From generalized Langevin equations to Brownian dynamics and embedded Brownian dynamics

Ma, Lina; Li, Xiantao; Li, Chun

doi:10.1063/1.4962419

Cited by 10 publications

(12 citation statements)

References 45 publications

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“…We present the idealized equilibrium derivation to connect with the widely read textbook literature (Jackson 1999) and to provide enough detail so others may learn to extend the derivation to the nonequilibrium case relevant to devices and other systems with long-range current flow, driven by (for example) spatially inhomogeneous boundary conditions, with (for example) different potentials at different locations on their boundaries. Temporal averaging is another approach, under intensive study by Chun Liu and associates (Ma, Li et al 2016a, Ma, Li et al 2016b).…”

Section: Macroscopic Charge Density and Gauss' Law In Isolated Ideali...mentioning

confidence: 99%

Dynamics of Current, Charge and Mass

Eisenberg

Oriols

Ferry

2017

Computational and Mathematical Biophysics

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Electricity plays a special role in our lives and life. Equations of electron dynamics are nearly exact and apply from nuclear particles to stars. These Maxwell equations include a special term the displacement current (of vacuum). Displacement current allows electrical signals to propagate through space. Displacement current guarantees that current is exactly conserved from inside atoms to between stars, as long as current is defined as Maxwell did, as the entire source of the curl of the magnetic field. We show how the Bohm formulation of quantum mechanics allows easy definition of current. We show how conservation of current can be derived without mention of the polarization or dielectric properties of matter. Matter does not behave the way physicists of the 1800's thought it does with a single dielectric constant, a real positive number independent of everything. Charge moves in enormously complicated ways that cannot be described in that way, when studied on time scales important today for electronic technology and molecular biology. Life occurs in ionic solutions in which charge moves in response to forces not mentioned or described in the Maxwell equations, like convection and diffusion. Classical derivations of conservation of current involve classical treatments of dielectrics and polarization in nearly every textbook. Because real dielectrics do not behave in a classical way, classical derivations of conservation of current are often distrusted or even ignored. We show that current is conserved exactly in any material no matter how complex the dielectric, polarization or conduction currents are. We believe models, simulations, and computations should conserve current on all scales, as accurately as possible, because physics conserves current that way. We believe models will be much more successful if they conserve current at every level of resolution, the way physics does.Comment: Version 4 slight reformattin

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Section: Macroscopic Charge Density and Gauss' Law In Isolated Ideali...mentioning

confidence: 99%

Dynamics of Current, Charge and Mass

Eisenberg

Oriols

Ferry

2017

Computational and Mathematical Biophysics

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“…The chaotic nature of the Newtonian dynamics, which in the long time drives the system to a stochastic equilibrium state, is recovered in the first-order in time dynamics through the use of an additive noise term, carefully chosen to guarantee that the system converges to the correct thermodynamical state in the long-time limit. While this approach has been widely used in studying the dynamics of soft matter systems as well as in biomolecular simulations [44,45,46], it has, to our knowledge, never been employed for the simulation of crystalline materials. In this section, we report the main equations used in the model.…”

Section: Modeling Approachmentioning

confidence: 99%

Atomistic simulation of martensite microstructural evolution during temperature driven β→α transition in pure titanium

Baruffi

Finel

Bouar

et al. 2022

Computational Materials Science

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HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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“…Ferry [84,85] provides a fine modern treatment of a classical literature [231] that includes [232][233][234][235]. This approach was extended to ions in channels by Schuss and collaborators [236] using the theory of stochastic processes (e.g., an adaption of renewal theory) to deal with the complicated shot noise produced when several types of ions move through channels, each with a different current voltage relation that is not independent. Each varies with concentration of every type of ion.…”

Section: Molecular Dynamicsmentioning

confidence: 99%

“…What is needed to provide atomic resolution of particle motion (in my opinion) is a molecular dynamics that exploits the special properties of total current, perhaps using the averaging-in-time methods introduced by Ma and Liu [235,236] that yield the Poisson Nernst Planck model as an approximation [237]. Or perhaps by introducing a quasi-particle, a conducton that automatically satisfies equality of total current in a series system.…”

Section: Updating the Maxwell Equationsmentioning

confidence: 99%

Thermostatics vs. Electrodynamics

Eisenberg¹

2020

Preprint

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Thermodynamics has been the foundation of many models of biological and technological systems. But thermodynamics is static and is misnamed. A more suitable name is thermostatics. Thermostatics does not include time as a variable and so has no velocity, flow or friction. Indeed, as usually formulated, thermostatics does not include boundary conditions. Devices require boundary conditions to define their input and output. They usually involve flow and friction. Thermostatics is an unsuitable foundation for understanding technological and biological devices. A time dependent generalization of thermostatics that might be called thermal dynamics is being developed by Chun Liu and collaborators to avoid these limitations. Electrodynamics is not restricted like thermostatics, but in its classical formulation involves drastic assumptions about polarization and an over-approximated dielectric constant. Once the Maxwell equations are rewritten without a dielectric constant, they are universal and exact. Conservation of total current, including displacement current, is a restatement of the Maxwell equations that leads to dramatic simplifications in the understanding of one dimensional systems, particularly those without branches, like the ion channel proteins of biological membranes and the two terminal devices of electronic systems. The Brownian fluctuations of concentrations and fluxes of ions become the spatially independent total current, because the displacement current acts as an unavoidable low pass filter, a consequence of the Maxwell equations for any material polarization. Electrodynamics and thermal dynamics together form a suitable foundation for models of technological and biological systems.

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From generalized Langevin equations to Brownian dynamics and embedded Brownian dynamics

Cited by 10 publications

References 45 publications

Dynamics of Current, Charge and Mass

Dynamics of Current, Charge and Mass

Atomistic simulation of martensite microstructural evolution during temperature driven β→α transition in pure titanium

Thermostatics vs. Electrodynamics

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