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Diffusion-based models have shown great promise in molecular generation but often require a large number of sampling steps to generate valid samples. In this paper, we introduce a novel Straight-Line Diffusion Model (SLDM) to tackle this…
We consider a discrete model of planar elasticity where the particles, in the reference configuration, sit on a regular triangular lattice and interact through nearest neighbor pairwise potentials, with bonds modeled as linearized elastic…
A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. In this work, we present a…
The transport of deformable particles through porous media underlies a wealth of applications ranging from filtration to oil recovery to the transport and spreading of biological agents. Using direct numerical simulations, we analyze the…
We present a novel method for precise 3D object localization in single images from a single calibrated camera using only 2D labels. No expensive 3D labels are needed. Thus, instead of using 3D labels, our model is trained with…
Monte Carlo (MC) simulations are used to study the dynamics of polymer translocation through a nanopore in the limit where the translocation rate is sufficiently slow that the polymer maintains a state of conformational quasi-equilibrium.…
A new geometric procedure to construct symplectic methods for constrained mechanical systems is developed in this paper. The definition of a map coming from the notion of retraction maps allows to adapt the continuous problem to the…
We derive an analytical expression for a novel large-scale structure observable: the line correlation function. The line correlation function, which is constructed from the three-point correlation function of the phase of the density field,…
The dynamics of dislocations can be formulated in terms of the evolution of continuous variables representing dislocation densities ('continuum dislocation dynamics'). We show for various variants of this approach that the resulting models…
We consider laminar flow in channels constrained geometrically to remain between two parallel planes; this geometry is typical of microchannels obtained with a single step by current microfabrication techniques. For pressure-driven Stokes…
Although continuum theory has been widely used to describe the long-range elastic behavior of dislocations, it is limited in its ability to describe mechanical behaviors that occur near dislocation cores. This limit of the continuum theory…
Understanding plastic deformation of crystals in terms of the fundamental physics of dislocations has remained a grand challenge in materials science for decades. To overcome this, the Discrete Dislocation Dynamics (DDD) method has been…
Many reduced order models are neither robust with respect to the parameter changes nor cost-effective enough for handling the nonlinear dependence of complex dynamical systems. In this study, we put forth a robust machine learning framework…
The long-time behavior of transport coefficients in a model for spatially heterogeneous media in two and three dimensions is investigated by Molecular Dynamics simulations. The behavior of the velocity auto-correlation function is…
We introduce a continuous-time random walk model on an infinite multilayer structure inspired by transportation networks. Each layer is a copy of $\mathbb{R}^d$, indexed by a non-negative integer. A walker moves within a layer by means of…
This study presents a physically consistent displacement-driven reformulation of the concept of action-at-a-distance, which is at the foundation of nonlocal elasticity. In contrast to existing approaches that adopts an integral…
Slow dynamics in a fluid are studied in one of the most basic systems possible: polydisperse hard spheres. Monodisperse hard spheres cannot be studied as the slow down in dynamics as the density is increased is preempted by crystallisation.…
The classic technique of Baker [J. ACM '94] is the most fundamental approach for designing approximation schemes on planar, or more generally topologically-constrained graphs, and it has been applied in a myriad of different variants and…
We introduce a phenomenological theory of dislocation motion appropriate for two dimensional lattices. A coarse grained description is proposed that involves as primitive variables local lattice rotation and Burgers vector densities along…
This note collects some results on the behaviour of screw dislocation in an elastic medium. By using a semi-discrete model, we are able to investigate two specific aspects of the dynamics, namely (i) the interaction with free boundaries and…