bifurcations with o 3 symmetry including applications to the benard problem this paper has two purposes to study from the singularity theory point of view certain bifurcation problems which commute with the five dimensional irreducible representation of the orthogonal group o 3 and to give some implications of this study for the benard problem in spherical geometry we shall now describe in general terms our results and compare them with the work of chossat 3 whose paper motivated our own interest in the problem the benard problem is concerned with convection in a viscous fluid when it is heated from below the fluid is assumed to be confined in a spherical shell of outer radius r and inner radius qro where q is near 0 3 this choice of q is partially motivated by considering convection within the molten layer of the core of the earth see busse l for further discussion we consider the binard problem in the boussinesq approximation in this model there is a trivial solution representing pure heat conduction radially outward as the temperature on the inner sphere that is the rayleigh number r is increased this trivial solution loses stability say at r r the benard problem is the study of the resulting bifurcation chossat studies this problem using the lyapunov schmidt reduction in the boussinesq approximation the fluid is driven from the pure conduction state by a term in the momentum equation involving the gravity vector g r and a term in the temperature equation involving the gradient of the conduction temperature vt assuming that the production of heat and the density are uniform throughout the shell these vectors have the form

bifurcations of subharmonic solutions in reversible systems soit f r r n r r n une application c periodique cut on dit que l equation differentielle x f t x est reversible s il existe un operateur symetrique s sur r n tel que s 2 i de telles equations differentielles sont aussi appelees systemes avec la propriete e par rapport a s on etudie les bifurcations des solutions sous harmoniques de tels systemes reversibles

ergodicity of probabilistic cellular automata a constructive criterion we give a sequence of criteria of increasing complexity for the exponential ergodicity of discrete time interacting particle systems each criterion involves estimating the dependence on initial conditions of the process on finite space time volumes it generalizes and improves the existing single site condition and is the analog of the dobrushin shlosmanc v condition in equilibrium statistical mechanics our dynamic criterion may also be used to prove the uniqueness of gibbs state in situations where thec v condition fails as a converse we prove that if there is a certain form of convergence to the stationary measure faster thann d wheren is the time andd is the dimension of the lattice then our condition holds for some space time volumes and hence the convergence must be exponentially fast

when is an interacting particle system ergodic we consider stochastic flip dynamics for an infinite number of ising spins on the lattice d we find a sequence of constructive criteria for the system to be exponentially ergodic the main idea is to approximate the continuous time process with discrete time processes itseuler polygon and to use an improved version of previous results ms about constructive ergodicity of discrete time processes

analytical solution of spatial elastica and its application to kinking problem abstract an analytical solution is presented for the spatially large deformation of a thin elastic rod spatial elastica which is naturally straight and uniform with equal principal stiffnesses and is subjected to terminal loads the elastica can suffer not only flexure and torsion as in the classical kirchhoff theory but also extension and shear the present solution is expressed in integral form and described in terms of only four parameters this solution clears the difficulty with the polar singularity in the use of euler angles hence the numerical analysis is possible for various boundary value problems with no limitation in this paper we study the post buckling behavior of an elastica under the terminal twist and uniaxial end shortening and give a theoretical explanation to commonly observed phenomena such as secondary bifurcation formation of a kink snap through behavior the contact problem is analyzed in the case where the elastica contacts with itself and forms a kink these results are available for other analysis e g based on finite element approximations

bifurcation from a normally degenerate manifold local bifurcation theory typically deals with the response of a degenerate but isolated equilibrium state or periodic orbit of a dynamical system to perturbations controlled by one or more independent parameters and characteristically uses tools from singularity theory there are many situations however in which the equilibrium state or periodic orbit is not isolated but belongs to a manifold s of such states typically as a result of continuous symmetries in the problem in this case the bifurcation analysis requires a combination of local and global methods and is most tractable in the case of normal nondegeneracy that is when the degeneracy is only along s itself and the system is nondegenerate in directions normal to s in this paper we consider the consequences of relaxing normal nondegeneracy which can generically occur within 1 parameter families of such systems we pay particular attention to the simplest but important case where dim s 1 and where the normal degeneracy occurs with corank 1 our main focus is on uniform degeneracy along s although we also consider aspects of the branching structure for solutions when the degeneracy varies at different places on s the tools are those of singularity theory adapted to global topology of s which allow us to explain the bifurcation geometry in a natural way in particular we extend and give a clear geometric setting for earlier analytical results of hale and taboas

iterated function systems ruelle operators and invariant projective measures we introduce a fourier based harmonic analysis for a class of discrete dynamical systems which arise from iterated function systems our starting point is the following pair of special features of these systems 1 we assume that a measurable space x comes with a finite to one endomorphism r x x which is onto but not one to one 2 in the case of affine iterated function systems ifss in r d this harmonic analysis arises naturally as a spectral duality defined from a given pair of finite subsets b l in r d of the same cardinality which generate complex hadamard matrices our harmonic analysis for these iterated function systems ifs x is based on a markov process on certain paths the probabilities are determined by a weight function w on x from w we define a transition operator r w acting on functions on x and a corresponding class h of continuous r w harmonic functions the properties of the functions in h are analyzed and they determine the spectral theory of l 2 for affine ifss we establish orthogonal bases in l 2 these bases are generated by paths with infinite repetition of finite words we use this in the last section to analyze tiles in r d

a group theoretic approach to the global bifurcation analysis of an axially compressed cylindrical shell abstract the accurate prediction of the buckling load of thin shell structures is an important yet elusive goal it is particularly important in the aerospace industry where thin shell members are commonly used as structural elements due to a lack of adequate analytical results current practices in industry put heavy reliance on experimental testing and empirical data to supplement theoretical analysis see d bushnell computerized buckling analysis of shells martinus nijhoff dordrecht 1985 this paper focuses on recent results of the group theoretic approach to a numerical global postbuckling analysis of a perfect axially compressed cylindrical shell with built in end conditions the built in end conditions obviate the existence of a trivial membrane solution branch the example of an axially compressed cylindrical shell was chosen because it is well known that for thin shells the primary axisymmetric solution branch is riddled with closely spaced symmetry breaking bifurcation points in a numerical arc length continuation scheme the close proximity of the bifurcation points on the primary path manifests itself in severe ill conditioning of the tangent stiffness matrix group theory helps one systematically find an optimal set of basis vectors or symmetry modes which reflect the symmetry of a given solution path the immediate payoff in using these symmetry modes as basis vectors is that the tangent stiffness matrix block diagonalizes and the numerical ill conditioning is avoided thus an efficient and accurate technique for computing solution branches of a specific type and a subsequent diagnosis for symmetry breaking bifurcations is made relatively simple understanding the global behavior of the perfect structure is crucial in identifying critical imperfections and will ultimately diminish the heavy reliance on expensive experimental verification

heteroclinic cycles in dynamical systems with broken spherical symmetry in mathematics and physics the phrase symmetry breaking has two distinct meanings the first refers to the frequently observed phenomenon that a configuration of a physical system satisfying a law a set of equations which is invariant under a group of transformations may itself only be invariant under a subgroup of this group this is referred to as spontaneous symmetry breaking the second meaning refers to the process of explicitly adding symmetry breaking terms to the equations which describe the system this we call induced or forced symmetry breaking over the past decade spontaneous symmetry breaking has attracted a considerable amount of attention within the context of bifurcation and dynamical systems theory see for example 13 previous work on forced symmetry breaking has mainly concentrated on the persistance of equilibrium solutions under small symmetry breaking perturbations of symmetric systems 3 4 2 7 8 12 22 231 the main aim of this paper is to show that such perturbations may also give rise to more complex dynamical behavior in particular to heteroclinic cycles we first present a simple example of our constructions for the particular choices of groups g so 3 h so 2 and k t described below in order to illustrate these general ideas without too many technicalities we return to a rigorous discussion of these types of problems in section 2

an efficient mathcal q tensor based algorithm for liquid crystal alignment away from defects we develop a fast and accurate approximation of the normally stiff equations which minimize the landau de gennes free energy of a nematic liquid crystal the resulting equations are suitable for all configurations in which defects are not present making them ideal for device simulation specifically they offer an increase in computational efficiency by a factor of 100 while maintaining an error of order 10 4 when compared to the full stiff equations as this approximation is based on a mathcal q tensor formalism the sign reversal symmetry of the liquid crystal is respected in this paper we derive these equations for a simple two dimensional case where the director is restricted to a plane and also for the full three dimensional case an approximation of the error in the perturbation scheme is derived in terms of the first order correction and a comparison to the full stiff equations is given

quantum cellular automata tensor networks and area laws quantum cellular automata are unitary maps that preserve locality and respect causality we identify them in any dimension with simple tensor networks projected entangled pair unitary whose bond dimension does not grow with the system size as a result they satisfy an area law for the entanglement entropy they can create we define other classes of nonunitary maps the so called quantum channels that either respect causality or preserve locality we show that whereas the latter obey an area law for the number of quantum correlations they can create as measured by the quantum mutual information the former may violate it we also show that neither of them can be expressed as tensor networks with a bond dimension that is independent of the system size

linearization stability and signorini series for the traction problems in elastostatics this paper uses previous results of chillingworth marsden and wan on symmetry and bifurcation for the traction problem in three dimensional elastostatics to establish new results on the signorini expansion we show that the signorini compatibility conditions are necessary and sufficient for linearization stability and analogies with results known for other field theories are pointed out under an explicit non degeneracy condition a new series expansion is given in which successive terms are inductively determined in pairs rather than singly our results include as special cases classical results of signorini tolotti and stopelli

finite dimensional approximation of bifurcation problems in presence of symmetries we give here a brief summary of the results of 4 14 the aim of our work was not only the finite dimensional approximation of the specific problem studied in 3 but we also wanted to show how to adapt to discrete problems and how to use in this case some classical mathematical tools e g the splitting lemma of gromoll meyer magnus the singularity theory etc such considerations are developed in 5 in particular we prove in 5 that in most cases e g in the examples given in 6 7 9 10 the discrete bifurcation problem behaves as an imperfect bifurcation problem and we improve the methods of 12 another way to use universal unfoldings in the approxima tion of bifurcation problems is suggested by 2

symmetry and bifurcations of momentum mappings the zero set of a momentum mapping is shown to have a singularity at each point with symmetry the zero set is diffeomorphic to the product of a manifold and the zero set of a homogeneous quadratic function the proof uses the kuranishi theory of deformations among the applications it is shown that the set of all solutions of the yang mills equations on a lorentz manifold has a singularity at any solution with symmetry in the sense of a pure gauge symmetry similarly the set of solutions of einstein s equations has a singularity at any solution that has spacelike killing fields provided the spacetime has a compact cauchy surface

statistical mechanics of probabilistic cellular automata we investigate the behavior of discrete time probabilistic cellular automata pca which are markov processes on spin configurations on ad dimensional lattice from a rigorous statistical mechanics point of view in particular we exploit whenever possible the correspondence between stationary measures on the space time histories of pcas on d and translation invariant gibbs states for a related hamiltonian on d 1 this leads to a simple large deviation formula for the space time histories of the pca and a proof that in a high temperature regime the stationary states of the pca are gibbsian we also obtain results about entropy fluctuations and correlation inequalities and demonstrate uniqueness of the invariant state and exponential decay of correlations in a high noise regime we discuss phase transitions in the low noise or low temperature regime and review toom s proof of nonergodicity of a certain class of pcas

a multiplicity of localised buckling modes for twisted rod equations the kirchhoff love equations governing the spatial equilibria of long thin elastic rods subject to end tension and moment are reviewed and used to examine the existence of localized buckling solutions the effects of shear and axial extension are not considered but the model does additionally allow for nonlinear constitutive laws under the assumption of infinite length the dynamical phase space analogy allows one to use techniques from dynamical systems theory to characterize many possible equilibrium paths localizing solutions correspond to homoclinic orbits of the dynamical system under non dimensionalization the twisted rod equations are shown to depend on a single load parameter and the bifurcation behaviour of localizing solutions of this problem is investigated using analytical and numerical techniques first in the case of a rod with equal principal bending stiffnesses where the equilibrium equations are completely integrable a known one parameter family of localizing solutions is computed for a variety of subcritical loads load deflection diagrams are computed for this family and certain materially nonlinear constitutive laws are shown to make little difference to the qualitative picture the breaking of the geometrical circular symmetry destroys complete integrability and in particular breaks the non transverse intersection of the stable and unstable manifolds of the trivial steady state the resulting transverse intersection which is already known to lead to spatial chaos is explicitly demonstrated to imply a multitude of localized buckling modes a sample of primary and multi modal solutions are computed numerically aided by the reversibility of the differential equations finally parallels are drawn with the conceptually simpler problem of a strut resting on a nonlinear elastic foundation for which much more information is known about the global behaviour of localized buckling modes

systematic description of imperfect bifurcation behavior of symmetric systems abstract a systematic method is presented for describing experimental curves of force vs strain of a system with regular polygonal dihedral group symmetry subject to bifurcation behavior with an aim toward overcoming the following problems 1 it is difficult to judge whether the system is undergoing bifurcation or not 2 the perfect behavior of the system cannot be known due to the presence of initial imperfections 3 those curves are often qualitatively different from bifurcation diagrams predicted by mathematics the tools employed are the asymptotic theory for imperfect bifurcation such as the koiter law and the stochastic theory of initial imperfections the former theory is extended in this paper to the system with regular polygonal symmetry to present asymptotic laws for recovering perfect curves with reference to the experimental ones these laws are formulated for physically observable displacements instead of the variables in the mathematical bifurcation diagrams in order to make them readily applicable to the experimental curves the stochastic theory is combined with an asymptotic law to develop a means to identify the multiplicity of the bifurcation point the systematic method for describing the experimental curves developed in this manner is applied to the bifurcation analysis of regular polygonal truss domes to testify its validity furthermore this method is applied to the shear behavior of cylindrical sand specimens to show that they in fact are undergoing bifurcation and in turn to demonstrate the importance of a viewpoint of bifurcation in the study of shear behavior of materials the need of a dual viewpoint of bifurcation and plasticity in the study of constitutive relationship of materials is emphasized to conclude the paper

classification and unfolding of degenerate hopf bifurcations with o 2 symmetry no distinguished parameter abstract the hopf bifurcation in the presence of o 2 symmetry is considered when the bifurcation breaks the symmetry the critical imaginary eigenvalues have multiplicity two and generically there are two primary branches of periodic orbits which bifurcate simultaneously in applications these correspond to rotating traveling waves and standing waves using equivariant singularity theory a classification of all such bifurcations up to and including codimension three is presented no distinguished parameter is assumed the universal unfoldings reveal the existence of both 2 tori and 3 tori corresponding to quasiperiodic waves with two and three independent frequencies respectively

computational methods for bifurcation problems with symmetries with special attention to steady state and hopf bifurcation points we show how group theoretical methods can be employed to utilize the symmetry of a bifurcation problem in numerical computations we extend the approach by werner 1988 by presenting methods for the detection of bifurcation points and the computation of multiple hopf points the essential numerical point is the utilization of certain reduced instead of full systems involving appropriate subgroups of the underlying symmetry group the group theoretical tool is an a priori knowledge of the interaction of certain subgroups 0 and of at possibly multiple steady state or hopf bifurcation points minimal 0 breaking bifurcation we introduce a bifurcation graph which shows graphically this a priori information its edges represent possible symmetry breaking bifurcations our analysis follows the lines of golubitsky stewart and schaeffer 1988 but it is aimed to numerical applications we have chosen a 4 box brusselator model in order to explain our notions and ideas and to discuss the numerical procedure

the aperture admittance of a circumferential slot in a circular cylinder a circumferential slot in an infinitely long cylinder when fed with a tangential electric field is considered parseval s theorem in which fourier integrals appear is used to express the aperture admittance as the integral from zero to infinity of an infinite series recognizing that the first two terms of this infinite series have a nonintegrable singularity when the variable of integration w is equal to the wavenumber k the authors distort slightly the contour of integration to avoid k the terms of the infinite series are then approximated when w is close to k a combination of numerical and analytical schemes employing both large and small argument approximations of hankel functions is used to perform the integration it has been found that these integration schemes work very well and a simple and fast algorithm has resulted

post bifurcation and stability of a finitely strained hexagonal honeycomb subjected to equi biaxial in plane loading abstract the buckling and crushing mechanics of cellular honeycomb materials is an important engineering problem motivated by the pioneering experimental and numerical studies of papka and kyriakides 1994 1999a b we review the literature on finitely strained honeycombs subjected to in plane loading and identify two open questions i how does the mechanical response of the honeycomb depend on the applied loading device and ii what can the bloch wave representation of all bounded perturbations contribute to our understanding of the stability of post bifurcated equilibrium configurations to address these issues we model the honeycomb as a two dimensional infinite perfect periodic medium we use analytical group theory methods as opposed to the more common but less robust imperfection method to study the honeycomb s bifurcation behavior under three different far field loadings that produce initially the same equi biaxial contractive dilatation using an fem discretization of the honeycomb walls struts we solve the equilibrium equations to find the principal and bifurcated equilibrium paths for each of the three loading cases we evaluate the structure s stability using two criteria rank one convexity of the homogenized continuum long wavelength perturbations and bloch wave stability bounded perturbations of arbitrary wavelength we find that the post bifurcation behavior is extremely sensitive to the applied loading device in spite of a common principal solution we confirm that the flower mode is always unstable as previously reported however our first ever bloch wave stability analysis of the post bifurcated equilibrium paths shows that the flower mode is stable for all sufficiently short wavelength perturbations this new result provides a realistic explanation for why this mode has been observed in the finite size specimen experiments of papka and kyriakides 1999a

lock on to tape like behaviour in the torsional buckling of anisotropic rods abstract through nonlinear normal form analysis of the equilibrium equations developed in a neighbourhood of the straight rod solution we show the existence of a phase transition from mildly anisotropic to full tape like buckling in non symmetric rods subject to terminal loads provided the material has a sufficiently low poisson s ratio for a solid elliptical rod with a poisson s ratio of 0 2 the critical point is found to occur at a cross sectional aspect ratio of just over 3 for larger aspect ratios the rod locks on to a one twist per wave buckling mode with no internal twist in the mildly anisotropic regime there turn out to be two physically distinct pairs of symmetric so called primary localised buckling modes differing in the phase of the internal twist these four modes homoclinic orbits remain of the full circle of localised buckling modes existing in the symmetric case after breaking of the circular symmetry of the rod s cross section in the strongly anisotropic regime only the energetically favourable pair of flat buckling modes survives

the g invariant implicit function theorem in infinite dimensions ii our basic theorem is a version of the implicit function theorem in the case of continuous groups of symmetries the result is sufficiently general to cover a great many applications it generalizes some earlier work of the author and corrects and improves some work of vanderbauwhede we also consider the breaking of symmetries problem and the variational case finally we apply our results to study the periodic solutions of an ordinary differential equation

quasiconvexity and uniqueness of equilibrium solutions in nonlinear elasticity in this paper we prove the uniqueness of the solution to certain simple displacement boundary value problems in the nonlinear theory of homogeneous hyperelasticity for a body occupying a star shaped reference configuration rn whose boundary is subjected to an affine deformation i e there exists a constant n n matrix f and a constant n vector b such that x fx b for all x we consider all smooth equilibrium configurations satisfying this boundary condition clearly the homogeneous deformation x fx b for all x in bar omega is one such solution our aim is to prove under suitable hypotheses that it is the only such solution

analysis of cylindrical antennas a spectral iteration technique the cylindrical antenna problem has been tackled using the spectral iteration technique an iterative scheme is employed for improving on an initially assumed form of the current distribution use is made of the fast fourier transform fft algorithm and the cumbersome process of matrix inversion is circumvented consequently this method is capable of handling a larger number of unknown coefficients in the expansion of the current distribution furthermore it provides a convenient means of testing for the satisfaction of the boundary conditions on the surface of the antenna convergence criteria for the iteration process have been established and the use of an acceleration procedure is illustrated different types of source models have been investigated and the convergence of both local and nonlocal parameters is also discussed

finitely correlated states on quantum spin chains we study a construction that yields a class of translation invariant states on quantum spin chains characterized by the property that the correlations across any bond can be modeled on a finite dimensional vector space these states can be considered as generalized valence bond states and they are dense in the set of all translation invariant states we develop a complete theory of the ergodic decomposition of such states including the decomposition into periodic neel ordered states the ergodic components have exponential decay of correlations all states considered can be obtained as local functions of states of a special kind so called purely generated states which are shown to be ground states for suitably chosen finite range vbs interactions we show that all these generalized vbs models have a spectral gap our theory does not require symmetry of the state with respect to a local gauge group in particular we illustrate our results with a one parameter family of examples which are not isotropic except for one special case this isotropic model coincides with the one dimensional antiferromagnet recently studied by affleck kennedy lieb and tasaki

ground states of fermions on lattices we consider fermion systems on integer lattices we establish the existence of dynamics for a class of long range interactions the infinite volume ground states are considered the equivalence of the variational principle and ground state conditions is proved for long range interactions we also prove that any pure translationally invariant ground state of the gauge invariant algebra is extendible to a ground state of the full car algebra for the hamiltonian with a chemical potential equivalence of ensemble for canonical and ground canonical states at the zero temperature

almost global tracking of simple mechanical systems on a general class of lie groups we present a general intrinsic tracking controller design for fully actuated simple mechanical systems when the configuration space is one of a general class of lie groups we first express a state feedback controller in terms of a function the error function satisfying certain regularity conditions if an error function can be found then a general smooth and bounded reference trajectory may be tracked asymptotically from almost every initial condition with locally exponential convergence asymptotic convergence from almost every initial condition is referred to as almost global asymptotic stability error functions may be shown to exist on any compact lie group or any lie group diffeomorphic to the product of a compact lie group and r sup n this covers many cases of practical interest such as so n se n their subgroups and direct products we show here that for compact lie groups the dynamic configuration feedback controller obtained by composing the full state feedback law with an exponentially convergent velocity observer is also almost globally asymptotically stable with respect to the tracking error we emphasize that no invariance is needed for these results however for the special case where the kinetic energy is left invariant we show that the explicit expression of these controllers does not require coordinates on the lie group the controller constructions are demonstrated on so 3 and simulated for the axi symmetric top results show excellent performance

the traction problem for incompressible materials on traite ce probleme comme un probleme de bifurcation en utilisant une approche variationnelle et une approche en series de puissance classique

symmetry and bifurcation in three dimensional elasticity part i in part i of this paper chillingworth marsden and wan 1982 hereafter referred to as 1 we reformulated the traction problem in elastostatics in various forms gave a classification of loads and gave complete analysis of solutions of the traction problem that are nearly stress free for loads near loads of type 0 and type 1 this part develops the basic theory as well as giving an analysis of solutions for loads of types 2 3 and 4 it includes a count of the numbers of solutions and an analysis of their stability and the structural stability of the bifurcation diagrams we begin in section 2 with a derivation of a potential formulation of the problem on so 3 the second order potential used in 1 can be recovered as a special case it follows from this that the traction problem always has at least four solutions at least one of which is neutrally stable for loads of type 0 we showed in 1 that there are exactly four solutions near so 3 for the other types there can be many more up to 40 section 3 4 and 5 examine types 2 3 and 4 respectively in a manner analogous to our treatment of types 0 and 1 in 1 loads of type 3 and 4 have some special features already studied in the literature in connection with parallel loads these special features will be discussed and other connections with the existing literature will be made at appropriate points throughout the paper

the equivalent parameters for the radiating slot on a sectoral waveguide formulas for the field components of the te sub pq mode and the dominant mode te sub 11 in a sectoral waveguide are given using the equivalence principle the electric field distribution on the aperture surface of a narrow longitudinal slot cut in the curved broad wall of a sectoral waveguide is solved by the moment method galerkin s method important results such as the scattering parameters the equivalent shunt admittance and the resonant conductance and length are studied the method used in this paper has good precision and has been adopted in the design of a linear slot array

radiation from narrow circumferential slots on a conducting circular cylinder radiation from narrow circumferential slots on a conducting circular cylinder is analyzed the incident tm sub 01 mode is assumed to propagate along a thick conducting cylinder multiply slotted in the axial direction the fourier transform and mode matching are utilized to obtain a set of simultaneous equations for the discrete modal coefficients simple fast convergent series solutions are presented using residue calculus the radiation transmission and reflection characteristics are investigated in terms of the operating frequency and slot geometry our numerical results agree favorably with other existing data as well as measurements at x band

abstract forced symmetry breaking and forced frequency locking of modulated waves we consider abstract forced symmetry breaking problems of the typef x y it is supposed that for all the mapsf are equivariant with respect to the action of a compact lie group thatf x0 0 0 and hence thatf x 0 0 for all elementsxof the group orbit o x0 ofx0 we look for solutionsxwhich bifurcate from the solution family o x0 as andymove away from 0and zero respectively especially we describe the number of different solutionsx for fixed control parameters andy their dynamic stability and their asymptotic behavior forytending to zero further generalizations are given to problems of the typef x y x finally our results are applied to a forced frequency locking problem of the typex t f x t y t here it is supposed that the vector fieldsf ares1 equivariant that the unperturbed equationx f x 0 has an orbitally stable modulated wave solution and that the forcingy t is a modulated wave

radiation from multiple circumferential slots on a conducting circular cylinder electromagnetic wave radiation from multiple circumferential slots on a conducting circular cylinder is theoretically investigated the fourier transform series technique is used to represent the continuous and discrete modes of the scattered field the mode matching is utilized to constitute a set of simultaneous equations for the discrete modal coefficients the residue calculus is applied to transform the scattered field integral representations into fast converging series forms thereby facilitating the numerical computations numerical computations illustrate the behavior of radiation in terms of the slot geometry the incident mode and the operating frequency

from equilibrium spin models to probabilistic cellular automata the general equivalence betweend dimensional probabilistic cellular automata pca and d 1 dimensional equilibrium spin models satisfying a disorder condition is first described in a pedagogical way and then used to analyze the phase diagrams the critical behavior and the universality classes of some automata diagrammatic representations of time dependent correlation functions of pca are introduced two important classes of pca are singled out for which these correlation functions simplify 1 quasi hamiltonian automata which have a current carrying steady state and for which some correlation functions are those of ad dimensional static model pca satisfying the detailed balance condition appear as a particular case of these rules for which the current vanishes 2 linear and more generally affine pca for which the diagrammatics reduces to a random walk problem closely related to d 1 dimensional directed saws both problems display a critical behavior with mean field exponents in any dimension the correlation length and effective velocity of propagation of excitations can be calculated for affine pca as is shown on an explicitd 1 example we conclude with some remarks on nonlinear pca for which the diagrammatics is related to reaction diffusion processes and which belong in some cases to the universality class of reggeon field theory

ergodicity of quantum cellular automata we define a class of dynamical maps on the quasi local algebra of a quantum spin system which are quantum analoges of probabilistic cellular automata we develop criteria for such a system to be ergodic i e to posses a unique invariant state intuitively ergodicity obtains if the local transition operators exhibit sufficiently large disorder the ergodicity criteria also imply bounds for the exponential decay of correlations in the unique invariant state the main technical tool is a quantum version of oscillation norms defined in the classical case as the sum over all sites of the variations of an observable with respect to local spin flips

finitely correlated pure states this paper is a report on joint work with mark fannes and bruno nachtergaele on a class of states on one dimensional quantum spin systems called finitely correlated these states can be constructed quite explicitly which in itself is remarkable since apart from quasi free states or convex combinations of product states there seem to be no states allowing a similarly complete control one of their characteristic properties is the absence of a certain typically quantum mechanical frustration phenomenon in this sense they do not exhibit the full complexity of quantum mechanical correla tions on the other hand the structure of this class is very rich and it is large enough to approximate any translationally invariant state in the weak topology moreover finitely correlated states appear as the exact ground states in physical models particu larly of antiferromagnetism therefore their study is an ideal vantage point from which to begin an exploration of the complexities of quantum mechanical correlations the aim of the present article is to give an overview of some of the results obtained so far emphasizing motivations and intuitive ideas and referring to the journal articles for the technical aspects and further references

cellular automata for nanometer scale computation abstract cellular automata have recently been proposed as an architecture for dense locally interacting arrays of submicron devices however because conventional von neumann cellular automata do not correctly reflect the long range behavior of typical inter device interactions they do not provide a suitable theoretical model for the proposed device arrays in this paper we define replica cellular automata a class of cellular automata that can be generated from lattice gas cellular automata we show that for inter device interactions that have a well defined screening length d replica cellular automata provide a suitable formal model as an example of their applicability we exhibit a computation universal cellular automata architecture in which the cells consist of charge transfer quantum dot devices

invariance under the dihedral group and application to bifurcation problems soit un groupe d ordre agissant lineairement sur r s et soient 1 2 t des generateurs homogenes de r x 1 x s l algebre de tous les polynomes invariants a s variables si f est une fonction invariante de classe c m sur r s avec 0 m alors il existe une fonction f c p r t telle que f f 1 t avec p sup 0 m s 1 on considere ici le cas s 2 d n le groupe diedre d ordre 2n avec n 2

admittance of rectangular waveguide radiating from a conducting cylinder theory and experiment are compared for the admittance presented to a rectangular waveguide which terminates at an arbitrary angle in the surface of a conducting cylinder two methods are described for calculating the admittance a single mode approximation from the modal solution and an alternative asymptotic solution using these methods the effect of aperture orientation on admittance and the results obtained are compared with the experiment the single mode approximation is in good agreement with experimental results for the case when the input waveguide supports the te sub 10 mode only the accuracy of the approximate formula for waveguide admittance was also verified the admittance is shown to be weakly dependent on aperture orientation for moderately large cylinders

ein operatorwertiger hahn banach satz abstract we generalize arveson s extension theorem for completely positive mappings 1 to a hahn banach principle for matricial sublinear functionals with values in an injective c algebra or an ideal in b h we characterize injective w algebras by a matricial order condition we illustrate the matricial hahn banach principle by three applications 1 let a b b be unital c algebras b a subalgebra of a and b b injective if a b is a completely bounded self adjoint b bihomomorphism then it can be expressed as the difference of two completely positive b bihomomorphism 2 let m be a w algebra containing 1 h on a hilbert space h if m is finite and hyperfinite there exists an invariant expectation mapping p of b h onto m p is an extension of the center trace 3 combes 7 proved that a lower semicontinuous scalar weight on a c algebra is the upper envelope of bounded positive functionals we generalize this result to unbounded completely positive mappings with values in an injective w algebra

on perturbations of a translationally invariant differential equation on etudie certaines perturbations de l equation differentielle u u up 0 sur tout l espace euclidien a n dimensions on obtient des conditions qui assurent l existence d une solution a l equation perturbee pres d une solution donnee de l equation non perturbee

passive velocity field control pvfc part ii application to contour following when the contour following task is represented by a velocity field on the configuration manifold of the system the coordination aspect of the problem is made explicit the pvfc scheme developed in the part i ibid vol 29 9 2001 can then be applied to track the defined velocity field however for some contours an encoding velocity held on the configuration manifold does not exist or is difficult to define and as a consequence the pvfc cannot be directly applied for systems whose configuration manifolds are compact lie groups and the desired contour is represented by a parameterized trajectory a general methodology is developed using a suspension technique to define a velocity field on a manifold related to the configuration manifold of the system for which pvfc can be applied with this strategy timing along the contour can be naturally varied online by a self pacing scheme so that the contour tracking performance can be improved the experimental results for a 2 dof robot following a lissajous contour illustrates and verifies the convergence and robustness properties of the pvfc methodology