Pendulum Integration and Elliptic Functions

Revisiting canonical integration of the classical pendulum around its unstable equilibrium, normal hyperbolic canonical coordinates are constructe

Reply to comment on "Simple one-dimensional model of heat conduction which obeys Fourier's law"

In this reply we answer the comment by A. Dhar (cond-mat/0203077) on our Letter "Simple one dimensional model of heat conduction which obeys Fourier's law" (Phys. Rev. Lett. 86, 5486 (2001), cond-mat/0104453)Comment: 1 pag., 1 fi

Symmetries in Fluctuations Far from Equilibrium

Fluctuations arise universally in Nature as a reflection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, fluctuations encode fundamental aspects of the physics of the system at hand, crucial to understand irreversibility and nonequilibrium behavior. In order to sustain a given fluctuation, a system traverses a precise optimal path in phase space. Here we show that by demanding invariance of optimal paths under symmetry transformations, new and general fluctuation relations valid arbitrarily far from equilibrium are unveiled. This opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations. We illustrate this concept studying symmetries of the current distribution out of equilibrium. In particular we derive an isometric fluctuation relation which links in a strikingly simple manner the probabilities of any pair of isometric current fluctuations. This relation, which results from the time-reversibility of the dynamics, includes as a particular instance the Gallavotti-Cohen fluctuation theorem in this context but adds a completely new perspective on the high level of symmetry imposed by time-reversibility on the statistics of nonequilibrium fluctuations. The new symmetry implies remarkable hierarchies of equations for the current cumulants and the nonlinear response coefficients, going far beyond Onsager's reciprocity relations and Green-Kubo formulae. We confirm the validity of the new symmetry relation in extensive numerical simulations, and suggest that the idea of symmetry in fluctuations as invariance of optimal paths has far-reaching consequences in diverse fields.Comment: 8 pages, 4 figure

Temporal video transcoding from H.264/AVC-to-SVC for digital TV broadcasting

Mobile digital TV environments demand flexible video compression like scalable video coding (SVC) because of varying bandwidths and devices. Since existing infrastructures highly rely on H.264/AVC video compression, network providers could adapt the current H.264/AVC encoded video to SVC. This adaptation needs to be done efficiently to reduce processing power and operational cost. This paper proposes two techniques to convert an H.264/AVC bitstream in Baseline (P-pictures based) and Main Profile (B-pictures based) without scalability to a scalable bitstream with temporal scalability as part of a framework for low-complexity video adaptation for digital TV broadcasting. Our approaches are based on accelerating the interprediction, focusing on reducing the coding complexity of mode decision and motion estimation tasks of the encoder stage by using information available after the H. 264/AVC decoding stage. The results show that when our techniques are applied, the complexity is reduced by 98 % while maintaining coding efficiency