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This article is devoted to the analysis of inverse source problems for Stokes systems in unbounded domains where the corresponding velocity flow is observed on a surface. Our main objective is to study the unique determination of general…

This paper presents a real-time solution for collision detection between objects based on the physics properties. Traditional approaches on collision detection often rely on the geometric relationships that computing the intersections…

This work introduces a novel, simple, and flexible method to quantify irreversibility in generic high-dimensional time series based on the well-known mapping to a binary classification problem. Our approach utilizes gradient boosting for…

A multidimensional chaos is generated by a special initial value problem for the non-autonomous impulsive differential equation. The existence of a chaotic attractor is shown, where density of periodic solutions, sensitivity of solutions…

Fatigue simulation requires accurate modeling of unloading and reloading. However, classical ductile damage models treat deformations after complete failure as irrecoverable -- which leads to unphysical behavior during unloading. This…

We consider weak solutions to dispersive partial differential equations with periodic boundary conditions and initial data with jump discontinuities. These are already known to be continuous at irrational times and piecewise constant at…

Computational intractability has for decades motivated the development of a plethora of methodologies that mainly aimed at a quality-time trade-off. The use of Machine Learning techniques has finally emerged as one of the possible tools to…

Modern robotics is gravitating toward increasingly collaborative human robot interaction. Tools such as acceleration policies can naturally support the realization of reactive, adaptive, and compliant robots. These tools require us to model…

We propose a one-dimensional, nonconvex elastic constitutive model with higher gradients that can predict spontaneous fracture at a critical load via a bifurcation analysis. It overcomes the problem of discontinuous deformations without…

Solutions to optimal control problems can be discontinuous, even if all the functionals defining the problem are smooth. This can cause difficulties when numerically computing solutions to these problems. While conventional numerical…

This paper is about output-feedback control problems for general linear systems in the presence of given state-, control-, disturbance-, and measurement error constraints. Because the traditional separation theorem in stochastic control is…

An actual infinity of colliding balls can be in a configuration in which the laws of mechanics lead to logical inconsistency. It is argued that one should therefore limit the domain of these laws to a finite, or only a potentially infinite…

Possibility of the diverging gradient of the macroscopic quantity near the boundary is investigated by a mono-speed Lorentz-gas model, with a special attention to the regularizing effect of the grazing collision for the infinite-range…

The ability to learn disentangled representations that split underlying sources of variation in high dimensional, unstructured data is important for data efficient and robust use of neural networks. While various approaches aiming towards…

Learning representations that capture the underlying data generating process is a key problem for data efficient and robust use of neural networks. One key property for robustness which the learned representation should capture and which…

In many biological systems, motile agents exhibit random motion with short-term directional persistence, together with crowding effects arising from spatial exclusion. We formulate and study a class of lattice-based models for multiple…

Cooperative localization is fundamental to autonomous multirobot systems, but most algorithms couple inter-robot communication with observation, making these algorithms susceptible to failures in both communication and observation steps. To…

We prove that nonlocal minimal graphs in the plane exhibit generically stickiness effects and boundary discontinuities. More precisely, we show that if a nonlocal minimal graph in a slab is continuous up to the boundary, then arbitrarily…

Closure problems are omnipresent when simulating multiscale systems, where some quantities and processes cannot be fully prescribed despite their effects on the simulation's accuracy. Recently, scientific machine learning approaches have…

Motor adaptation displays a structure-learning effect: adaptation to a new perturbation occurs more quickly when the subject has prior exposure to perturbations with related structure. Although this `learning-to-learn' effect is well…