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Understanding and accounting for uncertainty helps to ensure next-step tokamaks such as SPARC will robustly achieve their goals. While traditional Plasma OPerating CONtour (POPCON) analyses guide design, they often overlook the significant…
Surface reconstruction from point clouds is a fundamental step in many applications in computer vision. In this paper, we develop an efficient iterative method on a variational model for the surface reconstruction from point clouds. The…
An electrostatic gyrokinetic-based model is applied to simulate parallel plasma transport in the scrape-off layer to a divertor plate. The authors focus on a test problem that has been studied previously, using parameters chosen to model a…
The Lagrangian point of view is adopted to study turbulent premixed combustion. The evolution of the volume fraction of combustion products is established by the Reynolds transport theorem. It emerges that the burned-mass fraction is led by…
A parameterized surface can be represented as a projection from a certain toric surface. This generalizes the classical homogeneous and bihomogeneous parameterizations. We extend to the toric case two methods for computing the implicit…
We develop a geometric framework to describe the thermodynamics of microscopic heat engines driven by slow periodic temperature variations and modulations of a mechanical control parameter. Covering both the classical and the quantum…
The path-integral formulation of the statistical mechanics of quantum many-body systems is described, with the purpose of introducing practicaltechniques for the simulation of solids. Monte Carlo and molecular dynamics methods for…
Recently, the problem of boundary stabilization and estimation for unstable linear constant-coefficient reaction-diffusion equation on n-balls (in particular, disks and spheres) has been solved by means of the backstepping method. However,…
The process by which jet algorithms construct jets and subjets is inherently ambiguous and equally well motivated algorithms often return very different answers. The Qjets procedure was introduced by the authors to account for this…
The form of the kernel that controls the dynamics of the Bethe-Salpeter equations is essential for obtaining quantitatively accurate predictions for the observable properties of hadrons. In the present work we briefly review the basic…
Kinematics of rigid bodies can be analyzed in many different ways. The advantage of using Euler parameters is that the resulting equations are polynomials and hence computational algebra, in particular Gr\"obner bases, can be used to study…
This article reviews recent developments in multiresolution analysis which make it a powerful tool for the systematic treatment of the multiple length-scales inherent in the electronic structure of matter. Although the article focuses on…
The airplane refueling problem is a nonlinear combinatorial optimization problem, and its equivalent problem the $n$-vehicle exploration problem is proved to be NP-complete (arXiv:2304.03965v1, The $n$-vehicle exploration problem is…
Physics-Informed Neural Network (PINN) is a novel multi-task learning framework useful for solving physical problems modeled using differential equations (DEs) by integrating the knowledge of physics and known constraints into the…
The difficulty of identifying the physical model of complex systems has led to exploring methods that do not rely on such complex modeling of the systems. Deep reinforcement learning has been the pioneer for solving this problem without the…
Recent advances in deep learning makes solving parabolic partial differential equations (PDEs) in high dimensional spaces possible via forward-backward stochastic differential equation (FBSDE) formulations. The implementation of most…
Several aspects influence corrosive processes in RC structures, such as environmental conditions, structural geometry, and mechanical properties. Since these aspects present large randomnesses, probabilistic models allow a more accurate…
The existence of radial solutions of a nonlinear Dirichlet problem in a ball is translated to the language of Mechanics, i.e. to requirements on the time of motion of a particle in an external potential and under the action of a viscosity…
Spatially developing round jet flows are fundamental to numerous engineering applications. This letter applies the wave-particle turbulence simulation (WPTS) method, a recently developed multiscale approach, to simulate a spatially…
The diffusion forecasting is a nonparametric approach that provably solves the Fokker-Planck PDE corresponding to It\^o diffusion without knowing the underlying equation. The key idea of this method is to approximate the solution of the…