相关论文: Formulation of small-strain magneto-elastic proble…
The development of stellarators that use permanent magnet arrays to shape their confining magnetic fields has been a topic of recent interest, but the requirements for how such magnets must be shaped, manufactured, and assembled remain to…
In this paper we develop adaptive numerical schemes for certain nonlinear variational problems. The discretization of the variational problems is done by representing the solution as a suitable frame decomposition, i.e., a complete, stable,…
Group Theory techniques can aid greatly the determination of magnetic structures. The integration of their calculations into new and existing refinement programs is an ongoing development that will simplify and make more rigorous the…
We consider a setting in which an evolving surface is implicitly characterized as the zero level of a level set function. Such an implicit surface does not encode any information about the path of a single point on the evolving surface. In…
This article reports on the confluence of two streams of research, one emanating from the fields of numerical analysis and scientific computation, the other from topology and geometry. In it we consider the numerical discretization of…
Magnetic relaxation drives plasma toward lower-energy equilibria under helicity constraints. In ideal magnetohydrodynamics (MHD), helicity is locally conserved, while resistive theories such as Taylor relaxation preserve only global…
Using dimensionally reduced models for the numerical simulation of thin objects is highly attractive as this reduces the computational work substantially. The case of narrow thin elastic bands is considered and a convergent finite element…
Frustrated magnetism plays a central role in the phenomenology of exotic quantum states. However, because the magnetic structures of frustrated systems are aperiodic, there has always been the problem that they cannot be determined using…
In this work, we define a set of analytic tools to describe the dynamic response of the magnetization to small perturbations, which can be used on its own or in combination with micromagnetic simulations and does not require saturation. We…
The a posteriori analysis of the discretization error and the modeling error is studied for a compliance cost functional in the context of the optimization of composite elastic materials and a two-scale linearized elasticity model. A…
Finite elasticity problems commonly include material and geometric nonlinearities and are solved using various numerical methods. However, for highly nonlinear problems, achieving convergence is relatively difficult and requires small load…
This paper addresses different aspects of "coupled" model descriptions in computational electromagnetics. This includes domain decomposition, multiscale problems, multiple or hybrid discrete field formulation and multi-physics problems.…
A comparison is given of the fundamental works of S. V. Vonsovsky on the many-electron polar and s-d(f) exchange models with the subsequent development of the theory of magnetism of transition and rare earth metals and their compounds.…
In this paper, we first prove the local-in-time existence of the evolutionary model for magnetoelasticity with finite initial energy by employing the nonlinear iterative approach given in \cite{Jiang-Luo-2019-SIAM} to deal with the…
Magnetic properties of electrical steel are usually measured on Single Sheet Testers, Epstein frames or ring cores. Due to the geometric dimensions and measurement principles of these standardized setups, the fundamental microstructural…
Inverse design of morphing slender structures with programmable curvature has significant applications in various engineering fields. Most existing studies formulate it as an optimization problem, which requires repeatedly solving the…
When describing elastic deformations of a body sometimes it is worth to take in account elastic spatial dispersion. If spatial dispersion is weak, as usually happens, then it can be reduced to dependence of thermodynamic potential on strain…
We study compressible and incompressible nonlinear elasticity variational problems in a general context. Our main result gives a sufficient condition for an equilibrium to be a global energy minimizer, in terms of convexity properties of…
We review basic computational techniques for simulations of various magnetic properties of solids. Several applications to compute magnetic anisotropy energy, spin wave spectra, magnetic susceptibilities and temperature dependent…
Micro-Electro-Mechanical Systems (MEMS) normally have fixed or moving structures (plates or array of thin beams) with cross-sections of the order of microns and lengths of the order of tens or hundreds of microns. Electrostatic forces play…