1,656 research outputs found
New derivation for the equations of motion for particles in electromagnetism
We present equations of motion for charged particles using balanced
equations, and without introducing explicitly divergent quantities. This
derivation contains as particular cases some well known equations of motion, as
the Lorentz-Dirac equations. An study of our main equations in terms of order
of the interaction with the external field conduces us to the Landau-Lifshitz
equations. We find that the analysis in second order show a special behavior.
We give an explicit presentation up to third order of our main equations, and
expressions for the calculation of general orders.Comment: 11 pages, 2 figures. Minor changes. Closer to published versio
Monte Carlo simulation for statistical mechanics model of ion channel cooperativity in cell membranes
Voltage-gated ion channels are key molecules for the generation and
propagation of electrical signals in excitable cell membranes. The
voltage-dependent switching of these channels between conducting and
nonconducting states is a major factor in controlling the transmembrane
voltage. In this study, a statistical mechanics model of these molecules has
been discussed on the basis of a two-dimensional spin model. A new Hamiltonian
and a new Monte Carlo simulation algorithm are introduced to simulate such a
model. It was shown that the results well match the experimental data obtained
from batrachotoxin-modified sodium channels in the squid giant axon using the
cut-open axon technique.Comment: Paper has been revise
Cosmology and the Korteweg-de Vries Equation
The Korteweg-de Vries (KdV) equation is a non-linear wave equation that has
played a fundamental role in diverse branches of mathematical and theoretical
physics. In the present paper, we consider its significance to cosmology. It is
found that the KdV equation arises in a number of important scenarios,
including inflationary cosmology, the cyclic universe, loop quantum cosmology
and braneworld models. Analogies can be drawn between cosmic dynamics and the
propagation of the solitonic wave solution to the equation, whereby quantities
such as the speed and amplitude profile of the wave can be identified with
cosmological parameters such as the spectral index of the density perturbation
spectrum and the energy density of the universe. The unique mathematical
properties of the Schwarzian derivative operator are important to the analysis.
A connection with dark solitons in Bose-Einstein condensates is briefly
discussed.Comment: 7 pages; References adde
On a certain class of semigroups of operators
We define an interesting class of semigroups of operators in Banach spaces,
namely, the randomly generated semigroups. This class contains as a remarkable
subclass a special type of quantum dynamical semigroups introduced by
Kossakowski in the early 1970s. Each randomly generated semigroup is
associated, in a natural way, with a pair formed by a representation or an
antirepresentation of a locally compact group in a Banach space and by a
convolution semigroup of probability measures on this group. Examples of
randomly generated semigroups having important applications in physics are
briefly illustrated.Comment: 11 page
Biased Brownian motion in extreme corrugated tubes
Biased Brownian motion of point-size particles in a three-dimensional tube
with smoothly varying cross-section is investigated. In the fashion of our
recent work [Martens et al., PRE 83,051135] we employ an asymptotic analysis to
the stationary probability density in a geometric parameter of the tube
geometry. We demonstrate that the leading order term is equivalent to the
Fick-Jacobs approximation. Expression for the higher order corrections to the
probability density are derived. Using this expansion orders we obtain that in
the diffusion dominated regime the average particle current equals the
zeroth-order Fick-Jacobs result corrected by a factor including the corrugation
of the tube geometry. In particular we demonstrate that this estimate is more
accurate for extreme corrugated geometries compared to the common applied
method using the spatially dependent diffusion coefficient D(x,f). The analytic
findings are corroborated with the finite element calculation of a
sinusoidal-shaped tube.Comment: 10 pages, 4 figure
Effective zero-thickness model for a conductive membrane driven by an electric field
The behavior of a conductive membrane in a static (DC) electric field is
investigated theoretically. An effective zero-thickness model is constructed
based on a Robin-type boundary condition for the electric potential at the
membrane, originally developed for electrochemical systems. Within such a
framework, corrections to the elastic moduli of the membrane are obtained,
which arise from charge accumulation in the Debye layers due to capacitive
effects and electric currents through the membrane and can lead to an
undulation instability of the membrane. The fluid flow surrounding the membrane
is also calculated, which clarifies issues regarding these flows sharing many
similarities with flows produced by induced charge electro-osmosis (ICEO).
Non-equilibrium steady states of the membrane and of the fluid can be
effectively described by this method. It is both simpler, due to the zero
thickness approximation which is widely used in the literature on fluid
membranes, and more general than previous approaches. The predictions of this
model are compared to recent experiments on supported membranes in an electric
field.Comment: 14 pages, 5 figure
On a complex differential Riccati equation
We consider a nonlinear partial differential equation for complex-valued
functions which is related to the two-dimensional stationary Schrodinger
equation and enjoys many properties similar to those of the ordinary
differential Riccati equation as, e.g., the famous Euler theorems, the Picard
theorem and others. Besides these generalizations of the classical
"one-dimensional" results we discuss new features of the considered equation
like, e.g., an analogue of the Cauchy integral theorem
Movable algebraic singularities of second-order ordinary differential equations
Any nonlinear equation of the form y''=\sum_{n=0}^N a_n(z)y^n has a
(generally branched) solution with leading order behaviour proportional to
(z-z_0)^{-2/(N-1)} about a point z_0, where the coefficients a_n are analytic
at z_0 and a_N(z_0)\ne 0. We consider the subclass of equations for which each
possible leading order term of this form corresponds to a one-parameter family
of solutions represented near z_0 by a Laurent series in fractional powers of
z-z_0. For this class of equations we show that the only movable singularities
that can be reached by analytic continuation along finite-length curves are of
the algebraic type just described. This work generalizes previous results of S.
Shimomura. The only other possible kind of movable singularity that might occur
is an accumulation point of algebraic singularities that can be reached by
analytic continuation along infinitely long paths ending at a finite point in
the complex plane. This behaviour cannot occur for constant coefficient
equations in the class considered. However, an example of R. A. Smith shows
that such singularities do occur in solutions of a simple autonomous
second-order differential equation outside the class we consider here
On the Plants Leaves Boundary, "Jupe \`a Godets" and Conformal Embeddings
The stable profile of the boundary of a plant's leaf fluctuating in the
direction transversal to the leaf's surface is described in the framework of a
model called a "surface \`a godets". It is shown that the information on the
profile is encoded in the Jacobian of a conformal mapping (the coefficient of
deformation) corresponding to an isometric embedding of a uniform Cayley tree
into the 3D Euclidean space. The geometric characteristics of the leaf's
boundary (like the perimeter and the height) are calculated. In addition a
symbolic language allowing to investigate statistical properties of a "surface
\`a godets" with annealed random defects of curvature of density is
developed. It is found that at the surface exhibits a phase transition
with critical exponent from the exponentially growing to the flat
structure.Comment: 17 pages (revtex), 8 eps-figures, to appear in Journal of Physics
Linear superposition in nonlinear wave dynamics
We study nonlinear dispersive wave systems described by hyperbolic PDE's in
R^{d} and difference equations on the lattice Z^{d}. The systems involve two
small parameters: one is the ratio of the slow and the fast time scales, and
another one is the ratio of the small and the large space scales. We show that
a wide class of such systems, including nonlinear Schrodinger and Maxwell
equations, Fermi-Pasta-Ulam model and many other not completely integrable
systems, satisfy a superposition principle. The principle essentially states
that if a nonlinear evolution of a wave starts initially as a sum of generic
wavepackets (defined as almost monochromatic waves), then this wave with a high
accuracy remains a sum of separate wavepacket waves undergoing independent
nonlinear evolution. The time intervals for which the evolution is considered
are long enough to observe fully developed nonlinear phenomena for involved
wavepackets. In particular, our approach provides a simple justification for
numerically observed effect of almost non-interaction of solitons passing
through each other without any recourse to the complete integrability. Our
analysis does not rely on any ansatz or common asymptotic expansions with
respect to the two small parameters but it uses rather explicit and
constructive representation for solutions as functions of the initial data in
the form of functional analytic series.Comment: New introduction written, style changed, references added and typos
correcte
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