Related papers: Continuum limit and preconditioned Langevin sampli…
We prove, under mild conditions, that the stochastic gradient Langevin dynamics converges to a limiting law as time tends to infinity, even in the case where the driving data sequence is dependent.
We numerically solve the underdamped Langevin equation to obtain the trajectories of a particle in a sinusoidal potential driven by a temporally sinusoidal force in a medium with coefficient of friction periodic in space as the potential…
Polymers are an effective test-bed for studying topological constraints in condensed matter due to a wide array of synthetically-available chain topologies. When linear and ring polymers are blended together, emergent rheological properties…
Pathwise predictability of continuous time processes is studied in deterministic setting. We discuss uniform prediction in some weak sense with respect to certain classes of inputs. More precisely, we study possibility of approximation of…
A common problem to all applications of linear finite dynamical systems is analyzing the dynamics without enumerating every possible state transition. Of particular interest is the long term dynamical behaviour. In this paper, we study the…
Considering the standard abelian sandpile model in one dimension, we construct an infinite volume Markov process corresponding to its thermodynamic (infinite volume) limit. The main difficulty we overcome is the strong non-locality of the…
We present computer simulations of a simple bead-spring model for polymer melts with intramolecular barriers. By systematically tuning the strength of the barriers, we investigate their role on the glass transition. Dynamic observables are…
We discuss the generalization of a classical problem involving an $N$-step ideal polymer adsorption at a sticky boundary (potential well of depth $U$). It is known that as $N$ approaches infinity, the path undergoes a 2nd-order localization…
We describe methods for proving upper and lower bounds on infinite-time averages in deterministic dynamical systems and on stationary expectations in stochastic systems. The dynamics and the quantities to be bounded are assumed to be…
We present molecular dynamics simulations on the structural relaxation of a simple bead-spring model for polymer blends. The introduction of a different monomer size induces a large time scale separation for the dynamics of the two…
This paper introduces a method for predicting the likely behaviors of continuous nonlinear systems in equilibrium in which the input values can vary. The method uses a parameterized equation model and a lower bound on the input joint…
The dynamics of a freely jointed chain in the continuous limit is described by a field theory which closely resembles the nonlinear sigma model. The generating functional $\Psi[J]$ of this field theory contains nonholonomic constraints,…
We construct and study a family random continuum polymer measures $\mathbf{M}_{r}$ corresponding to limiting partition function laws recently derived in a weak-coupling regime of polymer models on hierarchical graphs with marginally…
We study the adsorption-desorption of fluid molecules on a solid substrate by introducing a schematic model in which the adsorption/desorption transition probabilities are given by irreversible kinetic constraints with a tunable violation…
We derived quantum trajectories for a system interacting with the environment prepared in a continuous mode single photon state as the limit of discrete filtering model with an environment defined as series of independent qubits prepared…
We study a (1+1)-dimensional directed polymer in a random environment on the integer lattice with log-gamma distributed weights. Among directed polymers, this model is special in the same way as the last-passage percolation model with…
Quantum circuit dynamics with local projective measurements can realize a rich spectrum of entangled states of quantum matter. Motivated by the physics of the Kitaev quantum spin liquid [1], we study quantum circuit dynamics in…
The article considers systems of interacting particles on networks with adaptively coupled dynamics. Such processes appear frequently in natural processes and applications. Relying on the notion of graph convergence, we prove that for large…
One of the main applications of the bound state in the continuum (BIC) is the low-threshold lasing. Ideally, the infinite quality factor of the BIC results in the zero-threshold and zero-linewidth lasing. However, various effects disturb…
The first goal of this paper is to prove multiple asymptotic results for a time-discrete and space-continuous polymer model of a random walk in a random potential. These results include: existence of deterministic free energy density in the…