Pattern formation outside of equilibrium

A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. Examples include patterns in hydrodynamic systems such as thermal convection in pure fluids and binary mixtures, Taylor-Couette flow, parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions and excitable biological media. The theoretical starting point is usually a set of deterministic equations of motion, typically in the form of nonlinear partial differential equations. These are sometimes supplemented by stochastic terms representing thermal or instrumental noise, but for macroscopic systems and carefully designed experiments the stochastic forces are often negligible. An aim of theory is to describe solutions of the deterministic equations that are likely to be reached starting from typical initial conditions and to persist at long times. A unified description is developed, based on the linear instabilities of a homogeneous state, which leads naturally to a classification of patterns in terms of the characteristic wave vector q0 and frequency ω0 of the instability. Type Is systems (ω0=0, q0≠0) are stationary in time and periodic in space; type IIIo systems (ω0≠0, q0=0) are periodic in time and uniform in space; and type Io systems (ω0≠0, q0≠0) are periodic in both space and time. Near a continuous (or supercritical) instability, the dynamics may be accurately described via "amplitude equations," whose form is universal for each type of instability. The specifics of each system enter only through the nonuniversal coefficients. Far from the instability threshold a different universal description known as the "phase equation" may be derived, but it is restricted to slow distortions of an ideal pattern. For many systems appropriate starting equations are either not known or too complicated to analyze conveniently. It is thus useful to introduce phenomenological order-parameter models, which lead to the correct amplitude equations near threshold, and which may be solved analytically or numerically in the nonlinear regime away from the instability. The above theoretical methods are useful in analyzing "real pattern effects" such as the influence of external boundaries, or the formation and dynamics of defects in ideal structures. An important element in nonequilibrium systems is the appearance of deterministic chaos. A greal deal is known about systems with a small number of degrees of freedom displaying "temporal chaos," where the structure of the phase space can be analyzed in detail. For spatially extended systems with many degrees of freedom, on the other hand, one is dealing with spatiotemporal chaos and appropriate methods of analysis need to be developed. In addition to the general features of nonequilibrium pattern formation discussed above, detailed reviews of theoretical and experimental work on many specific systems are presented. These include Rayleigh-Bénard convection in a pure fluid, convection in binary-fluid mixtures, electrohydrodynamic convection in nematic liquid crystals, Taylor-Couette flow between rotating cylinders, parametric surface waves, patterns in certain open flow systems, oscillatory chemical reactions, static and dynamic patterns in biological media, crystallization fronts, and patterns in nonlinear optics. A concluding section summarizes what has and has not been accomplished, and attempts to assess the prospects for the future

Localization and Pattern Formation in Quantum Physics. I. Phenomena of Localization

In these two related parts we present a set of methods, analytical and numerical, which can illuminate the behaviour of quantum system, especially in the complex systems. The key points demonstrating advantages of this approach are: (i) effects of localization of possible quantum states, more proper than "gaussian-like states"; (ii) effects of non-perturbative multiscales which cannot be calculated by means of perturbation approaches; (iii) effects of formation of complex quantum patterns from localized modes or classification and possible control of the full zoo of quantum states, including (meta) stable localized patterns (waveletons). We'll consider calculations of Wigner functions as the solution of Wigner-Moyal-von Neumann equation(s) corresponding to polynomial Hamiltonians. Modeling demonstrates the appearance of (meta) stable patterns generated by high-localized (coherent) structures or entangled/chaotic behaviour. We can control the type of behaviour on the level of reduced algebraical variational system. At the end we presented the qualitative definition of the Quantum Objects in comparison with their Classical Counterparts, which natural domain of definition is the category of multiscale/multiresolution decompositions according to the action of internal/hidden symmetry of the proper realization of scales of functional spaces. It gives rational natural explanation of such pure quantum effects as ``self-interaction''(self-interference) and instantaneous quantum interaction.Comment: LaTeX2e, spie.cls, 13 pages, 15 figures, submitted to Proc. of SPIE Meeting, The Nature of Light: What is a Photon? Optics & Photonics, SP200, San Diego, CA, July-August, 200

Flux flow spin Hall effect in type-II superconductors with spin-splitting field

We predict the very large spin Hall effect in type-II superconductors which mechanism is drastically different from the previously known ones. We find that in the flux-flow regime the spin is transported by the spin-polarized Abrikosov vortices moving under the action of the Lorenz force in the direction perpendicular to the applied electric current. Due to the large vortex velocities the spin Hall angle can be of the order of unity in realistic systems based on the high-field superconductors or the recently developed superconductor/ferromagnetic insulator proximity structures. We propose the realization of high-frequency pure spin current generator based on the periodic structure of moving vortex lattices. We find the patterns of charge imbalance and spin accumulation generated by moving vortices, which can be used for the electrical detection of individual vortex motion. The new mechanism of inverse flux-flow spin Hall effect is found based on the driving force acting on the vortices in the presence of injected spin current which results in the generation of transverse voltage.Comment: 12 pages, 4 figure

Reconciling cooperation, biodiversity and stability in complex ecological communities

Empirical observations show that ecological communities can have a huge number of coexisting species, also with few or limited number of resources. These ecosystems are characterized by multiple type of interactions, in particular displaying cooperative behaviors. However, standard modeling of population dynamics based on Lotka-Volterra type of equations predicts that ecosystem stability should decrease as the number of species in the community increases and that cooperative systems are less stable than communities with only competitive and/or exploitative interactions. Here we propose a stochastic model of population dynamics, which includes exploitative interactions as well as cooperative interactions induced by cross-feeding. The model is exactly solved and we obtain results for relevant macro-ecological patterns, such as species abundance distributions and correlation functions. In the large system size limit, any number of species can coexist for a very general class of interaction networks and stability increases as the number of species grows. For pure mutualistic/commensalistic interactions we determine the topological properties of the network that guarantee species coexistence. We also show that the stationary state is globally stable and that inferring species interactions through species abundance correlation analysis may be misleading. Our theoretical approach thus show that appropriate models of cooperation naturally leads to a solution of the long-standing question about complexity-stability paradox and on how highly biodiverse communities can coexist.Comment: 25 pages, 10 figure

Comparing ion conductance recordings of synthetic lipid bilayers with cell membranes containing TRP channels

In this article we compare electrical conductance events from single channel recordings of three TRP channel proteins (TRPA1, TRPM2 and TRPM8) expressed in human embryonic kidney cells with channel events recorded on synthetic lipid membranes close to melting transitions. Ion channels from the TRP family are involved in a variety of sensory processes including thermo- and mechano-reception. Synthetic lipid membranes close to phase transitions display channel-like events that respond to stimuli related to changes in intensive thermodynamic variables such as pressure and temperature. TRP channel activity is characterized by typical patterns of current events dependent on the type of protein expressed. Synthetic lipid bilayers show a wide spectrum of electrical phenomena that are considered typical for the activity of protein ion channels. We find unitary currents, burst behavior, flickering, multistep-conductances, and spikes behavior in both preparations. Moreover, we report conductances and lifetimes for lipid channels as described for protein channels. Non-linear and asymmetric current-voltage relationships are seen in both systems. Without further knowledge of the recording conditions, no easy decision can be made whether short current traces originate from a channel protein or from a pure lipid membraneComment: 13 pages, 9 Figure

Biodegradable materials based on silk fibroin and keratin

Wool and silk were dissolved and used for the preparation of blended films. Two systems are proposed: (1) blend films of silk fibroin and keratin aqueous solutions and (2) silk fibroin and keratin dissolved in formic acid. The FTIR spectra of pure films cast from aqueous solutions indicated that the keratin secondary structure mainly consists of alpha-helix and random coil conformations. The IR spectrum of pure SF is characteristic of films with prevalently amorphous structure (random coil conformation). Pure keratin film cast from formic acid shows an increase in the amount of beta-sheet and disordered keratin structures. The FTIR pattern of SF dissolved in formic acid is characteristic of films with prevalently beta-sheet conformations with beta-sheet crystallites embedded in an amorphous matrix. The thermal behavior of the blends confirmed the FTIR results. DSC curve of pure SF is typical of amorphous SF and the curve of pure keratin show the characteristic melting peak of alpha-helices for the aqueous system. These patterns are no longer observed in the films cast from formic acid due to the ability of formic acid to induce crystallization of SF and to increase the amount of beta-sheet structures on keratin. The nonlinear trend of the different parameters obtained from FTIR analysis and DSC curves of both SF/keratin systems indicate that when proteins are mixed they do not follow additives rules but are able to establish intermolecular interactions. Degradable polymeric biomaterials are preferred candidates for medical applications. It was investigated the degradation behavior of both SF/keratin systems by in vitro enzymatic incubation with trypsin. The SF/keratin films cast from water underwent a slower biological degradation than the films cast from formic acid. The weight loss obtained is a function of the amount of keratin in the blend. This study encourages the further investigation of the type of matrices presented here to be applied whether in scaffolds for tissue engineering or as controlled release drug delivery vehicles

A classical morphological analysis of galaxies in the Spitzer Survey of Stellar Structure in Galaxies (S ^(4) G)

The Spitzer Survey of Stellar Structure in Galaxies (S(4)G) is the largest available database of deep, homogeneous middle-infrared (mid-IR) images of galaxies of all types. The survey, which includes 2352 nearby galaxies, reveals galaxy morphology only minimally affected by interstellar extinction. This paper presents an atlas and classifications of S(4)G galaxies in the Comprehensive de Vaucouleurs revised Hubble-Sandage (CVRHS) system. The CVRHS system follows the precepts of classical de Vaucouleurs morphology, modified to include recognition of other features such as inner, outer, and nuclear lenses, nuclear rings, bars, and disks, spheroidal galaxies, X patterns and box/peanut structures, OLR subclass outer rings and pseudorings, bar ansae and barlenses, parallel sequence latetypes, thick disks, and embedded disks in 3D early-type systems. We show that our CVRHS classifications are internally consistent, and that nearly half of the S(4)G sample consists of extreme late-type systems (mostly bulgeless, pure disk galaxies) in the range Scd-Im. The most common family classification for mid-IR types S0/a to Sc is SA while that for types Scd to Sm is SB. The bars in these two type domains are very different in mid-IR structure and morphology. This paper examines the bar, ring, and type classification fractions in the sample, and also includes several montages of images highlighting the various kinds of "stellar structures" seen in mid-IR galaxy morphology

Parameter domains for Turing and stationary flow-distributed waves: I. The influence of nonlinearity

new type of instability in coupled reaction-diffusion-advection systems is analysed in a one-dimensional domain. This instability, arising due to the combined action of flow and diffusion, creates spatially periodic stationary waves termed flow and diffusion-distributed structures (FDS). Here we show, via linear stability analysis, that FDS are predicted in a considerably wider domain and are more robust (in the parameter domain) than the classical Turing instability patterns. FDS also represent a natural extension of the recently discovered flow-distributed oscillations (FDO). Nonlinear bifurcation analysis and numerical simulations in one-dimensional spatial domains show that FDS also have much richer solution behaviour than Turing structures. In the framework presented here Turing structures can be viewed as a particular instance of FDS. We conclude that FDS should be more easily obtainable in chemical systems than Turing (and FDO) structures and that they may play a potentially important role in biological pattern formation