Acoplamientos óptimos de caminos de longitud dos

96 páginas. Maestría en Optimización.Let P be a set of 3k points in the Euclidean plane. A 3-matching is a partition of P into k subsets of 3 points each, called triplets. The cost of each triplet fa; b; cg is given by minfjabj + jbcj; jbcj + jcaj; jcaj + jabjg, and the cost of the 3-matching is the sum of the costs of its triplets. The Euclidean 3-matching problem consists on finding a minimum cost 3-matching of P under the Euclidean metric. In the usual formulation of the Euclidean 3- matching problem we need to find a minimum cost 3-matching of P. This problem has several applications, especially in the insertion of components on a printed circuit board. Johnsson, Magyar, and Nevalainen introduced two integer programming formulations for this problem, and proved that its decision version is NP-complete if each triplet has an arbitrary positive cost (i.e., not necessarily Euclidean). The problem remains NP-complete even if the points of P correspond to vertices of a unit distance graph (a metric cost function). In this work, we prove that the linear programming relaxations of these two models are equivalent. Then we introduce three new integer programming models that use fewer variables than those from Johnsson, Magyar, and Nevalainen. We also compare the linear programming relaxations of the models. Besides the minimization problem, we are also interested in a similar maximization problem: finding a maximum cost non-crossing Euclidean 3-matching of P, where non-crossing means that no two segments intersect in a common interior point. Both problems, minimum cost and maximum cost non-crossing, are challenging, and we believe that both are NP-hard. Exact solutions to both problems can be attained through integer programming; however, in order to obtain good solutions in feasible times, we fix our attention to heuristics. We present three heuristics specially designed for our problems and compare their solutions and execution times against solving the exact models

Violations of local equilibrium and linear response in classical lattice theories

We study the dynamics of $\phi^4$ theory and the FPU $\beta$ model under thermal gradients, from first principles. We analyze quantitatively how local equilibrium and linear response are violated, paying special care to how we find observables that unambiguously display these violations. Relations between these quantities to equations of state are also examined. Further, we discuss how we can approach similar dynamical problems in continuum quantum field theory. We analyze how close we are to obtaining the continuum results.Comment: 7pp, 4figs, talk given by KA at "Thermal field theory and applications" workshop 200

Entropy and Entropy Production in Some Applications

By using entropy and entropy production, we calculate the steady flux of some phenomena. The method we use is a competition method, $S_S/\tau+\sigma={\it maximum}$, where $S_S$ is system entropy, $\sigma$ is entropy production and $\tau$ is microscopic interaction time. System entropy is calculated from the equilibrium state by studying the flux fluctuations. The phenomena we study include ionic conduction, atomic diffusion, thermal conduction and viscosity of a dilute gas

Tris{N-[(anthracen-9-yl)methyl­ene­amino]thio­ureato}cobalt(III) tetra­hydrate

In the title complex, [Co(C16H12N3S)3]·4H2O, the central CoIII atom is in a distorted octa­hedral coordination environment. There are three N-[(anthracen-9-yl)­methyl­ene­amino]­thio­ureate ligands coordinated to the CoIII atom via three imine N and three thio­amide S atoms. The Co—S and Co—N bond distances are in expected ranges [2.2194 (8)—2.2545 (8) and 1.926 (2)—1.985 (2)Å, respectively]. The endocyclic S—Co—N bond angles in the five-membered chelate rings range from 82.91 (7) to 85.33 (7)°. The structure contains four water mol­ecules which are disordered over 12 sites and link the complex mol­ecules into a three-dimensional network through N—H⋯O, O—H⋯O, O—H⋯N, and O—H⋯S hydrogen bonds

Thermodynamic Variables In The Context Of A Nonequilibrium Statistical Ensemble Approach

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Large Deviation Property of Free Energy in p-Body Sherrington-Kirkpatrick Model

Cumulant generating function phi(n) and rate function Sigma(f) of the free energy is evaluated in p-body Sherrington-Kirkpatrick model by using the replica method with the replica number n finite. From a perturbational argument, we show that the cumulant generating function is constant in the vicinity of n = 0. On the other hand, with the help of two analytic properties of phi(n), the behavior of phi(n) is derived again. However this is also shown to be broken at a finite value of n, which gives a characteristic value in the rate function near the thermodynamic value of the free energy. Through the continuation of phi(n) as a function of n, we find out a way to derive the 1RSB solution at least in this model, which is to fix the RS solution to be a monotone increasing function.Comment: 7 pages, 5 figures. accepted for publication in J.Phs.Soc.Jp

Violations of local equilibrium and stochastic thermostats

We quantitatively investigate the violations of local equilibrium in the $\phi^4$ theory under thermal gradients, using stochastic thermostats. We find that the deviations from local equilibrium can be quite well described by a behavior $\sim(\nabla T)^2$. The dependence of the quantities on the thermostat type is analyzed and its physical implications are discussed.Comment: 5pp, 3 fig

Higher-order hydrodynamics: Extended Fick's Law, evolution equation, and Bobylev's instability

A higher-order hydrodynamics for material motion in fluids, under arbitrary nonequilibrium conditions, is constructed. We obtain what is a generalized-to that conditions-Fick-type Law. It includes a representation of Burnett-type contributions of all order, in the form of a continuous-fraction expansion. Also, the equation includes generalized thermodynamic forces. which are characterized and discussed. All kinetic coefficients are given as correlations of microscopic mechanical quantities averaged over the nonequilibrium ensemble, and then are time- and space-dependent as a consequence of accounting for the dissipative processes that are unfolding in the medium. An extended evolution equation for the density of particles is derived, and the conditions when it goes over restricted forms of the type of the telegraphist equation and Fick's diffusion equation are presented. (C) 2002 American Institute of Physics.11641571158

Status of QCD

I have been asked to discuss the status of QCD. It seems to me that there are three main points to be made about the present status of QCD: $\bullet$ QCD is right, and we can do many beautiful things with it. $\bullet$ There are several important concrete problems that lie just beyond the edge of our current understanding. $\bullet$ There are some foundational issues in QCD, and some recent developments, that may point toward entirely new directions. These points will, I believe, emerge quite clearly from the following more detailed discussion. The discussion will be in three parts. I'll first discuss elementary processes, then more complicated processes, and then finally foundational issues.Comment: 28 pages, use Phyzzx, figures available by FAX or mail on request, IASSNS-HEP-93/6

Evolution of dissipative processes via a statistical thermodynamic approach. II. Thermodynamic properties of a fluid of bosons

On the basis of the generalized Mori-Heisenberg-Langevin equations presented in the preceding paper, we derive and analyze the informational-statistical thermodynamic properties of a fluid of bosons away from equilibrium. We derive the informational entropy and its production, proceeding to an analysis of the several contributions to these state functions arising out of the evolution of dissipative processes in the system. (C) 1998 American Institute of Physics.108187580758