相关论文: Variational methods for a singular SPDE yielding t…
The magnetization ripple is a microstructure formed by the magnetization in a thin-film ferromagnet. It is triggered by the random orientation of the grains in the poly-crystalline material. In an approximation of the micromagnetic model,…
We consider the variance renormalisation of a singular SPDE for which a Da Prato-Debussche trick is not applicable. The example taken is the $2$-dimensional generalised parabolic Anderson model (gPAM), driven by a much rougher than white…
Reconstructing magnetizations from measurements of the generated magnetic potential is generally non-unique. The non-uniqueness still remains if one restricts the magnetization to those induced by an ambient magnetic dipole field (i.e., the…
Ferromagnetic materials are governed by a variational principle which is nonlocal, nonconvex and multiscale. The main object is given by a unit-length three-dimensional vector field, the magnetization, that corresponds to the stable states…
We consider $\mathbb{S}^2$-valued maps on a domain $\Omega\subset\mathbb{R}^N$ minimizing a perturbation of the Dirichlet energy with vertical penalization in $\Omega$ and horizontal penalization on $\partial\Omega$. We first show the…
Global minimality, boundedness, and uniqueness are established for a general, physically motivated class of inverse source problems in non-homogeneous electromagnetic media with generalized constitutive parameters. The existence of a…
Two principal scenarios of magnetization reversal are considered. In the first scenario all spins perform coherent motion and an excess of magnetic energy directly goes to a nonmagnetic thermal bath. A general dynamic equation is derived…
In electrical impedance tomography, algorithms based on minimizing a linearized residual functional have been widely used due to their flexibility and good performance in practice. However, no rigorous convergence results have been…
We consider the inverse problem of recovering a continuous-domain function from a finite number of noisy linear measurements. The unknown signal is modeled as the sum of a slowly varying trend and a periodic or quasi-periodic seasonal…
A new electronic structure principle, viz. the minimum magnetizability principle (MMP) has been proposed and also has been verified through ab initio calculations, to extend the domain of applicability of the conceptual density functional…
This work is concerned with the recovery of piecewise constant images from noisy linear measurements. We study the noise robustness of a variational reconstruction method, which is based on total (gradient) variation regularization. We show…
A magnetic particle with atomic spins ordered in an unstable direction is an example of a false vacuum that decays via excitation of internal spin waves. Coupled evolution of the particle's magnetization (or the vacuum state) and spin…
We investigate a variational theory for magnetoelastic solids under the incompressibility constraint. The state of the system is described by deformation and magnetization. While the former is classically related to the reference…
Magnetic resonance is a widely-established phenomenon that probes magnetic properties such as magnetic damping and anisotropy. Even though the typical resonance frequency of a magnet ranges from gigahertz to terahertz, experiments also…
By numerically solving the equations of motion for atomic spins we show that internal spin-wave processes in large enough magnetic particles, initially in unstable states, lead to complete magnetization reversal and thermalization. The…
The study of singular perturbations of the Dirichlet energy is at the core of the phenomenological-description paradigm in soft condensed matter. Being able to pass to the limit plays a crucial role in the understanding of the…
A minimal surface in a random environment (MSRE) is a surface which minimizes the sum of its elastic energy and its environment potential energy, subject to prescribed boundary conditions. Apart from their intrinsic interest, such surfaces…
Transverse NMR relaxation from spins diffusing through a random magnetic medium is sensitive to its structure on a mesoscopic scale. In particular, this results in the time-dependent relaxation rate. We show analytically and numerically…
We relate the anomalous noise found experimentally in spin ice to the subdiffusion of magnetic monopoles. Because monopoles are emergent particles, they do not move in a structureless vacuum. Rather, the underlying spin ensemble filters the…
Magnetic nanoparticles (MNPs) have been proposed as an ultimate solution for diverse applications including nanomedicine and logic devices over decades. However, none has emerged revolutionary because realizing their magnetization response…