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Model off-lattice sequences in two dimensions are constructed so that their native states are close to an on-lattice target. The Hamiltonian involves the Lennard-Jones and harmonic interactions. The native states of these sequences are…
Lattice models with long-range interactions of power-law type are suggested as a new type of microscopic model for fractional non-local elasticity. Using the transform operation, we map the lattice equations into continuum equation with…
We report on a microscopic evaluation of electrodynamic response for the vortex lattice state of a model s-wave superconductor. Our calculation accounts self-consistently for both quasiparticle and order parameter response and establishes…
For a one-dimensional model in which the two-body interactions are long-range and strong, the system almost crystallizes. The harmonic modes of such a lattice can be used to compute the ground state wave function and the dynamical…
We present a study of electric transport at high temperature in a model of strongly interacting spinless fermions without disorder. We use exact diagonalization to study the statistics of the energy eigenvalues, eigenstates, and the matrix…
Nodal topological lattice is a form of magnetic crystal with topologically non-trivial spin texture, which further exhibits a periodic array of nodes with vanishing magnetization. Electronic structure for conduction electrons strongly…
We study the phase transition phenomena for long-range oriented percolation and contact process. We studied a contact process in which the range of each vertex are independent, updated dynamically and given by some distribution $N$. We also…
We establish an abstract local ergodic theorem, under suitable space-time scaling, for the (boundary-driven) symmetric exclusion process on an increasing sequence of balls covering an infinite weighted graph. The proofs are based on 1-block…
We introduce a contact law for the normal force generated between two contacting, elastically anisotropic bodies of arbitrary geometry. The only requirement is that their surfaces be smooth and frictionless. This anisotropic contact law is…
The study of random graphs has become very popular for real-life network modeling such as social networks or financial networks. Inhomogeneous long-range percolation (or scale-free percolation) on the lattice $\mathbb Z^d$, $d\ge1$, is a…
We study loop percolation models in two and in three space dimensions, in which configurations of occupied bonds are forced to form closed loop. We show that the uncorrelated occupation of elementary plaquettes of the square and the simple…
Elastic effects in a model of disordered nematic elastomers are numerically investigated in two dimensions. Networks crosslinked in the isotropic phase exhibit unusual soft mechanical response against stretching. It arises from gradual…
This paper studies the dynamics of isometries in the curtain model, which is used to capture the hyperbolicity in a fixed CAT(0) space. We establish several fundamental properties, fully classify the behavior of semisimple isometries of a…
Persistent currents and transport properties are investigated for the nano-graphite ribbons with zigzag shaped edges with paying attention to system length $L$ dependence. It is found that both the persistent current in the isolated ring…
Two-dimensional orbital compass model is studied as an interacting itinerant electron model. A Hubbard-type tight-binding model, from which the orbital compass model is derived in the strong coupling limit, is identified. This model is…
We explain how to build invisible isotropic conductivity perturbations of the unit conductivity in the framework of the point electrode model for two-dimensional electrical impedance tomography. The theoretical approach, based on solving a…
Using a tight binding model we calculate the conductance of monovalent atomic chains for different contact geometries. The leads connected to the chains are modelled as semi-infinite fcc lattices with different orientations and couplings.…
In this article we propose a discrete lattice model to simulate the elastic, plastic and failure behaviour of isotropic materials. Focus is given on the mathematical derivation of the lattice elements, nodes and edges, in the presence of…
A spatially one dimensional coupled map lattice possessing the same symmetries as the Miller Huse model is introduced. Our model is studied analytically by means of a formal perturbation expansion which uses weak coupling and the vicinity…
We investigate the phase diagram of the \tj Model on a triangular lattice using a Variational Monte-Carlo approach. We use an extended set of Gutzwiller projected fermionic trial wave-functions allowing for simultaneous magnetic and…