相关论文: Homogenization at different linear scales, bounded…

This paper considers a family of second-order periodic parabolic equations with highly oscillating potentials, which have been considered many times for the time-varying potentials in stochastic homogenization. Following a standard…

A heterostructure composed of two parallel homogeneous layers is studied in the limit as their widths $l_1$ and $l_2$, and the distance between them $r$ shrinks to zero simultaneously. The problem is investigated in one dimension and the…

We consider a one-dimensional diffusion process with coefficients that are periodic outside of a finite 'interface region'. The question investigated in this article is the limiting long time / large scale behaviour of such a process under…

The paper studies homogenization problem for a non-autonomous parabolic equation with a large random rapidly oscillating potential in the case of one dimensional spatial variable. We show that if the potential is a statistically homogeneous…

We consider one-dimensional infinite chains of harmonic oscillators with random exchanges of momenta and long-range interaction potentials which have polynomial decay rate $|x|^{-\theta}, x \to \infty, \theta > 1$ where $x \in \mathbb{Z}$…

We consider a one dimensional infinite acoustic chain of harmonic oscillators whose dynamics is perturbed by a random exchange of velocities, such that the energy and momentum of the chain are conserved. Consequently, the evolution of the…

In this work, we study the two-point entanglement S(i,j), which measures the entanglement between two separated degrees of freedom (ij) and the rest of system, near a quantum phase transition. Away from the critical point, S(i,j) saturates…

Competing time scales generate novelty. Here, we show that a coupling between the time scales imposed by instrument inertia and the formation of inter-particle frictional contacts in shear-thickening suspensions leads to highly asymmetric…

In piecewise-smooth differential systems, a hyperbolic limit cycle of a subsystem loses its structural stability if it grazes the switching manifold at a tangent point. Such a cycle is called a grazing loop and in this paper we investigate…

Hamiltonian mixed systems with unbounded phase space are typically characterized by two asymptotic algebraic laws: decay of recurrence time statistics ($\gamma$) and superdiffusion ($\beta$). We conjecture the universal exponents…

We use the notion of stochastic two-scale convergence to solve the problem of stochastic homogenization of the elastic plate in the bending regime.

We study a random model of deep multi-head self-attention in which the weights are resampled independently across layers and heads, as at initialization of training. Viewing depth as a time variable, the residual stream defines a…

We consider a homogenous fragmentation process with killing at an exponential barrier. With the help of two families of martingales we analyse the growth of the largest fragment for parameter values that allow for survival. In this respect…

In this work, we study the effective behavior of a two-dimensional variational model within finite crystal plasticity for high-contrast bilayered composites. Precisely, we consider materials arranged into periodically alternating thin…

In [CSZ23], the authors proved the convergence of the finite dimensional time distribution of the rescaled random fields derived from the discrete stochastic heat equation of $2d$-directed polymers in random environment in the critical…

Two time scale stochastic approximation algorithms emulate singularly perturbed deterministic differential equations in a certain limiting sense, i.e., the interpolated iterates on each time scale approach certain differential equations in…

The interplay between multiscale homogenization and dimension reduction for nonlinear elastic thin plates is analyzed in the case in which the scaling of the energy corresponds to Kirchhoff's nonlinear bending theory for plates. Different…

A variational model for the interaction between homogenization and phase separation is considered. The focus is on the regime where the latter happens at a smaller scale than the former, and when the wells of the double well potential are…

We consider the probability of having two intervals (gaps) without eigenvalues in the bulk scaling limit of the Gaussian Unitary Ensemble of random matrices. We describe uniform asymptotics for the transition between a single large gap and…

This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…