a new super kp system and a characterization of the jacobians of arbitrary algebraic super curves a set of super commuting vector fields is defined on the super grassmannians a characterization of the jacobian varieties of super curves super schottky problem is established in the following manner every finite dimensional integral manifold of these vector fields has a canonical structure of the jacobian variety of an algebraic super curve and conversely the jacobian variety of an arbitrary algebraic super curve is obtained in this way the vector fields restricted on the super grassmannian of index 0 0 give a completely integrable system of partial super differential equations which gives a new supersymmetric generalization of the kp system thus every finite dimensional solution of this new system gives rise to a jacobian variety of an algebraic super curve the correspondence between this super grassmannian and the group of monic super pseudo differential operators of order zero the super sato correspondence is also established table of

n 2 super riemann surfaces and algebraic geometry the geometric framework for n 2 superconformal field theories are described by studying susy2 curves a nickname for n 2 super riemann surfaces it is proved that single susy2 curves are actually split supermanifolds and their local model is a serre self dual locally free sheaf of rank two over a smooth algebraic curve superconformal structures on these sheaves are then examined by setting up deformation theory as a first step in studying moduli problems

odd periodic window and bifurcations on 2d parameter space of low frequency oscillations low frequency current oscillations have been usually investigated under the influence of the external applied voltage temperature and illumination a parallel applied magnetic field has been used in the present work in order to obtain odd periodic windows and bifurcations inside them in a two dimension parameter space for a semi insulating gaas sample grown by molecular beam epitaxy two kinds of parameter spaces have been used in order to stabilize the odd periodic windows and the bifurcations namely the external applied voltage versus the parallel magnetic field and the illumination versus the parallel magnetic field we report on a successful observation of stable cycles of periodicity 3 4 5 6 7 and 8 inside a period 3 window an example of bifurcation route is presented following the sequence from chaos to 4 3 6 3 5 7 5 and back to chaos in the parameter space of voltage versus magnetic field for this bifurcation route we will show which branch of the cycle is bifurcating and which are coalescing with the control parameters

unstable dimension variability a source of nonhyperbolicity in chaotic systems the hyperbolicity or nonhyperbolicity of a chaotic set has profound implications for the dynamics on the set a familiar mechanism causing nonhyperbolicity is the tangency of the stable and unstable manifolds at points on the chaotic set here we investigate a different mechanism that can lead to nonhyperbolicity in typical invertible respectively noninvertible maps of dimension 3 respectively 2 and higher in particular we investigate a situation first considered by abraham and smale in 1970 for different purposes in which the dimension of the unstable and stable tangent spaces are not constant over the chaotic set we call this unstable dimension variability a simple two dimensional map that displays behavior typical of this phenomenon is presented and analyzed

controlling chaotic dynamical systems we review the major ideas involved in the control of chaos we present the ott grebogi yorke ogy method of controlling chaos which is a particular case of the pole placement technique but which is the one leading to the shortest time to achieve the control of chaotic systems implementation using only measured time series in experimental settings is also described

a new approach to analyticity of dirichlet neumann operators this paper outlines the theoretical background of a new approach towards an accurate and well conditioned perturbative calculation of dirichlet neumann operators dnos on domains that are perturbations of simple geometries previous work on the analyticity of dnos has produced formulae that as we have found are very ill conditioned we show how a simple change of variables can lead to recursions that satisfy analyticity estimates without relying on subtle cancellation properties at the heart of previous formulae

spatiotemporal chaos in mixed linear nonlinear coupled logistic map lattice abstract we investigate the spatiotemporal dynamics with mixing degrees of nonlinear chaotic maps in coupling connections here the coupling methods between lattices are both linear neighborhood coupling and the nonlinear chaotic map coupling of lattices while strictly nearest neighborhood coupling is only a special case in the proposed system we employed the criteria such as kolmogorov sinai entropy density and universality bifurcation diagrams space amplitude and space time diagrams to investigate the chaotic behaviors of the proposed system in this paper in fact the proposed system contains new features for applications of cryptography such as the larger range of parameters for chaotic behaviors the higher percentage of lattices in chaotic behaviors for most of parameters and less periodic windows in bifurcation diagrams furthermore we also show the parameter ranges of the proposed system which hold those features in cryptography compared with those of the cml system finally we design the encryption scheme based on the proposed system for an explicit illustration

crossing bifurcations and unstable dimension variability a crisis is a global bifurcation in which a chaotic attractor has a discontinuous change in size or suddenly disappears as a scalar parameter of the system is varied in this letter we describe a global bifurcation in three dimensions which can result in a crisis this bifurcation does not involve a tangency and cannot occur in maps of dimension smaller than 3 we present evidence of unstable dimension variability as a result of the crisis we then derive a new scaling law describing the density of the new portion of the attractor formed in the crisis we illustrate this new type of bifurcation with a specific example of a three dimensional chaotic attractor undergoing a crisis

expansion shock waves in regularized shallow water theory we identify a new type of shock wave by constructing a stationary expansion shock solution of a class of regularized shallow water equations that include the benjamin bona mahony and boussinesq equations an expansion shock exhibits divergent characteristics thereby contravening the classical lax entropy condition the persistence of the expansion shock in initial value problems is analysed and justified using matched asymptotic expansions and numerical simulations the expansion shock s existence is traced to the presence of a non local dispersive term in the governing equation we establish the algebraic decay of the shock as it is gradually eroded by a simple wave on either side more generally we observe a robustness of the expansion shock in the presence of weak dissipation and in simulations of asymmetric initial conditions where a train of solitary waves is shed from one side of the shock

superconformal geometry and string theory we give a formula for the determinant of the super laplace operator in a holomorphic hermitian line bundle over a superconformal manifold this is then used to obtain an expression for the fermion string measure

a numerical approach to blow up issues for dispersive perturbations of burgers equation abstract we provide a detailed numerical study of various issues pertaining to the dynamics of the burgers equation perturbed by a weak dispersive term blow up in finite time versus global existence nature of the blow up existence for long times and the decomposition of the initial data into solitary waves plus radiation we numerically construct solitary waves for fractional korteweg de vries equations

dissecting shrimps results for some one dimensional physical models this paper describes how certain shrimp like clusters of stability organize themselves in the parameter space of dynamical systems clusters are composed of an infinite affine similar repetition of a basic elementary cell containing two primary noble points a head and a tail defining an axis of approximate symmetry knowledge of the axis and the skewness of the k periodic main cell of a k 2 cluster is enough to define the orientation of the whole cluster in space peculiarly simple directions along which shrimp like clusters align are formed by the locus of doubly degenerate saddle zero multipliers corresponding to the main shrimp head in addition we report a family of models having the boundaries of all isoperiodic domains of stability totally degenerate and describe different aspects of their mathematical arrangement and some of their consequences for example that shrimps are diffeomorphic copies of shrimps

a superanalog of the selberg trace formula and multiloop contributions for fermionic strings an analog of the classical selberg trace formula is given for discrete groups acting on the upper complex half superplane applications to the fermionic string measure on the moduli superspace are discussed

validity of numerical trajectories in the synchronization transition of complex systems we investigate the relationship between the loss of synchronization and the onset of shadowing breakdown via unstable dimension variability in complex systems in the neighborhood of the critical transition to strongly nonhyperbolic behavior the system undergoes on off intermittency with respect to the synchronization state there are potentially severe consequences of these facts on the validity of the computer generated trajectories obtained from dynamical systems whose synchronization manifolds share the same nonhyperbolic properties

a numerical study of the whitham equation as a model for steady surface water waves the object of this article is the comparison of numerical solutions of the so called whitham equation to numerical approximations of solutions of the full euler free surface water wave problem the whitham equation t 3 2 c 0 h 0 x k h 0 x 0 was proposed by whitham 1967 as an alternative to the kdv equation for the description of wave motion at the surface of a perfect fluid by simplified evolution equations but the accuracy of this equation as a water wave model has not been investigated to date in order to understand whether the whitham equation is a viable water wave model numerical approximations of periodic solutions of the kdv and whitham equation are compared to numerical solutions of the surface water wave problem given by the full euler equations with free surface boundary conditions computed by a novel spectral element method technique the bifurcation curves for these three models are compared in the phase velocity waveheight parameter space and wave profiles are compared for different wavelengths and waveheights it is found that for small wavelengths the steady whitham waves compare more favorably to the euler waves than the kdv waves for larger wavelengths the kdv waves appear to be a better approximation of the euler waves

symmetry and decay of traveling wave solutions to the whitham equation abstract this paper is concerned with decay and symmetry properties of solitary wave solutions to a nonlocal shallow water wave model an exponential decay result for supercritical solitary wave solutions is given moreover it is shown that all such solitary wave solutions are symmetric and monotone on either side of the crest the proof is based on the method of moving planes furthermore a close relation between symmetric and traveling wave solutions is established

the geometry of super riemann surfaces we define super riemann surfaces as smooth 2 2 dimensional supermanifolds equipped with a reduction of their structure group to the group of invertible upper triangular 2 2 complex matrices the integrability conditions for such a reduction turn out to be most of the torsion constraints of 2d supergravity we show that they are both necessary and sufficient for a frame to admit local superconformal coordinates the other torsion constraints are merely conditions to fix some of the gauge freedom in this description or to specify a particular connection on such a manifold analogous to the levi civita connection in riemannian geometry unlike ordinary riemann surfaces a super riemann surface cannot be regarded as having only one complex dimension nevertheless in certain important aspects super riemann surfaces behave as nicely as if they had only one dimension in particular they posses an analog widehat partial of the cauchy riemann operator on ordinary riemann surfaces a differential operator taking values in the bundle of half volume forms this operator furnishes a short resolution of the structure sheaf making possible a quillen theory of determinant line bundles finally we show that the moduli space of super riemann surfaces is embedded in the larger space of complex curves of dimension 1 1

an easily implementable fourth order method for the time integration of wave problems abstract we are concerned with the time integration of systems of ordinary differential equations arising from the space discretization of partial differential wave equations with smooth solutions a method is suggested that while being as easily implementable as the standard implicit mid point rule is fourth order accurate the new method is symplectic so that it is very well suited for long time integrations of problems with a hamiltonian structure numerical experiments are reported that refer to a fourth order galerkin space discretization of the korteweg de vries equation and to a pseudospectral space discretization of the same equation

on n 4 super riemann surfaces and the superconformal semigroup the finite n 4superconformal scf transformations areobtained and classified into three types by means of the permanent of specific matrices the properties of the latter are studied in connection with complex plane non euclidean geometry the explicit expression for the n 4 scf transformations allows them to be used as the transition functions for n 4 split and non split super riemann surfaces and scf embeddings the existence of the semigroup of scf transformations is indicated

moduli of super riemann surfaces the basic properties of super riemann surfaces are presented and their supermoduli spaces are constructed in a manner suitable for the application of algebro geometric techniques to string theory

the whitham equation as a model for surface water waves the whitham equation was proposed as an alternate model equation for the simplified description of uni directional wave motion at the surface of an inviscid fluid as the whitham equation incorporates the full linear dispersion relation of the water wave problem it is thought to provide a more faithful description of shorter waves of small amplitude than traditional long wave models such as the kdv equation in this work we identify a scaling regime in which the whitham equation can be derived from the hamiltonian theory of surface water waves the whitham equation is integrated numerically and it is shown that the equation gives a close approximation of inviscid free surface dynamics as described by the euler equations the performance of the whitham equation as a model for free surface dynamics is also compared to two standard free surface models the kdv and the bbm equation it is found that in a wide parameter range of amplitudes and wavelengths the whitham equation performs on par with or better than both the kdv and bbm equations

bifurcation diagram noise reduction and period four cycle on low frequency current oscillations in a semi insulating gaas sample abstract low frequency oscillations lfo on current i v t curves were studied in a gaas sample grown by molecular beam epitaxy our measurements were carried out at a temperature of 200 k and under infrared illumination the nonlinear i v characteristics give rise to spontaneous oscillations under constant applied bias v the attractors were constructed by the delay vector technique with the delay value given by minimal mutual information a bifurcation diagram was constructed from the minima sequence as a function of the applied bias a noise reduction algorithm applied to the raw data allowed the cleaning of the bifurcation diagram we have identified a bifurcation route of periodicity following the sequence 0 1 2 4 2 having the applied bias as the control parameter fourier transforms is a merit figure of the noise reduction procedure and also a qualitative proof of the chaotic regime

numerical bifurcation for the capillary whitham equation abstract the so called whitham equation arises in the modeling of free surface water waves and combines a generic nonlinear quadratic term with the exact linear dispersion relation for gravity waves on the free surface of a fluid with finite depth in this work the effect of incorporating capillarity into the whitham equation is in focus the capillary whitham equation is a nonlocal equation similar to the usual whitham equation but containing an additional term with a coefficient depending on the bond number which measures the relative strength of capillary and gravity effects on the wave motion a spectral collocation scheme for computing approximations to periodic traveling waves for the capillary whitham equation is put forward numerical approximations of periodic traveling waves are computed using a bifurcation approach and a number of bifurcation curves are found our analysis uncovers a rich structure of bifurcation patterns including subharmonic bifurcations as well as connecting and crossing branches indeed for some values of the bond number the bifurcation diagram features distinct branches of solutions which intersect at a secondary bifurcation point the same branches may also cross without connecting and some bifurcation curves feature self crossings without self connections

experimental observation of a complex periodic window the existence of a special periodic window in the two dimensional parameter space of an experimental chua s circuit is reported one of the main reasons that makes such a window special is that the observation of one implies that other similar periodic windows must exist for other parameter values however such a window has never been experimentally observed since its size in parameter space decreases exponentially with the period of the periodic attractor this property imposes clear limitations for its experimental detection

unstable dimension variability and synchronization of chaotic systems the nonhyperbolic structure of synchronization dynamics is investigated in this work we argue analytically and confirm numerically that the chaotic dynamics on the synchronization manifold exhibits an unstable dimension variability which is an extreme form of nonhyperbolicity we analyze the dynamics in the synchronization manifold and in its transversal direction where a tonguelike structure is formed through a system of two coupled chaotic maps the unstable dimension variability is revealed in the statistical distribution of the finite time transversal lyapunov exponent having both negative and positive values we also point out that unstable dimension variability is a cause of severe modeling difficulty

controlling chaotic dynamical systems abstract we describe a method that converts the motion on a chaotic attractor to a desired attracting time periodic motion by making only small time dependent perturbations of a control parameter the time periodic motion results from the stabilization of one of the infinite number of previously unstable periodic orbits embedded in the attractor the present paper extends that of ott grebogi and yorke phys rev lett 64 1990 1196 allowing for a more general choice of the feedback matrix and implementation to higher dimensional systems the method is illustrated by an application to the control of a periodically impulsively kicked dissipative mechanical system with two degrees of freedom resulting in a four dimensional map the double rotor map a key issue addressed is that of the dependence of the average time to achieve control on the size of the perturbations and on the choice of the feedback matrix

theta functions modular invariance and strings we use quillen s theorem and algebraic geometry to investigate the modular transformation properties of some quantities of interest in string theory in particular we show that the spin structure dependence of the chiral dirac determinant on a riemann surface is given by riemann s theta function we use this result to investigate the modular invariance of multiloop heterotic string amplitudes

the mumford form and the polyakov measure in string theory an explicit formula is derived for the mumford form on the moduli space of algebraic curves according to the belavin knizhnik theorem this gives a formula for the polyakov bosonic string measure

selberg supertrace formula for super riemann surfaces analytic properties of selberg super zeta functions and multiloop contributions for the fermionic string in this paper a complete derivation of the selberg supertrace formula for super riemann surfaces and a discussion of the analytic properties of the selberg super zeta functions is presented the selberg supertrace formula is based on laplace dirac operators m of weightm on super riemann surfaces the trace formula for allm z is derived and it is shown that one must discriminate between even and oddm particularly the term in the trace formula proportional to the identity transformation is sensitive to this discrimination the analytic properties of the two selberg super zeta functions are discussed in detail first with and the second without consideration of the spin structure we find for the selberg super zeta functions similarities as well as differences in comparison to the ordinary selberg zeta function also functional equations for the two selberg super zeta functions are derived the results are applied to discuss the spectrum of the laplace dirac operators and to ccalculate their determinants for the spectrum it is found that the nontrivial eigenvalues are the same for m and 0 up to a constant depending onm which is analogous to the bosonic case the analytic properties of the determinants can be deduced from the analytic properties of the selberg super zeta functions and it is shown that they are well defined special cases m 0 2 for the determinants are important in the polyakov approach for the fermionic string with these results it is deduced that the fermionic string integrand of the polyakov functional integral is well defined

modulational instability in the whitham equation with surface tension and vorticity abstract we study modulational stability and instability in the whitham equation combining the dispersion relation of water waves and a nonlinearity of the shallow water equations and modified to permit the effects of surface tension and constant vorticity when the surface tension coefficient is large we show that a periodic traveling wave of sufficiently small amplitude is unstable to long wavelength perturbations if the wave number is greater than a critical value and stable otherwise similarly to the benjamin feir instability of gravity waves in the case of weak surface tension we find intervals of stable and unstable wave numbers whose boundaries are associated with the extremum of the group velocity the resonance between the first and second harmonics the resonance between long and short waves and a resonance between dispersion and the nonlinearity for each constant vorticity we show that a periodic traveling wave of sufficiently small amplitude is unstable if the wave number is greater than a critical value and stable otherwise moreover it can be made stable for a sufficiently large vorticity the results agree with those based upon numerical computations or formal multiple scale expansions to the physical problem

two state on off intermittency caused by unstable dimension variability in periodically forced drift waves certain high dimensional dynamical systems present two or more attractors characterized by different energy branches for some parameter values the dynamics oscillates between these two branches in a seemingly random fashion a phenomenon called two state on off intermittency in this work we show that the dynamical mechanism underlying this intermittency involves the severe breakdown of hyperbolicity of the attractors through a mechanism known as unstable dimension variability we characterize the parametric evolution of this variability using statistical properties of the finite time lyapunov exponents as a model system that exhibits this behavior we consider periodically forced and damped drift waves in this spatiotemporal example there is a low dimensional chaotic attractor that is created by an interior crisis already presenting unstable dimension variability

hamiltonian long wave expansions for free surfaces and interfaces the theory of internal waves between two bodies of immiscible fluid is important both for its interest to ocean engineering and as a source of numerous interesting mathematical model equations which exhibit nonlinearity and dispersion in this paper we derive a hamiltonian formulation of the problem of a dynamic free interface with rigid lid upper boundary conditions and of a free surface and a free interface this latter situation occurring more commonly in experiment and in nature from the formulation we develop a hamiltonian perturbation theory for the long wave limits and we carry out a systematic analysis of the principal long wave scaling regimes this analysis provides a uniform treatment of the classical works of peters and stoker 28 benjamin 3 4 ono 26 and many others our considerations include the boussinesq and kdv regimes over finite depth fluids the benjamin ono regimes in the situation in which one fluid layer is infinitely deep and the intermediate long wave regimes in addition we describe a novel class of scaling regimes of the problem in which the amplitude of the interface disturbance is of the same order as the mean fluid depth and the characteristic small parameter corresponds to the slope of the interface our principal results are that we highlight the discrepancies between the case of rigid lid and of free surface upper boundary conditions which in some circumstances can be significant motivated by the recent results of choi and camassa 6 7 we also derive novel systems of nonlinear dispersive long wave equations in the large amplitude small slope regime our formulation of the dynamical free surface free interface problem is shown to be very effective for perturbation calculations and as well it holds promise as a basis for numerical simulations c 2000 wiley periodicals inc

geometry of superconformal manifolds the main facts about complex curves are generalized to superconformal manifolds the results thus obtained are relevant to the fermion string theory and in particular they are useful for computation of determinants of super laplacians which enter the string partition function

n 2 supertori and their representation as algebraic curves n 2 supertori n 2 super riemann surfaces of genus 1 are classified according to their superconformal equivalence classes a detailed description of the corresponding supermoduli space is based on this classification superelliptic functions are constructed and used for representing the supertori as algebraic varieties in projective superspace the boundary of n 2 genus 1 supermoduli space is discussed

the geometry of the super kp flows a supersymmetric generalization of the krichever map is used to construct algebro geometric solutions to the various super kadomtsev petviashvili skp hierarchies the geometric data required consist of a suitable algebraic supercurve of genusg generallynot a super riemann surface with a distinguished point and local coordinates z there and a generic line bundle of degreeg 1 with a local trivialization near the point the resulting solutions to the manin radul skp system describe coupled deformations of the line bundle and the supercurve itself in contrast to the ordinary kp system which deforms line bundles but not curves two new skp systems are introduced an integrable jacobian system whose solutions describe genuine jacobian flows deforming the bundle but not the curve and a nonintegrable maximal system describing independent deformations of bundle and curve the kac van de leur skp system describes the same deformations as the maximal system but in a different parametrization

numerical simulation of gravity waves abstract we present a new spectral method to simulate numerically the waterwave problem in a channel for a fluid of finite or infinite depth it is formulated in terms of the free surface elevation and the velocity potential the numerical method is based on the reduction of this problem to a lower dimensional computation involving surface variables alone to accomplish this we describe the taylor expansion of the dirichlet neumann operator in homogeneous powers of the surface elevation each term is a concatenation of fourier multipliers with powers of and its derivatives and is valid uniformly in wavenumber these are easily calculated using the fast fourier transform the method is illustrated by computing the long time evolution of modulated wave packets and of approximations to the stokes steady wave train by imposing a surface pressure we observe surface steepening in large amplitude evolution and wake and bow wave development for flows with a close to critical froude number finally we give an example of nonlinear evolution of the distribution of energy among normal modes

unstable dimension variability in coupled chaotic systems systems of coupled chaotic maps and flows arise in many situations of physical and biological interest the aim of this paper is to analyze and to present numerical evidence for a common type of nonhyperbolic behavior in these systems unstable dimension variability we show that unstable periodic orbits embedded in the dynamical invariant set of such a system can typically have different numbers of unstable directions the consequence of this may be severe the system cannot be modeled deterministically in the sense that no trajectory of the model can be realized by the natural chaotic system that the model is supposed to describe and quantify we argue that unstable dimension variability can arise for small values of the coupling parameter severe modeling difficulties nonetheless occur only for reasonable coupling when the unstable dimension variability is appreciable we speculate about the possible physical consequences in this case

unstable dimension variability structure in the parameter space of coupled henon maps coupled maps have been investigated to model the applications of periodic and chaotic dynamics of spatially extended systems we have studied the parameter space of coupled henon maps and showed that attractors possessing unstable dimension variability udv appear for parameters neighbouring the so called shrimp domains representing parameters leading to stable periodic behaviour therefore the udv should be very likely to be found in the same large class of natural and man made systems that present shrimp domains