105 research outputs found
Hopf-Turing mixed mode and pattern selection in reaction diffusion systems
The amplitude equation of Gierer-Mainhardt model has been actually derived
near the boundary abuot which Turing and Hopf modes exist. In a parameter
region where Hopf-Turing mixed mode solution is stable, a chaotic state that
generally results from interaction between mixed modes, is observed. This
chaotic region follows a strong selection of a spatially periodic order
followed by a local, resonant, very large frequency temporal oscillation. A
spatio-temporal forcing, responsible for what obseved, has been identified.Comment: 7 pages and 9 figure
Harmonic oscillator states as oscillating localized structures near Hopf-Turing instability boundary
A set of coupled complex Ginzburg-landau type amplitude equations which
operates near a Hopf-Turing instability boundary is analytically investigated
to show localized oscillatory patterns. The spatial structure of those patterns
are the same as quantum mechanical harmonic oscillator stationary states and
can have even or odd symmetry depending on the order of the state. It has been
seen that the underlying Turing state plays a major role in the selection of
the order of such solutions.Comment: 6 page
Generalized fluctuation-dissipation relation and statistics for the equilibrium of a system with conformation dependent damping
Liouville's theorem, based on the Hamiltonian flow (micro-canonical ensemble)
for a many particle system, indicates that the (stationary) equilibrium
probability distribution is a function of the Hamiltonian. A canonical ensemble
corresponds to a micro-canonical one at thermodynamic limit. On the contrary,
the dynamics of a single Brownian particle (BP) being explicitly
non-Hamiltonian with a force and damping term in it and at the other extreme to
thermodynamic limit admits the Maxwell-distribution (MD) for its velocity and
Boltmann-distribution (BD) for positions (when in a potential). This is due to
the fluctuation-dissipation relation (FDR), as was first introduced by
Einstein, which forces the Maxwell distribution to the Brownian particles. For
a structureless BP, that, this theory works is an experimentally verified fact
over a century now. Considering a structured Brownian particle we will show
that the BD and MD fails to ensure equilibrium. We will derive a generalized
FDR on the basis of the demand of zero current on inhomogeneous space. Our FDR
and resulting generalized equilibrium distributions recover the standard ones
at appropriate limits.Comment: 11 pages, no figures, a discussion on It\^o vs Stratonovich
conventions in the context of present theory is added in the en
A theory for one dimensional asynchronous chemical wave
We present a theory for experimentally observed phenomenon of one dimensional
asynchronous waves. The general principle of coexistence of linear and
nonlinear solutions of a dynamical system is underlying the present theoretical
work. The result has been proposed analytically and numerical simulations are
produced in support of the analytical results.Comment: 9 pages, five figure
Equilibrium stochastic dynamics of a Brownian particle in inhomogeneous space: derivation of an alternative model
An alternative equilibrium stochastic dynamics for a Brownian particle in
inhomogeneous space is derived. Such a dynamics can model the motion of a
complex molecule in its conformation space when in equilibrium with a uniform
heat bath. The derivation is done by a simple generalization of the formulation
due to Zwanzig for a Brownian particle in homogeneous heat bath. We show that
if the system couples to different number of bath degrees of freedom at
different conformations then the alternative model is derived. We discuss
results of an experiment by Faucheux and Libchaber which probably has indicated
possible limitation of the Boltzmann distribution as equilibrium distribution
of a Brownian particle in inhomogeneous space and propose experimental
verification of the present theory using similar methods.Comment: This revised version more clearly describes the cases of vertical and
horizontal diffusivity as could be seen in an experiment as has been
previously done by Faucheux and Libchaber. This version also includes
proposal of a new experiment involving complex molecule
Galaxy rotation curves from external influence on Schwarzschild geometry
We present a modified Schwarzschild metric to introduce a weak breakdown of
asymptotic flatness. The kinematics of the metric captures a wide range of
galaxy rotation curves. We show baryonic Tully-Fisher relation on the basis of
this modified Schwarzschild metric. On the basis of the kinematics of this
modified metric we also show some connections between the size and ordinary
matter content of the observable universe and the rotation curves of spiral
galaxies.Comment: 7 pages and 1 figur
The lower bound of barrier-energy in spin glasses: a calculation of the exponent on hierarchical lattice
We argue that the lower bound to the barrier energy to flip an up/down spin
domain embedded in a down/up spin environment for Ising spin glass is
independent of the size of the system. The argument shows the existence of at
least one dynamical way through which it is possible to bypass local maxima in
the phase space. For an arbitrary case where one flips any cluster of spin of
size , we have numerically calculated a lower bound to the exponent
characterizing the barrier one has to overcome. In this case
corresponding to the lower bound calculated on hierarchical lattice comes out
to be equal to the exponent characterizing the domain wall energy in
ground state.Comment: 4 pages, 2 figure
Model of amplitude modulations induced by phase slips in one-dimensional superconductors
We propose a linear model for the dynamics of amplitudes associated with
formation of phase slip centers in a one-dimensional superconductor. The model
is derived taking into account the fact that, during the formation of phase
slip centers the wave number of the superconducting phase remains practically
constant. The model captures various forms of amplitude modulations associated
with PSCs in closed analytic forms.Comment: 11 pages, 2 figur
Directional transport induced by elasticity and volume exclusion
We investigate an exactly solvable model for directional transport in 1D. The
structured system, which has strong elastic interactions in its parts,
explicitly demonstrates the role of volume exclusion in producing directional
transport. We capture the complementary role of the elasticity and volume
exclusion as the basic ingredient for showing up of broken microscopic symmetry
at the scale of macroscopic motions. We compare the analytic results with the
numerical simulation.Comment: 11 pages 4 figure
Equilibrium of a Brownian particle with coordinate dependent diffusivity and damping: Generalized Boltzmann distribution
Fick's law for coordinate dependent diffusivity is derived. Corresponding
diffusion current in the presence of coordinate dependent diffusivity is
consistent with the form as given by Kramers-Moyal expansion. We have obtained
the equilibrium solution of the corresponding Smoluchowski equation. The
equilibrium distribution is a generalization of the Boltzmann distribution.
This generalized Boltzmann distribution involves an effective potential which
is a function of coordinate dependent diffusivity. We discuss various
implications of the existence of this generalized Boltzmann distribution for
equilibrium of systems with coordinate dependent diffusivity and damping.Comment: 11 pages, 1 figur
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