158,190 research outputs found
Benchmarking the nonperturbative functional renormalization group approach on the random elastic manifold model in and out of equilibrium
Criticality in the class of disordered systems comprising the random-field
Ising model (RFIM) and elastic manifolds in a random environment is controlled
by zero-temperature fixed points that must be treated through a functional
renormalization group. We apply the nonperturbative functional renormalization
group approach that we have previously used to describe the RFIM in and out of
equilibrium [Balog-Tarjus-Tissier, Phys. Rev. B 97, 094204 (2018)] to the
simpler and by now well-studied case of the random elastic manifold model. We
recover the main known properties, critical exponents and scaling functions, of
both the pinned phase of the manifold at equilibrium and the depinning
threshold in the athermally and quasi-statically driven case for any dimension
. This successful benchmarking of our theoretical approach gives
strong support to the results that we have previously obtained for the RFIM, in
particular concerning the distinct universality classes of the equilibrium and
out-of-equilibrium (hysteresis) critical points below a critical dimension
.Comment: 38 pages, 6 figure
Elastic theory of flux lattices in presence of weak disorder
The effect of disorder on flux lattices at equilibrium is studied
quantitatively in the absence of free dislocations using both the Gaussian
variational method and the renormalization group. Our results for the mean
square relative displacements clarify the nature of the crossovers with
distance. We find three regimes: (i) a short distance regime (``Larkin
regime'') where elasticity holds (ii) an intermediate regime (``Random
Manifold'') where vortices are pinned independently (iii) a large distance,
quasi-ordered regime where the periodicity of the lattice becomes important and
there is universal logarithmic growth of displacements for and
persistence of algebraic quasi-long range translational order. The functional
renormalization group to and the variational method, agree
within on the value of the exponent. In we compute the crossover
function between the three regimes. We discuss the observable signature of this
crossover in decoration experiments and in neutron diffraction experiments on
flux lattices. Qualitative arguments are given suggesting the existence for
weak disorder in of a `` Bragg glass '' phase without free dislocations
and with algebraically divergent Bragg peaks. In both the variational
method and the Cardy-Ostlund renormalization group predict a glassy state below
the same transition temperature , but with different behaviors.
Applications to systems and experiments on magnetic bubbles are
discussed.Comment: 59 pages; RevTeX 3.0; 5 postscript figures uuencode
Kernel-based stochastic collocation for the random two-phase Navier-Stokes equations
In this work, we apply stochastic collocation methods with radial kernel
basis functions for an uncertainty quantification of the random incompressible
two-phase Navier-Stokes equations. Our approach is non-intrusive and we use the
existing fluid dynamics solver NaSt3DGPF to solve the incompressible two-phase
Navier-Stokes equation for each given realization. We are able to empirically
show that the resulting kernel-based stochastic collocation is highly
competitive in this setting and even outperforms some other standard methods
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