Related papers: Existence results in large-strain magnetoelasticit…
We present three-dimensional force-free electrodynamics simulations of magnetar magnetospheres that demonstrate the instability of certain degenerate, high energy equilibrium solutions of the Grad-Shafranov equation. This result indicates…
The aim of this paper is to prove the existence of minimizers for a variational problem involving the minimization under volume constraint of the sum of the perimeter and a non-local energy of Wasserstein type. This extends previous partial…
We study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is…
Motivated by experiments in electroconvection in nematic liquid crystals with homeotropic alignment we study the coupled amplitude equations describing the formation of a stationary roll pattern in the presence of a weakly-damped mode that…
The existence and the regularity results obtained in [37] for the variational model introduced in [36] to study the optimal shape of crystalline materials in the setting of stress-driven rearrangement instabilities (SDRI) are extended from…
Motivated by applications to cell biology, we study the constrained minimization of the Helfrich energy among closed surfaces confined to a container. We show existence of minimizers in the class of bubble trees of spherical weak branched…
This paper studies equality-constrained composite minimization problems. This class of problems, capturing regularization terms and inequality constraints, naturally arises in a wide range of engineering and machine learning applications.…
The dynamical equation of the magnetization has been reconsidered with enlarging the phase space of the ferromagnetic degrees of freedom to the angular momentum. The generalized Landau-Lifshitz-Gilbert equation that includes inertial terms,…
We formulate a large-strain model of single-slip crystal elastoplasticity in the framework of energetic solutions. Numerical performance of the model is compared with lab experiments on the compression of a stack of note papers.
We study the multiplicity and concentration of complex valued solutions for a fractional magnetic Schr\"odinger equation involving a scalar continuous electric potential satisfying a local condition and a continuous nonlinearity with…
We present the application of the variational-wavelet analysis to the quasiclassical calculations of the solutions of Wigner/von Neumann/Moyal and related equations corresponding to the nonlinear (polynomial) dynamical problems. (Naive)…
The mechanism of appearance of exponentially large number of metastable states in magnetic phases of disordered Ising magnets with short-range random exchange is suggested. It is based on the assumption that transitions into inhomogeneous…
Magnetic gels and elastomers are promising candidates to construct reversibly excitable soft actuators, triggered from outside by magnetic fields. These magnetic fields induce or alter the magnetic interactions between discrete rigid…
This paper investigates the existence and properties of stable, uniformly rotating star-planet systems, i.e. mass ratio is sufficiently small. It is modeled by the Euler-Poisson equations. Following the framework established by McCann for…
We approximate an elliptic problem with oscillatory coefficients using a problem of the same type, but with constant coefficients. We deliberately take an engineering perspective, where the information on the oscillatory coefficients in the…
We derive the equations of nonlinear magnetoelastostatics using several variational formulations involving the mechanical deformation and an independent field representing the magnetic component. An equivalence is also discussed, modulo…
Nonconvex functionals with spherical symmetry are studied. Existence of one and radial symmetry of all global minimizers is shown with an approach based on convex relaxation.
This work considers two related families of nonlinear and nonlocal problems in the plane $\mathbb{R}^2$. The first main result derives the general integrable solution to a generalized Liouville equation using the Wronskian of two coprime…
We suggest an alternative mathematical model for the massless neutrino. Consider an elastic continuum in 3-dimensional Euclidean space and assume that points of this continuum can experience no displacements, only rotations. This framework…
We use a variational approach to study existence and regularity of solutions for a Neumann $p$-Laplacian problem with a reaction term on metric spaces equipped with a doubling measure and supporting a Poincar\'e inequality. Trace theorems…