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 $l$, we have numerically calculated a lower bound to the exponent $\psi$ characterizing the barrier one has to overcome. In this case $\psi$ corresponding to the lower bound calculated on hierarchical lattice comes out to be equal to $\theta$ 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