Global Langevin model of multidimensional biomolecular dynamics
Schaudinnus, Norbert; Lickert, Benjamin; Biswas, Mithun; Stock, Gerhard
2016-11-01
Molecular dynamics simulations of biomolecular processes are often discussed in terms of diffusive motion on a low-dimensional free energy landscape F ( 𝒙 ) . To provide a theoretical basis for this interpretation, one may invoke the system-bath ansatz á la Zwanzig. That is, by assuming a time scale separation between the slow motion along the system coordinate x and the fast fluctuations of the bath, a memory-free Langevin equation can be derived that describes the system's motion on the free energy landscape F ( 𝒙 ) , which is damped by a friction field and driven by a stochastic force that is related to the friction via the fluctuation-dissipation theorem. While the theoretical formulation of Zwanzig typically assumes a highly idealized form of the bath Hamiltonian and the system-bath coupling, one would like to extend the approach to realistic data-based biomolecular systems. Here a practical method is proposed to construct an analytically defined global model of structural dynamics. Given a molecular dynamics simulation and adequate collective coordinates, the approach employs an "empirical valence bond"-type model which is suitable to represent multidimensional free energy landscapes as well as an approximate description of the friction field. Adopting alanine dipeptide and a three-dimensional model of heptaalanine as simple examples, the resulting Langevin model is shown to reproduce the results of the underlying all-atom simulations. Because the Langevin equation can also be shown to satisfy the underlying assumptions of the theory (such as a delta-correlated Gaussian-distributed noise), the global model provides a correct, albeit empirical, realization of Zwanzig's formulation. As an application, the model can be used to investigate the dependence of the system on parameter changes and to predict the effect of site-selective mutations on the dynamics.
A Langevin model for low density pedestrian dynamics
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.
Nonlinear Dynamic Modeling of Langevin-Type Piezoelectric Transducers
Nicolás Peréz Alvarez
2015-11-01
Full Text Available Langevin transducers are employed in several applications, such as power ultrasound systems, naval hydrophones, and high-displacement actuators. Nonlinear effects can influence their performance, especially at high vibration amplitude levels. These nonlinear effects produce variations in the resonant frequency, harmonics of the excitation frequency, in addition to loss of symmetry in the frequency response and “frequency domain hysteresis”. In this context, this paper presents a simplified nonlinear dynamic model of power ultrasound transducers requiring only two parameters for simulating the most relevant nonlinear effects. One parameter reproduces the changes in the resonance frequency and the other introduces the dependence of the frequency response on the history of the system. The piezoelectric constitutive equations are extended by a linear dependence of the elastic constant on the mechanical displacement amplitude. For introducing the frequency hysteresis, the elastic constant is computed by combining the current value of the mechanical amplitude with the previous state amplitude. The model developed in this work is applied for predicting the dynamic responses of a 26 kHz ultrasonic transducer. The comparison of theoretical and experimental responses, obtained at several input voltages around the tuned frequency, shows a good agreement, indicating that the model can accurately describe the transducer nonlinear behavior.
Li, Daming
2016-01-01
We consider the massive Thirring model at finite density in 0+1 dimension. The fermion bag approach, Langevin dynamics and complex Langevin dynamics are adopted to attack the sign problem for this model. Compared with the complex Langevin dynamics, both fermion bag approach and Langvin dynamics avoid the sign problem. The fermion density and chiral condensate, which are obtained by these numerical methods, are compared with the exact results. The advantages of the fermion bag approach over the other numerical methods are also discussed.
Langevin model of the temperature and hydration dependence of protein vibrational dynamics.
Moritsugu, Kei; Smith, Jeremy C
2005-06-23
The modification of internal vibrational modes in a protein due to intraprotein anharmonicity and solvation effects is determined by performing molecular dynamics (MD) simulations of myoglobin, analyzing them using a Langevin model of the vibrational dynamics and comparing the Langevin results to a harmonic, normal mode model of the protein in vacuum. The diagonal and off-diagonal Langevin friction matrix elements, which model the roughness of the vibrational potential energy surfaces, are determined together with the vibrational potentials of mean force from the MD trajectories at 120 K and 300 K in vacuum and in solution. The frictional properties are found to be describable using simple phenomenological functions of the mode frequency, the accessible surface area, and the intraprotein interaction (the displacement vector overlap of any given mode with the other modes in the protein). The frictional damping of a vibrational mode in vacuum is found to be directly proportional to the intraprotein interaction of the mode, whereas in solution, the friction is proportional to the accessible surface area of the mode. In vacuum, the MD frequencies are lower than those of the normal modes, indicating intramolecular anharmonic broadening of the associated potential energy surfaces. Solvation has the opposite effect, increasing the large-amplitude vibrational frequencies relative to in vacuum and thus vibrationally confining the protein atoms. Frictional damping of the low-frequency modes is highly frequency dependent. In contrast to the damping effect of the solvent, the vibrational frequency increase due to solvation is relatively temperature independent, indicating that it is primarily a structural effect. The MD-derived vibrational dynamic structure factor and density of states are well reproduced by a model in which the Langevin friction and potential of mean force parameters are applied to the harmonic normal modes.
A Langevin model for the Dynamic Contact Angle Parameterised Using Molecular Dynamics
Smith, Edward; Muller, Erich; Craster, Richard; Matar, Omar
2016-11-01
An understanding of droplet spreading is essential in a diverse range of applications, including coating processes, dip feed reactors, crop spraying and biomedical treatments such as surfactant replacement theory. The default modelling tools for engineering fluid dynamics assume that the continuum hypothesis is valid. The contact line motion is very difficult to capture in this paradigm and requires some form of closure model, often tuned a priori to experiments. Molecular dynamics (MD), by assuming only an inter-molecular potential, reproduces the full detail of the three-phase contact line with no additional modelling assumptions. This provides an ideal test-bed to understand contact line motion. In this talk, MD results for a sheared liquid bridge are presented. The evolution and fluctuations of the dynamic contact angle are paramterised over a range of wall sliding speeds and temperatures. A Langevin model is proposed to reproduce the fluctuations and evolution of the contact angle. Results from this model are compared to molecular simulation data showing excellent agreement. The potential applications of this model, as well as limitation and possible extensions, are discussed. EPSRC UK platform Grant MACIPh (EP/L020564/1).
Non-linear Langevin model for the early-stage dynamics of electrospinning jets
Lauricella, Marco; Pisignano, Dario; Succi, Sauro
2015-01-01
We present a non-linear Langevin model to investigate the early-stage dynamics of electrified polymer jets in electrospinning experiments. In particular, we study the effects of air drag force on the uniaxial elongation of the charged jet, right after ejection from the nozzle. Numerical simulations show that the elongation of the jet filament close to the injection point is significantly affected by the non-linear drag exerted by the surrounding air. These result provide useful insights for the optimal design of current and future electrospinning experiments.
Controlling complex Langevin dynamics at finite density
Aarts, Gert; Bongiovanni, Lorenzo [Swansea University, Department of Physics, College of Science, Swansea (United Kingdom); Seiler, Erhard [Max-Planck-Institut fuer Physik (Werner-Heisenberg-Institut), Muenchen (Germany); Sexty, Denes [Universitaet Heidelberg, Institut fuer Theoretische Physik, Heidelberg (Germany); Stamatescu, Ion-Olimpiu [Universitaet Heidelberg, Institut fuer Theoretische Physik, Heidelberg (Germany); FEST, Heidelberg (Germany)
2013-07-15
At nonzero chemical potential the numerical sign problem in lattice field theory limits the use of standard algorithms based on importance sampling. Complex Langevin dynamics provides a possible solution, but it has to be applied with care. In this review, we first summarise our current understanding of the approach, combining analytical and numerical insight. In the second part we study SL(N,C) gauge cooling, which was introduced recently as a tool to control complex Langevin dynamics in nonabelian gauge theories. We present new results in Polyakov chain models and in QCD with heavy quarks and compare various adaptive cooling implementations. (orig.)
Aarts, Gert
2010-01-01
The three-dimensional XY model is studied at finite chemical potential using complex Langevin dynamics. The validity of the approach is probed at small chemical potential using imaginary chemical potential and continuity arguments, and at larger chemical potential by comparison with the world line method. While complex Langevin works for larger beta, we find that it fails for smaller beta, in the region of the phase diagram corresponding to the disordered phase. Diagnostic tests are developed to identify symptoms correlated with incorrect convergence. We argue that the erroneous behaviour at smaller beta is not due to the sign problem, but rather resembles dynamics observed in complex Langevin simulations of simple models with complex noise.
Hasegawa, Hideo
2007-02-01
We have studied the finite N-unit Langevin model subjected to multiplicative noises, by using the augmented moment method (AMM), as a continuation of our previous paper [H. Hasegawa, J. Phys. Soc. Japan 75 (2006) 033001]. Effects of couplings on stationary and dynamical properties of the model have been investigated. The difference and similarity between the results of diffusive and sigmoid couplings are studied in details. Time dependences of average and fluctuations in local and global variables calculated by the AMM are in good agreement with those of direct simulations (DSs). We also discuss stationary distributions of local and global variables with the use of the Fokker-Planck equation (FPE) method and DSs. It is demonstrated that stationary distributions show much variety when multiplicative noise and external inputs are taken into account.
He Zhuo-Ran; Wu Tai-Lin; Ouyang Qi; Tu Yu-Hai
2012-01-01
Recent extensive studies of Escherichia coli (E.coli) chemotaxis have achieved a deep understanding of its microscopic control dynamics.As a result,various quantitatively predictive models have been developed to describe the chemotactic behavior of E.coli motion.However,a population-level partial differential equation (PDE) that rationally incorporates such microscopic dynamics is still insufficient.Apart from the traditional Keller-Segel (K-S) equation,many existing population-level models developed from the microscopic dynamics are integro-PDEs.The difficulty comes mainly from cell tumbles which yield a velocity jumping process.Here,we propose a Langevin approximation method that avoids such a difficulty without appreciable loss of precision.The resulting model not only quantitatively reproduces the results of pathway-based single-cell simulators,but also provides new inside information on the mechanism of E.coli chemotaxis.Our study demonstrates a possible alternative in establishing a simple population-level model that allows for the complex microscopic mechanisms in bacterial chemotaxis.
Haas, Kevin R; Yang, Haw; Chu, Jhih-Wei
2013-09-28
The evaluation of the Fisher information matrix for the probability density of trajectories generated by the over-damped Langevin dynamics at equilibrium is presented. The framework we developed is general and applicable to any arbitrary potential of mean force where the parameter set is now the full space dependent function. Leveraging an innovative Hermitian form of the corresponding Fokker-Planck equation allows for an eigenbasis decomposition of the time propagation probability density. This formulation motivates the use of the square root of the equilibrium probability density as the basis for evaluating the Fisher information of trajectories with the essential advantage that the Fisher information matrix in the specified parameter space is constant. This outcome greatly eases the calculation of information content in the parameter space via a line integral. In the continuum limit, a simple analytical form can be derived to explicitly reveal the physical origin of the information content in equilibrium trajectories. This methodology also allows deduction of least informative dynamics models from known or available observables that are either dynamical or static in nature. The minimum information optimization of dynamics is performed for a set of different constraints to illustrate the generality of the proposed methodology.
A Langevin model for fluctuating contact angle behaviour parametrised using molecular dynamics.
Smith, E R; Müller, E A; Craster, R V; Matar, O K
2016-12-06
Molecular dynamics simulations are employed to develop a theoretical model to predict the fluid-solid contact angle as a function of wall-sliding speed incorporating thermal fluctuations. A liquid bridge between counter-sliding walls is studied, with liquid-vapour interface-tracking, to explore the impact of wall-sliding speed on contact angle. The behaviour of the macroscopic contact angle varies linearly over a range of capillary numbers beyond which the liquid bridge pinches off, a behaviour supported by experimental results. Nonetheless, the liquid bridge provides an ideal test case to study molecular scale thermal fluctuations, which are shown to be well described by Gaussian distributions. A Langevin model for contact angle is parametrised to incorporate the mean, fluctuation and auto-correlations over a range of sliding speeds and temperatures. The resulting equations can be used as a proxy for the fully-detailed molecular dynamics simulation allowing them to be integrated within a continuum-scale solver.
Self-guided Langevin dynamics via generalized Langevin equation.
Wu, Xiongwu; Brooks, Bernard R; Vanden-Eijnden, Eric
2016-03-05
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.
On complex Langevin dynamics and zeroes of the measure I: Formal proof and simple models
Aarts, Gert; Sexty, Denes; Stamatescu, Ion-Olimpiu
2016-01-01
In the complex Langevin approach to lattice simulations at nonzero density, zeroes of the fermion determinant lead to a meromorphic drift and hence a need to revisit the theoretical derivation. We discuss how poles in the drift affect the formal justification of the approach and then explore the various potential issues in simple models, in a manner that is applicable to heavy dense and full QCD.
Testing dynamic stabilisation in complex Langevin simulations
Attanasio, Felipe
2016-01-01
Complex Langevin methods have been successfully applied in theories that suffer from a sign problem such as QCD with a chemical potential. We present and illustrate a novel method (dynamic stabilisation) that ensures that Complex Langevin simulations stay close to the SU(3) manifold, which lead to correct and improved results in the framework of pure Yang-Mills simulations and QCD in the limit of heavy quarks.
Some remarks on Lefschetz thimbles and complex Langevin dynamics
Aarts, Gert; Seiler, Erhard; Sexty, Denes
2014-01-01
Lefschetz thimbles and complex Langevin dynamics both provide a means to tackle the numerical sign problem prevalent in theories with a complex weight in the partition function, e.g. due to nonzero chemical potential. Here we collect some findings for the quartic model, and for U(1) and SU(2) models in the presence of a determinant, which have some features not discussed before, due to a singular drift. We find evidence for a relation between classical runaways and stable thimbles, and give an example of a degenerate fixed point. We typically find that the distributions sampled in complex Langevin dynamics are related to the thimble(s), but with some important caveats, for instance due to the presence of unstable fixed points in the Langevin dynamics.
Error Analysis of Modified Langevin Dynamics
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.
Efficient Algorithms for Langevin and DPD Dynamics.
Goga, N; Rzepiela, A J; de Vries, A H; Marrink, S J; Berendsen, H J C
2012-10-09
In this article, we present several algorithms for stochastic dynamics, including Langevin dynamics and different variants of Dissipative Particle Dynamics (DPD), applicable to systems with or without constraints. The algorithms are based on the impulsive application of friction and noise, thus avoiding the computational complexity of algorithms that apply continuous friction and noise. Simulation results on thermostat strength and diffusion properties for ideal gas, coarse-grained (MARTINI) water, and constrained atomic (SPC/E) water systems are discussed. We show that the measured thermal relaxation rates agree well with theoretical predictions. The influence of various parameters on the diffusion coefficient is discussed.
Applications of Langevin and Molecular Dynamics methods
Lomdahl, P. S.
Computer simulation of complex nonlinear and disordered phenomena from materials science is rapidly becoming an active and new area serving as a guide for experiments and for testing of theoretical concepts. This is especially true when novel massively parallel computer systems and techniques are used on these problems. In particular the Langevin dynamics simulation technique has proven useful in situations where the time evolution of a system in contact with a heat bath is to be studied. The traditional way to study systems in contact with a heat bath has been via the Monte Carlo method. While this method has indeed been used successfully in many applications, it has difficulty addressing true dynamical questions. Large systems of coupled stochastic ODE's (or Langevin equations) are commonly the end result of a theoretical description of higher dimensional nonlinear systems in contact with a heat bath. The coupling is often local in nature, because it reflects local interactions formulated on a lattice, the lattice for example represents the underlying discreteness of a substrate of atoms or discrete k-values in Fourier space. The fundamental unit of parallelism thus has a direct analog in the physical system the authors are interested in. In these lecture notes the authors illustrate the use of Langevin stochastic simulation techniques on a number of nonlinear problems from materials science and condensed matter physics that have attracted attention in recent years. First, the authors review the idea behind the fluctuation-dissipation theorem which forms that basis for the numerical Langevin stochastic simulation scheme. The authors then show applications of the technique to various problems from condensed matter and materials science.
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.
An attempt toward the generalized Langevin dynamics simulation
B.Kim
2008-03-01
Full Text Available An attempt to generalize the Langevin dynamics simulation method is presented based on the generalized Langevin theory of liquids, in which the dynamics of both solute and solvent is treated by the generalized Langevin equations, but the integration of the equation of motion of solute is made in the manner similar to the ordinary molecular dynamics simulation with discretized time steps along a trajectory. A preliminary result is derived based on an assumption of the uniform solvent density. The result is regarded to be a microscopic generalization of the phenomenological Langevin theory for the harmonic oscillator immersed in a continuum solvent developed by Wang and Uhlenbeck.
Complex Langevin dynamics for chiral random matrix theory
Mollgaard, A.; Splittorff, K.
2013-12-01
We apply complex Langevin dynamics to chiral random matrix theory at nonzero chemical potential. At large quark mass, the simulations agree with the analytical results while incorrect convergence is found for small quark masses. The region of quark masses for which the complex Langevin dynamics converges incorrectly is identified as the region where the fermion determinant frequently traces out a path surrounding the origin of the complex plane during the Langevin flow. This links the incorrect convergence to an ambiguity in the Langevin force due to the presence of the logarithm of the fermion determinant in the action.
Complex Langevin Dynamics for chiral Random Matrix Theory
Mollgaard, A
2013-01-01
We apply complex Langevin dynamics to chiral random matrix theory at nonzero chemical potential. At large quark mass the simulations agree with the analytical results while incorrect convergence is found for small quark masses. The region of quark masses for which the complex Langevin dynamics converges incorrectly is identified as the region where the fermion determinant frequently traces out a path surrounding the origin of the complex plane during the Langevin flow. This links the incorrect convergence to an ambiguity in the Langevin force due to the presence of the logarithm of the fermion determinant in the action.
Localised distributions and criteria for correctness in complex Langevin dynamics
Aarts, Gert, E-mail: g.aarts@swan.ac.uk [Department of Physics, College of Science, Swansea University, Swansea (United Kingdom); Giudice, Pietro, E-mail: p.giudice@uni-muenster.de [Department of Physics, College of Science, Swansea University, Swansea (United Kingdom); Seiler, Erhard, E-mail: ehs@mppmu.mpg.de [Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), München (Germany)
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.
On Complex Langevin Dynamics and the Evaluation of Observables
Durakovic, Amel; Tranberg, Anders
2014-01-01
In stochastic quantisation, quantum mechanical expectation values are computed as averages over the time history of a stochastic process described by a Langevin equation. Complex stochastic quantisation, though theoretically not rigorously established, extends this idea to cases where the action is complex-valued by complexifying the basic degrees of freedom, all observables and allowing the stochastic process to probe the complexified configuration space. We review the method for a previously studied one-dimensional toy model, the U(1) one link model. We confirm that complex Langevin dynamics only works for a certain range of parameters, misestimating observables otherwise. A curious effect is observed where all moments of the basic stochastic variable are misestimated, although these misestimated moments may be used to construct, by a Taylor series, other observables that are reproduced correctly. This suggests a subtle but not completely resolved relationship between the original complex integration measur...
Huang, Yandong; Rüdiger, Sten; Shuai, Jianwei
2013-12-01
The random opening and closing of ion channels establishes channel noise, which can be approximated and included into stochastic differential equations (Langevin approach). The Langevin approach is often incorporated to model stochastic ion channel dynamics for systems with a large number of channels. Here, we introduce a discretization procedure of a channel-based Langevin approach to simulate the stochastic channel dynamics with small and intermediate numbers of channels. We show that our Langevin approach with discrete channel open fractions can give a good approximation of the original Markov dynamics even for only 10 K channels. We suggest that the better approximation by the discretized Langevin approach originates from the improved representation of events that trigger action potentials.
Huang, Yandong [Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005 (China); Rüdiger, Sten [Institute of Physics, Humboldt-Universität zu Berlin (Germany); Shuai, Jianwei, E-mail: jianweishuai@xmu.edu.cn [Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005 (China)
2013-12-13
The random opening and closing of ion channels establishes channel noise, which can be approximated and included into stochastic differential equations (Langevin approach). The Langevin approach is often incorporated to model stochastic ion channel dynamics for systems with a large number of channels. Here, we introduce a discretization procedure of a channel-based Langevin approach to simulate the stochastic channel dynamics with small and intermediate numbers of channels. We show that our Langevin approach with discrete channel open fractions can give a good approximation of the original Markov dynamics even for only 10 K{sup +} channels. We suggest that the better approximation by the discretized Langevin approach originates from the improved representation of events that trigger action potentials.
Uncertainty quantification for generalized Langevin dynamics
Hall, Eric J.; Katsoulakis, Markos A.; Rey-Bellet, Luc
2016-12-01
We present efficient finite difference estimators for goal-oriented sensitivity indices with applications to the generalized Langevin equation (GLE). In particular, we apply these estimators to analyze an extended variable formulation of the GLE where other well known sensitivity analysis techniques such as the likelihood ratio method are not applicable to key parameters of interest. These easily implemented estimators are formed by coupling the nominal and perturbed dynamics appearing in the finite difference through a common driving noise or common random path. After developing a general framework for variance reduction via coupling, we demonstrate the optimality of the common random path coupling in the sense that it produces a minimal variance surrogate for the difference estimator relative to sampling dynamics driven by independent paths. In order to build intuition for the common random path coupling, we evaluate the efficiency of the proposed estimators for a comprehensive set of examples of interest in particle dynamics. These reduced variance difference estimators are also a useful tool for performing global sensitivity analysis and for investigating non-local perturbations of parameters, such as increasing the number of Prony modes active in an extended variable GLE.
Nattino, Francesco; Galparsoro, Oihana; Costanzo, Francesca; Díez Muiño, Ricardo; Alducin, Maite; Kroes, Geert-Jan
2016-06-01
Accurately modeling surface temperature and surface motion effects is necessary to study molecule-surface reactions in which the energy dissipation to surface phonons can largely affect the observables of interest. We present here a critical comparison of two methods that allow to model such effects, namely, the ab initio molecular dynamics (AIMD) method and the generalized Langevin oscillator (GLO) model, using the dissociation of N2 on W(110) as a benchmark. AIMD is highly accurate as the surface atoms are explicitly part of the dynamics, but this advantage comes with a large computational cost. The GLO model is much more computationally convenient, but accounts for lattice motion effects in a very approximate way. Results show that, despite its simplicity, the GLO model is able to capture the physics of the system to a large extent, returning dissociation probabilities which are in better agreement with AIMD than static-surface results. Furthermore, the GLO model and the AIMD method predict very similar energy transfer to the lattice degrees of freedom in the non-reactive events, and similar dissociation dynamics.
Langevin approach with rescaled noise for stochastic channel dynamics in Hodgkin-Huxley neurons
Huang, Yan-Dong; Xiang, Li; Shuai, Jian-Wei
2015-12-01
The Langevin approach has been applied to model the random open and closing dynamics of ion channels. It has long been known that the gate-based Langevin approach is not sufficiently accurate to reproduce the statistics of stochastic channel dynamics in Hodgkin-Huxley neurons. Here, we introduce a modified gate-based Langevin approach with rescaled noise strength to simulate stochastic channel dynamics. The rescaled independent gate and identical gate Langevin approaches improve the statistical results for the mean membrane voltage, inter-spike interval, and spike amplitude. Project supported by the National Natural Science Foundation for Distinguished Young Scholars of China (Grant No. 11125419), the National Natural Science Foundation of China (Grant No. 10925525), and the Funds for the Leading Talents of Fujian Province, China.
The derivation and approximation of coarse-grained dynamics from Langevin dynamics
Ma, Lina; Li, Xiantao; Liu, Chun
2016-11-01
We present a derivation of a coarse-grained description, in the form of a generalized Langevin equation, from the Langevin dynamics model that describes the dynamics of bio-molecules. The focus is placed on the form of the memory kernel function, the colored noise, and the second fluctuation-dissipation theorem that connects them. Also presented is a hierarchy of approximations for the memory and random noise terms, using rational approximations in the Laplace domain. These approximations offer increasing accuracy. More importantly, they eliminate the need to evaluate the integral associated with the memory term at each time step. Direct sampling of the colored noise can also be avoided within this framework. Therefore, the numerical implementation of the generalized Langevin equation is much more efficient.
Snook, Ian
2007-01-01
The Langevin and Generalised Langevin Approach To The Dynamics Of Atomic, Polymeric And Colloidal Systems is concerned with the description of aspects of the theory and use of so-called random processes to describe the properties of atomic, polymeric and colloidal systems in terms of the dynamics of the particles in the system. It provides derivations of the basic equations, the development of numerical schemes to solve them on computers and gives illustrations of application to typical systems.Extensive appendices are given to enable the reader to carry out computations to illustrate many of the points made in the main body of the book.* Starts from fundamental equations* Gives up-to-date illustration of the application of these techniques to typical systems of interest* Contains extensive appendices including derivations, equations to be used in practice and elementary computer codes
From the Underdamped Generalized Elastic Model to the Single Particle Langevin Description
Alessandro Taloni
2017-01-01
Full Text Available The generalized elastic model encompasses several linear stochastic models describing the dynamics of polymers, membranes, rough surfaces, and fluctuating interfaces. While usually defined in the overdamped case, in this paper we formally include the inertial term to account for the initial diffusive stages of the stochastic dynamics. We derive the generalized Langevin equation for a probe particle and we show that this equation reduces to the usual Langevin equation for Brownian motion, and to the fractional Langevin equation on the long-time limit.
Generalized Langevin equation formulation for anomalous polymer dynamics
Panja, D.
2010-01-01
For reproducing the anomalous—i.e., sub-diffusive or super-diffusive—behavior in some stochastic dynamical systems, the generalized Langevin equation (GLE) has gained considerable popularity in recent years. Motivated by the question of whether or not a system with anomalous dynamics can have the GL
Langevin model for a Brownian system with directed motion
Ambía, Francisco; Híjar, Humberto
2016-08-01
We propose a model for an active Brownian system that exhibits one-dimensional directed motion. This system consists of two Brownian spherical particles that interact through an elastic potential and have time-dependent radii. We suggest an algorithm by which the sizes of the particles can be varied, such that the center of mass of the system is able to move at an average constant speed in one direction. The dynamics of the system is studied theoretically using a Langevin model, as well as from Brownian Dynamics simulations.
Langevin dynamics of the pure SU(2) deconfining transition
Fraga, E S; Mizher, A J
2007-01-01
We investigate the dissipative real-time evolution of the order parameter for the deconfining transition in the pure SU(2) gauge theory. The approach to equilibrium after a quench to temperatures well above the critical one is described by a Langevin equation. To fix completely the markovian Langevin dynamics we choose the dissipation coefficient, that is a function of the temperature, guided by preliminary Monte Carlo simulations for various temperatures. Assuming a relationship between Monte Carlo time and real time, we estimate the delay in thermalization brought about by dissipation and noise.
Description of dynamics of stock prices by a Langevin approach
Huang Zi-Gang; Chen Yong; Zhang Yong; Wang Ying-Hai
2007-01-01
We have studied the Langevin description of stochastic dynamics of financial time series. A sliding-window algorithm is used for our analysis. We find that the fluctuation of stock prices can be understood from the view of a time-dependent drift force corresponding to the drift parameter in Langevin equation. It is revealed that the statistical results of the drift force estimated from financial time series can be approximately considered as a linear restoring force. We investigate the significance of this linear restoring force to the prices evolution from its two coefficients, the equilibrium position and the slope coefficient. The daily log-returns of S&P 500 index from 1950 to 1999 are especially analysed. The new simple form of the restoring force obtained both from mathematical and numerical analyses suggests that the Langevin approach can effectively present not only the macroscopical but also the detailed properties of the price evolution.
Langevin model for reactive transport in porous media
Tartakovsky, Alexandre M.
2010-08-01
Existing continuum models for reactive transport in porous media tend to overestimate the extent of solute mixing and mixing-controlled reactions because the continuum models treat both the mechanical and diffusive mixings as an effective Fickian process. Recently, we have proposed a phenomenological Langevin model for flow and transport in porous media [A. M. Tartakovsky, D. M. Tartakovsky, and P. Meakin, Phys. Rev. Lett. 101, 044502 (2008)10.1103/PhysRevLett.101.044502]. In the Langevin model, the fluid flow in a porous continuum is governed by a combination of a Langevin equation and a continuity equation. Pore-scale velocity fluctuations, the source of mechanical dispersion, are represented by the white noise. The advective velocity (the solution of the Langevin flow equation) causes the mechanical dispersion of a solute. Molecular diffusion and sub-pore-scale Taylor-type dispersion are modeled by an effective stochastic advection-diffusion equation. Here, we propose a method for parameterization of the model for a synthetic porous medium, and we use the model to simulate multicomponent reactive transport in the porous medium. The detailed comparison of the results of the Langevin model with pore-scale and continuum (Darcy) simulations shows that: (1) for a wide range of Peclet numbers the Langevin model predicts the mass of reaction product more accurately than the Darcy model; (2) for small Peclet numbers predictions of both the Langevin and the Darcy models agree well with a prediction of the pore-scale model; and (3) the accuracy of the Langevin and Darcy model deteriorates with the increasing Peclet number but the accuracy of the Langevin model decreases more slowly than the accuracy of the Darcy model. These results show that the separate treatment of advective and diffusive mixing in the stochastic transport model is more accurate than the classical advection-dispersion theory, which uses a single effective diffusion coefficient (the dispersion
Parametrizing linear generalized Langevin dynamics from explicit molecular dynamics simulations
Gottwald, Fabian; Ivanov, Sergei D; Kühn, Oliver
2015-01-01
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 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 (GLE), which can be rigorously derived by means of a linear projection (LP) 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 most 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. Importa...
Fractional Langevin model of gait variability
Latka Miroslaw
2005-08-01
Full Text Available Abstract The stride interval in healthy human gait fluctuates from step to step in a random manner and scaling of the interstride interval time series motivated previous investigators to conclude that this time series is fractal. Early studies suggested that gait is a monofractal process, but more recent work indicates the time series is weakly multifractal. Herein we present additional evidence for the weakly multifractal nature of gait. We use the stride interval time series obtained from ten healthy adults walking at a normal relaxed pace for approximately fifteen minutes each as our data set. A fractional Langevin equation is constructed to model the underlying motor control system in which the order of the fractional derivative is itself a stochastic quantity. Using this model we find the fractal dimension for each of the ten data sets to be in agreement with earlier analyses. However, with the present model we are able to draw additional conclusions regarding the nature of the control system guiding walking. The analysis presented herein suggests that the observed scaling in interstride interval data may not be due to long-term memory alone, but may, in fact, be due partly to the statistics.
Fractional Langevin model of memory in financial markets.
Picozzi, Sergio; West, Bruce J
2002-10-01
The separation of the microscopic and macroscopic time scales is necessary for the validity of ordinary statistical physics and the dynamical description embodied in the Langevin equation. When the microscopic time scale diverges, the differential equations on the macroscopic level are no longer valid and must be replaced with fractional differential equations of motion; in particular, we obtain a fractional-differential stochastic equation of motion. After decades of statistical analysis of financial time series certain "stylized facts" have emerged, including the statistics of stock price fluctuations having "fat tails" and their linear correlations in time being exceedingly short lived. On the other hand, the magnitude of these fluctuations and other such measures of market volatility possess temporal correlations that decay as an inverse power law. One explanation of this long-term memory is that it is a consequence of the time-scale separation between "microscopic" and "macroscopic" economic variables. We propose a fractional Langevin equation as a dynamical model of the observed memory in financial time series.
Parametrizing linear generalized Langevin dynamics from explicit molecular dynamics simulations
Gottwald, Fabian; Karsten, Sven; Ivanov, Sergei D.; Kühn, Oliver
2015-06-01
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.
Parametrizing linear generalized Langevin dynamics from explicit molecular dynamics simulations
Gottwald, Fabian; Karsten, Sven; Ivanov, Sergei D., E-mail: sergei.ivanov@uni-rostock.de; Kühn, Oliver [Institute of Physics, Rostock University, Universitätsplatz 3, 18055 Rostock (Germany)
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.
Boltzmann-Langevin one-body dynamics for fermionic systems
Napolitani P.
2012-07-01
Full Text Available A full implementation of the Boltzmann-Langevin equation for fermionic systems is introduced in a transport model for dissipative collisions among heavy nuclei. Fluctuations are injected in phase space and not, like in more conventional approaches, as a projection on suitable subspaces. The advantage of this model is to be specifically adapted to describe processes characterised by instabilities, like the formation of fragments from a hot nuclear system, and by dissipation, like the transparency in nucleus-nucleus collisions.
Entropy and enthalpy of polyelectrolyte complexation: Langevin dynamics simulations.
Ou, Zhaoyang; Muthukumar, M
2006-04-21
We report a systematic study by Langevin dynamics simulation on the energetics of complexation between two oppositely charged polyelectrolytes of same charge density in dilute solutions of a good solvent with counterions and salt ions explicitly included. The enthalpy of polyelectrolyte complexation is quantified by comparisons of the Coulomb energy before and after complexation. The entropy of polyelectrolyte complexation is determined directly from simulations and compared with that from a mean-field lattice model explicitly accounting for counterion adsorption. At weak Coulomb interaction strengths, e.g., in solvents of high dielectric constant or with weakly charged polyelectrolytes, complexation is driven by a negative enthalpy due to electrostatic attraction between two oppositely charged chains, with counterion release entropy playing only a subsidiary role. In the strong interaction regime, complexation is driven by a large counterion release entropy and opposed by a positive enthalpy change. The addition of salt reduces the enthalpy of polyelectrolyte complexation by screening electrostatic interaction at all Coulomb interaction strengths. The counterion release entropy also decreases in the presence of salt, but the reduction only becomes significant at higher Coulomb interaction strengths. More significantly, in the range of Coulomb interaction strengths appropriate for highly charged polymers in aqueous solutions, complexation enthalpy depends weakly on salt concentration and counterion release entropy exhibits a large variation as a function of salt concentration. Our study quantitatively establishes that polyelectrolyte complexation in highly charged Coulomb systems is of entropic origin.
Study of dissipative dynamics in fission of hot nuclei using Langevin equation
Chaudhuri, G
2004-01-01
The fission of highly excited compound nuclei formed in heavy ion induced fusion reactions has emerged as a topic of considerable interest in the recent years. Dissipative dynamical models based on the Langevin equation were developed and were applied successfully for fission dynamics of highly excited heavy nuclei. However, Wall Friction(WF), the standard version of nuclear friction when incorporated in the Langevin dynamical model was not able to reproduce simultaneously experimental data for both prescission neutron multiplicity and fission probability. Consequently, an empirical reduction in the strength of the wall friction was found necessary to reproduce the experimental numbers by many workers. Interestingly, a modification of the wall friction was proposed recently where the reduction was achieved microscopically. This modified version is known as the chaos weighted wall friction(CWWF) which takes into account non-integrability of single particle motion. The work in my thesis aims at using this stron...
Langevin dynamics of financial systems: A second-order analysis
Canessa, E.
2001-07-01
We address the issue of stock market fluctuations within Langevin Dynamics (LD) and the thermodynamics definitions of multifractality in order to study its second-order characterization given by the analogous specific heat Cq, where q is an analogous temperature relating the moments of the generating partition function for the financial data signals. Due to non-linear and additive noise terms within the LD, we found that Cq can display a shoulder to the right of its main peak as also found in the S&P500 historical data which may resemble a classical phase transition at a critical point.
Correlations in a generalized elastic model: fractional Langevin equation approach.
Taloni, Alessandro; Chechkin, Aleksei; Klafter, Joseph
2010-12-01
The generalized elastic model (GEM) provides the evolution equation which governs the stochastic motion of several many-body systems in nature, such as polymers, membranes, and growing interfaces. On the other hand a probe (tracer) particle in these systems performs a fractional Brownian motion due to the spatial interactions with the other system's components. The tracer's anomalous dynamics can be described by a fractional Langevin equation (FLE) with a space-time correlated noise. We demonstrate that the description given in terms of GEM coincides with that furnished by the relative FLE, by showing that the correlation functions of the stochastic field obtained within the FLE framework agree with the corresponding quantities calculated from the GEM. Furthermore we show that the Fox H -function formalism appears to be very convenient to describe the correlation properties within the FLE approach.
Langevin equation model of dispersion in the convective boundary layer
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
Hamilton dynamics for the Lefschetz thimble integration akin to the complex Langevin method
Fukushima, Kenji
2015-01-01
The Lefschetz thimble method, i.e., the integration along the steepest descent cycles, is an idea to evade the sign problem by complexifying the theory. We discuss that such steepest descent cycles can be identified as ground-state wave-functions of a supersymmetric Hamilton dynamics, which is described with a framework akin to the complex Langevin method. We numerically construct the wave-functions on a grid using a toy model and confirm their well-localized behavior.
Bifurcation dynamics of the tempered fractional Langevin equation
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.
Bifurcation dynamics of the tempered fractional Langevin equation.
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.
Bifurcation dynamics of the tempered fractional Langevin equation
Zeng, Caibin, E-mail: macbzeng@scut.edu.cn; Yang, Qigui, E-mail: qgyang@scut.edu.cn [School of Mathematics, South China University of Technology, Guangzhou 510640 (China); Chen, YangQuan, E-mail: ychen53@ucmerced.edu [MESA LAB, School of Engineering, University of California, Merced, 5200 N. Lake Road, Merced, California 95343 (United States)
2016-08-15
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.
Recovering hidden dynamical modes from the generalized Langevin equation
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.
Bifurcations in Boltzmann–Langevin one body dynamics for fermionic systems
Napolitani, P., E-mail: napolita@ipno.in2p3.fr [IPN, CNRS/IN2P3, Université Paris-Sud 11, 91406 Orsay cedex (France); Colonna, M. [INFN-LNS, Laboratori Nazionali del Sud, 95123 Catania (Italy)
2013-10-07
We investigate the occurrence of bifurcations in the dynamical trajectories depicting central nuclear collisions at Fermi energies. The quantitative description of the reaction dynamics is obtained within a new transport model, based on the solution of the Boltzmann–Langevin equation in three dimensions, with a broad applicability for dissipative fermionic dynamics. Dilute systems formed in central collisions are shown to fluctuate between two energetically favourable mechanisms: reverting to a compact shape or rather disintegrating into several fragments. The latter result can be connected to the recent observation of bimodal distributions for quantities characterising fragmentation processes and may suggest new investigations.
From generalized Langevin equations to Brownian dynamics and embedded Brownian dynamics
Ma, Lina; Li, Xiantao; Liu, Chun
2016-09-01
We present the reduction of generalized Langevin equations to a coordinate-only stochastic model, which in its exact form involves a forcing term with memory and a general Gaussian noise. It will be shown that a similar fluctuation-dissipation theorem still holds at this level. We study the approximation by the typical Brownian dynamics as a first approximation. Our numerical test indicates how the intrinsic frequency of the kernel function influences the accuracy of this approximation. In the case when such an approximate is inadequate, further approximations can be derived by embedding the nonlocal model into an extended dynamics without memory. By imposing noises in the auxiliary variables, we show how the second fluctuation-dissipation theorem is still exactly satisfied.
Pastorino, C; Kreer, T; Müller, M; Binder, K
2007-08-01
In this work we compare and characterize the behavior of Langevin and dissipative particle dynamics (DPD) thermostats in a broad range of nonequilibrium simulations of polymeric systems. Polymer brushes in relative sliding motion, polymeric liquids in Poiseuille and Couette flows, and brush-melt interfaces are used as model systems to analyze the efficiency and limitations of different Langevin and DPD thermostat implementations. Widely used coarse-grained bead-spring models under good and poor solvent conditions are employed to assess the effects of the thermostats. We considered equilibrium, transient, and steady state examples for testing the ability of the thermostats to maintain constant temperature and to reproduce the underlying physical phenomena in nonequilibrium situations. The common practice of switching off the Langevin thermostat in the flow direction is also critically revisited. The efficiency of different weight functions for the DPD thermostat is quantitatively analyzed as a function of the solvent quality and the nonequilibrium situation.
Langevin dynamics for the chiral transition and DCC formation
Kroff, Daniel; Fraga, Eduardo S. [Universidade Federal do Rio de Janeiro (IF/UFRJ), RJ (Brazil). Inst. de Fisica
2011-07-01
Full text: The theory of the strong interactions allows for the formation of metastable exotic configurations of the vacuum. Such metastable states can, in principle, be produced in high-energy heavy ion collisions taking place in accelerators like the LHC and in cosmic rays in the atmosphere. In this work, we consider disoriented chiral condensates (DCC), treating them through an effective field theory - the linear-sigma model couple to quarks - and consider possible consequences for ultra-energetic cosmic ray observations performed by the Pierre Auger observatory. After a high-energy collision, the state of the system can be chirally rotated from its true vacuum orientation. Later, this disoriented state (DCC) will relax into the ordinary vacuum configuration, emitting pions. This leads to an asymmetry between charged and neutral pions. This is especially interesting in the context of cosmic rays, where the primary collision in the atmosphere presents favorable conditions for the formation of DCCs. Such exotics might be related to the Centauro and Anti-Centauro events observed by Lattes and collaborators in high-energy cosmic rays experiments. We consider the possibility of DCC formation during a first-order chiral transition, studying the order parameter evolution in a Langevin description. We analyse the DCC influence on the typical time scales of transition and also calculate the pion production rate. (author)
A simulation method of combinding boundary element method with generalized Langevin dynamics
无
2000-01-01
A new simulation approach to incorporate hydration force into generalized Langevin dynamics (GLD) is developed in this note. The hydration force determined by the boundary element method (BEM) is taken into account as the mean force terms of solvent including Coulombic interactions with the induced surface charge and the surface pressure of solvent. The exponential model is taken for the friction kernel. A simulation study has been performed on the cyclic undecapeptide cyclosporin A (CPA). The results obtained from the new method (GLDBEM) have been analyzed and compared with that obtained from the molecular dynamics (MD) simulation and the conventional stochastic dynamics (SD) simulation. We have found that the results obtained from GLDBEM show the obvious improvement over the SD simulation technique in the study of molecular structure and dynamic properties.
Scaling of Langevin and molecular dynamics persistence times of nonhomogeneous fluids.
Olivares-Rivas, Wilmer; Colmenares, Pedro J
2012-01-01
The existing solution for the Langevin equation of an anisotropic fluid allowed the evaluation of the position-dependent perpendicular and parallel diffusion coefficients, using molecular dynamics data. However, the time scale of the Langevin dynamics and molecular dynamics are different and an ansatz for the persistence probability relaxation time was needed. Here we show how the solution for the average persistence probability obtained from the backward Smoluchowski-Fokker-Planck equation (SE), associated to the Langevin dynamics, scales with the corresponding molecular dynamics quantity. Our SE perpendicular persistence time is evaluated in terms of simple integrals over the equilibrium local density. When properly scaled by the perpendicular diffusion coefficient, it gives a good match with that obtained from molecular dynamics.
Mücke, Tanja A; Milan, Patrick; Peinke, Joachim
2015-01-01
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...
Dynamic arrest within the self-consistent generalized Langevin equation of colloid dynamics.
Yeomans-Reyna, L; Chávez-Rojo, M A; Ramírez-González, P E; Juárez-Maldonado, R; Chávez-Páez, M; Medina-Noyola, M
2007-10-01
This paper presents a recently developed theory of colloid dynamics as an alternative approach to the description of phenomena of dynamic arrest in monodisperse colloidal systems. Such theory, referred to as the self-consistent generalized Langevin equation (SCGLE) theory, was devised to describe the tracer and collective diffusion properties of colloidal dispersions in the short- and intermediate-time regimes. Its self-consistent character, however, introduces a nonlinear dynamic feedback, leading to the prediction of dynamic arrest in these systems, similar to that exhibited by the well-established mode coupling theory of the ideal glass transition. The full numerical solution of this self-consistent theory provides in principle a route to the location of the fluid-glass transition in the space of macroscopic parameters of the system, given the interparticle forces (i.e., a nonequilibrium analog of the statistical-thermodynamic prediction of an equilibrium phase diagram). In this paper we focus on the derivation from the same self-consistent theory of the more straightforward route to the location of the fluid-glass transition boundary, consisting of the equation for the nonergodic parameters, whose nonzero values are the signature of the glass state. This allows us to decide if a system, at given macroscopic conditions, is in an ergodic or in a dynamically arrested state, given the microscopic interactions, which enter only through the static structure factor. We present a selection of results that illustrate the concrete application of our theory to model colloidal systems. This involves the comparison of the predictions of our theory with available experimental data for the nonergodic parameters of model dispersions with hard-sphere and with screened Coulomb interactions.
Langevin dynamics of the deconfinement transition for pure gauge theory
Fraga, E S; Krein, G; Fraga, Eduardo S.; Mizher, Ana J\\'ulia; Krein, Gast\\~ao
2007-01-01
We investigate the effects of dissipation in the deconfinement transition for pure SU(2) and SU(3) gauge theories. Using an effective theory for the order parameter, we study its Langevin evolution numerically. Noise effects are included for the case of SU(2). We find that both dissipation and noise have dramatic effects on the spinodal decomposition of the order parameter and delay considerably its thermalization. For SU(3) the effects of dissipation are even larger than for SU(2).
Langevin dynamics of the deconfinement transition for pure gauge theory
Mizher, Ana Júlia; Fraga, Eduardo S.; Krein, Gastão Inácio [UNESP
2006-01-01
We investigate the effects of dissipation in the deconfinement transition for pure SU(2) and SU(3) gauge theories. Using an effective theory for the order parameter, we study its Langevin evolution numerically. Noise effects are included for the case of SU(2). We find that both dissipation and noise have dramatic effects on the spinodal decomposition of the order parameter and delay considerably its thermalization. For SU(3) the effects of dissipation are even larger than for SU(2).
Langevin dynamics of the deconfinement transition for pure gauge theory
Mizher, Ana Julia; Fraga, Eduardo S. [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil). Inst. de Fisica; Krein, Gastao [Universidade Estadual Paulista (UNESP), Sao Paulo, SP (Brazil). Inst. de Fisica Teorica
2007-06-15
We investigate the effects of dissipation in the deconfinement transition for pure SU(2) and SU(3) gauge theories. Using an effective theory for the order parameter, we study its Langevin evolution numerically. Noise effects are included for the case of SU(2). We find that both dissipation and noise have dramatic effects on the spinodal decomposition of the order parameter and delay considerably its thermalization. For SU(3) the effects of dissipation are even larger than for SU(2). (author)
Accelerating the convergence of path integral dynamics with a generalized Langevin equation.
Ceriotti, Michele; Manolopoulos, David E; Parrinello, Michele
2011-02-28
The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that zero-point energy effects can be included comparatively cheaply in simulations of harmonic and quasiharmonic systems by augmenting classical molecular dynamics with a generalized Langevin equation (GLE). Here we describe how a similar approach can be used to accelerate the convergence of path integral (PI) molecular dynamics to the exact quantum mechanical result in more strongly anharmonic systems exhibiting both zero point energy and tunnelling effects. The resulting PI-GLE method is illustrated with applications to a double-well tunnelling problem and to liquid water.
Majka, M.; Góra, P. F.
2016-10-01
While the origins of temporal correlations in Langevin dynamics have been thoroughly researched, the understanding of spatially correlated noise (SCN) is rather incomplete. In particular, very little is known about the relation between friction and SCN. In this article, starting from the microscopic, deterministic model, we derive the analytical formula for the spatial correlation function in the particle-bath interactions. This expression shows that SCN is the inherent component of binary mixtures, originating from the effective (entropic) interactions. Further, employing this spatial correlation function, we postulate the thermodynamically consistent Langevin equation driven by the Gaussian SCN and calculate the adequate fluctuation-dissipation relation. The thermodynamical consistency is achieved by introducing the spatially variant friction coefficient, which can be also derived analytically. This coefficient exhibits a number of intriguing properties, e.g., the singular behavior for certain types of interactions. Eventually, we apply this new theory to the system of two charged particles in the presence of counter-ions. Such particles interact via the screened-charge Yukawa potential and the inclusion of SCN leads to the emergence of the anomalous frictionless regime. In this regime the particles can experience active propulsion leading to the transient attraction effect. This effect suggests a nonequilibrium mechanism facilitating the molecular binding of the like-charged particles.
Some properties of the Langevin model for dispersion
De Baas, A.F.
1988-01-01
The Langevin Equation is used to describe dispersion of pollutants in the atmosphere. The theoretical background for the equation is discussed in length and a review on previous treatments and applications is given. It is shown that the Langevin equation can describe dispersion in complex circumstan
Generalized elastic model yields a fractional Langevin equation description.
Taloni, Alessandro; Chechkin, Aleksei; Klafter, Joseph
2010-04-23
Starting from a generalized elastic model which accounts for the stochastic motion of several physical systems such as membranes, (semi)flexible polymers, and fluctuating interfaces among others, we derive the fractional Langevin equation (FLE) for a probe particle in such systems, in the case of thermal initial conditions. We show that this FLE is the only one fulfilling the fluctuation-dissipation relation within a new family of fractional Brownian motion equations. The FLE for the time-dependent fluctuations of the donor-acceptor distance in a protein is shown to be recovered. When the system starts from nonthermal conditions, the corresponding FLE, which does not fulfill the fluctuation-dissipation relation, is derived.
A strong diffusive ion mode in dense ionized matter predicted by Langevin dynamics.
Mabey, P; Richardson, S; White, T G; Fletcher, L B; Glenzer, S H; Hartley, N J; Vorberger, J; Gericke, D O; Gregori, G
2017-01-30
The state and evolution of planets, brown dwarfs and neutron star crusts is determined by the properties of dense and compressed matter. Due to the inherent difficulties in modelling strongly coupled plasmas, however, current predictions of transport coefficients differ by orders of magnitude. Collective modes are a prominent feature, whose spectra may serve as an important tool to validate theoretical predictions for dense matter. With recent advances in free electron laser technology, X-rays with small enough bandwidth have become available, allowing the investigation of the low-frequency ion modes in dense matter. Here, we present numerical predictions for these ion modes and demonstrate significant changes to their strength and dispersion if dissipative processes are included by Langevin dynamics. Notably, a strong diffusive mode around zero frequency arises, which is not present, or much weaker, in standard simulations. Our results have profound consequences in the interpretation of transport coefficients in dense plasmas.
A simple and accurate algorithm for path integral molecular dynamics with the Langevin thermostat
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.
A simple and accurate algorithm for path integral molecular dynamics with the Langevin thermostat.
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.
Sanghi, T; Aluru, N R
2013-03-28
In this work, we combine our earlier proposed empirical potential based quasi-continuum theory, (EQT) [A. V. Raghunathan, J. H. Park, and N. R. Aluru, J. Chem. Phys. 127, 174701 (2007)], which is a coarse-grained multiscale framework to predict the static structure of confined fluids, with a phenomenological Langevin equation to simulate the dynamics of confined fluids in thermal equilibrium. An attractive feature of this approach is that all the input parameters to the Langevin equation (mean force profile of the confined fluid and the static friction coefficient) can be determined using the outputs of the EQT and the self-diffusivity data of the corresponding bulk fluid. The potential of mean force profile, which is a direct output from EQT is used to compute the mean force profile of the confined fluid. The density profile, which is also a direct output from EQT, along with the self-diffusivity data of the bulk fluid is used to determine the static friction coefficient of the confined fluid. We use this approach to compute the mean square displacement and survival probabilities of some important fluids such as carbon-dioxide, water, and Lennard-Jones argon confined inside slit pores. The predictions from the model are compared with those obtained using molecular dynamics simulations. This approach of combining EQT with a phenomenological Langevin equation provides a mathematically simple and computationally efficient means to study the impact of structural inhomogeneity on the self-diffusion dynamics of confined fluids.
Notes on the Langevin model for turbulent diffusion of ``marked`` particles
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.
Mass-energy distribution of fragments in Langevin dynamics of fission induced by heavy ions
Vanin D. V.
2012-12-01
Full Text Available Four-dimensional Langevin equation was employed to calculate mass-energy distributions of fission fragments of highly excited compound nuclei. The research took into account not only three shape collective coordinates introduced on the basis of {c,h,α}-parametrization but also orientation degree of freedom (K-state— spin about the symmetry axis. Overdamped Langevin equation was used to describe the evolution of the K-state. Friction tensor was calculated using the “wall+window” model of the modified one-body dissipation mechanism with a reduction coeffcient from the “wall” formula ks. The calculations have been performed with ks = 0:25 and ks = 1:0. To learn more about the role of the dissipation effects the calculations have also been done with use of the chaoticity measure of nucleon movements in the nuclear shape configuration as ks parameter. Calculations were performed for the large number of compound nuclei with Z2/A parameter in the range 21 ≤ Z2/A ≤ 44. The goal was to study the mass-energy distributions not only for heavy nuclei but also for light nuclei close to the Businaro-Gallone point. Mass-energy distributions and variances of the mass fragments are well reproduced in the applied calculations for all considered compound nuclei. It was shown that inclusion of the K-state in the dynamical model produces considerable increase of the mass and energy variances. Inclusion of the chaoticity measure to the friction tensor provides a better agreement with the experiment results on mass variances.
Exact series model of Langevin transducers with internal losses.
Nishamol, P A; Ebenezer, D D
2014-03-01
An exact series method is presented to analyze classical Langevin transducers with arbitrary boundary conditions. The transducers consist of an axially polarized piezoelectric solid cylinder sandwiched between two elastic solid cylinders. All three cylinders are of the same diameter. The length to diameter ratio is arbitrary. Complex piezoelectric and elastic coefficients are used to model internal losses. Solutions to the exact linearized governing equations for each cylinder include four series. Each term in each series is an exact solution to the governing equations. Bessel and trigonometric functions that form complete and orthogonal sets in the radial and axial directions, respectively, are used in the series. Asymmetric transducers and boundary conditions are modeled by using axially symmetric and anti-symmetric sets of functions. All interface and boundary conditions are satisfied in a weighted-average sense. The computed input electrical admittance, displacement, and stress in transducers are presented in tables and figures, and are in very good agreement with those obtained using atila-a finite element package for the analysis of sonar transducers. For all the transducers considered in the analysis, the maximum difference between the first three resonance frequencies calculated using the present method and atila is less than 0.03%.
Molecular Dynamics, Monte Carlo Simulations, and Langevin Dynamics: A Computational Review
Eric Paquet
2015-01-01
Full Text Available Macromolecular structures, such as neuraminidases, hemagglutinins, and monoclonal antibodies, are not rigid entities. Rather, they are characterised by their flexibility, which is the result of the interaction and collective motion of their constituent atoms. This conformational diversity has a significant impact on their physicochemical and biological properties. Among these are their structural stability, the transport of ions through the M2 channel, drug resistance, macromolecular docking, binding energy, and rational epitope design. To assess these properties and to calculate the associated thermodynamical observables, the conformational space must be efficiently sampled and the dynamic of the constituent atoms must be simulated. This paper presents algorithms and techniques that address the abovementioned issues. To this end, a computational review of molecular dynamics, Monte Carlo simulations, Langevin dynamics, and free energy calculation is presented. The exposition is made from first principles to promote a better understanding of the potentialities, limitations, applications, and interrelations of these computational methods.
Langevin Formalism as the Basis for the Unification of Population Dynamics
de Vladar, Harold P.
2005-03-01
We are presenting a simple reformulation to population dynamics that generalizes many growth functions. The reformulation consists of two equations, one for population size, and one for the growth rate. The model shows that even when a population is density-dependent the dynamics of its growth rate does not depend explicitly neither on population size nor on the carrying capacity. Actually, the growth rate is uncoupled from the population size equation. The model has only two parameters: a Malthusian parameter ρ and an interaction coefficient θ. Distinct values of these parameters reproduce the family of θ-logistics, the van Bertalanffy, Gompertz and Potential Growth equations, among other possibilities. Stochastic perturbations to the Malthusian parameter leads to a Langevin form of stochastic differential equation consisting of a family of cubic potentials perturbed with multiplicative noise. Using these equtions, we derive the stationary Fokker Plank distribution which which shows that in the stationary dynamics, density dependent populations fluctuate around a mean size that is shifted from the carrying capacity proportionally to the noise intensity. We also study which kinds of populations are susceptible to noise induced transitions.
Bernoulli-Langevin Wind Speed Model for Simulation of Storm Events
Fürstenau, Norbert; Mittendorf, Monika
2016-12-01
We present a simple nonlinear dynamics Langevin model for predicting the instationary wind speed profile during storm events typically accompanying extreme low-pressure situations. It is based on a second-degree Bernoulli equation with δ-correlated Gaussian noise and may complement stationary stochastic wind models. Transition between increasing and decreasing wind speed and (quasi) stationary normal wind and storm states are induced by the sign change of the controlling time-dependent rate parameter k(t). This approach corresponds to the simplified nonlinear laser dynamics for the incoherent to coherent transition of light emission that can be understood by a phase transition analogy within equilibrium thermodynamics [H. Haken, Synergetics, 3rd ed., Springer, Berlin, Heidelberg, New York 1983/2004.]. Evidence for the nonlinear dynamics two-state approach is generated by fitting of two historical wind speed profiles (low-pressure situations "Xaver" and "Christian", 2013) taken from Meteorological Terminal Air Report weather data, with a logistic approximation (i.e. constant rate coefficients k) to the solution of our dynamical model using a sum of sigmoid functions. The analytical solution of our dynamical two-state Bernoulli equation as obtained with a sinusoidal rate ansatz k(t) of period T (=storm duration) exhibits reasonable agreement with the logistic fit to the empirical data. Noise parameter estimates of speed fluctuations are derived from empirical fit residuals and by means of a stationary solution of the corresponding Fokker-Planck equation. Numerical simulations with the Bernoulli-Langevin equation demonstrate the potential for stochastic wind speed profile modeling and predictive filtering under extreme storm events that is suggested for applications in anticipative air traffic management.
Constant pressure and temperature discrete-time Langevin molecular dynamics.
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.
Quantum corrected Langevin dynamics for adsorbates on metal surfaces interacting with hot electrons
Olsen, Thomas; Schiøtz, Jakob
2010-01-01
quantum mechanical probabilities from the classical phase space distributions resulting from the dynamics. At short time scales, classical and quasiclassical initial conditions lead to wrong results and only correctly quantized initial conditions give a close agreement with an inherently quantum......We investigate the importance of including quantized initial conditions in Langevin dynamics for adsorbates interacting with a thermal reservoir of electrons. For quadratic potentials the time evolution is exactly described by a classical Langevin equation and it is shown how to rigorously obtain...... mechanical master equation approach. With CO on Cu(100) as an example, we demonstrate the effect for a system with ab initio frictional tensor and potential energy surfaces and show that quantizing the initial conditions can have a large impact on both the desorption probability and the distribution...
Complex Langevin in Lattice QCD: dynamic stabilisation and the phase diagram
Aarts, Gert; Jäger, Benjamin; Sexty, Dénes
2016-01-01
Complex Langevin simulations provide an alternative to sample path integrals with complex weights and therefore are suited to determine the phase diagram of QCD from first principles. We use our proposed method of Dynamic Stabilisation (DS) to ensure improved convergence to the right limit and present new systematic tests of this technique. We also show results on QCD in the limit of heavy quarks and an analysis of DS compared to known results from reweighting.
Langevin equation with fluctuating diffusivity: A two-state model.
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.
Isothermal Langevin dynamics in systems with power-law spatially dependent friction.
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 c1, 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.
Copperman, J; Guenza, M G
2015-07-23
We utilize a multiscale approach where molecular dynamic simulations are performed to obtain quantitative structural averages used as input to a coarse-grained Langevin equation for protein dynamics, which can be solved analytically. The approach describes proteins as fundamentally semiflexible objects collapsed into the free energy well representing the folded state. The normal-mode analytical solution to this Langevin equation naturally separates into global modes describing the fully anisotropic tumbling of the macromolecule as a whole and internal modes which describe local fluctuations about the folded structure. Complexity in the configurational free-energy landscape of the macromolecule leads to a renormalization of the internal modes, while the global modes provide a basis set in which the dipolar orientation and global anisotropy can be accounted for when comparing to experiments. This simple approach predicts the dynamics of both global rotational diffusion and internal motion from the picosecond to the nanosecond regime and is quantitative when compared to time correlation functions calculated from molecular dynamic simulations and in good agreement with nuclear magnetic resonance relaxation experiments. Fundamental to this approach is the inclusion of internal dissipation, which is absent in any rigid-body hydrodynamical modeling scheme.
Critical scaling in hidden state inference for linear Langevin dynamics
Bravi, Barbara; Sollich, Peter
2016-01-01
We consider the problem of inferring the dynamics of unknown (i.e. hidden) nodes from a set of observed trajectories and we study analytically the average prediction error given by the Extended Plefka Expansion applied to it, as presented in [1]. We focus on a stochastic linear dynamics of continuous degrees of freedom interacting via random Gaussian couplings in the infinite network size limit. The expected error on the hidden time courses can be found as the equal-time hidden-to-hidden cova...
Kawai, Shinnosuke; Komatsuzaki, Tamiki
2010-12-21
A framework recently developed for the extraction of a dynamic reaction coordinate to mediate reactions buried in a multidimensional Langevin equation is extended to the generalized Langevin equations without a priori assumption of the forms of the potential (in general, nonlinearly coupled systems) and the friction kernel. The equation of motion with memory effect can be transformed into an equation without memory at the cost of an increase in the dimensionality of the system, and hence the theoretical framework developed for the (nonlinear) Langevin formulation can be generalized to the non-Markovian process with colored noise. It is found that the increased dimension can be physically interpreted as effective modes of the fluctuating environment. As an illustrative example, we apply this theory to a multidimensional generalized Langevin equation for motion on the Müller-Brown potential surface with an exponential friction kernel. Numerical simulations find a boundary between the highly reactive region and the less reactive region in the space of initial conditions. The location of the boundary is found to depend significantly on both the memory kernel and the nonlinear couplings. The theory extracts a reaction coordinate whose sign determines the fate of the reaction taking into account thermally fluctuating environments, memory effect, and nonlinearities. It is found that the location of the boundary of reactivity is satisfactorily reproduced as the zero of the statistical average of the new reaction coordinate, which is an analytical functional of both the original position coordinates and velocities of the system, and of the properties of the environment.
Langevin equation with colored noise for constant-temperature molecular dynamics simulations.
Ceriotti, Michele; Bussi, Giovanni; Parrinello, Michele
2009-01-16
We discuss the use of a Langevin equation with a colored (correlated) noise to perform constant-temperature molecular dynamics. Since the equations of motion are linear in nature, it is easy to predict the response of a Hamiltonian system to such a thermostat and to tune at will the relaxation time of modes of different frequency. This allows one to optimize the time needed for equilibration and to generate independent configurations. We show how this frequency-dependent response can be exploited to control the temperature of Car-Parrinello-like dynamics without affecting the adiabatic separation of the electronic degrees of freedom from the vibrations of the ions.
Dynamics of protein-protein encounter: a Langevin equation approach with reaction patches.
Schluttig, Jakob; Alamanova, Denitsa; Helms, Volkhard; Schwarz, Ulrich S
2008-10-21
We study the formation of protein-protein encounter complexes with a Langevin equation approach that considers direct, steric, and thermal forces. As three model systems with distinctly different properties we consider the pairs barnase:barstar, cytochrome c-cytochrome c peroxidase, and p53:MDM2. In each case, proteins are modeled either as spherical particles, as dipolar spheres, or as collection of several small beads with one dipole. Spherical reaction patches are placed on the model proteins according to the known experimental structures of the protein complexes. In the computer simulations, concentration is varied by changing box size. Encounter is defined as overlap of the reaction patches and the corresponding first passage times are recorded together with the number of unsuccessful contacts before encounter. We find that encounter frequency scales linearly with protein concentration, thus proving that our microscopic model results in a well-defined macroscopic encounter rate. The number of unsuccessful contacts before encounter decreases with increasing encounter rate and ranges from 20 to 9000. For all three models, encounter rates are obtained within one order of magnitude of the experimentally measured association rates. Electrostatic steering enhances association up to 50-fold. If diffusional encounter is dominant (p53:MDM2) or similarly important as electrostatic steering (barnase:barstar), then encounter rate decreases with decreasing patch radius. More detailed modeling of protein shapes decreases encounter rates by 5%-95%. Our study shows how generic principles of protein-protein association are modulated by molecular features of the systems under consideration. Moreover it allows us to assess different coarse-graining strategies for the future modeling of the dynamics of large protein complexes.
Event Driven Langevin simulations of Hard Spheres
Scala, Antonio
2011-01-01
The blossoming of interest in colloids and nano-particles has given renewed impulse to the study of hard-body systems. In particular, hard spheres have become a real test system for theories and experiments. It is therefore necessary to study the complex dynamics of such systems in presence of a solvent; disregarding hydrodynamic interactions, the simplest model is the Langevin equation. Unfortunately, standard algorithms for the numerical integration of the Langevin equation require that interactions are slowly varying during an integration timestep. This in not the case for hard-body systems, where there is no clearcut between the correlation time of the noise and the timescale of the interactions. Starting first from a splitting of the Fokker-Plank operator associated with the Langevin dynamics, and then from an approximation of the two-body Green's function, we introduce and test two new algorithms for the simulation of the Langevin dynamics of hard-spheres.
C. S. Leung; J. Y. Wei; T. Harko; Z. Kovacs
2011-03-01
In this paper, we introduce a simplified model for explaining the observations of optical intra-day variability (IDV) of the BL Lac Objects. We assume that the source of the IDV are the stochastic oscillations of an accretion disk around a supermassive black hole. The stochastic fluctuations on the vertical direction of the accretion disk are described by using a Langevin type equation with a damping term and a random, white noise type force. Furthermore, preliminary numerical simulation results are presented, which are based on the numerical analysis of the Langevin stochastic differential equation.
A simple model for Brownian motion leading to the Langevin equation
Grooth, de Bart G.
1999-01-01
A simple one-dimensional model is presented for the motion of a Brownian particle. It is shown how the collisions between a Brownian particle and its surrounding molecules lead to the Langevin equation, the power spectrum of the stochastic force, and the equipartition of kinetic energy.
Langevin equation for the extended Rayleigh model with an asymmetric bath.
Plyukhin, Alexander V; Schofield, Jeremy
2004-02-01
In this paper a one-dimensional model of two infinite gases separated by a movable heavy piston is considered. The nonlinear Langevin equation for the motion of the piston is derived from first principles for the case when the thermodynamic parameters and/or the molecular masses of gas particles on the left and right sides of the piston are different. Microscopic expressions involving time correlation functions of the force between bath particles and the piston are obtained for all parameters appearing in the nonlinear Langevin equation. It is demonstrated that the equation has stationary solutions corresponding to directional fluctuation-induced drift in the absence of systematic forces. In the case of ideal gases interacting with the piston via a quadratic repulsive potential, the model is exactly solvable and explicit expressions for the kinetic coefficients in the nonlinear Langevin equation are derived. The transient solution of the nonlinear Langevin equation is analyzed perturbatively and it is demonstrated that previously obtained results for systems with the hard-wall interaction are recovered.
Liu Jian; Wang Hai-Yan; Bao Jing-Dong
2013-01-01
A minimal system-plus-reservoir model yielding a nonergodic Langevin equation is proposed,which originates from the cubic-spectral density of environmental oscillators and momentum-dependent coupling.This model allows ballistic diffusion and classical localization simultaneously,in which the fluctuation-dissipation relation is still satisfied but the Khinchin theorem is broken.The asymptotical equilibrium for a nonergodic system requires the initial thermal equilibrium,however,when the system starts from nonthermal conditions,it does not approach the equilibration even though a nonlinear potential is used to bound the particle,this can be confirmed by the zeroth law of thermodynamics.In the dynamics of Brownian localization,due to the memory damping function inducing a constant term,our results show that the stationary distribution of the system depends on its initial preparation of coordinate rather than momentum.The coupled oscillator chain with a fixed end boundary acts as a heat bath,which has long been used in studies of collinear atom/solid-surface scattering and lattice vibration,we investigate this problem from the viewpoint of nonergodicity.
Bashir Ahmad
2010-01-01
Full Text Available We study a Dirichlet boundary value problem for Langevin equation involving two fractional orders. Langevin equation has been widely used to describe the evolution of physical phenomena in fluctuating environments. However, ordinary Langevin equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical processes in a fractal medium, numerous generalizations of Langevin equation have been proposed. One such generalization replaces the ordinary derivative by a fractional derivative in the Langevin equation. This gives rise to the fractional Langevin equation with a single index. Recently, a new type of Langevin equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index. The contraction mapping principle and Krasnoselskii's fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space.
Lázaro-Lázaro, Edilio; Mendoza-Méndez, Patricia; Elizondo-Aguilera, Luis Fernando; Perera-Burgos, Jorge Adrián; Ramírez-González, Pedro Ezequiel; Pérez-Ángel, Gabriel; Castañeda-Priego, Ramón; Medina-Noyola, Magdaleno
2017-05-01
A fundamental challenge of the theory of liquids is to understand the similarities and differences in the macroscopic dynamics of both colloidal and atomic liquids, which originate in the (Newtonian or Brownian) nature of the microscopic motion of their constituents. Starting from the recently discovered long-time dynamic equivalence between a colloidal and an atomic liquid that share the same interparticle pair potential, in this work we develop a self-consistent generalized Langevin equation theory for the dynamics of equilibrium multicomponent atomic liquids, applicable as an approximate but quantitative theory describing the long-time diffusive dynamical properties of simple equilibrium atomic liquids. When complemented with a Gaussian-like approximation, this theory is also able to provide a reasonable representation of the passage from a ballistic to diffusive behavior. We illustrate the applicability of the resulting theory with three particular examples, namely, a monodisperse and a polydisperse monocomponent hard-sphere liquid and a highly size-asymmetric binary hard-sphere mixture. To assess the quantitative accuracy of our results, we perform event-driven molecular dynamics simulations, which corroborate the general features of the theoretical predictions.
General Laser Intensity Langevin Equation in a Single-Mode Laser Model
KE Sheng-Zhi; CAO Li; WU Da-Jin; YAO Kai-Lun
2001-01-01
A two-dimensional single-mode laser model is investigated, with cross-correlations between the real and imaginary parts of the quantum noise as well as the pump noise. The general closed form of the laser intensity Langevin equation (GILE) is obtained under a stable locked phase resulting from the cross-correlation λq between the real and imaginary parts of the quantum noise. Because of the presence of a new term containing λq, we can unify the two opposite intensity Langevin equations which correspond to the two special cases for ｜λq｜ → 0 and ｜λq｜ → 1 in the GILE. It is expected that the transient and stationary properties of the laser model can be changed qualitatively when λq varies.
Nadtochy, P. N.; Ryabov, E. G.; Cheredov, A. V.; Adeev, G. D.
2016-10-01
A stochastic approach based on four-dimensional Langevin fission dynamics is applied to the calculation of a wide set of experimental observables of excited compound nuclei from 199Pb to 248Cf formed in reactions induced by heavy ions. In the model under investigation, the tilting degree of freedom ( K coordinate) representing the projection of the total angular momentum onto the symmetry axis of the nucleus is taken into account in addition to three collective shape coordinates introduced on the basis of {c,h,α} parametrization. The evolution of the K coordinate is described by means of the Langevin equation in the overdamped regime. The friction tensor for the shape collective coordinates is calculated under the assumption of the modified version of the one-body dissipation mechanism, where the reduction coefficient ks of the contribution from the "wall" formula is introduced. The calculations are performed both for the constant values of the coefficient ks and for the coordinate-dependent reduction coefficient ks(q) which is found on the basis of the "chaos-weighted wall formula". Different possibilities of the deformation-dependent dissipation coefficient (γK) for the K coordinate are investigated. The presented results demonstrate that an impact of the ks and γK parameters on the calculated observable fission characteristics can be selectively probed. It was found that it is possible to describe the experimental data consistently with the deformation-dependent γK(q) coefficient for shapes featuring a neck, which predicts quite small values of γK=0.0077 (MeV zs)-1/2 and constant γK=0.1-0.4 (MeV zs)-1/2 for compact shapes featuring no neck.
PSPICE controlled-source models of analogous circuit for Langevin type piezoelectric transducer
2007-01-01
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.
PSPICE controlled-source models of analogous circuit for Langevin type piezoelectric transducer
CHEN YeongChin; WU MenqJiun; LIU WeiKuo
2007-01-01
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.
Shen, Tonghao; Su, Neil Qiang; Wu, Anan; Xu, Xin
2014-03-05
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.
The Langevin Approach: An R Package for Modeling Markov Processes
Philip Rinn
2016-08-01
Full Text Available We describe an 'R' package developed by the research group 'Turbulence, Wind energy' 'and Stochastics' (TWiSt at the Carl von Ossietzky University of Oldenburg, which extracts the (stochastic evolution equation underlying a set of data or measurements. The method can be directly applied to data sets with one or two stochastic variables. Examples for the one-dimensional and two-dimensional cases are provided. This framework is valid under a small set of conditions which are explicitly presented and which imply simple preliminary test procedures to the data. For Markovian processes involving Gaussian white noise, a stochastic differential equation is derived straightforwardly from the time series and captures the full dynamical properties of the underlying process. Still, even in the case such conditions are not fulfilled, there are alternative versions of this method which we discuss briefly and provide the user with the necessary bibliography.
The Langevin Approach: An R Package for Modeling Markov Processes
Rinn, Philip; Wächter, Matthias; Peinke, Joachim
2016-01-01
We describe an R package developed by the research group Turbulence, Wind energy and Stochastics (TWiSt) at the Carl von Ossietzky University of Oldenburg, which extracts the (stochastic) evolution equation underlying a set of data or measurements. The method can be directly applied to data sets with one or two stochastic variables. Examples for the one-dimensional and two-dimensional cases are provided. This framework is valid under a small set of conditions which are explicitly presented and which imply simple preliminary test procedures to the data. For Markovian processes involving Gaussian white noise, a stochastic differential equation is derived straightforwardly from the time series and captures the full dynamical properties of the underlying process. Still, even in the case such conditions are not fulfilled, there are alternative versions of this method which we discuss briefly and provide the user with the necessary bibliography.
Modeling near-barrier collisions of heavy ions based on a Langevin-type approach
Karpov, A. V.; Saiko, V. V.
2017-08-01
Background: Multinucleon transfer in low-energy nucleus-nucleus collisions is proposed as a method of production of yet-unknown neutron-rich nuclei hardly reachable by other methods. Purpose: Modeling of dynamics of nuclear reactions induced by heavy ions in their full complexity of competing reaction channels remains to be a challenging task. The work is aimed at development of such a model and its application to the analysis of multinucleon transfer in deep inelastic collisions of heavy ions leading, in particular, to formation of neutron-rich isotopes in the vicinity of the N =126 shell closure. Method: Multidimensional dynamical model of nucleus-nucleus collisions based on the Langevin equations has been proposed. It is combined with a statistical model for simulation of de-excitation of primary reaction fragments. The model provides a continuous description of the system evolution starting from the well-separated target and projectile in the entrance channel of the reaction up to the formation of final reaction products. Results: A rather complete set of experimental data available for reactions 136Xe+198Pt,208Pb,209Bi was analyzed within the developed model. The model parameters have been determined. The calculated energy, mass, charge, and angular distributions of reaction products, their various correlations as well as cross sections for production of specific isotopes agree well with the data. On this basis, optimal experimental conditions for synthesizing the neutron-rich nuclei in the vicinity of the N =126 shell were formulated and the corresponding cross sections were predicted. Conclusions: The production yields of neutron-rich nuclei with N =126 weakly depend on the incident energy. At the same time, the corresponding angular distributions are strongly energy dependent. They are peaked at grazing angles for larger energies and extend up to the forward angles at low near-barrier collision energies. The corresponding cross sections exceed 100 nb for
Sule, N; Rice, S A; Gray, S K; Scherer, N F
2015-11-16
Understanding the formation of electrodynamically interacting assemblies of metal nanoparticles requires accurate computational methods for determining the forces and propagating trajectories. However, since computation of electromagnetic forces occurs on attosecond to femtosecond timescales, simulating the motion of colloidal nanoparticles on milliseconds to seconds timescales is a challenging multi-scale computational problem. Here, we present a computational technique for performing accurate simulations of laser-illuminated metal nanoparticles. In the simulation, we self-consistently combine the finite-difference time-domain method for electrodynamics (ED) with Langevin dynamics (LD) for the particle motions. We demonstrate the ED-LD method by calculating the 3D trajectories of a single 100-nm-diameter Ag nanoparticle and optical trapping and optical binding of two and three 150-nm-diameter Ag nanoparticles in simulated optical tweezers. We show that surface charge on the colloidal metal nanoparticles plays an important role in their optically driven self-organization. In fact, these simulations provide a more complete understanding of the assembly of different structures of two and three Ag nanoparticles that have been observed experimentally, demonstrating that the ED-LD method will be a very useful tool for understanding the self-organization of optical matter.
A Langevin dynamics simulation study of the tribology of polymer loop brushes.
Yin, Fang; Bedrov, Dmitry; Smith, Grant D; Kilbey, S Michael
2007-08-28
The tribology of surfaces modified with doubly bound polymer chains (loops) has been investigated in good solvent conditions using Langevin dynamics simulations. The density profiles, brush interpenetration, chain inclination, normal forces, and shear forces for two flat substrates modified by doubly bound bead-necklace polymers and equivalent singly bound polymers (twice as many polymer chains of 12 the molecular weight of the loop chains) were determined and compared as a function of surface separation, grafting density, and shear velocity. The doubly bound polymer layers showed less interpenetration with decreasing separation than the equivalent singly bound layers. Surprisingly, this difference in interpenetration between doubly bound polymer and singly bound polymer did not result in decreased friction at high shear velocity possibly due to the decreased ability of the doubly bound chains to deform in response to the applied shear. However, at lower shear velocity, where deformation of the chains in the flow direction is less pronounced and the difference in interpenetration is greater between the doubly bound and singly bound chains, some reduction in friction was observed.
Examination of isospin effects in multi-dimensional Langevin fission dynamics
Nadtochy, P.N., E-mail: nadtochy@na.infn.i [Istituto Nazionale di Fisica Nucleare, Universita di Napoli ' Federico II' , Via Cinthia, 80126 Napoli (Italy); Vardaci, E.; Di Nitto, A.; Brondi, A.; La Rana, G.; Moro, R. [Istituto Nazionale di Fisica Nucleare, Universita di Napoli ' Federico II' , Via Cinthia, 80126 Napoli (Italy); Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' , Via Cinthia, 80126 Napoli (Italy); Cinausero, M.; Prete, G. [Laboratori Nazionali di Legnaro dell' Istituto Nazionale di Fisica Nucleare, Legnaro (Padova) (Italy); Gelli, N.; Lucarelli, F. [Istituto Nazionale di Fisica Nucleare and Dipartimento di Fisica, Firenze (Italy)
2010-03-08
One-dimensional and three-dimensional dynamical fission calculations based on Langevin equations are performed for the compound nuclei {sup 194}Pb, {sup 200}Pb, {sup 206}Pb, {sup 182}Hg, and {sup 204}Hg to investigate the influence of the compound nucleus isospin on the prescission particle multiplicities and on the fission fragment mass-energy distribution. It is found that the prescission neutron, proton, and alpha particle multiplicities have approximately the same sensitivity to the dissipation strength for a given nucleus. This is at variance with conclusions of recent papers. The sensitivity of the calculated prescission particle multiplicities to the dissipation strength becomes higher with decreasing isospin of fissioning compound nucleus, and the increase of prescission particle multiplicities could reach 200%, when the reduction coefficient of one-body viscosity k{sub s} increases from 0.1 to 1, for the most neutron deficient nuclei considered. The variances of fission fragment mass and kinetic energy distributions are less sensitive to the change of dissipation strength than the prescission light particle multiplicities. A comparison to experimental data concerning {sup 200}Pb nucleus is also presented.
Finite-Temperature Non-equilibrium Quasicontinuum Method based on Langevin Dynamics
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.
Popov, Alexander V; Hernandez, Rigoberto
2013-09-01
Kawai and Komatsuzaki [J. Chem. Phys. 134, 114523 (2011)] recently derived the nonequilibrium generalized Langevin equation (GLE) for a nonstationary system using the projection operator technique. In the limit when the environment is slowly changing (that is, a quasi-equilibrium bath), it should reduce to the irreversible GLE approach (iGLE) [J. Chem. Phys. 111, 7701 (1999)]. Kawai and Komatsuzaki, however, found that the driven harmonic oscillator, an example of a nonequilibrium system does not obey the iGLE presumably because it did not quite satisfy the limiting conditions of the latter. Notwithstanding the lack of a massive quasi-equilibrium bath (one of the conditions under which the iGLE had been derived earlier), we found that the temperature-driven iGLE (T-iGLE) [J. Chem. Phys. 126, 244506 (2007)] can reproduce the nonequilibrium dynamics of a driven dissipated pair of harmonic oscillators. It requires a choice of the function representing the coupling between the oscillator coordinate and the bath and shows that the T-iGLE representation is consistent with the projection operator formalism if only dominant bath modes are taken into account. Moreover, we also show that the more readily applicable phenomenological iGLE model is recoverable from the Kawai and Komatsuzaki model beyond the adiabatic limit used in the original T-iGLE theory.
Langevin dynamics for vector variables driven by multiplicative white noise: A functional formalism.
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.
Mouhat, Félix; Sorella, Sandro; Vuilleumier, Rodolphe; Saitta, Antonino Marco; Casula, Michele
2017-06-13
We introduce a novel approach for a fully quantum description of coupled electron-ion systems from first principles. It combines the variational quantum Monte Carlo solution of the electronic part with the path integral formalism for the quantum nuclear dynamics. On the one hand, the path integral molecular dynamics includes nuclear quantum effects by adding a set of fictitious classical particles (beads) aimed at reproducing nuclear quantum fluctuations via a harmonic kinetic term. On the other hand, variational quantum Monte Carlo can provide Born-Oppenheimer potential energy surfaces with a precision comparable to the most-advanced post-Hartree-Fock approaches, and with a favorable scaling with the system size. In order to cope with the intrinsic noise due to the stochastic nature of quantum Monte Carlo methods, we generalize the path integral molecular dynamics using a Langevin thermostat correlated according to the covariance matrix of quantum Monte Carlo nuclear forces. The variational parameters of the quantum Monte Carlo wave function are evolved during the nuclear dynamics, such that the Born-Oppenheimer potential energy surface is unbiased. Statistical errors on the wave function parameters are reduced by resorting to bead grouping average, which we show to be accurate and well-controlled. Our general algorithm relies on a Trotter breakup between the dynamics driven by ionic forces and the one set by the harmonic interbead couplings. The latter is exactly integrated, even in the presence of the Langevin thermostat, thanks to the mapping onto an Ornstein-Uhlenbeck process. This framework turns out to be also very efficient in the case of noiseless (deterministic) ionic forces. The new implementation is validated on the Zundel ion (H5O2(+)) by direct comparison with standard path integral Langevin dynamics calculations made with a coupled cluster potential energy surface. Nuclear quantum effects are confirmed to be dominant over thermal effects well beyond
Quasirelativistic Langevin equation.
Plyukhin, A V
2013-11-01
We address the problem of a microscopic derivation of the Langevin equation for a weakly relativistic Brownian particle. A noncovariant Hamiltonian model is adopted, in which the free motion of particles is described relativistically while their interaction is treated classically, i.e., by means of action-to-a-distance interaction potentials. Relativistic corrections to the classical Langevin equation emerge as nonlinear dissipation terms and originate from the nonlinear dependence of the relativistic velocity on momentum. On the other hand, similar nonlinear dissipation forces also appear as classical (nonrelativistic) corrections to the weak-coupling approximation. It is shown that these classical corrections, which are usually ignored in phenomenological models, may be of the same order of magnitude, if not larger than, relativistic ones. The interplay of relativistic corrections and classical beyond-the-weak-coupling contributions determines the sign of the leading nonlinear dissipation term in the Langevin equation and thus is qualitatively important.
Relativistic Brownian motion: from a microscopic binary collision model to the Langevin equation.
Dunkel, Jörn; Hänggi, Peter
2006-11-01
The Langevin equation (LE) for the one-dimensional relativistic Brownian motion is derived from a microscopic collision model. The model assumes that a heavy pointlike Brownian particle interacts with the lighter heat bath particles via elastic hard-core collisions. First, the commonly known, nonrelativistic LE is deduced from this model, by taking into account the nonrelativistic conservation laws for momentum and kinetic energy. Subsequently, this procedure is generalized to the relativistic case. There, it is found that the relativistic stochastic force is still delta correlated (white noise) but no longer corresponds to a Gaussian white noise process. Explicit results for the friction and momentum-space diffusion coefficients are presented and discussed.
Bettencourt, L M A
2001-01-01
I consider several Langevin and Fokker-Planck classes of dynamics for scalar field theories in contact with a thermal bath at temperature T. These models have been applied recently in the numerical description of the dynamics of second order phase transitions and associated topological defect formation as well as in other studies of these critical phenomena. Closed form solutions of the Fokker-Planck equation are given for the harmonic potential and a dynamical mean-field approximation is developed. These methods allow for an analytical discussion of the behavior of the theories in several circumstances of interest such as critical slowing down at a second order transition and the development of spinodal instabilities. These insights allow for a more detailed understanding of several numerical studies in the literature.
Wen, Kai; Sakata, Fumihiko; Li, Zhu-Xia; Wu, Xi-Zhen; Zhang, Ying-Xun; Zhou, Shan-Gui
2013-07-05
Macroscopic parameters as well as precise information on the random force characterizing the Langevin-type description of the nuclear fusion process around the Coulomb barrier are extracted from the microscopic dynamics of individual nucleons by exploiting the numerical simulation of the improved quantum molecular dynamics. It turns out that the dissipation dynamics of the relative motion between two fusing nuclei is caused by a non-Gaussian distribution of the random force. We find that the friction coefficient as well as the time correlation function of the random force takes particularly large values in a region a little bit inside of the Coulomb barrier. A clear non-Markovian effect is observed in the time correlation function of the random force. It is further shown that an emergent dynamics of the fusion process can be described by the generalized Langevin equation with memory effects by appropriately incorporating the microscopic information of individual nucleons through the random force and its time correlation function.
Complex Langevin Dynamics in 1+1d QCD at Non-Zero Densities
Schmalzbauer, Sebastian
2016-01-01
We present our results obtained from gauge cooled complex Langevin simulations in 1+1d QCD at non-zero densities in the strong coupling regime with unrooted staggered fermions. For small quark masses there are regions of the chemical potential where this method fails to reproduce correct results. In these parameter ranges we studied the effect of different gauge cooling schemes on the distributions of the fermion determinant as well as of observables.
Internal noise-driven generalized Langevin equation from a nonlocal continuum model.
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.
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.
Sharma, A. S.; Setty, V. A.
2015-12-01
Multiscale fluctuations in large and complex data are usually characterized by a power law with a scaling exponent but many systems require more than one exponent and thus exhibit crossover behavior. The scaling exponents, such as Hurst exponents, represent the nature of correlation in the system and the crossover shows the presence of more than one type of correlation. An accurate characterization of the crossover behavior is thus needed for a better understanding of the inherent correlations in the system, and is an important method of Big Data analysis. A multi-step process is developed for accurate computation of the crossover behavior. First the detrended fluctuation analysis is used to remove the trends in the data and the scaling exponents are computed. The crossover point is then computed by a Hyperbolic regression technique, with no prior assumptions. The time series data of the magnetic field variations during substorms in the Earth's magnetosphere is analyzed with these techniques and yields a crossover behavior with a time scale of ~4 hrs. A Langevin model derived from the data provides an excellent fit to the crossover in the scaling exponents and a good model of magnetospheric dynamics. The combination of fluctuation analysis and mathematical modeling thus yields a comprehensive approach in the analysis of Big Data.
Fodor, Z; Sexty, D; Török, C
2015-01-01
We study lattice QCD at non-vanishing chemical potential using the complex Langevin equation. We compare the results with multi-parameter reweighting both from $\\mu=0$ and phase quenched ensembles. We find a good agreement for lattice spacings below $\\approx$0.15 fm. On coarser lattices the complex Langevin approach breaks down. Four flavors of staggered fermions are used on $N_t=4, 6$ and 8 lattices. For one ensemble we also use two flavors to investigate the effects of rooting.
Supersymmetric Langevin equation to explore free-energy landscapes.
Mossa, Alessandro; Clementi, Cecilia
2007-04-01
The recently discovered supersymmetric generalizations of the Langevin dynamics and Kramers equation can be utilized for the exploration of free-energy landscapes of systems whose large time-scale separation hampers the usefulness of standard molecular dynamics techniques. The first realistic application is here presented. The system chosen is a minimalist model for a short alanine peptide exhibiting a helix-coil transition.
On complex Langevin dynamics and zeroes of the measure II: Fermionic determinant
Aarts, G; Sexty, D; Stamatescu, I -O
2016-01-01
Lattice QCD at non-vanishing chemical potential is studied using the complex Langevin equation (CLE). One of the conditions for the correctness of the results of the CLE is that the zeroes of the measure coming from the fermionic determinant are outside of the distribution of the configurations, or at least in a region where support for the distribution is very much suppressed. We investigate this issue for Heavy Dense QCD (HDQCD) and full QCD at high temperatures. In HDQCD it is found that the configurations move closest to the zeroes of the measure around the critical chemical potential of the onset transition, where the sign problem is diminished, but results remain largely unaffected. In full QCD at high temperatures the investigation of the spectrum of the Dirac operator yields a similar observation: the results are unaffected by the issue of the poles.
Reeves, Daniel B., E-mail: dbr@Dartmouth.edu [Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755 (United States); Weaver, John B. [Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755 (United States); Department of Radiology, Geisel School of Medicine, Hanover, New Hampshire 03755 (United States)
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.
Kong, Wei; Yang, Fang; Liu, Songfen; Shi, Feng
2016-10-01
A Langevin dynamics simulation method is used to study the two-dimensional (2D) equilibrium structure of complex plasmas while considering an external magnetic field. The traditional Yukawa potential and a modified Yukawa potential according to Shukla et al. [Phys. Lett. A 291, 413 (2001); Shukla and Mendonca, Phys. Scr. T113 82 (2004)] and Salimullah et al. [Phys. Plasmas 10, 3047 (2003)] respectively, are employed to account for the interaction of the charged dust particles. It is found that the collisions between neutral gas and charged dust particles have minor effects on the 2D equilibrium structure of the system. Based on the modified Yukawa potential, studies on the 2D equilibrium structure show that the traditional Yukawa potential is still suitable for describing the magnetized complex plasmas, even if the shielding distance of charged dust particles is affected by the strong external magnetic field.
Numerical simulation of the fractional Langevin equation
Guo Peng
2012-01-01
Full Text Available In this paper, we study the fractional Langevin equation, whose derivative is in Caputo sense. By using the derived numerical algorithm, we obtain the displacement and the mean square displacement which describe the dynamic behaviors of the fractional Langevin equation.
Data-driven parameterization of the generalized Langevin equation
Lei, Huan; Baker, Nathan A.; Li, Xiantao
2016-11-29
We present a data-driven approach to determine the memory kernel and random noise of the generalized Langevin equation. To facilitate practical implementations, we parameterize the kernel function in the Laplace domain by a rational function, with coefficients directly linked to the equilibrium statistics of the coarse-grain variables. Further, we show that such an approximation can be constructed to arbitrarily high order. Within these approximations, the generalized Langevin dynamics can be embedded in an extended stochastic model without memory. We demonstrate how to introduce the stochastic noise so that the fluctuation-dissipation theorem is exactly satisfied.
Turchenkov, D A; Boronovskiĭ, S E; Nartsissov, Ia R
2013-01-01
Changes in the state of the central nervous system, leading to the development of pathological processes, are directly associated with a state of neurons, particularly with their conductivity in synaptic cleft region. The synaptic flexibility plays a key role in environmental adaptation, which manifests in dynamic changes of synaptic properties. However more attention was paid rather to their functional, than physical-chemical properties. We present the results of simulation of potential determining ions in synaptic contact area using Langevin dynamics. Diffusion and self-diffusion coefficients were calculated. It is shown that the range of variability of the diffusion coefficient of ions in perimembrane space, caused by variable viscosity and dielectric conductivity of electrolyte can reach 20%. These physical-chemical synaptic parameters can be considered as relevant for synaptic flexibility.
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.
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.
Inferring hidden states in Langevin dynamics on large networks: Average case performance
Bravi, B.; Opper, M.; Sollich, P.
2017-01-01
We present average performance results for dynamical inference problems in large networks, where a set of nodes is hidden while the time trajectories of the others are observed. Examples of this scenario can occur in signal transduction and gene regulation networks. We focus on the linear stochastic dynamics of continuous variables interacting via random Gaussian couplings of generic symmetry. We analyze the inference error, given by the variance of the posterior distribution over hidden paths, in the thermodynamic limit and as a function of the system parameters and the ratio α between the number of hidden and observed nodes. By applying Kalman filter recursions we find that the posterior dynamics is governed by an "effective" drift that incorporates the effect of the observations. We present two approaches for characterizing the posterior variance that allow us to tackle, respectively, equilibrium and nonequilibrium dynamics. The first appeals to Random Matrix Theory and reveals average spectral properties of the inference error and typical posterior relaxation times; the second is based on dynamical functionals and yields the inference error as the solution of an algebraic equation.
Panja, D.
2010-01-01
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 tagge
Reactive Boundary Conditions as Limits of Interaction Potentials for Brownian and Langevin Dynamics
Chapman, S Jonathan; Isaacson, Samuel A
2015-01-01
A popular approach to modeling bimolecular reactions between diffusing molecules is through the use of reactive boundary conditions. One common model is the Smoluchowski partial absorption condition, which uses a Robin boundary condition in the separation coordinate between two possible reactants. This boundary condition can be interpreted as an idealization of a reactive interaction potential model, in which a potential barrier must be surmounted before reactions can occur. In this work we show how the reactive boundary condition arises as the limit of an interaction potential encoding a steep barrier within a shrinking region in the particle separation, where molecules react instantly upon reaching the peak of the barrier. The limiting boundary condition is derived by the method of matched asymptotic expansions, and shown to depend critically on the relative rate of increase of the barrier height as the width of the potential is decreased. Limiting boundary conditions for the same interaction potential in b...
The Langevin Limit of the Nosé-Hoover-Langevin Thermostat
Frank, J.E.; Gottwald, G.A.
2011-01-01
In this note we study the asymptotic limit of large variance in a stochastically perturbed thermostat model, the Nos\\'{e}-Hoover-Langevin device. We show that in this limit, the model reduces to a Langevin equation with one-dimensional Wiener process, and that the perturbation is in the direction of
The Langevin limit of the Nosé-Hoover-Langevin thermostat
Frank, J.; Gottwald, G.A.
2011-01-01
In this note we study the asymptotic limit of large variance in a stochastically perturbed thermostat model, the Nosé-Hoover-Langevin device. We show that in this limit, the model reduces to a Langevin equation with one-dimensional Wiener process, and that the perturbation is in the direction of the
Vortex polarity in 2-D magnetic dots by Langevin dynamics simulations
Depondt, Ph., E-mail: depondt@insp.jussieu.f [Institut des NanoSciences de Paris, Universite Pierre et Marie Curie, UMR 7588 CNRS, 75252 Paris Cedex 05 (France); Levy, J.-C.S., E-mail: jean-claude.levy@univ-paris-diderot.f [Materiaux et Phenomenes Quantiques, Universite Denis Diderot, UMR 7162 CNRS, 75013 Paris (France); Mertens, F.G., E-mail: franz.mertens@uni-bayreuth.d [Physikalisches Institut, Universitaet Bayreuth, D-95440 Bayreuth (Germany)
2011-01-17
Two-dimensional magnetic plots of finite size were simulated by integrating the Landau-Lifshitz equation for the isotropic Heisenberg model with a systematic exploration of the effect of dipole-dipole interactions of various strengths d, at a low temperature. Structures with or without vortices are observed, and in the cases in which vortices are present, out-of-plane contributions show only for relatively weak dipolar strengths: the integrated intensity of the out-of-plane component decreases roughly as 1/d with increasing dipolar strength while the vortex core width decreases as d{sup -1/2}. The coexistence of several vortices with an out-of-plane component seems limited to a narrow d-range, at least for the sample sizes studied. The size limit below which the vortices disappear decreases roughly as 1/d.
Roy, Dibyendu
2008-06-01
Through an exact analysis using quantum Langevin dynamics, we demonstrate the crossover from ballistic to diffusive thermal transport in a harmonic chain with each site connected to Ohmic heat reservoirs. The temperatures of the two heat baths at the boundaries are specified from the beginning, whereas the temperatures of the interior heat reservoirs are determined self-consistently by demanding that in the steady state, on average, there is no heat current between any such (self-consistent) reservoir and the harmonic chain. The essence of our study is that the effective mean free path separating the ballistic regime of transport from the diffusive one emerges naturally.
Relativistic Langevin equation for runaway electrons
Mier, J. A.; Martin-Solis, J. R.; Sanchez, R.
2016-10-01
The Langevin approach to the kinetics of a collisional plasma is developed for relativistic electrons such as runaway electrons in tokamak plasmas. In this work, we consider Coulomb collisions between very fast, relativistic electrons and a relatively cool, thermal background plasma. The model is developed using the stochastic equivalence of the Fokker-Planck and Langevin equations. The resulting Langevin model equation for relativistic electrons is an stochastic differential equation, amenable to numerical simulations by means of Monte-Carlo type codes. Results of the simulations will be presented and compared with the non-relativistic Langevin equation for RE electrons used in the past. Supported by MINECO (Spain), Projects ENE2012-31753, ENE2015-66444-R.
Baczewski, Andrew D
2013-01-01
Generalized Langevin dynamics (GLD) arise in the modeling of a number of systems, ranging from structured fluids that exhibit a viscoelastic mechanical response, to biological systems, and other media that exhibit anomalous diffusive phenomena. Molecular dynamics (MD) simulations that include GLD in conjunction with external and/or pairwise forces require the development of numerical integrators that are efficient, stable, and have known convergence properties. In this article, we derive a family of extended variable integrators for the Generalized Langevin equation (GLE) with a positive Prony series memory kernel. Using stability and error analysis, we identify a superlative choice of parameters and implement the corresponding numerical algorithm in the LAMMPS MD software package. Salient features of the algorithm include exact conservation of the first and second moments of the equilibrium velocity distribution in some important cases, stable behavior in the limit of conventional Langevin dynamics, and the ...
Nuclear fission problem and Langevin equation
M Sakhaee
2011-12-01
Full Text Available A combined dynamical and statistical model for fission was employed in our calculation. There is no doubt that a Langevin description plus a Monte Carlo treatment of the evaporation processes provide the most adequate dynamical description. In this paper, we would consider a strongly shaped dependent friction force and we use the numerical method rather than the analytical one. The objective of this article is to calculate the time dependent fission widths of the 224Th nucleus. The fission widths were calculated with both chaos-weighted wall friction (CWWF and wall friction (WF dissipations. The calculations are repeated for 100000 trajectories. The result was compared to the others' work. We use nuclear elongation coordinate with time and it is necessary to repeat the small steps many times to improve the accuracy.
Critical exponent of the fractional Langevin equation.
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.
An adaptive stepsize method for the chemical Langevin equation.
Ilie, Silvana; Teslya, Alexandra
2012-05-14
Mathematical and computational modeling are key tools in analyzing important biological processes in cells and living organisms. In particular, stochastic models are essential to accurately describe the cellular dynamics, when the assumption of the thermodynamic limit can no longer be applied. However, stochastic models are computationally much more challenging than the traditional deterministic models. Moreover, many biochemical systems arising in applications have multiple time-scales, which lead to mathematical stiffness. In this paper we investigate the numerical solution of a stochastic continuous model of well-stirred biochemical systems, the chemical Langevin equation. The chemical Langevin equation is a stochastic differential equation with multiplicative, non-commutative noise. We propose an adaptive stepsize algorithm for approximating the solution of models of biochemical systems in the Langevin regime, with small noise, based on estimates of the local error. The underlying numerical method is the Milstein scheme. The proposed adaptive method is tested on several examples arising in applications and it is shown to have improved efficiency and accuracy compared to the existing fixed stepsize schemes.
Phase-space geometry of the generalized Langevin equation.
Bartsch, Thomas
2009-09-28
The generalized Langevin equation is widely used to model the influence of a heat bath upon a reactive system. This equation will here be studied from a geometric point of view. A dynamical phase space that represents all possible states of the system will be constructed, the generalized Langevin equation will be formally rewritten as a pair of coupled ordinary differential equations, and the fundamental geometric structures in phase space will be described. It will be shown that the phase space itself and its geometric structure depend critically on the preparation of the system: A system that is assumed to have been in existence forever has a larger phase space with a simpler structure than a system that is prepared at a finite time. These differences persist even in the long-time limit, where one might expect the details of preparation to become irrelevant.
Data-driven parameterization of the generalized Langevin equation.
Lei, Huan; Baker, Nathan A; Li, Xiantao
2016-12-13
We present a data-driven approach to determine the memory kernel and random noise in generalized Langevin equations. To facilitate practical implementations, we parameterize the kernel function in the Laplace domain by a rational function, with coefficients directly linked to the equilibrium statistics of the coarse-grain variables. We show that such an approximation can be constructed to arbitrarily high order and the resulting generalized Langevin dynamics can be embedded in an extended stochastic model without explicit memory. We demonstrate how to introduce the stochastic noise so that the second fluctuation-dissipation theorem is exactly satisfied. Results from several numerical tests are presented to demonstrate the effectiveness of the proposed method.
Data-driven parameterization of the generalized Langevin equation
Lei, Huan; Li, Xiantao
2016-01-01
We present a data-driven approach to determine the memory kernel and random noise in generalized Langevin equations. To facilitate practical implementations, we parameterize the kernel function in the Laplace domain by a rational function, with coefficients directly linked to the equilibrium statistics of the coarse-grain variables. We show that such an approximation can be constructed to arbitrarily high order and the resulting generalized Langevin dynamics can be embedded in an extended stochastic model without explicit memory. We demonstrate how to introduce the stochastic noise so that the second fluctuation-dissipation theorem is exactly satisfied. Results from several numerical tests are presented to demonstrate the effectiveness of the proposed method.
Kawai, Shinnosuke; Komatsuzaki, Tamiki
2009-12-14
We present a novel theory which enables us to explore the mechanism of reaction selectivity and robust functions in complex systems persisting under thermal fluctuation. The theory constructs a nonlinear coordinate transformation so that the equation of motion for the new reaction coordinate is independent of the other nonreactive coordinates in the presence of thermal fluctuation. In this article we suppose that reacting systems subject to thermal noise are described by a multidimensional Langevin equation without a priori assumption for the form of potential. The reaction coordinate is composed not only of all the coordinates and velocities associated with the system (solute) but also of the random force exerted by the environment (solvent) with friction constants. The sign of the reaction coordinate at any instantaneous moment in the region of a saddle determines the fate of the reaction, i.e., whether the reaction will proceed through to the products or go back to the reactants. By assuming the statistical properties of the random force, one can know a priori a well-defined boundary of the reaction which separates the full position-velocity space in the saddle region into mainly reactive and mainly nonreactive regions even under thermal fluctuation. The analytical expression of the reaction coordinate provides the firm foundation on the mechanism of how and why reaction proceeds in thermal fluctuating environments.
Manufactured Turbulence with Langevin equations
Mishra, Aashwin
2016-01-01
By definition, Manufactured turbulence(MT) is purported to mimic physical turbulence rather than model it. The MT equations are constrained to be simple to solve and provide an inexpensive surrogate to Navier-Stokes based Direct Numerical Simulations (DNS) for use in engineering applications or theoretical analyses. In this article, we investigate one approach in which the linear inviscid aspects of MT are derived from a linear approximation of the Navier-Stokes equations while the non-linear and viscous physics are approximated via stochastic modeling. The ensuing Langevin MT equations are used to compute planar, quadratic turbulent flows. While much work needs to be done, the preliminary results appear promising.
Langevin Monte Carlo filtering for target tracking
Iglesias Garcia, Fernando; Bocquel, Melanie; Driessen, Hans
2015-01-01
This paper introduces the Langevin Monte Carlo Filter (LMCF), a particle filter with a Markov chain Monte Carlo algorithm which draws proposals by simulating Hamiltonian dynamics. This approach is well suited to non-linear filtering problems in high dimensional state spaces where the bootstrap filte
From shape to randomness: A classification of Langevin stochasticity
Eliazar, Iddo; Cohen, Morrel H.
2013-01-01
The Langevin equation-perhaps the most elemental stochastic differential equation in the physical sciences-describes the dynamics of a random motion driven simultaneously by a deterministic potential field and by a stochastic white noise. The Langevin equation is, in effect, a mechanism that maps the stochastic white-noise input to a stochastic output: a stationary steady state distribution in the case of potential wells, and a transient extremum distribution in the case of potential gradients. In this paper we explore the degree of randomness of the Langevin equation’s stochastic output, and classify it à la Mandelbrot into five states of randomness ranging from “infra-mild” to “ultra-wild”. We establish closed-form and highly implementable analytic results that determine the randomness of the Langevin equation’s stochastic output-based on the shape of the Langevin equation’s potential field.
Langevin equation path integral ground state.
Constable, Steve; Schmidt, Matthew; Ing, Christopher; Zeng, Tao; Roy, Pierre-Nicholas
2013-08-15
We propose a Langevin equation path integral ground state (LePIGS) approach for the calculation of ground state (zero temperature) properties of molecular systems. The approach is based on a modification of the finite temperature path integral Langevin equation (PILE) method (J. Chem. Phys. 2010, 133, 124104) to the case of open Feynman paths. Such open paths are necessary for a ground state formulation. We illustrate the applicability of the method using model systems and the weakly bound water-parahydrogen dimer. We show that the method can lead to converged zero point energies and structural properties.
Fluctuation theorems for total entropy production in generalized Langevin systems
Ghosh, Bappa; Chaudhury, Srabanti
2017-01-01
The validity of the fluctuation theorems for total entropy production of a colloidal particle embedded in a non-Markovian heat bath driven by a time-dependent force in a harmonic potential is probed here. The dynamics of the system is modeled by the generalized Langevin equation with colored noise. The distribution function of the total entropy production is calculated and the detailed fluctuation theorem contains a renormalized temperature term which arises due to the non-Markovian characteristics of the thermal bath.
Minier, J P; Chibbaro, S
2010-01-01
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, Physics Reports, Vol. 352/1-3, 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 analysed : the necessity to add an extra term in the equation for the velocity of the fluid seen in the case of twoway coupling, the theoretical and numerical evaluations of particle averages and the fulfilment of the particle mass-continuity constraint. The theoretical model is developed within the 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 (SDE) written in continuous time (Langevin equations) for the veloci...
Conditions for the validity of the quantum Langevin equation.
Frenkel, J; Taylor, J C
2012-01-01
From microscopic models, a Langevin equation can, in general, be derived only as an approximation. Two possible conditions to validate this approximation are studied. One is, for a linear Langevin equation, that the frequency of the Fourier transform should be close to the natural frequency of the system. The other is by the assumption of "slow" variables. We test this method by comparison with an exactly soluble model and point out its limitations. We base our discussion on two approaches. The first is a direct, elementary treatment of Senitzky. The second is via a generalized Langevin equation as an intermediate step.
vanVlimmeren, BAC; Fraaije, JGEM
1996-01-01
We present a simple method for the numerical calculation of the noise distribution in multicomponent functional Langevin models. The topic is of considerable importance, in view of the increased interest in the application of mesoscopic dynamics simulation models to phase separation of complex
Critical fluctuations and anomalous transport in soft Yukawa-Langevin systems.
Ratynskaia, S; Regnoli, G; Rypdal, K; Klumov, B; Morfill, G
2009-10-01
Simulation of a Langevin-dynamics model demonstrates emergence of critical fluctuations and anomalous grain transport which have been observed in experiments on "soft" quasi-two-dimensional dusty plasma clusters. Our model does not contain external drive or plasma interactions that serve to drive the system away from thermodynamic equilibrium. The grains are confined by an external potential, interact via static Yukawa forces, and are subject to stochastic heating and dissipation from neutrals. One remarkable feature is emergence of leptokurtic probability distributions of grain displacements xi(tau) on time scales tau tau(Delta). The latter is a signature of intermittency, here interpreted as a transition from bursty transport associated with hopping on intermediate time scales to vortical flows on longer time scales. These intermittency features are quantitatively modeled by a single-particle Itô-Langevin stochastic equation with a nonlinear drift term.
The complex chemical Langevin equation
Schnoerr, David [School of Biological Sciences, University of Edinburgh (United Kingdom); School of Informatics, University of Edinburgh (United Kingdom); Sanguinetti, Guido [School of Informatics, University of Edinburgh (United Kingdom); Grima, Ramon [School of Biological Sciences, University of Edinburgh (United Kingdom)
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.
The complex chemical Langevin equation.
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.
Langevin Simulation of Non-Uniform Granular Gases
张端明; 雷雅洁; 潘贵军; 郁伯铭
2003-01-01
We present and study a fractal model of a non-uniform granular system for the first time, based on which we numerically solve the dynamics actions in the system successfully in one-dimensional case. The multi-mixture is composed of N different particles, whose granularity distribution has the fractal characteristic. The particles are subject to inelastic mutual collisions and obey to Langevin equation between collisions. Far from the equilibrium,i.e. the given typical relaxation time T of the driving Brownian process is much larger than the mean collision time Tc, the results of simulation indicate that the degree of inhomogeneity in the granularity distribution signed by the fractal dimension D of size distribution has great influence on the dynamics actions of the system. The velocity distribution deviates obviously from the Gaussian distribution and the particles cluster more pronouncedly with the larger value of D in the system. The velocity distribution and spatial clusterization change with D are presented.
Self-consistent generalized Langevin equation for colloidal mixtures.
Chávez-Rojo, Marco Antonio; Medina-Noyola, Magdaleno
2005-09-01
A self-consistent theory of collective and tracer diffusion in colloidal mixtures is presented. This theory is based on exact results for the partial intermediate scattering functions derived within the framework of the generalized Langevin equation formalism, plus a number of conceptually simple and sensible approximations. The first of these consists of a Vineyard-like approximation between collective and tracer diffusion, which writes the collective dynamics in terms of the memory function related to tracer diffusion. The second consists of interpolating this only unknown memory function between its two exact limits at small and large wave vectors; for this, a phenomenologically determined, but not arbitrary, interpolating function is introduced: a Lorentzian with its inflection point located at the first minimum of the partial static structure factor. The small wave-vector exact limit involves a time-dependent friction function, for which we take a general approximate result, previously derived within the generalized Langevin equation formalism. This general result expresses the time-dependent friction function in terms of the partial intermediate scattering functions, thus closing the system of equations into a fully self-consistent scheme. This extends to mixtures a recently proposed self-consistent theory developed for monodisperse suspensions [Yeomans-Reyna and Medina-Noyola, Phys. Rev. E 64, 066114 (2001)]. As an illustration of its quantitative accuracy, its application to a simple model of a binary dispersion in the absence of hydrodynamic interactions is reported.
Baczewski, Andrew D; Bond, Stephen D
2013-07-28
Generalized Langevin dynamics (GLD) arise in the modeling of a number of systems, ranging from structured fluids that exhibit a viscoelastic mechanical response, to biological systems, and other media that exhibit anomalous diffusive phenomena. Molecular dynamics (MD) simulations that include GLD in conjunction with external and/or pairwise forces require the development of numerical integrators that are efficient, stable, and have known convergence properties. In this article, we derive a family of extended variable integrators for the Generalized Langevin equation with a positive Prony series memory kernel. Using stability and error analysis, we identify a superlative choice of parameters and implement the corresponding numerical algorithm in the LAMMPS MD software package. Salient features of the algorithm include exact conservation of the first and second moments of the equilibrium velocity distribution in some important cases, stable behavior in the limit of conventional Langevin dynamics, and the use of a convolution-free formalism that obviates the need for explicit storage of the time history of particle velocities. Capability is demonstrated with respect to accuracy in numerous canonical examples, stability in certain limits, and an exemplary application in which the effect of a harmonic confining potential is mapped onto a memory kernel.
Baczewski, Andrew D.; Bond, Stephen D.
2013-07-01
Generalized Langevin dynamics (GLD) arise in the modeling of a number of systems, ranging from structured fluids that exhibit a viscoelastic mechanical response, to biological systems, and other media that exhibit anomalous diffusive phenomena. Molecular dynamics (MD) simulations that include GLD in conjunction with external and/or pairwise forces require the development of numerical integrators that are efficient, stable, and have known convergence properties. In this article, we derive a family of extended variable integrators for the Generalized Langevin equation with a positive Prony series memory kernel. Using stability and error analysis, we identify a superlative choice of parameters and implement the corresponding numerical algorithm in the LAMMPS MD software package. Salient features of the algorithm include exact conservation of the first and second moments of the equilibrium velocity distribution in some important cases, stable behavior in the limit of conventional Langevin dynamics, and the use of a convolution-free formalism that obviates the need for explicit storage of the time history of particle velocities. Capability is demonstrated with respect to accuracy in numerous canonical examples, stability in certain limits, and an exemplary application in which the effect of a harmonic confining potential is mapped onto a memory kernel.
Variable time-stepping in the pathwise numerical solution of the chemical Langevin equation.
Ilie, Silvana
2012-12-21
Stochastic modeling is essential for an accurate description of the biochemical network dynamics at the level of a single cell. Biochemically reacting systems often evolve on multiple time-scales, thus their stochastic mathematical models manifest stiffness. Stochastic models which, in addition, are stiff and computationally very challenging, therefore the need for developing effective and accurate numerical methods for approximating their solution. An important stochastic model of well-stirred biochemical systems is the chemical Langevin Equation. The chemical Langevin equation is a system of stochastic differential equation with multidimensional non-commutative noise. This model is valid in the regime of large molecular populations, far from the thermodynamic limit. In this paper, we propose a variable time-stepping strategy for the numerical solution of a general chemical Langevin equation, which applies for any level of randomness in the system. Our variable stepsize method allows arbitrary values of the time-step. Numerical results on several models arising in applications show significant improvement in accuracy and efficiency of the proposed adaptive scheme over the existing methods, the strategies based on halving/doubling of the stepsize and the fixed step-size ones.
Particle-scale modelling of financial price dynamics
Liu, David
2017-02-01
This paper proposes a particle-based computational framework for modeling of financial price dynamics, which is an extension of the recent empirical work of Financial Brownian Particle (FBP), and discretizes and solves the Langevin equation that is the continuum representation of a financial market. The framework enables us to simulate the limit order book of the USD/JPY exchange rates. The research yields results that are in good agreement with the published empirical results. Our framework of modelling financial prices is of multidisciplinary nature, and can bridge the fields of empirical studies of financial order books, particle dynamics simulation, and modelling of financial market.
The Fractional Langevin Equation: Brownian Motion Revisited
Mainardi, Francesco
2008-01-01
We have revisited the Brownian motion on the basis of the fractional Langevin equation which turns out to be a particular case of the generalized Langevin equation introduced by Kubo on 1966. The importance of our approach is to model the Brownian motion more realistically than the usual one based on the classical Langevin equation, in that it takes into account also the retarding effects due to hydrodynamic backflow, i.e. the added mass and the Basset memory drag. On the basis of the two fluctuation-dissipation theorems and of the techniques of the Fractional Calculus we have provided the analytical expressions of the correlation functions (both for the random force and the particle velocity) and of the mean squared particle displacement. The random force has been shown to be represented by a superposition of the usual white noise with a "fractional" noise. The velocity correlation function is no longer expressed by a simple exponential but exhibits a slower decay, proportional to $t^{-3/2}$ as $t \\to \\infty...
Langevin simulation of scalar fields: Additive and multiplicative noises and lattice renormalization
Cassol-Seewald, N. C.; Farias, R. L. S.; Fraga, E. S.; Krein, G.; Ramos, Rudnei O.
2012-08-01
We consider the Langevin lattice dynamics for a spontaneously broken λϕ4 scalar field theory where both additive and multiplicative noise terms are incorporated. The lattice renormalization for the corresponding stochastic Ginzburg-Landau-Langevin and the subtleties related to the multiplicative noise are investigated.
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.
Reconstruction of the modified discrete Langevin equation from persistent time series.
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.
Brett, Tobias; Galla, Tobias
2013-06-21
We develop a systematic approach to the linear-noise approximation for stochastic reaction systems with distributed delays. Unlike most existing work our formalism does not rely on a master equation; instead it is based upon a dynamical generating functional describing the probability measure over all possible paths of the dynamics. We derive general expressions for the chemical Langevin equation for a broad class of non-Markovian systems with distributed delay. Exemplars of a model of gene regulation with delayed autoinhibition and a model of epidemic spread with delayed recovery provide evidence of the applicability of our results.
A Langevin equation approach to electron transfer reactions in the diabatic basis.
Song, XiaoGeng; Wang, Haobin; Van Voorhis, Troy
2008-10-14
A linear Langevin equation that governs the population dynamics of electron transfer reactions is derived. The noise in the Langevin equation is eliminated by treating the diabatic population fluctuations as the relevant variables, leaving only the memory kernel responsible for the population relaxation. Within the memory kernel, the diabatic coupling is treated perturbatively and a second order expansion is found to give a simple closed form expression for the kernel. The accuracy of the second order truncation is maximized by performing a fixed rotation of the diabatic electronic states that minimizes the first order free energy of the system and thus minimizes the effect of the perturbation on the thermodynamics. The resulting two-hop Langevin equation (THLE) is then validated by applying it to a simple spin-boson model, where exact results exist. Excellent agreement is found in a wide parameter range, even where the perturbation is moderately strong. Results obtained in the rotated electronic basis are found to be consistently more accurate than those from the unrotated basis. These benchmark calculations also allow us to demonstrate the advantage of treating the population fluctuations instead of the populations as the relevant variables, as only the former lead to reliable results at long time. Thus, the THLE appears to provide a viable alternative to established methods--such as Ehrenfest dynamics or surface hopping--for the treatment of nonadiabatic effects in electron transfer simulations.
A path-integral Langevin equation treatment of low-temperature doped helium clusters.
Ing, Christopher; Hinsen, Konrad; Yang, Jing; Zeng, Toby; Li, Hui; Roy, Pierre-Nicholas
2012-06-14
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)] 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 He(N)-CO(2) 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)], an open-source molecular simulation package.
Ness, H; Stella, L; Lorenz, C D; Kantorovich, L
2017-04-28
We use a generalised Langevin equation scheme to study the thermal transport of low dimensional systems. In this approach, the central classical region is connected to two realistic thermal baths kept at two different temperatures [H. Ness et al., Phys. Rev. B 93, 174303 (2016)]. We consider model Al systems, i.e., one-dimensional atomic chains connected to three-dimensional baths. The thermal transport properties are studied as a function of the chain length N and the temperature difference ΔT between the baths. We calculate the transport properties both in the linear response regime and in the non-linear regime. Two different laws are obtained for the linear conductance versus the length of the chains. For large temperatures (T≳500 K) and temperature differences (ΔT≳500 K), the chains, with N>18 atoms, present a diffusive transport regime with the presence of a temperature gradient across the system. For lower temperatures (T≲500 K) and temperature differences (ΔT≲400 K), a regime similar to the ballistic regime is observed. Such a ballistic-like regime is also obtained for shorter chains (N≤15). Our detailed analysis suggests that the behaviour at higher temperatures and temperature differences is mainly due to anharmonic effects within the long chains.
Nguyen, Trong-Nghia; Lee, Yun-Min; Wu, Jong-Shinn; Lin, Ming-Chang
2017-02-01
H, H2, and SiH x + (x ≤ 4) ions coexist under plasma-enhanced chemical vapor deposition (PECVD) conditions. We have studied the kinetics of their interactions by high-level quantum chemical and statistical theory calculations, and compared the results with classical Langevin values (˜2 × 10-9 cm3 molecule-1 s-1 independent of temperature). The results indicate that, for H capturing by SiH x + (x ≤ 4), both theories agree within a factor of 2-4, whereas for H2 capturing by SiH x + (x ≤ 3), the modern theory gives higher and weakly temperature-dependent values by up to more than one order of magnitude, attributable to reaction path degeneracies and increased entropies of activation. The heats of formation and structural parameters of SiH x + ions (x ≤ 5) in this work agree well with available experimental data. For practical applications, we have provided tables of rate constants for modeling various processes of relevance to the PECVD of a-Si:H films.
Two critical issues in Langevin simulation of gas flows
Zhang, Jun [James Weir Fluids Laboratory, Department of Mechanical and Aerospace Engineering, University of Strathclyde, Glasgow G1 1XJ, United Kingdom and State Key Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences (China); Fan, Jing [State Key Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190 (China)
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.
Upsilon suppression in the Schrödinger-Langevin approach
Gossiaux, P. B.; Katz, R.
2016-12-01
We treat the question of bottomonia suppression in ultrarelativistic heavy ion collisions (URHIC) as a dynamical open quantum problem, tackled for the first time using the Schrödinger-Langevin equation. Coupling this equation to the EPOS2 event generator, predictions are made for the nuclear modification factor of ϒ (1 S) and ϒ (2 S).
Upsilon suppression in the Schr\\"odinger-Langevin approach
Gossiaux, Pol Bernard
2016-01-01
We treat the question of bottomonia suppression in ultrarelativistic heavy ion collisions (URHIC) as a dynamical open quantum problem, tackled for the first time using the Schr\\"odinger-Langevin equation. Coupling this equation to the EPOS2 event generator, predictions are made for the nuclear modification factor of $\\Upsilon (1S)$ and $\\Upsilon (2S)$.
Foundation of fractional Langevin equation: harmonization of a many-body problem.
Lizana, Ludvig; Ambjörnsson, Tobias; Taloni, Alessandro; Barkai, Eli; Lomholt, Michael A
2010-05-01
In this study we derive a single-particle equation of motion, from first principles, starting out with a microscopic description of a tracer particle in a one-dimensional many-particle system with a general two-body interaction potential. Using a harmonization technique, we show that the resulting dynamical equation belongs to the class of fractional Langevin equations, a stochastic framework which has been proposed in a large body of works as a means of describing anomalous dynamics. Our work sheds light on the fundamental assumptions of these phenomenological models and a relation derived by Kollmann.
Einstein's Clocks and Langevin's Twins
Weinstein, Galina
2012-01-01
In 1905 Einstein presented the Clock Paradox and in 1911 Paul Langevin expanded Einstein's result to human observers, the "Twin Paradox." I will explain the crucial difference between Einstein and Langevin. Einstein did not present the so-called "Twin Paradox." Later Einstein continued to speak about the clock paradox. Einstein might not have been interested in the question: what happens to the observers themselves. The reason for this could be the following; Einstein dealt with measurement procedures, clocks and measuring rods. Einstein's observers were measuring time with these clocks and measuring rods. Einstein might not have been interested in so-called biology of the observers, whether these observers were getting older, younger, or whether they have gone any other changes; these changes appeared to be out of the scope of his "Principle of relativity" or kinematics. The processes and changes occurring within observers seemed to be good for philosophical discussions. Later writers criticized Einstein's c...
Diffusive dynamics and stochastic models of turbulent axisymmetric wakes
Rigas, G; Brackston, R D; Morrison, J F
2015-01-01
A modelling methodology to reproduce the experimental measurements of a turbulent flow under the presence of symmetry is presented. The flow is a three-dimensional wake generated by an axisymmetric body. We show that the dynamics of the turbulent wake- flow can be assimilated by a nonlinear two-dimensional Langevin equation, the deterministic part of which accounts for the broken symmetries which occur at the laminar and transitional regimes at low Reynolds numbers and the stochastic part of which accounts for the turbulent fluctuations. Comparison between theoretical and experimental results allows the extraction of the model parameters.
Scaling of ballistic deposition from a Langevin equation.
Haselwandter, Christoph A; Vvedensky, Dimitri D
2006-04-01
An exact lattice Langevin equation is derived for the ballistic deposition model of surface growth. The continuum limit of this equation is dominated by the Kardar-Parisi-Zhang (KPZ) equation at all length and time scales. For a one-dimensional substrate the solution of the exact lattice Langevin equation yields the KPZ scaling exponents without any extrapolation. For a two-dimensional substrate the scaling exponents are different from those found from computer simulations. This discrepancy is discussed in relation to analytic approaches to the KPZ equation in higher dimensions.
Mathematical Modeling to Study the Dynamics of A Diatomic Molecule N2 in Water
Sharma, Nitin
2010-01-01
In the present work an attempt has been made to study the dynamics of a diatomic molecule N2 in water. The proposed model consists of Langevin stochastic differential equation whose solution is obtained through Euler's method. The proposed work has been concluded by studying the behavior of statistical parameters like variance in position, variance in velocity and covariance between position and velocity. This model incorporates the important parameters like acceleration, intermolecular force, frictional force and random force.
Galatà, A., E-mail: alessio.galata@lnl.infn.it [INFN–Laboratori Nazionali di Legnaro, Viale dell’Università 2, 35020 Legnaro, Padova (Italy); Mascali, D.; Neri, L.; Torrisi, G.; Celona, L. [INFN–Laboratori Nazionali del Sud, Via S. Sofia 62, 95123 Catania (Italy)
2016-02-15
A Charge Breeder (CB) is a crucial device of an ISOL facility, allowing post-acceleration of radioactive ions: it accepts an incoming 1+ beam, then multiplying its charge with a highly charged q+ beam as an output. The overall performances of the facility (intensity and attainable final energy) critically depend on the charge breeder optimization. Experimental results collected along the years confirm that the breeding process is still not fully understood and room for improvements still exists: a new numerical approach has been therefore developed and applied to the description of a {sup 85}Rb{sup 1+} beam capture by the plasma of the 14.5 GHz PHOENIX ECR-based CB, installed at the Laboratoire de Physique Subatomique et de Cosmologie (LPSC), and adopted for the Selective Production of Exotic Species project under construction at Laboratori Nazionali di Legnaro. The results of the numerical simulations, obtained implementing a plasma-target model of increasing accuracy and different values for the plasma potential, will be described along the paper: results very well agree with the theoretical predictions and with the experimental results obtained on the LPSC test bench.
Langevin- Science and vigilance; Langevin - Science et vigilance
Bensaude-Vincent, B.
1987-12-31
Paul Langevin personifies the figure of popular scientist, buried in the Pantheon, because he was in all great fights: to diffuse knowledge, for improvement and democratization of teaching, for justice and peace. Great theoretician of physics, comparable to Einstein whom he rejoined the approach, he was a fertile discoverer, author, in particular, of a proceeding to detect submarines. He fought politically, regardless of his career, in the ranges of pacifists and opponents of fascism. This book reveals, in his warm diversity, a badly known personality, in spite of the legend in his lifetime. (N.C.).
GOLDSCHMIDT, YADIN Y.; LIU, Jin-Tao
2007-08-07
In this paper we use London Langevin molecular dynamics simulations to investigate the vortex matter melting transition in the highly anisotropic high-temperature superconductor material Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+{delta}} in the presence of low concentration of columnar defects (CDs). We reproduce with further details our previous results obtained by using Multilevel Monte Carlo simulations that showed that the melting of the nanocrystalline vortex matter occurs in two stages: a first stage melting into nanoliquid vortex matter and a second stage delocalization transition into a homogeneous liquid. Furthermore, we report on new dynamical measurements in the presence of a current that identifies clearly the irreversibility line and the second stage delocalization transition. In addition to CDs aligned along the c-axis we also simulate the case of tilted CDs which are aligned at an angle with respect to the applied magnetic field. Results for CDs tilted by 45{degree} with respect to c-axis show that the locations of the melting and delocalization transitions are not affected by the tilt when the ratio of flux lines to CDs remains constant. On the other hand we argue that some dynamical properties and in particular the position of the irreversibility line should be affected.
Numerical simulation of generalized Langevin equation with arbitrary correlated noise.
Lü, Kun; Bao, Jing-Dong
2005-12-01
A generalized Langevin equation with arbitrary correlated noise and associated frequency-dependent friction is simulated, which can lead to anomalous diffusion. The algorithm is realized by using the Fourier transform technique to generate noise and the stochastic Runge-Kutta method to solve the whole equation. Application to an acoustic phonon model, initial preparation-dependent ballistic diffusion, is shown.
Davtyan, Aram; Dama, James F.; Voth, Gregory A. [Department of Chemistry, The James Franck Institute, Institute for Biophysical Dynamics, and Computation Institute, The University of Chicago, Chicago, Illinois 60637 (United States); Andersen, Hans C., E-mail: hca@stanford.edu [Department of Chemistry, Stanford University, Stanford, California 94305 (United States)
2015-04-21
Coarse-grained (CG) models of molecular systems, with fewer mechanical degrees of freedom than an all-atom model, are used extensively in chemical physics. It is generally accepted that a coarse-grained model that accurately describes equilibrium structural properties (as a result of having a well constructed CG potential energy function) does not necessarily exhibit appropriate dynamical behavior when simulated using conservative Hamiltonian dynamics for the CG degrees of freedom on the CG potential energy surface. Attempts to develop accurate CG dynamic models usually focus on replacing Hamiltonian motion by stochastic but Markovian dynamics on that surface, such as Langevin or Brownian dynamics. However, depending on the nature of the system and the extent of the coarse-graining, a Markovian dynamics for the CG degrees of freedom may not be appropriate. In this paper, we consider the problem of constructing dynamic CG models within the context of the Multi-Scale Coarse-graining (MS-CG) method of Voth and coworkers. We propose a method of converting a MS-CG model into a dynamic CG model by adding degrees of freedom to it in the form of a small number of fictitious particles that interact with the CG degrees of freedom in simple ways and that are subject to Langevin forces. The dynamic models are members of a class of nonlinear systems interacting with special heat baths that were studied by Zwanzig [J. Stat. Phys. 9, 215 (1973)]. The properties of the fictitious particles can be inferred from analysis of the dynamics of all-atom simulations of the system of interest. This is analogous to the fact that the MS-CG method generates the CG potential from analysis of equilibrium structures observed in all-atom simulation data. The dynamic models generate a non-Markovian dynamics for the CG degrees of freedom, but they can be easily simulated using standard molecular dynamics programs. We present tests of this method on a series of simple examples that demonstrate that
Grothaus, Martin
2012-01-01
In this article we develop geometric versions of the classical Langevin equation on regular submanifolds in euclidean space in an easy, natural way and combine them with a bunch of applications. The equations are formulated as Stratonovich stochastic differential equations on manifolds. The first version of the geometric Langevin equation has already been detected before by Leli\\`evre, Rousset and Stoltz with a different derivation. We propose an additional extension of the models, the geometric Langevin equations with velocity of constant absolute value. The latters are seemingly new and provide a galaxy of new, beautiful and powerful mathematical models. Up to the authors best knowledge there are not many mathematical papers available dealing with geometric Langevin processes. We connect the first version of the geometric Langevin equation via proving that its generator coincides with the generalized Langevin operator proposed by Soloveitchik, Jorgensen and Kolokoltsov. All our studies are strongly motivate...
Asymptotic dynamics of a frustrated model with spherical constraint
Mendoza-Coto, Alejandro [Departamento de Física, Universidade Federal do Rio Grande do Sul, CP 15051, 91501-970 Porto Alegre (Brazil); Díaz-Méndez, Rogelio, E-mail: rogelio@fisica.uh.cu [Nanophysics Group, Electric Engineering Faculty, CUJAE, CP 19390, La Habana (Cuba); Group of Complex Systems, Physics Faculty, University of Havana, CP 10400, La Habana (Cuba)
2013-11-15
We solve the Langevin dynamics of a continuum model with a spherical constraint, considering a ferromagnetic exchange and a long-range antiferromagnetic interaction. Analytical results within the Hartree approximation show an equivalence in the form of spatial and auto-correlation functions in the long time regime between this model and the recently studied Ginzburg–Landau frustrated model. The low-temperature behavior is discussed in the context of glassy dynamics. The emergence of interesting features regarding the establishment of the saturated phase is also analyzed in the view of recent literature. - Highlights: • We solve the long-time dynamics of a model with ferro and antiferromagnetic interactions and spherical restriction. • We find the critical behavior of spatial and self-correlations. • The new results are analyzed in the frame of existing literature on glassy states and thin films.
Viana, A., E-mail: Antoine.Viana@g2elab.grenoble-inp.f [Grenoble Electrical Engineering Lab (CNRS UMR5269), Universite de Grenoble, ENSE3, BP 46, 38402 Saint Martin d' Heres (France); Coulomb, J.-L.; Rouve, L.-L.; Cauffet, G. [Grenoble Electrical Engineering Lab (CNRS UMR5269), Universite de Grenoble, ENSE3, BP 46, 38402 Saint Martin d' Heres (France)
2010-01-15
The Langevin equation is classically used to model the anhysteretic magnetization curve. A modified version of this equation has been introduced by Jiles to take into account the effects of magnetostriction on the anhysteretic magnetization behavior when a ferromagnetic material undergoes mechanical stresses. The numerical resolution of the modified Langevin equation is usually performed with a root-finding algorithm. In this paper, a differential form of the modified Langevin equation is proposed, allowing a faster numerical resolution.
Gradient-based MCMC samplers for dynamic causal modelling.
Sengupta, Biswa; Friston, Karl J; Penny, Will D
2016-01-15
In this technical note, we derive two MCMC (Markov chain Monte Carlo) samplers for dynamic causal models (DCMs). Specifically, we use (a) Hamiltonian MCMC (HMC-E) where sampling is simulated using Hamilton's equation of motion and (b) Langevin Monte Carlo algorithm (LMC-R and LMC-E) that simulates the Langevin diffusion of samples using gradients either on a Euclidean (E) or on a Riemannian (R) manifold. While LMC-R requires minimal tuning, the implementation of HMC-E is heavily dependent on its tuning parameters. These parameters are therefore optimised by learning a Gaussian process model of the time-normalised sample correlation matrix. This allows one to formulate an objective function that balances tuning parameter exploration and exploitation, furnishing an intervention-free inference scheme. Using neural mass models (NMMs)-a class of biophysically motivated DCMs-we find that HMC-E is statistically more efficient than LMC-R (with a Riemannian metric); yet both gradient-based samplers are far superior to the random walk Metropolis algorithm, which proves inadequate to steer away from dynamical instability.
Langevin description of fission fragment charge distribution from excited nuclei
Karpov, A V
2002-01-01
A stochastic approach to fission dynamics based on a set of three-dimensional Langevin equations was applied to calculate fission-fragment charge distribution of compound nucleus sup 2 sup 3 sup 6 U. The following collective coordinates have been chosen - elongation coordinate, neck-thickness coordinate, and charge-asymmetry coordinate. The friction coefficient of charge mode has been calculated in the framework of one-body and two-body dissipation mechanisms. Analysis of the results has shown that Langevin approach is appropriate for investigation of isobaric distribution. Moreover, the dependences of the variance of the charge distribution on excitation energy and on the two-body viscosity coefficient has been studied
Gottschall, Julia; Courtney, Michael
2015-01-01
In this paper, we review a dynamical power curve concept that was introduced in earlier publications and shown to provide results for a wind turbine’s power characteristic with several benefits compared with the IEC 61400-12-1 standard procedure. After summarizing the theoretical concept based...
Fission dynamics of hot nuclei
Santanu Pal; Jhilam Sadhukhan
2014-04-01
Experimental evidence accumulated during the last two decades indicates that the fission of excited heavy nuclei involves a dissipative dynamical process. We shall briefly review the relevant dynamical model, namely the Langevin equations for fission. Statistical model predictions using the Kramers’ fission width will also be discussed.
An Analysis of Vehicular Traffic Flow Using Langevin Equation
Çağlar Koşun
2015-08-01
Full Text Available Traffic flow data are stochastic in nature, and an abundance of literature exists thereof. One way to express stochastic data is the Langevin equation. Langevin equation consists of two parts. The first part is known as the deterministic drift term, the other as the stochastic diffusion term. Langevin equation does not only help derive the deterministic and random terms of the selected portion of the city of Istanbul traffic empirically, but also sheds light on the underlying dynamics of the flow. Drift diagrams have shown that slow lane tends to get congested faster when vehicle speeds attain a value of 25 km/h, and it is 20 km/h for the fast lane. Three or four distinct regimes may be discriminated again from the drift diagrams; congested, intermediate, and free-flow regimes. At places, even the intermediate regime may be divided in two, often with readiness to congestion. This has revealed the fact that for the selected portion of the highway, there are two main states of flow, namely, congestion and free-flow, with an intermediate state where the noise-driven traffic flow forces the flow into either of the distinct regimes.
Dynamic Latent Classification Model
Zhong, Shengtong; Martínez, Ana M.; Nielsen, Thomas Dyhre
as possible. Motivated by this problem setting, we propose a generative model for dynamic classification in continuous domains. At each time point the model can be seen as combining a naive Bayes model with a mixture of factor analyzers (FA). The latent variables of the FA are used to capture the dynamics...... in the process as well as modeling dependences between attributes....
The modified Langevin description for probes in a nonlinear medium
Krüger, Matthias; Maes, Christian
2017-02-01
When the motion of a probe strongly disturbs the thermal equilibrium of the solvent or bath, the nonlinear response of the latter must enter the probe’s effective evolution equation. We derive that induced stochastic dynamics using second order response around the bath thermal equilibrium. We discuss the nature of the new term in the evolution equation which is no longer purely dissipative, and the appearance of a novel time-scale for the probe related to changes in the dynamical activity of the bath. A major application for the obtained nonlinear generalized Langevin equation is in the study of colloid motion in a visco-elastic medium.
白玉林; 陈向荣; 杨向东; 芦鹏飞
2003-01-01
A first-principles density-functional theory method, i.e. the finite-difference pseudopotential density-functional theory in real space and Langevin molecular dynamics annealing technique (PDFMD), is introduced to describe the structures and properties of small sulfur clusters S n ( n = 2 ～ 8). It is found that the ground state structures of S3, S4, S5, S6, S7 and S8 are C2v, D2h, envelope-shaped Cs, D3d(or boat-shaped C2v), a chair-shaped Cs and D4d symmetry structures, respectively, which are in good agreement with experiment. It is shown that the more the number of atom in the cluster, the more stable it is for small sulfur clusters.%引入第一原理密度泛函理论,即赝势密度泛函在实空间的有限差分方法和朗之万分子动力学退火技术,对硫团簇Sn(n=2～8)的结构等进行了计算.结果表明,S3,S4,S5,S6,S7和S8的结构对应为C2v,D2h,信封式Cs,D3d(或船式C2v),椅式C5和D4d的对称结构,其结构参数与有实验数据的S和S6-8吻合较好.从平均原子结合能看,原子数目越多,硫团簇越为稳定.
SELF-CONSISTENT LANGEVIN SIMULATION OF COULOMB COLLISIONS IN CHARGED-PARTICLE BEAMS
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.
A stochastic phase-field model determined from molecular dynamics
von Schwerin, Erik
2010-03-17
The dynamics of dendritic growth of a crystal in an undercooled melt is determined by macroscopic diffusion-convection of heat and by capillary forces acting on the nanometer scale of the solid-liquid interface width. Its modelling is useful for instance in processing techniques based on casting. The phase-field method is widely used to study evolution of such microstructural phase transformations on a continuum level; it couples the energy equation to a phenomenological Allen-Cahn/Ginzburg-Landau equation modelling the dynamics of an order parameter determining the solid and liquid phases, including also stochastic fluctuations to obtain the qualitatively correct result of dendritic side branching. This work presents a method to determine stochastic phase-field models from atomistic formulations by coarse-graining molecular dynamics. It has three steps: (1) a precise quantitative atomistic definition of the phase-field variable, based on the local potential energy; (2) derivation of its coarse-grained dynamics model, from microscopic Smoluchowski molecular dynamics (that is Brownian or over damped Langevin dynamics); and (3) numerical computation of the coarse-grained model functions. The coarse-grained model approximates Gibbs ensemble averages of the atomistic phase-field, by choosing coarse-grained drift and diffusion functions that minimize the approximation error of observables in this ensemble average. © EDP Sciences, SMAI, 2010.
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.
Justification of the complex Langevin method with the gauge cooling procedure
Nagata, Keitaro; Shimasaki, Shinji
2015-01-01
Recently there has been remarkable progress in the complex Langevin method, which aims at solving the complex action problem by complexifying the dynamical variables in the original path integral. In particular, a new technique called the gauge cooling was introduced and the full QCD simulation at finite density has been made possible in the high temperature (deconfined) phase or with heavy quarks. Here we provide a rigorous justification of the complex Langevin method including the gauge cooling procedure. We first show that the gauge cooling can be formulated as an extra term in the complex Langevin equation involving a gauge transformation parameter, which is chosen appropriately as a function of the configuration before cooling. The probability distribution of the complexified dynamical variables is modified by this extra term. However, this modification is shown not to affect the Fokker-Planck equation for the corresponding complex weight as far as observables are restricted to gauge invariant ones. Thus...
Inelastic X-ray scattering on liquid benzene analyzed using a generalized Langevin equation
Yoshida, Koji; Fukuyama, Nami; Yamaguchi, Toshio; Hosokawa, Shinya; Uchiyama, Hiroshi; Tsutsui, Satoshi; Baron, Alfred Q. R.
2017-07-01
The dynamic structure factor, S(Q,ω), of liquid benzene was measured by meV-resolved inelastic X-ray scattering (IXS) and analyzed using a generalized Langevin model with a memory function including fast, μ-relaxation and slow, structural, α-relaxation. The model well reproduced the experimental S(Q,ω) of liquid benzene. The dispersion relation of the collective excitation energy yields the high-frequency sound velocity for liquid benzene as related to the α-relaxation. The ratio of the high-frequency to the adiabatic sound velocity is approximately 1.5, larger to that of carbon tetrachloride and smaller than those of methanol and water, reflecting the nature of intermolecular interactions.
Collinearly improved JIMWLK evolution in Langevin form
Hatta, Yoshitaka
2016-01-01
The high-energy evolution of Wilson line operators, which at leading order is described by the Balitsky-JIMWLK equations, receives large radiative corrections enhanced by single and double collinear logarithms at next-to-leading order and beyond. We propose a method for resumming such logarithmic corrections to all orders, at the level of the Langevin formulation of the JIMWLK equation. The ensuing, collinearly-improved Langevin equation features generalized Wilson line operators, which depend not only upon rapidity (the logarithm of the longitudinal momentum), but also upon the transverse size of the color neutral projectile to which the Wilson lines belong. This additional scale dependence is built up during the evolution, via the condition that the successive emissions of soft gluons be ordered in time. The presence of this transverse scale in the Langevin equation furthermore allows for the resummation of the one-loop running coupling corrections.
Stochastic heart-rate model can reveal pathologic cardiac dynamics
Kuusela, Tom
2004-03-01
A simple one-dimensional Langevin-type stochastic difference equation can simulate the heart-rate fluctuations in a time scale from minutes to hours. The model consists of a deterministic nonlinear part and a stochastic part typical of Gaussian noise, and both parts can be directly determined from measured heart-rate data. Data from healthy subjects typically exhibit the deterministic part with two or more stable fixed points. Studies of 15 congestive heart-failure subjects reveal that the deterministic part of pathologic heart dynamics has no clear stable fixed points. Direct simulations of the stochastic model for normal and pathologic cases can produce statistical parameters similar to those of real subjects. Results directly indicate that pathologic situations simplify the heart-rate control system.
Models for Dynamic Applications
2011-01-01
be applied to formulate, analyse and solve these dynamic problems and how in the case of the fuel cell problem the model consists of coupledmeso and micro scale models. It is shown how data flows are handled between the models and how the solution is obtained within the modelling environment....
On the environmental modes for the generalized Langevin equation.
Kawai, Shinnosuke
2015-09-07
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.
樊华; 李理; 袁坚; 山秀明
2009-01-01
为互联网中的流量控制协议构建恰当模型,从而阐明具体协议算法与网络宏观性能间的关系,一直是互联网研究者面临的重大挑战,本文通过逻辑演绎,建立了互联网传输控制协议下流量的朗之万方程.在此基础上,细致分析了主动队列管理算法的有效性,在理论上证明了.此类算法存在从畅通态到拥塞态到瘫痪态的相变过程,并给出了相变临界点与系统参数的显式关系.本建模与分析方法虽以具体的主动队列管理算法为例,但其方法可以应用于一般的网络流量控制问题.%One of the big challenges in the field of Intemet research is to elucidate the relationship between micro-algorithms of the flow control protocols and macro-properties of the Intemet with a proper model. In this paper, we build up a Langevin equation under the transmission control protocol using deductive method. Then we analyze the effectiveness of the active queue management based on the Langevin model. We have proved that there is a phase transition sequence from smooth state to congestion state then to paralysis state in all such kind of algorithms. We also provide explicit formulas of the critical points in terms of the system parameters. Although the model used in this paper focuses on a specific algorithm, we believe this method has a great potential in analyzing and understanding various network congestion control algorithms.
A Langevin Canonical Approach to the Study of Quantum Stochastic Resonance in Chiral Molecules
Germán Rojas-Lorenzo
2016-09-01
Full Text Available A Langevin canonical framework for a chiral two-level system coupled to a bath of harmonic oscillators is used within a coupling scheme different from the well-known spin-boson model to study the quantum stochastic resonance for chiral molecules. This process refers to the amplification of the response to an external periodic signal at a certain value of the noise strength, being a cooperative effect of friction, noise, and periodic driving occurring in a bistable system. Furthermore, from this stochastic dynamics within the Markovian regime and Ohmic friction, the competing process between tunneling and the parity violating energy difference present in this type of chiral systems plays a fundamental role. This mechanism is finally proposed to observe the so-far elusive parity-violating energy difference in chiral molecules.
Protein Conformational Change Based on a Two-dimensional Generalized Langevin Equation
Ying-xi Wang; Shuang-mu Linguang; Nan-rong Zhao; Yi-jing Yan
2011-01-01
A two-dimensional generalized Langevin equation is proposed to describe the protein conformational change,compatible to the electron transfer process governed by atomic packing density model.We assume a fractional Gaussian noise and a white noise through bond and through space coordinates respectively,and introduce the coupling effect coming from both fluctuations and equilibrium variances.The general expressions for autocorrelation functions of distance fluctuation and fluorescence lifetime variation are derived,based on which the exact conformational change dynamics can be evaluated with the aid of numerical Laplace inversion technique.We explicitly elaborate the short time and long time approximations.The relationship between the two-dimensional description and the one-dimensional theory is also discussed.
Nonergodic solutions of the generalized Langevin equation.
Plyukhin, A V
2011-06-01
It is known that in the regime of superlinear diffusion, characterized by zero integral friction (vanishing integral of the memory function), the generalized Langevin equation may have nonergodic solutions that do not relax to equilibrium values. It is shown that the equation may have nonergodic (nonstationary) solutions even if the integral of the memory function is finite and diffusion is normal.
Analysis of multifrequency langevin composite ultrasonic transducers.
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.
Andreasen, Martin Møller; Meldrum, Andrew
This paper studies whether dynamic term structure models for US nominal bond yields should enforce the zero lower bound by a quadratic policy rate or a shadow rate specification. We address the question by estimating quadratic term structure models (QTSMs) and shadow rate models with at most four...
Causal influence in linear Langevin networks without feedback
Auconi, Andrea; Giansanti, Andrea; Klipp, Edda
2017-04-01
The intuition of causation is so fundamental that almost every research study in life sciences refers to this concept. However, a widely accepted formal definition of causal influence between observables is still missing. In the framework of linear Langevin networks without feedback (linear response models) we propose a measure of causal influence based on a new decomposition of information flows over time. We discuss its main properties and we compare it with other information measures like the transfer entropy. We are currently unable to extend the definition of causal influence to systems with a general feedback structure and nonlinearities.
Salinelli, Ernesto
2014-01-01
This book provides an introduction to the analysis of discrete dynamical systems. The content is presented by an unitary approach that blends the perspective of mathematical modeling together with the ones of several discipline as Mathematical Analysis, Linear Algebra, Numerical Analysis, Systems Theory and Probability. After a preliminary discussion of several models, the main tools for the study of linear and non-linear scalar dynamical systems are presented, paying particular attention to the stability analysis. Linear difference equations are studied in detail and an elementary introduction of Z and Discrete Fourier Transform is presented. A whole chapter is devoted to the study of bifurcations and chaotic dynamics. One-step vector-valued dynamical systems are the subject of three chapters, where the reader can find the applications to positive systems, Markov chains, networks and search engines. The book is addressed mainly to students in Mathematics, Engineering, Physics, Chemistry, Biology and Economic...
Fokker-Planck description for a linear delayed Langevin equation with additive Gaussian noise
Giuggioli, Luca; McKetterick, Thomas John; Kenkre, V. M.; Chase, Matthew
2016-09-01
We construct an equivalent probability description of linear multi-delay Langevin equations subject to additive Gaussian white noise. By exploiting the time-convolutionless transform and a time variable transformation we are able to write a Fokker-Planck equation (FPE) for the 1-time and for the 2-time probability distributions valid irrespective of the regime of stability of the Langevin equations. We solve exactly the derived FPEs and analyze the aging dynamics by studying analytically the conditional probability distribution. We discuss explicitly why the initially conditioned distribution is not sufficient to describe fully out a non-Markov process as both preparation and observation times have bearing on its dynamics. As our analytic procedure can also be applied to linear Langevin equations with memory kernels, we compare the non-Markov dynamics of a one-delay system with that of a generalized Langevin equation with an exponential as well as a power law memory. Application to a generalization of the Green-Kubo formula is also presented.
Ghanem, Bernard
2013-01-01
This paper proposes the problem of modeling video sequences of dynamic swarms (DSs). We define a DS as a large layout of stochastically repetitive spatial configurations of dynamic objects (swarm elements) whose motions exhibit local spatiotemporal interdependency and stationarity, i.e., the motions are similar in any small spatiotemporal neighborhood. Examples of DS abound in nature, e.g., herds of animals and flocks of birds. To capture the local spatiotemporal properties of the DS, we present a probabilistic model that learns both the spatial layout of swarm elements (based on low-level image segmentation) and their joint dynamics that are modeled as linear transformations. To this end, a spatiotemporal neighborhood is associated with each swarm element, in which local stationarity is enforced both spatially and temporally. We assume that the prior on the swarm dynamics is distributed according to an MRF in both space and time. Embedding this model in a MAP framework, we iterate between learning the spatial layout of the swarm and its dynamics. We learn the swarm transformations using ICM, which iterates between estimating these transformations and updating their distribution in the spatiotemporal neighborhoods. We demonstrate the validity of our method by conducting experiments on real and synthetic video sequences. Real sequences of birds, geese, robot swarms, and pedestrians evaluate the applicability of our model to real world data. © 2012 Elsevier Inc. All rights reserved.
Kirchner, Jens; Meyer, Wolfgang; Elsholz, Markus; Hensel, Bernhard
2007-08-01
Using the Langevin equation we develop the model of a stochastic process subject to a given time-dependent regulatory mechanism. The effects of this nonstationarity on the statistical properties of the time series, i.e., on global and conditional probability densities and on the moments of the distribution, are derived. Application of these results on simple model trends allows one to approximate cardiological data and thus to explain effects recently observed in the reconstruction of the deterministic part of the Langevin equation for time series of heart rate.
Heavy Flavor in Medium Momentum Evolution: Langevin vs Boltzmann
Das, Santosh K; Greco, Vincenzo
2013-01-01
The propagation of heavy quarks through the quark-gluon plasma (QGP) has been often treated within the framework of Langevin equation (LV), i.e. assuming the heavy flavor momentum transfer is small or the scatterings are sufficiently forward peaked, small screening mass $m_D$. We address a thorough study of the approximations involved in Langevin dynamics by mean of a direct comparison with the solution of the Boltzmann collisional integral (BM) when a bulk medium is in equilibrium at fixed temperature. We show that unless the cross section is quite forward peaked ($m_D\\cong T $) or the mass to temperature ratio is quite large ($M_q/T \\gtrsim 8-10$) there are significant differences in the evolution of the $p-$spectra with time and consequently on the so-called nuclear modification factor $R_{AA}(p_T)$. However for charm quark we find that very similar $R_{AA}(p_T)$ between the LV and BM can be obtained, but the estimate of the underlying diffusion coefficient can differ by about $\\sim 15-50\\%$ depending on t...
Dynamic causal modelling revisited.
Friston, K J; Preller, Katrin H; Mathys, Chris; Cagnan, Hayriye; Heinzle, Jakob; Razi, Adeel; Zeidman, Peter
2017-02-17
This paper revisits the dynamic causal modelling of fMRI timeseries by replacing the usual (Taylor) approximation to neuronal dynamics with a neural mass model of the canonical microcircuit. This provides a generative or dynamic causal model of laminar specific responses that can generate haemodynamic and electrophysiological measurements. In principle, this allows the fusion of haemodynamic and (event related or induced) electrophysiological responses. Furthermore, it enables Bayesian model comparison of competing hypotheses about physiologically plausible synaptic effects; for example, does attentional modulation act on superficial or deep pyramidal cells - or both? In this technical note, we describe the resulting dynamic causal model and provide an illustrative application to the attention to visual motion dataset used in previous papers. Our focus here is on how to answer long-standing questions in fMRI; for example, do haemodynamic responses reflect extrinsic (afferent) input from distant cortical regions, or do they reflect intrinsic (recurrent) neuronal activity? To what extent do inhibitory interneurons contribute to neurovascular coupling? What is the relationship between haemodynamic responses and the frequency of induced neuronal activity? This paper does not pretend to answer these questions; rather it shows how they can be addressed using neural mass models of fMRI timeseries. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.
Lucarini, Valerio; Willeit, Matteo
2011-01-01
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 and show, 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...
Exactly solvable nonequilibrium Langevin relaxation of a trapped nanoparticle
Salazar, Domingos S. P.; Lira, Sérgio A.
2016-11-01
In this work, we study the nonequilibrium statistical properties of the relaxation dynamics of a nanoparticle trapped in a harmonic potential. We report an exact time-dependent analytical solution to the Langevin dynamics that arises from the stochastic differential equation of our system’s energy in the underdamped regime. By utilizing this stochastic thermodynamics approach, we are able to completely describe the heat exchange process between the nanoparticle and the surrounding environment. As an important consequence of our results, we observe the validity of the heat exchange fluctuation theorem in our setup, which holds for systems arbitrarily far from equilibrium conditions. By extending our results for the case of N noninterating nanoparticles, we perform analytical asymptotic limits and direct numerical simulations that corroborate our analytical predictions.
Fractional Langevin equation: overdamped, underdamped, and critical behaviors.
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.
Langevin Equations for Reaction-Diffusion Processes
Benitez, Federico; Duclut, Charlie; Chaté, Hugues; Delamotte, Bertrand; Dornic, Ivan; Muñoz, Miguel A.
2016-09-01
For reaction-diffusion processes with at most bimolecular reactants, we derive well-behaved, numerically tractable, exact Langevin equations that govern a stochastic variable related to the response field in field theory. Using duality relations, we show how the particle number and other quantities of interest can be computed. Our work clarifies long-standing conceptual issues encountered in field-theoretical approaches and paves the way for systematic numerical and theoretical analyses of reaction-diffusion problems.
Langevin equation with two fractional orders
Lim, S.C. [Faculty of Engineering, Multimedia University, Jalan Multimedia, Cyberjaya 63100, Selangor Darul Ehsan (Malaysia)], E-mail: sclim@mmu.edu.my; Li Ming [School of Information Science and Technology, East China Normal University, No. 500, Dong-Chuan Road, Shanghai 200241 (China)], E-mail: mli@ee.ecnu.edu.cn; Teo, L.P. [Faculty of Information Technology, Multimedia University, Jalan Multimedia, Cyberjaya 63100, Selangor Darul Ehsan (Malaysia)], E-mail: lpteo@mmu.edu.my
2008-10-13
A new type of fractional Langevin equation of two different orders is introduced. The solutions for this equation, known as the fractional Ornstein-Uhlenbeck processes, based on Weyl and Riemann-Liouville fractional derivatives are obtained. The basic properties of these processes are studied. An example of the spectral density of ocean wind speed which has similar spectral density as that of Weyl fractional Ornstein-Uhlenbeck process is given.
Conformally-related Einstein-Langevin equations for metric fluctuations in stochastic gravity
Satin, Seema; Hu, Bei Lok
2016-01-01
For a conformally-coupled scalar field we obtain the conformally-related Einstein-Langevin equations, using appropriate transformations for all the quantities in the equations between two conformally-related spacetimes. In particular, we analyze the transformations of the influence action, the stress energy tensor, the noise kernel and the dissipation kernel. In due course the fluctuation-dissipation relation is also discussed. The analysis in this paper thereby facilitates a general solution to the Einstein-Langevin equation once the solution of the equation in a simpler, conformally-related spacetime is known. For example, from the Minkowski solution of Martin and Verdaguer, those of the Einstein-Langevin equations in conformally-flat spacetimes, especially for spatially-flat Friedmann-Robertson-Walker models, can be readily obtained.
Conformally related Einstein-Langevin equations for metric fluctuations in stochastic gravity
Satin, Seema; Cho, H. T.; Hu, Bei Lok
2016-09-01
For a conformally coupled scalar field we obtain the conformally related Einstein-Langevin equations, using appropriate transformations for all the quantities in the equations between two conformally related spacetimes. In particular, we analyze the transformations of the influence action, the stress energy tensor, the noise kernel and the dissipation kernel. In due course the fluctuation-dissipation relation is also discussed. The analysis in this paper thereby facilitates a general solution to the Einstein-Langevin equation once the solution of the equation in a simpler, conformally related spacetime is known. For example, from the Minkowski solution of Martín and Verdaguer, those of the Einstein-Langevin equations in conformally flat spacetimes, especially for spatially flat Friedmann-Robertson-Walker models, can be readily obtained.
Generalized Langevin equation with tempered memory kernel
Liemert, André; Sandev, Trifce; Kantz, Holger
2017-01-01
We study a generalized Langevin equation for a free particle in presence of a truncated power-law and Mittag-Leffler memory kernel. It is shown that in presence of truncation, the particle from subdiffusive behavior in the short time limit, turns to normal diffusion in the long time limit. The case of harmonic oscillator is considered as well, and the relaxation functions and the normalized displacement correlation function are represented in an exact form. By considering external time-dependent periodic force we obtain resonant behavior even in case of a free particle due to the influence of the environment on the particle movement. Additionally, the double-peak phenomenon in the imaginary part of the complex susceptibility is observed. It is obtained that the truncation parameter has a huge influence on the behavior of these quantities, and it is shown how the truncation parameter changes the critical frequencies. The normalized displacement correlation function for a fractional generalized Langevin equation is investigated as well. All the results are exact and given in terms of the three parameter Mittag-Leffler function and the Prabhakar generalized integral operator, which in the kernel contains a three parameter Mittag-Leffler function. Such kind of truncated Langevin equation motion can be of high relevance for the description of lateral diffusion of lipids and proteins in cell membranes.
Malafeyev, O. A.; Nemnyugin, S. A.; Rylow, D.; Kolpak, E. P.; Awasthi, Achal
2017-07-01
The corruption dynamics is analyzed by means of the lattice model which is similar to the three-dimensional Ising model. Agents placed at nodes of the corrupt network periodically choose to perfom or not to perform the act of corruption at gain or loss while making decisions based on the process history. The gain value and its dynamics are defined by means of the Markov stochastic process modelling with parameters established in accordance with the influence of external and individual factors on the agent's gain. The model is formulated algorithmically and is studied by means of the computer simulation. Numerical results are obtained which demonstrate asymptotic behaviour of the corruption network under various conditions.
Sorin Dan ŞANDOR
2003-01-01
Full Text Available System Dynamics was introduced by Jay W. Forrester in the 1960s. Since then the methodology was adopted in many areas of natural or social sciences. This article tries to present briefly how this methodology works, both as Systems Thinking and as Modelling with Vensim computer software.
Dynamic modelling of windmills
Akhmatov, Vladislav; Knudsen, Hans
1999-01-01
An empirical dynamic model of windmills is set up based on analysis of measured Fourier spectra of the active electric power from a wind farm. The model is based on the assumption that eigenswings of the mechanical construction of the windmills excited by the phenomenon of vortex tower interaction...... will be transferred through the shaft to the electrical generator and result in disturbances of the active electric power supplied by the windmills. The results of the model are found to be in agreement with measurements in the frequency range of the model that is from 0.1 to 10 Hz....
Armbruster, Benjamin
2011-01-01
We analyze random networks that change over time. First we analyze a dynamic Erdos-Renyi model, whose edges change over time. We describe its stationary distribution, its convergence thereto, and the SI contact process on the network, which has relevance for connectivity and the spread of infections. Second, we analyze the effect of node turnover, when nodes enter and leave the network, which has relevance for network models incorporating births, deaths, aging, and other demographic factors.
Fluctuation-Response Relation and modeling in systems with fast and slow dynamics
G. Lacorata
2007-10-01
Full Text Available We show how a general formulation of the Fluctuation-Response Relation is able to describe in detail the connection between response properties to external perturbations and spontaneous fluctuations in systems with fast and slow variables. The method is tested by using the 360-variable Lorenz-96 model, where slow and fast variables are coupled to one another with reciprocal feedback, and a simplified low dimensional system. In the Fluctuation-Response context, the influence of the fast dynamics on the slow dynamics relies in a non trivial behavior of a suitable quadratic response function. This has important consequences for the modeling of the slow dynamics in terms of a Langevin equation: beyond a certain intrinsic time interval even the optimal model can give just statistical prediction.
Modal aerosol dynamics modeling
Whitby, E.R.; McMurry, P.H.; Shankar, U.; Binkowski, F.S.
1991-02-01
The report presents the governing equations for representing aerosol dynamics, based on several different representations of the aerosol size distribution. Analytical and numerical solution techniques for these governing equations are also reviewed. Described in detail is a computationally efficient numerical technique for simulating aerosol behavior in systems undergoing simultaneous heat transfer, fluid flow, and mass transfer in and between the gas and condensed phases. The technique belongs to a general class of models known as modal aerosol dynamics (MAD) models. These models solve for the temporal and spatial evolution of the particle size distribution function. Computational efficiency is achieved by representing the complete aerosol population as a sum of additive overlapping populations (modes), and solving for the time rate of change of integral moments of each mode. Applications of MAD models for simulating aerosol dynamics in continuous stirred tank aerosol reactors and flow aerosol reactors are provided. For the application to flow aerosol reactors, the discussion is developed in terms of considerations for merging a MAD model with the SIMPLER routine described by Patankar (1980). Considerations for incorporating a MAD model into the U.S. Environmental Protection Agency's Regional Particulate Model are also described. Numerical and analytical techniques for evaluating the size-space integrals of the modal dynamics equations (MDEs) are described. For multimodal logonormal distributions, an analytical expression for the coagulation integrals of the MDEs, applicable for all size regimes, is derived, and is within 20% of accurate numerical evaluation of the same moment coagulation integrals. A computationally efficient integration technique, based on Gauss-Hermite numerical integration, is also derived.
Murawski, Jens; Kleine, Eckhard
2017-04-01
Sea ice remains one of the frontiers of ocean modelling and is of vital importance for the correct forecasts of the northern oceans. At large scale, it is commonly considered a continuous medium whose dynamics is modelled in terms of continuum mechanics. Its specifics are a matter of constitutive behaviour which may be characterised as rigid-plastic. The new developed sea ice dynamic module bases on general principles and follows a systematic approach to the problem. Both drift field and stress field are modelled by a variational property. Rigidity is treated by Lagrangian relaxation. Thus one is led to a sensible numerical method. Modelling fast ice remains to be a challenge. It is understood that ridging and the formation of grounded ice keels plays a role in the process. The ice dynamic model includes a parameterisation of the stress associated with grounded ice keels. Shear against the grounded bottom contact might lead to plastic deformation and the loss of integrity. The numerical scheme involves a potentially large system of linear equations which is solved by pre-conditioned iteration. The entire algorithm consists of several components which result from decomposing the problem. The algorithm has been implemented and tested in practice.
Pusch, Andreas; Wuestner, Sebastian; Hamm, Joachim M; Tsakmakidis, Kosmas L; Hess, Ortwin
2012-03-27
Nanoplasmonic metamaterials are an exciting new class of engineered media that promise a range of important applications, such as subwavelength focusing, cloaking, and slowing/stopping of light. At optical frequencies, using gain to overcome potentially not insignificant losses has recently emerged as a viable solution to ultra-low-loss operation that may lead to next-generation active metamaterials. Maxwell-Bloch models for active nanoplasmonic metamaterials are able to describe the coherent spatiotemporal and nonlinear gain-plasmon dynamics. Here, we extend the Maxwell-Bloch theory to a Maxwell-Bloch Langevin approach-a spatially resolved model that describes the light field and noise dynamics in gain-enhanced nanoplasmonic structures. Using the example of an optically pumped nanofishnet metamaterial with an embedded laser dye (four-level) medium exhibiting a negative refractive index, we demonstrate the transition from loss-compensation to amplification and to nanolasing. We observe ultrafast relaxation oscillations of the bright negative-index mode with frequencies just below the THz regime. The influence of noise on mode competition and the onset and magnitude of the relaxation oscillations is elucidated, and the dynamics and spectra of the emitted light indicate that coherent amplification and lasing are maintained even in the presence of noise and amplified spontaneous emission.
Dynamic wake meandering modeling
Larsen, Gunner C.; Aagaard Madsen, H.; Bingoel, F. (and others)
2007-06-15
We present a consistent, physically based theory for the wake meandering phenomenon, which we consider of crucial importance for the overall description of wind turbine loadings in wind farms. In its present version the model is confined to single wake situations. The model philosophy does, however, have the potential to include also mutual wake interaction phenomenons. The basic conjecture behind the dynamic wake meandering model is that wake transportation in the atmospheric boundary layer is driven by the large scale lateral- and vertical turbulence components. Based on this conjecture a stochastic model of the downstream wake meandering is formulated. In addition to the kinematic formulation of the dynamics of the 'meandering frame of reference', models characterizing the mean wake deficit as well as the added wake turbulence, described in the meandering frame of reference, are an integrated part the model complex. For design applications, the computational efficiency of wake deficit prediction is a key issue. Two computationally low cost models are developed for this purpose. The character of the added wake turbulence, generated by the up-stream turbine in the form of shed and trailed vorticity, has been approached by analytical as well as by numerical studies. The dynamic wake meandering philosophy has been verified by comparing model predictions with extensive full-scale measurements. These comparisons have demonstrated good agreement, both qualitatively and quantitatively, concerning both flow characteristics and turbine load characteristics. Contrary to previous attempts to model wake loading, the dynamic wake meandering approach opens for a unifying description in the sense that turbine power and load aspects can be treated simultaneously. This capability is a direct and attractive consequence of the model being based on the underlying physical process, and it potentially opens for optimization of wind farm topology, of wind farm operation as
Perturbative and non-perturbative aspects non-Abelian Boltzmann-Langevin equation
Boedeker, Dietrich. E-mail: bodeker@physik.uni-bielefeld.de
2002-12-30
We study the Boltzmann-Langevin equation which describes the dynamics of hot Yang-Mills fields with typical momenta of order of the magnetic screening scale g{sup 2}T. It is transformed into a path integral and Feynman rules are obtained. We find that the leading log Langevin equation can be systematically improved in a well behaved expansion in log(1/g){sup -1}. The result by Arnold and Yaffe that the leading log Langevin equation is still valid at next-to-leading-log order is confirmed. We also confirm their result for the next-to-leading-log damping coefficient, or color conductivity, which is shown to be gauge fixing independent for a certain class of gauges. The frequency scale g{sup 2}T does not contribute to this result, but it does contribute, by power counting, to the transverse gauge field propagator. Going beyond a perturbative expansion we find 1-loop ultraviolet divergences which cannot be removed by renormalizing the parameters in the Boltzmann-Langevin equation.
Dynamic wake meandering modeling
Larsen, Gunner Chr.; Madsen Aagaard, Helge; Bingöl, Ferhat;
, are an integrated part the model complex. For design applications, the computational efficiency of wake deficit prediction is a key issue. Two computationally low cost models are developed for this purpose. The character of the added wake turbulence, generated by the up-stream turbine in the form of shed......We present a consistent, physically based theory for the wake meandering phenomenon, which we consider of crucial importance for the overall description of wind turbine loadings in wind farms. In its present version the model is confined to single wake situations. The model philosophy does, however......, have the potential to include also mutual wake interaction phenomenons. The basic conjecture behind the dynamic wake meandering model is that wake transportation in the atmospheric boundary layer is driven by the large scale lateral- and vertical turbulence components. Based on this conjecture...
Charpentier, Arthur; Durand, Marilou
2015-07-01
In this paper, we investigate questions arising in Parsons and Geist (Bull Seismol Soc Am 102:1-11, 2012). Pseudo causal models connecting magnitudes and waiting times are considered, through generalized regression. We do use conditional model (magnitude given previous waiting time, and conversely) as an extension to joint distribution model described in Nikoloulopoulos and Karlis (Environmetrics 19: 251-269, 2008). On the one hand, we fit a Pareto distribution for earthquake magnitudes, where the tail index is a function of waiting time following previous earthquake; on the other hand, waiting times are modeled using a Gamma or a Weibull distribution, where parameters are functions of the magnitude of the previous earthquake. We use those two models, alternatively, to generate the dynamics of earthquake occurrence, and to estimate the probability of occurrence of several earthquakes within a year or a decade.
Jansen, Thomas la Cour; Knoester, Jasper
2007-01-01
We combine numerical Langevin simulations with numerical integration of the Schrodinger equation to calculate two-dimensional infrared spectra of ultrafast chemical exchange. This provides a tool to model and interpret such spectra of molecules undergoing chemical processes, such as isomerization an
Structural dynamic modifications via models
T K Kundra
2000-06-01
Structural dynamic modification techniques attempt to reduce dynamic design time and can be implemented beginning with spatial models of structures, dynamic test data or updated models. The models assumed in this discussion are mathematical models, namely mass, stiffness, and damping matrices of the equations of motion of a structure. These models are identified/extracted from dynamic test data viz. frequency response functions (FRFs). Alternatively these models could have been obtained by adjusting or updating the finite element model of the structure in the light of the test data. The methods of structural modification for getting desired dynamic characteristics by using modifiers namely mass, beams and tuned absorbers are discussed.
Electron-hole recombination in disordered organic semiconductors: Validity of the Langevin formula
van der Holst, J. J. M.; van Oost, F. W. A.; Coehoorn, R.; Bobbert, P. A.
2009-12-01
Accurate modeling of electron-hole recombination in organic light-emitting diodes (OLEDs) is essential for developing a complete description of their functioning. Traditionally, the recombination rate is described by the Langevin formula, with a proportionality factor equal to the sum of the electron and hole mobilities. In the disordered organic semiconductors used in OLEDs these mobilities have been shown to depend strongly on the carrier densities and on the electric field. Moreover, the energetic disorder leads to percolating pathways for the electron and hole currents, which may or may not be correlated. To answer the question whether the Langevin formula is still valid under such circumstances we perform Monte Carlo simulations of the recombination rate for Gaussian energetic disorder. We vary the disorder energy, the temperature, the densities, and mobility ratio of electrons and holes, the electric field, and the type of correlation between the electron and hole energies. We find that at zero electric field the Langevin formula is surprisingly well obeyed, provided that a change in the charge-carrier mobilities due to the presence of charge carriers of the opposite type is taken into account. Deviations from the Langevin formula at finite electric field are small at the field scale relevant for OLED modeling.
Complex Langevin: Etiology and Diagnostics of its Main Problem
Aarts, Gert; Seiler, Erhard; Stamatescu, Ion-Olimpiu
2011-01-01
The complex Langevin method is a leading candidate for solving the so-called sign problem occurring in various physical situations. Its most vexing problem is that in some cases it produces `convergence to the wrong limit'. In the first part of the paper we go through the formal justification of the method, identify points at which it may fail and identify a necessary and sufficient criterion for correctness. This criterion would, however, require checking infinitely many identities, and therefore is somewhat academic. We propose instead a truncation to the check of a few identities; this still gives a necessary criterion, but a priori it is not clear whether it remains sufficient. In the second part we carry out a detailed study of two toy models: first we identify the reasons why in some cases the method fails, second we test the efficiency of the truncated criterion and find that it works perfectly at least in the toy models studied.
Langevin Simulation of Scalar Fields: Additive and Multiplicative Noises and Lattice Renormalization
Cassol-Seewald, N C; Fraga, E S; Krein, G; Ramos, R O
2007-01-01
We consider the nonequilibrium dynamics of the formation of a condensate in a spontaneously broken lambda phi4 scalar field theory, incorporating additive and multiplicative noise terms to study the role of fluctuation and dissipation. The corresponding stochastic Ginzburg-Landau-Langevin (GLL) equation is derived from the effective action, and solved on a (3+1)-dimensional lattice. Particular attention is devoted to the renormalization of the stochastic GLL equation in order to obtain lattice-independent equilibrium results.
Viñales, A. D.; Despósito, M. A.
2006-01-01
We study the effect of a disordered or fractal environment in the irreversible dynamics of a harmonic oscillator. Starting from a generalized Langevin equation and using Laplace analysis, we derive exact expressions for the mean values, variances, and velocity autocorrelation function of the particle in terms of generalized Mittag-Leffler functions. The long-time behaviors of these quantities are obtained and the presence of a whip-back effect is analyzed.
Naqvi, K R
2005-01-01
Ornstein and his coauthors, who constructed a dynamical theory of Brownian motion, taking the equation $mdv/dt =-\\zeta v+X$ as their starting point, usually named the equation after Einstein alone or after both Einstein and Langevin; furthermore, Ornstein, who was the first to extract from this equation the correct expression for $\\bar{\\Delta^2}$, the mean-squared distance covered by a Brownian particle, credited de Haas-Lorentz, rather than Langevin, for finding the stationary limit of $\\bar{\\Delta^2}$. A glance at Einstein's 1907 paper, titled ``Theoretical remarks on Brownian motion'', should suffice to convince one that it is not unfair to attribute the {\\it conception} of the above equation, now universally known as the Langevin equation, to Einstein. Langevin's avowed aim in his 1908 article was to recover, through a route that was `infinitely more simple', Einstein's 1905 expression for the diffusion coefficient, but a careful reading of Langevin's paper shows that--depending on how one interprets his ...
Langevin process reflected on a partially elastic boundary II
Jacob, Emmanuel
2011-01-01
A particle subject to a white noise external forcing moves like a Langevin process. Consider now that the particle is reflected at a boundary which restores a portion c of the incoming speed at each bounce. For c strictly smaller than the critical value 0.1630, the bounces of the reflected process accumulate in a finite time. We show that nonetheless the particle is not necessarily absorbed after this time. We define a "resurrected" reflected process as a recurrent extension of the absorbed process, and study some of its properties. We also prove that this resurrected reflected process is the unique solution to the stochastic partial differential equation describing the model. Our approach consists in defining the process conditioned on never being absorbed, via an h-transform, and then giving the Ito excursion measure of the recurrent extension thanks to a formula fairly similar to Imhof's relation.
Berthoumieux, Hélène
2016-01-01
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 non-equilibrium 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, estimate the deviation of the fluctuation-dissipation theorem and the range of...
Comparing different dynamic stall models
Holierhoek, J.G. [Unit Wind Energy, Energy research Centre of the Netherlands, ZG, Petten (Netherlands); De Vaal, J.B.; Van Zuijlen, A.H.; Bijl, H. [Aerospace Engineering, Delft University of Technology, Delft (Netherlands)
2012-07-16
The dynamic stall phenomenon and its importance for load calculations and aeroelastic simulations is well known. Different models exist to model the effect of dynamic stall; however, a systematic comparison is still lacking. To investigate if one is performing better than another, three models are used to simulate the Ohio State University measurements and a set of data from the National Aeronautics and Space Administration Ames experimental study of dynamic stall and compare results. These measurements were at conditions and for aerofoils that are typical for wind turbines, and the results are publicly available. The three selected dynamic stall models are the ONERA model, the Beddoes-Leishman model and the Snel model. The simulations show that there are still significant differences between measurements and models and that none of the models is significantly better in all cases than the other models. Especially in the deep stall regime, the accuracy of each of the dynamic stall models is limited.
Campagnoli, Patrizia; Petris, Giovanni
2009-01-01
State space models have gained tremendous popularity in as disparate fields as engineering, economics, genetics and ecology. Introducing general state space models, this book focuses on dynamic linear models, emphasizing their Bayesian analysis. It illustrates the fundamental steps needed to use dynamic linear models in practice, using R package.
Langevin-Poisson-EQT: A dipolar solvent based quasi-continuum approach for electric double layers
Mashayak, S. Y.; Aluru, N. R.
2017-01-01
Water is a highly polar solvent. As a result, electrostatic interactions of interfacial water molecules play a dominant role in determining the distribution of ions in electric double layers (EDLs). Near a surface, an inhomogeneous and anisotropic arrangement of water molecules gives rise to pronounced variations in the electrostatic and hydration energies of ions. Therefore, a detailed description of the structural and dielectric properties of water is important to study EDLs. However, most theoretical models ignore the molecular effects of water and treat water as a background continuum with a uniform dielectric permittivity. Explicit consideration of water polarization and hydration of ions is both theoretically and numerically challenging. In this work, we present an empirical potential-based quasi-continuum theory (EQT) for EDL, which incorporates the polarization and hydration effects of water explicitly. In EQT, water molecules are modeled as Langevin point dipoles and a point dipole based coarse-grained model for water is developed systematically. The space dependence of the dielectric permittivity of water is included in the Poisson equation to compute the electrostatic potential. In addition, to reproduce hydration of ions, ion-water coarse-grained potentials are developed. We demonstrate the EQT framework for EDL by simulating NaCl aqueous electrolyte confined inside slit-like capacitor channels at various ion concentrations and surface charge densities. We show that the ion and water density predictions from EQT agree well with the reference molecular dynamics simulations.
Mazurek K.
2013-12-01
Full Text Available The fission dynamics described by solving differential equations of the Langevin type in three dimensional space of the deformation parameters is very sensitive on the choice of the macroscopic components such as potential energy models. The mass or charge distribution or total kinetic energy has been already shown to be different when one uses the Finite Range Liquid Drop Model or Lublin - Strasbourg Drop model. Also the shape-dependent congruence or shape-dependent Wigner energy and A0 terms are important especially for the fission of medium mass nuclei. We would like to make step forward and answer the question about the varying of the post-scission multiplicity by including different PES. Up to now there are only few experimental data for the medium mass nuclei where the pre- and post- scission emission has been estimated and isotopic distributions have been shown. The isotopic distributions of the fission products for light compound nucleus such as 111 In with two beam energies (Ebeam = 10.6 AMeV and 5.9 AMeV and two heavy systems: 229Np with Ebeam = 7.4 AMeV and 260 No (Ebeam = 6 AMeV and 7.5 AMeV have been studied theoretically. The agreement with the experimental data is discussed.
Pahlavani, M. R.; Mirfathi, S. M.
2017-07-01
Neutron multiplicity prior to scission and evaluation of mass distribution of fission fragments with the fission time scale for neutron induced fission of plutonium isotopes are investigated using a dynamical Langevin approach. Also, mass yield of fragments and prompt neutron multiplicity in different time scales of the fission process are compared with experimental data. Reasonable agreement is achieved between calculated and available experimental data.
Another derivation of generalized Langevin equations
Dengler, R
2015-01-01
The formal derivation of Langevin equations (and, equivalently Fokker-Planck equations) with projection operator techniques of Mori, Zwanzig, Kawasaki and others can well be called a pearl of theoretical physics. The derivation relies on classical mechanics, and encompasses everything an omnipotent engineer can construct from point particles and potentials: solids, liquids, liquid crystals, conductors, polymers, systems with spin-like degrees of freedom ... Einstein relations and Onsager reciprocity theorem come for free. It apparently not has widely found its way into textbooks, but has been reproduced dozens of times on the fly with many references to the literature and without adding much substantially new. Here we follow the tradition, but strive to produce a self-contained text. Furthermore, we address questions that naturally arise in the derivation. Among other things the meaning of the divergence of the Poisson brackets is explained, and the role of nonlinear damping coefficients is clarified.
Stochastic thermodynamics for delayed Langevin systems.
Jiang, Huijun; Xiao, Tiejun; Hou, Zhonghuai
2011-06-01
We discuss stochastic thermodynamics (ST) for delayed Langevin systems in this paper. By using the general principles of ST, the first-law-like energy balance and trajectory-dependent entropy s(t) can be well defined in a way that is similar to that in a system without delay. Because the presence of time delay brings an additional entropy flux into the system, the conventional second law (Δs(tot))≥0 no longer holds true, where Δs(tot) denotes the total entropy change along a stochastic path and (·) stands for the average over the path ensemble. With the help of a Fokker-Planck description, we introduce a delay-averaged trajectory-dependent dissipation functional η[χ(t)] which involves the work done by a delay-averaged force F(x,t) along the path χ(t) and equals the medium entropy change Δs(m)[x(t)] in the absence of delay. We show that the total dissipation functional R=Δs+η, where Δs denotes the system entropy change along a path, obeys (R)≥0, which could be viewed as the second law in the delayed system. In addition, the integral fluctuation theorem (e(-R))=1 also holds true. We apply these concepts to a linear Langevin system with time delay and periodic external force. Numerical results demonstrate that the total entropy change (Δs(tot)) could indeed be negative when the delay feedback is positive. By using an inversing-mapping approach, we are able to obtain the delay-averaged force F(x,t) from the stationary distribution and then calculate the functional R as well as its distribution. The second law (R)≥0 and the fluctuation theorem are successfully validated.
Harko, Tiberiu; Mocanu, Gabriela
2014-01-01
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, which accounts for the general memory and retarded effects of the frictional force, and on the fluctuation-dissipation theorem. The presence of the memory effects influences the response of the disk to external random interactions, and 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 (PSD) of the disk luminosity is also obtained. As a possible astrophysical application of the formalism we investigate the possibility that the Intra...
Modelling dynamic roughness during floods
Paarlberg, Andries; Dohmen-Janssen, Catarine M.; Hulscher, Suzanne J.M.H.; Termes, A.P.P.
2007-01-01
In this paper, we present a dynamic roughness model to predict water levels during floods. Hysteresis effects of dune development are explicitly included. It is shown that differences between the new dynamic roughness model, and models where the roughness coefficient is calibrated, are most
Friston, K J; Harrison, L; Penny, W
2003-08-01
In this paper we present an approach to the identification of nonlinear input-state-output systems. By using a bilinear approximation to the dynamics of interactions among states, the parameters of the implicit causal model reduce to three sets. These comprise (1) parameters that mediate the influence of extrinsic inputs on the states, (2) parameters that mediate intrinsic coupling among the states, and (3) [bilinear] parameters that allow the inputs to modulate that coupling. Identification proceeds in a Bayesian framework given known, deterministic inputs and the observed responses of the system. We developed this approach for the analysis of effective connectivity using experimentally designed inputs and fMRI responses. In this context, the coupling parameters correspond to effective connectivity and the bilinear parameters reflect the changes in connectivity induced by inputs. The ensuing framework allows one to characterise fMRI experiments, conceptually, as an experimental manipulation of integration among brain regions (by contextual or trial-free inputs, like time or attentional set) that is revealed using evoked responses (to perturbations or trial-bound inputs, like stimuli). As with previous analyses of effective connectivity, the focus is on experimentally induced changes in coupling (cf., psychophysiologic interactions). However, unlike previous approaches in neuroimaging, the causal model ascribes responses to designed deterministic inputs, as opposed to treating inputs as unknown and stochastic.
Mankin, R; Laas, K; Sauga, A
2011-06-01
The temporal behavior of the mean-square displacement and the velocity autocorrelation function of a particle subjected to a periodic force in a harmonic potential well is investigated for viscoelastic media using the generalized Langevin equation. The interaction with fluctuations of environmental parameters is modeled by a multiplicative white noise, by an internal Mittag-Leffler noise with a finite memory time, and by an additive external noise. It is shown that the presence of a multiplicative noise has a profound effect on the behavior of the autocorrelation functions. Particularly, for correlation functions the model predicts a crossover between two different asymptotic power-law regimes. Moreover, a dependence of the correlation function on the frequency of the external periodic forcing occurs that gives a simple criterion to discern the multiplicative noise in future experiments. It is established that additive external and internal noises cause qualitatively different dependences of the autocorrelation functions on the external forcing and also on the time lag. The influence of the memory time of the internal noise on the dynamics of the system is also discussed.
Dynamic-structure-factor measurements on a model Lorentz gas
Egelstaff, P. A.; Eder, O. J.; Glaser, W.; Polo, J.; Renker, B.; Soper, A. K.
1990-02-01
A model system for the Lorentz gas can be made [Eder, Chen, and Egelstaff, Proc. Phys. Soc. London 89, 833 (1966); McPherson and Egelstaff, Can. J. Phys. 58, 289 (1980)] by mixing small quantities of hydrogen with an argon host. For neutron-scattering experiments the large H-to-Ar cross section ratio (~200) makes the argon relatively invisible. Dynamic-structure-factor [S(Q,ω) for H2] measurements at room temperature have been made on this system using the IN4 spectrometer at the Institute Laue Langevin, Grenoble, France. Argon densities between 1.9 and 10.5 atoms/nm3 were used for 0.4model, but slightly less complicated than a computer simulation so showing the significance of multiple-collision processes.
Derivation of the generalized Langevin equation in nonstationary environments.
Kawai, Shinnosuke; Komatsuzaki, Tamiki
2011-03-21
The generalized Langevin equation (GLE) is extended to the case of nonstationary bath. The derivation starts with the Hamiltonian equation of motion of the total system including the bath, without any assumption on the form of Hamiltonian or the distribution of the initial condition. Then the projection operator formulation is utilized to obtain a low-dimensional description of the system dynamics surrounded by the nonstationary bath modes. In contrast to the ordinary GLE, the mean force becomes a time-dependent function of the position and the velocity of the system. The friction kernel is found to depend on both the past and the current times, in contrast to the stationary case where it only depends on their difference. The fluctuation-dissipation theorem, which relates the statistical property of the random force to the friction kernel, is also derived for general nonstationary cases. The resulting equation of motion is as simple as the ordinary GLE, and is expected to give a powerful framework to analyze the dynamics of the system surrounded by a nonstationary bath.
Sasanka ARE; Markos A.KATSOULAKIS; Anders SZEPESSY
2009-01-01
Kinetic Monte Carlo methods provide a powerful computational tool for the simulation of microscopic processes such as the diffusion of interacting particles on a surface, at a detailed atomistic level. However such algorithms are typically computationally expensive and are restricted to fairly small spatiotemporal scales. One approach towards overcoming this problem was the development of coarse-grained Monte Carlo algorithms. In recent literature, these methods were shown to be capable of efficiently describing much larger length scales while still incorporating information on microscopic interactions and fluctuations. In this paper, a coarse-grained Langevin system of stochastic differential equations as approximations of diffusion of interacting particles is derived, based on these earlier coarse-grained models. The authors demonstrate the asymptotic equivalence of transient and long time behavior of the Langevin approximation and the underlying microscopic process, using asymptotics methods such as large deviations for interacting particles systems, and furthermore, present corresponding numerical simulations, comparing statistical quantities like mean paths, auto correlations and power spectra of the microscopic and the approximating Langevin processes. Finally, it is shown that the Langevin approximations presented here are much more computationally efficient than conventional Kinetic Monte Carlo methods, since in addition to the reduction in the number of spatial degrees of freedom in coarse-grained Monte Carlo methods, the Langevin system of stochastic differential equations allows for multiple particle moves in a single timestep.
Florian Ion Tiberiu Petrescu; Relly Victoria Virgil Petrescu
2016-01-01
Otto engine dynamics are similar in almost all common internal combustion engines. We can speak so about dynamics of engines: Lenoir, Otto, and Diesel. The dynamic presented model is simple and original. The first thing necessary in the calculation of Otto engine dynamics, is to determine the inertial mass reduced at the piston. One uses then the Lagrange equation. Kinetic energy conservation shows angular speed variation (from the shaft) with inertial masses. One uses and elastic constant of...
Fractional Langevin equation and Riemann-Liouville fractional derivative.
Sau Fa, Kwok
2007-10-01
In this present work we consider a fractional Langevin equation with Riemann-Liouville fractional time derivative which modifies the classical Newtonian force, nonlocal dissipative force, and long-time correlation. We investigate the first two moments, variances and position and velocity correlation functions of this system. We also compare them with the results obtained from the same fractional Langevin equation which uses the Caputo fractional derivative.
Dynamical features of nuclear fission
Santanu Pal
2015-08-01
It is now established that the transition-state theory of nuclear fission due to Bohr and Wheeler underestimates several observables in heavy-ion-induced fusion–fission reactions. Dissipative dynamical models employing either the Langevin equation or equivalently the Fokker–Planck equation have been developed for fission of heavy nuclei at high excitations (T ∼1 MeV or higher). Here, we first present the physical picture underlying the dissipative fission dynamics. We mainly concentrate upon the Kramers’ prescription for including dissipation in fission dynamics. We discuss, in some detail, the results of a statistical model analysis of the pre-scission neutron multiplicity data from the reactions 19F+194,196,198Pt using Kramers’ fission width. We also discuss the multi-dimensional Langevin equation in the context of kinetic energy and mass distribution of the fission fragments.
Nagata, Keitaro; Shimasaki, Shinji
2016-01-01
The complex Langevin method is a promising approach to the complex-action problem based on a fictitious time evolution of complexified dynamical variables under the influence of a Gaussian noise. Although it is known to have a restricted range of applicability, the use of gauge cooling made it applicable to various interesting cases including finite density QCD in certain parameter regions. In this paper we revisit the argument for justification of the method. Starting with a finite Langevin step-size $\\epsilon$, we find that the $\\epsilon\\rightarrow 0$ limit is actually subtle, although the previous argument used a continuous Langevin time from the outset. We also point out a subtlety in the use of time-evolved observables, which play a crucial role in the argument. This subtlety appears when the probability of the drift term is not suppressed exponentially at large magnitude. We claim that the failures of the method previously considered to occur for different reasons should be understood in this way. Using...
Kwok, Sau Fa, E-mail: kwok@dfi.uem.br
2012-08-15
A Langevin equation with multiplicative white noise and its corresponding Fokker-Planck equation are considered in this work. From the Fokker-Planck equation a transformation into the Wiener process is provided for different orders of prescription in discretization rule for the stochastic integrals. A few applications are also discussed. - Highlights: Black-Right-Pointing-Pointer Fokker-Planck equation corresponding to the Langevin equation with mul- tiplicative white noise is presented. Black-Right-Pointing-Pointer Transformation of diffusion processes into the Wiener process in different prescriptions is provided. Black-Right-Pointing-Pointer The prescription parameter is associated with the growth rate for a Gompertz-type model.
Deriving Langevin equations in curved spacetime
Ramos, Rudnei O.; Tavares, Romulo F. [Universidade do Estado do Rio de Janeiro (UERJ), Rio de Janeiro, RJ (Brazil)
2013-07-01
Full text: Warm inflation is an inflationary scenario where the interactions between the inflaton and other degrees of freedom are considered. The effective equation of motion for the inflaton is in general of the form of a Langevin equation, that includes both quantum and thermal effects and where these effects manifest in the form of dissipation and stochastic noise terms, which are related by a generalized fluctuation-dissipation relation. The dissipation term is related to the interactions of the inflaton with other degrees of freedom of the thermal bath that can be obtained from the appropriate Feynman propagators. As the inflaton evolves into an expanding metric, these effects have to be taken into account when calculating the Green functions and consequently the Feynman propagators. In this work we present the considerations that must be made to calculate the Green functions in curved space (expanding metric) and in the presence of radiation in order to proper derive the effective evolution of the inflaton in the warm-inflation scenario. (author)
c -number quantum generalized Langevin equation for an open system
Kantorovich, L.; Ness, H.; Stella, L.; Lorenz, C. D.
2016-11-01
We derive a c -number generalized Langevin equation (GLE) describing the evolution of the expectation values xixit of the atomic position operators xi of an open system. The latter is coupled linearly to a harmonic bath kept at a fixed temperature. The equations of motion contain a non-Markovian friction term with the classical kernel [L. Kantorovich, Phys. Rev. B 78, 094304 (2008), 10.1103/PhysRevB.78.094304] and a zero mean non-Gaussian random force with correlation functions that depend on the initial preparation of the open system. We used a density operator formalism without assuming that initially the combined system was decoupled. The only approximation made in deriving quantum GLE consists of assuming that the Hamiltonian of the open system at time t can be expanded up to the second order with respect to operators of atomic displacements ui=xi-t (the "harmonization" approximation). The noise is introduced to ensure that sampling many quantum GLE trajectories yields exactly the average one. An explicit expression for the pair correlation function of the noise, consistent with the classical limit, is also proposed. Unlike the usually considered quantum operator GLE, the proposed c -number quantum GLE can be used in direct molecular dynamic simulations of open systems under general equilibrium or nonequilibrium conditions.
Description of quantum noise by a Langevin equation
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.
Computer Modelling of Dynamic Processes
B. Rybakin
2000-10-01
Full Text Available Results of numerical modeling of dynamic problems are summed in the article up. These problems are characteristic for various areas of human activity, in particular for problem solving in ecology. The following problems are considered in the present work: computer modeling of dynamic effects on elastic-plastic bodies, calculation and determination of performances of gas streams in gas cleaning equipment, modeling of biogas formation processes.
Launch Vehicle Dynamics Demonstrator Model
1963-01-01
Launch Vehicle Dynamics Demonstrator Model. The effect of vibration on launch vehicle dynamics was studied. Conditions included three modes of instability. The film includes close up views of the simulator fuel tank with and without stability control. [Entire movie available on DVD from CASI as Doc ID 20070030984. Contact help@sti.nasa.gov
Generative models of conformational dynamics.
Langmead, Christopher James
2014-01-01
Atomistic simulations of the conformational dynamics of proteins can be performed using either Molecular Dynamics or Monte Carlo procedures. The ensembles of three-dimensional structures produced during simulation can be analyzed in a number of ways to elucidate the thermodynamic and kinetic properties of the system. The goal of this chapter is to review both traditional and emerging methods for learning generative models from atomistic simulation data. Here, the term 'generative' refers to a model of the joint probability distribution over the behaviors of the constituent atoms. In the context of molecular modeling, generative models reveal the correlation structure between the atoms, and may be used to predict how the system will respond to structural perturbations. We begin by discussing traditional methods, which produce multivariate Gaussian models. We then discuss GAMELAN (GRAPHICAL MODELS OF ENERGY LANDSCAPES), which produces generative models of complex, non-Gaussian conformational dynamics (e.g., allostery, binding, folding, etc.) from long timescale simulation data.
Fractal Models of Earthquake Dynamics
Bhattacharya, Pathikrit; Kamal,; Samanta, Debashis
2009-01-01
Our understanding of earthquakes is based on the theory of plate tectonics. Earthquake dynamics is the study of the interactions of plates (solid disjoint parts of the lithosphere) which produce seismic activity. Over the last about fifty years many models have come up which try to simulate seismic activity by mimicking plate plate interactions. The validity of a given model is subject to the compliance of the synthetic seismic activity it produces to the well known empirical laws which describe the statistical features of observed seismic activity. Here we present a review of two such models of earthquake dynamics with main focus on a relatively new model namely The Two Fractal Overlap Model.
Dynamic programming models and applications
Denardo, Eric V
2003-01-01
Introduction to sequential decision processes covers use of dynamic programming in studying models of resource allocation, methods for approximating solutions of control problems in continuous time, production control, more. 1982 edition.
Building dynamic spatial environmental models
Karssenberg, D.J.
2003-01-01
An environmental model is a representation or imitation of complex natural phenomena that can be discerned by human cognitive processes. This thesis deals with the type of environmental models referred to as dynamic spatial environmental models. The word spatial refers to the geographic domain whi
Dynamical models of the Galaxy
McMillan P.J.
2012-02-01
Full Text Available I discuss the importance of dynamical models for exploiting survey data, focusing on the advantages of “torus” models. I summarize a number of applications of these models to the study of the Milky Way, including the determination of the peculiar Solar velocity and investigation of the Hyades moving group.
Knudsen, Torben
2011-01-01
The purpose with this deliverable 2.5 is to use fresh experimental data for validation and selection of a flow model to be used for control design in WP3-4. Initially the idea was to investigate the models developed in WP2. However, in the project it was agreed to include and focus on a additive...... model turns out not to be useful for prediction of the flow. Moreover, standard Box Jenkins model structures and multiple output auto regressive models proves to be superior as they can give useful predictions of the flow....
Predictive models of forest dynamics.
Purves, Drew; Pacala, Stephen
2008-06-13
Dynamic global vegetation models (DGVMs) have shown that forest dynamics could dramatically alter the response of the global climate system to increased atmospheric carbon dioxide over the next century. But there is little agreement between different DGVMs, making forest dynamics one of the greatest sources of uncertainty in predicting future climate. DGVM predictions could be strengthened by integrating the ecological realities of biodiversity and height-structured competition for light, facilitated by recent advances in the mathematics of forest modeling, ecological understanding of diverse forest communities, and the availability of forest inventory data.
Adams, Neil S.; Bollenbacher, Gary
1992-01-01
This report discusses the development and underlying mathematics of a rigid-body computer model of a proposed cryogenic on-orbit liquid depot storage, acquisition, and transfer spacecraft (COLD-SAT). This model, referred to in this report as the COLD-SAT dynamic model, consists of both a trajectory model and an attitudinal model. All disturbance forces and torques expected to be significant for the actual COLD-SAT spacecraft are modeled to the required degree of accuracy. Control and experimental thrusters are modeled, as well as fluid slosh. The model also computes microgravity disturbance accelerations at any specified point in the spacecraft. The model was developed by using the Boeing EASY5 dynamic analysis package and will run on Apollo, Cray, and other computing platforms.
Soto-Aquino, D; Rosso, D; Rinaldi, C
2011-11-01
Ferrofluids are colloidal suspensions of magnetic nanoparticles that exhibit normal liquid behavior in the absence of magnetic fields but respond to imposed magnetic fields by changing their viscosity without loss of fluidity. The response of ferrofluids to constant shear and magnetic fields has received a lot of attention, but the response of ferrofluids to oscillatory shear remains largely unexplored. In the present work we used rotational Brownian dynamics to study the dynamic properties of ferrofluids with thermally blocked nanoparticles under oscillatory shear and constant magnetic fields. Comparisons between simulations and modeling using the ferrohydrodynamics equations were also made. Simulation results show that, for small rotational Péclet number, the in-phase and out-of-phase components of the complex viscosity depend on the magnitude of the magnetic field and frequency of the shear, following a Maxwell-like model with field-dependent viscosity and characteristic time equal to the field-dependent transverse magnetic relaxation time of the nanoparticles. Comparison between simulations and the numerical solution of the ferrohydrodynamic equations shows that the oscillatory rotational magnetoviscosity for an oscillating shear field obtained using the kinetic magnetization relaxation equation quantitatively agrees with simulations for a wide range of Péclet number and Langevin parameter but has quantitative deviations from the simulations at high values of the Langevin parameter. These predictions indicate an apparent elastic character to the rheology of these suspensions, even though we are considering the infinitely dilute limit in which there are negligible particle-particle interactions and, as such, chains do not form. Additionally, an asymptotic analytical solution of the ferrohydrodynamics equations, valid for Pe<2, was used to demonstrate that the Cox-Merz rule applies for dilute ferrofluids under conditions of small shear rates. At higher shear
Self-diffusion in a system of interacting Langevin particles.
Dean, D S; Lefèvre, A
2004-06-01
The behavior of the self-diffusion constant of Langevin particles interacting via a pairwise interaction is considered. The diffusion constant is calculated approximately within a perturbation theory in the potential strength about the bare diffusion constant. It is shown how this expansion leads to a systematic double expansion in the inverse temperature beta and the particle density rho. The one-loop diagrams in this expansion can be summed exactly and we show that this result is exact in the limit of small beta and rhobeta constants. The one-loop result can also be resummed using a semiphenomenological renormalization group method which has proved useful in the study of diffusion in random media. In certain cases the renormalization group calculation predicts the existence of a diverging relaxation time signaled by the vanishing of the diffusion constant, possible forms of divergence coming from this approximation are discussed. Finally, at a more quantitative level, the results are compared with numerical simulations, in two dimensions, of particles interacting via a soft potential recently used to model the interaction between coiled polymers.
Berg, van den, Aad; Meester, R.; White, Damien
1997-01-01
Consider an ordinary Boolean model, that is, a homogeneous Poisson point process in Rd, where the points are all centres of random balls with i.i.d. radii. Now let these points move around according to i.i.d. stochastic processes. It is not hard to show that at each xed time t we again have a Boolean model with the original distribution. Hence if the original model is supercritical then, for any t, the probability of having an unbounded occupied component at time t equals 1. We show that unde...
Sotiropoulos, Vassilios; Kaznessis, Yiannis N
2008-01-07
Models involving stochastic differential equations (SDEs) play a prominent role in a wide range of applications where systems are not at the thermodynamic limit, for example, biological population dynamics. Therefore there is a need for numerical schemes that are capable of accurately and efficiently integrating systems of SDEs. In this work we introduce a variable size step algorithm and apply it to systems of stiff SDEs with multiple multiplicative noise. The algorithm is validated using a subclass of SDEs called chemical Langevin equations that appear in the description of dilute chemical kinetics models, with important applications mainly in biology. Three representative examples are used to test and report on the behavior of the proposed scheme. We demonstrate the advantages and disadvantages over fixed time step integration schemes of the proposed method, showing that the adaptive time step method is considerably more stable than fixed step methods with no excessive additional computational overhead.
Anomalous diffusion in nonhomogeneous media: time-subordinated Langevin equation approach.
Srokowski, Tomasz
2014-03-01
Diffusion in nonhomogeneous media is described by a dynamical process driven by a general Lévy noise and subordinated to a random time; the subordinator depends on the position. This problem is approximated by a multiplicative process subordinated to a random time: it separately takes into account effects related to the medium structure and the memory. Density distributions and moments are derived from the solutions of the corresponding Langevin equation and compared with the numerical calculations for the exact problem. Both subdiffusion and enhanced diffusion are predicted. Distribution of the process satisfies the fractional Fokker-Planck equation.
The Langevin Approach: a simple stochastic method for complex phenomena
Reinke, Nico; Medjroubi, Wided; Lind, Pedro G; Wächter, Matthias; Peinke, Joachim
2015-01-01
We describe a simple stochastic method, so-called Langevin approach, which enables one to extract evolution equations of stochastic variables from a set of measurements. Our method is parameter-free and it is based on the nonlinear Langevin equation. Moreover, it can be applied not only to processes in time, but also to processes in scale, given that the data available shows ergodicity. This chapter introduces the mathematical foundations of the Langevin approach and describes how to implement it numerically. A specific application of the method is presented, namely to a turbulent velocity field measured in the laboratory, retrieving the corresponding energy cascade and comparing with the results from a computational simulation of that experiment. In addition, we describe a physical interpretation bridging between processes in time and in scale. Finally, we describe extensions of the method for time series reconstruction and applications to other fields such as finance, medicine, geophysics and renewable ener...
Modelling group dynamic animal movement
Langrock, Roland; Hopcraft, J. Grant C.; Blackwell, Paul G.
2014-01-01
Group dynamic movement is a fundamental aspect of many species' movements. The need to adequately model individuals' interactions with other group members has been recognised, particularly in order to differentiate the role of social forces in individual movement from environmental factors. However......, to date, practical statistical methods which can include group dynamics in animal movement models have been lacking. We consider a flexible modelling framework that distinguishes a group-level model, describing the movement of the group's centre, and an individual-level model, such that each individual...... makes its movement decisions relative to the group centroid. The basic idea is framed within the flexible class of hidden Markov models, extending previous work on modelling animal movement by means of multi-state random walks. While in simulation experiments parameter estimators exhibit some bias...
Eslamizadeh, H.
2017-02-01
Evaporation residue cross section, fission probability, anisotropy of fission fragment angular distribution, mass and energy distributions of fission fragments and the pre-scission neutron multiplicity for the excited compound nuclei {}168{{Y}}{{b}}, {}172{{Y}}{{b}}, {}178{{W}} and {}227{{P}}{{a}} produced in fusion reactions have been calculated in the framework of the modified statistical model and multidimensional dynamical model. In the dynamical calculations, the dynamics of fission of excited nuclei has been studied by solving three- and four-dimensional Langevin equations with dissipation generated through the chaos-weighted wall and window friction formula. Three collective shape coordinates plus the projection of total spin of the compound nucleus to the symmetry axis, K, were considered in the four-dimensional dynamical model. A non-constant dissipation coefficient of K, {γ }k, was applied in the four-dimensional dynamical calculations. A comparison of the results of the three- and four-dimensional dynamical models with the experimental data showed that the results of the four-dimensional dynamical model for the evaporation residue cross section, fission probability, anisotropy of fission fragment angular distribution, mass and energy distributions of fission fragments and the pre-scission neutron multiplicity are in better agreement with the experimental data. It was also shown that the modified statistical model can reproduce the above-mentioned experimental data by choosing appropriate values of the temperature coefficient of the effective potential, λ , and the scaling factor of the fission-barrier height, {r}s.
Gabora, Liane
2008-01-01
EVOC (for EVOlution of Culture) is a computer model of culture that enables us to investigate how various factors such as barriers to cultural diffusion, the presence and choice of leaders, or changes in the ratio of innovation to imitation affect the diversity and effectiveness of ideas. It consists of neural network based agents that invent ideas for actions, and imitate neighbors' actions. The model is based on a theory of culture according to which what evolves through culture is not memes or artifacts, but the internal models of the world that give rise to them, and they evolve not through a Darwinian process of competitive exclusion but a Lamarckian process involving exchange of innovation protocols. EVOC shows an increase in mean fitness of actions over time, and an increase and then decrease in the diversity of actions. Diversity of actions is positively correlated with population size and density, and with barriers between populations. Slowly eroding borders increase fitness without sacrificing diver...
Swimmers’ Collective Dynamics Modelization
Ferré Porta, Guillem
2011-01-01
English: We describe a new model in order to study the properties of collections of self-propelled particles swimming in a two-dimensional fluid. Our model consist in two types of particles, the first interacting with each other with a soft potential and thus representing the fluid while the second type are self-propelled particles of biological nature capable of changing its orientation following the velocity field of the fluid. The results of the simulations show how a super-diffusive regim...
Model of THz Magnetization Dynamics
Bocklage, Lars
2016-01-01
Magnetization dynamics can be coherently controlled by THz laser excitation, which can be applied in ultrafast magnetization control and switching. Here, transient magnetization dynamics are calculated for excitation with THz magnetic field pulses. We use the ansatz of Smit and Beljers, to formulate dynamic properties of the magnetization via partial derivatives of the samples free energy density, and extend it to solve the Landau-Lifshitz-equation to obtain the THz transients of the magnetization. The model is used to determine the magnetization response to ultrafast multi- and single-cycle THz pulses. Control of the magnetization trajectory by utilizing the THz pulse shape and polarization is demonstrated. PMID:26956997
Modeling Internet Topology Dynamics
Haddadi, H.; Uhlig, S.; Moore, A.; Mortier, R.; Rio, M.
Despite the large number of papers on network topology modeling and inference, there still exists ambiguity about the real nature of the Internet AS and router level topology. While recent findings have illustrated the inaccuracies in maps inferred from BGP peering and traceroute measurements, exist
Langevin equation for systems with a preferred spatial direction
Belousov, Roman; Cohen, E. G. D.; Rondoni, Lamberto
2016-09-01
In this paper, we generalize the theory of Brownian motion and the Onsager-Machlup theory of fluctuations for spatially symmetric systems to equilibrium and nonequilibrium steady-state systems with a preferred spatial direction, due to an external force. To do this, we extend the Langevin equation to include a bias, which is introduced by an external force and alters the Gaussian structure of the system's fluctuations. In addition, by solving this extended equation, we provide a physical interpretation for the statistical properties of the fluctuations in these systems. Connections of the extended Langevin equation with the theory of active Brownian motion are discussed as well.
Langevin equation approach to diffusion magnetic resonance imaging.
Cooke, Jennie M; Kalmykov, Yuri P; Coffey, William T; Kerskens, Christian M
2009-12-01
The normal phase diffusion problem in magnetic resonance imaging (MRI) is treated by means of the Langevin equation for the phase variable using only the properties of the characteristic function of Gaussian random variables. The calculation may be simply extended to anomalous diffusion using a fractional generalization of the Langevin equation proposed by Lutz [E. Lutz, Phys. Rev. E 64, 051106 (2001)] pertaining to the fractional Brownian motion of a free particle coupled to a fractal heat bath. The results compare favorably with diffusion-weighted experiments acquired in human neuronal tissue using a 3 T MRI scanner.
Nonergodic dynamics of force-free granular gases
Bodrova, Anna; Chechkin, Aleksei V.; Cherstvy, Andrey G.; Metzler, Ralf
2015-01-01
We study analytically and by event-driven molecular dynamics simulations the nonergodic and aging properties of force-free cooling granular gases with both constant and velocity-dependent (viscoelastic) restitution coefficient $\\varepsilon$ for particle pair collisions. We compare the granular gas dynamics with an effective single particle stochastic model based on an underdamped Langevin equation with time dependent diffusivity. We find that both models share the same behavior of the ensembl...
Vehicle dynamics modeling and simulation
Schramm, Dieter; Bardini, Roberto
2014-01-01
The authors examine in detail the fundamentals and mathematical descriptions of the dynamics of automobiles. In this context different levels of complexity will be presented, starting with basic single-track models up to complex three-dimensional multi-body models. A particular focus is on the process of establishing mathematical models on the basis of real cars and the validation of simulation results. The methods presented are explained in detail by means of selected application scenarios.
Paty, M. [Paris-7 Univ., 75 (France)
1999-05-01
This article is a short biography of the French physicist Paul Langevin. P.Langevin epitomizes the whole physics of the first half of the last century. His formation made him both an experimenter and a theorist of a great value. His fields of interest were: ionized gas, electron physics, radiation physics and the electrodynamics of moving bodies. P.Langevin was one of the first to fully understand the implications of the relativity theory set up by A.Einstein and he became a fervent supporter of new ideas in physics, he discussed and analysed the interpretations of quantum physics since the very beginning of this new branch of physics. (A.C.)
Dynamic Characteristics and Models
Pedersen, Lars
2007-01-01
Vibration levels of flooring-systems are generally difficult to predict. Nevertheless an estimate may be needed for flooring-systems that are prone to vibrate to actions of humans in motion (e.g. grandstands, footbridges or long-span office floors). One reason for the difficulties...... and the paper therefore looks into this mechanism which is done by carrying out controlled modal identification tests on a test floor. The paper describes the experimental investigations and the basic principles adopted for modal identification. Since there is an interest in being able to model the scenario...
Pfeffer, A; Das, S; Lawless, D; Ng, B
2006-10-10
Many dynamic systems involve a number of entities that are largely independent of each other but interact with each other via a subset of state variables. We present global/local dynamic models (GLDMs) to capture these kinds of systems. In a GLDM, the state of an entity is decomposed into a globally influenced state that depends on other entities, and a locally influenced state that depends only on the entity itself. We present an inference algorithm for GLDMs called global/local particle filtering, that introduces the principle of reasoning globally about global dynamics and locally about local dynamics. We have applied GLDMs to an asymmetric urban warfare environment, in which enemy units form teams to attack important targets, and the task is to detect such teams as they form. Experimental results for this application show that global/local particle filtering outperforms ordinary particle filtering and factored particle filtering.
A dynamical model of terrorism
Firdaus Udwadia
2006-01-01
Full Text Available This paper develops a dynamical model of terrorism. We consider the population in a given region as being made up of three primary components: terrorists, those susceptible to both terrorist and pacifist propaganda, and nonsusceptibles, or pacifists. The dynamical behavior of these three populations is studied using a model that incorporates the effects of both direct military/police intervention to reduce the terrorist population, and nonviolent, persuasive intervention to influence the susceptibles to become pacifists. The paper proposes a new paradigm for studying terrorism, and looks at the long-term dynamical evolution in time of these three population components when such interventions are carried out. Many important features—some intuitive, others not nearly so—of the nature of terrorism emerge from the dynamical model proposed, and they lead to several important policy implications for the management of terrorism. The different circumstances in which nonviolent intervention and/or military/police intervention may be beneficial, and the specific conditions under which each mode of intervention, or a combination of both, may be useful, are obtained. The novelty of the model presented herein is that it deals with the time evolution of terrorist activity. It appears to be one of the few models that can be tested, evaluated, and improved upon, through the use of actual field data.
Langevin Diffusion in Holographic Backgrounds with Hyperscaling Violation
J. Sadeghi
2014-01-01
Full Text Available We consider a relativistic heavy quark which moves in the quark-gluon plasmas. By using the holographic methods, we analyze the Langevin diffusion process of this relativistic heavy quark. This heavy quark is described by a trailing string attached to a flavor brane and moving at constant velocity. The fluctuations of this string are related to the thermal correlators and the correlation functions are precisely the kinds of objects that we compute in the gravity dual picture. We obtain the action of the trailing string in hyperscaling violation backgrounds and we then find the equations of motion. These equations lead us to constructing the Langevin correlator which helps us to obtain the Langevin constants. Using the Langevin correlators we derive the spectral densities and simple analytic expressions in the small- and large-frequency limits. We examine our works for planar and R-charged black holes with hyperscaling violation and find new constraints on θ in the presence of velocity v.
Temperature dependent fission fragment distribution in the Langevin equation
WANG Kun; MA Yu-Gang; ZHENG Qing-Shan; CAI Xiang-Zhou; FANG De-Qing; FU Yao; LU Guang-Cheng; TIAN Wen-Dong; WANG Hong-Wei
2009-01-01
The temperature dependent width of the fission fragment distributions was simulated in the Langevin equation by taking two-parameter exponential form of the fission fragment mass variance at scission point for each fission event. The result can reproduce experimental data well, and it permits to make reliable estimate for unmeasured product yields near symmetry fission.
Experimental Modeling of Dynamic Systems
Knudsen, Morten Haack
2006-01-01
An engineering course, Simulation and Experimental Modeling, has been developed that is based on a method for direct estimation of physical parameters in dynamic systems. Compared with classical system identification, the method appears to be easier to understand, apply, and combine with physical...
Nonlinear Dynamic Model Explains The Solar Dynamic
Kuman, Maria
Nonlinear mathematical model in torus representation describes the solar dynamic. Its graphic presentation shows that without perturbing force the orbits of the planets would be circles; only perturbing force could elongate the circular orbits into ellipses. Since the Hubble telescope found that the planetary orbits of other stars in the Milky Way are also ellipses, powerful perturbing force must be present in our galaxy. Such perturbing force is the Sagittarius Dwarf Galaxy with its heavy Black Hole and leftover stars, which we see orbiting around the center of our galaxy. Since observations of NASA's SDO found that magnetic fields rule the solar activity, we can expect when the planets align and their magnetic moments sum up, the already perturbed stars to reverse their magnetic parity (represented graphically as periodic looping through the hole of the torus). We predict that planets aligned on both sides of the Sun, when their magnetic moments sum-up, would induce more flares in the turbulent equatorial zone, which would bulge. When planets align only on one side of the Sun, the strong magnetic gradient of their asymmetric pull would flip the magnetic poles of the Sun. The Sun would elongate pole-to-pole, emit some energy through the poles, and the solar activity would cease. Similar reshaping and emission was observed in stars called magnetars and experimentally observed in super-liquid fast-spinning Helium nanodroplets. We are certain that NASA's SDO will confirm our predictions.
Florian Ion Tiberiu Petrescu
2016-03-01
Full Text Available Otto engine dynamics are similar in almost all common internal combustion engines. We can speak so about dynamics of engines: Lenoir, Otto, and Diesel. The dynamic presented model is simple and original. The first thing necessary in the calculation of Otto engine dynamics, is to determine the inertial mass reduced at the piston. One uses then the Lagrange equation. Kinetic energy conservation shows angular speed variation (from the shaft with inertial masses. One uses and elastic constant of the crank shaft, k. Calculations should be made for an engine with a single cylinder. Finally it makes a dynamic analysis of the mechanism with discussion and conclusions. The ratio between the crank length r and the length of the connecting-rod l is noted with landa. When landa increases the mechanism dynamics is deteriorating. For a proper operation is necessary the reduction of the ratio landa, especially if we want to increase the engine speed. We can reduce the acceleration values by reducing the dimensions r and l.
Usang, M. D.; Ivanyuk, F. A.; Ishizuka, C.; Chiba, S.
2016-10-01
Nuclear fission is treated by using the Langevin dynamical description with macroscopic and microscopic transport coefficients (mass and friction tensors), and it is elucidated how the microscopic (shell and pairing) effects in the transport coefficients, especially their dependence on temperature, affects various fission observables. We found that the microscopic transport coefficients, calculated by linear response theory, change drastically as a function of temperature: in general, the friction increases with growing temperature while the mass tensor decreases. This temperature dependence brings a noticeable change in the mass distribution and kinetic energies of fission fragments from nuclei around 236U at an excitation energy of 20 MeV. The prescission kinetic energy decreases from 25 MeV at low temperature to about 2.5 MeV at high temperature. In contrast, the Coulomb kinetic energy increases as the temperature increases. Interpolating the microscopic transport coefficients among the various temperatures enabled our Langevin equation to use the microscopic transport coefficients at a deformation-dependent local temperature of the dynamical evolution. This allowed us to compare directly the fission observables of both macroscopic and microscopic calculations, and we found almost identical results under the conditions considered in this work.
On the Generalized Langevin Equation for a Rouse Bead in a Nonequilibrium Bath
Vandebroek, Hans; Vanderzande, Carlo
2017-04-01
We present the reduced dynamics of a bead in a Rouse chain which is submerged in a bath containing a driving agent that renders it out-of-equilibrium. We first review the generalized Langevin equation of the middle bead in an equilibrated bath. Thereafter, we introduce two driving forces. Firstly, we add a constant force that is applied to the first bead of the chain. We investigate how the generalized Langevin equation changes due to this perturbation for which the system evolves towards a steady state after some time. Secondly, we consider the case of stochastic active forces which will drive the system to a nonequilibrium state. Including these active forces results in an extra contribution to the second fluctuation-dissipation relation. The form of this active contribution is analysed for the specific case of Gaussian, exponentially correlated active forces. We also discuss the resulting rich dynamics of the middle bead in which various regimes of normal diffusion, subdiffusion and superdiffusion can be present.
Business model dynamics and innovation
Cavalcante, Sergio Andre; Kesting, Peter; Ulhøi, John Parm
2011-01-01
Purpose – This paper aims to discuss the need to dynamize the existing conceptualization of business model, and proposes a new typology to distinguish different types of business model change. Design/methodology/approach – The paper integrates basic insights of innovation, business process...... and routine research into the concept of business model. The main focus of the paper is on strategic and terminological issues. Findings – The paper offers a new, process-based conceptualization of business model, which recognizes and integrates the role of individual agency. Based on this, it distinguishes...... and specifies four different types of business model change: business model creation, extension, revision, and termination. Each type of business model change is associated with specific challenges. Practical implications – The proposed typology can serve as a basis for developing a management tool to evaluate...
DYNAMIC TEACHING RATIO PEDAGOGIC MODEL
Chen Jiaying
2010-11-01
Full Text Available This paper outlines an innovative pedagogic model, Dynamic Teaching Ratio (DTR Pedagogic Model, for learning design and teaching strategy aimed at the postsecondary technical education. The model draws on the theory of differential learning, which is widely recognized as an important tool for engaging students and addressing the individual needs of all students. The DTR model caters to the different abilities, interest or learning needs of students and provides different learning approaches based on a student’s learning ability. The model aims to improve students’ academic performance through increasing the lecturer-to-student ratio in the classroom setting. An experimental case study on the model was conducted and the outcome was favourable. Hence, a large-scale implementation was carried out upon the successful trial run. The paper discusses the methodology of the model and its application through the case study and the large-scale implementation.
Soheilifard, Reza; Makarov, Dmitrii E; Rodin, Gregory J
2011-08-07
Reduced-dimensionality, coarse-grained models are commonly employed to describe the structure and dynamics of large molecular systems. In those models, the dynamics is often described by Langevin equations of motion with phenomenological parameters. This paper presents a rigorous coarse-graining method for the dynamics of linear systems. In this method, as usual, the conformational space of the original atomistic system is divided into master and slave degrees of freedom. Under the assumption that the characteristic timescales of the masters are slower than those of the slaves, the method results in Langevin-type equations of motion governed by an effective potential of mean force. In addition, coarse-graining introduces hydrodynamic-like coupling among the masters as well as non-trivial inertial effects. Application of our method to the long-timescale part of the relaxation spectra of proteins shows that such dynamic coupling is essential for reproducing their relaxation rates and modes.
DYNAMIC MODELING OF METAMORPHIC MECHANISM
无
2003-01-01
The concept of metamorphic mechanism is put forward according to the change of configurations from one state to another. Different configurations of metamorphic mechanism are described through the method of Huston lower body arrays. Kinematics analyses for metamorphic mechanism with generalized topological structure, including the velocity, angular velocity, acceleration and angular acceleration, are given. Dynamic equations for an arbitrary configuration, including close-loop constraints, are formed by using Kane's equations. For an arbitrary metamorphic mechanism, the transformation matrix of generalized speeds between configuration (*)and(*)+1 is obtained for the first time. Furthermore, configuration-complete dynamic modeling of metamorphic mechanism including all configurations is completely established.
Stochastic Model of Microtubule Dynamics
Hryniv, Ostap; Martínez Esteban, Antonio
2017-10-01
We introduce a continuous time stochastic process on strings made of two types of particle, whose dynamics mimics that of microtubules in a living cell. The long term behaviour of the system is described in terms of the velocity v of the string end. We show that v is an analytic function of its parameters and study its monotonicity properties. We give a complete characterisation of the phase diagram of the model and derive several criteria of the growth (v>0) and the shrinking (v<0) regimes of the dynamics.
Metastable states and quasicycles in a stochastic Wilson-Cowan model of neuronal population dynamics
Bressloff, Paul C.
2010-11-03
We analyze a stochastic model of neuronal population dynamics with intrinsic noise. In the thermodynamic limit N→∞, where N determines the size of each population, the dynamics is described by deterministic Wilson-Cowan equations. On the other hand, for finite N the dynamics is described by a master equation that determines the probability of spiking activity within each population. We first consider a single excitatory population that exhibits bistability in the deterministic limit. The steady-state probability distribution of the stochastic network has maxima at points corresponding to the stable fixed points of the deterministic network; the relative weighting of the two maxima depends on the system size. For large but finite N, we calculate the exponentially small rate of noise-induced transitions between the resulting metastable states using a Wentzel-Kramers- Brillouin (WKB) approximation and matched asymptotic expansions. We then consider a two-population excitatory or inhibitory network that supports limit cycle oscillations. Using a diffusion approximation, we reduce the dynamics to a neural Langevin equation, and show how the intrinsic noise amplifies subthreshold oscillations (quasicycles). © 2010 The American Physical Society.
Dynamical Modelling of Meteoroid Streams
Clark, David; Wiegert, P. A.
2012-10-01
Accurate simulations of meteoroid streams permit the prediction of stream interaction with Earth, and provide a measure of risk to Earth satellites and interplanetary spacecraft. Current cometary ejecta and meteoroid stream models have been somewhat successful in predicting some stream observations, but have required questionable assumptions and significant simplifications. Extending on the approach of Vaubaillon et al. (2005)1, we model dust ejection from the cometary nucleus, and generate sample particles representing bins of distinct dynamical evolution-regulating characteristics (size, density, direction, albedo). Ephemerides of the sample particles are integrated and recorded for later assignment of frequency based on model parameter changes. To assist in model analysis we are developing interactive software to permit the “turning of knobs” of model parameters, allowing for near-real-time 3D visualization of resulting stream structure. With this tool, we will revisit prior assumptions made, and will observe the impact of introducing non-uniform cometary surface attributes and temporal activity. The software uses a single model definition and implementation throughout model verification, sample particle bin generation and integration, and analysis. It supports the adjustment with feedback of both independent and independent model values, with the intent of providing an interface supporting multivariate analysis. Propagations of measurement uncertainties and model parameter precisions are tracked rigorously throughout. We maintain a separation of the model itself from the abstract concepts of model definition, parameter manipulation, and real-time analysis and visualization. Therefore we are able to quickly adapt to fundamental model changes. It is hoped the tool will also be of use in other solar system dynamics problems. 1 Vaubaillon, J.; Colas, F.; Jorda, L. (2005) A new method to predict meteor showers. I. Description of the model. Astronomy and
Dynamic Model of Mesoscale Eddies
Dubovikov, Mikhail S.
2003-04-01
Oceanic mesoscale eddies which are analogs of well known synoptic eddies (cyclones and anticyclones), are studied on the basis of the turbulence model originated by Dubovikov (Dubovikov, M.S., "Dynamical model of turbulent eddies", Int. J. Mod. Phys.B7, 4631-4645 (1993).) and further developed by Canuto and Dubovikov (Canuto, V.M. and Dubovikov, M.S., "A dynamical model for turbulence: I. General formalism", Phys. Fluids8, 571-586 (1996a) (CD96a); Canuto, V.M. and Dubovikov, M.S., "A dynamical model for turbulence: II. Sheardriven flows", Phys. Fluids8, 587-598 (1996b) (CD96b); Canuto, V.M., Dubovikov, M.S., Cheng, Y. and Dienstfrey, A., "A dynamical model for turbulence: III. Numerical results", Phys. Fluids8, 599-613 (1996c)(CD96c); Canuto, V.M., Dubovikov, M.S. and Dienstfrey, A., "A dynamical model for turbulence: IV. Buoyancy-driven flows", Phys. Fluids9, 2118-2131 (1997a) (CD97a); Canuto, V.M. and Dubovikov, M.S., "A dynamical model for turbulence: V. The effect of rotation", Phys. Fluids9, 2132-2140 (1997b) (CD97b); Canuto, V.M., Dubovikov, M.S. and Wielaard, D.J., "A dynamical model for turbulence: VI. Two dimensional turbulence", Phys. Fluids9, 2141-2147 (1997c) (CD97c); Canuto, V.M. and Dubovikov, M.S., "Physical regimes and dimensional structure of rotating turbulence", Phys. Rev. Lett. 78, 666-669 (1997d) (CD97d); Canuto, V.M., Dubovikov, M.S. and Dienstfrey, A., "Turbulent convection in a spectral model", Phys. Rev. Lett. 78, 662-665 (1997e) (CD97e); Canuto, V.M. and Dubovikov, M.S., "A new approach to turbulence", Int. J. Mod. Phys.12, 3121-3152 (1997f) (CD97f); Canuto, V.M. and Dubovikov, M.S., "Two scaling regimes for rotating Raleigh-Benard convection", Phys. Rev. Letters78, 281-284, (1998) (CD98); Canuto, V.M. and Dubovikov, M.S., "A dynamical model for turbulence: VII. The five invariants for shear driven flows", Phys. Fluids11, 659-664 (1999a) (CD99a); Canuto, V.M., Dubovikov, M.S. and Yu, G., "A dynamical model for turbulence: VIII. IR and UV
Dynamic queuing transmission model for dynamic network loading
Raovic, Nevena; Nielsen, Otto Anker; Prato, Carlo Giacomo
2017-01-01
This paper presents a new macroscopic multi-class dynamic network loading model called Dynamic Queuing Transmission Model (DQTM). The model utilizes ‘good’ properties of the Dynamic Queuing Model (DQM) and the Link Transmission Model (LTM) by offering a DQM consistent with the kinematic wave theory...... and allowing for the representation of multiple vehicle classes, queue spillbacks and shock waves. The model assumes that a link is split into a moving part plus a queuing part, and p that traffic dynamics are given by a triangular fundamental diagram. A case-study is investigated and the DQTM is compared...
Relating structure and dynamics in organisation models
Jonkers, C.M.; Treur, J.
To understand how an organisational structure relates to dynamics is an interesting fundamental challenge in the area of social modelling. Specifications of organisational structure usually have a diagrammatic form that abstracts from more detailed dynamics. Dynamic properties of agent systems,
Leung, Chun Sing; Harko, Tiberiu
2013-01-01
We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects based on the generalized Langevin equation, which accounts for the general retarded effects of the frictional force, and on the fluctuation-dissipation theorems. 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 luminosity it is also obtained, and it is shown that it has non-standard values. The theoretical predictions of the model are compared with the observational data for the luminosity time variation of the BL Lac S5 0716+714 object.
Generalized Langevin Equation Description of Stochastic Oscillations of General Relativistic Disks
Chun Sing Leung; Gabriela Mocanu; Tiberiu Harko
2014-09-01
We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects based on the generalized Langevin equation, which accounts for the general retarded effects of the frictional force, and on the fluctuation–dissipation theorems. The vertical displacements, velocities and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and Kerr cases. The power spectral distribution of the luminosity is also obtained, and it is shown that it has non-standard values. The theoretical predictions of the model are compared with the observational data for the luminosity time variation of the BL Lac S5 0716+714 object.
Laws of large numbers and langevin approximations for stochastic neural field equations.
Riedler, Martin G; Buckwar, Evelyn
2013-01-23
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.
Memory effects in nonadiabatic molecular dynamics at metal surfaces
Olsen, Thomas; Schiøtz, Jakob
2010-01-01
We study the effect of temporal correlation in a Langevin equation describing nonadiabatic dynamics at metal surfaces. For a harmonic oscillator, the Langevin equation preserves the quantum dynamics exactly and it is demonstrated that memory effects are needed in order to conserve the ground state...... energy of the oscillator. We then compare the result of Langevin dynamics in a harmonic potential with a perturbative master equation approach and show that the Langevin equation gives a better description in the nonperturbative range of high temperatures and large friction. Unlike the master equation...... the temporal correlation function and dynamical friction within density functional theory....
Dynamics Modeling of Heavy Special Driving Simulator
无
2008-01-01
Based on the dynamical characteristic parameters of the real vehicle, the modeling approach and procedure of dynamics of vehicles are expatiated. The layout of vehicle dynamics is proposed, and the sub-models of the diesel engine, drivetrain system and vehicle multi-body dynamics are introduced. Finally, the running characteristic data of the virtual and real vehicles are compared, which shows that the dynamics model is similar closely to the real vehicle system.
Models of ungulate population dynamics
L. L. Eberhardt
1991-10-01
Full Text Available A useful theory for analyzing ungulate population dynamics is available in the form of equations based on the work of A. J. Lotka. Because the Leslie matrix model yields identical results and is widely known, it is convenient to label the resulting equations as the "Lotka-Leslie" model. The approach is useful for assessing population trends and attempting to predict the outcomes of various management actions. A broad list of applications to large mammals, and two examples specific to caribou are presented with a simple spreadsheet approach to calculations.
Dynamical model of brushite precipitation
Oliveira, Cristina; Georgieva, Petia; Rocha, Fernando; Ferreira, António; Feyo de Azevedo, Sebastião
2007-07-01
The objectives of this work are twofold. From academic point of view the aim is to build a dynamical macro model to fit the material balance and explain the main kinetic mechanisms that govern the transformation of the hydroxyapatite (HAP) into brushite and the growth of brushite, based on laboratory experiments and collected database. From practical point of view, the aim is to design a reliable process simulator that can be easily imbedded in industrial software for model driven monitoring, optimization and control purposes. Based upon a databank of laboratory measurements of the calcium concentration in solution (on-line) and the particle size distribution (off-line) a reliable dynamical model of the dual nature of brushite particle formation for a range of initial concentrations of the reagents was derived as a system of ordinary differential equations of time. The performance of the model is tested with respect to the predicted evolution of mass of calcium in solution and the average (in mass) particle size along time. Results obtained demonstrate a good agreement between the model time trajectories and the available experimental data for a number of different initial concentrations of reagents.
Stochastic dynamics of phase singularities under ventricular fibrillation in 2D Beeler-Reuter model
Suzuki, Akio; Konno, Hidetoshi
2011-09-01
The dynamics of ventricular fibrillation (VF) has been studied extensively, and the initiation mechanism of VF has been elucidated to some extent. However, the stochastic dynamical nature of sustained VF remains unclear so far due to the complexity of high dimensional chaos in a heterogeneous system. In this paper, various statistical mechanical properties of sustained VF are studied numerically in 2D Beeler-Reuter-Drouhard-Roberge (BRDR) model with normal and modified ionic current conductance. The nature of sustained VF is analyzed by measuring various fluctuations of spatial phase singularity (PS) such as velocity, lifetime, the rates of birth and death. It is found that the probability density function (pdf) for lifetime of PSs is independent of system size. It is also found that the hyper-Gamma distribution serves as a universal pdf for the counting number of PSs for various system sizes and various parameters of our model tissue under VF. Further, it is demonstrated that the nonlinear Langevin equation associated with a hyper-Gamma process can mimic the pdf and temporal variation of the number of PSs in the 2D BRDR model.
Stochastic dynamics of phase singularities under ventricular fibrillation in 2D Beeler-Reuter model
Akio Suzuki
2011-09-01
Full Text Available The dynamics of ventricular fibrillation (VF has been studied extensively, and the initiation mechanism of VF has been elucidated to some extent. However, the stochastic dynamical nature of sustained VF remains unclear so far due to the complexity of high dimensional chaos in a heterogeneous system. In this paper, various statistical mechanical properties of sustained VF are studied numerically in 2D Beeler-Reuter-Drouhard-Roberge (BRDR model with normal and modified ionic current conductance. The nature of sustained VF is analyzed by measuring various fluctuations of spatial phase singularity (PS such as velocity, lifetime, the rates of birth and death. It is found that the probability density function (pdf for lifetime of PSs is independent of system size. It is also found that the hyper-Gamma distribution serves as a universal pdf for the counting number of PSs for various system sizes and various parameters of our model tissue under VF. Further, it is demonstrated that the nonlinear Langevin equation associated with a hyper-Gamma process can mimic the pdf and temporal variation of the number of PSs in the 2D BRDR model.
Dynamic pricing models for electronic business
Y Narahari; C V L Raju; K Ravikumar; Sourabh Shah
2005-04-01
Dynamic pricing is the dynamic adjustment of prices to consumers depending upon the value these customers attribute to a product or service. Today’s digital economy is ready for dynamic pricing; however recent research has shown that the prices will have to be adjusted in fairly sophisticated ways, based on sound mathematical models, to derive the beneﬁts of dynamic pricing. This article attempts to survey different models that have been used in dynamic pricing. We ﬁrst motivate dynamic pricing and present underlying concepts, with several examples, and explain conditions under which dynamic pricing is likely to succeed. We then bring out the role of models in computing dynamic prices. The models surveyed include inventory-based models, data-driven models, auctions, and machine learning. We present a detailed example of an e-business market to show the use of reinforcement learning in dynamic pricing.
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.
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.
Stochastic dynamics and irreversibility
Tomé, Tânia
2015-01-01
This textbook presents an exposition of stochastic dynamics and irreversibility. It comprises the principles of probability theory and the stochastic dynamics in continuous spaces, described by Langevin and Fokker-Planck equations, and in discrete spaces, described by Markov chains and master equations. Special concern is given to the study of irreversibility, both in systems that evolve to equilibrium and in nonequilibrium stationary states. Attention is also given to the study of models displaying phase transitions and critical phenomema both in thermodynamic equilibrium and out of equilibrium. These models include the linear Glauber model, the Glauber-Ising model, lattice models with absorbing states such as the contact process and those used in population dynamic and spreading of epidemic, probabilistic cellular automata, reaction-diffusion processes, random sequential adsorption and dynamic percolation. A stochastic approach to chemical reaction is also presented.The textbook is intended for students of ...
Isoscaling of the Fission Fragments with Langevin Equation
WANG Kun; TIAN Wen-Dong; ZHONG Chen; ZHOU Xing-Fei; MA Yu-Gang; WEI Yi-Bin; CAI Xiang-Zhou; CHEN Jin-Gen; FANG De-Qing; GUO Wei; MA Guo-Liang; SHEN Wen-Qing
2005-01-01
@@ The Langevin equation is used to simulate the fission process of 112Sn + 112Sn and 116Sn + 116Sn. The mass distribution of the fission fragments are given by assuming the process of symmetric fission or asymmetric fission with the Gaussian probability sampling. The isoscaling behaviour has been observed from the analysis of fission fragments of both the reactions, and the isoscaling parameter α seems to be sensitive to the width of fission probability and the beam energy.
Modelling of the Manifold Filling Dynamics
Hendricks, Elbert; Chevalier, Alain Marie Roger; Jensen, Michael
1996-01-01
Mean Value Engine Models (MVEMs) are dynamic models which describe dynamic engine variable (or state) responses on time scales slightly longer than an engine event. This paper describes a new model of the intake manifold filling dynamics which is simple and easy to calibrate for use in engine con...
Lin, Chien Y.; Huang, Jung Y.; Lo, Leu-Wei
2014-12-01
We developed an energetic model by integrating the generalized Langevin equation with the Cahn-Hilliard equation to simulate the diffusive behaviors of receptor proteins in the plasma membrane of a living cell. Simulation results are presented to elaborate the confinement effects from actin corrals and protein-induced lipid domains. Single-molecule tracking data of epidermal growth factor receptors (EGFR) acquired on live HeLa cells agree with the simulation results and the mechanism that controls the diffusion of single-molecule receptors is clarified. We discovered that after ligand binding, EGFR molecules move into lipid nanodomains. The transition rates between different diffusion states of liganded EGFR molecules are regulated by the lipid domains. Our method successfully captures dynamic interactions of receptors at the single-molecule level and provides insight into the functional architecture of both the diffusing EGFR molecules and their local cellular environment.
Multiscale modeling of pedestrian dynamics
Cristiani, Emiliano; Tosin, Andrea
2014-01-01
This book presents mathematical models and numerical simulations of crowd dynamics. The core topic is the development of a new multiscale paradigm, which bridges the microscopic and macroscopic scales taking the most from each of them for capturing the relevant clues of complexity of crowds. The background idea is indeed that most of the complex trends exhibited by crowds are due to an intrinsic interplay between individual and collective behaviors. The modeling approach promoted in this book pursues actively this intuition and profits from it for designing general mathematical structures susceptible of application also in fields different from the inspiring original one. The book considers also the two most traditional points of view: the microscopic one, in which pedestrians are tracked individually, and the macroscopic one, in which pedestrians are assimilated to a continuum. Selected existing models are critically analyzed. The work is addressed to researchers and graduate students.
Langevin and diffusion equation of turbulent fluid flow
Brouwers, J. J. H.
2010-08-01
A derivation of the Langevin and diffusion equations describing the statistics of fluid particle displacement and passive admixture in turbulent flow is presented. Use is made of perturbation expansions. The small parameter is the inverse of the Kolmogorov constant C 0 , which arises from Lagrangian similarity theory. The value of C 0 in high Reynolds number turbulence is 5-6. To achieve sufficient accuracy, formulations are not limited to terms of leading order in C0 - 1 including terms next to leading order in C0 - 1 as well. Results of turbulence theory and statistical mechanics are invoked to arrive at the descriptions of the Langevin and diffusion equations, which are unique up to truncated terms of O ( C0 - 2 ) in displacement statistics. Errors due to truncation are indicated to amount to a few percent. The coefficients of the presented Langevin and diffusion equations are specified by fixed-point averages of the Eulerian velocity field. The equations apply to general turbulent flow in which fixed-point Eulerian velocity statistics are non-Gaussian to a degree of O ( C0 - 1 ) . The equations provide the means to calculate and analyze turbulent dispersion of passive or almost passive admixture such as fumes, smoke, and aerosols in areas ranging from atmospheric fluid motion to flows in engineering devices.
Does the complex Langevin method give unbiased results?
Salcedo, L L
2016-01-01
We investigate whether the stationary solution of the Fokker-Planck equation of the complex Langevin algorithm reproduces the correct expectation values. When the complex Langevin algorithm for an action $S(x)$ is convergent, it produces an equivalent complex probability distribution $P(x)$ which ideally would coincide with $e^{-S(x)}$. We show that the projected Fokker-Planck equation fulfilled by $P(x)$ may contain an anomalous term whose form is made explicit. Such term spoils the relation $P(x)=e^{-S(x)}$, introducing a bias in the expectation values. Through the analysis of several periodic and non-periodic one-dimensional problems, using either exact or numerical solutions of the Fokker-Planck equation on the complex plane, it is shown that the anomaly is present quite generally. In fact, an anomaly is expected whenever the Langevin walker needs only a finite time to go to infinity and come back, and this is the case for typical actions. We conjecture that the anomaly is the rule rather than the excepti...
Does the complex Langevin method give unbiased results?
Salcedo, L. L.
2016-12-01
We investigate whether the stationary solution of the Fokker-Planck equation of the complex Langevin algorithm reproduces the correct expectation values. When the complex Langevin algorithm for an action S (x ) is convergent, it produces an equivalent complex probability distribution P (x ) which ideally would coincide with e-S (x ). We show that the projected Fokker-Planck equation fulfilled by P (x ) may contain an anomalous term whose form is made explicit. Such a term spoils the relation P (x )=e-S (x ), introducing a bias in the expectation values. Through the analysis of several periodic and nonperiodic one-dimensional problems, using either exact or numerical solutions of the Fokker-Planck equation on the complex plane, it is shown that the anomaly is present quite generally. In fact, an anomaly is expected whenever the Langevin walker needs only a finite time to go to infinity and come back, and this is the case for typical actions. We conjecture that the anomaly is the rule rather than the exception in the one-dimensional case; however, this could change as the number of variables involved increases.
Transient aging in fractional Brownian and Langevin-equation motion.
Kursawe, Jochen; Schulz, Johannes; Metzler, Ralf
2013-12-01
Stochastic processes driven by stationary fractional Gaussian noise, that is, fractional Brownian motion and fractional Langevin-equation motion, are usually considered to be ergodic in the sense that, after an algebraic relaxation, time and ensemble averages of physical observables coincide. Recently it was demonstrated that fractional Brownian motion and fractional Langevin-equation motion under external confinement are transiently nonergodic-time and ensemble averages behave differently-from the moment when the particle starts to sense the confinement. Here we show that these processes also exhibit transient aging, that is, physical observables such as the time-averaged mean-squared displacement depend on the time lag between the initiation of the system at time t=0 and the start of the measurement at the aging time t(a). In particular, it turns out that for fractional Langevin-equation motion the aging dependence on t(a) is different between the cases of free and confined motion. We obtain explicit analytical expressions for the aged moments of the particle position as well as the time-averaged mean-squared displacement and present a numerical analysis of this transient aging phenomenon.
Complex reaction noise in a molecular quasispecies model
Hochberg, David; Zorzano, María-Paz; Morán, Federico
2006-05-01
We have derived exact Langevin equations for a model of quasispecies dynamics. The inherent multiplicative reaction noise is complex and its statistical properties are specified completely. The numerical simulation of the complex Langevin equations is carried out using the Cholesky decomposition for the noise covariance matrix. This internal noise, which is due to diffusion-limited reactions, produces unavoidable spatio-temporal density fluctuations about the mean field value. In two dimensions, this noise strictly vanishes only in the perfectly mixed limit, a situation difficult to attain in practice.
DYNAMICAL MODEL OF ELECTROMAGNETIC DRIVE
Trunev A. P.
2016-02-01
Full Text Available The article discusses the dynamic model of the rocket motor electromagnetic type, consisting of a source of electromagnetic waves of radio frequency band and a conical cavity in which electromagnetic waves are excited. The processes of excitation of electromagnetic oscillations in a cavity with conducting walls, as well as the waves of the YangMills field have been investigated. Multi-dimensional transient numerical model describing the processes of establishment of electromagnetic oscillations in a cavity with the conducting wall was created Separately, the case of standing waves in the cavity with conducting walls been tested. It is shown that the oscillation mode in the conducting resonator different from that in an ideal resonator, both in the steady and unsteady processes. The mechanism of formation of traction for the changes in the space-time metric, the contribution of particle currents, the Yang-Mills and electromagnetic field proposed. It is shown that the effect of the Yang-Mills field calls change the dielectric properties of vacuum, which leads to a change in capacitance of the resonator. Developed a dynamic model, which enables optimal traction on a significant number of parameters. It was found that the thrust increases in the Yang-Mills field parameters near the main resonance frequency. In the presence of thermal fluctuations and the Yang-Mills field as well the traction force changes sign, indicating the presence of various oscillation modes
Eigenvalue dynamics for multimatrix models
de Mello Koch, Robert; Gossman, David; Nkumane, Lwazi; Tribelhorn, Laila
2017-07-01
By performing explicit computations of correlation functions, we find evidence that there is a sector of the two matrix model defined by the S U (2 ) sector of N =4 super Yang-Mills theory that can be reduced to eigenvalue dynamics. There is an interesting generalization of the usual Van der Monde determinant that plays a role. The observables we study are the Bogomol'nyi-Prasad-Sommerfield operators of the S U (2 ) sector and include traces of products of both matrices, which are genuine multimatrix observables. These operators are associated with supergravity solutions of string theory.
Eigenvalue Dynamics for Multimatrix Models
Koch, Robert de Mello; Nkumane, Lwazi; Tribelhorn, Laila
2016-01-01
By performing explicit computations of correlation functions, we find evidence that there is a sector of the two matrix model defined by the $SU(2)$ sector of ${\\cal N}=4$ super Yang-Mills theory, that can be reduced to eigenvalue dynamics. There is an interesting generalization of the usual Van der Monde determinant that plays a role. The observables we study are the BPS operators of the $SU(2)$ sector and include traces of products of both matrices, which are genuine multi matrix observables. These operators are associated to supergravity solutions of string theory.
Effective reduced diffusion-models: a data driven approach to the analysis of neuronal dynamics.
Gustavo Deco
2009-12-01
Full Text Available We introduce in this paper a new method for reducing neurodynamical data to an effective diffusion equation, either experimentally or using simulations of biophysically detailed models. The dimensionality of the data is first reduced to the first principal component, and then fitted by the stationary solution of a mean-field-like one-dimensional Langevin equation, which describes the motion of a Brownian particle in a potential. The advantage of such description is that the stationary probability density of the dynamical variable can be easily derived. We applied this method to the analysis of cortical network dynamics during up and down states in an anesthetized animal. During deep anesthesia, intracellularly recorded up and down states transitions occurred with high regularity and could not be adequately described by a one-dimensional diffusion equation. Under lighter anesthesia, however, the distributions of the times spent in the up and down states were better fitted by such a model, suggesting a role for noise in determining the time spent in a particular state.
Bayesian Estimation of Categorical Dynamic Factor Models
Zhang, Zhiyong; Nesselroade, John R.
2007-01-01
Dynamic factor models have been used to analyze continuous time series behavioral data. We extend 2 main dynamic factor model variations--the direct autoregressive factor score (DAFS) model and the white noise factor score (WNFS) model--to categorical DAFS and WNFS models in the framework of the underlying variable method and illustrate them with…
Emsellem, E; Bacon, R; Emsellem, Eric; Dejonghe, Herwig; Bacon, Roland
1998-01-01
We present new dynamical models of the S0 galaxy N3115, making use of the available published photometry and kinematics as well as of two-dimensional TIGER spectrography. We first examined the kinematics in the central 40 arcsec in the light of two integral f(E,J) models. Jeans equations were used to constrain the mass to light ratio, and the central dark mass whose existence was suggested by previous studies. The even part of the distribution function was then retrieved via the Hunter & Qian formalism. We thus confirmed that the velocity and dispersion profiles in the central region could be well fit with a two-integral model, given the presence of a central dark mass of ~10^9 Msun. However, no two integral model could fit the h_3 profile around a radius of 25 arcsec where the outer disc dominates the surface brightness distribution. Three integral analytical models were therefore built using a Quadratic Programming technique. These models showed that three integral components do indeed provide a reasona...
Cipiti, Benjamin B. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2017-03-01
The Co-Decontamination (CoDCon) Demonstration project is designed to test the separation of a mixed U and Pu product from dissolved spent nuclear fuel. The primary purpose of the project is to quantify the accuracy and precision to which a U/Pu mass ratio can be achieved without removing a pure Pu product. The system includes an on-line monitoring system using spectroscopy to monitor the ratios throughout the process. A dynamic model of the CoDCon flowsheet and on-line monitoring system was developed in order to expand the range of scenarios that can be examined for process control and determine overall measurement uncertainty. The model development and initial results are presented here.
Characterizing and modeling citation dynamics
Eom, Young-Ho; 10.1371/journal.pone.0024926
2011-01-01
Citation distributions are crucial for the analysis and modeling of the activity of scientists. We investigated bibliometric data of papers published in journals of the American Physical Society, searching for the type of function which best describes the observed citation distributions. We used the goodness of fit with Kolmogorov-Smirnov statistics for three classes of functions: log-normal, simple power law and shifted power law. The shifted power law turns out to be the most reliable hypothesis for all citation networks we derived, which correspond to different time spans. We find that citation dynamics is characterized by bursts, usually occurring within a few years since publication of a paper, and the burst size spans several orders of magnitude. We also investigated the microscopic mechanisms for the evolution of citation networks, by proposing a linear preferential attachment with time dependent initial attractiveness. The model successfully reproduces the empirical citation distributions and accounts...
闫勇; 姜泽军; 梅冬成; 周凌云
2002-01-01
本文对具有加性和乘性白噪声关联的单模激光模型的统计性质进行了研究.从一个具有交叉关联噪声与单模激光与立方模随机等价郎之万方程,计算了稳态激光光强度的平均值、协方差和偏斜率.并与早期结果比较,阐明了考虑郎之万方程修正项对描述激光系统统计性质的重要性.%The stationary properties of a singlemode laser with correlations between additive and multiplicative whitenoise terms are investigated.The mean,variance,and skewness of the steadystate laser intensity are calculated through a Langevin equation(LE) derived by Long which is always stochastically equivalent to the single mode cubic laser model when additive and multiplicative noises are correlated.Compared with the result obtained by Zhu,the consideration of modification item in LE when addivtive and multiplicative noises are correlated is important for describing statistical properties of the laser system.
Scholz, Robert; Floß, Gereon; Saalfrank, Peter; Füchsel, Gernot; Lončarić, Ivor; Juaristi, J. I.
2016-10-01
A Langevin model accounting for all six molecular degrees of freedom is applied to femtosecond-laser induced, hot-electron driven dynamics of Ru(0001)(2 ×2 ):CO. In our molecular dynamics with electronic friction approach, a recently developed potential energy surface based on gradient-corrected density functional theory accounting for van der Waals interactions is adopted. Electronic friction due to the coupling of molecular degrees of freedom to electron-hole pairs in the metal are included via a local density friction approximation, and surface phonons by a generalized Langevin oscillator model. The action of ultrashort laser pulses enters through a substrate-mediated, hot-electron mechanism via a time-dependent electronic temperature (derived from a two-temperature model), causing random forces acting on the molecule. The model is applied to laser induced lateral diffusion of CO on the surface, "hot adsorbate" formation, and laser induced desorption. Reaction probabilities are strongly enhanced compared to purely thermal processes, both for diffusion and desorption. Reaction yields depend in a characteristic (nonlinear) fashion on the applied laser fluence, as well as branching ratios for various reaction channels. Computed two-pulse correlation traces for desorption and other indicators suggest that aside from electron-hole pairs, phonons play a non-negligible role for laser induced dynamics in this system, acting on a surprisingly short time scale. Our simulations on precomputed potentials allow for good statistics and the treatment of long-time dynamics (300 ps), giving insight into this system which hitherto has not been reached. We find generally good agreement with experimental data where available and make predictions in addition. A recently proposed laser induced population of physisorbed precursor states could not be observed with the present low-coverage model.
Modeling Structural Dynamics of Biomolecular Complexes by Coarse-Grained Molecular Simulations.
Takada, Shoji; Kanada, Ryo; Tan, Cheng; Terakawa, Tsuyoshi; Li, Wenfei; Kenzaki, Hiroo
2015-12-15
Due to hierarchic nature of biomolecular systems, their computational modeling calls for multiscale approaches, in which coarse-grained (CG) simulations are used to address long-time dynamics of large systems. Here, we review recent developments and applications of CG modeling methods, focusing on our methods primarily for proteins, DNA, and their complexes. These methods have been implemented in the CG biomolecular simulator, CafeMol. Our CG model has resolution such that ∼10 non-hydrogen atoms are grouped into one CG particle on average. For proteins, each amino acid is represented by one CG particle. For DNA, one nucleotide is simplified by three CG particles, representing sugar, phosphate, and base. The protein modeling is based on the idea that proteins have a globally funnel-like energy landscape, which is encoded in the structure-based potential energy function. We first describe two representative minimal models of proteins, called the elastic network model and the classic Go̅ model. We then present a more elaborate protein model, which extends the minimal model to incorporate sequence and context dependent local flexibility and nonlocal contacts. For DNA, we describe a model developed by de Pablo's group that was tuned to well reproduce sequence-dependent structural and thermodynamic experimental data for single- and double-stranded DNAs. Protein-DNA interactions are modeled either by the structure-based term for specific cases or by electrostatic and excluded volume terms for nonspecific cases. We also discuss the time scale mapping in CG molecular dynamics simulations. While the apparent single time step of our CGMD is about 10 times larger than that in the fully atomistic molecular dynamics for small-scale dynamics, large-scale motions can be further accelerated by two-orders of magnitude with the use of CG model and a low friction constant in Langevin dynamics. Next, we present four examples of applications. First, the classic Go̅ model was used to
A model of shape memory materials with hierarchical twinning: Statics and dynamics
Saxena, A.; Bishop, A.R. [Los Alamos National Lab., NM (United States); Shenoy, S.R. [International Center for Theoretical Physics, Trieste (Italy); Wu, Y.; Lookman, T. [Western Ontario Univ., London, Ontario (Canada). Dept. of Applied Mathematics
1995-07-01
We consider a model of shape memory material in which hierarchical twinning near the habit plane (austenite-martensite interface) is a new and crucial ingredient. The model includes (1) a triple-well potential ({phi} model) in local shear strain, (2) strain gradient terms up to second order in strain and fourth order in gradient, and (3) all symmetry allowed compositional fluctuation induced strain gradient terms. The last term favors hierarchy which enables communication between macroscopic (cm) and microscopic ({Angstrom}) regions essential for shape memory. Hierarchy also stabilizes between formation (critical pattern of twins). External stress or pressure (pattern) modulates the spacing of domain walls. Therefore the ``pattern`` is encoded in the modulated hierarchical variation of the depth and width of the twins. This hierarchy of length scales provides a hierarchy of time scales and thus the possibility of non-exponential decay. The four processes of the complete shape memory cycle -- write, record, erase and recall -- are explained within this model. Preliminary results based on 2D Langevin dynamics are shown for tweed and hierarchy formation.
Dynamical Modeling of Mars' Paleoclimate
Richardson, Mark I.
2004-01-01
This report summarizes work undertaken under a one-year grant from the NASA Mars Fundamental Research Program. The goal of the project was to initiate studies of the response of the Martian climate to changes in planetary obliquity and orbital elements. This work was undertaken with a three-dimensional numerical climate model based on the Geophysical Fluid Dynamics Laboratory (GFDL) Skyhi General Circulation Model (GCM). The Mars GCM code was adapted to simulate various obliquity and orbital parameter states. Using a version of the model with a basic water cycle (ice caps, vapor, and clouds), we examined changes in atmospheric water abundances and in the distribution of water ice sheets on the surface. This work resulted in a paper published in the Journal of Geophysical Research - Planets. In addition, the project saw the initial incorporation of a regolith water transport and storage scheme into the model. This scheme allows for interaction between water in the pores of the near subsurface (<3m) and the atmosphere. This work was not complete by the end of the one-year grant, but is now continuing within the auspices of a three-year grant of the same title awarded by the Mars Fundamental Research Program in late 2003.
A Langevin Approach to a Classical Brownian Oscillator in an Electromagnetic Field
Espinoza Ortiz, J. S.; Bauke, F. C.; Lagos, R. E.
2016-08-01
We consider a charged Brownian particle bounded by an harmonic potential, embedded in a Markovian heat bath and driven from equilibrium by external electric and magnetic fields. We develop a quaternionic-like (or Pauli spinor-like) representation, hitherto exploited in classical Lorentz related dynamics. Within this formalism, in a very straight forward and elegant fashion, we compute the exact solution for the resulting generalized Langevin equation, for the case of a constant magnetic field. For the case the source electromagnetic fields satisfy Maxwell's equations, yielding spinor-like Mathieu equations, we compute the solutions within the JWKB approximation. With the solutions at hand we further compute spatial, velocities and crossed time correlations. In particular we study the (kinetically defined) nonequilbrium temperature. Therefore, we can display the system's time evolution towards equilibrium or towards non equilibrium (steady or not) states.
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.
Grebenkov, Denis S; Vahabi, Mahsa
2014-01-01
We consider a generalized Langevin equation that can be used to describe thermal motion of a tracer in a viscoelastic medium by accounting for inertial and hydrodynamic effects at short times, subdiffusive scaling at intermediate times, and eventual optical trapping at long times. We derive a Laplace-type integral representation for the linear response function that governs the diffusive dynamics. This representation is particularly well suited for rapid numerical computation and theoretical analysis. In particular, we deduce explicit formulas for the mean and variance of the time averaged (TA) mean square displacement (MSD) and velocity autocorrelation function (VACF). The asymptotic behavior of the TA MSD and TA VACF is investigated at different time scales. Some biophysical and microrheological applications are discussed, with an emphasis on the statistical analysis of optical tweezers' single-particle tracking experiments in polymer networks and living cells.
Han, Jie
2014-01-01
We investigate time-dependent probability for a Brownian particle passing over the barrier to stay at a metastable potential pocket against escaping over the barrier. This is related to whole fusion-fission dynamical process and can be called the reverse Kramers problem. By the passing probability over the saddle point of inverse harmonic potential multiplying the exponential decay factor of a particle in the metastable potential, we present an approximate expression for the modified passing probability over the barrier, in which the effect of reflection boundary of potential is taken into account. Our analytical result and Langevin Monte-Carlo simulation show that the probability passing and against escaping over the barrier is a non-monotonous function of time and its maximal value is less than the stationary result of passing probability over the saddle point of inverse harmonic potential.
On the condition for correct convergence in the complex Langevin method
Shimasaki, Shinji; Nishimura, Jun
2016-01-01
The complex Langevin method (CLM) provides a promising way to perform the path integral with a complex action using a stochastic equation for complexified dynamical variables. It is known, however, that the method gives wrong results in some cases, while it works, for instance, in finite density QCD in the deconfinement phase or in the heavy dense limit. Here we revisit the argument for justification of the CLM and point out a subtlety in using the time-evolved observables, which play a crucial role in the argument. This subtlety requires that the probability distribution of the drift term should fall off exponentially or faster at large magnitude. We demonstrate our claim in some examples such as chiral Random Matrix Theory and show that our criterion is indeed useful in judging whether the results obtained by the CLM are trustable or not.
Dynamic nature at the QCD Critical End Point
Ohnishi, K; Ohnishi, Kazuaki; Teiji Kunihiro
2005-01-01
We discuss the dynamic nature of the critical end point (CEP) which is the end point of the first order chiral phase transition. In the earlier work, Son and Stephanov analyzed the Langevin equation for CEP taking care of the mixing effect between the chiral condensate and the baryon number density and showed that the dynamic universality class of CEP is the model H, the same as that of the end point of the liquid-gas transition. We point out a difficulty in their treatment that the theory does not correctly reduce to CEP in the limiting situation where the mixing effect disappears. We give a reanalysis of the Langevin equation to conclude that CEP belongs to the model C apart from the energy and momentum densities, which is the same conclusion as given by Berdnikov and Rajagopal. We also propose a new signal for CEP in the heavy-ion collision experiments.
Dynamical approach to fusion-fission process in superheavy mass region
Aritomo Y.
2012-10-01
Full Text Available In order to describe heavy-ion fusion reactions around the Coulomb barrier with an actinide target nucleus, we propose a model which combines the coupled-channels approach and a fluctuation-dissipation model for dynamical calculations. This model takes into account couplings to the collective states of the interacting nuclei in the penetration of the Coulomb barrier and the subsequent dynamical evolution of a nuclear shape from the contact configuration. In the fluctuation-dissipation model with a Langevin equation, the effect of nuclear orientation at the initial impact on the prolately deformed target nucleus is considered. Fusion-fission, quasifission and deep quasifission are separated as different Langevin trajectories on the potential energy surface. Using this model, we analyze the experimental data for the mass distribution of fission fragments (MDFF in the reaction of 36S+238U at several incident energies around the Coulomb barrier.
Wind Farm Decentralized Dynamic Modeling With Parameters
Soltani, Mohsen; Shakeri, Sayyed Mojtaba; Grunnet, Jacob Deleuran;
2010-01-01
Development of dynamic wind flow models for wind farms is part of the research in European research FP7 project AEOLUS. The objective of this report is to provide decentralized dynamic wind flow models with parameters. The report presents a structure for decentralized flow models with inputs from...
Dynamical model for virus spread
Camelo-Neto, G
1995-01-01
The steady state properties of the mean density population of infected cells in a viral spread is simulated by a general forest fire like cellular automaton model with two distinct populations of cells ( permissive and resistant ones) and studied in the framework of the mean field approximation. Stochastic dynamical ingredients are introduced in this model to mimic cells regeneration (with probability {\\it p}) and to consider infection processes by other means than contiguity (with probability {\\it f}). Simulations are carried on a L \\times L square lattice considering the eight first neighbors. The mean density population of infected cells (D_i) is measured as function of the regeneration probability {\\it p}, and analyzed for small values of the ratio {\\it f/p } and for distinct degrees of the cell resistance. The results obtained by a mean field like approach recovers the simulations results. The role of the resistant parameter R (R \\geq 2) on the steady state properties is investigated and discussed in com...
Characterizing and modeling citation dynamics.
Young-Ho Eom
Full Text Available Citation distributions are crucial for the analysis and modeling of the activity of scientists. We investigated bibliometric data of papers published in journals of the American Physical Society, searching for the type of function which best describes the observed citation distributions. We used the goodness of fit with Kolmogorov-Smirnov statistics for three classes of functions: log-normal, simple power law and shifted power law. The shifted power law turns out to be the most reliable hypothesis for all citation networks we derived, which correspond to different time spans. We find that citation dynamics is characterized by bursts, usually occurring within a few years since publication of a paper, and the burst size spans several orders of magnitude. We also investigated the microscopic mechanisms for the evolution of citation networks, by proposing a linear preferential attachment with time dependent initial attractiveness. The model successfully reproduces the empirical citation distributions and accounts for the presence of citation bursts as well.
Michael, Fredrick; Johnson, M. D.
2003-03-01
A necessary precondition for modeling financial markets is a complete understanding of their statistics, including dynamics. Distributions derived from nonextensive Tsallis statistics are closely connected with dynamics described by a nonlinear Fokker-Planck equation. The combination shows promise in describing stochastic processes with power-law distributions and superdiffusive dynamics. We investigate intra-day price changes in the S& P500 stock index within this framework. We find that the power-law tails of the distributions, and the index's anomalously diffusing dynamics, are very accurately described by this approach. Our results show good agreement between market data and Fokker-Planck dynamics. This approach may be applicable in any anomalously diffusing system in which the correlations in time can be accounted for by an Ito-Langevin process with a simple time-dependent diffusion coefficient.
Despósito, M A; Viñales, A D
2008-03-01
We investigate the memory effects present in the asymptotic dynamics of a classical harmonic oscillator governed by a generalized Langevin equation. Using Laplace analysis together with Tauberian theorems we derive asymptotic expressions for the mean values, variances, and velocity autocorrelation function in terms of the long-time behavior of the memory kernel and the correlation function of the random force. The internal and external noise cases are analyzed. A simple criterion to determine if the diffusion process is normal or anomalous is established.
Correlated L\\'evy noise in linear dynamical systems
Srokowski, Tomasz
2010-01-01
Linear dynamical systems, driven by a non-white noise which has the Levy distribution, are analysed. Noise is modelled by a specific stochastic process which is defined by the Langevin equation with a linear force and the Levy distributed symmetric white noise. Correlation properties of the process are discussed. The Fokker-Planck equation driven by that noise is solved. Distributions have the Levy shape and their width, for a given time, is smaller than for processes in the white noise limit...
Relating structure and dynamics in organisation models
Jonkers, C.M.; Treur, J.
2008-01-01
To understand how an organisational structure relates to dynamics is an interesting fundamental challenge in the area of social modelling. Specifications of organisational structure usually have a diagrammatic form that abstracts from more detailed dynamics. Dynamic properties of agent systems, on t
Modelling the dynamics of youth subcultures
Holme, P; Holme, Petter; Gronlund, Andreas
2005-01-01
What are the dynamics behind youth subcultures such as punk, hippie, or hip-hop cultures? How does the global dynamics of these subcultures relate to the individual's search for a personal identity? We propose a simple dynamical model to address these questions and find that only a few assumptions of the individual's behaviour are necessary to regenerate known features of youth culture.
Detailed balance condition and effective free energy in the primitive chain network model
Uneyama, Takashi; Masubuchi, Yuichi
2011-11-01
We consider statistical mechanical properties of the primitive chain network (PCN) model for entangled polymers from its dynamic equations. We show that the dynamic equation for the segment number of the PCN model does not reduce to the standard Langevin equation which satisfies the detailed balance condition. We propose heuristic modifications for the PCN dynamic equation for the segment number, to make it reduce to the standard Langevin equation. We analyse some equilibrium statistical properties of the modified PCN model, by using the effective free energy obtained from the modified PCN dynamic equations. The PCN effective free energy can be interpreted as the sum of the ideal Gaussian chain free energy and the repulsive interaction energy between slip-links. By using the single chain approximation, we calculate several distribution functions of the PCN model. The obtained distribution functions are qualitatively different from ones for the simple slip-link model without any direct interactions between slip-links.
Detailed balance condition and effective free energy in the primitive chain network model.
Uneyama, Takashi; Masubuchi, Yuichi
2011-11-14
We consider statistical mechanical properties of the primitive chain network (PCN) model for entangled polymers from its dynamic equations. We show that the dynamic equation for the segment number of the PCN model does not reduce to the standard Langevin equation which satisfies the detailed balance condition. We propose heuristic modifications for the PCN dynamic equation for the segment number, to make it reduce to the standard Langevin equation. We analyse some equilibrium statistical properties of the modified PCN model, by using the effective free energy obtained from the modified PCN dynamic equations. The PCN effective free energy can be interpreted as the sum of the ideal Gaussian chain free energy and the repulsive interaction energy between slip-links. By using the single chain approximation, we calculate several distribution functions of the PCN model. The obtained distribution functions are qualitatively different from ones for the simple slip-link model without any direct interactions between slip-links.
Dynamic stall model for wind turbine airfoils
Larsen, J.W.; Nielsen, S.R.K.; Krenk, Steen
2007-01-01
A model is presented for aerodynamic lift of wind turbine profiles under dynamic stall. The model combines memory delay effects under attached flow with reduced lift due to flow separation under dynamic stall conditions. The model is based on a backbone curve in the form of the static lift...... conditions, nonstationary effects are included by three mechanisms: a delay of the lift coefficient of fully attached flow via a second-order filter, a delay of the development of separation represented via a first-order filter, and a lift contribution due to leading edge separation also represented via...... during dynamic stall conditions. The proposed model is compared with five other dynamic stall models including, among others, the Beddoes-Leishman model and the ONERA model. It is demonstrated that the proposed model performs equally well or even better than more complicated models and that the included...
Reprint of : The Boltzmann--Langevin approach: A simple quantum-mechanical derivation
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.
Model dynamics for quantum computing
Tabakin, Frank
2017-08-01
A model master equation suitable for quantum computing dynamics is presented. In an ideal quantum computer (QC), a system of qubits evolves in time unitarily and, by virtue of their entanglement, interfere quantum mechanically to solve otherwise intractable problems. In the real situation, a QC is subject to decoherence and attenuation effects due to interaction with an environment and with possible short-term random disturbances and gate deficiencies. The stability of a QC under such attacks is a key issue for the development of realistic devices. We assume that the influence of the environment can be incorporated by a master equation that includes unitary evolution with gates, supplemented by a Lindblad term. Lindblad operators of various types are explored; namely, steady, pulsed, gate friction, and measurement operators. In the master equation, we use the Lindblad term to describe short time intrusions by random Lindblad pulses. The phenomenological master equation is then extended to include a nonlinear Beretta term that describes the evolution of a closed system with increasing entropy. An external Bath environment is stipulated by a fixed temperature in two different ways. Here we explore the case of a simple one-qubit system in preparation for generalization to multi-qubit, qutrit and hybrid qubit-qutrit systems. This model master equation can be used to test the stability of memory and the efficacy of quantum gates. The properties of such hybrid master equations are explored, with emphasis on the role of thermal equilibrium and entropy constraints. Several significant properties of time-dependent qubit evolution are revealed by this simple study.
An immune based dynamic intrusion detection model
LI Tao
2005-01-01
With the dynamic description method for self and antigen, and the concept of dynamic immune tolerance for lymphocytes in network-security domain presented in this paper, a new immune based dynamic intrusion detection model (Idid) is proposed. In Idid, the dynamic models and the corresponding recursive equations of the lifecycle of mature lymphocytes, and the immune memory are built. Therefore, the problem of the dynamic description of self and nonself in computer immune systems is solved, and the defect of the low efficiency of mature lymphocyte generating in traditional computer immune systems is overcome. Simulations of this model are performed, and the comparison experiment results show that the proposed dynamic intrusion detection model has a better adaptability than the traditional methods.
Workflow-Based Dynamic Enterprise Modeling
黄双喜; 范玉顺; 罗海滨; 林慧萍
2002-01-01
Traditional systems for enterprise modeling and business process control are often static and cannot adapt to the changing environment. This paper presents a workflow-based method to dynamically execute the enterprise model. This method gives an explicit representation of the business process logic and the relationships between the elements involved in the process. An execution-oriented integrated enterprise modeling system is proposed in combination with other enterprise views. The enterprise model can be established and executed dynamically in the actual environment due to the dynamic properties of the workflow model.
Dynamical model of the kinesin protein motor
Nesterov, Alexander I; Ramírez, Mónica F
2016-01-01
We model and simulate the stepping dynamics of the kinesin motor including electric and mechanical forces, environmental noise, and the complicated potentials produced by tracking and neighboring protofilaments. Our dynamical model supports the hand-over-hand mechanism of the kinesin stepping. Our theoretical predictions and numerical simulations include the off-axis displacements of the kinesin heads while the steps are performed. The results obtained are in a good agreement with recent experiments on the kinesin dynamics.
A simplified model of software project dynamics
Ruiz Carreira, Mercedes; Ramos Román, Isabel; Toro Bonilla, Miguel
2001-01-01
The simulation of a dynamic model for software development projects (hereinafter SDPs) helps to investigate the impact of a technological change, of different management policies, and of maturity level of organisations over the whole project. In the beginning of the 1990s, with the appearance of the dynamic model for SDPs by Abdel-Hamid and Madnick [Software Project Dynamics: An Integrated Approach, Prentice-Hall, Englewood Cliffs, NJ, 1991], a significant advance took place in the field of p...
Explicit models for dynamic software
Bosloper, Ivor; Siljee, Johanneke; Nijhuis, Jos; Nord, R; Medvidovic, N; Krikhaar, R; Khrhaar, R; Stafford, J; Bosch, J
2006-01-01
A key aspect in creating autonomous dynamic software systems is the possibility of reasoning about properties of runtime variability and dynamic behavior, e.g. when and how to reconfigure the system. Currently these properties are often not made explicit in the software architecture. We argue that
Explicit models for dynamic software
Bosloper, Ivor; Siljee, Johanneke; Nijhuis, Jos; Nord, R; Medvidovic, N; Krikhaar, R; Khrhaar, R; Stafford, J; Bosch, J
2006-01-01
A key aspect in creating autonomous dynamic software systems is the possibility of reasoning about properties of runtime variability and dynamic behavior, e.g. when and how to reconfigure the system. Currently these properties are often not made explicit in the software architecture. We argue that h
Comparative dynamics in a health investment model.
Eisenring, C
1999-10-01
The method of comparative dynamics fully exploits the inter-temporal structure of optimal control models. I derive comparative dynamic results in a simplified demand for health model. The effect of a change in the depreciation rate on the optimal paths for health capital and investment in health is studied by use of a phase diagram.
Dynamic Heat Transfer Model of Refrigerated Foodstuff
Cai, Junping; Risum, Jørgen; Thybo, Claus
2006-01-01
their temperature relation. This paper discusses the dynamic heat transfer model of foodstuff inside the display cabinet, one-dimensional dynamic model is developed, and the Explicit Finite Difference Method is applied, to handle the unsteady heat transfer problem with phase change, as well as time varying boundary...
System dynamics modelling of situation awareness
Oosthuizen, R
2015-11-01
Full Text Available . The feedback loops and delays in the Command and Control system also contribute to the complex dynamic behavior. This paper will build on existing situation awareness models to develop a System Dynamics model to support a qualitative investigation through...
The Challenges to Coupling Dynamic Geospatial Models
Goldstein, N
2006-06-23
Many applications of modeling spatial dynamic systems focus on a single system and a single process, ignoring the geographic and systemic context of the processes being modeled. A solution to this problem is the coupled modeling of spatial dynamic systems. Coupled modeling is challenging for both technical reasons, as well as conceptual reasons. This paper explores the benefits and challenges to coupling or linking spatial dynamic models, from loose coupling, where information transfer between models is done by hand, to tight coupling, where two (or more) models are merged as one. To illustrate the challenges, a coupled model of Urbanization and Wildfire Risk is presented. This model, called Vesta, was applied to the Santa Barbara, California region (using real geospatial data), where Urbanization and Wildfires occur and recur, respectively. The preliminary results of the model coupling illustrate that coupled modeling can lead to insight into the consequences of processes acting on their own.
Multiscale approach to modeling intrinsic dissipation in solids
Kunal, K.; Aluru, N. R.
2016-08-01
In this paper, we develop a multiscale approach to model intrinsic dissipation under high frequency of vibrations in solids. For vibrations with a timescale comparable to the phonon relaxation time, the local phonon distribution deviates from the equilibrium distribution. We extend the quasiharmonic (QHM) method to describe the dynamics under such a condition. The local deviation from the equilibrium state is characterized using a nonequilibrium stress tensor. A constitutive relation for the time evolution of the stress component is obtained. We then parametrize the evolution equation using the QHM method and a stochastic sampling approach. The stress relaxation dynamics is obtained using mode Langevin dynamics. Methods to obtain the input variables for the Langevin dynamics are discussed. The proposed methodology is used to obtain the dissipation rate Edissip for different cases. Frequency and size effect on Edissip are studied. The results are compared with those obtained using nonequilibrium molecular dynamics (MD).
Hydration dynamics near a model protein surface
Russo, Daniela; Hura, Greg; Head-Gordon, Teresa
2003-09-01
The evolution of water dynamics from dilute to very high concentration solutions of a prototypical hydrophobic amino acid with its polar backbone, N-acetyl-leucine-methylamide (NALMA), is studied by quasi-elastic neutron scattering and molecular dynamics simulation for both the completely deuterated and completely hydrogenated leucine monomer. We observe several unexpected features in the dynamics of these biological solutions under ambient conditions. The NALMA dynamics shows evidence of de Gennes narrowing, an indication of coherent long timescale structural relaxation dynamics. The translational water dynamics are analyzed in a first approximation with a jump diffusion model. At the highest solute concentrations, the hydration water dynamics is significantly suppressed and characterized by a long residential time and a slow diffusion coefficient. The analysis of the more dilute concentration solutions takes into account the results of the 2.0M solution as a model of the first hydration shell. Subtracting the first hydration layer based on the 2.0M spectra, the translational diffusion dynamics is still suppressed, although the rotational relaxation time and residential time are converged to bulk-water values. Molecular dynamics analysis shows spatially heterogeneous dynamics at high concentration that becomes homogeneous at more dilute concentrations. We discuss the hydration dynamics results of this model protein system in the context of glassy systems, protein function, and protein-protein interfaces.
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.
Satin, Seema
2015-01-01
We attempt to introduce an new approach towards study of certain interesting issues in classical gravity. This can be done for few confined, but interesting and meaningful physical situations, which can be modeled by a classical stochastic Einstein equation. The Einstein equation can be looked upon as an equation of motion, while introducing to it a classical stochastic source or classical fluctuations as driving source. This is analogous to the Langevin equation formalism, in Brownian motion studies. A justification for the validity of such an ansatz for classical gravity is given. The regime of validity of such an approach and the consequences and possible outcomes of this formulation are discussed. We also mention, further relevant directions and applications of the same,that act as motivation towards the new proposal. This field of study can be seen to emerge out of well established ideas and results in Brownian motion theory as well as the Stochastic Semiclassical Gravity (which is already an active area...
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.
Dynamic Factor Models for the Volatility Surface
van der Wel, Michel; Ozturk, Sait R.; Dijk, Dick van
The implied volatility surface is the collection of volatilities implied by option contracts for different strike prices and time-to-maturity. We study factor models to capture the dynamics of this three-dimensional implied volatility surface. Three model types are considered to examine desirable...... features for representing the surface and its dynamics: a general dynamic factor model, restricted factor models designed to capture the key features of the surface along the moneyness and maturity dimensions, and in-between spline-based methods. Key findings are that: (i) the restricted and spline......-based models are both rejected against the general dynamic factor model, (ii) the factors driving the surface are highly persistent, (iii) for the restricted models option Delta is preferred over the more often used strike relative to spot price as measure for moneyness....
Comprehensive Survey on Dynamic Graph Models
Aya Zaki
2016-02-01
Full Text Available Most of the critical real-world networks are con-tinuously changing and evolving with time. Motivated by the growing importance and widespread impact of this type of networks, the dynamic nature of these networks have gained a lot of attention. Because of their intrinsic and special characteristics, these networks are best represented by dynamic graph models. To cope with their evolving nature, the representation model must keep the historical information of the network along with its temporal time. Storing such amount of data, poses many problems from the perspective of dynamic graph data management. This survey provides an in-depth overview on dynamic graph related problems. Novel categorization and classification of the state of the art dynamic graph models are also presented in a systematic and comprehensive way. Finally, we discuss dynamic graph processing including the output representation of its algorithms.
Luis L. Bonilla
2017-05-01
Full Text Available In this work, we present a numerical study of the influence of matrix degrading enzyme (MDE dynamics and haptotaxis on the development of vessel networks in tumor-induced angiogenesis. Avascular tumors produce growth factors that induce nearby blood vessels to emit sprouts formed by endothelial cells. These capillary sprouts advance toward the tumor by chemotaxis (gradients of growth factor and haptotaxis (adhesion to the tissue matrix outside blood vessels. The motion of the capillaries in this constrained space is modelled by stochastic processes (Langevin equations, branching and merging of sprouts coupled to continuum equations for concentrations of involved substances. There is a complementary deterministic description in terms of the density of actively moving tips of vessel sprouts. The latter forms a stable soliton-like wave whose motion is influenced by the different taxis mechanisms. We show the delaying effect of haptotaxis on the advance of the angiogenic vessel network by direct numerical simulations of the stochastic process and by a study of the soliton motion.
Molecular dynamics model for nano-motions of FePd nanohelices
Taya, M.; Xu, C.; Matsuse, T.; Muraishi, S.
2017-04-01
Shrinkage and relaxation motions of flexible FePd nanohelices of FePd nanorobots are simulated by a molecular dynamics (MD) model where FePd is a paramagnetic shape memory alloy that can exhibit phase transformation accompanied by softening of the nanohelix under an applied magnetic field (H-field). Two designs of FePd nanorobots are used: (i) a FePd cylindrical head connected to a FePd nanohelix tail and (ii) a FePd nanohelix alone. The geometry and dimensions of the FePd robots are taken after the as-processed FePd nanorobots. In the MD simulation, the FePd head and nanohelix are divided into a number of segmented FePd spheres, each having its magnetic moment. The results of the MD model reveal that upon the applied constant magnetic field, the initial gaps (g = 3 nm) between the adjacent turns of the FePd nanohelix are closed, resulting in the total shrinkage (Stot) of 47 nm of the FePd nanorobot. The effects of the applied H-field on Stot are examined by using the MD model and the M-H curve of FePd fitted with Langevin type, resulting in the smaller applied magnetic field leading to the smaller Stot. The results of the MD model provide us with an effective tool in the analysis and design of new nanorobots based on the paramagnetic shape memory alloy of FePd nanohelices that can exert dynamic vibrations on target cells under the oscillating magnetic field.
Modelling the dynamics of turbulent floods
Mei, Z; Li, Z; Li, Zhenquan
1999-01-01
Consider the dynamics of turbulent flow in rivers, estuaries and floods. Based on the widely used k-epsilon model for turbulence, we use the techniques of centre manifold theory to derive dynamical models for the evolution of the water depth and of vertically averaged flow velocity and turbulent parameters. This new model for the shallow water dynamics of turbulent flow: resolves the vertical structure of the flow and the turbulence; includes interaction between turbulence and long waves; and gives a rational alternative to classical models for turbulent environmental flows.
Cosseddu, Salvatore M; Allen, Michael P; Rodger, P M; Luchinsky, Dmitry G; McClintock, Peter V E
2013-01-01
The statistical and dynamical properties of ions in the selectivity filter of the KcsA ion channel are considered on the basis of molecular dynamics (MD) simulations of the KcsA protein embedded in a lipid membrane surrounded by an ionic solution. A new approach to the derivation of a Brownian dynamics (BD) model of ion permeation through the filter is discussed, based on unbiased MD simulations. It is shown that depending on additional assumptions, ion's dynamics can be described either by under-damped Langevin equation with constant damping and white noise or by Langevin equation with a fractional memory kernel. A comparison of the potential of the mean force derived from unbiased MD simulations with the potential produced by the umbrella sampling method demonstrates significant differences in these potentials. The origin of these differences is an open question that requires further clarifications.
Flapping Wing Flight Dynamic Modeling
2011-08-22
von Karman, T. and Burgers, J. M., Gerneral Aerodynamic Theory - Perfect Fluids , Vol. II, Julius Springer , Berlin, 1935. [24] Pesavento, U. and Wang...L., Methods of Analytical Dynamics , McGraw-Hill Book Company, New York, 1970. [34] Deng, X., Schenato, L., Wu, W. C., and Sastry, S. S., Flapping...Micro air vehicle- motivated computational biomechanics in bio ights: aerodynamics, ight dynamics and maneuvering stability, Acta Mechanica
Modeling Mitochondrial Bioenergetics with Integrated Volume Dynamics
Bazil, Jason N.; Buzzard, Gregery T.; Ann E Rundell
2010-01-01
Author Summary Mathematically modeling biological systems challenges our current understanding of the physical and biochemical events contributing to the observed dynamics. It requires careful consideration of hypothesized mechanisms, model development assumptions and details regarding the experimental conditions. We have adopted a modeling approach to translate these factors that explicitly considers the thermodynamic constraints, biochemical states and reaction mechanisms during model devel...
Dynamical CP violation in composite Higgs models
Hashimoto, S.; Inagaki, Tomohiro; Muta, Taizo
1993-01-01
The dynamical origin of the CP violation in electroweak theory is investigated in composite Higgs models. The mechanism of the spontaneous CP violation proposed in other context by Dashen is adopted to construct simple models of the dynamical CP violation. Within the models the size of the neutron electric dipole moment is estimated and the constraint on the $\\varepsilon$-parameter in K-meson decays is discussed.
Very Large System Dynamics Models - Lessons Learned
Jacob J. Jacobson; Leonard Malczynski
2008-10-01
This paper provides lessons learned from developing several large system dynamics (SD) models. System dynamics modeling practice emphasize the need to keep models small so that they are manageable and understandable. This practice is generally reasonable and prudent; however, there are times that large SD models are necessary. This paper outlines two large SD projects that were done at two Department of Energy National Laboratories, the Idaho National Laboratory and Sandia National Laboratories. This paper summarizes the models and then discusses some of the valuable lessons learned during these two modeling efforts.
QUANTUM LANGEVIN THEORY OF WHISPERING-GALLERY-MODE MICROSPHERE LASER
CHAI JIN-HUA; LU YI-QUN; LEUNG PUI-TANG
2000-01-01
A quantum Langevin theory of whispering-gallery-mode microsphere laser theory is developed. The linear and nonlinear analysis are made for laser operation below and above the threshold. In these analysis, corresponding to the specific property of microsphere, the effect of inversion fluctuation is treated. The coherence functions of laser field are calculated, and the intensity, the amplitude fluctuation and the linewidth of the field are obtained, which are connected with the enhancement factor of whispering-gallery-mode microsphere. It is shown that the strong couple and strong pumping are useful for the amplification of intensity and the decrease of linewidth below the threshold. It is also shown that, for the laser action above threshold, the variances of photon number and the linewidth of internal field are related to the enhancement factor and the square of the enhancement factor, respectively.
Comparing models of Red Knot population dynamics
McGowan, Conor
2015-01-01
Predictive population modeling contributes to our basic scientific understanding of population dynamics, but can also inform management decisions by evaluating alternative actions in virtual environments. Quantitative models mathematically reflect scientific hypotheses about how a system functions. In Delaware Bay, mid-Atlantic Coast, USA, to more effectively manage horseshoe crab (Limulus polyphemus) harvests and protect Red Knot (Calidris canutus rufa) populations, models are used to compare harvest actions and predict the impacts on crab and knot populations. Management has been chiefly driven by the core hypothesis that horseshoe crab egg abundance governs the survival and reproduction of migrating Red Knots that stopover in the Bay during spring migration. However, recently, hypotheses proposing that knot dynamics are governed by cyclical lemming dynamics garnered some support in data analyses. In this paper, I present alternative models of Red Knot population dynamics to reflect alternative hypotheses. Using 2 models with different lemming population cycle lengths and 2 models with different horseshoe crab effects, I project the knot population into the future under environmental stochasticity and parametric uncertainty with each model. I then compare each model's predictions to 10 yr of population monitoring from Delaware Bay. Using Bayes' theorem and model weight updating, models can accrue weight or support for one or another hypothesis of population dynamics. With 4 models of Red Knot population dynamics and only 10 yr of data, no hypothesis clearly predicted population count data better than another. The collapsed lemming cycle model performed best, accruing ~35% of the model weight, followed closely by the horseshoe crab egg abundance model, which accrued ~30% of the weight. The models that predicted no decline or stable populations (i.e. the 4-yr lemming cycle model and the weak horseshoe crab effect model) were the most weakly supported.
A Stochastic Cobweb Dynamical Model
Serena Brianzoni
2008-01-01
_,__0__1, and the forward predictor with probability (1−, so that the expected price at time is a random variable and consequently the dynamics describing the price evolution in time is governed by a stochastic dynamical system. The dynamical system becomes a Markov process when the memory rate vanishes. In particular, we study the Markov chain in the cases of discrete and continuous time. Using a mixture of analytical tools and numerical methods, we show that, when prices take discrete values, the corresponding Markov chain is asymptotically stable. In the case with continuous prices and nonnecessarily zero memory rate, numerical evidence of bounded price oscillations is shown. The role of the memory rate is studied through numerical experiments, this study confirms the stabilizing effects of the presence of resistant memory.
Modeling the Dynamics of an Information System
Jacek Unold
2003-11-01
Full Text Available The article concentrates on the nature of a social subsystem of an information system. It analyzes the nature of information processes of collectivity within an IS and introduces a model of IS dynamics. The model is based on the assumption that a social subsystem of an information system works as a nonlinear dynamic system. The model of IS dynamics is verified on the indexes of the stock market. It arises from the basic assumption of the technical analysis of the markets, that is, the index chart reflects the play of demand and supply, which in turn represents the crowd sentiment on the market.
Structural Dynamics Model of a Cartesian Robot
1985-10-01
34 D FILE COPY AD-A198 053 *.CC Technical Report 1009 Structural Dynamics Model of a Cartesian Robot "DTIC SELEC T E 0 Alfonso Garcia Reynoso MIT...COVERED Structural Dynamics Model of a Cartesian Robot technical report G. PERFORMING ORG. REPORT NUM9ER 7. AUTHO0R(@) S. CONTRACT On GRANT NUMSER...8217 %S S Structural Dynamics Model of a Cartesian Robot by Alfonso Garcia Reynoso BSME Instituto Tecnol6gico de Veracruz (1967) MSME Instituto Tecnol6gico
Equivalent dynamic model of DEMES rotary joint
Zhao, Jianwen; Wang, Shu; Xing, Zhiguang; McCoul, David; Niu, Junyang; Huang, Bo; Liu, Liwu; Leng, Jinsong
2016-07-01
The dielectric elastomer minimum energy structure (DEMES) can realize large angular deformations by a small voltage-induced strain of the dielectric elastomer (DE), so it is a suitable candidate to make a rotary joint for a soft robot. Dynamic analysis is necessary for some applications, but the dynamic response of DEMESs is difficult to model because of the complicated morphology and viscoelasticity of the DE film. In this paper, a method composed of theoretical analysis and experimental measurement is presented to model the dynamic response of a DEMES rotary joint under an alternating voltage. Based on measurements of equivalent driving force and damping of the DEMES, the model can be derived. Some experiments were carried out to validate the equivalent dynamic model. The maximum angle error between model and experiment is greater than ten degrees, but it is acceptable to predict angular velocity of the DEMES, therefore, it can be applied in feedforward-feedback compound control.
Modeling microbial growth and dynamics.
Esser, Daniel S; Leveau, Johan H J; Meyer, Katrin M
2015-11-01
Modeling has become an important tool for widening our understanding of microbial growth in the context of applied microbiology and related to such processes as safe food production, wastewater treatment, bioremediation, or microbe-mediated mining. Various modeling techniques, such as primary, secondary and tertiary mathematical models, phenomenological models, mechanistic or kinetic models, reactive transport models, Bayesian network models, artificial neural networks, as well as agent-, individual-, and particle-based models have been applied to model microbial growth and activity in many applied fields. In this mini-review, we summarize the basic concepts of these models using examples and applications from food safety and wastewater treatment systems. We further review recent developments in other applied fields focusing on models that explicitly include spatial relationships. Using these examples, we point out the conceptual similarities across fields of application and encourage the combined use of different modeling techniques in hybrid models as well as their cross-disciplinary exchange. For instance, pattern-oriented modeling has its origin in ecology but may be employed to parameterize microbial growth models when experimental data are scarce. Models could also be used as virtual laboratories to optimize experimental design analogous to the virtual ecologist approach. Future microbial growth models will likely become more complex to benefit from the rich toolbox that is now available to microbial growth modelers.
The resonant behavior of an over-damped linear fractional Langevin equation%线性过阻尼分数阶Langevin方程的共振行为
钟苏川; 高仕龙; 韦鹍; 马洪
2012-01-01
通过将广义Langevin方程中的系统内噪声建模为分数阶高斯噪声，推导出分数阶Langevin方程，其分数阶导数项阶数由系统内噪声的Hurst指数所确定．讨论了处于强噪声环境下的线性过阻尼分数阶Langevin方程在周期信号激励下的共振行为，利用Shapiro—Loginov公式和Laplace变换，推导了系统响应的一、二阶稳态矩和稳态响应振幅、方差的解析表达式．分析表明，适当参数下，系统稳态响应振幅和方差随噪声的某些特征参数、周期激励信号的频率及系统部分参数的变化出现了广义的随机共振现象．%By choosing the internal noise as a fractional Gaussian noise, we obtain the fractional Langevin equation. We explore the phenomenon of stochastic resonance in an over-damped linear fractional Langevin equation subjected to an external sinusoidal forcing. The influence of fluctuations of environmental parameters on the dynamics of the system is modeled by a dichotomous noise.Using the Shapiro-Loginov formula and the Laplace transformation technique, we obtain the exact expressions of the first and second moment of the output signal, the mean particle displacement and the variance of the output signal in the long-time limit t→∞.Finally, the numerical simulation shows that the over-damped linear fractional Langevin equation reveals a lot of dynamic behaviors and the stochastic resonance （SR） in a wide sense can be found with internal noise and external noise.
Relaxation Dynamics of Semiflexible Fractal Macromolecules
Jonas Mielke
2016-07-01
Full Text Available We study the dynamics of semiflexible hyperbranched macromolecules having only dendritic units and no linear spacers, while the structure of these macromolecules is modeled through T-fractals. We construct a full set of eigenmodes of the dynamical matrix, which couples the set of Langevin equations. Based on the ensuing relaxation spectra, we analyze the mechanical relaxation moduli. The fractal character of the macromolecules reveals itself in the storage and loss moduli in the intermediate region of frequencies through scaling, whereas at higher frequencies, we observe the locally-dendritic structure that is more pronounced for higher stiffness.
Dynamics of the chiral phase transition
van Hees, H; Meistrenko, A; Greiner, C
2013-01-01
The intention of this study is the search for signatures of the chiral phase transition in heavy-ion collisions. To investigate the impact of fluctuations, e.g., of the baryon number, at the transition or at a critical point, the linear sigma model is treated in a dynamical (3+1)-dimensional numerical simulation. Chiral fields are approximated as classical mean fields, and quarks are described as quasi particles in a Vlasov equation. Additional dynamics is implemented by quark-quark and quark-sigma-field interactions. For a consistent description of field-particle interactions, a new Monte-Carlo-Langevin-like formalism has been developed and is discussed.
Forecasting house prices in the 50 states using Dynamic Model Averaging and Dynamic Model Selection
Bork, Lasse; Møller, Stig Vinther
2015-01-01
We examine house price forecastability across the 50 states using Dynamic Model Averaging and Dynamic Model Selection, which allow for model change and parameter shifts. By allowing the entire forecasting model to change over time and across locations, the forecasting accuracy improves...
Colmenero, J
2015-07-28
We show that the universal behavior of the Rouse-mode relaxation in polymer systems - which has been recently reported from experimental data [S. Arrese-Igor, et al., Phys. Rev. Lett., 2014, 113, 078302] - can be quantitatively explained in the framework of a theoretical approach based on: (i) a generalized Langevin equation formalism and (ii) a memory function which takes into account the coupling between intra-chain dynamics and collective dynamics. This approach opens the way for generalizing the magnitudes probing chain dynamics in polymer systems.
Phone Routing using the Dynamic Memory Model
Bendtsen, Claus Nicolaj; Krink, Thiemo
2002-01-01
In earlier studies a genetic algorithm (GA) extended with the dynamic memory model has shown remarkable performance on real-world-like problems. In this paper we experiment with routing in communication networks and show that the dynamic memory GA performs remarkable well compared to ant colony o...
System Dynamics Modelling for a Balanced Scorecard
Nielsen, Steen; Nielsen, Erland Hejn
2008-01-01
Purpose - To construct a dynamic model/framework inspired by a case study based on an international company. As described by the theory, one of the main difficulties of BSC is to foresee the time lag dimension of different types of indicators and their combined dynamic effects. Design/methodology...
Nonlinear dynamic phenomena in the beer model
Mosekilde, Erik; Laugesen, Jakob Lund
2007-01-01
The production-distribution system or "beer game" is one of the most well-known system dynamics models. Notorious for the complex dynamics it produces, the beer game has been used for nearly five decades to illustrate how structure generates behavior and to explore human decision making. Here we...
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.
A new dynamics model for traffic flow
无
2001-01-01
As a study method of traffic flow, dynamics models were developedand applied in the last few decades. However, there exist some flaws in most existing models. In this note, a new dynamics model is proposed by using car-following theory and the usual connection method of micro-macro variables, which can overcome some ubiquitous problems in the existing models. Numerical results show that the new model can very well simulate traffic flow conditions, such as congestion, evacuation of congestion, stop-and-go phenomena and phantom jam.
Complex saddle points and the sign problem in complex Langevin simulation
Hayata, Tomoya; Tanizaki, Yuya
2015-01-01
We show that complex Langevin simulation converges to a wrong result, by relating it to the Lefschetz-thimble path integral, when the path-integral weight has different phases among dominant complex saddle points. Equilibrium solution of the complex Langevin equation forms local distributions around complex saddle points. Its ensemble average approximately becomes a direct sum of the average in each local distribution, where relative phases among them are dropped. We propose that by taking these phases into account through reweighting, we can solve the wrong convergence problem. However, this prescription may lead to a recurrence of the sign problem in the complex Langevin method for quantum many-body systems.
Full simulation of chiral Random Matrix Theory at non-zero chemical potential by Complex Langevin
Mollgaard, A
2014-01-01
It is demonstrated that the complex Langevin method can simulate chiral random matrix theory at non-zero chemical potential. The successful match with the analytic prediction for the chiral condensate is established through a shift of matrix integration variables and choosing a polar representation for the new matrix elements before complexification. Furthermore, we test the proposal to work with a Langevin-time dependent quark mass and find that it allows us to control the fluctuations of the phase of the fermion determinant throughout the Langevin trajectory.
Full simulation of chiral random matrix theory at nonzero chemical potential by complex Langevin
Mollgaard, A.; Splittorff, K.
2015-02-01
It is demonstrated that the complex Langevin method can simulate chiral random matrix theory at nonzero chemical potential. The successful match with the analytic prediction for the chiral condensate is established through a shift of matrix integration variables and choosing a polar representation for the new matrix elements before complexification. Furthermore, we test the proposal to work with a Langevin-time-dependent quark mass and find that it allows us to control the fluctuations of the phase of the fermion determinant throughout the Langevin trajectory.
Langevin study of neutron emission in the reactions 16O+181Ta and 19F+178Hf
YE Wei; WU Feng; YANG Hong-Wei
2008-01-01
The pre-scission neutrons measured in the reactions 16O+181Ta and 19F+178Hf are studied via a Langevin equation coupled with a statistical decay model.We find that because of the mass asymmetry of different entrance channels,the spin distributions of compound nuclei would be different,consequently,the measured neutrons in these two reactions would also different.This means that the entrance channel will affect the particle emission in the fission process of hot nuclei.
MODELING MICROBUBBLE DYNAMICS IN BIOMEDICAL APPLICATIONS
CHAHINE Georges L.; HSIAO Chao-Tsung
2012-01-01
Controlling mierobubble dynamics to produce desirable biomedical outcomes when and where necessary and avoid deleterious effects requires advanced knowledge,which can be achieved only through a combination of experimental and numerical/analytical techniques.The present communication presents a multi-physics approach to study the dynamics combining viscousinviseid effects,liquid and structure dynamics,and multi bubble interaction.While complex numerical tools are developed and used,the study aims at identifying the key parameters influencing the dynamics,which need to be included in simpler models.
Airship dynamics modeling: A literature review
Li, Yuwen; Nahon, Meyer; Sharf, Inna
2011-04-01
The resurgence of airships has created a need for dynamics models and simulation capabilities adapted to these lighter-than-air vehicles. However, the modeling techniques for airship dynamics have lagged behind and are less systematic than those for fixed-wing aircraft. A state-of-the-art literature review is presented on airship dynamics modeling, aiming to provide a comprehensive description of the main problems in this area and a useful source of references for researchers and engineers interested in modern airship applications. The references are categorized according to the major topics in this area: aerodynamics, flight dynamics, incorporation of structural flexibility, incorporation of atmospheric turbulence, and effects of ballonets. Relevant analytical, numerical, and semi-empirical techniques are discussed, with a particular focus on how the main differences between lighter-than-air and heavier-than-air aircraft have been addressed in the modeling. Directions are suggested for future research on each of these topics.
Computational fluid dynamics modeling in yarn engineering
Patanaik, A
2011-07-01
Full Text Available This chapter deals with the application of computational fluid dynamics (CFD) modeling in reducing yarn hairiness during the ring spinning process and thereby “engineering” yarn with desired properties. Hairiness significantly affects the appearance...
Molecular dynamics model of dimethyl ether
Lin, B.; Halley, W.J. [Univ. of Minnesota, Minneapolis, MN (United States)
1995-11-02
We report a molecular dynamics model of the monomeric liquid dimethyl ether. The united atom approach is used to treat CH{sub 3} groups as point source centers. Partial charges are derived from the experimental dipole moment. Harmonic force constants are used for intramolecular interactions, and their values are so chosen that the model`s fundamental frequencies agree with experimental results. Because we are interested in solvation properties, the model contains flexible molecules, allowing molecular distortion and internal dynamical quantities. We report radial distribution functions and the static structure factors as well as some dynamical quantities such as the dynamical structure factor, infrared absorption, and Raman scattering spectra. Calculated results agree reasonably well with experimental and other simulation results. 25 refs., 8 figs., 1 tab.
Stochastic population dynamic models as probability networks
M.E. and D.C. Lee. Borsuk
2009-01-01
The dynamics of a population and its response to environmental change depend on the balance of birth, death and age-at-maturity, and there have been many attempts to mathematically model populations based on these characteristics. Historically, most of these models were deterministic, meaning that the results were strictly determined by the equations of the model and...
System Identification by Dynamic Factor Models
C. Heij (Christiaan); W. Scherrer; M. Destler
1996-01-01
textabstractThis paper concerns the modelling of stochastic processes by means of dynamic factor models. In such models the observed process is decomposed into a structured part called the latent process, and a remainder that is called noise. The observed variables are treated in a symmetric way, so
Damping mechanisms and models in structural dynamics
Krenk, Steen
2002-01-01
Several aspects of damping models for dynamic analysis of structures are investigated. First the causality condition for structural response is used to identify rules for the use of complex-valued frequency dependent material models, illustrated by the shortcomings of the elastic hysteretic model...
Bayesian semiparametric dynamic Nelson-Siegel model
C. Cakmakli
2011-01-01
This paper proposes the Bayesian semiparametric dynamic Nelson-Siegel model where the density of the yield curve factors and thereby the density of the yields are estimated along with other model parameters. This is accomplished by modeling the error distributions of the factors according to a Diric
Probabilistic Modeling in Dynamic Information Retrieval
Sloan, M. C.
2016-01-01
Dynamic modeling is used to design systems that are adaptive to their changing environment and is currently poorly understood in information retrieval systems. Common elements in the information retrieval methodology, such as documents, relevance, users and tasks, are dynamic entities that may evolve over the course of several interactions, which is increasingly captured in search log datasets. Conventional frameworks and models in information retrieval treat these elements as static, or only...
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.
Identification and Modelling of Linear Dynamic Systems
Stanislav Kocur
2006-01-01
Full Text Available System identification and modelling are very important parts of system control theory. System control is only as good as good is created model of system. So this article deals with identification and modelling problems. There are simple classification and evolution of identification methods, and then the modelling problem is described. Rest of paper is devoted to two most known and used models of linear dynamic systems.
Properties of low-dimensional collective variables in the molecular dynamics of biopolymers
Meloni, Roberto; Camilloni, Carlo; Tiana, Guido
2016-11-01
The description of the dynamics of a complex, high-dimensional system in terms of a low-dimensional set of collective variables Y can be fruitful if the low-dimensional representation satisfies a Langevin equation with drift and diffusion coefficients that depend only on Y . We present a computational scheme to evaluate whether a given collective variable provides a faithful low-dimensional representation of the dynamics of a high-dimensional system. The scheme is based on the framework of a finite-difference Langevin equation, similar to that used for molecular-dynamics simulations. This allows one to calculate the drift and diffusion coefficients in any point of the full-dimensional system. The width of the distribution of drift and diffusion coefficients in an ensemble of microscopic points at the same value of Y indicates to what extent the dynamics of Y is described by a simple Langevin equation. Using a simple protein model, we show that collective variables often used to describe biopolymers display a non-negligible width both in the drift and in the diffusion coefficients. We also show that the associated effective force is compatible with the equilibrium free energy calculated from a microscopic sampling, but it results in markedly different dynamical properties.
A stochastic model of human gait dynamics
Ashkenazy, Yosef; M. Hausdorff, Jeffrey; Ch. Ivanov, Plamen; Eugene Stanley, H.
2002-12-01
We present a stochastic model of gait rhythm dynamics, based on transitions between different “neural centers”, that reproduces distinctive statistical properties of normal human walking. By tuning one model parameter, the transition (hopping) range, the model can describe alterations in gait dynamics from childhood to adulthood-including a decrease in the correlation and volatility exponents with maturation. The model also generates time series with multifractal spectra whose broadness depends only on this parameter. Moreover, we find that the volatility exponent increases monotonically as a function of the width of the multifractal spectrum, suggesting the possibility of a change in multifractality with maturation.
Integration of Dynamic Models in Range Operations
Bardina, Jorge; Thirumalainambi, Rajkumar
2004-01-01
This work addresses the various model interactions in real-time to make an efficient internet based decision making tool for Shuttle launch. The decision making tool depends on the launch commit criteria coupled with physical models. Dynamic interaction between a wide variety of simulation applications and techniques, embedded algorithms, and data visualizations are needed to exploit the full potential of modeling and simulation. This paper also discusses in depth details of web based 3-D graphics and applications to range safety. The advantages of this dynamic model integration are secure accessibility and distribution of real time information to other NASA centers.
Long-term dynamics simulation: Modeling requirements
Morched, A.S.; Kar, P.K.; Rogers, G.J.; Morison, G.K. (Ontario Hydro, Toronto, ON (Canada))
1989-12-01
This report details the required performance and modelling capabilities of a computer program intended for the study of the long term dynamics of power systems. Following a general introduction which outlines the need for long term dynamic studies, the modelling requirements for the conduct of such studies is discussed in detail. Particular emphasis is placed on models for system elements not normally modelled in power system stability programs, which will have a significant impact in the long term time frame of minutes to hours following the initiating disturbance. The report concludes with a discussion of the special computational and programming requirements for a long term stability program. 43 refs., 36 figs.
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, 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.
Schmidt, Matthew; Constable, Steve; Ing, Christopher; Roy, Pierre-Nicholas, E-mail: pnroy@uwaterloo.ca [Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada)
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.
Uncertainty and Sensitivity in Surface Dynamics Modeling
Kettner, Albert J.; Syvitski, James P. M.
2016-05-01
Papers for this special issue on 'Uncertainty and Sensitivity in Surface Dynamics Modeling' heralds from papers submitted after the 2014 annual meeting of the Community Surface Dynamics Modeling System or CSDMS. CSDMS facilitates a diverse community of experts (now in 68 countries) that collectively investigate the Earth's surface-the dynamic interface between lithosphere, hydrosphere, cryosphere, and atmosphere, by promoting, developing, supporting and disseminating integrated open source software modules. By organizing more than 1500 researchers, CSDMS has the privilege of identifying community strengths and weaknesses in the practice of software development. We recognize, for example, that progress has been slow on identifying and quantifying uncertainty and sensitivity in numerical modeling of earth's surface dynamics. This special issue is meant to raise awareness for these important subjects and highlight state-of-the-art progress.
The future dynamic world model
Karr, Thomas J.
2014-10-01
Defense and security forces exploit sensor data by means of a model of the world. They use a world model to geolocate sensor data, fuse it with other data, navigate platforms, recognize features and feature changes, etc. However, their need for situational awareness today exceeds the capabilities of their current world model for defense operations, despite the great advances of sensing technology in recent decades. I review emerging technologies that may enable a great improvement in the spatial and spectral coverage, the timeliness, and the functional insight of their world model.
Brand Equity Evolution: a System Dynamics Model
Edson Crescitelli
2009-04-01
Full Text Available One of the greatest challenges in brand management lies in monitoring brand equity over time. This paper aimsto present a simulation model able to represent this evolution. The model was drawn on brand equity concepts developed by Aaker and Joachimsthaler (2000, using the system dynamics methodology. The use ofcomputational dynamic models aims to create new sources of information able to sensitize academics and managers alike to the dynamic implications of their brand management. As a result, an easily implementable model was generated, capable of executing continuous scenario simulations by surveying casual relations among the variables that explain brand equity. Moreover, the existence of a number of system modeling tools will allow extensive application of the concepts used in this study in practical situations, both in professional and educational settings
Dynamic stiffness model of spherical parallel robots
Cammarata, Alessandro; Caliò, Ivo; D`Urso, Domenico; Greco, Annalisa; Lacagnina, Michele; Fichera, Gabriele
2016-12-01
A novel approach to study the elastodynamics of Spherical Parallel Robots is described through an exact dynamic model. Timoshenko arches are used to simulate flexible curved links while the base and mobile platforms are modelled as rigid bodies. Spatial joints are inherently included into the model without Lagrangian multipliers. At first, the equivalent dynamic stiffness matrix of each leg, made up of curved links joined by spatial joints, is derived; then these matrices are assembled to obtain the Global Dynamic Stiffness Matrix of the robot at a given pose. Actuator stiffness is also included into the model to verify its influence on vibrations and modes. The latter are found by applying the Wittrick-Williams algorithm. Finally, numerical simulations and direct comparison to commercial FE results are used to validate the proposed model.
Stirling Engine Dynamic System Modeling
Nakis, Christopher G.
2004-01-01
The Thermo-Mechanical systems branch at the Glenn Research Center focuses a large amount time on Stirling engines. These engines will be used on missions where solar power is inefficient, especially in deep space. I work with Tim Regan and Ed Lewandowski who are currently developing and validating a mathematical model for the Stirling engines. This model incorporates all aspects of the system including, mechanical, electrical and thermodynamic components. Modeling is done through Simplorer, a program capable of running simulations of the model. Once created and then proven to be accurate, a model is used for developing new ideas for engine design. My largest specific project involves varying key parameters in the model and quantifying the results. This can all be done relatively trouble-free with the help of Simplorer. Once the model is complete, Simplorer will do all the necessary calculations. The more complicated part of this project is determining which parameters to vary. Finding key parameters depends on the potential for a value to be independently altered in the design. For example, a change in one dimension may lead to a proportional change to the rest of the model, and no real progress is made. Also, the ability for a changed value to have a substantial impact on the outputs of the system is important. Results will be condensed into graphs and tables with the purpose of better communication and understanding of the data. With the changing of these parameters, a more optimal design can be created without having to purchase or build any models. Also, hours and hours of results can be simulated in minutes. In the long run, using mathematical models can save time and money. Along with this project, I have many other smaller assignments throughout the summer. My main goal is to assist in the processes of model development, validation and testing.
Haptics-based dynamic implicit solid modeling.
Hua, Jing; Qin, Hong
2004-01-01
This paper systematically presents a novel, interactive solid modeling framework, Haptics-based Dynamic Implicit Solid Modeling, which is founded upon volumetric implicit functions and powerful physics-based modeling. In particular, we augment our modeling framework with a haptic mechanism in order to take advantage of additional realism associated with a 3D haptic interface. Our dynamic implicit solids are semi-algebraic sets of volumetric implicit functions and are governed by the principles of dynamics, hence responding to sculpting forces in a natural and predictable manner. In order to directly manipulate existing volumetric data sets as well as point clouds, we develop a hierarchical fitting algorithm to reconstruct and represent discrete data sets using our continuous implicit functions, which permit users to further design and edit those existing 3D models in real-time using a large variety of haptic and geometric toolkits, and visualize their interactive deformation at arbitrary resolution. The additional geometric and physical constraints afford more sophisticated control of the dynamic implicit solids. The versatility of our dynamic implicit modeling enables the user to easily modify both the geometry and the topology of modeled objects, while the inherent physical properties can offer an intuitive haptic interface for direct manipulation with force feedback.
Synaptic dynamics: linear model and adaptation algorithm.
Yousefi, Ali; Dibazar, Alireza A; Berger, Theodore W
2014-08-01
In this research, temporal processing in brain neural circuitries is addressed by a dynamic model of synaptic connections in which the synapse model accounts for both pre- and post-synaptic processes determining its temporal dynamics and strength. Neurons, which are excited by the post-synaptic potentials of hundred of the synapses, build the computational engine capable of processing dynamic neural stimuli. Temporal dynamics in neural models with dynamic synapses will be analyzed, and learning algorithms for synaptic adaptation of neural networks with hundreds of synaptic connections are proposed. The paper starts by introducing a linear approximate model for the temporal dynamics of synaptic transmission. The proposed linear model substantially simplifies the analysis and training of spiking neural networks. Furthermore, it is capable of replicating the synaptic response of the non-linear facilitation-depression model with an accuracy better than 92.5%. In the second part of the paper, a supervised spike-in-spike-out learning rule for synaptic adaptation in dynamic synapse neural networks (DSNN) is proposed. The proposed learning rule is a biologically plausible process, and it is capable of simultaneously adjusting both pre- and post-synaptic components of individual synapses. The last section of the paper starts with presenting the rigorous analysis of the learning algorithm in a system identification task with hundreds of synaptic connections which confirms the learning algorithm's accuracy, repeatability and scalability. The DSNN is utilized to predict the spiking activity of cortical neurons and pattern recognition tasks. The DSNN model is demonstrated to be a generative model capable of producing different cortical neuron spiking patterns and CA1 Pyramidal neurons recordings. A single-layer DSNN classifier on a benchmark pattern recognition task outperforms a 2-Layer Neural Network and GMM classifiers while having fewer numbers of free parameters and
Dynamics modeling and simulation of flexible airships
Li, Yuwen
The resurgence of airships has created a need for dynamics models and simulation capabilities of these lighter-than-air vehicles. The focus of this thesis is a theoretical framework that integrates the flight dynamics, structural dynamics, aerostatics and aerodynamics of flexible airships. The study begins with a dynamics model based on a rigid-body assumption. A comprehensive computation of aerodynamic effects is presented, where the aerodynamic forces and moments are categorized into various terms based on different physical effects. A series of prediction approaches for different aerodynamic effects are unified and applied to airships. The numerical results of aerodynamic derivatives and the simulated responses to control surface deflection inputs are verified by comparing to existing wind-tunnel and flight test data. With the validated aerodynamics and rigid-body modeling, the equations of motion of an elastic airship are derived by the Lagrangian formulation. The airship is modeled as a free-free Euler-Bernoulli beam and the bending deformations are represented by shape functions chosen as the free-free normal modes. In order to capture the coupling between the aerodynamic forces and the structural elasticity, local velocity on the deformed vehicle is used in the computation of aerodynamic forces. Finally, with the inertial, gravity, aerostatic and control forces incorporated, the dynamics model of a flexible airship is represented by a single set of nonlinear ordinary differential equations. The proposed model is implemented as a dynamics simulation program to analyze the dynamics characteristics of the Skyship-500 airship. Simulation results are presented to demonstrate the influence of structural deformation on the aerodynamic forces and the dynamics behavior of the airship. The nonlinear equations of motion are linearized numerically for the purpose of frequency domain analysis and for aeroelastic stability analysis. The results from the latter for the
Smarandache F.
2010-04-01
Full Text Available In this article, we find out some analytical and numerical solutions to the problem of barrier tunneling for cluster deuterium, in particular using Langevin method to solve the time-independent Schroedinger equation.
Chen Yi
2011-01-01
Full Text Available We study a boundary value problem to Langevin equation involving two fractional orders. The Banach fixed point theorem and Krasnoselskii's fixed point theorem are applied to establish the existence results.
Barocchi, Fabrizio; Bafile, Ubaldo; Sampoli, Marco
2012-02-01
We show that an exact solution of the generalized Langevin equation (GLE) for the autocorrelations of a many-body classical system can be given in an exponential functionality (EF) form. As a consequence, the power spectrum of the correlation has a Lorentzian functionality, i.e., is represented by an infinite sum of Lorentzian functions corresponding to the eigenmodes of the considered correlation. By means of the simple derivation of the GLE by M. H. Lee [Phys. Rev. B 26, 2547 (1982)], we also show that, in practical cases of interest to experimental spectroscopies, possible approximations of the EF are related to a reduction of the relevant dynamical variables via a restriction of the dimensions of the orthogonalized space onto which the dynamics of the system is projected.
Model Reduction of Nonlinear Fire Dynamics Models
Lattimer, Alan Martin
2016-01-01
Due to the complexity, multi-scale, and multi-physics nature of the mathematical models for fires, current numerical models require too much computational effort to be useful in design and real-time decision making, especially when dealing with fires over large domains. To reduce the computational time while retaining the complexity of the domain and physics, our research has focused on several reduced-order modeling techniques. Our contributions are improving wildland fire reduced-order mod...
On anomalous diffusion and the fractional generalized Langevin equation for a harmonic oscillator
Figueiredo Camargo, R.; Capelas de Oliveira, E.; Vaz, J.
2009-12-01
The fractional generalized Langevin equation (FGLE) is proposed to discuss the anomalous diffusive behavior of a harmonic oscillator driven by a two-parameter Mittag-Leffler noise. The solution of this FGLE is discussed by means of the Laplace transform methodology and the kernels are presented in terms of the three-parameter Mittag-Leffler functions. Recent results associated with a generalized Langevin equation are recovered.
Heat dissipation and information flow for delayed bistable Langevin systems near coherence resonance
Xiao, Tiejun
2016-11-01
In this paper, stochastic thermodynamics of delayed bistable Langevin systems near coherence resonance is discussed. We calculate the heat dissipation rate and the information flow of a delayed bistable Langevin system under various noise intensities. Both the heat dissipation rate and the information flow are found to be bell-shaped functions of the noise intensity, which implies that coherence resonance manifests itself in the thermodynamic properties.
Rapid sampling of reactive Langevin trajectories via noise-space Monte Carlo.
Dickson, B M
2007-08-14
A noise-space Monte Carlo approach to sampling reactive Langevin trajectories is introduced and compared to a configuration based approach. The noise sampling is shown to overcome the slow relaxation of the configuration based method. Furthermore, the noise sampling is shown to sample multiple pathways with the correct probabilities without any additional work being required formally or algorithmically. The path sampling proceeds without any introduction of fictitious interactions and includes only the parameters appearing in Langevin's equation.
Simulation of stationary Gaussian noise with regard to the Langevin equation with memory effect.
Schmidt, Julian; Meistrenko, Alex; van Hees, Hendrik; Xu, Zhe; Greiner, Carsten
2015-03-01
We present an efficient method for simulating a stationary Gaussian noise with an arbitrary covariance function, and then we study numerically the impact of time-correlated noise on the time evolution of a (1+1)-dimensional generalized Langevin equation by comparing also to analytical results. Finally, we apply our method to the generalized Langevin equation with an external harmonic and double-well potential.
Forecasting with Dynamic Regression Models
Pankratz, Alan
2012-01-01
One of the most widely used tools in statistical forecasting, single equation regression models is examined here. A companion to the author's earlier work, Forecasting with Univariate Box-Jenkins Models: Concepts and Cases, the present text pulls together recent time series ideas and gives special attention to possible intertemporal patterns, distributed lag responses of output to input series and the auto correlation patterns of regression disturbance. It also includes six case studies.
Online Learning of Industrial Manipulators' Dynamics Models
Polydoros, Athanasios
2017-01-01
The robotics industry has introduced light-weight compliant manipulators to increase the safety during human-robot interaction. This characteristic is achieved by replacing the stiff actuators of the traditional robots with compliant ones which creates challenges in the analytical derivation...... of the dynamics models. Those mainly derive from physics-based methods and thus they are based on physical properties which are hard to be calculated. In this thesis, is presented, a novel online machine learning approach which is able to model both inverse and forward dynamics models of industrial manipulators...
A stochastic evolutionary model for survival dynamics
Fenner, Trevor; Loizou, George
2014-01-01
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in different contexts. Here we propose a generative model to capture the essential dynamics of survival analysis, traditionally employed in clinical trials and reliability analysis in engineering. In our model, the only implicit assumption made is that the longer an actor has been in the system, the more likely it is to have failed. We derive a power-law distribution for the process and provide preliminary empirical evidence for the validity of the model from two well-known survival analysis data sets.
Cellular automata modeling of pedestrian's crossing dynamics
张晋; 王慧; 李平
2004-01-01
Cellular automata modeling techniques and the characteristics of mixed traffic flow were used to derive the 2-dimensional model presented here for simulation of pedestrian's crossing dynamics.A conception of "stop point" is introduced to deal with traffic obstacles and resolve conflicts among pedestrians or between pedestrians and the other vehicles on the crosswalk.The model can be easily extended,is very efficient for simulation of pedestrian's crossing dynamics,can be integrated into traffic simulation software,and has been proved feasible by simulation experiments.
Dynamical modelling of coordinated multiple robot systems
Hayati, Samad
1987-01-01
The state of the art in the modeling of the dynamics of coordinated multiple robot manipulators is summarized and various problems related to this subject are discussed. It is recognized that dynamics modeling is a component used in the design of controllers for multiple cooperating robots. As such, the discussion addresses some problems related to the control of multiple robots. The techniques used to date in the modeling of closed kinematic chains are summarized. Various efforts made to date for the control of coordinated multiple manipulators is summarized.
Stochastic transition model for pedestrian dynamics
Schultz, Michael
2012-01-01
The proposed stochastic model for pedestrian dynamics is based on existing approaches using cellular automata, combined with substantial extensions, to compensate the deficiencies resulting of the discrete grid structure. This agent motion model is extended by both a grid-based path planning and mid-range agent interaction component. The stochastic model proves its capabilities for a quantitative reproduction of the characteristic shape of the common fundamental diagram of pedestrian dynamics. Moreover, effects of self-organizing behavior are successfully reproduced. The stochastic cellular automata approach is found to be adequate with respect to uncertainties in human motion patterns, a feature previously held by artificial noise terms alone.
Quantum Dynamics of the HMF Model
Plestid, Ryan; Mahon, Perry; O'Dell, Duncan
2016-01-01
We study the dynamics of the quantized Hamiltonian Mean Field (HMF) model assuming a gas of bosons in the large N limit. We characterize the full set of stationary states, and study the dynamics of the model numerically focussing on competition between classical and quantum effects. We make contact with the existing literature on the HMF model as a classical system, and stress universal features which can be inferred in the semi-classical limit.In particular we show that the characteristic ch...
Towards Disaggregate Dynamic Travel Forecasting Models
Moshe Ben-Akiva; Jon Bottom; Song Gao; Haris N. Koutsopoulos; Yang Wen
2007-01-01
The authors argue that travel forecasting models should be dynamic and disaggregate in their representation of demand, supply, and supply-demand interactions, and propose a framework for such models.The proposed framework consists of disaggregate activity-based representation of travel choices of individual motorists on the demand side integrated with disaggregate dynamic modeling of network performance,through vehicle-based traffic simulation models on the supply side. The demand model generates individual members of the population and assigns to them socioeconomic characteristics. The generated motorists maintain these characteristics when they are loaded on the network by the supply model. In an equilibrium setting, the framework lends itself to a fixed-point formulation to represent and resolve demand-supply interactions. The paper discusses some of the remaining development challenges and presents an example of an existing travel forecasting model system that incorporates many of the proposed elements.
Dynamical effects of overparametrization in nonlinear models
Aguirre, Luis Antonio; Billings, S. A.
1995-01-01
This paper is concemed with dynamical reconstruction for nonlinear systems. The effects of the driving function and of the complexity of a given representation on the bifurcation patter are investigated. It is shown that the use of different driving functions to excite the system may yield models with different bifurcation patterns. The complexity of the reconstructions considered is quantified by the embedding dimension and the number of estimated parameters. In this respect it appears that models which reproduce the original bifurcation behaviour are of limited complexity and that excessively complex models tend to induce ghost bifurcations and spurious dynamical regimes. Moreover, some results suggest that the effects of overparametrization on the global dynamical behaviour of a nonlinear model may be more deleterious than the presence of moderate noise levels. In order to precisely quantify the complexity of the reconstructions, global polynomials are used although the results are believed to apply to a much wider class of representations including neural networks.
Dynamic optimization deterministic and stochastic models
Hinderer, Karl; Stieglitz, Michael
2016-01-01
This book explores discrete-time dynamic optimization and provides a detailed introduction to both deterministic and stochastic models. Covering problems with finite and infinite horizon, as well as Markov renewal programs, Bayesian control models and partially observable processes, the book focuses on the precise modelling of applications in a variety of areas, including operations research, computer science, mathematics, statistics, engineering, economics and finance. Dynamic Optimization is a carefully presented textbook which starts with discrete-time deterministic dynamic optimization problems, providing readers with the tools for sequential decision-making, before proceeding to the more complicated stochastic models. The authors present complete and simple proofs and illustrate the main results with numerous examples and exercises (without solutions). With relevant material covered in four appendices, this book is completely self-contained.
MODELS FOR NETWORK DYNAMICS - A MARKOVIAN FRAMEWORK
LEENDERS, RTAJ
1995-01-01
A question not very often addressed in social network analysis relates to network dynamics and focuses on how networks arise and change. It alludes to the idea that ties do not arise or vanish randomly, but (partly) as a consequence of human behavior and preferences. Statistical models for modeling
Dynamic modeling of the INAPRO aquaponic system
Karimanzira, Divas; Keesman, Karel J.; Kloas, Werner; Baganz, Daniela; Rauschenbach, Thomas
2016-01-01
The use of modeling techniques to analyze aquaponics systems is demonstrated with an example of dynamic modeling for the production of Nile tilapia (Oreochromis niloticus) and tomatoes (Solanum lycopersicon) using the innovative double recirculating aquaponic system ASTAF-PRO. For the management and
Dynamic spatial panels : models, methods, and inferences
Elhorst, J. Paul
This paper provides a survey of the existing literature on the specification and estimation of dynamic spatial panel data models, a collection of models for spatial panels extended to include one or more of the following variables and/or error terms: a dependent variable lagged in time, a dependent
A Discrete Dynamical Model of Signed Partitions
G. Chiaselotti
2013-01-01
Full Text Available We use a discrete dynamical model with three evolution rules in order to analyze the structure of a partially ordered set of signed integer partitions whose main properties are actually not known. This model is related to the study of some extremal combinatorial sum problems.
A system dynamics model for communications networks
Awcock, A. J.; King, T. E. G.
1985-09-01
An abstract model of a communications network in system dynamics terminology is developed as implementation of this model by a FORTRAN program package developed at RSRE is discussed. The result of this work is a high-level simulation package in which the performance of adaptive routing algorithms and other network controls may be assessed for a network of arbitrary topology.
Concept-Oriented Modeling of Dynamic Behavior
Breedveld, P.C.; Borutzky, Wolfgang
2011-01-01
This chapter introduces the reader to the concept-oriented approach to modeling that clearly separates ideal concepts from the physical components of a system when modeling its dynamic behavior for a specific problem context. This is done from a port-based point of view for which the domain-independ
A dynamical model for the Utricularia trap
Llorens, Coraline; Argentina, Médéric; Bouret, Yann; Marmottant, Philippe; Vincent, Olivier
2012-01-01
We propose a model that captures the dynamics of a carnivorous plant, Utricularia inflata. This plant possesses tiny traps for capturing small aquatic animals. Glands pump water out of the trap, yielding a negative pressure difference between the plant and its surroundings. The trap door is set into a meta-stable state and opens quickly as an extra pressure is generated by the displacement of a potential prey. As the door opens, the pressure difference sucks the animal into the trap. We write an ODE model that captures all the physics at play. We show that the dynamics of the plant is quite similar to neuronal dynamics and we analyse the effect of a white noise on the dynamics of the trap. PMID:22859569
Adaptation dynamics of the quasispecies model
Kavita Jain
2008-08-01
We study the adaptation dynamics of an initially maladapted population evolving via the elementary processes of mutation and selection. The evolution occurs on rugged fitness landscapes which are defined on the multi-dimensional genotypic space and have many local peaks separated by low fitness valleys. We mainly focus on the Eigen’s model that describes the deterministic dynamics of an infinite number of self-replicating molecules. In the stationary state, for small mutation rates such a population forms a quasispecies which consists of the fittest genotype and its closely related mutants. The quasispecies dynamics on rugged fitness landscape follow a punctuated (or step-like) pattern in which a population jumps from a low fitness peak to a higher one, stays there for a considerable time before shifting the peak again and eventually reaches the global maximum of the fitness landscape. We calculate exactly several properties of this dynamical process within a simplified version of the quasispecies model.
Adaptation dynamics of the quasispecies model
Jain, Kavita
2009-02-01
We study the adaptation dynamics of an initially maladapted population evolving via the elementary processes of mutation and selection. The evolution occurs on rugged fitness landscapes which are defined on the multi-dimensional genotypic space and have many local peaks separated by low fitness valleys. We mainly focus on the Eigen's model that describes the deterministic dynamics of an infinite number of self-replicating molecules. In the stationary state, for small mutation rates such a population forms a {\\it quasispecies} which consists of the fittest genotype and its closely related mutants. The quasispecies dynamics on rugged fitness landscape follow a punctuated (or step-like) pattern in which a population jumps from a low fitness peak to a higher one, stays there for a considerable time before shifting the peak again and eventually reaches the global maximum of the fitness landscape. We calculate exactly several properties of this dynamical process within a simplified version of the quasispecies model.
Replicator-dynamics models of sexual conflict.
Kimura, Mariko; Ihara, Yasuo
2009-09-07
Evolutionary conflict between the sexes has been studied in various taxa and in various contexts. When the sexes are in conflict over mating rates, natural selection favors both males that induce higher mating rates and females that are more successful at resisting mating attempts. Such sexual conflict may result in an escalating coevolutionary arms race between males and females. In this article, we develop simple replicator-dynamics models of sexual conflict in order to investigate its evolutionary dynamics. Two specific models of the dependence of a female's fitness on her number of matings are considered: in model 1, female fitness decreases linearly with increasing number of matings and in model 2, there is an optimal number of matings that maximizes female fitness. For each of these models, we obtain the conditions for a coevolutionary process to establish costly male and female traits and examine under what circumstances polymorphism is maintained at equilibrium. Then we discuss how assumptions in previous models of sexual conflict are translated to fit to our model framework and compare our results with those of the previous studies. The simplicity of our models allows us to consider sexual conflict in various contexts within a single framework. In addition, we find that our model 2 shows more complicated evolutionary dynamics than model 1. In particular, the population exhibits bistability, where the evolutionary outcome depends on the initial state, only in model 2.
Cosmological model with dynamical curvature
Stichel, Peter C
2016-01-01
We generalize the recently introduced relativistic Lagrangian darkon fluid model (EPJ C (2015) 75:9) by starting with a self-gravitating geodesic fluid whose energy-momentum tensor is dust-like with a nontrivial energy flow. The corresponding covariant propagation and constraint equations are considered in a shear-free nonrelativistic limit whose analytic solutions determine the 1st-order relativistic correction to the spatial curvature. This leads to a cosmological model where the accelerated expansion of the Universe is driven by a time-dependent spatial curvature without the need for introducing any kind of dark energy. We derive the differential equation to be satisfied by the area distance for this model.
Modeling hybrid perovskites by molecular dynamics.
Mattoni, Alessandro; Filippetti, Alessio; Caddeo, Claudia
2017-02-01
The topical review describes the recent progress in the modeling of hybrid perovskites by molecular dynamics simulations. Hybrid perovskites and in particular methylammonium lead halide (MAPI) have a tremendous technological relevance representing the fastest-advancing solar material to date. They also represent the paradigm of an organic-inorganic crystalline material with some conceptual peculiarities: an inorganic semiconductor for what concerns the electronic and absorption properties with a hybrid and solution processable organic-inorganic body. After briefly explaining the basic concepts of ab initio and classical molecular dynamics, the model potential recently developed for hybrid perovskites is described together with its physical motivation as a simple ionic model able to reproduce the main dynamical properties of the material. Advantages and limits of the two strategies (either ab initio or classical) are discussed in comparison with the time and length scales (from pico to microsecond scale) necessary to comprehensively study the relevant properties of hybrid perovskites from molecular reorientations to electrocaloric effects. The state-of-the-art of the molecular dynamics modeling of hybrid perovskites is reviewed by focusing on a selection of showcase applications of methylammonium lead halide: molecular cations disorder; temperature evolution of vibrations; thermally activated defects diffusion; thermal transport. We finally discuss the perspectives in the modeling of hybrid perovskites by molecular dynamics.
Modeling hybrid perovskites by molecular dynamics
Mattoni, Alessandro; Filippetti, Alessio; Caddeo, Claudia
2017-02-01
The topical review describes the recent progress in the modeling of hybrid perovskites by molecular dynamics simulations. Hybrid perovskites and in particular methylammonium lead halide (MAPI) have a tremendous technological relevance representing the fastest-advancing solar material to date. They also represent the paradigm of an organic-inorganic crystalline material with some conceptual peculiarities: an inorganic semiconductor for what concerns the electronic and absorption properties with a hybrid and solution processable organic-inorganic body. After briefly explaining the basic concepts of ab initio and classical molecular dynamics, the model potential recently developed for hybrid perovskites is described together with its physical motivation as a simple ionic model able to reproduce the main dynamical properties of the material. Advantages and limits of the two strategies (either ab initio or classical) are discussed in comparison with the time and length scales (from pico to microsecond scale) necessary to comprehensively study the relevant properties of hybrid perovskites from molecular reorientations to electrocaloric effects. The state-of-the-art of the molecular dynamics modeling of hybrid perovskites is reviewed by focusing on a selection of showcase applications of methylammonium lead halide: molecular cations disorder; temperature evolution of vibrations; thermally activated defects diffusion; thermal transport. We finally discuss the perspectives in the modeling of hybrid perovskites by molecular dynamics.
Dispersive models describing mosquitoes’ population dynamics
Yamashita, W. M. S.; Takahashi, L. T.; Chapiro, G.
2016-08-01
The global incidences of dengue and, more recently, zica virus have increased the interest in studying and understanding the mosquito population dynamics. Understanding this dynamics is important for public health in countries where climatic and environmental conditions are favorable for the propagation of these diseases. This work is based on the study of nonlinear mathematical models dealing with the life cycle of the dengue mosquito using partial differential equations. We investigate the existence of traveling wave solutions using semi-analytical method combining dynamical systems techniques and numerical integration. Obtained solutions are validated through numerical simulations using finite difference schemes.
Induction generator models in dynamic simulation tools
Knudsen, Hans; Akhmatov, Vladislav
1999-01-01
. It is found to be possible to include a transient model in dynamic stability tools and, then, obtain correct results also in dynamic tools. The representation of the rotating system influences on the voltage recovery shape which is an important observation in case of windmills, where a heavy mill is connected......For AC network with large amount of induction generators (windmills) the paper demonstrates a significant discrepancy in the simulated voltage recovery after fault in weak networks when comparing dynamic and transient stability descriptions and the reasons of discrepancies are explained...
Dynamics of the supermarket model
MacPhee, I M; Vachkovskaia, M
2010-01-01
We consider the long term behaviour of a Markov chain \\xi(t) on \\Z^N based on the N station supermarket model. Different routing policies for the supermarket model give different Markov chains. We show that for a general class of local routing policies, "join the least weighted queue" (JLW), the N one-dimensional components \\xi_i(t) can be partitioned into disjoint clusters C_k. Within each cluster C_k the "speed" of each component \\xi_j converges to a constant V_k and under certain conditions \\xi is recurrent in shape on each cluster. To establish these results we have assembled methods from two distinct areas of mathematics, semi-martingale techniques used for showing stability of Markov chains together with the theory of optimal flows in networks. As corollaries to our main result we obtain the stability classification of the supermarket model under any JLW policy and can explicitly compute the C_k and V_k for any instance of the model and specific JLW policy.
Exploring Complex-Langevin Methods for Finite-Density QCD
Sinclair, D K
2015-01-01
QCD at non-zero chemical potential ($\\mu$) for quark number has a complex fermion determinant and thus standard simulation methods for lattice QCD cannot be applied. We therefore simulate this theory using the Complex-Langevin algorithm with Gauge Cooling in addition to adaptive methods, to prevent runaway behaviour. Simulations are performed at zero temperature on a $12^4$ lattice with 2 quarks which are light enough that $m_N/3$ is significantly larger than $m_\\pi/2$. Preliminary results are qualitatively as expected. The quark-number density is close to zero for $\\mu < m_N/3$, beyond which it increases, eventually reaching its saturation value of $3$ for $\\mu$ sufficiently large. The chiral condensate decreases as $\\mu$ is increased approaching zero at saturation, while the plaquette increases towards its quenched value. We have yet to observe the transition to nuclear matter at $\\mu \\approx m_N/3$, presumably because the runs for $\\mu$ between $m_N/3$ and saturation have yet to equilibrate.
On fractional Langevin equation involving two fractional orders
Baghani, Omid
2017-01-01
In numerical analysis, it is frequently needed to examine how far a numerical solution is from the exact one. To investigate this issue quantitatively, we need a tool to measure the difference between them and obviously this task is accomplished by the aid of an appropriate norm on a certain space of functions. For example, Sobolev spaces are indispensable part of theoretical analysis of partial differential equations and boundary integral equations, as well as are necessary for the analysis of some numerical methods for the solving of such equations. But most of articles that appear in this field usually use ‖.‖∞ in the space of C[a, b] which is very restrictive. In this paper, we introduce a new norm that is convenient for the fractional and singular differential equations. Using this norm, the existence and uniqueness of initial value problems for nonlinear Langevin equation with two different fractional orders are studied. In fact, the obtained results could be used for the classical cases. Finally, by two examples we show that we cannot always speak about the existence and uniqueness of solutions just by using the previous methods.
Intermittent rainfall in dynamic multimedia fate modeling.
Hertwich, E G
2001-03-01
It has been shown that steady-state multimedia models (level III fugacity models) lead to a substantial underestimate of air concentrations for chemicals with a low Henry's law constant (H multimedia models are used to estimate the spatial range or inhalation exposure. A dynamic model of pollutant fate is developed for conditions of intermittent rainfall to calculate the time profile of pollutant concentrations in different environmental compartments. The model utilizes a new, mathematically efficient approach to dynamic multimedia fate modeling that is based on the convolution of solutions to the initial conditions problem. For the first time, this approach is applied to intermittent conditions. The investigation indicates that the time-averaged pollutant concentrations under intermittent rainfall can be approximated by the appropriately weighted average of steady-state concentrations under conditions with and without rainfall.
Argument for justification of the complex Langevin method and the condition for correct convergence
Nagata, Keitaro; Nishimura, Jun; Shimasaki, Shinji
2016-12-01
The complex Langevin method is a promising approach to the complex-action problem based on a fictitious time evolution of complexified dynamical variables under the influence of a Gaussian noise. Although it is known to have a restricted range of applicability, the use of gauge cooling made it applicable to various interesting cases including finite density QCD in certain parameter regions. In this paper we revisit the argument for justification of the method. In particular, we point out a subtlety in the use of time-evolved observables, which play a crucial role in the previous argument. This requires that the probability of the drift term should fall off exponentially or faster at large magnitude. We argue that this is actually a necessary and sufficient condition for the method to be justified. Using two simple examples, we show that our condition tells us clearly whether the results obtained by the method are trustable or not. We also discuss a new possibility for the gauge cooling, which can reduce the magnitude of the drift term directly.
Dynamic exponents for potts model cluster algorithms
Coddington, Paul D.; Baillie, Clive F.
We have studied the Swendsen-Wang and Wolff cluster update algorithms for the Ising model in 2, 3 and 4 dimensions. The data indicate simple relations between the specific heat and the Wolff autocorrelations, and between the magnetization and the Swendsen-Wang autocorrelations. This implies that the dynamic critical exponents are related to the static exponents of the Ising model. We also investigate the possibility of similar relationships for the Q-state Potts model.
The dynamic model of enterprise revenue management
Mitsel, A. A.; Kataev, M. Yu; Kozlov, S. V.; Korepanov, K. V.
2017-01-01
The article presents the dynamic model of enterprise revenue management. This model is based on the quadratic criterion and linear control law. The model is founded on multiple regression that links revenues with the financial performance of the enterprise. As a result, optimal management is obtained so as to provide the given enterprise revenue, namely, the values of financial indicators that ensure the planned profit of the organization are acquired.
Feature Extraction for Structural Dynamics Model Validation
Farrar, Charles [Los Alamos National Laboratory; Nishio, Mayuko [Yokohama University; Hemez, Francois [Los Alamos National Laboratory; Stull, Chris [Los Alamos National Laboratory; Park, Gyuhae [Chonnam Univesity; Cornwell, Phil [Rose-Hulman Institute of Technology; Figueiredo, Eloi [Universidade Lusófona; Luscher, D. J. [Los Alamos National Laboratory; Worden, Keith [University of Sheffield
2016-01-13
As structural dynamics becomes increasingly non-modal, stochastic and nonlinear, finite element model-updating technology must adopt the broader notions of model validation and uncertainty quantification. For example, particular re-sampling procedures must be implemented to propagate uncertainty through a forward calculation, and non-modal features must be defined to analyze nonlinear data sets. The latter topic is the focus of this report, but first, some more general comments regarding the concept of model validation will be discussed.
A Dynamic Model for Energy Structure Analysis
无
2006-01-01
Energy structure is a complicated system concerning economic development, natural resources, technological innovation, ecological balance, social progress and many other elements. It is not easy to explain clearly the developmental mechanism of an energy system and the mutual relations between the energy system and its related environments by the traditional methods. It is necessary to develop a suitable dynamic model, which can reflect the dynamic characteristics and the mutual relations of the energy system and its related environments. In this paper, the historical development of China's energy structure was analyzed. A new quantitative analysis model was developed based on system dynamics principles through analysis of energy resources, and the production and consumption of energy in China and comparison with the world. Finally, this model was used to predict China's future energy structures under different conditions.
Dynamic Model Identification for Industrial Robots
Ngoc Dung Vuong
2009-12-01
Full Text Available In this paper, a systematic procedure for identifying the dynamics of industrialrobots is presented. Since joint friction can be highly nonlinearwith time varyingcharacteristics in the low speed region,a simple and yet effective scheme has been used toidentify the boundary velocity that separates this “dynamic” friction region from its staticregion. The robot’s dynamic model is then identified in this static region, where thenonlinnear friction model is reduced to the linear-in-parameter form. To overcome thedrawbacks of the least squares estimator, which does not take in any constraints, anonlinear optimization problem is formulated to guarantee the physical feasibility of theidentified parameters. The proposed procedure has been demonstrated on the first fourlinks of the Mitsubishi PA10 manipulator, an improved dynamic model was obtained andthe the effectiveness of the proposed identification procedure is demonstrated.
Dynamic Model for Life History of Scyphozoa.
Congbo Xie
Full Text Available A two-state life history model governed by ODEs is formulated to elucidate the population dynamics of jellyfish and to illuminate the triggering mechanism of its blooms. The polyp-medusa model admits trichotomous global dynamic scenarios: extinction, polyps survival only, and both survival. The population dynamics sensitively depend on several biotic and abiotic limiting factors such as substrate, temperature, and predation. The combination of temperature increase, substrate expansion, and predator diminishment acts synergistically to create a habitat that is more favorable for jellyfishes. Reducing artificial marine constructions, aiding predator populations, and directly controlling the jellyfish population would help to manage the jellyfish blooms. The theoretical analyses and numerical experiments yield several insights into the nature underlying the model and shed some new light on the general control strategy for jellyfish.
Modeling Of Ballistic Missile Dynamics
Salih Mahmoud Attiya
2013-05-01
Full Text Available Aerodynamic modeling of ballistic missile in pitch plane is performed and the open-loop transfer function related to the jet deflector angle as input and pitch rate, normal acceleration as output has been derived with certain acceptable assumptions. For typical values of ballistic missile parameters such as mass, velocity, altitude, moment of inertia, thrust, moment and lift coefficient show that, the step time response and frequency response of the missile is unstable. The steady state gain, damping ratio and undraped natural frequency depend on the missile parameters. To stabilize the missile a lead compensator must be added to the forward loop.
Dynamic modeling of solar dynamic components and systems
Hochstein, John I.; Korakianitis, T.
1992-09-01
The purpose of this grant was to support NASA in modeling efforts to predict the transient dynamic and thermodynamic response of the space station solar dynamic power generation system. In order to meet the initial schedule requirement of providing results in time to support installation of the system as part of the initial phase of space station, early efforts were executed with alacrity and often in parallel. Initially, methods to predict the transient response of a Rankine as well as a Brayton cycle were developed. Review of preliminary design concepts led NASA to select a regenerative gas-turbine cycle using a helium-xenon mixture as the working fluid and, from that point forward, the modeling effort focused exclusively on that system. Although initial project planning called for a three year period of performance, revised NASA schedules moved system installation to later and later phases of station deployment. Eventually, NASA selected to halt development of the solar dynamic power generation system for space station and to reduce support for this project to two-thirds of the original level.
Dynamical properties of the Rabi model
Hu, Binglu; Zhou, Huili; Chen, Shujie; Xianlong, Gao; Wang, Kelin
2017-02-01
We study the dynamical properties of the quantum Rabi model using a systematic expansion method. Based on the observation that the parity symmetry of the Rabi model is kept during evolution of the states, we decompose the initial state and the time-dependent one into positive and negative parity parts expanded by superposition of the coherent states. The evolutions of the corresponding positive and the negative parities are obtained, in which the expansion coefficients in the dynamical equations are known from the derived recurrence relation.
Dynamical Model of Weak Pion Production Reactions
Sato, T; Lee, T S H
2003-01-01
The dynamical model of pion electroproduction has been extended to investigate the weak pion production reactions. The predicted cross sections of neutrino-induced pion production reactions are in good agreement with the existing data. We show that the renormalized(dressed) axial N-$\\Delta$ form factor contains large dynamical pion cloud effects and this renormalization effects are crucial in getting agreement with the data. We conclude that the N-$\\Delta$ transitions predicted by the constituent quark model are consistent with the existing neutrino induced pion production data in the $\\Delta$ region.
Research on nonlinear stochastic dynamical price model
Li Jiaorui [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China); School of Statistics, Xi' an University of Finance and Economics, Xi' an 710061 (China)], E-mail: jiaoruili@mail.nwpu.edu.cn; Xu Wei; Xie Wenxian; Ren Zhengzheng [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China)
2008-09-15
In consideration of many uncertain factors existing in economic system, nonlinear stochastic dynamical price model which is subjected to Gaussian white noise excitation is proposed based on deterministic model. One-dimensional averaged Ito stochastic differential equation for the model is derived by using the stochastic averaging method, and applied to investigate the stability of the trivial solution and the first-passage failure of the stochastic price model. The stochastic price model and the methods presented in this paper are verified by numerical studies.
Dynamic model for the popularity of websites
Lee, Chang-Yong; Kim, Seungwhan
2002-03-01
In this paper, we have studied a dynamic model to explain the observed characteristics of websites in the World Wide Web. The dynamic model consists of the self-growth term for each website and the external force term acting on the website. With simulations of the model, we can explain most of the important characteristics of websites. These characteristics include a power-law distribution of the number of visitors to websites, fluctuation in the fractional growth of individual websites, and the relationship between the age and the popularity of the websites. We also investigated a few variants of the model and showed that the ingredients included in the model adequately explain the behavior of the websites.
Modelling environmental dynamics. Advances in goematic solutions
Paegelow, Martin [Toulouse-2 Univ., 31 (France). GEODE UMR 5602 CNRS; Camacho Olmedo, Maria Teresa (eds.) [Granada Univ (Spain). Dpto. de Analisis Geografico Regional y Geografia Fisica
2008-07-01
Modelling environmental dynamics is critical to understanding and predicting the evolution of the environment in response to the large number of influences including urbanisation, climate change and deforestation. Simulation and modelling provide support for decision making in environmental management. The first chapter introduces terminology and provides an overview of methodological modelling approaches which may be applied to environmental and complex dynamics. Based on this introduction this book illustrates various models applied to a large variety of themes: deforestation in tropical regions, fire risk, natural reforestation in European mountains, agriculture, biodiversity, urbanism, climate change and land management for decision support, etc. These case studies, provided by a large international spectrum of researchers and presented in a uniform structure, focus particularly on methods and model validation so that this book is not only aimed at researchers and graduates but also at professionals. (orig.)
Modeling emotional dynamics : currency versus field.
Sallach, D .L.; Decision and Information Sciences; Univ. of Chicago
2008-08-01
Randall Collins has introduced a simplified model of emotional dynamics in which emotional energy, heightened and focused by interaction rituals, serves as a common denominator for social exchange: a generic form of currency, except that it is active in a far broader range of social transactions. While the scope of this theory is attractive, the specifics of the model remain unconvincing. After a critical assessment of the currency theory of emotion, a field model of emotion is introduced that adds expressiveness by locating emotional valence within its cognitive context, thereby creating an integrated orientation field. The result is a model which claims less in the way of motivational specificity, but is more satisfactory in modeling the dynamic interaction between cognitive and emotional orientations at both individual and social levels.
Modeling dynamic functional connectivity using a wishart mixture model
Nielsen, Søren Føns Vind; Madsen, Kristoffer Hougaard; Schmidt, Mikkel Nørgaard
2017-01-01
.e. the window length. In this work we use the Wishart Mixture Model (WMM) as a probabilistic model for dFC based on variational inference. The framework admits arbitrary window lengths and number of dynamic components and includes the static one-component model as a special case. We exploit that the WMM...
Modeling the dynamics of dissent
Lee, Eun; Lee, Sang Hoon
2016-01-01
We investigate opinion formation against authority in an authoritarian society composed of agents with different levels of authority. We explore a (symbolically) "right" opinion, held by lower-ranking, obedient, less authoritative people, spreading in an environment of a "wrong" opinion held by authoritative leaders. The mental picture would be that of a corrupt society where the ruled people revolts against authority, but it could be argued to hold in more general situations. In our model, agents can change their opinion depending on the relative authority to their neighbors and their own confidence level. In addition, with a certain probability, agents can override the authority to take the right opinion of a neighbor. Based on analytic derivation and numerical simulations, we observe that both the network structure and heterogeneity in authority, and their correlation significantly affect the possibility of the right opinion to spread in the population. In particular, the right opinion is suppressed when t...
Mélykúti, Bence; Burrage, Kevin; Zygalakis, Konstantinos C
2010-04-28
The Chemical Langevin Equation (CLE), which is a stochastic differential equation driven by a multidimensional Wiener process, acts as a bridge between the discrete stochastic simulation algorithm and the deterministic reaction rate equation when simulating (bio)chemical kinetics. The CLE model is valid in the regime where molecular populations are abundant enough to assume their concentrations change continuously, but stochastic fluctuations still play a major role. The contribution of this work is that we observe and explore that the CLE is not a single equation, but a parametric family of equations, all of which give the same finite-dimensional distribution of the variables. On the theoretical side, we prove that as many Wiener processes are sufficient to formulate the CLE as there are independent variables in the equation, which is just the rank of the stoichiometric matrix. On the practical side, we show that in the case where there are m(1) pairs of reversible reactions and m(2) irreversible reactions there is another, simple formulation of the CLE with only m(1) + m(2) Wiener processes, whereas the standard approach uses 2(m(1) + m(2)). We demonstrate that there are considerable computational savings when using this latter formulation. Such transformations of the CLE do not cause a loss of accuracy and are therefore distinct from model reduction techniques. We illustrate our findings by considering alternative formulations of the CLE for a human ether a-go-go related gene ion channel model and the Goldbeter-Koshland switch.
Induction generator models in dynamic simulation tools
Knudsen, Hans; Akhmatov, Vladislav
1999-01-01
For AC network with large amount of induction generators (windmills) the paper demonstrates a significant discrepancy in the simulated voltage recovery after fault in weak networks when comparing dynamic and transient stability descriptions and the reasons of discrepancies are explained. It is fo......For AC network with large amount of induction generators (windmills) the paper demonstrates a significant discrepancy in the simulated voltage recovery after fault in weak networks when comparing dynamic and transient stability descriptions and the reasons of discrepancies are explained....... It is found to be possible to include a transient model in dynamic stability tools and, then, obtain correct results also in dynamic tools. The representation of the rotating system influences on the voltage recovery shape which is an important observation in case of windmills, where a heavy mill is connected...
Jump Markov models and transition state theory: the quasi-stationary distribution approach.
Di Gesù, Giacomo; Lelièvre, Tony; Le Peutrec, Dorian; Nectoux, Boris
2016-12-22
We are interested in the connection between a metastable continuous state space Markov process (satisfying e.g. the Langevin or overdamped Langevin equation) and a jump Markov process in a discrete state space. More precisely, we use the notion of quasi-stationary distribution within a metastable state for the continuous state space Markov process to parametrize the exit event from the state. This approach is useful to analyze and justify methods which use the jump Markov process underlying a metastable dynamics as a support to efficiently sample the state-to-state dynamics (accelerated dynamics techniques). Moreover, it is possible by this approach to quantify the error on the exit event when the parametrization of the jump Markov model is based on the Eyring-Kramers formula. This therefore provides a mathematical framework to justify the use of transition state theory and the Eyring-Kramers formula to build kinetic Monte Carlo or Markov state models.
Jump Markov models and transition state theory: the Quasi-Stationary Distribution approach
Di Gesù, Giacomo; Peutrec, Dorian Le; Nectoux, Boris
2016-01-01
We are interested in the connection between a metastable continuous state space Markov process (satisfying e.g. the Langevin or overdamped Langevin equation) and a jump Markov process in a discrete state space. More precisely, we use the notion of quasi-stationary distribution within a metastable state for the continuous state space Markov process to parametrize the exit event from the state. This approach is useful to analyze and justify methods which use the jump Markov process underlying a metastable dynamics as a support to efficiently sample the state-to-state dynamics (accelerated dynamics techniques). Moreover, it is possible by this approach to quantify the error on the exit event when the parametrization of the jump Markov model is based on the Eyring-Kramers formula. This therefore provides a mathematical framework to justify the use of transition state theory and the Eyring-Kramers formula to build kinetic Monte Carlo or Markov state models.