Memory Effects and Scaling Laws in Slowly Driven Systems

This article deals with dynamical systems depending on a slowly varying parameter. We present several physical examples illustrating memory effects, such as metastability and hysteresis, which frequently appear in these systems. A mathematical theory is outlined, which allows to show existence of hysteresis cycles, and determine related scaling laws.Comment: 28 pages (AMS-LaTeX), 18 PS figure

Metastability in Interacting Nonlinear Stochastic Differential Equations II: Large-N Behaviour

We consider the dynamics of a periodic chain of N coupled overdamped particles under the influence of noise, in the limit of large N. Each particle is subjected to a bistable local potential, to a linear coupling with its nearest neighbours, and to an independent source of white noise. For strong coupling (of the order N^2), the system synchronises, in the sense that all oscillators assume almost the same position in their respective local potential most of the time. In a previous paper, we showed that the transition from strong to weak coupling involves a sequence of symmetry-breaking bifurcations of the system's stationary configurations, and analysed in particular the behaviour for coupling intensities slightly below the synchronisation threshold, for arbitrary N. Here we describe the behaviour for any positive coupling intensity \gamma of order N^2, provided the particle number N is sufficiently large (as a function of \gamma/N^2). In particular, we determine the transition time between synchronised states, as well as the shape of the "critical droplet", to leading order in 1/N. Our techniques involve the control of the exact number of periodic orbits of a near-integrable twist map, allowing us to give a detailed description of the system's potential landscape, in which the metastable behaviour is encoded

Relating the Cosmological Constant and Supersymmetry Breaking in Warped Compactifications of IIB String Theory

It has been suggested that the observed value of the cosmological constant is related to the supersymmetry breaking scale M_{susy} through the formula Lambda \sim M_p^4 (M_{susy}/M_p)^8. We point out that a similar relation naturally arises in the codimension two solutions of warped space-time varying compactifications of string theory in which non-isotropic stringy moduli induce a small but positive cosmological constant.Comment: 7 pages, LaTeX, references added and minor changes made, (v3) map between deSitter and global cosmic brane solutions clarified, supersymmetry breaking discussion improved and references adde

Modular space station Phase B extension

The modular space station concept and preliminary design are outlined. The premission operations, reference programs, baseline program costs, sortie analysis, and program options are covered

New Calabi–Yau manifolds from genetic algorithms

Calabi–Yau manifolds can be obtained as hypersurfaces in toric varieties built from reflexive polytopes. We generate reflexive polytopes in various dimensions using a genetic algorithm. As a proof of principle, we demonstrate that our algorithm reproduces the full set of reflexive polytopes in two and three dimensions, and in four dimensions with a small number of vertices and points. Motivated by this result, we construct five-dimensional reflexive polytopes with the lowest number of vertices and points. By calculating the normal form of the polytopes, we establish that many of these are not in existing datasets and therefore give rise to new Calabi–Yau four-folds. In some instances, the Hodge numbers we compute are new as well

Chaotic hysteresis in an adiabatically oscillating double well

We consider the motion of a damped particle in a potential oscillating slowly between a simple and a double well. The system displays hysteresis effects which can be of periodic or chaotic type. We explain this behaviour by computing an analytic expression of a Poincar'e map.Comment: 4 pages RevTeX, 3 PS figs, uses psfig.sty. Submitted to Phys. Rev. Letters. PS file also available at http://dpwww.epfl.ch/instituts/ipt/berglund.htm

Mechanical performance of yew (Taxus baccata L.) from a longbow perspective

Yew (Taxus baccata L.) longbow was the preferred weapon in the Middle Ages until the emergence of guns. In this study, the tensile, compression, and bending properties of yew were investigated. The advantage of yew over the other species in the study was also confirmed by a simple beam model. The superior toughness of yew has the effect that a yew longbow has a higher range compared with bows made from other species. Unexpectedly, the mechanical performance of a bow made from yew is influenced by the juvenile-to-mature wood ratio rather than by the heartwood-to-sapwood ratio. A yew bow is predicted to have maximized performance at a juvenile wood content of 30-50%, and located at the concave side (the compressive side facing the bowyer). Here, the stiffness and yield stress in compression should be as high as possibl

Evaluating matrix elements relevant to some Lorenz violating operators

Carlson, Carone and Lebed have derived the Feynman rules for a consistent formulation of noncommutative QCD. The results they obtained were used to constrain the noncommutativity parameter in Lorentz violating noncommutative field theories. However, their constraint depended upon an estimate of the matrix element of the quark level operator (gamma.p - m) in a nucleon. In this paper we calculate the matrix element of (gamma.p - m), using a variety of confinement potential models. Our results are within an order of magnitude agreement with the estimate made by Carlson et al. The constraints placed on the noncommutativity parameter were very strong, and are still quite severe even if weakened by an order of magnitude.Comment: 4 pages, 3 figures, RevTex, minor change