1,644 research outputs found
Dynamics of Current, Charge and Mass
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
Stochastic Dynamics of Bionanosystems: Multiscale Analysis and Specialized Ensembles
An approach for simulating bionanosystems, such as viruses and ribosomes, is
presented. This calibration-free approach is based on an all-atom description
for bionanosystems, a universal interatomic force field, and a multiscale
perspective. The supramillion-atom nature of these bionanosystems prohibits the
use of a direct molecular dynamics approach for phenomena like viral structural
transitions or self-assembly that develop over milliseconds or longer. A key
element of these multiscale systems is the cross-talk between, and consequent
strong coupling of, processes over many scales in space and time. We elucidate
the role of interscale cross-talk and overcome bionanosystem simulation
difficulties with automated construction of order parameters (OPs) describing
supra-nanometer scale structural features, construction of OP dependent
ensembles describing the statistical properties of atomistic variables that
ultimately contribute to the entropies driving the dynamics of the OPs, and the
derivation of a rigorous equation for the stochastic dynamics of the OPs. Since
the atomic scale features of the system are treated statistically, several
ensembles are constructed that reflect various experimental conditions. The
theory provides a basis for a practical, quantitative bionanosystem modeling
approach that preserves the cross-talk between the atomic and nanoscale
features. A method for integrating information from nanotechnical experimental
data in the derivation of equations of stochastic OP dynamics is also
introduced.Comment: 24 page
Charge migration mechanisms in the DNA at finite temperature revisited; from quasi-ballistic to subdiffusive transport
Various charge migration mechanisms in the DNA are studied within the
framework of the Peyrard-Bishop-Holstein model which has been widely used to
address charge dynamics in this macromolecule. To analyze these mechanisms we
consider characteristic size and time scales of the fluctuations of the
electronic and vibrational subsystems. It is shown, in particular, that due to
substantial differences in these timescales polaron formation is unlikely
within a broad range of temperatures. We demonstrate that at low temperatures
electronic transport can be quasi-ballistic. For high temperatures, we propose
an alternative to polaronic charge migration mechanism: the
fluctuation-assisted one, in which the electron dynamics is governed by
relatively slow fluctuations of the vibrational subsystem. We argue also that
the discussed methods and mechanisms can be relevant for other organic
macromolecular systems, such as conjugated polymers and molecular aggregates
Partial differential equations for self-organization in cellular and developmental biology
Understanding the mechanisms governing and regulating the emergence of structure and heterogeneity within cellular systems, such as the developing embryo, represents a multiscale challenge typifying current integrative biology research, namely, explaining the macroscale behaviour of a system from microscale dynamics. This review will focus upon modelling how cell-based dynamics orchestrate the emergence of higher level structure. After surveying representative biological examples and the models used to describe them, we will assess how developments at the scale of molecular biology have impacted on current theoretical frameworks, and the new modelling opportunities that are emerging as a result. We shall restrict our survey of mathematical approaches to partial differential equations and the tools required for their analysis. We will discuss the gap between the modelling abstraction and biological reality, the challenges this presents and highlight some open problems in the field
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