Search results for "Zero mean"
showing 5 items of 5 documents
On delocalization of eigenvectors of random non-Hermitian matrices
2019
We study delocalization of null vectors and eigenvectors of random matrices with i.i.d entries. Let $A$ be an $n\times n$ random matrix with i.i.d real subgaussian entries of zero mean and unit variance. We show that with probability at least $1-e^{-\log^{2} n}$ $$ \min\limits_{I\subset[n],\,|I|= m}\|{\bf v}_I\| \geq \frac{m^{3/2}}{n^{3/2}\log^Cn}\|{\bf v}\| $$ for any real eigenvector ${\bf v}$ and any $m\in[\log^C n,n]$, where ${\bf v}_I$ denotes the restriction of ${\bf v}$ to $I$. Further, when the entries of $A$ are complex, with i.i.d real and imaginary parts, we show that with probability at least $1-e^{-\log^{2} n}$ all eigenvectors of $A$ are delocalized in the sense that $$ \min\l…
Numerical Evidences of Polarization Switching in PMN Type Relaxor Ferroelectrics
2011
We present a conceptual and computational framework for chemically ordered Pb(Mg 1/3 Nb 2/3 O 3) (PMN) type supercells violating disorder of the host lattice. The effective Hamiltonian is specified by invariance under permutations of supercells and by the dipole-dipole interaction supporting both local nonzero and zero mean polarization of the structure. Statistics treated in canonical ensemble within the mean field approach reveals emergence of polar nanoregions as supported by interplay between the (random) initial state polarization of supercells and their interactions increased at cooling.
Relations between cavitation erosion resistance of materials and their fatigue strength under random loading
1999
Abstract The paper contains results of tests on fatigue strength under uniaxial random loading and cavitation erosion resistance for three steels: 10HNAP, 18G2A and 15G2ANb. The obtained fatigue and cavitation characteristics were used for determination of relations between these two phenomena. From the analysis it appears that there is correlation between fatigue strength of the material under random loading and its cavitation erosion resistance. It has been shown that fatigue tests under random loading and tests on cavitation erosion of 10HNAP, 18G2A and 15G2ANb steels may be described with a mathematical model of the same type. It has been also found that there is a linear relation, in t…
Exact constants in Poincaré type inequalities for functions with zero mean boundary traces
2014
In this paper, we investigate Poincare type inequalities for the functions having zero mean value on the whole boundary of a Lipschitz domain or on a measurable part of the boundary. We find exact and easily computable constants in these inequalities for some basic domains (rectangles, cubes, and right triangles) and discuss applications of the inequalities to quantitative analysis of partial differential equations. Copyright © 2014 John Wiley & Sons, Ltd.
FATIGUE FAILURE CRITERIA FOR MATERIALS UNDER RANDOM TRIAXIAL STATE OF STRESS
1984
SUMMARY Five fatigue failure criteria are formulated for a random triaxial state of stress whose components have zero mean values. It is assumed that fatigue failure is determined by the stress and strain components that act on an expected fracture plane. It is shown that in some special cases the proposed failure theories reduce to classical theories applied for sinusoidal stresses.