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The statistical mechanics of a linear non-interacting polymer chain with a large number of monomers is considered with fixed angular momentum. The radius of gyration for a linear polymer is derived exactly by functional integration. This…
We investigate polymers pulled away from an interacting surface, where the force is applied to the untethered endpoint and at an angle $\theta$ to the surface. We use the canonical self-avoiding walk model of polymers and obtain the phase…
In a variety of biological situations, swimming cells have to move through complex fluids. Similarly, mucociliary clearance involves the transport of polymeric fluids by beating cilia. Here, we consider the extent to which complex fluids…
The research is important for a molecular theory of liquid and has a wide interest as an example solving the problem when dynamic parameters of systems can be indirectly connected with their equilibrium properties. In frameworks of the…
We study the phenomenon of lack of reversibility in molecular dynamics algorithms for the case of Wilson's lattice QCD. We demonstrate that the classical equations of motion that are employed in these algorithms are chaotic in nature. The…
We present simulation data for the motion of a polymer chain through a regular lattice of impenetrable obstacles (Evans-Edwards model). Chain lengths range from N=20 to N=640, and time up to $10^{7}$ Monte Carlo steps. For $N \geq 160$ we…
We investigate the anomalous dynamics of unentangled polymer melts. The proposed equation of motion formally relates the anomalous center-of-mass diffusion, as observed in computer simulations and experiments, to the nature of the effective…
We consider a large class of bullet models that contains, in particular, the colliding bullet model with creations and a new loop model. For this large class of bullet models, we give sufficient conditions on their parameter to be…
Nematic elastomers are programmable soft materials that display large, reversible and predictable deformation under an external stimulus such as a change in temperature or light. While much of the work in the field has focused on actuation…
Some recent results on the rotational dynamics of polymers are reviewed and extended. We focus here on the relaxation of a polymer, either flexible or semiflexible, initially wrapped around a rigid rod. We also study the steady polymer…
Given a demonstration of a complex manipulation task, such as pouring liquid from one container to another, we seek to generate a motion plan for a new task instance involving objects with different geometries. This is nontrivial since we…
Plasticisers (PLs) are small additives commonly incorporated into polymer composites to enhance processability and improve mechanical properties. Their effectiveness depends heavily on their miscibility within the polymer melt, yet…
We recently demonstrated that standard fixed-time lattice random-walk models cannot be modified to properly represent biased diffusion processes in more than two dimensions. The origin of this fundamental limitation appears to be the fact…
Monte Carlo simulations of proteins are hindered by the system's high density which often makes local moves ineffective. Here we devise and test a set of long range moves that work well even when all sites of a lattice simulation are…
In this paper we create a model of particle motion on a three-dimensional lattice using discrete random walk with small steps. We rigorously construct a probability space of the particle trajectories. Unlike deterministic approach in…
A polymer repelled by unfavorable interactions with a uniform flat surface may still be pinned to attractive edges and corners. This is demonstrated by considering adsorption of a two-dimensional ideal polymer to an attractive corner of a…
This paper proposes an adaptive lattice-based motion planning solution to address the problem of generating feasible trajectories for systems, represented by a linearly parameterizable non-linear model operating within a cluttered…
We consider an inverse problem for the compressible Euler's equations in polytropic fluid. We show that by taking active measurements near a particle trajectory one can determine the background flow in a set where pressure waves can…
We study the dynamics of an Airy wavepacket moving in a one-dimensional lattice potential. In contrast to the usual case of propagation in a continuum, for which such a wavepacket experiences a uniform acceleration, the lattice bounds its…
This is erratum of the paper [Phys. Rev. Lett. {\bf 84}, 4260 (2000)]