arXiv subjects

L. Molinari

Publications and source records attributed to L. Molinari.

10 recordsLinked to original sources

arXiv2026

Volumetric locking-free Mixed Virtual Element Methods for Contact Problems

We consider the approximation of the 2D frictionless contact problem in elasticity using the Virtual Element Methods (VEMs). To overcome the volumetric locking phenomenon in the nearly incompressible case, we adopt a mixed displacement/pressure ($u/p$) variational formulation, where pressure is introduced as an independent unknown. We present the VEM discretization and develop a general error analysis, keeping explicit track of the constants involved in the error estimates, thus allowing to consider meshes with "small edges". As examples, we consider two possible VEM schemes: a first-order scheme and a second-order scheme. The numerical results confirm the theoretical predictions, specifically both schemes show: 1) robustness with respect to the volumetric parameter $\lambda$, thus preventing the occurrence of the volumetric locking phenomenon; 2) good behavior even in the presence of "small edges"; 3) achievement of the expected theoretical convergence rates.

math.NA↗

arXiv2003

Spectral duality and distribution of exponents for transfer matrices of block tridiagonal Hamiltonians

I consider a general block tridiagonal matrix and the corresponding transfer matrix. By allowing for a complex Bloch parameter in the boundary conditions, the two matrices are related by a spectral duality. As a consequence, I derive some analytic properties of the exponents of the transfer matrix in terms of the eigenvalues of the (non-Hermitian) block matrix. Some of them are the single-matrix analogue of results holding for Lyapunov exponents of an ensemble of block matrices, which occur in models of transport. The counting function of exponents is related to winding numbers of eigenvalues. I discuss some implications of duality on the distribution (real bands and complex arcs) and the dynamics of eigenvalues.

math-ph↗

arXiv2002

Virtual Photon Contribution to Frictional Drag in double-layer Devices

The first order contribution to frictional drag in bi-layered fermion gas is examined. We discuss the relevance of single photon exchange in the evaluation of transresistance, which is usually explained by second order effects such as Coulomb and phonon drag. Since the effective e.m. interaction is unscreened, in the d.c. limit we obtain a finite (and large) contribution to transconductivity.

cond-mat.mes-hall↗

arXiv2002

Enumeration of simple random walks and tridiagonal matrices

We present some old and new results in the enumeration of random walks in one dimension, mostly developed in works of enumerative combinatorics. The relation between the trace of the $n$-th power of a tridiagonal matrix and the enumeration of weighted paths of $n$ steps allows an easier combinatorial enumeration of the paths. It also seems promising for the theory of tridiagonal random matrices .

cond-mat.stat-mech↗

arXiv2001

Yang-Mills Integrals

Two results are presented for reduced Yang-Mills integrals with different symmetry groups and dimensions: the first is a compact integral representation in terms of the relevant variables of the integral, the second is a method to analytically evaluate the integrals in cases of low order. This is exhibited by evaluating a Yang-Mills integral over real symmetric matrices of order 3.

hep-th↗

arXiv1999

Non-Hermitian tridiagonal random matrices and returns to the origin of a random walk

We study a class of tridiagonal matrix models, the "q-roots of unity" models, which includes the sign ($q=2$) and the clock ($q=\infty$) models by Feinberg and Zee. We find that the eigenvalue densities are bounded by and have the symmetries of the regular polygon with $2 q$ sides, in the complex plane. Furthermore the averaged traces of $M^k$ are integers that count closed random walks on the line, such that each site is visited a number of times multiple of $q$. We obtain an explicit evaluation for them.

cond-mat.stat-mech↗

arXiv1999

Non-universality of compact support probability distributions in random matrix theory

The two-point resolvent is calculated in the large-n limit for the generalized fixed and bounded trace ensembles. It is shown to disagree with the one of the canonical Gaussian ensemble by a non-universal part which is given explicitly for all monomial potentials $V(M)=M^{2p}$. Moreover, we prove that for the generalized fixed and bounded trace ensemble all k-point resolvents agree in the large-n limit, despite their non-universality.

cond-mat↗

arXiv1998

Compact support probability distributions in random matrix theory

We consider a generalization of the fixed and bounded trace ensembles introduced by Bronk and Rosenzweig up to an arbitrary polynomial potential. In the large-N limit we prove that the two are equivalent and that their eigenvalue distribution coincides with that of the "canonical" ensemble with measure exp[-$n$Tr V(M)]. The mapping of the corresponding phase boundaries is illuminated in an explicit example. In the case of a Gaussian potential we are able to derive exact expressions for the one- and two-point correlator for finite $n$, having finite support.

cond-mat↗

arXiv1995

Parametric Spectral Correlations of Disordered Systems in the Fourier Domain

A Fourier analysis of parametric level dynamics for random matrices periodically depending on a phase is developed. We demonstrate both theoretically and numerically that under very general conditions the correlation $C(φ)$ of level velocities is singular at $φ=0$ for any symmetry class; the singularity is revealed by algebraic tails in Fourier transforms, and is milder, the stronger the level repulsion in the chosen ensemble. The singularity is strictly connected with the divergence of the 2nd moments of level derivatives of appropriate order, and its type is specified to leading terms for Gaussian, stationary ensembles of GOE, GUE, GSE types, and for the Gaussian ensemble of Periodic Banded Random Matrices, in which a breaking of symmetry occurs. In the latter case, we examine the behaviour of correlations in the diffusive regime and in the localized one as well, finding a singularity like that of pure GUE cases. In all the considered ensembles we study the statistics of the Fourier coefficients of eigenvalues, which are Gaussian distributed for low harmonics, but not for high ones, and the distribution of kinetic energies.

chao-dyn↗

arXiv1994

A Matrix Model for Random Surfaces with Dynamical Holes

A matrix model to describe dynamical loops on random planar graphs is analyzed. It has similarities with a model studied by Kazakov, few years ago, and the O(n) model by Kostov and collaborators. The main difference is that all loops are coherently oriented and empty. The free energy is analytically evaluated and the two critical phases are analyzed, where the free energy exhibits the same critical behaviour of Kazakov's model, thus confirming the universality of the description in the continuum limit (surface with small holes, and the tearing phase). A third phase occurs on the boundary separating the above phase regions, and is characterized by a different singular behaviour, presumably due to the orientation of loops.

hep-th↗