466 research outputs found
X-ray diffraction of a disordered charge density wave
We study the X-ray diffraction spectrum produced by a collectively pinned
charge density wave (CDW), for which one can expect a Bragg glass phase. The
spectrum consists of two asymmetric divergent peaks. We compute the shape of
the peaks, and discuss the experimental consequences.Comment: 5 pages, 2 figure
From microstructural features to effective toughness in disordered brittle solids
The relevant parameters at the microstructure scale that govern the
macroscopic toughness of disordered brittle materials are investigated
theoretically. We focus on planar crack propagation and describe the front
evolution as the propagation of a long-range elastic line within a plane with
random distribution of toughness. Our study reveals two regimes: in the
collective pinning regime, the macroscopic toughness can be expressed as a
function of a few parameters only, namely the average and the standard
deviation of the local toughness distribution and the correlation lengths of
the heterogeneous toughness field; in the individual pinning regime, the
passage from micro to macroscale is more subtle and the full distribution of
local toughness is required to be predictive. Beyond the failure of brittle
solids, our findings illustrate the complex filtering process of microscale
quantities towards the larger scales into play in a broad range of systems
governed by the propagation of an elastic interface in a disordered medium.Comment: 7 pages, 4 figure
Effect of disorder geometry on the critical force in disordered elastic systems
We address the effect of disorder geometry on the critical force in
disordered elastic systems. We focus on the model system of a long-range
elastic line driven in a random landscape. In the collective pinning regime, we
compute the critical force perturbatively. Not only our expression for the
critical force confirms previous results on its scaling with respect to the
microscopic disorder parameters, it also provides its precise dependence on the
disorder geometry (represented by the disorder two-point correlation function).
Our results are successfully compared to the results of numerical simulations
for random field and random bond disorders.Comment: 18 pages, 7 figure
Maximum of N Independent Brownian Walkers till the First Exit From the Half Space
We consider the one-dimensional target search process that involves an
immobile target located at the origin and searchers performing independent
Brownian motions starting at the initial positions all on the positive half space. The process stops when the target is
first found by one of the searchers. We compute the probability distribution of
the maximum distance visited by the searchers till the stopping time and
show that it has a power law tail: for large . Thus all moments of up to the order
are finite, while the higher moments diverge. The prefactor increases
with faster than exponentially. Our solution gives the exit probability of
a set of particles from a box through the left boundary.
Incidentally, it also provides an exact solution of the Laplace's equation in
an -dimensional hypercube with some prescribed boundary conditions. The
analytical results are in excellent agreement with Monte Carlo simulations.Comment: 18 pages, 9 figure
Eigenstate versus Zeeman-based approaches to the solid-effect
The solid effect is one of the simplest and most effective mechanisms for
Dynamic Nuclear Polarization. It involves the exchange of polarization between
one electron and one nuclear spin coupled via the hyperfine interaction. Even
for such a small spin system, the theoretical understanding is complicated by
the contact with the lattice and the microwave irradiation. Both being weak,
they can be treated within perturbation theory. In this work, we analyze the
two most popular perturbation schemes: the Zeeman and the eigenstate-based
approaches which differ in the way the hyperfine interaction is treated. For
both schemes, we derive from first principles an effective Liouville equation
which describes the density matrix of the spin system; we then study
numerically the behavior of the nuclear polarization for several values of the
hyperfine coupling. In general, we obtain that the Zeeman-based approach
underestimates the value of the nuclear polarization. By performing a
projection onto the diagonal part of the spin-system density matrix, we are
able to understand the origin of the discrepancy, which is due to the presence
of parasite leakage transitions appearing whenever the Zeeman basis is
employed.Comment: 9 pages, 4 figures, 7 pages of supplementary materia
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