Mathematical and numerical models for transfer of low-density lipoproteins through the arterial walls: A new methodology for the model set up with applications to the study of disturbed lumenal flow
We study the compact support property for solutions of the following stochastic partial differential equations: partial derivative tu=aijuxixj(t,x)+biuxi(t,x)+cu+h(t,x,u(t,x))F-center dot(t,x),(t,x)is an element of(0,infinity)xRd,where F-center dot is a sp ...
In the context of SARS-CoV-2 pandemic, mathematical modelling has played a funda-mental role for making forecasts, simulating scenarios and evaluating the impact of pre-ventive political, social and pharmaceutical measures. Optimal control theory represent ...
In this work we consider solutions to stochastic partial differential equations with transport noise, which are known to converge, in a suitable scaling limit, to solution of the corresponding deterministic PDE with an additional viscosity term. Large devi ...
Deep learning (DL) has been wildly successful in practice, and most of the state-of-the-art machine learning methods are based on neural networks (NNs). Lacking, however, is a rigorous mathematical theory that adequately explains the amazing performance of ...
Modern manufacturing engineering is based on a ``design-through-analysis'' workflow. According to this paradigm, a prototype is first designed with Computer-aided-design (CAD) software and then finalized by simulating its physical behavior, which usually i ...
The Internodes method is a general purpose method to deal with non-conforming discretizations of partial differential equations on 2D and 3D regions partitioned into disjoint subdomains. In this paper we are interested in measuring how much the Internodes ...
Mitochondrial diseases are rare and severe conditions with debilitating symptoms. Biochemical defects in mitochondria however are common. The difference between these two frequencies is suspected to lie in the capability of the cells to adapt to the homeos ...
Removing geometrical details from a complex domain is a classical operation in computer aided design for simulation and manufacturing. This procedure simplifies the meshing process, and it enables faster simulations with less memory requirements. But depen ...
In this work, we present a PDE-aware deep learning model for the numerical solution to the inverse problem of electrocardiography. The model both leverages data availability and exploits the knowledge of a physically based mathematical model, expressed by ...
Removing geometrical details from a complex domain is a classical operation in computer aided design for simulation and manufacturing. This procedure simplifies the meshing process, and it enables faster simulations with less memory requirements. However, ...
Global spectral methods offer the potential to compute solutions of partial differential equations numerically to very high accuracy. In this work, we develop a novel global spectral method for linear partial differential equations on cubes by extending th ...
