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A Geometric Interpretation of the Second-Order Structure Function Arising in Turbulence
Springer Science and Business Media LLC - Tập 12 - Trang 1-18 - 2008
We primarily deal with homogeneous isotropic turbulence and use a closure model
for the von Kármán-Howarth equation to study several geometric properties of
turbulent fluid dynamics. We focus our attention on the application of
Riemannian geometry methods in turbulence. Some advantage of this approach
consists in exploring the specific form of a closure model for the von
Kármán-Howarth equation th...
Stationary currents in long-range interacting magnetic systems
Springer Science and Business Media LLC - Tập 23 - Trang 1-25 - 2020
We construct a solution for the 1d integro-differential stationary equation
derived from a finite-volume version of the mesoscopic model proposed in
Giacomin and Lebowitz (J. Stat. Phys. 87(1), 37–61, 1997). This is the
continuous limit of an Ising spin chain interacting at long range through Kac
potentials, staying in contact at the two edges with reservoirs of fixed
magnetizations. The stationar...
Supersymmetric Polar Coordinates with Applications to the Lloyd Model
Springer Science and Business Media LLC - Tập 23 Số 1 - Trang 1-21 - 2020
Spectral properties of random Schrödinger operators are encoded in the average
of products of Greens functions. For probability distributions with enough
finite moments, the supersymmetric approach offers a useful dual representation.
Here we use supersymmetric polar coordinates to derive a dual representation
that holds for general distributions. We apply this result to study the density
of state...
On the AC Spectrum of One-dimensional Random Schrödinger Operators with Matrix-valued Potentials
Springer Science and Business Media LLC - Tập 13 - Trang 219-233 - 2010
We consider discrete one-dimensional random Schrödinger operators with decaying
matrix-valued, independent potentials. We show that if the ℓ2-norm of this
potential has finite expectation value with respect to the product measure then
almost surely the Schrödinger operator has an interval of purely absolutely
continuous (ac) spectrum. We apply this result to Schrödinger operators on a
strip. This ...
Height Fluctuations for the Stationary KPZ Equation
Springer Science and Business Media LLC - Tập 18 - Trang 1-95 - 2015
We compute the one-point probability distribution for the stationary KPZ
equation (i.e. initial data $\mathcal {H}(0,X)=B(X)$ , for B(X) a two-sided
standard Brownian motion) and show that as time T goes to infinity, the
fluctuations of the height function $\mathcal {H}(T,X)$ grow like T 1/3 and
converge to those previously encountered in the study of the stationary totally
asymmetric simple exclu...
The Representation of Isometric Operators on C (1)(X)
Springer Science and Business Media LLC - Tập 13 - Trang 287-297 - 2010
In this paper,we introduce a new norm on C (1)(X), which is induced by a hexagon
on R 2, and prove that every isometric operator on C (1)(X) can be induced by a
homeomorphism of X, where X is a connected subset of R.
How One can Repair Non-integrable Kahan Discretizations. II. A Planar System with Invariant Curves of Degree 6
Springer Science and Business Media LLC - Tập 24 - Trang 1-19 - 2021
We find a novel one-parameter family of integrable quadratic Cremona maps of the
plane preserving a pencil of curves of degree 6 and of genus 1. They turn out to
serve as Kahan-type discretizations of a novel family of quadratic vector fields
possessing a polynomial integral of degree 6 whose level curves are of genus 1,
as well. These vector fields are non-homogeneous generalizations of reduced N...
Existence, Non-existence, and Uniqueness for a Heat Equation with Exponential Nonlinearity in ℝ2
Springer Science and Business Media LLC - - 2015
Weakly Periodic Gibbs Measures of the Ising Model on the Cayley Tree of Order Five and Six
Springer Science and Business Media LLC - - 2018
Phase Transition in the Density of States of Quantum Spin Glasses
Springer Science and Business Media LLC - Tập 17 - Trang 441-464 - 2014
We prove that the empirical density of states of quantum spin glasses on
arbitrary graphs converges to a normal distribution as long as the maximal
degree is negligible compared with the total number of edges. This extends the
recent results of Keating et al. (2014) that were proved for graphs with bounded
chromatic number and with symmetric coupling distribution. Furthermore, we
generalise the re...
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