Heat fluctuations and fluctuation theorems in the case of multiple reservoirs

We consider heat fluctuations and fluctuation theorems for systems driven by multiple reservoirs. We establish a fundamental symmetry obeyed by the joint probability distribution for the heat transfers and system coordinates. The symmetry leads to a generalisation of the asymptotic fluctuation theorem for large deviations at large times. As a result the presence of multiple reservoirs influence the tails in the heat distribution. The symmetry, moreover, allows for a simple derivation of a recent exact fluctuation theorem valid at all times. Including a time dependent work protocol we also present a derivation of the integral fluctuation theorem.Comment: 27 pages, 1 figure, new extended version, to appear in J. Stat. Mech, (2014

Chaotic oscillations in singularly perturbed FitzHugh-Nagumo systems

We consider the singularly perturbed limit of periodically excited two-dimensional FitzHugh-Nagumo systems. We show that the dynamics of such systems are essentially governed by an one-dimensional map and present a numerical scheme to accurately compute it together with its Lyapunov exponent. We then investigate the occurrence of chaos by varying the parameters of the system, with especial emphasis on the simplest possible chaotic oscillations. Our results corroborate and complement some recent works on bifurcations and routes to chaos in certain particular cases corresponding to piecewise linear FitzHugh-Nagumo-like systems.Comment: 16 pages, 6 figures, final version to appear in Chaos, Solitons & Fractal

The Story of the Puerto Rican-Chicano Committee

The concept or idea for The Puerto Rican-Chicano Committee (PRCC) came from UB student Alberto O. Cappas, who also was the original founder of PODER, at the time known as the Puerto Rican Organization for Dignity, Elevation, and Responsibility

Shape fluctuations and elastic properties of two-component bilayer membranes

The elastic properties of two-component bilayer membranes are studied using a coarse grain model for amphiphilic molecules. The two species of amphiphiles considered here differ only in their length. Molecular Dynamics simulations are performed in order to analyze the shape fluctuations of the two-component bilayer membranes and to determine their bending rigidity. Both the bending rigidity and its inverse are found to be nonmonotonic functions of the mole fraction $x_{\rm B}$ of the shorter B-amphiphiles and, thus, do not satisfy a simple lever rule. The intrinsic area of the bilayer also exhibits a nonmonotonic dependence on $x_{\rm B}$ and a maximum close to $x_{\rm B} \simeq 1/2$.Comment: To appear on Europhysics Letter

Instability and trade in currency areas

We present a model of a currency area in which labor markets of country members are isolated but there is trade among these countries. When a country experiences a negative (resp. positive) shock, inflation goes down (up). This causes two effects. On the one hand the real interest rate of this country increases (decreases). On the other hand the goods produced in this country become more (less) competitive. We show that the stability of the system depends on several factors, including a large competitive effect, how inflation expectations are formed and fiscal policy. In general, stability requires a trade-off between the rationality of expectations and budget balance

The Yang-Mills gradient flow and SU(3) gauge theory with 12 massless fundamental fermions in a colour-twisted box

We perform the step-scaling investigation of the running coupling constant, using the gradient-flow scheme, in SU(3) gauge theory with twelve massless fermions in the fundamental representation. The Wilson plaquette gauge action and massless unimproved staggered fermions are used in the simulations. Our lattice data are prepared at high accuracy, such that the statistical error for the renormalised coupling, g_GF, is at the subpercentage level. To investigate the reliability of the continuum extrapolation, we employ two different lattice discretisations to obtain g_GF. For our simulation setting, the corresponding gauge-field averaging radius in the gradient flow has to be almost half of the lattice size, in order to have this extrapolation under control. We can determine the renormalisation group evolution of the coupling up to g^2_GF ~ 6, before the onset of the bulk phase structure. In this infrared regime, the running of the coupling is significantly slower than the two-loop perturbative prediction, although we cannot draw definite conclusion regarding possible infrared conformality of this theory. Furthermore, we comment on the issue regarding the continuum extrapolation near an infrared fixed point. In addition to adopting the fit ansatz a'la Symanzik for performing this task, we discuss a possible alternative procedure inspired by properties derived from low-energy scale invariance at strong coupling. Based on this procedure, we propose a finite-size scaling method for the renormalised coupling as a means to search for infrared fixed point. Using this method, it can be shown that the behaviour of the theory around g^2_GF ~ 6 is still not governed by possible infrared conformality.Comment: 24 pages, 6 figures; Published version; Appendix A added for tabulating data; One reference included; Typos correcte

Error Analysis and Correction for Weighted A*'s Suboptimality (Extended Version)

Weighted A* (wA*) is a widely used algorithm for rapidly, but suboptimally, solving planning and search problems. The cost of the solution it produces is guaranteed to be at most W times the optimal solution cost, where W is the weight wA* uses in prioritizing open nodes. W is therefore a suboptimality bound for the solution produced by wA*. There is broad consensus that this bound is not very accurate, that the actual suboptimality of wA*'s solution is often much less than W times optimal. However, there is very little published evidence supporting that view, and no existing explanation of why W is a poor bound. This paper fills in these gaps in the literature. We begin with a large-scale experiment demonstrating that, across a wide variety of domains and heuristics for those domains, W is indeed very often far from the true suboptimality of wA*'s solution. We then analytically identify the potential sources of error. Finally, we present a practical method for correcting for two of these sources of error and experimentally show that the correction frequently eliminates much of the error.Comment: Published as a short paper in the 12th Annual Symposium on Combinatorial Search, SoCS 201