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Interfaces in a model with a single, real nonconserved order parameter and purely dissipative evolution equation are considered. We show that a systematic perturbative approach, called the expansion in width and developed for curved domain…
World models are central to LLM agents that must evaluate actions over long horizons. Yet much existing work focuses on environments governed by physical dynamics or spatial structure, whereas many high-impact domains, including supply…
Out-of-equilibrium systems, inherently complex and challenging to understand, are prevalent across various disciplines, including physics where they arise in contexts such as fluid dynamics. In particular, critical out-of-equilibrium…
Studying extreme events and how they evolve in a changing climate is one of the most important current scientific challenges. Starting from complex climate models, a key difficulty is to be able to run long enough simulations in order to…
A robust and efficient anomaly detection technique is proposed, capable of dealing with crowded scenes where traditional tracking based approaches tend to fail. Initial foreground segmentation of the input frames confines the analysis to…
This work considers the problem of finding analytical expressions for the expected values of dis- tributed computing performance metrics when the underlying communication network has a complex structure. Through active probing tests a real…
We use a Convolutional Recurrent Neural Network approach to learn morphological evolution driven by surface diffusion. To this aim we first produce a training set using phase field simulations. Intentionally, we insert in such a set only…
We propose a level-set approach to characterize the region occupied by the solid in Stefan problems with and without surface tension, based on their recent probabilistic reformulation. The level-set function is parameterized by a…
We develop a method for the evaluation of extreme event statistics associated with nonlinear dynamical systems, using a small number of samples. From an initial dataset of design points, we formulate a sequential strategy that provides the…
A numerical method for coupled 3D-1D problems with discontinuous solutions at the interfaces is derived and discussed. This extends a previous work on the subject where only continuous solutions were considered. Thanks to properly defined…
In this work we study the dynamic behaviour of compound shells of revolution partially filled with an ideal incompressible fluid based on boundary-value problems. New analytical mathematical model with corresponding discrete scheme for the…
Generalizing the well-known relations on characteristic functions on a plane to the case of a one-dimensional regular surface (curve) with compact support, we establish implicit equations for these functions. Introducing an approximation,…
Using offline observational data for policy evaluation and learning allows decision-makers to evaluate and learn a policy that connects characteristics and interventions. Most existing literature has focused on either discrete treatment…
In this paper we present a high-order kernel method for numerically solving diffusion and reaction-diffusion partial differential equations (PDEs) on smooth, closed surfaces embedded in $\mathbb{R}^d$. For two-dimensional surfaces embedded…
A proof of convergence is given for semi- and full discretizations of mean curvature flow of closed two-dimensional surfaces. The numerical method proposed and studied here combines evolving finite elements, whose nodes determine the…
Numerous models for supervised and reinforcement learning benefit from combinations of discrete and continuous model components. End-to-end learnable discrete-continuous models are compositional, tend to generalize better, and are more…
We present a newly developed approach for the calculation of interfacial stiffness and contact area evolution between two rough bodies exhibiting self affine surface structures. Using spline assisted discretization to define localised…
A new class of asynchronous discrete-event simulation schemes for advection-diffusion-reaction equations are introduced, which is based on the principle of allowing quanta of mass to pass through faces of a Cartesian finite volume grid. The…
Liquid wetting of a surface is omnipresent in nature and the advance of micro-fabrication and assembly techniques in recent years offers increasing ability to control this phenomenon. Here, we identify how surface roughness influences the…
The scaling properties of one-dimensional deconstructed surfaces are studied by numerical simulations of a disaggregation model. The model presented here for the disaggregation process takes into account the possibility of having quenched…