) for the factorization formula by the compact integrals of the DA at {mu}{approx}1 GeV.

  15. Evolution equation for the B-meson distribution amplitude in the heavy-quark effective theory in coordinate space

    NASA Astrophysics Data System (ADS)

    Kawamura, Hiroyuki; Tanaka, Kazuhiro

    2010-06-01

    The B-meson distribution amplitude (DA) is defined as the matrix element of a quark-antiquark bilocal light-cone operator in the heavy-quark effective theory, corresponding to a long-distance component in the factorization formula for exclusive B-meson decays. The evolution equation for the B-meson DA is governed by the cusp anomalous dimension as well as the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi-type anomalous dimension, and these anomalous dimensions give the “quasilocal” kernel in the coordinate-space representation. We show that this evolution equation can be solved analytically in the coordinate space, accomplishing the relevant Sudakov resummation at the next-to-leading logarithmic accuracy. The quasilocal nature leads to a quite simple form of our solution which determines the B-meson DA with a quark-antiquark light-cone separation t in terms of the DA at a lower renormalization scale μ with smaller interquark separations zt (z≤1). This formula allows us to present rigorous calculation of the B-meson DA at the factorization scale ˜mbΛQCD for t less than ˜1GeV-1, using the recently obtained operator product expansion of the DA as the input at μ˜1GeV. We also derive the master formula, which reexpresses the integrals of the DA at μ˜mbΛQCD for the factorization formula by the compact integrals of the DA at μ˜1GeV.

  16. Equation of state of warm dense deuterium and its isotopes from density-functional theory molecular dynamics.

    PubMed

    Danel, J-F; Kazandjian, L; Piron, R

    2016-04-01

    Of the two approaches of density-functional theory molecular dynamics, quantum molecular dynamics is limited at high temperature by computational cost whereas orbital-free molecular dynamics, based on an approximation of the kinetic electronic free energy, can be implemented in this domain. In the case of deuterium, it is shown how orbital-free molecular dynamics can be regarded as the limit of quantum molecular dynamics at high temperature for the calculation of the equation of state. To this end, accurate quantum molecular dynamics calculations are performed up to 20 eV at mass densities as low as 0.5g/cm^{3} and up to 10 eV at mass densities as low as 0.2g/cm^{3}. As a result, the limitation in temperature so far attributed to quantum molecular dynamics is overcome and an approach combining quantum and orbital-free molecular dynamics is used to construct an equation of state of deuterium. The thermodynamic domain addressed is that of the fluid phase above 1 eV and 0.2g/cm^{3}. Both pressure and internal energy are calculated as functions of temperature and mass density, and various exchange-correlation contributions are compared. The generalized gradient approximation of the exchange-correlation functional, corrected to approximately include the influence of temperature, is retained and the results obtained are compared to other approaches and to experimental shock data; in parts of the thermodynamic domain addressed, these results significantly differ from those obtained in other first-principles investigations which themselves disagree. The equations of state of hydrogen and tritium above 1 eV and above, respectively, 0.1g/cm^{3} and 0.3g/cm^{3}, can be simply obtained by mass density scaling from the results found for deuterium. This ab initio approach allows one to consistently cover a very large domain of temperature on the domain of mass density outlined above. PMID:27176421

  17. Testing the social cognitive career theory in Thai nurses' interest to become nurse educators: A structural equation modeling analysis.

    PubMed

    Thungjaroenkul, Petsunee; G Cummings, Greta; Tate, Kaitlyn

    2016-09-01

    A shortage of nurse educators generates a systemic problem in nursing education. A model to develop interventions directed at enhancing graduate nursing student interest in assuming a future faculty role is needed. This study used a social cognitive career theory perspective to examine the effects of past performance in teaching and supervision, social influence, observing others teaching, perceived task demands for nurse educators, self-efficacy, and outcome expectations on Thai graduate nursing students' (n=236) interest to become a nurse educator. Results of structural equation modeling analyses revealed that social influence and past performance in teaching and supervision had significant effects on interest to become a nurse educator when mediated by self-efficacy and outcome expectations. Observing others teaching and perceived task demands for nurse educators did not significantly predict interest in faculty roles. These findings provide new knowledge about factors and their influence on the development of interest to assume faculty roles. Implications for nursing education include the design of feasible graduate curricula that enhance students' abilities in faculty role and increases valuation of teaching careers. PMID:27429345

  18. Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media: II. The nonlinear theory

    NASA Astrophysics Data System (ADS)

    Bona, J. L.; Chen, M.; Saut, J.-C.

    2004-05-01

    In part I of this work (Bona J L, Chen M and Saut J-C 2002 Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media I: Derivation and the linear theory J. Nonlinear Sci. 12 283-318), a four-parameter family of Boussinesq systems was derived to describe the propagation of surface water waves. Similar systems are expected to arise in other physical settings where the dominant aspects of propagation are a balance between the nonlinear effects of convection and the linear effects of frequency dispersion. In addition to deriving these systems, we determined in part I exactly which of them are linearly well posed in various natural function classes. It was argued that linear well-posedness is a natural necessary requirement for the possible physical relevance of the model in question. In this paper, it is shown that the first-order correct models that are linearly well posed are in fact locally nonlinearly well posed. Moreover, in certain specific cases, global well-posedness is established for physically relevant initial data. In part I, higher-order correct models were also derived. A preliminary analysis of a promising subclass of these models shows them to be well posed.

  19. Fast and General Method To Predict the Physicochemical Properties of Druglike Molecules Using the Integral Equation Theory of Molecular Liquids.

    PubMed

    Palmer, David S; Mišin, Maksim; Fedorov, Maxim V; Llinas, Antonio

    2015-09-01

    We report a method to predict physicochemical properties of druglike molecules using a classical statistical mechanics based solvent model combined with machine learning. The RISM-MOL-INF method introduced here provides an accurate technique to characterize solvation and desolvation processes based on solute-solvent correlation functions computed by the 1D reference interaction site model of the integral equation theory of molecular liquids. These functions can be obtained in a matter of minutes for most small organic and druglike molecules using existing software (RISM-MOL) (Sergiievskyi, V. P.; Hackbusch, W.; Fedorov, M. V. J. Comput. Chem. 2011, 32, 1982-1992). Predictions of caco-2 cell permeability and hydration free energy obtained using the RISM-MOL-INF method are shown to be more accurate than the state-of-the-art tools for benchmark data sets. Due to the importance of solvation and desolvation effects in biological systems, it is anticipated that the RISM-MOL-INF approach will find many applications in biophysical and biomedical property prediction. PMID:26212723

  20. Laser flash photolysis and integral equation theory to investigate reactions of dilute solutes with oxygen in supercritical fluids

    SciTech Connect

    Roberts, C.B.; Zhang, J.; Chateauneuf, J.E.; Brennecke, J.F.

    1995-06-21

    The absolute reactivity of triplet benzophenone ({sup 3}BP) and benzyl free radical (PhCH{sub 2}) toward molecular oxygen (O{sub 2}) in supercritical CO{sub 2} and CHF{sub 3} has been measured by laser flash photolysis (LFP). The transient reactants may be considered to be infinitely dilute solutes reacting with a gaseous cosolvent in a supercritical fluid mixture. Both reactants were found to undergo kinetically controlled reactivity with O{sub 2} and the measured bimolecular rate constants (k{sub hi}) were found to decrease with a decrease in solvent density at reduced pressures between 1.0 and 2.5. These results are consistent with solute reactivity with a `nonattractive` cosolvent. The results are compared with those previously obtained for the reaction of {sup 3}BP with an `attractive` cosolvent, 1,4-cyclohexadiene, in supercritical CO{sub 2} and CHF{sub 3}, in which enhanced {sup 3}BP reactivity was observed due to preferential cosolvent/solute solvation. Integral equation theory has also been applied to model these ternary systems, and the results indicate how the strengths of local solvation forces can influence kinetically controlled reactions in supercritical fluids. 36 refs., 8 figs., 3 tabs.

  1. Loop equation in D=4, N=4 super Yang-Mills theory and string field equation on AdS{sub 5}xS{sup 5}

    SciTech Connect

    Hata, Hiroyuki; Miwa, Akitsugu

    2006-02-15

    We consider the loop equation in four-dimensional N=4 SYM, which is a functional differential equation for the Wilson loop W(C) and expresses the propagation and the interaction of the string C. Our W(C) consists of the scalar and the gaugino fields as well as the gauge field. The loop C is specified by six bosonic coordinates y{sup i}(s) and two fermionic coordinates {zeta}(s) and {eta}(s) besides the four-dimensional spacetime coordinates x{sup {mu}}(s). We have successfully determined, to quadratic order in {zeta} and {eta}, the parameters in W(C) and the loop differential operator so that the equation of motion of SYM can be correctly reproduced to give the nonlinear term of W(C). We extract the most singular and linear part of our loop equation and compare it with the Hamiltonian constraint of the string propagating on AdS{sub 5}xS{sup 5} background.

  2. Obtaining Some Degree of Correspondence Between Unequatable Scores: A Comparison of Item Response Theory and Equipercentile Equating Methods.

    ERIC Educational Resources Information Center

    Yen, Wendy M.

    Test scores that are not perfectly reliable cannot be strictly equated unless they are strictly parallel. This fact implies that tau equivalence can be lost if an equipercentile equating is applied to observed scores that are not strictly parallel. Thirty-six simulated data sets are produced to simulate equating tests with different difficulties…

  3. Applications of deuterium-tritium equation of state based on density functional theory in inertial confinement fusion

    SciTech Connect

    Wang, Cong; He, Xian-Tu; Ye, Wen-Hua; Zhang, Ping; Fan, Zheng-Feng

    2015-06-15

    An accurate equation of state for deuterium-tritium mixture is of crucial importance in inertial confinement fusion. The equation of state can determine the compressibility of the imploding target and the energy deposited into the fusion fuel. In the present work, a new deuterium-tritium equation of state, which is calculated according to quantum molecular dynamic and orbital free molecular dynamic simulations, has been used to study the target implosion hydrodynamics. The results indicate that the peak density predicted by the new equation of state is ∼10% higher than the quotidian equation of state data. During the implosion, the areal density and neutron yield are also discussed.

  4. Uniformly Asymptotic Frequency Domain Green's Functions for the Acoustic Equation - Theory and Applications in Two and Three Dimensions

    NASA Astrophysics Data System (ADS)

    Yedlin, Matthew; Virieux, Jean

    2010-05-01

    As data collection in both seismic data acquisition and radar continues to improve, more emphasis is being placed on data pre-processing and inversion, in particular frequency domain waveform inversion in seismology [1], and, for example, time-domain waveform inversion in crosshole radar measurements [2]. Complementary to these methods are the sensitivity kernel techniques established initially in seismology [3, 4]. However, these methods have also been employed in crosshole radar tomography [5]. The sensitivity kernel technique has most recently been applied to the analysis of diffraction of waves in shallow water [6]. Central to the sensitivity kernel techniques is the use of an appropriate Green's function in either two or three dimensions and a background model is assumed for the calculation of the Green's function. In some situations, the constant velocity Green's function is used [5] but in other situations a smooth background model is used in a ray-type approximation. In the case of the smooth background model, computation of a ray-tracing type Green's function is problematic since at the source point the rays convergence, creating a singularity in the computation of the Jacobian used in the amplitude calculation. In fact the source is an axial caustic in two dimensions and a point caustic in three dimensions [7]. To obviate this problem, we will create a uniform asymptotic ansatz [8], explaining in detail how it is obtained in two dimensions. We will then show how to extend the results to three dimensions. In both cases, the Green's function will be obtained in the frequency domain for the acoustic equation with smoothly varying density and bulk modulus. The application of the new Green's function technique will provide more flexibility in the computation of sensitivities, both in seismological and radar applications. References [1] R. G. Pratt. 1999, Seismic waveform inversion in the frequency domain, part 1: Theory and verification in a physical scale

  5. Spin-orbit couplings within the equation-of-motion coupled-cluster framework: Theory, implementation, and benchmark calculations

    NASA Astrophysics Data System (ADS)

    Epifanovsky, Evgeny; Klein, Kerstin; Stopkowicz, Stella; Gauss, Jürgen; Krylov, Anna I.

    2015-08-01

    We present a formalism and an implementation for calculating spin-orbit couplings (SOCs) within the EOM-CCSD (equation-of-motion coupled-cluster with single and double substitutions) approach. The following variants of EOM-CCSD are considered: EOM-CCSD for excitation energies (EOM-EE-CCSD), EOM-CCSD with spin-flip (EOM-SF-CCSD), EOM-CCSD for ionization potentials (EOM-IP-CCSD) and electron attachment (EOM-EA-CCSD). We employ a perturbative approach in which the SOCs are computed as matrix elements of the respective part of the Breit-Pauli Hamiltonian using zeroth-order non-relativistic wave functions. We follow the expectation-value approach rather than the response-theory formulation for property calculations. Both the full two-electron treatment and the mean-field approximation (a partial account of the two-electron contributions) have been implemented and benchmarked using several small molecules containing elements up to the fourth row of the periodic table. The benchmark results show the excellent performance of the perturbative treatment and the mean-field approximation. When used with an appropriate basis set, the errors with respect to experiment are below 5% for the considered examples. The findings regarding basis-set requirements are in agreement with previous studies. The impact of different correlation treatment in zeroth-order wave functions is analyzed. Overall, the EOM-IP-CCSD, EOM-EA-CCSD, EOM-EE-CCSD, and EOM-SF-CCSD wave functions yield SOCs that agree well with each other (and with the experimental values when available). Using an EOM-CCSD approach that provides a more balanced description of the target states yields more accurate results.

  6. NEW HYPERON EQUATIONS OF STATE FOR SUPERNOVAE AND NEUTRON STARS IN DENSITY-DEPENDENT HADRON FIELD THEORY

    SciTech Connect

    Banik, Sarmistha; Hempel, Matthias; Bandyopadhyay, Debades

    2014-10-01

    We develop new hyperon equation of state (EoS) tables for core-collapse supernova simulations and neutron stars. These EoS tables are based on a density-dependent relativistic hadron field theory where baryon-baryon interaction is mediated by mesons, using the parameter set DD2 for nucleons. Furthermore, light and heavy nuclei along with interacting nucleons are treated in the nuclear statistical equilibrium model of Hempel and Schaffner-Bielich which includes excluded volume effects. Of all possible hyperons, we consider only the contribution of Λs. We have developed two variants of hyperonic EoS tables: in the npΛφ case the repulsive hyperon-hyperon interaction mediated by the strange φ meson is taken into account, and in the npΛ case it is not. The EoS tables for the two cases encompass a wide range of densities (10{sup –12} to ∼1 fm{sup –3}), temperatures (0.1 to 158.48 MeV), and proton fractions (0.01 to 0.60). The effects of Λ hyperons on thermodynamic quantities such as free energy per baryon, pressure, or entropy per baryon are investigated and found to be significant at higher densities. The cold, β-equilibrated EoS (with the crust included self-consistently) results in a 2.1 M {sub ☉} maximum mass neutron star for the npΛφ case, whereas that for the npΛ case is 1.95 M {sub ☉}. The npΛφ EoS represents the first supernova EoS table involving hyperons that is directly compatible with the recently measured 2 M {sub ☉} neutron stars.

  7. Spin-orbit couplings within the equation-of-motion coupled-cluster framework: Theory, implementation, and benchmark calculations.

    PubMed

    Epifanovsky, Evgeny; Klein, Kerstin; Stopkowicz, Stella; Gauss, Jürgen; Krylov, Anna I

    2015-08-14

    We present a formalism and an implementation for calculating spin-orbit couplings (SOCs) within the EOM-CCSD (equation-of-motion coupled-cluster with single and double substitutions) approach. The following variants of EOM-CCSD are considered: EOM-CCSD for excitation energies (EOM-EE-CCSD), EOM-CCSD with spin-flip (EOM-SF-CCSD), EOM-CCSD for ionization potentials (EOM-IP-CCSD) and electron attachment (EOM-EA-CCSD). We employ a perturbative approach in which the SOCs are computed as matrix elements of the respective part of the Breit-Pauli Hamiltonian using zeroth-order non-relativistic wave functions. We follow the expectation-value approach rather than the response-theory formulation for property calculations. Both the full two-electron treatment and the mean-field approximation (a partial account of the two-electron contributions) have been implemented and benchmarked using several small molecules containing elements up to the fourth row of the periodic table. The benchmark results show the excellent performance of the perturbative treatment and the mean-field approximation. When used with an appropriate basis set, the errors with respect to experiment are below 5% for the considered examples. The findings regarding basis-set requirements are in agreement with previous studies. The impact of different correlation treatment in zeroth-order wave functions is analyzed. Overall, the EOM-IP-CCSD, EOM-EA-CCSD, EOM-EE-CCSD, and EOM-SF-CCSD wave functions yield SOCs that agree well with each other (and with the experimental values when available). Using an EOM-CCSD approach that provides a more balanced description of the target states yields more accurate results. PMID:26277122

  8. Spin-orbit couplings within the equation-of-motion coupled-cluster framework: Theory, implementation, and benchmark calculations

    SciTech Connect

    Epifanovsky, Evgeny; Klein, Kerstin; Gauss, Jürgen; Stopkowicz, Stella; Krylov, Anna I.

    2015-08-14

    We present a formalism and an implementation for calculating spin-orbit couplings (SOCs) within the EOM-CCSD (equation-of-motion coupled-cluster with single and double substitutions) approach. The following variants of EOM-CCSD are considered: EOM-CCSD for excitation energies (EOM-EE-CCSD), EOM-CCSD with spin-flip (EOM-SF-CCSD), EOM-CCSD for ionization potentials (EOM-IP-CCSD) and electron attachment (EOM-EA-CCSD). We employ a perturbative approach in which the SOCs are computed as matrix elements of the respective part of the Breit-Pauli Hamiltonian using zeroth-order non-relativistic wave functions. We follow the expectation-value approach rather than the response-theory formulation for property calculations. Both the full two-electron treatment and the mean-field approximation (a partial account of the two-electron contributions) have been implemented and benchmarked using several small molecules containing elements up to the fourth row of the periodic table. The benchmark results show the excellent performance of the perturbative treatment and the mean-field approximation. When used with an appropriate basis set, the errors with respect to experiment are below 5% for the considered examples. The findings regarding basis-set requirements are in agreement with previous studies. The impact of different correlation treatment in zeroth-order wave functions is analyzed. Overall, the EOM-IP-CCSD, EOM-EA-CCSD, EOM-EE-CCSD, and EOM-SF-CCSD wave functions yield SOCs that agree well with each other (and with the experimental values when available). Using an EOM-CCSD approach that provides a more balanced description of the target states yields more accurate results.

  9. The Langevin Hull: Constant pressure and temperature dynamics for non-periodic systems

    PubMed Central

    Vardeman, Charles F.; Stocker, Kelsey M.; Gezelter, J. Daniel

    2011-01-01

    We have developed a new isobaric-isothermal (NPT) algorithm which applies an external pressure to the facets comprising the convex hull surrounding the system. A Langevin thermostat is also applied to the facets to mimic contact with an external heat bath. This new method, the “Langevin Hull”, can handle heterogeneous mixtures of materials with different compressibilities. These systems are problematic for traditional affine transform methods. The Langevin Hull does not suffer from the edge effects of boundary potential methods, and allows realistic treatment of both external pressure and thermal conductivity due to the presence of an implicit solvent. We apply this method to several different systems including bare metal nanoparticles, nanoparticles in an explicit solvent, as well as clusters of liquid water. The predicted mechanical properties of these systems are in good agreement with experimental data and previous simulation work. PMID:21547015

  10. Chain entanglements. I. Theory

    NASA Astrophysics Data System (ADS)

    Fixman, Marshall

    1988-09-01

    A model of concentrated polymer solution dynamics is described. The forces in a linear generalized Langevin equation for the motion of a probe chain are derived on the assumption that all relaxation of the forces is due to motion of the surrounding matrix. Vicinal chain displacements are classified as viscoelastic deformation, reptation, and minor residual fluctuations. The latter provide a torsional relaxation of the primitive path that minimizes the significance of transverse forces on the probe chain. All displacements of vicinal segments are assumed proportional to the forces that they exert on the probe chain. In response to an external force, the displacement of the probe chain relative to a laboratory frame is increased by viscoelastic deformation of the matrix, but reptative diffusion relative to the deforming matrix is slowed down. The net effect on translational diffusion is negligible if the probe and vicinal chains have the same chain length N, but the friction constant for reptative motion is increased by a factor N1-xs. xs=1/2 if Gaussian conformational statistics applies during the disengagement process, while xs =0.6 if excluded volume statistics applies. The translational friction constant is βp ˜N2, as in reptation theory, but the viscosity is η˜N4-xs . The persistence of entanglements during the translational diffusion of the probe chain across many radii of gyration is rationalized pictorially in terms of correlated reptative motion of the probe and vicinal chains.

  11. The screen effect of the earth in the TETG - Theory of a screening experiment of a sample body at the equator, using the earth as a screen

    NASA Astrophysics Data System (ADS)

    Adamuti, I. A.

    1982-04-01

    The acceleration of gravity, g, is calculated at the same point on the earth's surface for the cases of the equator at midday and at midnight. The calculations are for an ellipsoid of revolution of the earth around an axis projected from the plane of the equator. Values of g are calculated in terms of the Newton and electrothermodynamical theories, for the earth, sun, and the centrifugal rotation and revolution of the earth. The results are presented in tabular form for the midday and midnight cases, and calculations are conducted to verify the total differences between the two points, for the two theoretical frameworks, by means of a pendulum and a ballistic gravimeter.

  12. Numerical Solution of 3D Poisson-Nernst-Planck Equations Coupled with Classical Density Functional Theory for Modeling Ion and Electron Transport in a Confined Environment

    SciTech Connect

    Meng, Da; Zheng, Bin; Lin, Guang; Sushko, Maria L.

    2014-08-29

    We have developed efficient numerical algorithms for the solution of 3D steady-state Poisson-Nernst-Planck equations (PNP) with excess chemical potentials described by the classical density functional theory (cDFT). The coupled PNP equations are discretized by finite difference scheme and solved iteratively by Gummel method with relaxation. The Nernst-Planck equations are transformed into Laplace equations through the Slotboom transformation. Algebraic multigrid method is then applied to efficiently solve the Poisson equation and the transformed Nernst-Planck equations. A novel strategy for calculating excess chemical potentials through fast Fourier transforms is proposed which reduces computational complexity from O(N2) to O(NlogN) where N is the number of grid points. Integrals involving Dirac delta function are evaluated directly by coordinate transformation which yields more accurate result compared to applying numerical quadrature to an approximated delta function. Numerical results for ion and electron transport in solid electrolyte for Li ion batteries are shown to be in good agreement with the experimental data and the results from previous studies.

  13. Boltzmann equation modelling of Learning Dynamics. Comment on "Collective learning modeling based on the kinetic theory of active particles" by D. Burini et al.

    NASA Astrophysics Data System (ADS)

    Shizgal, Bernie

    2016-03-01

    The paper by Burini et al. [7] presents an interesting use of the Boltzmann equation of kinetic theory to model real learning processes. The authors provide a comprehensive discussion of the basic concepts involved in their modelling work. The Boltzmann equation as used by physicists and chemists to model a variety of transport processes in many diverse fields is based on the notion of the binary collisions between identifiable particles in the defined system [9]. The particles exchange energy on collision and the distribution function, which depends on the three velocity components and the three spatial coordinates, varies with time. The classical or quantum collision dynamics between particles play a central role in the definition of the kernels in the integral operators that define the Boltzmann equation [8].

  14. Wavy film flows down an inclined plane: Perturbation theory and general evolution equation for the film thickness

    SciTech Connect

    Frenkel, A.L.; Indireshkumar, K.

    1999-10-01

    Wavy film flow of incompressible Newtonian fluid down an inclined plane is considered. The question is posed as to the parametric conditions under which the description of evolution can be approximately reduced for all time to a single evolution equation for the film thickness. An unconventional perturbation approach yields the most general evolution equation and least restrictive conditions on its validity. The advantages of this equation for analytical and numerical studies of three-dimensional waves in inclined films are pointed out. {copyright} {ital 1999} {ital The American Physical Society}

  15. Spectral Decomposition of a Fokker-Planck Equation at Criticality

    NASA Astrophysics Data System (ADS)

    Bologna, M.; Beig, M. T.; Svenkeson, A.; Grigolini, P.; West, B. J.

    2015-07-01

    The mean field for a complex network consisting of a large but finite number of random two-state elements, , has been shown to satisfy a nonlinear Langevin equation. The noise intensity is inversely proportional to . In the limiting case , the solution to the Langevin equation exhibits a transition from exponential to inverse power law relaxation as criticality is approached from above or below the critical point. When , the inverse power law is truncated by an exponential decay with rate , the evaluation of which is the main purpose of this article. An analytic/numeric approach is used to obtain the lowest-order eigenvalues in the spectral decomposition of the solution to the corresponding Fokker-Planck equation and its equivalent Schrödinger equation representation.

  16. Evolutionary game theory for physical and biological scientists. II. Population dynamics equations can be associated with interpretations.

    PubMed

    Liao, David; Tlsty, Thea D

    2014-08-01

    The use of mathematical equations to analyse population dynamics measurements is being increasingly applied to elucidate complex dynamic processes in biological systems, including cancer. Purely 'empirical' equations may provide sufficient accuracy to support predictions and therapy design. Nevertheless, interpretation of fitting equations in terms of physical and biological propositions can provide additional insights that can be used both to refine models that prove inconsistent with data and to understand the scope of applicability of models that validate. The purpose of this tutorial is to assist readers in mathematically associating interpretations with equations and to provide guidance in choosing interpretations and experimental systems to investigate based on currently available biological knowledge, techniques in mathematical and computational analysis and methods for in vitro and in vivo experiments. PMID:25097752

  17. Aerodynamic airfoil design using the Euler equations based on the dynamic evolution method and the control theory

    NASA Astrophysics Data System (ADS)

    Gao, YingYing; He, Feng; Shen, MengYu

    2011-04-01

    Based on the idea of adjoint method and the dynamic evolution method, a new optimum aerodynamic design technique is presented in this paper. It can be applied to the optimum problems with a large number of design variables and is time saving. The key of the new method lies in that the optimization process is regarded as an unsteady evolution, i.e., the optimization is executed, simultaneously with solving the unsteady flow governing equations and adjoint equations. Numerical examples for both the inverse problem and drag minimization using Euler equations have been presented, and the results show that the method presented in this paper is more efficient than the optimum methods based on the steady flow solution and the steady solution of adjoint equations.

  18. Evolutionary game theory for physical and biological scientists. II. Population dynamics equations can be associated with interpretations

    PubMed Central

    Liao, David; Tlsty, Thea D.

    2014-01-01

    The use of mathematical equations to analyse population dynamics measurements is being increasingly applied to elucidate complex dynamic processes in biological systems, including cancer. Purely ‘empirical’ equations may provide sufficient accuracy to support predictions and therapy design. Nevertheless, interpretation of fitting equations in terms of physical and biological propositions can provide additional insights that can be used both to refine models that prove inconsistent with data and to understand the scope of applicability of models that validate. The purpose of this tutorial is to assist readers in mathematically associating interpretations with equations and to provide guidance in choosing interpretations and experimental systems to investigate based on currently available biological knowledge, techniques in mathematical and computational analysis and methods for in vitro and in vivo experiments. PMID:25097752

  19. Equation of Motion Theory for Excited States in Variational Monte Carlo and the Jastrow Antisymmetric Geminal Power in Hilbert Space.

    PubMed

    Zhao, Luning; Neuscamman, Eric

    2016-08-01

    An equation of motion formalism for excited states in variational Monte Carlo is derived, and a pilot implementation for the Jastrow-modified antisymmetric geminal power is tested. In single excitations across a range of small molecules, this combination is shown to be intermediate in accuracy between configuration interaction singles and equation of motion coupled cluster with singles and doubles. For double excitations, energy errors are found to be similar to those for coupled cluster. PMID:27398808

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

    NASA Astrophysics Data System (ADS)

    Bommier, Véronique

    2016-06-01

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

  1. Analysis of the methods for the derivation of binary kinetic equations in the theory of fluorescence concentration quenching

    SciTech Connect

    Doktorov, A. B.

    2014-09-14

    In the framework of unified many-particle approach the familiar problem of fluorescence concentration quenching in the presence of pumping (light pulse) of arbitrary intensity is considered. This process is a vivid and the simplest example of multistage bulk reaction including bimolecular irreversible quenching reaction and reversible monomolecular transformation as elementary stages. General relation between the kinetics of multistage bulk reaction and that of the elementary stage of quenching has been established. This allows one to derive general kinetic equations (of two types) for the multistage reaction in question on the basis of general kinetic equations (differential and integro-differential) of elementary stage of quenching. Relying on the same unified many-particle approach we have developed binary approximations with the use of two (frequently employed in the literature) many-particle methods (such as simple superposition approximation and the method of extracting pair channels in three-particle correlation evolution) to the derivation of non-Markovian binary kinetic equations. The possibility of reducing the obtained binary equations to the Markovian equations of formal chemical kinetics has been considered. As an example the exact solution of the problem (for the specific case) is examined, and the applicability of two many particle methods of derivation of binary equations is analyzed.

  2. Theory of relativistic Brownian motion: the (1+3) -dimensional case.

    PubMed

    Dunkel, Jörn; Hänggi, Peter

    2005-09-01

    A theory for (1+3) -dimensional relativistic Brownian motion under the influence of external force fields is put forward. Starting out from a set of relativistically covariant, but multiplicative Langevin equations we describe the relativistic stochastic dynamics of a forced Brownian particle. The corresponding Fokker-Planck equations are studied in the laboratory frame coordinates. In particular, the stochastic integration prescription--i.e., the discretization rule dilemma--is elucidated (prepoint discretization rule versus midpoint discretization rule versus postpoint discretization rule). Remarkably, within our relativistic scheme we find that the postpoint rule (or the transport form) yields the only Fokker-Planck dynamics from which the relativistic Maxwell-Boltzmann statistics is recovered as the stationary solution. The relativistic velocity effects become distinctly more pronounced by going from one to three spatial dimensions. Moreover, we present numerical results for the asymptotic mean-square displacement of a free relativistic Brownian particle moving in 1+3 dimensions. PMID:16241514

  3. Theory for non-equilibrium statistical mechanics.

    PubMed

    Attard, Phil

    2006-08-21

    This paper reviews a new theory for non-equilibrium statistical mechanics. This gives the non-equilibrium analogue of the Boltzmann probability distribution, and the generalization of entropy to dynamic states. It is shown that this so-called second entropy is maximized in the steady state, in contrast to the rate of production of the conventional entropy, which is not an extremum. The relationships of the new theory to Onsager's regression hypothesis, Prigogine's minimal entropy production theorem, the Langevin equation, the formula of Green and Kubo, the Kawasaki distribution, and the non-equilibrium fluctuation and work theorems, are discussed. The theory is worked through in full detail for the case of steady heat flow down an imposed temperature gradient. A Monte Carlo algorithm based upon the steady state probability density is summarized, and results for the thermal conductivity of a Lennard-Jones fluid are shown to be in agreement with known values. Also discussed is the generalization to non-equilibrium mechanical work, and to non-equilibrium quantum statistical mechanics. As examples of the new theory two general applications are briefly explored: a non-equilibrium version of the second law of thermodynamics, and the origin and evolution of life. PMID:16883388

  4. The Theory of Planned Behavior (TPB) and Pre-Service Teachers' Technology Acceptance: A Validation Study Using Structural Equation Modeling

    ERIC Educational Resources Information Center

    Teo, Timothy; Tan, Lynde

    2012-01-01

    This study applies the theory of planned behavior (TPB), a theory that is commonly used in commercial settings, to the educational context to explain pre-service teachers' technology acceptance. It is also interested in examining its validity when used for this purpose. It has found evidence that the TPB is a valid model to explain pre-service…

  5. Role of the Charge-Transfer State in Reduced Langevin Recombination in Organic Solar Cells: A Theoretical Study

    PubMed Central

    2015-01-01

    Reduced Langevin recombination has been observed in organic solar cells (OSCs) for many years, but its origin is still unclear. A recent work by Burke et al. (Adv. Energy Mater.2015, 5, 1500123-1) was inspired by this reduced Langevin recombination, and they proposed an equilibrium model of charge-transfer (CT) states that correlates the open-circuit voltage of OSCs with experimentally available device parameters. In this work, we extend Burke et al.’s CT model further and for the first time directly correlate the reduced Langevin recombination with the energetic and dynamic behavior of the CT state. Recombination through CT states leads in a straightforward manner to a decrease in the Langevin reduction factor with increasing temperature, without explicit consideration of the temperature dependence of the mobility. To verify the correlation between the CT states and reduced Langevin recombination, we incorporated this CT model and the reduced Langevin model into drift-diffusion simulations of a bilayer OSC. The simulations not only successfully reproduced realistic current–voltage (J–V) characteristics of the bilayer OSC, but also demonstrate that the two models consistently lead to same value of the apparent Langevin reduction factor. PMID:26640611

  6. Fluctuation paraconductivity within the framework of time-dependent Ginzburg Landau theory

    NASA Astrophysics Data System (ADS)

    Damianov, Damian Ch.; Mishonov, Todor M.

    1997-04-01

    Above the critical temperatureTcthe fluctuations of the superconducting order parameter Ψ are described within the framework of time-dependent Ginzburt-Landua theory using Langevin's approach of stochastic differential equations. The excess Aslamazov-Larkin conductivity is derived as an improtant test example for the case of non interacting fluctuations. It is shown at what conditions the kinetic arguments can be successively derived. A fluctuation Hall conductivity σxy(fl)and Nernst coefficient νxy(fl)are calculated for the case of weak magnetic field. The comparison with the BCS will result by Varlamov and Livanov [A. A. Varlamov and D. V. Livanov, Phys. Lett. A 157, 519 (1991)] gives the final determination of all the coefficients of the phenomenological TDGL theory.

  7. A study of Kramers' turnover theory in the presence of exponential memory friction

    NASA Astrophysics Data System (ADS)

    Ianconescu, Reuven; Pollak, Eli

    2015-09-01

    Originally, the challenge of solving Kramers' turnover theory was limited to Ohmic friction, or equivalently, motion of the escaping particle governed by a Langevin equation. Mel'nikov and Meshkov [J. Chem. Phys. 85, 1018 (1986)] (MM) presented a solution valid for Ohmic friction. The turnover theory was derived more generally and for memory friction by Pollak, Grabert, and Hänggi [J. Chem. Phys. 91, 4073 (1989)] (PGH). Mel'nikov proceeded to also provide finite barrier corrections to his theory [Phys. Rev. E 48, 3271 (1993)]. Finite barrier corrections were derived only recently within the framework of PGH theory [E. Pollak and R. Ianconescu, J. Chem. Phys. 140, 154108 (2014)]. A comprehensive comparison between MM and PGH theories including finite barrier corrections and using Ohmic friction showed that the two methods gave quantitatively similar results and were in quantitative agreement with numerical simulation data. In the present paper, we extend the study of the turnover theories to exponential memory friction. By comparing with numerical simulation, we find that PGH theory is rather accurate, even in the strong friction long memory time limit, while MM theory fails. However, inclusion of finite barrier corrections to PGH theory leads to failure in this limit. The long memory time invalidates the fundamental assumption that consecutive traversals of the well are independent of each other. Why PGH theory without finite barrier corrections remains accurate is a puzzle.

  8. Efficient quantum mechanical calculation of solvation free energies based on density functional theory, numerical atomic orbitals and Poisson Boltzmann equation

    NASA Astrophysics Data System (ADS)

    Wang, Mingliang; Wong, Chung F.; Liu, Jianhong; Zhang, Peixin

    2007-07-01

    We have successfully coupled the Kohn-Sham with Poisson-Boltzmann equations to predict the solvation free energy, where the Kohn-Sham equations were solved by implementing the flexible pseudo atomic orbitals as in S IESTA package. It was found that the calculated solvation free energy is in good agreement with experimental results for small neutral molecules, and its standard error is 1.33 kcal/mol, the correlation coefficient is 0.97. Due to its high efficiency and accuracy, the proposed model can be a promising tool for computing solvation free energies in computer aided drug design in future.

  9. A general theory of motion for the eight major satellites of Saturn. I - Equations and method of resolution

    NASA Astrophysics Data System (ADS)

    Duriez, L.; Vienne, A.

    1991-03-01

    A new method to construct an analytical theory of motion of Saturn's satellites is presented. It is an extension of the methods already used by Duriez (1979) and Laskar (1984) to construct a general planetary theory, using the same formalism to deal with the multiple resonances occurring in the saturnian system. The present goal is to obtain accurate representations of motions, adequate to future space observations. Thus, great care is taken in the construction of the models, which remains completely analytical with respect to physical parameters and constants of motion. Some preliminary results are given, which indicate good agreement with previous theories.

  10. Langevin approach to noise modelling of bipolar microwave transistors

    NASA Astrophysics Data System (ADS)

    Patti, F.; Miceli, V.; Spagnolo, B.

    2000-04-01

    We present a new approach to study the complete stochastic properties of fluctuations of the output current of microwave transistors. We obtain the π-hybrid model of bipolar microwave transistors with the noise internal sources starting from experimental on-wafer measurements of the scattering and noise parameters. We derive the stochastic differential equations of the Giacoletto model for different loads and source admittances. We give the analytical temporal behavior of the second moment of the output current, assuming particular given correlation functions between the internal noise sources.

  11. Constant pressure and temperature discrete-time Langevin molecular dynamics.

    PubMed

    Grønbech-Jensen, Niels; Farago, Oded

    2014-11-21

    We present a new and improved method for simultaneous control of temperature and pressure in molecular dynamics simulations with periodic boundary conditions. The thermostat-barostat equations are built on our previously developed stochastic thermostat, which has been shown to provide correct statistical configurational sampling for any time step that yields stable trajectories. Here, we extend the method and develop a set of discrete-time equations of motion for both particle dynamics and system volume in order to seek pressure control that is insensitive to the choice of the numerical time step. The resulting method is simple, practical, and efficient. The method is demonstrated through direct numerical simulations of two characteristic model systems-a one-dimensional particle chain for which exact statistical results can be obtained and used as benchmarks, and a three-dimensional system of Lennard-Jones interacting particles simulated in both solid and liquid phases. The results, which are compared against the method of Kolb and Dünweg [J. Chem. Phys. 111, 4453 (1999)], show that the new method behaves according to the objective, namely that acquired statistical averages and fluctuations of configurational measures are accurate and robust against the chosen time step applied to the simulation. PMID:25416875

  12. Constant pressure and temperature discrete-time Langevin molecular dynamics

    SciTech Connect

    Grønbech-Jensen, Niels; Farago, Oded

    2014-11-21

    We present a new and improved method for simultaneous control of temperature and pressure in molecular dynamics simulations with periodic boundary conditions. The thermostat-barostat equations are built on our previously developed stochastic thermostat, which has been shown to provide correct statistical configurational sampling for any time step that yields stable trajectories. Here, we extend the method and develop a set of discrete-time equations of motion for both particle dynamics and system volume in order to seek pressure control that is insensitive to the choice of the numerical time step. The resulting method is simple, practical, and efficient. The method is demonstrated through direct numerical simulations of two characteristic model systems—a one-dimensional particle chain for which exact statistical results can be obtained and used as benchmarks, and a three-dimensional system of Lennard-Jones interacting particles simulated in both solid and liquid phases. The results, which are compared against the method of Kolb and Dünweg [J. Chem. Phys. 111, 4453 (1999)], show that the new method behaves according to the objective, namely that acquired statistical averages and fluctuations of configurational measures are accurate and robust against the chosen time step applied to the simulation.

  13. Boussinesq Equations and Other Systems for Small-Amplitude Long Waves in Nonlinear Dispersive Media. I: Derivation and Linear Theory

    NASA Astrophysics Data System (ADS)

    Bona, G.; Chen, J. A.; Saut, Jing Ping

    2002-08-01

    Considered herein are a number of variants of the classical Boussinesq system and their higher-order generalizations. Such equations were first derived by Boussinesq to describe the two-way propagation of small-amplitude, long wavelength, gravity waves on the surface of water in a canal. These systems arise also when modeling the propagation of long-crested waves on large lakes or the ocean and in other contexts. Depending on the modeling of dispersion, the resulting system may or may not have a linearization about the rest state which is well posed. Even when well posed, the linearized system may exhibit a lack of conservation of energy that is at odds with its status as an approximation to the Euler equations. In the present script, we derive a four-parameter family of Boussinesq systems from the two-dimensional Euler equations for free-surface flow and formulate criteria to help decide which of these equations one might choose in a given modeling situation. The analysis of the systems according to these criteria is initiated.

  14. Phase-Space Reconstruction: a Path Towards the Next Generation of Nonlinear Differential Equation Based Models and Its Implications Towards Non-Uniform Sampling Theory

    SciTech Connect

    Charles R. Tolle; Mark Pengitore

    2009-08-01

    This paper explores the overlaps between the Control community’s work on System Identification (SysID) and the Physics, Mathematics, Chaos, and Complexity communities’ work on phase-space reconstruction via time-delay embedding. There are numerous overlaps between the goals of each community. Nevertheless, the Controls community can gain new insight as well as some new very powerful tools for SysID from the latest developments within the Physics, Mathematics, Chaos, and Complexity communities. These insights are gained via the work on phase-space reconstruction of non-linear dynamics. New methods for discovering non-linear differential based equations that evolved from embedding operations can shed new light on hybrid-systems theory, Nyquest-Shannon’s Theories, and network based control theory. This paper strives to guide the Controls community towards a closer inspection of the tools and additional insights being developed within the Physics, Mathematics, Chaos, and Complexity communities for discovery of system dynamics, the first step in control system development. The paper introduces the concepts of phase-space reconstruction via time-delay embedding (made famous byWhitney, Takens, and Sauer’s Thoreoms), intergrate-and-fire embedding, and non-linear differential equation discovery based on Perona’s method.

  15. Mixed Quantum/Classical Theory for Molecule-Molecule Inelastic Scattering: Derivations of Equations and Application to N2 + H2 System.

    PubMed

    Semenov, Alexander; Babikov, Dmitri

    2015-12-17

    The mixed quantum classical theory, MQCT, for inelastic scattering of two molecules is developed, in which the internal (rotational, vibrational) motion of both collision partners is treated with quantum mechanics, and the molecule-molecule scattering (translational motion) is described by classical trajectories. The resultant MQCT formalism includes a system of coupled differential equations for quantum probability amplitudes, and the classical equations of motion in the mean-field potential. Numerical tests of this theory are carried out for several most important rotational state-to-state transitions in the N2 + H2 system, in a broad range of collision energies. Besides scattering resonances (at low collision energies) excellent agreement with full-quantum results is obtained, including the excitation thresholds, the maxima of cross sections, and even some smaller features, such as slight oscillations of energy dependencies. Most importantly, at higher energies the results of MQCT are nearly identical to the full quantum results, which makes this approach a good alternative to the full-quantum calculations that become computationally expensive at higher collision energies and for heavier collision partners. Extensions of this theory to include vibrational transitions or general asymmetric-top rotor (polyatomic) molecules are relatively straightforward. PMID:26323089

  16. Structure of Poly(dialkylsiloxane) Melts: Comparisons of Wide Angle X-ray Scattering, Molecular Dynamics Simulations, and Integral Equation Theory

    SciTech Connect

    Habenschuss, Anton {Tony}; Tsige, Mesfin; Curro, John G.; Grest, Gary S.; Nath, Shyamal

    2007-01-01

    Wide-angle X-ray scattering, molecular dynamics (MD) simulations, and integral equation theory are used to study the structure of poly(diethylsiloxane) (PDES), poly(ethylmethylsiloxane) (PEMS), and poly(dimethylsiloxane) (PDMS) melts. The structure functions of PDES, PEMS, and PDMS are similar, but systematic trends in the intermolecular packing are observed. The local intramolecular structure is extracted from the experimental structure functions. The bond distances and bond angles obtained, including the large Si-O-Si angle, are in good agreement with the explicit atom (EA) and united atom (UA) potentials used in the simulations and theory and from other sources. Very good agreement is found between the MD simulations using the EA potentials and the experimental scattering results. Good agreement is also found between the polymer reference interaction site model (PRISM theory) and the UA MD simulations. The intermolecular structure is examined experimentally using an appropriately weighted radial distribution function and with theory and simulation using intermolecular site/site pair correlation functions. Experiment, simulation, and theory show systematic increases in the chain/chain packing distances in the siloxanes as the number of sites in the pendant side chains is increased.

  17. Structure of Poly(dialkylsiloxane) Melts: Comparisons of Wide-Angle X-ray Scattering, Molecular Dynamics Simualations, and Integral Equation Theory

    SciTech Connect

    Habenschuss, Anton {Tony}; Tsige, Mesfin; Curro, John G.; Grest, Gary S.; Nath, Shyamal

    2007-01-01

    Wide-angle X-ray scattering, molecular dynamics (MD) simulations, and integral equation theory are used to study the structure of poly(diethylsiloxane) (PDES), poly(ethylmethylsiloxane) (PEMS), and poly(dimethylsiloxane) (PDMS) melts. The structure functions of PDES, PEMS, and PDMS are similar, but systematic trends in the intermolecular packing are observed. The local intramolecular structure is extracted from the experimental structure functions. The bond distances and bond angles obtained, including the large Si-O-Si angle, are in good agreement with the explicit atom (EA) and united atom (UA) potentials used in the simulations and theory and from other sources. Very good agreement is found between the MD simulations using the EA potentials and the experimental scattering results. Good agreement is also found between the polymer reference interaction site model (PRISM theory) and the UA MD simulations. The intermolecular structure is examined experimentally using an appropriately weighted radial distribution function and with theory and simulation using intermolecular site/site pair correlation functions. Experiment, simulation, and theory show systematic increases in the chain/chain packing distances in the siloxanes as the number of sites in the pendant side chains is increased.

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

    NASA Astrophysics Data System (ADS)

    Haussmann, Rudolf

    2016-03-01

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

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

    PubMed

    Haussmann, Rudolf

    2016-03-23

    Starting from the microscopic description of a normal fluid in terms of any kind of local interacting many-particle theory we present a well defined step by step procedure to derive the hydrodynamic equations for the macroscopic phenomena. We specify the densities of the conserved quantities as the relevant hydrodynamic variables and apply the methods of non-equilibrium statistical mechanics with projection operator techniques. As a result we obtain time-evolution equations for the hydrodynamic variables with three kinds of terms on the right-hand sides: reversible, dissipative and fluctuating terms. In their original form these equations are completely exact and contain nonlocal terms in space and time which describe nonlocal memory effects. Applying a few approximations the nonlocal properties and the memory effects are removed. As a result we find the well known hydrodynamic equations of a normal fluid with Gaussian fluctuating forces. In the following we investigate if and how the time-inversion invariance is broken and how the second law of thermodynamics comes about. Furthermore, we show that the hydrodynamic equations with fluctuating forces are equivalent to stochastic Langevin equations and the related Fokker-Planck equation. Finally, we investigate the fluctuation theorem and find a modification by an additional term. PMID:26902659

  20. Republication of: Geometrodynamics in the null case. Exact solutions of the field equations of the general theory of relativity III

    NASA Astrophysics Data System (ADS)

    Jordan, Pascual; Kundt, Wolfgang

    2014-03-01

    This is an English translation of a paper by Pascual Jordan and Wolfgang Kundt, first published in 1961 in the proceedings of the Academy of Sciences and Literature in Mainz (Germany). The original paper was part 3 of a five-part series of articles containing the first summary of knowledge about exact solutions of Einstein's equations found until then. (Parts 1, 2 and 4 of the series have already been reprinted, part 5 will be printed as a Golden Oldie in near future.) This third paper shows how solutions of the Einstein-Maxwell equations with null Maxwell field can be incorporated into the scheme of geometrodynamics. It has been selected by the Editors of General Relativity and Gravitation for republication in the Golden Oldies series of the journal. The republication is accompanied by an editorial note written by Charles Misner.