The role of the nature of the noise in the thermal conductance of mechanical systems

Focussing on a paradigmatic small system consisting of two coupled damped oscillators, we survey the role of the L\'evy-It\^o nature of the noise in the thermal conductance. For white noises, we prove that the L\'evy-It\^o composition (Lebesgue measure) of the noise is irrelevant for the thermal conductance of a non-equilibrium linearly coupled chain, which signals the independence between mechanical and thermodynamical properties. On the other hand, for the non-linearly coupled case, the two types of properties mix and the explicit definition of the noise plays a central role.Comment: 9 pages, 2 figures. To be published in Physical Review

Critical scaling in standard biased random walks

The spatial coverage produced by a single discrete-time random walk, with asymmetric jump probability $p\neq 1/2$ and non-uniform steps, moving on an infinite one-dimensional lattice is investigated. Analytical calculations are complemented with Monte Carlo simulations. We show that, for appropriate step sizes, the model displays a critical phenomenon, at $p=p_c$. Its scaling properties as well as the main features of the fragmented coverage occurring in the vicinity of the critical point are shown. In particular, in the limit $p\to p_c$, the distribution of fragment lengths is scale-free, with nontrivial exponents. Moreover, the spatial distribution of cracks (unvisited sites) defines a fractal set over the spanned interval. Thus, from the perspective of the covered territory, a very rich critical phenomenology is revealed in a simple one-dimensional standard model.Comment: 4 pages, 4 figure

Exact Nonequilibrium Work Generating Function for a Small Classical System

We obtain the exact nonequilibrium work generating function (NEWGF), for a small system consisting of a massive Brownian particle connected to internal and external springs. The external work is provided to the system for a finite time interval. The Jarzynski equality (JE), obtained in this case directly from the NEWGF, is shown to be valid for the present model, in an exact way regardless of the rate of external work

On exact time-averages of a massive Poisson particle

In this work we study, under the Stratonovich definition, the problem of the damped oscillatory massive particle subject to a heterogeneous Poisson noise characterised by a rate of events, \lambda (t), and a magnitude, \Phi, following an exponential distribution. We tackle the problem by performing exact time-averages over the noise in a similar way to previous works analysing the problem of the Brownian particle. From this procedure we obtain the long-term equilibrium distributions of position and velocity as well as analytical asymptotic expressions for the injection and dissipation of energy terms. Considerations on the emergence of stochastic resonance in this type of system are also set forth.Comment: 21 pages, 5 figures. To be published in Journal of Statistical Mechanics: Theory and Experimen

Short-Range Ising Spin Glass: Multifractal Properties

The multifractal properties of the Edwards-Anderson order parameter of the short-range Ising spin glass model on d=3 diamond hierarchical lattices is studied via an exact recursion procedure. The profiles of the local order parameter are calculated and analysed within a range of temperatures close to the critical point with four symmetric distributions of the coupling constants (Gaussian, Bimodal, Uniform and Exponential). Unlike the pure case, the multifractal analysis of these profiles reveals that a large spectrum of the $\alpha$-H\"older exponent is required to describe the singularities of the measure defined by the normalized local order parameter, at and below the critical point. Minor changes in these spectra are observed for distinct initial distributions of coupling constants, suggesting an universal spectra behavior. For temperatures slightly above T_{c}, a dramatic change in the $F(\alpha)$ function is found, signalizing the transition.Comment: 8 pages, LaTex, PostScript-figures included but also available upon request. To be published in Physical Review E (01/March 97

On Tackling the Limits of Resolution in SAT Solving

The practical success of Boolean Satisfiability (SAT) solvers stems from the CDCL (Conflict-Driven Clause Learning) approach to SAT solving. However, from a propositional proof complexity perspective, CDCL is no more powerful than the resolution proof system, for which many hard examples exist. This paper proposes a new problem transformation, which enables reducing the decision problem for formulas in conjunctive normal form (CNF) to the problem of solving maximum satisfiability over Horn formulas. Given the new transformation, the paper proves a polynomial bound on the number of MaxSAT resolution steps for pigeonhole formulas. This result is in clear contrast with earlier results on the length of proofs of MaxSAT resolution for pigeonhole formulas. The paper also establishes the same polynomial bound in the case of modern core-guided MaxSAT solvers. Experimental results, obtained on CNF formulas known to be hard for CDCL SAT solvers, show that these can be efficiently solved with modern MaxSAT solvers

Substratos no desenvolvimento inicial de quatro cultivares de pessegueiro e uma nectarineira.

Entre os fatores que contribuem para melhor desenvolvimento inicial das plantas, estão a qualidade da semente e o substrato utilizado.Objetivou-se avaliar o efeito do substrato na formação inicial de pessegueiro e nectarineira. O trabalho foi realizado no Departamento de Fitotecnia, da Universidade Federal de Viçosa, de fevereiro a março de 2004. Foram utilizados quatro cultivares de pessegueiro, 'Alô Doçura', 'Campinas 1', 'Relíquia' e 'Ouromel' e uma cultivar de nectarineira 'Josefina'. Sementes retiradas de frutos maturos, foram estratificadas em câmara fria, com temperatura de 5±1ºC e ausência de luz. Após a germinação, no interior da casa-de-vegetação, procedeu-se à semeadura em recipientes plásticos (3 litros), contendo os substratos: Plantmax®; Plantmax® + Areia (1:1 v/v); Plantmax® + Latossolo Vermelho (1:1 v/v); Plantmax® + Latossolo Vermelho + Areia (1:1:1 v/v). Foi utilizado o delineamento experimental inteiramente casualizado, num fatorial 5 x 4 (cultivar x substrato), com cinco repetições, considerando-se como unidade experimental cada recipiente plástico. Após 38 dias da semeadura foram analisadas: porcentagem de emergência, número de folhas, comprimento total, altura e comprimento de raiz, diâmetro do caule, massa da matéria seca total, da parte aérea e da raiz e o número de brotações primárias. O substrato teve efeito no desenvolvimento inicial de pessegueiro, obtendo-se os melhores resultados com o substrato comercial Plantmax®. O maior acúmulo de massa de matéria seca total e da parte aérea foi obtido com os cultivares 'Campinas 1' e 'Relíquia', sendo que esse último, também proporcionou maior número de brotações primárias