Two-dimensional Finite Lattice Research Articles

In-plane vibration analysis of plates with periodic skeletal truss microstructures

The dynamic in-plane behavior of two-dimensional finite lattices with periodic microskeletal truss structures, made either by bar or beam elements, is studied adopting a homogenization asymptotic technique. The resulting equations are then analyzed for deriving relationships between reference cell properties and homogenized continuum properties. Specific selection criteria are found for geometric and material parameters of the reference cell in view of getting orthotropic as well as isotropic homogenized plates. Finally, the effects of microstructural properties on the vibrating behavior of the homogenized plate are investigated in terms of modal analysis, studying their influence on natural frequencies.

Localization Parameters for Two Interacting Particles in Disordered Two-Dimensional Finite Lattices

I study spreading of two interacting hardcore bosons in disordered two-dimensional finite lattices from an initial occupation of two adjacent sites. The parameters related to the spreading of the particles provide an insight on the effect of interaction. I find that the presence of interaction makes the particles less localized than the non-interacting ones within the range of disorder strength W ≤ 4 and interaction strength V ≤ 4 . If the interaction strength is higher, then particles localize more. A transition with changes in the character of dominant correlations is found at critical disorder strengths for each chosen strength of interaction. The nature of correlations between the particles as nearest neighbours becomes dominant beyond these disorder strengths.

Critical behavior of a two-species reaction–diffusion problem in 2D

In this work we study the critical behavior of a model that simulates the propagation of an epidemic process over a population. We simulate the model on two-dimensional finite lattices to determine the critical density of the diffusive population. A finite size scaling analysis is employed to determine the order parameter and correlation length critical exponents.

Spin magnetization of a strongly correlated electron gas confined in a two-dimensional finite lattice

The influence of disorder and interaction on the ground state polarization of the two-dimensional (2D) correlated electron gas is studied by numerical investigations of unrestricted Hartree-Fock equations. The ferromagnetic ground state is found to be plausible when the electron number is lowered and the interaction and disorder parameters are suitably chosen. For a finite system at constant electronic density the disorder induced spin polarization is cut off when the electron orbitals become strongly localized to the individual network sites. The fluctuations of the interaction matrix elements are calculated and brought out as favoring the ferromagnetic instability in the extended and weak localization regime. The localization effect of the Hubbard interaction term is discussed.

Nonlocal lattice fermionic models on a two-dimensional torus

Abelian fermionic models described by the SLAC action on a two-dimensional finite lattice are considered. In vector U(1) models modified by introducing additional Pauli-Villars regularization, nonlocal effects are suppressed, and the results are in good agreement with the continuous-theory results. For chiral fermions, the lattice determinant phase differs from the determinant phase in the continuous theory.

Kinetic theory of ligand recombination of myoglobin: a model for a combination of entropic and enthalpic effects

A kinetic theory of ligand recombination of myoglobin is obtained through a microscopic model. The macroscopic time dependent rate constant is obtained by the first passage time distribution random walk method. When the ligand is outside the haem pocket, it diffuses in a continuum space. In this process, this rate corresponds to a Smoluchowski rate constant times the concentration of myoglobin. After penetrating through the hydration shell, the ligand waits in front of the gate or diffuses on the myoglobin surface for entering the gate. This waiting time refers to a large scale fluctuation of protein to open the gate. When the ligand is inside the pocket, the motion of the ligand ranges from a ballistic to a diffusive limit. To cover the whole range of friction, it is necessary to solve exactly a finite area random walk model with periodic gating in one- and two-dimensional finite lattices with slippery boundary conditions. Protein dynamics influence the ligand motion indirectly through the collision between the ligand and the heme pocket well. The first step corresponds to an adiabatic dissociation process. A branching diagram method is used to show a detailed pathway analysis of the adiabaticity by introducing intermediate states in the quintet states for the CO ligand binding. The rate theories of ligand recombination of myoglobin are a combination of entropic and enthalpic effects.

Infrared renormalons and finite volume

We analyze the perturbative expansion of a condensate in the O( N) non-linear sigma model for large N on a two-dimensional finite lattice. On an infinite volume this expansion is affected by an infrared renormalon. We extrapolate this analysis to the case of the gluon condensate of Yang-Mills theory and argue that infrared renormalons can be detected by performing perturbative studies even on relatively small lattices.

On the static approximation for the Hubbard Hamiltonian

We study the validity of the static approximation for the Hubbard model. We compare results obtained within the static approximation on two-dimensional finite lattices with results obtained from exact diagonalization and Monte Carlo simulations. We find that the static approximation is quite accurate at high temperatures but breaks down at low temperatures. One reason for its failure is that the static approximation destroys the rotational invariance in spin space.

Random walks on finite lattices with traps

We consider dissipative processes involving both chemical reaction and physical diffusion in systems for which the influence of boundaries and system size on the dynamics cannot be neglected. We report the results of Monte Carlo simulations on an irreversible reaction in a confined system subject to two sorts of finite boundary conditions. The problem is posed in such a way as to take maximal advantage of two earlier studies: Montroll's work on random walks on $d$-dimensional periodic lattices with traps, and the work of Sanders, Ruijgrok, and ten Bosch on random walks on two-dimensional finite lattices with traps. Our results are used to discuss the concept of reduction of dimensionality as introduced by Adam and Delbr\"uck in their study of biological diffusion processes.