International Journal of Modern Physics C

This paper discusses a computing architecture that uses both classical parallelism and quantum parallelism. We consider a large parallel array of small quantum computers, connected together by classical communication channels. This kind of computer is called a type-II quantum computer, to differentiate it from a globally phase-coherent quantum computer, which is the first type of quantum computer that has received nearly exclusive attention in the literature. Although a hybrid, a type-II quantum computer retains the crucial advantage allowed by quantum mechanical superposition that its computational power grows exponentially in the number of phase-coherent qubits per node, only short-range and short time phase-coherence is needed, which significantly reduces the level of engineering facility required to achieve its construction. Therefore, the primary factor limiting its computational power is an economic one and not a technological one, since the volume of its computational medium can in principle scale indefinitely.

Presented is a factorized quantum lattice-gas algorithm to model the diffusion equation. It is a minimal model with two qubits per node of a one-dimensional lattice and it is suitable for implementation on a large array of small quantum computers interconnected by nearest-neighbor classical communication channels. The quantum lattice-gas system is described at the mesoscopic scale by a lattice-Boltzmann equation whose collision term is unconditionally stable and obeys the principle of detailed balance. An analytical treatment of the model is given to predict a macroscopic effective field theory. The numerical simulations are in excellent agreement with the analytical results. In particular, numerical simulations confirm the value of the analytically calculated diffusion constant. The algorithm is time-explicit with numerical convergence that is first-order accurate in time and second-order accurate in space.

The problem of obtaining the material systems with more enhanced material constants characterizing physical property is considered within the framework of Suh's theory of design. The design problem is to find the mapping between the functional requirements (FR) and the design parameters (DP). The material parameters (the design parameters) for the material design are unable to move freely. Thus, our strategy is to substantially decrease the number of design parameters and to learn which directions to move the design parameters in order to efficiently enhance the material constants. To accomplish, we study the mathematical properties of the relationship, called design function, between the FRs and the DPs to find the decomposition property. The decomposition has several effective properties. We apply our method to a special case where the third-order nonlinear optical susceptibility is enhanced. We also discuss some methods for moving the material parameters as well as the scope of problems where the concept of decomposition seems to be effective.

We present the effect of regulations on self-organized market by using biological model of Bak–Sneppen in higher dimensions. This study extends the idea of Cuniberti et al. The higher-dimensional description of the market receives less effect of regulation than that of lower one.

The Korteweg-de Vries-typed equations are the most important class of nonlinear evolution equations, with numerous applications in physical and engineering sciences. In this paper, for the deformed Korteweg-de Vries equation of the form , we make use of computerized symbolic computation and obtain several families of new exact analytic solutions, some of which are solitonic.

A standard Genetic Algorithm is applied to a set of test problems, three of them taken from physics and the rest analytical expressions explicitly constructed to test search procedures. The relation between mutation rate and population size in the search for optimum performance is obtained showing similar behavior in these problems.

With computerized symbolic computation, we present an auto-Bäcklund transformation and three families of soliton-like solutions to the modified dispersive water wave equations.

In this work, we have proposed a new geometrical method for calculating the critical temperature and critical exponents by introducing a set of bond breaking probability values. The probability value P_c corresponding to the Coniglio–Klein probability for the transition temperature is obtained among this set of trial probabilities. Critical temperature, thermal and magnetic exponents are presented for d = 2 and d = 3, q = 2 Potts model and for the application of the method to the system with first order phase transition, q = 7 Potts model on different size lattices are employed.

The advantage of this method can be that the bond breaking probability can be applied, where the clusters are defined on a set of dynamic variables, which are different from the dynamic quantities of the actual Hamiltonian or the action of the full system. An immediate application can be to use the method on finite temperature lattice gauge theories.

We study the simple evolutionary process in which we repeatedly find the least fit agent in a population of agents and give it a new fitness, which is chosen independently at random from a specified distribution. We show that many of the average properties of this process can be calculated exactly using analytic methods. In particular, we find the distribution of fitnesses at arbitrary time, and the distribution of the lengths of runs of hits on the same agent, the latter being found to follow a power law with exponent -1, similar to the distribution of times between evolutionary events in the Bak–Sneppen model and models based on the so-called record dynamics. We confirm our analytic results with extensive numerical simulations.

The modified Kadomtsev–Petviashvili (MKP) models describe the large-scale motion of such rotating fluids as the atmosphere and oceans. Based on the computerized symbolic computation, we in this paper extend the power of the variable-coefficient balancing-act method, which is recently proposed, to a variable-coefficient MKP model. The model is re-written as a coupled set of partial differential equations, and the algorithm is re-written correspondingly. We obtain a new family of the soliton-like, exact analytic solutions, beyond the traveling waves.

The structural stability of carbon nanoballs (fullerenes) C₂₀, C₆₀, and onion type C₂₀@C₆₀ has been investigated by performing molecular-dynamics computer simulations. Calculations have been realized by using an empirical many-body potential energy function for carbon. It has been found that C₂₀ is relatively resistive to heat treatment, however, the onion type structure is relatively less strong against heat treatment. The electronic structure of the systems considered has been also studied by performing density functional theory type calculations.

The two-dimensional ferromagnetic Blume–Capel model is simulated on a cellular automaton, which based on the Creutz cellular automaton for square lattice. The values of the critical temperature and the static critical exponents are estimated within the framework of the finite-size scaling theory for 0 ≤ D/J ≤ 1.5. The results are compatible with the universal Ising critical behavior.