arXiv subjects

Vishal Mehra

Publications and source records attributed to Vishal Mehra.

11 recordsLinked to original sources

arXiv2003

Structure optimization in an off-lattice protein model

We study an off-lattice protein toy model with two species of monomers interacting through modified Lennard-Jones interactions. Low energy configurations are optimized using the pruned-enriched-Rosenbluth method (PERM), hitherto employed to native state searches only for off lattice models. For 2 dimensions we found states with lower energy than previously proposed putative ground states, for all chain lengths $\ge 13$. This indicates that PERM has the potential to produce native states also for more realistic protein models. For $d=3$, where no published ground states exist, we present some putative lowest energy states for future comparison with other methods.

cond-mat.stat-mech↗

arXiv2003

Growth Algorithms for Lattice Heteropolymers at Low Temperatures

Two improved versions of the pruned-enriched-Rosenbluth method (PERM) are proposed and tested on simple models of lattice heteropolymers. Both are found to outperform not only the previous version of PERM, but also all other stochastic algorithms which have been employed on this problem, except for the core directed chain growth method (CG) of Beutler & Dill. In nearly all test cases they are faster in finding low-energy states, and in many cases they found new lowest energy states missed in previous papers. The CG method is superior to our method in some cases, but less efficient in others. On the other hand, the CG method uses heavily heuristics based on presumptions about the hydrophobic core and does not give thermodynamic properties, while the present method is a fully blind general purpose algorithm giving correct Boltzmann-Gibbs weights, and can be applied in principle to any stochastic sampling problem.

cond-mat.stat-mech↗

arXiv2003

A Growth-based Optimization Algorithm for Lattice Heteropolymers

An improved version of the pruned-enriched-Rosenbluth method (PERM) is proposed and tested on finding lowest energy states in simple models of lattice heteropolymers. It is found to outperform not only the previous version of PERM, but also all other fully blind general purpose stochastic algorithms which have been employed on this problem. In many cases it found new lowest energy states missed in previous papers. Limitations are discussed.

cond-mat.stat-mech↗

arXiv2001

On the trapping reaction with mobile traps

We present Monte Carlo results for the two-species trapping reaction $A+B \to B$ with diffusing $A$ and $B$ on lattices in one, two and three dimension. We use a novel algorithm which permits to simulate survival probabilities of $A$ partic les down to $<10^{-30}$ with high accuracy. The results for the survival probability agree much better with the exact asymptotic predictions of Bramson and Lebowitz (Phys. Rev. Lett. {\bf 61}, 2397 (1988)) than with the heuristics of Kang and Redner (J. Phys. A {\bf 17}, L451 (1984)). But there are very large deviations from either which show that even these simulations are far from asymptotia. This is supported by the rms. displacement of $A$ particles which clearly show that the asymptotic regime has not been reached, at least for $d=2$ and $d=3$.

cond-mat.stat-mech↗

arXiv2001

Transition to Localization of Biased Walkers in a Randomly Absorbing Enviroment

We study biased random walkers on lattices with randomly dispersed static traps in one, two and three dimensions. As the external bias is increased from zero the system undergoes a phase transition, most clearly manifested in the asymptotic drift velocity of survivors which is zero below a critical bias. This transition is second-order in one dimension but of first order in higher dimensions. The model can be mapped to a stretched polymer with attractive interaction between monomers, and this phase transition would then describe sudden unfolding of the polymer when the stretching force exceeds a critical value. We also present precise simulations of the zero bias case where we show unambiguously that the transition between the Rosenstock and Donsker-Varadhan regimes is first order in dimension $\ge 2$.

cond-mat.stat-mech↗

arXiv2001

Perfectly Translating Lattices on a Cylinder

We perform molecular dynamics simulations on an interacting electron gas confined to a cylindrical surface and subject to a radial magnetic field and the field of the positive background. In order to study the system at lowest energy states that still carry a current, initial configurations are obtained by a special quenching procedure. We observe the formation of a steady state in which the entire electron-lattice cycles with a common uniform velocity. Certain runs show an intermediate instability leading to lattice rearrangements. A Hall resistance can be defined and depends linearly on the magnetic field with an anomalous coefficient reflecting the manybody contributions peculiar to two dimensions.

cond-mat.stat-mech↗

arXiv1999

Long Range Magnetic Order and the Darwin Lagrangian

We simulate a finite system of $N$ confined electrons with inclusion of the Darwin magnetic interaction in two- and three-dimensions. The lowest energy states are located using the steepest descent quenching adapted for velocity dependent potentials. Below a critical density the ground state is a static Wigner lattice. For supercritical density the ground state has a non-zero kinetic energy. The critical density decreases with $N$ for exponential confinement but not for harmonic confinement. The lowest energy state also depends on the confinement and dimension: an antiferromagnetic cluster forms for harmonic confinement in two dimensions.

cond-mat.stat-mech↗

arXiv1997

Strange Nonchaotic Attractors in the Quasiperiodically forced Logistic Map

Different mechanisms for the creation of strange non-chaotic dynamics in the quasiperiodically forced logistic map are studied. These routes to strange nonchaos are characterised through the behavior of the largest nontrivial Lyapunov exponent, as well as through the characteristic distributions of finite time Lyapunov exponents. Strange nonchaotic attractors can be created at a saddle-node bifurcation when the dynamics shows Type-I intermittency; this intermittent transition, which is studied in detail, is characterised through scaling exponents. Band-merging crises through which dynamics remains nonchaotic are also studied, and correspondence is made with analogous behavior in the unforced logistic map. Robustness of these phenomena with respect to additive noise is investigated.

chao-dyn↗

arXiv1997

Intermittency Route to Strange Nonchaotic Attractors

Strange nonchaotic attractors (SNA) arise in quasiperiodically driven systems in the neighborhood of a saddle node bifurcation whereby a strange attractor is replaced by a periodic (torus) attractor. This transition is accompanied by Type-I intermittency. The largest nontrivial Lyapunov exponent $Λ$ is a good order-parameter for this route from chaos to SNA to periodic motion: the signature is distinctive and unlike that for other routes to SNA. In particular, $Λ$ changes sharply at the SNA to torus transition, as does the distribution of finite-time or N--step Lyapunov exponents, P(Λ_N).

chao-dyn↗

arXiv1997

Curvature fluctuations and Lyapunov exponent at Melting

We calculate the maximal Lyapunov exponent in constant-energy molecular dynamics simulations at the melting transition for finite clusters of 6 to 13 particles (model rare-gas and metallic systems) as well as for bulk rare-gas solid. For clusters, the Lyapunov exponent generally varies linearly with the total energy, but the slope changes sharply at the melting transition. In the bulk system, melting corresponds to a jump in the Lyapunov exponent, and this corresponds to a singularity in the variance of the curvature of the potential energy surface. In these systems there are two mechanisms of chaos -- local instability and parametric instability. We calculate the contribution of the parametric instability towards the chaoticity of these systems using a recently proposed formalism. The contribution of parametric instability is a continuous function of energy in small clusters but not in the bulk where the melting corresponds to a decrease in this quantity. This implies that the melting in small clusters does not lead to enhanced local instability.

chao-dyn↗

arXiv1995

Maximal Lyapunov exponent at Crises

We study the variation of Lyapunov exponents of simple dynamical systems near attractor-widening and attractor-merging crises. The largest Lyapunov exponent has universal behaviour, showing abrupt variation as a function of the control parameter as the system passes through the crisis point, either in the value itself, in the case of the attractor-widening crisis, or in the slope, for attractor merging crises. The distribution of local Lyapunov exponents is very different for the two cases: the fluctuations remain constant through a merging crisis, but there is a dramatic increase in the fluctuations at a widening crisis.

chao-dyn↗