Ground-State Properties and Phase Separation of Binary Mixtures in Mesoscopic Ring Lattices

We investigated the spatial phase separation of the two components forming a bosonic mixture distributed in a four-well lattice with a ring geometry. We studied the ground state of this system, described by means of a binary Bose–Hubbard Hamiltonian, by implementing a well-known coherent-state picture which allowed us to find the semi-classical equations determining the distribution of boson components in the ring lattice. Their fully analytic solutions, in the limit of large boson numbers, provide the boson populations at each well as a function of the interspecies interaction and of other significant model parameters, while allowing to reconstruct the non-trivial architecture of the ground-state four-well phase diagram. The comparison with the L-well (L=2,3) phase diagrams highlights how increasing the number of wells considerably modifies the phase diagram structure and the transition mechanism from the full-mixing to the full-demixing phase controlled by the interspecies interaction. Despite the fact that the phase diagrams for L=2,3,4 share various general properties, we show that, unlike attractive binary mixtures, repulsive mixtures do not feature a transition mechanism which can be extended to an arbitrary lattice of size L.

Finite size scaling in the heterogeneous reaction 2A + B2 → 2AB

In the present paper we extend the exact solution previously obtained for the heterogeneous catalytic reaction 2A + B2 → 2AB on small domains, to arbitrary lattice sizes () and calculate the average number of reactive steps necessary to poison the lattice first, . We determine as a function of through Monte Carlo simulations previously contrasted with the exact solution in lattices. We show that follows a power law with , without appreciable transient behaviors, and a scale factor () dependent on the two parameters of the model, the sticking coefficient probability and the desorption probability . The dependence of on both and is determined.

ON THE CONSTRUCTION OF PARTIAL DIFFERENCE SCHEMES II: DISCRETE VARIABLES AND SCHWARZIAN LATTICES

In the process of constructing invariant difference schemes which approximate partial differential equations we write down a procedure for discretizing a partial differential equation on an arbitrary lattice. An open problem is the meaning of a lattice which does not satisfy the Clairaut–Schwarz–Young theorem. To analyze it we apply the procedure on a simple example, the potential Burgers equation with two different lattices, an orthogonal lattice which is invariant under the symmetries of the equation and satisfies the commutativity of the partial difference operators and an exponential lattice which is not invariant and does not satisfy the Clairaut–Schwarz–Young theorem. A discussion on the numerical results is presented showing the different behavior of both schemes for two different exact solutions and their numerical approximations.

An efficient algorithm for computing the primitive bases of a general lattice plane

The atomistic structures of interfaces and their properties are profoundly influenced by the underlying crystallographic symmetries. Whereas the theory of bicrystallography helps in understanding the symmetries of interfaces, an efficient methodology for computing the primitive basis vectors of the two-dimensional lattice of an interface does not exist. In this article, an algorithm for computing the basis vectors for a plane with Miller indices (hkl) in an arbitrary lattice system is presented. This technique is expected to become a routine tool for both computational and experimental analysis of interface structures.

Nonnegative basis of a lattice

A nonnegative basis of a complete lattice is constructed. The criterion of existence of a nonnegative basis of an arbitrary lattice is proved. The problem of existence of a lattice basis from an arbitrary convex cone is investigated.

Research of the Minimum Vertex-Cover Solutions on the Tree and Lattice Structures

We focus the solution space of a most fundamental problem - Minimum Vertex-Cover problem - in theoretical computer science. After some rigorous analysis, we provide the formation mechanism of minimum vertex-cover solutions on the tree and give the organization of these solutions on arbitrary lattice structure. By the results, we can easily calculate the solution numbers on these structures and have better understanding of the hardness of Minimum Vertex-Cover problem. The proposed study and algorithm can make a new way on detecting the essential difficulty of NP-complete problems and designing efficient algorithms on solving them.