Noise and dynamical pattern selection

In pattern forming systems such as Rayleigh-Benard convection or directional solidification, a large number of linearly stable, patterned steady states exist when the basic, simple steady state is unstable. Which of these steady states will be realized in a given experiment appears to depend on unobservable details of the system's initial conditions. We show, however, that weak, Gaussian white noise drives such a system toward a preferred wave number which depends only on the system parameters and is independent of initial conditions. We give a prescription for calculating this wave number, analytically near the onset of instability and numerically otherwise.Comment: 12 pages, REVTEX, no figures. Submitted to Phys. Rev. Let

Well-posedness and asymptotic behavior of a multidimensional model of morphogen transport

Morphogen transport is a biological process, occurring in the tissue of living organisms, which is a determining step in cell differentiation. We present rigorous analysis of a simple model of this process, which is a system coupling parabolic PDE with ODE. We prove existence and uniqueness of solutions for both stationary and evolution problems. Moreover we show that the solution converges exponentially to the equilibrium in $C^1\times C^0$ topology. We prove all results for arbitrary dimension of the domain. Our results improve significantly previously known results for the same model in the case of one dimensional domain

Complex-valued Burgers and KdV-Burgers equations

Spatially periodic complex-valued solutions of the Burgers and KdV-Burgers equations are studied in this paper. It is shown that for any sufficiently large time T, there exists an explicit initial data such that its corresponding solution of the Burgers equation blows up at T. In addition, the global convergence and regularity of series solutions is established for initial data satisfying mild conditions

Phase diagrams, critical and multicritical behavior of hard-core Bose-Hubbard models

We determine the zero-temperature phase diagram of the hard-core Bose-Hubbard model on a square lattice by mean-field theory supplemented by a linear spin-wave analysis. Due to the interplay between nearest and next-nearest neighbor interaction and cubic anisotropy several supersolid phases with checkerboard, stripe domain or intermediate symmetry are stabilized. The phase diagrams show three different topologies depending on the relative strength of nearest and next-nearest neighbor interaction. We also find a rich variety of new quantum critical behavior and multicritical points and discuss the corresponding effective actions and universality classes.Comment: 19 pages, ReVTeX, 18 figures included, submitted to PR

Serial Search Based Code Acquisition in the Cooperative MIMO Aided DS-CDMA Downlink

Full text of this paper is not available in UHRAFocal blockade of postsynaptic acetylcholine receptors (AChRs) in a small region of the neuromuscular junction may cause long-term synapse elimination at that site. Blockade of the whole junction does not cause synapse loss, indicating that it is the contrast in postsynaptic activity between the blocked and unblocked regions which causes withdrawal of the synaptic terminals. This phenomenon can be explained by the dual role of calcium, both in controlling AChR gene transcription and influencing AChR aggregation. A computational model is provided and the stability of the solutions is confirmed by theoretical analysis and computer simulation

Statistical mechanics of temporal association in neural networks with transmission delays

We study the representation of static patterns and temporal sequences in neural networks with signal delays and a stochastic parallel dynamics. For a wide class of delay distributions, the asymptotic network behavior can be described by a generalized Gibbs distribution, generated by a novel Lyapunov functional for the determination dynamics. We extend techniques of equilibrium statistical mechanics so as to deal with time-dependent phenomena, derive analytic results for both retrieval quality and storage capacity, and compare them with numerical simulations

Phase Diagram of a Superconducting and Antiferromagnetic System with SO(5) Symmetry

Temperature vs. chemical-potential phase diagrams of an SO(5) model for high-(T_c) cuprates are calculated by Monte Carlo simulation. There is a bicritical point where the second-order antiferromagnetism (AF) and superconductivity transition lines merge tangentially into a first-order line, and the SO(5) symmetry is achieved. In an external magnetic field, the AF ordering is first order in the region where the first-order melting line of flux lattice joins in. There is a tricritical point on the AF transition line from which the AF ordering becomes second order.Comment: 6 pages, 5 postscript figures, RevTe

From segment to somite: segmentation to epithelialization analyzed within quantitative frameworks

One of the most visually striking patterns in the early developing embryo is somite segmentation. Somites form as repeated, periodic structures in pairs along nearly the entire caudal vertebrate axis. The morphological process involves short- and long-range signals that drive cell rearrangements and cell shaping to create discrete, epithelialized segments. Key to developing novel strategies to prevent somite birth defects that involve axial bone and skeletal muscle development is understanding how the molecular choreography is coordinated across multiple spatial scales and in a repeating temporal manner. Mathematical models have emerged as useful tools to integrate spatiotemporal data and simulate model mechanisms to provide unique insights into somite pattern formation. In this short review, we present two quantitative frameworks that address the morphogenesis from segment to somite and discuss recent data of segmentation and epithelialization

De Sitter and Schwarzschild-De Sitter According to Schwarzschild and De Sitter

When de Sitter first introduced his celebrated spacetime, he claimed, following Schwarzschild, that its spatial sections have the topology of the real projective space RP^3 (that is, the topology of the group manifold SO(3)) rather than, as is almost universally assumed today, that of the sphere S^3. (In modern language, Schwarzschild was disturbed by the non-local correlations enforced by S^3 geometry.) Thus, what we today call "de Sitter space" would not have been accepted as such by de Sitter. There is no real basis within classical cosmology for preferring S^3 to RP^3, but the general feeling appears to be that the distinction is in any case of little importance. We wish to argue that, in the light of current concerns about the nature of de Sitter space, this is a mistake. In particular, we argue that the difference between "dS(S^3)" and "dS(RP^3)" may be very important in attacking the problem of understanding horizon entropies. In the approach to de Sitter entropy via Schwarzschild-de Sitter spacetime, we find that the apparently trivial difference between RP^3 and S^3 actually leads to very different perspectives on this major question of quantum cosmology.Comment: 26 pages, 8 figures, typos fixed, references added, equation numbers finally fixed, JHEP versio

Detection of variable VHE gamma-ray emission from the extra-galactic gamma-ray binary LMC P3

Context. Recently, the high-energy (HE, 0.1-100 GeV) $\gamma$-ray emission from the object LMC P3 in the Large Magellanic Cloud (LMC) has been discovered to be modulated with a 10.3-day period, making it the first extra-galactic $\gamma$-ray binary. Aims. This work aims at the detection of very-high-energy (VHE, >100 GeV) $\gamma$-ray emission and the search for modulation of the VHE signal with the orbital period of the binary system. Methods. LMC P3 has been observed with the High Energy Stereoscopic System (H.E.S.S.); the acceptance-corrected exposure time is 100 h. The data set has been folded with the known orbital period of the system in order to test for variability of the emission. Energy spectra are obtained for the orbit-averaged data set, and for the orbital phase bin around the VHE maximum. Results. VHE $\gamma$-ray emission is detected with a statistical significance of 6.4 $\sigma$. The data clearly show variability which is phase-locked to the orbital period of the system. Periodicity cannot be deduced from the H.E.S.S. data set alone. The orbit-averaged luminosity in the $1-10$ TeV energy range is $(1.4 \pm 0.2) \times 10^{35}$ erg/s. A luminosity of $(5 \pm 1) \times 10^{35}$ erg/s is reached during 20% of the orbit. HE and VHE $\gamma$-ray emissions are anti-correlated. LMC P3 is the most luminous $\gamma$-ray binary known so far.Comment: 5 pages, 3 figures, 1 table, accepted for publication in A&