Related papers: Comment on ``Statistical Mechanics of a Nonlinear …
The hypothesis that phase transitions originate from some topological change of the critical level hypersurface of the potential energy receives direct evident support by our study of the Bishop--Peyrard model of DNA thermal denaturation.
The modeling of realistic magnetic materials requires the inclusion of defects. Based on the pseudospectral Landau-Lifshitz description of magnetisation dynamics, we propose a statistical model that takes into account defects, specifically…
The melting curves of short heterogeneous DNA chains in solution are calculated on the basis of statistical thermodynamics and compared to experiments. The computation of the partition function is based on the Peyrard-Bishop hamiltonian,…
A study of the micromechanical unzipping of DNA in the framework of the Peyrard-Bishop-Dauxois model is presented. We introduce a Monte Carlo technique that allows accurate determination of the dependence of the unzipping forces on…
Long length-scale structural deformations of DNA play a central role in many biological processes including gene expression. The elastic rod model, which uses a continuum approximation, has emerged as a viable tool to model deformations of…
THis work is a survey of a few nonlinear PDE based models in image restoring.
This article is written in memory of Pierre Hohenberg with appreciation for his deep commitment to the basic principles of theoretical physics. I summarize recent developments in the theory of dislocation-enabled deformation of crystalline…
Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial…
A unifying theory of the denaturation transition of DNA, driven by temperature T or induced by an external mechanical torque Gamma is presented. Our model couples the hydrogen-bond opening and the untwisting of the helicoidal molecular…
Most image deblurring methods assume an over-simplistic image formation model and as a result are sensitive to more realistic image degradations. We propose a novel variational framework, that explicitly handles pixel saturation, noise,…
We report the complete statistical treatment of a system of particles interacting via Newtonian forces in continuous boundary-driven flow, far from equilibrium. By numerically time-stepping the force-balance equations of a model fluid we…
The statistical mechanics of DNA denaturation under fixed linking number is qualitatively different from that of the unconstrained DNA. Quantitatively different melting scenarios are reached from two alternative assumptions, namely, that…
A nonlinear inequality is formulated in the paper. An estimate of the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can be…
The thermodynamical properties of heterogeneous DNA sequences are computed by path integral techniques applied to a nonlinear model Hamiltonian. The base pairs relative displacements are interpreted as time dependent paths whose amplitudes…
In this paper, we investigate DNA denaturation through Statistical Mechanics and show that exceptional polynomials lead to DNA mutation. We consider a DNA model with two chains connected by Morse potential representing the H bonds, and then…
We give a bird's-eye view of the plastic deformation of crystals aimed at the statistical physics community, and a broad introduction into the statistical theories of forced rigid systems aimed at the plasticity community. Memory effects in…
We introduce a coarse-grained model of DNA with bases modeled as rigid-body ellipsoids to capture their anisotropic stereochemistry. Interaction potentials are all physicochemical and generated from all-atom simulation/parameterization with…
The damping effect to the DNA bubble is investigated within the Peyrard-Bishop model. In the continuum limit, the dynamics of the bubble of DNA is described by the damped nonlinear Schrodinger equation and studied by means of variational…
A quadratic inequality is formulated in the paper. An estimate on the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations.
The aim of this paper is to establish a nonlinear variational approach to the reconstruction of moving density images from indirect dynamic measurements. Our approach is to model the dynamics as a hyperelastic deformation of an initial…