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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
Vladimir N. Grebenev, Martin Oberlack
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...... hiện toàn bộ
Stationary currents in long-range interacting magnetic systems
Springer Science and Business Media LLC - Tập 23 - Trang 1-25 - 2020
Roberto Boccagna
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...... hiện toàn bộ
Supersymmetric Polar Coordinates with Applications to the Lloyd Model
Springer Science and Business Media LLC - Tập 23 Số 1 - Trang 1-21 - 2020
Disertori, Margherita, Lager, Mareike
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...... hiện toàn bộ
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
Richard Froese, David Hasler, Wolfgang Spitzer
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 ...... hiện toàn bộ
Height Fluctuations for the Stationary KPZ Equation
Springer Science and Business Media LLC - Tập 18 - Trang 1-95 - 2015
Alexei Borodin, Ivan Corwin, Patrik Ferrari, Bálint Vető
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 ...... hiện toàn bộ
The Representation of Isometric Operators on C (1)(X)
Springer Science and Business Media LLC - Tập 13 - Trang 287-297 - 2010
Jingke Li
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
Misha Schmalian, Yuri B. Suris, Yuriy Tumarkin
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...... hiện toàn bộ
Existence, Non-existence, and Uniqueness for a Heat Equation with Exponential Nonlinearity in ℝ2
Springer Science and Business Media LLC - - 2015
Norisuke Ioku, Bernhard Ruf, Elide Terraneo
Weakly Periodic Gibbs Measures of the Ising Model on the Cayley Tree of Order Five and Six
Springer Science and Business Media LLC - - 2018
Nasir Ganikhodjaev, Музаффар Мухаммаджанович Рахматуллаев, Mohd Hirzie Rodzhan
Phase Transition in the Density of States of Quantum Spin Glasses
Springer Science and Business Media LLC - Tập 17 - Trang 441-464 - 2014
László Erdős, Dominik Schröder
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...... hiện toàn bộ
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