Related papers: Reissner-Mindlin shell theory based on tangential …
In this paper, we study the consequences of the fundamental theorem of calculus from an algebraic point of view. For functions with singularities, this leads to a generalized notion of evaluation. We investigate properties of such…
The classical nucleation theory (CNT) concept of a nucleus as a fragment of the bulk new phase fails for nanosized nuclei. An extension of CNT taking into account the properties of the transition region between coexisting bulk phases is…
We discuss recent advances made in modelling the complex magnetohydrodynamics of the Sun using our anelastic spherical harmonics (ASH) code. We have conducted extensive 3--D simulations of compressible convection in rotating spherical…
Modelling of turbine blade-induced turbulence (BIT) is discussed within the framework of three-dimensional Reynolds-averaged Navier-Stokes (RANS) actuator disk computations. We first propose a generic (baseline) BIT model, which is applied…
A multilevel Monte Carlo (MLMC) method for quantifying model-form uncertainties associated with the Reynolds-Averaged Navier-Stokes (RANS) simulations is presented. Two, high-dimensional, stochastic extensions of the RANS equations are…
In this article a surprising result is demonstrated using the neural tangent kernel. This kernel is defined as the inner product of the vector of the gradient of an underlying model evaluated at training points. This kernel is used to…
Physical processes that manifest as tangential vector fields on a sphere are common in geophysical and environmental sciences. These naturally occurring vector fields are often subject to physical constraints, such as being curl-free or…
We survey structure-preserving discretizations of minimal surfaces in Euclidean space. Our focus is on a discretization defined via parallel face offsets of polyhedral surfaces, which naturally leads to a notion of vanishing mean curvature…
Neural network models are one of the most successful approaches to machine learning, enjoying an enormous amount of development and research over recent years and finding concrete real-world applications in almost any conceivable area of…
The purpose of this paper is to present a new mathematical model for the deformation of thin Cosserat elastic plates. Our approach, which is based on a generalization of the classical Reissner plate theory, takes into account the transverse…
For multilayer materials in thin substrate systems, interfacial failure is one of the most challenges. The traction-separation relations (TSR) quantitatively describe the mechanical behavior of a material interface undergoing openings,…
Several Tensor Basis Neural Network (TBNN) frameworks aimed at enhancing turbulence RANS modeling have recently been proposed in the literature as data-driven constitutive models for systems with known invariance properties. However,…
Three-dimensional nanoarchitectures are widely used across various areas of physics, including spintronics, photonics, and superconductivity. In this regard, thin curved 3D membranes are especially interesting for applications in nano- and…
In this paper, the surface of revolution discrete element method (SR-DEM) is introduced to simulate systems of particles with closed surfaces of revolution. Due to the cylindrical symmetry of a surface of revolution, the geometry of any…
In this paper, following the ideas in Marsden et al.[18], we set up the regular reduction theory of a regular controlled Lagrangian (RCL) system with symmetry and momentum map, by using Legendre transformation and Euler-Lagrange vector…
We apply the theory of functors of Artin rings to prove the existence of a universal formal solution to a exterior differential system. We compute the tangent space and the obstruction theory of the funtor of Artin ring governing the…
Shell models have found wide application in the study of hydrodynamic turbulence because they are easily solved numerically even at very large Reynolds numbers. Although bereft of spatial variation, they accurately reproduce the main…
We propose a data-driven mean-curvature solver for the level-set method. This work is the natural extension to $\mathbb{R}^3$ of our two-dimensional strategy in [DOI: 10.1007/s10915-022-01952-2][1] and the hybrid inference system of [DOI:…
Nuclear many-body theory is used to study nuclear matter and finite nuclei at extreme isospin. In-medium interactions in asymmetric nuclear matter are obtained from (Dirac-) Brueckner theory. Neutron skin formation in Ni and Sn isotopes is…
Realistic astrophysical environments are turbulent due to the extremely high Reynolds numbers. Therefore, the theories of reconnection intended for describing astrophysical reconnection should not ignore the effects of turbulence on…