7,377 research outputs found
Mott law as upper bound for a random walk in a random environment
We consider a random walk on the support of an ergodic simple point process
on R^d, d>1, furnished with independent energy marks. The jump rates of the
random walk decay exponentially in the jump length and depend on the energy
marks via a Boltzmann-type factor. This is an effective model for the
phonon-induced hopping of electrons in disordered solids in the regime of
strong Anderson localization. Under mild assumptions on the point process we
prove an upper bound of the asymptotic diffusion matrix of the random walk in
agreement with Mott law. A lower bound in agreement with Mott law was proved in
\cite{FSS}.Comment: 22 pages. Additional results and corrections
On the classical algebras
We analyze the W_N^l algebras according to their conjectured realization as
the second Hamiltonian structure of the integrable hierarchy resulting from the
interchange of x and t in the l^{th} flow of the sl(N) KdV hierarchy. The W_4^3
algebra is derived explicitly along these lines, thus providing further support
for the conjecture. This algebra is found to be equivalent to that obtained by
the method of Hamiltonian reduction. Furthermore, its twisted version
reproduces the algebra associated to a certain non-principal embedding of sl(2)
into sl(4), or equivalently, the u(2) quasi-superconformal algebra. The general
aspects of the W_N^l algebras are also presented.Comment: 28 page
Growth rate of Rayleigh-Taylor turbulent mixing layers with the foliation approach
For years, astrophysicists, plasma fusion and fluid physicists have puzzled
over Rayleigh-Taylor turbulent mixing layers. In particular, strong
discrepancies in the growth rates have been observed between experiments and
numerical simulations. Although two phenomenological mechanisms (mode-coupling
and mode-competition) have brought some insight on these differences,
convincing theoretical arguments are missing to explain the observed values. In
this paper, we provide an analytical expression of the growth rate compatible
with both mechanisms and is valide for a self-similar, low Atwood
Rayleigh-Taylor turbulent mixing subjected to a constant or time-varying
acceleration. The key step in this work is the introduction of {\it foliated}
averages and {\it foliated} turbulent spectra highlighted in our three
dimensional numerical simulations. We show that the exact value of the
Rayleigh-Taylor growth rate not only depends upon the acceleration history but
is also bound to the power-law exponent of the {\it foliated} spectra at large
scales
SM(2,4k) fermionic characters and restricted jagged partitions
A derivation of the basis of states for the superconformal minimal
models is presented. It relies on a general hypothesis concerning the role of
the null field of dimension . The basis is expressed solely in terms of
modes and it takes the form of simple exclusion conditions (being thus a
quasi-particle-type basis). Its elements are in correspondence with
-restricted jagged partitions. The generating functions of the latter
provide novel fermionic forms for the characters of the irreducible
representations in both Ramond and Neveu-Schwarz sectors.Comment: 12 page
Steady States, Fluctuation-Dissipation Theorems and Homogenization for Reversible Diffusions in a Random Environment
Accepted manuscript version. Published version available at https://doi.org/10.1007/s00205-018-1245-1.Prolongating our previous paper on the Einstein relation, we study the motion of a particle diffusing in a random reversible environment when subject to a small external forcing. In order to describe the long time behavior of the particle, we introduce the notions of steady state and weak steady state. We establish the continuity of weak steady states for an ergodic and uniformly elliptic environment. When the environment has finite range of dependence, we prove the existence of the steady state and weak steady state and compute its derivative at a vanishing force. Thus we obtain a complete ‘fluctuation–dissipation Theorem’ in this context as well as the continuity of the effective variance
Modelling the dynamics of turbulent floods
Consider the dynamics of turbulent flow in rivers, estuaries and floods. Based on the widely used k-epsilon model for turbulence, we use the techniques of centre manifold theory to derive dynamical models for the evolution of the water depth and of vertically averaged flow velocity and turbulent parameters. This new model for the shallow water dynamics of turbulent flow: resolves the vertical structure of the flow and the turbulence; includes interaction between turbulence and long waves; and gives a rational alternative to classical models for turbulent environmental flows
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