Network of inherent structures in spin glasses: scaling and scale-free distributions

The local minima (inherent structures) of a system and their associated transition links give rise to a network. Here we consider the topological and distance properties of such a network in the context of spin glasses. We use steepest descent dynamics, determining for each disorder sample the transition links appearing within a given barrier height. We find that differences between linked inherent structures are typically associated with local clusters of spins; we interpret this within a framework based on droplets in which the characteristic ``length scale'' grows with the barrier height. We also consider the network connectivity and the degrees of its nodes. Interestingly, for spin glasses based on random graphs, the degree distribution of the network of inherent structures exhibits a non-trivial scale-free tail.Comment: minor changes and references adde

Generation-free Agent-based Evolutionary Computing

AbstractMetaheuristics resulting from the hybridization of multi-agent systems with evolutionary computing are efficient in many optimization problems. Evolutionary multi-agent systems (EMAS) are more similar to biological evolution than classical evolutionary algorithms. However, technological limitations prevented the use of fully asynchronous agents in previous EMAS implementations. In this paper we present a new algorithm for agent-based evolutionary computations. The individuals are represented as fully autonomous and asynchronous agents. Evolutionary operations are performed continuously and no artificial generations need to be distinguished. Our results show that such asynchronous evolutionary operators and the resulting absence of explicit generations lead to significantly better results. An efficient implementation of this algorithm was possible through the use of Erlang technology, which natively supports lightweight processes and asynchronous communication

Network Transitivity and Matrix Models

This paper is a step towards a systematic theory of the transitivity (clustering) phenomenon in random networks. A static framework is used, with adjacency matrix playing the role of the dynamical variable. Hence, our model is a matrix model, where matrices are random, but their elements take values 0 and 1 only. Confusion present in some papers where earlier attempts to incorporate transitivity in a similar framework have been made is hopefully dissipated. Inspired by more conventional matrix models, new analytic techniques to develop a static model with non-trivial clustering are introduced. Computer simulations complete the analytic discussion.Comment: 11 pages, 7 eps figures, 2-column revtex format, print bug correcte

On the microscopic dynamics of DCC formation

The dynamics of the pion field after a quench is studied in the framework of the linear sigma model. Our aim is to determine to what extent the amplified pion field resembles the DCC picture originally proposed in the early '90s. We present the result of a computer experiment where, among other things, we study in detail the correlation between isospin orientations of the distinct modes of the field. We show that this correlation is absent. In a sense, the distinct modes behave as distinct DCCs. The implications of this observation are discussed.Comment: 19 pages, Latex2e, 7 figures in EPS, uses (included) boldgreek.sty and standard epsf package

Energy consumption and capacity utilization of galvanizing furnaces

An explicit equation leading to a method for improving furnace efficiency is presented. This equation is dimensionless and can be applied to furnaces of any size and fuel type for the purposes of comparison. The implications for current furnace design are discussed. Currently the technique most commonly used to reduce energy consumption in galvanizing furnaces is to increase burner turndown. This is shown by the analysis presented here actually to worsen the thermal efficiency of the furnace, particularly at low levels of capacity utilization. Galvanizing furnaces are different to many furnaces used within industry, as a quantity of material (in this case zinc) is kept molten within the furnace at all times, even outside production periods. The dimensionless analysis can, however, be applied to furnaces with the same operational function as a galvanizing furnace, such as some furnaces utilized within the glass industry. © IMechE 2004

Statistical ensemble of scale-free random graphs

A thorough discussion of the statistical ensemble of scale-free connected random tree graphs is presented. Methods borrowed from field theory are used to define the ensemble and to study analytically its properties. The ensemble is characterized by two global parameters, the fractal and the spectral dimensions, which are explicitly calculated. It is discussed in detail how the geometry of the graphs varies when the weights of the nodes are modified. The stability of the scale-free regime is also considered: when it breaks down, either a scale is spontaneously generated or else, a "singular" node appears and the graphs become crumpled. A new computer algorithm to generate these random graphs is proposed. Possible generalizations are also discussed. In particular, more general ensembles are defined along the same lines and the computer algorithm is extended to arbitrary (degenerate) scale-free random graphs.Comment: 10 pages, 6 eps figures, 2-column revtex format, minor correction

A Remark on the Renormalization Group Equation for the Penner Model

It is possible to extract values for critical couplings and gamma_string in matrix models by deriving a renormalization group equation for the variation of the of the free energy as the size N of the matrices in the theory is varied. In this paper we derive a ``renormalization group equation'' for the Penner model by direct differentiation of the partition function and show that it reproduces the correct values of the critical coupling and gamma_string and is consistent with the logarithmic corrections present for g=0,1.Comment: LaTeX, 5 pages, LPTHE-Orsay-94-5

An efficient method for the incompressible Navier-Stokes equations on irregular domains with no-slip boundary conditions, high order up to the boundary

Common efficient schemes for the incompressible Navier-Stokes equations, such as projection or fractional step methods, have limited temporal accuracy as a result of matrix splitting errors, or introduce errors near the domain boundaries (which destroy uniform convergence to the solution). In this paper we recast the incompressible (constant density) Navier-Stokes equations (with the velocity prescribed at the boundary) as an equivalent system, for the primary variables velocity and pressure. We do this in the usual way away from the boundaries, by replacing the incompressibility condition on the velocity by a Poisson equation for the pressure. The key difference from the usual approaches occurs at the boundaries, where we use boundary conditions that unequivocally allow the pressure to be recovered from knowledge of the velocity at any fixed time. This avoids the common difficulty of an, apparently, over-determined Poisson problem. Since in this alternative formulation the pressure can be accurately and efficiently recovered from the velocity, the recast equations are ideal for numerical marching methods. The new system can be discretized using a variety of methods, in principle to any desired order of accuracy. In this work we illustrate the approach with a 2-D second order finite difference scheme on a Cartesian grid, and devise an algorithm to solve the equations on domains with curved (non-conforming) boundaries, including a case with a non-trivial topology (a circular obstruction inside the domain). This algorithm achieves second order accuracy (in L-infinity), for both the velocity and the pressure. The scheme has a natural extension to 3-D.Comment: 50 pages, 14 figure