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Showing 1 to 20 of 43 for “"Langevin equation"”.
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A study of electrochemical transport and diffuse charge dynamics using a Langevin equation
… models based on the Poisson-Nernst-Planck equations and atomic simulations using molecular dynamics algorithms. Neither of them is easy to use or conducive to electrokinetic transport modeling in strong confinement or over long time scales. This work introduces a new approach based on a …
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Nonadiabatic electron transfer in the condensed phase, via semiclassical and Langevin equation approach
… the spin-coherent representation. The resulting equation of motion is a classical-like ordinary differential equation subject to a two-ended boundary condition. The boundary value problem is solved using the "near real trajectory" algorithm. This method is applied to three scattering problems to …
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A study of electrochemical transport and diffuse charge dynamics in nanoscale devices using a Langevin equation
… models based on the Poisson-Nernst-Planck equations and atomic simulations using molecular dynamics algorithms. Neither of them is easy to use or conducive to electrokinetic transport modeling in strong confinement or over long time scales. This work introduces a new approach based on a …
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Bödeker's Effective Theory: From Langevin Dynamics to Dyson-Schwinger Equations
… modes to leading logarithmic order by means of a Langevin equation. This effective theory has been used for lattice calculations so far. In this work we provide a complementary, more analytic approach based on Dyson-Schwinger equations. Using methods known from stochastic quantisation, we recast …
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A Brownian Dynamics Analysis of Ion Movement in Membrane Channels
… fundamental stochastic theory is based on the Langevin equation. A simulation technique based on this equation is presented. The technique called Brownian dynamics is then used to study ion transport through membrane channels. Four cases are considered: (1) no ion-ion interaction, no channel …
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Fundamental limitations between noise and back-action in bio-molecular networks
… model the system as a set of non-linear chemical Langevin equations and quantify the trade-off for two different approximations of this non-linear model. First we consider a system linearized about a fixed point and quantify the trade-off using transfer functions. Next we use a linear …
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Effects of an External Field and Dissipation on Decoherence
… using the solution of the initial value quantum Langevin equation. One of the key results obtained is that ”decoherence without dissipation” does not occur in the case of a free harmonic oscillator, in contrast to the case of a free particle.
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Modeling of the dynamics of autonomous catalytic nanomotors using the method of regularized stokeslets
… modeled as the stochastic solution to a Langevin Equation satisfying the fluctuation-dissipation theorem of statistical mechanics. A comparison of our numerically simulated results with the experimental observations is also presented here.
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Slow dynamics in supercooled liquids : matrix formalism, mode coupling and glass transition
… (MCT). Following the real-time generalized Langevin equation in Newtonian liquids, the dynamic Gaussian factorization scheme leads to mode-coupling (MC) closures. As an alternative approach to the projection operator technique, the matrix formalism based on the complete basis set is …
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Free products of operator spaces and free Markov processes
… as solutions to free stochastic differential equations driven by free Levy processes. A special and rather interesting kind of free Markov processes, free Ornstein-Uhlenbeck processes, is studied in some details. It is shown that a probability measure on R is free self-decomposable if and only …
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CRITICAL DYNAMICS OF LIQUID CRYSTAL ABOVE THE ISOTROPIC - NEMATIC PHASE TRANSITION
… We first derive the complete quadratic dynamic equations for molecular orientation and translational velocity, based on Mori's theory of the generalized Langevin equation. Our problem differs from the well studied problem of binary fluids in (1)the parameter is not conservative and (2)there are …
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Quasi-condensation in low-dimensional Bose gases
… on the basis of their excitation sprectum, equation of state, density fluctuations and related correlation functions. High-temperature expansions of the corresponding integrals are derived analytically for the numerical evaluation of the self-consistent integral equations. Apart from that, …
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Discrete 3D Model of Molecular Diffusion Through the Nuclear Pore Complex
… molecules. The basis of the model is a Langevin equation that was customized to the environment of the central channel of a NPC. The model incorporated not only the Brownian motion of the molecules, but also the geometry of the channel, the diffusion coefficient for molecules in the …
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Stochastic modelling of gene regulation with microRNAs
… the magnitude of noise in different systems. The Langevin Equation and Tau-Leaping methods (for which Matlab codes are developed here) are shown to be excellent approximations to the Gillespie Algorithm.
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Processing random signals in neuroscience, electrical engineering and operations research
… addressed by different versions of a generalized Langevin equation. Our mathematical models utilize stochastic differential equations (SDEs) and stochastic optimal control, both of which were born in the soil of electrical engineering. Central to this dissertation is a brain-physics based model of …
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Random-vortex-particle methods applied to broadband fan interaction noise
… and combine it with the linearised Euler equations to predict broadband fan interaction noise. In modern turbofan designs broadband fan noise is a dominant source of aircraft noise, the most efficient source being the interaction between upstream turbulence and the stator vanes. The …
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Channel Modelling of Blood Capillary-based Molecular Communication
… Fick's diffusion, this work involves microscopic Langevin diffusion to describe the propagation process with a frequency domain method being proposed to calculate the information-theoretical performance channel capacity. Secondly, a much more realistic blood capillary model with blood flow drift …
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Fourier-accelerated Langevin simulation of the frustrated XY model and simulation of the spinless and spin one-half Hubbard model
… two-dimensional XY model was simulated using the Langevin equation with Fourier transform acceleration. The speedup due to Fourier acceleration was measured for frustration one-half at the transition temperature. For comparison, the unfrustrated XY model was also studied. For the frustrated case, …
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The role of quenched disorder, interfaces and confinement on the glassy dynamics of colloidal suspensions, thermal liquids and films
… The Elastically Collective Nonlinear Langevin Equation (ECNLE) theory for activated relaxation in the bulk serves as the starting point to predict dynamical arrest, the shear modulus and alpha relaxation time. First, I construct a new theoretical framework for the dynamics of bulk …
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Diffusion, sub-diffusion, and escape: A study of over-damped Brownian motion
… rough potentials is studied, and a modified Langevin equation, valid on long time scales, is derived. This result is extended to higher dimensions and used to derive an expression for the effective diffusion coefficient. Comparison to that obtained from a lattice hopping model facilitates the …
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