radial symmetry of positive solutions in nonlinear polyharmonic dirichlet problems we extend the symmetry result of gidas ni nirenberg to semilinear polyharmonic dirichlet problems in the unit ball in the proof we develop a new variant of the method of moving planes relying on fine estimates for the green function of the polyharmonic operator we also consider minimizers for subcritical higher order sobolev embeddings for embeddings into weighted spaces with a radially symmetric weight function we show that the minimizers are at least axially symmetric this result is sharp since we exhibit examples of minimizers which do not have full radial symmetry

resonant suppression of turing patterns by periodic illumination we study the resonant behavior of turing pattern suppression in a model of the chlorine dioxide iodine malonic acid reaction with periodic illumination the results of simulations based on integration of partial differential equations display resonance at the frequency of autonomous oscillations in the corresponding well stirred system the resonance in turing pattern suppression is sharper at lower complexing agent concentration and is affected by the waveform of the periodic driving force square wave on off periodic forcing is more effective in suppressing turing patterns than sinusoidal forcing we compare the dynamics of periodically forced turing patterns with the dynamics of periodically forced nonhomogeneous states in a system of two identical coupled cells bifurcation analysis based on numerical continuation of the latter system gives good predictions for the boundaries of the major resonance regions of the periodically forced patterns

spatially periodic modulated rayleigh benard convection two dimensional thermal convection in a fluid layer between two rigid walls at different mean temperatures is investigated the top container boundary is undulated and the temperatures at the top and bottom boundaries are spatially periodic modulated with modulation wavelengths large compared to the thickness of the fluid layer the continuous translational invariance in the fluid layer is broken by these spatial modulations consequently phase differences between two periodic modulations give rise to an interesting drifting pattern with the drift direction depending on the sign of the relative phase between the modulations at distinguished ratios between the modulation wave numbers and relative phases the onset of convection changes as function of the modulation amplitudes from a stationary into an oscillatory one we call this phenomenon hopf bifurcation by frustrated drifts possible experiments are described in detail where this phenomenon can be expected textcopyright 1996 the american physical society

spatial synchronization of regular optical patterns we investigate an extended nonlinear optical experiment exhibiting the spontaneous formation of hexagonal patterns out of a stationary bifurcation the system is exposed to a two dimensional spatially periodic forcing namely static hexagonal patterns under variation of their spatial periodicity parameters are the strength of the forcing and the distance to pattern forming threshold the system response is quantitatively characterized with different methods we observe several locking regimes where the system is entrained by the forcing most of the locking regimes can be related to resonances between the different critical wave numbers and the forcing wave number or its spatial harmonics one particular locking appears to result from two of these simple resonances in a kind of generalized order m n synchronization the width of the locking regimes increases with forcing strength apparently representing a spatial analog of arnold tongues

using advection to control the velocity of patterns in rings of maps traveling patterns are well known features of rings of symmetrically coupled maps which however propagate with rather small velocities of the order of 10 3 sites per step we show that it is easy to produce traveling patterns with velocities tunable over three orders of magnitude by simply breaking the symmetry of the coupling between neighbors this asymmetry arises naturally when the usual model of coupled map lattices is generalized to also include advection in addition asymmetries change the wavelength of waves traveling on the lattice 2002 elsevier science b v all rights reserved

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

morphological instability and dynamics of fronts in bacterial growth models with nonlinear diffusion depending on the growth condition bacterial colonies can exhibit different morphologies as argued by ben jacob et al there is biological and modeling evidence that a nonlinear diffusion coefficient of the type d b d 0 b k is a basic mechanism that underlies almost all of the patterns and generates a long wavelength instability we study a reaction diffusion system with a nonlinear diffusion coefficient and find that a unique planar traveling front solution exists whose velocity is uniquely determined by k and d d 0 d n where d n is the diffusion coefficient of the nutrient due to the fact that the bacterial diffusion coefficient vanishes when stackrel ensuremath rightarrow b 0 in the front solution b vanishes in a singular way as a result the standard linear stability analysis for fronts cannot be used we introduce an extension of the stability analysis that can be applied to singular fronts and use the method to perform a linear stability analysis of the planar bacteriological growth front we show that a nonlinear diffusion coefficient generates a long wavelength instability for kg0 and dl d c k we map out the region of stability in the d ensuremath k plane and determine the onset of stability that is given by d c k both for stackrel ensuremath rightarrow d 0 and stackrel ensuremath rightarrow k ensuremath infty the dynamics of the growth zone essentially reduces to that of a sharp interface problem that is reminiscent of a so called one sided growth problem where the growth velocity is proportional to the gradient of a diffusion field ahead of the interface the moving boundary approximation that we derive in these limits is quite accurate but surprisingly does not become a proper asymptotic theory in the strict mathematical sense in the limit stackrel ensuremath rightarrow d 0 due to lack of full separation of scales on all dynamically relevant length scales our linear stability analysis and sharp interface formulation will also be applicable to other examples of interface formation due to nonlinear diffusion like in porous media or in the problem of vortex motion in superconductors

cellular automaton model for the simulation of laser dynamics the classical modeling approach for laser study relies on the differential equations in this paper a cellular automaton model is proposed as an alternative for the simulation of population dynamics even though the model is simplified it captures the essence of laser phenomenology i there is a threshold pumping rate that depends inversely on the decaying lifetime of the atoms and the photons and ii depending on these lifetimes and on the pumping rate a constant or an oscillatory behavior can be observed more complex behaviors such as spiking and pattern formation can also be studied with the cellular automaton model

stripe hexagon competition in forced pattern forming systems with broken up down symmetry we investigate the response of two dimensional pattern forming systems with a broken up down symmetry such as chemical reactions to spatially resonant forcing and propose related experiments the nonlinear behavior immediately above threshold is analyzed in terms of amplitude equations suggested for a 1 2 and 1 1 ratio between the wavelength of the spatial periodic forcing and the wavelength of the pattern of the respective system both sets of coupled amplitude equations are derived by a perturbative method from the lengyel epstein model describing a chemical reaction showing turing patterns which gives us the opportunity to relate the generic response scenarios to a specific pattern forming system the nonlinear competition between stripe patterns and distorted hexagons is explored and their range of existence stability and coexistence is determined whereas without modulations hexagonal patterns are always preferred near onset of pattern formation single mode solutions stripes are favored close to threshold for modulation amplitudes beyond some critical value hence distorted hexagons only occur in a finite range of the control parameter and their interval of existence shrinks to zero with increasing values of the modulation amplitude furthermore depending on the modulation amplitude the transition between stripes and distorted hexagons is either subcritical or supercritical

wavelike patterns in one dimensional coupled map lattices we investigate the existence of wavelike solution for the logistic coupled map lattices for which the spatiotemporal periodic patterns can be predicted by a simple two dimensional mapping the existence of such wavelike solutions is proved by the implicit function theorem with constraints we also examine the stabilities of these wave solutions under perturbations of uniform small deformation type we show that in some specific cases these perturbations are completely general the technique used in this paper is also applicable to investigate other space time regular patterns

symmetry breaking hopf bifurcation in anisotropic systems abstract symmetry breaking hopf bifurcation from a spatially uniform steady state of a spatially extended anisotropic system is considered this work is motivated by the experimental observation of a hopf bifurcation to oblique traveling rolls in electrohydrodynamic convection in planarly aligned nematic liquid crystals symmetry forces four traveling rolls to lose stability simultaneously four coupled complex ordinary differential equations describing the nonlinear interaction of the traveling rolls are analyzed using methods of equivariant bifurcation theory six branches of periodic solutions always bifurcate from the trivial state at the hopf bifurcation these correspond to traveling and standing wave patterns in an open region of coefficient space there is a primary bifurcation to a quasiperiodic standing wave solution the hopf bifurcation can also lead directly to an aperiodic attractor in the form of an asymptotically stable structurally stable heteroclinic cycle the theory is applied to a model for the transition from normal to oblique traveling rolls

one dimensional dynamics for traveling fronts in coupled map lattices multistable coupled map lattices typically support traveling fronts separating two adjacent stable phases we show how the existence of an invariant function describing the front profile allows a reduction of the infinitely dimensional dynamics to a one dimensional circle homeomorphism whose rotation number gives the propagation velocity the mode locking of the velocity with respect to the system parameters then typically follows we study the behavior of fronts near the boundary of parametric stability and we explain how the mode locking tends to disappear as we approach the continuum limit of an infinite density of sites

sporadicity and synchronization in one dimensional asymmetrically coupled maps a one dimensional chain of sporadic maps with asymmetric nearest neighbour couplings is studied numerically it is shown that in the region of strong asymmetry the system becomes spatially fully synchronized even in the thermodynamic limit while the lyapunov exponent is zero for weak asymmetry the synchronization is no more complete and the lyapunov exponent becomes positive at variance with the case of non sporadic maps where the coherence length does not change in time here the coherence length exhibits strong fluctuations in addition one has a clear relation between temporal and spatial chaos i e a positive effective lyapunov exponent corresponds to a lack of synchronization and vice versa

extended symbolic dynamics in bistable cml existence and stability of fronts abstract we consider a diffusive coupled map lattice cml for which the local map is piecewise affine and has two stable fixed points by introducing a spatio temporal coding we prove the one to one correspondence between the set of global orbits and the set of admissible codes this relationship is applied to the study of the uniform fronts dynamics it is shown that for any given velocity in 1 1 there is a parameter set for which the fronts with that velocity exist and their shape is unique the dependence of the fronts velocity on the local map s discontinuity is proved to be a devil s staircase moreover the linear stability of the global orbits which do not reach the discontinuity follows directly from our simple map for the fronts this statement is improved and as a consequence the velocity of all the propagating interfaces is computed for any parameter the fronts are shown to be also nonlinearly stable under some restrictions on the parameters actually these restrictions follow from the co existence of uniform fronts and non uniformly travelling fronts for strong coupling finally these results are extended to some c local maps

spatial forcing of spontaneous optical patterns a nonlinear optical system which spontaneously forms hexagonal patterns is exposed to a weak spatially modulated forcing as forcing stationary hexagonal patterns are used under variation of their transverse wave number in the experiment we observe a locking when the forcing wave number is close to one of the critical wave numbers of the unforced system outside the locking regimes forcing provokes spatiotemporal disorder the system response is characterized quantitatively with respect to its dynamics and to its spatial order

information capacity and pattern formation in a tent map network featuring statistical periodicity we provide quantitative support to the observation that lattices of coupled maps are efficient information coding devices it has been suggested recently that lattices of coupled maps may provide a model of information coding in the nervous system because of their ability to create structured and stimulus dependent activity patterns which have the potential to be used for storing information in this paper we give an upper bound to the effective number of patterns that can be used to store information in the lattice by evaluating numerically its information capacity or information rate as a function of the coupling strength between the maps we also estimate the time taken by the lattice to establish a limiting activity pattern

effects of parametric disorder on a stationary bifurcation abstract effects of a frozen random contribution to the control parameter are investigated in terms of the complex ginzburg landau equation with real coefficients the threshold of the bifurcation from the homogeneous basic state is reduced by a random contribution even with a vanishing spatial mean value as shown by three different approaches by a perturbation calculation by a self consistent iteration method and by a fully numerical solution of the linear part of the ginzburg landau equation for arbitrary random contributions the nonlinear stationary solutions are numerically determined and in the limit of small random amplitudes analytical expressions are derived in terms of two different perturbation expansions which cover already several related trends beyond threshold for instance the spatial modulations of the solutions increase with the noise amplitude but decrease with increasing distance from threshold

hints for universality in coupled map lattices a wide range of coupled map lattices is found to have identical pattern sequences providing numerical evidence for their universality in the class of systems studied it is furthermore found that the wave type solutions of the diffusively coupled logistic lattice scale linearly with the coupling range indicating the existence of a continuum limit the findings are used to introduce a very simple type of spatially extended map that can serve as a representative for the pattern sequence of this class of coupled maps

beamforming in the presence of correlated arrivals using structured correlation matrix expressions are derived for the snr signal to noise ratio at the output of two antenna array processors in the presence of correlated arrivals and the effect on the output snr of the magnitude and the phase of the correlation the number of elements in the array the direction of the level of the interference source and the level of the uncorrelated noise is investigated the two processes considered are the optimal element space processor esp and the optimal postbeamformer interference canceller pic the pic processes the signal by forming two beams and adjusting the weights of one beam in contrast to the esp where the signals from all the elements are weighted and all the weights are adjusted a method is proposed for decorrelating the correlated sources and an analytical expression is derived to show the decorrelation effect of the proposed technique for a line array of equispaced elements numerical examples are included

resolving uncorrelated and correlated sources by linear prediction the resolution and the estimation error are investigated for two linear prediction lp algorithms for bearing estimation with uniform linear array of sensors in the presence of incoherent and coherent sources the burg algorithm ba and the generalized burg algorithm gba the superresolution is easily achieved with both algorithms when the sources are incoherent for coherent sources however the ba estimate is somewhat more sensitive to the magnitude and the phase of the intersignal correlation than the gba thereby resulting in the increased error in the bearing estimates

chaotic traveling waves in a coupled map lattice traveling waves triggered by a phase slip are studied in a coupled map lattice a local phase slip affects globally the system which is in strong contrast with kink propagation attractors with different velocities coexist and form quantized bands determined by the number of phase slips if the system size is not far from an integer multiple of the selected wavelength attractors are tori otherwise weak chaos induces modulation of waves or a chaotic itinerancy of traveling states with a long ranged temporal correlation supertransients before the formation of traveling waves are noted in the high nonlinearity regime in the weaker nonlinearity there are fluctuations of domain sizes and brownian like motion of domains propagation of chaotic domains by phase slips is also found

translational and nontranslational motion of perturbed turing patterns when the front and rear boundaries of a turing pattern with nonzero flux boundary conditions move synchronously several modes of motion of the pattern are found traveling boundaries can be obtained experimentally by illuminating a turing unstable system through a moving mask consisting of a single dark stripe with a light intensity sufficient to suppress pattern formation all structured moving patterns belong to two general types smooth translation at low mask velocity v x and nontranslational hopping at intermediate v x at high v x turing patterns are unable to form and an unstructured striped image of the mask is seen when the mask width exceeds the turing wavelength bistability between different types of moving patterns can occur as v x is varied

pattern formation in diffusive advective coupled map lattices we investigate pattern formation and evolution in coupled map lattices when advection is incorporated inaddition to the usual diffusive term all patterns may be suitably grouped into ve classes three periodic supporting static patterns and traveling waves and two nonperiodic relative frequencies are determined as afunction of all model parameters diffusion advection local nonlinearity and lattice size advection plays animportant role in coupled map lattices being capable of considerably altering pattern evolution for instance advection may induce synchronization making chaotic patterns evolve periodically as a byproduct we de scribe a practical algorithm for classifying generic pattern evolutions and for measuring velocities of travelingwaves doi 10 1103 physreve 69 066206 pacs number s 89 75 kd 05 45 xt 05 45 rai introduction

strong resonances of spatially distributed oscillators a laboratory to study patterns and defects abstract this paper describes phenomena which arise in a continuous system of coupled oscillators subject to a strongly resonant forcing we show that the temporal forcing induces a new type of instability leading to the formation of spatial patterns such as stripes hexagons and spatio temporal intermittent states reminiscent of chemical and magnetical systems we also report the existence of localized states where the instability is confined in the core of a defect leading to an increased mobility and diffusive behaviour of the defect

a few basic structures determine the behavior of a coupled map lattice the stability and formation of structures in lattices of diffusively coupled logistic maps are investigated for high nonlinearity and medium and large coupling two stability statements are given that relate the presence of the predominant attractors i e cycles and quasiperiodic traveling waves to the stability of a few simple periodic structures they are supported by strong numerical evidence furthermore they are justified through the description of some mechanisms that connect the formation of a stable structure to the cycles of the uncoupled lattice as an important consequence for given parameter values an approximate prediction of the behavior of the lattice is allowed s1063 651x 98 15402 8

on stability of structures and patterns in extended systems abstract we study the stability of spatial structures in extended systems each spatial structure consists of some simple undecomposable structures that we call patterns we show numerically for some classes of coupled map lattices that the stability of a spatial structure is determined by the stability of its pattern with the minimal spatial scale i e by the most tiny detail of this structure

wavenumber locking and pattern formation in spatially forced systems we study wavenumber locking and pattern formation resulting from weak spatially periodic one dimensional forcing of two dimensional systems we consider systems that produce stationary or traveling stripe patterns when unforced and apply forcing aligned with the stripes forcing at close to twice the pattern wavenumber selects stabilizes or creates resonant stripes locked at half the forcing wavenumber if the mismatch between the forcing and pattern wavenumber is high we find that the pattern still locks but develops a wave vector component perpendicular to the forcing direction and forms rectangular and oblique patterns when the unforced system supports traveling waves resonant rectangular patterns remain stationary but oblique patterns travel in a direction orthogonal to the traveling waves

global spectral analysis for convection diffusion reaction equation in one and two dimensions effects of numerical anti diffusion and dispersion abstract convection diffusion reaction cdr equation plays a central role in many disciplines of engineering science and finances as a consequence importance of analysis of numerical methods for the accurate solution of cdr equation has motivated the present research we have used the global spectral analysis to characterize all the three important physical processes in terms of the non dimensional numerical parameters namely the non dimensional wavenumber kh courant friedrich lewy cfl number n c the peclet number pe and the damkohler number da for the purpose of illustration we have focused on two space time discretization schemes known for accuracy and robustness the basic properties relate to numerical issues arising for the numerical amplification factor numerical diffusion coefficient numerical phase speed and numerical group velocity with the help of model one dimensional 1d and two dimensional 2d cdr equations we have reported the numerical property charts for the cases i when all the processes of convection diffusion and reaction are of same order with critical numerical behaviour enforcing low values of da for the 1d cdr equation studied here ii the 2d cdr equation considered is diffusion reaction dominated and as a consequence this enforces da to be larger we have thoroughly analyzed these cases to identify the essential roles of anti diffusion on the critical n c and pe values which in turn decides admissible space and time steps to be used with the discretization schemes the property charts have been used to calibrate the analysis with two model equations one of which has an exact solution for a 1d cdr equation and the second case for the 2d cdr equation has numerical solution available in the literature these cases help to identify the importance of such analysis in explaining the utility of the choice one can exercise in fixing the numerical parameters this also identifies and explains some hitherto unknown numerical problems for cdr equation and their alleviation techniques

travelling stripe forcing of turing patterns we report on the effect of a spatio temporal forcing applied on turing stripe patterns under spatial resonance experiments conducted with the photosensitive cdima reaction unveil a large variety of dynamical responses of striped patterns from entrained to waving when changing the forcing velocity from small to large values in between and quite unexpectedly we also observe a symmetry breaking phenomenon leading to hexagonal lattices either entrained with the forcing or oscillating we propose a new set of coupled amplitude equations 1 which provides a theoretical framework where the experimental phenomena can be interpreted

pattern formation on trees networks having the geometry and the connectivity of trees are considered as the spatial support of spatiotemporal dynamical processes a tree is characterized by two parameters its ramification and its depth the local dynamics at the nodes of a tree is described by a nonlinear map giving rise to a coupled map lattice system the coupling is expressed by a matrix whose eigenvectors constitute a basis on which spatial patterns on trees can be expressed by linear combination the spectrum of eigenvalues of the coupling matrix exhibit a nonuniform distribution that manifests itself in the bifurcation structure of the spatially synchronized modes these models may describe reaction diffusion processes and several other phenomena occurring on heterogeneous media with hierarchical structure

on quasiperiodic travelling waves in coupled map lattices we investigate quasiperiodic travelling waves qtws in lattices of diffusively coupled logistic maps starting from the assumption that any spatial structure can be broken down into simpler elementary structures a classification scheme for qtws is introduced within this framework the phenomenon of discrete velocities is reviewed and further investigated in addition a new technique is proposed for predicting whether qtws can occur for given parameter values and which they might be