Global Existence of Classical Solutions for A Class Nonlinear Parabolic Equations

In this article we prove the existence of classical solutions for a class nonlinear parabolic equations. We propose new integral representation of the classical solutions. As an application we give continuous dependence and differentiability of the solutions with respect to the initial data and parameters

Chemo-dynamical evolution of Globular Cluster Systems

We studied the relation between the ratio of rotational velocity to velocity dispersion and the metallicity (/\sigma_{v}-metallicity relation) of globular cluster systems (GCS) of disk galaxies by comparing the relation predicted from simple chemo-dynamical models for the formation and evolution of disk galaxies with the observed kinematical and chemical properties of their GCSs. We conclude that proto disk galaxies underwent a slow initial collapse that was followed by a rapid contraction and derive that the ratio of the initial collapse time scale to the active star formation time scale is \sim 6 for our Galaxy and \sim 15 for M31. The fundamental formation process of disk galaxies was simulated based on simple chemo-dynamical models assuming the conservation of their angular momentum. We suggest that there is a typical universal pattern in the /\sigma_{v}-metallicity relation of the GCS of disk galaxies. This picture is supported by the observed properties of GCSs in the Galaxy and in M31. This relation would deviate from the universal pattern, however, if large-scale merging events took major role in chemo-dynamical evolution of galaxies and will reflect the epoch of such merging events. We discuss the properties of the GCS of M81 and suggest the presence of past major merging event.Comment: 25 pages, 8 figures, Accepted for publication in the Astrophysical Journa

Chiral persistent currents and magnetic susceptibilities in the parafermion quantum Hall states in the second Landau level with Aharonov-Bohm flux

Using the effective conformal field theory for the quantum Hall edge states we propose a compact and convenient scheme for the computation of the periods, amplitudes and temperature behavior of the chiral persistent currents and the magnetic susceptibilities in the mesoscopic disk version of the Z_k parafermion quantum Hall states in the second Landau level. Our numerical calculations show that the persistent currents are periodic in the Aharonov-Bohm flux with period exactly one flux quantum and have a diamagnetic nature. In the high-temperature regime their amplitudes decay exponentially with increasing the temperature and the corresponding exponents are universal characteristics of non-Fermi liquids. Our theoretical results for these exponents are in perfect agreement with those extracted from the numerical data and demonstrate that there is in general a non-trivial contribution coming from the neutral sector. We emphasize the crucial role of the non-holomorphic factors, first proposed by Cappelli and Zemba in the context of the conformal field theory partition functions for the quantum Hall states, which ensure the invariance of the annulus partition function under the Laughlin spectral flow.Comment: 14 pages, RevTeX4, 7 figures (eps

A Position-Space Renormalization-Group Approach for Driven Diffusive Systems Applied to the Asymmetric Exclusion Model

This paper introduces a position-space renormalization-group approach for nonequilibrium systems and applies the method to a driven stochastic one-dimensional gas with open boundaries. The dynamics are characterized by three parameters: the probability $\alpha$ that a particle will flow into the chain to the leftmost site, the probability $\beta$ that a particle will flow out from the rightmost site, and the probability $p$ that a particle will jump to the right if the site to the right is empty. The renormalization-group procedure is conducted within the space of these transition probabilities, which are relevant to the system's dynamics. The method yields a critical point at $\alpha_c=\beta_c=1/2$,in agreement with the exact values, and the critical exponent $\nu=2.71$, as compared with the exact value $\nu=2.00$.Comment: 14 pages, 4 figure

Voting and Catalytic Processes with Inhomogeneities

We consider the dynamics of the voter model and of the monomer-monomer catalytic process in the presence of many ``competing'' inhomogeneities and show, through exact calculations and numerical simulations, that their presence results in a nontrivial fluctuating steady state whose properties are studied and turn out to specifically depend on the dimensionality of the system, the strength of the inhomogeneities and their separating distances. In fact, in arbitrary dimensions, we obtain an exact (yet formal) expression of the order parameters (magnetization and concentration of adsorbed particles) in the presence of an arbitrary number $n$ of inhomogeneities (``zealots'' in the voter language) and formal similarities with {\it suitable electrostatic systems} are pointed out. In the nontrivial cases $n=1, 2$, we explicitly compute the static and long-time properties of the order parameters and therefore capture the generic features of the systems. When $n>2$, the problems are studied through numerical simulations. In one spatial dimension, we also compute the expressions of the stationary order parameters in the completely disordered case, where $n$ is arbitrary large. Particular attention is paid to the spatial dependence of the stationary order parameters and formal connections with electrostatics.Comment: 17 pages, 6 figures, revtex4 2-column format. Original title ("Are Voting and Catalytic Processes Electrostatic Problems ?") changed upon editorial request. Minor typos corrected. Published in Physical Review

The 2D/3D Best-Fit Problem

In computer systems, the best-fit problem can be described as a search for the best transformation matrix to transform input mea- sured points from their coordinate system into a CAD model coordinate system using a criteria function for optimization. For example, if the criterion is Mini- mum Sum of Deviations, we search for a transformation matrix M that minimizes the sum of all distances from an matrix-transformed measure points to a CAD model