Counting (3+1) - Avoiding permutations

A poset is {\it (\3+\1)-free} if it contains no induced subposet isomorphic to the disjoint union of a 3-element chain and a 1-element chain. These posets are of interest because of their connection with interval orders and their appearance in the (\3+\1)-free Conjecture of Stanley and Stembridge. The dimension 2 posets $P$ are exactly the ones which have an associated permutation $\pi$ where $i\prec j$ in $P$ if and only if $i<j$ as integers and $i$ comes before $j$ in the one-line notation of $\pi$. So we say that a permutation $\pi$ is {\it (\3+\1)-free} or {\it (\3+\1)-avoiding} if its poset is (\3+\1)-free. This is equivalent to $\pi$ avoiding the permutations 2341 and 4123 in the language of pattern avoidance. We give a complete structural characterization of such permutations. This permits us to find their generating function.Comment: 17 page

Aging, rejuvenation and memory effects in re-entrant ferromagnets

We have studied the slow dynamics of the ferromagnetic phases of the re-entrant CdCr_{2x}In_{2-2x}S_4 system for 0.85<x<=1 by means of low frequency ac susceptibility and magnetization measurements. Experimental procedures widely used in the investigation of the out-of-equilibrium dynamics of spin glasses (such as the x=0.85 compound) have been applied to search for aging, rejuvenation and memory effects, and to test their dependence on the disorder introduced by dilution of the magnetic ions. Whereas the rejuvenation effect is found in all studied samples, the memory effect is clearly enhanced for increasing dilutions. The results support a description of aging in both ferromagnetic and re-entrant spin-glass phases in terms of hierarchical reconformations of domain walls pinned by the disorder.Comment: Service de Physique de l'Etat Condense, DRECAM, DSM, CEA Saclay,91191 Gif sur Yvette Cedex, France, 9 pages, including 7 figures, To appear in Eur. Phys. J. B (2002

PyFR: An Open Source Framework for Solving Advection-Diffusion Type Problems on Streaming Architectures using the Flux Reconstruction Approach

High-order numerical methods for unstructured grids combine the superior accuracy of high-order spectral or finite difference methods with the geometric flexibility of low-order finite volume or finite element schemes. The Flux Reconstruction (FR) approach unifies various high-order schemes for unstructured grids within a single framework. Additionally, the FR approach exhibits a significant degree of element locality, and is thus able to run efficiently on modern streaming architectures, such as Graphical Processing Units (GPUs). The aforementioned properties of FR mean it offers a promising route to performing affordable, and hence industrially relevant, scale-resolving simulations of hitherto intractable unsteady flows within the vicinity of real-world engineering geometries. In this paper we present PyFR, an open-source Python based framework for solving advection-diffusion type problems on streaming architectures using the FR approach. The framework is designed to solve a range of governing systems on mixed unstructured grids containing various element types. It is also designed to target a range of hardware platforms via use of an in-built domain specific language based on the Mako templating engine. The current release of PyFR is able to solve the compressible Euler and Navier-Stokes equations on grids of quadrilateral and triangular elements in two dimensions, and hexahedral elements in three dimensions, targeting clusters of CPUs, and NVIDIA GPUs. Results are presented for various benchmark flow problems, single-node performance is discussed, and scalability of the code is demonstrated on up to 104 NVIDIA M2090 GPUs. The software is freely available under a 3-Clause New Style BSD license (see www.pyfr.org)

Ageing and relaxation times in disordered insulators

We focus on the slow relaxations observed in the conductance of disordered insulators at low temperature (especially granular aluminum films). They manifest themselves as a temporal logarithmic decrease of the conductance after a quench from high temperatures and the concomitant appearance of a field effect anomaly centered on the gate voltage maintained. We are first interested in ageing effects, i.e. the age dependence of the dynamical properties of the system. We stress that the formation of a second field effect anomaly at a different gate voltage is not a "history free" logarithmic (lnt) process, but departs from lnt in a way which encodes the system's age. The apparent relaxation time distribution extracted from the observed relaxations is thus not "constant" but evolves with time. We discuss what defines the age of the system and what external perturbation out of equilibrium does or does not rejuvenate it. We further discuss the problem of relaxation times and comment on the commonly used "two dip" experimental protocol aimed at extracting "characteristic times" for the glassy systems (granular aluminum, doped indium oxide...). We show that it is inoperable for systems like granular Al and probably highly doped InOx where it provides a trivial value only determined by the experimental protocol. But in cases where different values are obtained like in lightly doped InOx or some ultra thin metal films, potentially interesting information can be obtained, possibly about the "short time" dynamics of the different systems. Present ideas about the effect of doping on the glassiness of disordered insulators may also have to be reconsidered.Comment: to appear in the proceedings of the 14th International Conference on Transport and Interactions in Disordered Systems (TIDS14

Aging phenomena in spin glass and ferromagnetic phases: domain growth and wall dynamics

We compare aging in a disordered ferromagnet and in a spin glass, by studying the different phases of a reentrant system. We have measured the relaxation of the low-frequency ac susceptibility, in both the ferromagnetic and spin-glass phases of a CdCr_{1.9}In_{0.1}S_4 sample. A restart of aging processes when the temperature is lowered (`chaos-like' effect) is observed in both phases. The memory of previous aging at a higher temperature can be retrieved upon re-heating, but in the ferromagnetic phase it can rapidly be erased by the growth of ferromagnetic domains. We interpret the behaviour observed in the ferromagnetic phase in terms of a combination of domain growth and pinned wall reconformations, and suggest that aging in spin glasses is dominated by such wall reconformation processes.Comment: SPEC, CEA Saclay, 91191 Gif sur Yvette Cedex, France, to appear in Europhys. Lett. (2000

Polymer Maximum Drag Reduction: A Unique Transitional State

The upper bound of polymer drag reduction is identified as a unique transitional state between laminar and turbulent flow corresponding to the onset of the nonlinear breakdown of flow instabilities

Multiple Signaling Functions Of Song In A Polymorphic Species With Alternative Reproductive Strategies

Vocal traits can be sexually selected to reflect male quality, but may also evolve to serve additional signaling functions. We used a long-term dataset to examine the signaling potential of song in dimorphic white-throated sparrows (Zonotrichia albicollis). We investigated whether song conveys multifaceted information about the vocalizing individual, including fitness, species identity, individual identity, and morph. We also evaluated whether song traits correlate differently with fitness in the two morphs, as the more promiscuous strategy of white, relative to tan, morph males might impose stronger sexual selection. Males with high song rates achieved higher lifetime reproductive success, and this pattern was driven by white morph males. In addition, males that sang songs with many notes survived longer, but this pattern was less robust. Thus, song traits reflect differences in fitness and may more strongly affect fitness in the white morph. Song frequency was unrelated to fitness, body size, or morph, but was individual specific and could signal individual identity. Songs of the two morphs displayed similar frequency ratios and bandwidths. However, tan morph males sang songs with longer first notes, fewer notes, and higher variability. Thus, song could be used in morph discrimination. Variation in frequency ratios between notes was low and could function in conspecific recognition, but pitch change dynamics did differ between four different song types observed. Our results support a multiple messages model for white-throated sparrow song, in which different song traits communicate discrete information about the vocalizing individual

Low-Temperature Features of Nano-Particle Dynamics

In view of better characterizing possible quantum effects in the dynamics of nanometric particles, we measure the effect on the relaxation of a slight heating cycle. The effect of the field amplitude is studied; its magnitude is chosen in order to induce the relaxation of large particles (~7nm), even at very low temperatures (100mK). Below 1K, the results significantly depart from a simple thermal dynamics scenario.Comment: 1 tex file, 4 PostScript figure