166 research outputs found
Electric field formulation for thin film magnetization problems
We derive a variational formulation for thin film magnetization problems in
type-II superconductors written in terms of two variables, the electric field
and the magnetization function. A numerical method, based on this formulation,
makes it possible to accurately compute all variables of interest, including
the electric field, for any value of the power in the power law current-voltage
relation characterizing the superconducting material. For high power values we
obtain a good approximation to the critical state model solution. Numerical
simulation results are presented for simply and multiply connected films, and
also for an inhomogeneous film.Comment: 15 p., submitte
Partial L-1 Monge-Kantorovich problem: variational formulation and numerical approximation
Published versio
A mixed formulation of the Monge-Kantorovich equations
Published versio
Nonlinear Dynamics of Aeolian Sand Ripples
We study the initial instability of flat sand surface and further nonlinear
dynamics of wind ripples. The proposed continuous model of ripple formation
allowed us to simulate the development of a typical asymmetric ripple shape and
the evolution of sand ripple pattern. We suggest that this evolution occurs via
ripple merger preceded by several soliton-like interaction of ripples.Comment: 6 pages, 3 figures, corrected 2 typo
3D modeling of magnetic atom traps on type-II superconductor chips
Magnetic traps for cold atoms have become a powerful tool of cold atom
physics and condense matter research. The traps on superconducting chips allow
one to increase the trapped atom life- and coherence time by decreasing the
thermal noise by several orders of magnitude compared to that of the typical
normal-metal conductors. A thin superconducting film in the mixed state is,
usually, the main element of such a chip.
Using a finite element method to analyze thin film magnetization and
transport current in type-II superconductivity, we study magnetic traps
recently employed in experiments. The proposed approach allows us to predict
important characteristics of the magnetic traps (their depth, shape, distance
from the chip surface, etc.) necessary when designing magnetic traps in cold
atom experiments.Comment: Submitted to Superconductor Science and Technolog
On the energy-based variational model for vector magnetic hysteresis
We consider the quasi-static magnetic hysteresis model based on a dry-friction like representation of magnetization. The model has a consistent energy interpretation, is intrinsically vectorial, and ensures a direct calculation of the stored and dissipated energies at any moment in time, and hence not only on the completion of a closed hysteresis loop. We discuss the variational formulation of this model and derive an efficient numerical scheme, avoiding the usually employed approximation which can be inaccurate in the vectorial case. The parameters of this model for a nonoriented steel are identified using a set of first order reversal curves. Finally, the model is incorporated as a local constitutive relation into a 2D finite element simulation accounting for both the magnetic hysteresis and the eddy current
Stationary quasivariational inequalities with gradient constraint and nonhomogeneous boundary conditions
Publicado em "From particle systems to partial differential equations. Part 2. (Springer proceedings in mathematics & statistics, vol. 75). ISBN 978-3-642-54270-1We study existence of solution of stationary uasivariational inequalities with gradient constraint and nonhomogeneous boundary condition of Neumann or Dirichlet type.
Through two different approaches, one making use of a fixed point theorem and the other using a process of regularization and penalization, we obtain different sufficient conditions for the existence of solution.(undefined
Quasivariational solutions for first order quasilinear equations with gradient constraint
We prove the existence of solutions for an evolution quasi-variational
inequality with a first order quasilinear operator and a variable convex set,
which is characterized by a constraint on the absolute value of the gradient
that depends on the solution itself. The only required assumption on the
nonlinearity of this constraint is its continuity and positivity. The method
relies on an appropriate parabolic regularization and suitable {\em a priori}
estimates. We obtain also the existence of stationary solutions, by studying
the asymptotic behaviour in time. In the variational case, corresponding to a
constraint independent of the solution, we also give uniqueness results
A QUASI-VARIATIONAL INEQUALITY PROBLEM IN SUPERCONDUCTIVITY
Accepted versio
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