near field performance analysis of locally conformal perfectly matched absorbers via monte carlo simulations in the numerical solution of some boundary value problems by the finite element method fem the unbounded domain must be truncated by an artificial absorbing boundary or layer to have a bounded computational domain the perfectly matched layer pml approach is based on the truncation of the computational domain by a reflectionless artificial layer which absorbs outgoing waves regardless of their frequency and angle of incidence in this paper we present the near field numerical performance analysis of our new pml approach which we call as locally conformal pml using monte carlo simulations the locally conformal pml method is an easily implementable conformal pml implementation to the problem of mesh truncation in the fem the most distinguished feature of the method is its simplicity and flexibility to design conformal pmls over challenging geometries especially those with curvature discontinuities in a straightforward way without using artificial absorbers the method is based on a special complex coordinate transformation which is locally defined for each point inside the pml region the method can be implemented in an existing fem software by just replacing the nodal coordinates inside the pml region by their complex counterparts obtained via complex coordinate transformation we first introduce the analytical derivation of the locally conformal pml method for the fem solution of the two dimensional scalar helmholtz equation arising in the mathematical modeling of various steady state or time harmonic wave phenomena then we carry out its numerical performance analysis by means of some monte carlo simulations which consider both the problem of constructing the two dimensional green s function and some specific cases of electromagnetic scattering

coupled map lattices with complex order parameter abstract we introduce and study coupled map lattices with complex state variable the dynamical regimes of the finite length systems are classified naturally in terms of a topological invariant the overall phase shift accumulated along the whole length at fixed time a stability analysis of the spatially uniform states is presented and the results of numerical simulations of the spatio temporal dynamics are discussed we demonstrate that fast amplitude evolution including regular and chaotic spatio temporal behavior takes place on the background of a slower phase evolution for large values of the topological invariant the phase dynamics may give rise to an instability which in some cases results in a jump of the system to another value of the invariant we also consider the formation of long lived bubbles i e local domains of complicated dynamics in the spatial regions of locally reduced phase gradient our coupled map lattice model and its generalizations may be useful for understanding the dynamics in a larger range of parameters for such nonlinear dissipative media which allow small amplitude description in terms of the complex ginzburg landau equation as well as for time delay feedback systems with nonzero central frequency of the generated signal

a note on the one particle and hilbert schmidt cohomologies of the poincare group in three spacetime dimensions cocycles for p up arrow 2 1 with values in a hilbert space are studied it is found that cocycles for irreducible representations apart from the case of vanishing momentum are trivial further cocycles for the action v v 1 with values in the representation space of v are investigated and found to be trivial some consequences for physics are obtained

large deviations and nontrivial exponents in coarsening systems we investigate the statistics of the mean magnetization of its large deviations and persistent large deviations in simple coarsening systems in particular we consider more specifically the case of the diffusion equation of the ising chain at zero temperature and of the two dimensional voter model for the diffusion equation at large times the mean magnetization has a limit law which is studied analytically using the independent interval approximation the probability of persistent large deviations defined as the probability that the mean magnetization was for all previous times greater than some level x decays algebraically at large times with an exponent continuously varying with x when x 1 is the usual persistence exponent similar behaviour is found for the glauber ising chain at zero temperature for the two dimensional voter model large deviations of the mean magnetization are algebraic while the probability of persistent large deviations seem to behave as the usual persistence probability

combining perturbation theory and transformation electromagnetics for finite element solution of helmholtz type scattering problems a numerical method is proposed for efficient solution of scattering from objects with weakly perturbed surfaces by combining the perturbation theory transformation electromagnetics and the finite element method a transformation medium layer is designed over the smooth surface and the material parameters of the medium are determined by means of a coordinate transformation that maps the smooth surface to the perturbed surface the perturbed fields within the domain are computed by employing the material parameters and the fields of the smooth surface as source terms in the helmholtz equation the main advantage of the proposed approach is that if repeated solutions are needed such as in monte carlo technique or in optimization problems requiring multiple solutions for a set of perturbed surfaces computational resources considerably decrease because a single mesh is used and the global matrix is formed only once only the right hand side vector is changed with respect to the perturbed material parameters corresponding to each of the perturbed surfaces the technique is validated via finite element simulations

automorphisms of the canonical anticommutation relations and index theory let h be a complex hilbert space p an orthogonal projection on h and p the complementary projection if g is any symmetrically normed ideal in the ring of bounded operators on h then we consider the group of unitary operators on h such that p up and p u p lie in g when g is the hilbert schmidt class these unitaries define automorphisms of the c algebra b of the canonical anticommutation relations over h which are implementable in the representation of b determined by p we investigate the structure of the group u proving in particular that it has infinitely many connected components uk labelled by the fredholm index of p u p the connected component of the identity u0 is generated by unitaries of the form exp ia with a self adjoint and p a p in g finally we consider an application of these results to two dimensional field theory showing in particular that the charge and chiral charge quantum numbers arise as the fredholm indices of p up for certain unitary u on l2 r c2

a superversion of quasifree second quantization i charged particles a formalism comprising and extending quasifree second quantization of charged bosons and fermions is presented the second quantization of one particle observables leads to current superalgebras and a super schwinger term shows up anticommuting parameters are introduced in order to construct super bogoliubov transformations mixing bosons and fermions as an application representations of lie superalgebras are given which are semidirect products of extensions of affine kac moody algebras and the virasoro algebra and of the super virasoro algebra

twisted condensates of quantised fields the authors construct some quasi free pure states of three quantised fields in 1 1 dimensions that are localised in the sense of knight 1961 they consider massless or massive dirac fields forming a u n n or 1 multiplet and subject it to a local gauge transformation they also subject a doublet of massive klein gordon fields to local so 2 transformations they find the conditions that the resulting automorphisms are spatial in fock space in some cases the conditions turn out to require that certain parameters identified as the winding numbers of the gauge are integers it is argued that this integer labels states of various charge

software metamaterials transformation media based multiscale techniques for computational electromagnetics this paper presents computational models employing special transformation based media which we call software metamaterials for the purpose of enhancing the ability of numerical modeling methods for solving multi scale electromagnetic boundary value problems involving features with multiple length or frequency scales or both the multi scale problems in general suffer from difficulties in mesh generation and the number of unknowns due to certain meshing requirements dictated by the fine features of the problem the underlying idea in this study is to introduce transformation media into the computational domain of the finite element method or finite difference methods in order to allow uniform and easy to generate meshes by avoiding mesh refinement and therefore to develop efficient and simple computer aided simulation tools in other words a virtual equivalent problem is created which acts like the original problem the techniques proposed in this paper are validated via several finite element simulations in the context of tm z electromagnetic scattering problems

phase ordering and persistence relative effects of space discretization chaos and anisotropy abstract the peculiar phase ordering properties of a lattice of coupled chaotic maps studied recently lemaitre chate phys rev lett 82 1999 1140 are revisited with the help of detailed investigations of interface motion it is shown that normal curvature driven like domain growth is recovered at larger scales than considered before and that the persistence exponent seems to be universal using generalized persistence spectra the properties of interface motion in this deterministic chaotic lattice system are found to interpolate between those of the two canonical reference systems the probabilistic ising model and the deterministic space continuous time dependent ginzburg landau equation

domain compression via anisotropic metamaterials designed by coordinate transformations we introduce a spatial coordinate transformation technique to compress the excessive white space i e free space in the computational domain of finite methods this approach is based on the form invariance property of maxwell s equations under coordinate transformations clearly maxwell s equations are still satisfied inside the transformed space but the medium turns into an anisotropic medium whose constitutive parameters are determined by the coordinate transformation the proposed technique can be employed to reduce the number of unknowns especially in high frequency applications wherein a finite method requires an electrically large computational domain after developing the analytical background of this technique we report some numerical results for finite element simulations of electromagnetic scattering problems

local relativistic invariant flows for quantum fields for quantum fields with trigonometric interaction in arbitrary space dimension we construct a representation of the lorentz group by automorphisms on a banach space generated by the weyl algebra

displaced fock representations of the canonical commutation relations defines displaced fock representations of the canonical commutation relations in an algebraic framework then the author considers the problem of unitary implementability of the symmetry group which acts on the one particle space of the theory this action induces an automorphism of the algebra of the ccr and a condition is found to ensure that this automorphism be implemented by a unitary group representation in the space of the displaced fock representation using this condition the author proves the existence of infinitely many displaced fock representations in which the group automorphism is implemented by a unitary action this is done for a specific choice of a subgroup of the poincare group and for all cases of integer value of spin

some local covariant representations of the canonical anticommutation relations the authors find some non fock representations of the canonical anticommutation relations in 1 1 dimensions these representations obtained by a bogoliubov transformation of the fock annihilation and creation operators are poincare covariant have positive energy and are labelled by two conserved charges which take on continuous values in the interval 0 2 pi

galilei covariance and quasi free representations of fermi fields some quasi free irreducible representations of the car algebra of a non relativistic free fermi field are constructed which are covariant under certain subgroups of the extended galilei group the construction of fully covariant but reducible representations as direct integrals of partially covariant ones is described this method is also applicable to arbitrary c algebras and other covariance groups

c algebraic scattering theory and explicitly solvable quantum field theories a general theoretical framework is developed for the treatment of a class of quantum field theories that are explicitly exactly solvable but require the use of c algebraic techniques because time dependent scattering theory cannot be constructed in any one natural representation of the observable algebra the purpose is to exhibit mechanisms by which inequivalent representations of the observable algebra can arise in quantum field theory in a setting free of other complications commonly associated with the specification of dynamics one of two major results is the development of necessary and sufficient conditions for the concurrent unitary implementation of two automorphism groups in a class of quasifree representations of the algebra of the canonical commutation relations ccr the automorphism groups considered are induced by one parameter groups of symplectic transformations on the classical phase space over which the weyl algebra of the ccr is built each symplectic group is conjugate by a fixed

fermion currents in 1 1 dimensions let f denote the fock space for a free massless fermion field in two space time dimensions if q and q5 denote the charge and chiral charge operators then f n1 n2fn1 n2 where fn1 n2 is the joint eigenspace of q and q5 with corresponding eigenvalues n1 and n2 the smeared time zero free fermion currents formally given by j f x x f x dx 0 1 f s r are in fact self adjoint densely defined operators on f and their exponentials generate a c algebra which leaves each subspace fn1 n2 invariant if a periodic box cutoff for the fermions is introduced uhlenbrock has shown that this c algebra acts irreducibly in each sector fn1 n2 we prove this same result without any cutoffs and determine the properties of the representations in each sector the importance of this result for the problem of constructing fermion fields from observables in two dimensional models such as those of thirring and schwinger is discussed

perfectly matched layers for time harmonic elastodynamics of unbounded domains theory and finite element implementation abstract one approach to the numerical solution of a wave equation on an unbounded domain uses a bounded domain surrounded by an absorbing boundary or layer that absorbs waves propagating outwards from the bounded domain a perfectly matched layer pml is an unphysical absorbing layer model for linear wave equations that absorbs almost perfectly outgoing waves of all non tangential angles of incidence and of all non zero frequencies this paper develops the pml concept for time harmonic elastodynamics in cartesian coordinates utilising insights obtained with electromagnetics pmls and presents a novel displacement based symmetric finite element implementation of the pml for time harmonic plane strain or three dimensional motion the pml concept is illustrated through the example of a one dimensional rod on elastic foundation and through the anti plane motion of a two dimensional continuum the concept is explored in detail through analytical and numerical results from a pml model of the semi infinite rod on elastic foundation and through numerical results for the anti plane motion of a semi infinite layer on a rigid base numerical results are presented for the classical soil structure interaction problems of a rigid strip footing on a i half plane ii layer on a half plane and iii layer on a rigid base the analytical and numerical results obtained for these canonical problems demonstrate the high accuracy achievable by pml models even with small bounded domains

non maxwellian locally conformal pml absorbers for finite element mesh truncation we introduce the locally conformal perfectly matched layer pml approach which is an easy and straightforward pml implementation to the problem of mesh truncation in the finite element method fem this method is based on a locally defined complex coordinate transformation which has no explicit dependence on the differential geometric characteristics of the pml free space interface as a result it is possible to handle challenging pml geometries with interfaces having arbitrary curvature especially those with curvature discontinuities in order to implement this approach we also introduce the concept of complex space fem using elements with complex nodal coordinates after developing the analytical background of this method we present some numerical results to demonstrate the performance of this method in three dimensional electromagnetic scattering problems

some covariant representations of massless fermi fields studies the class of pure quasi free gauge invariant states of the fermion algebra the authors show that the question of g covariance of the corresponding representations i e implementability of some group g of one particle symmetry transformations is related to a cohomology group with values in the hilbert schmidt class in four dimensional space time this cohomology is nontrivial thus leading to g covariant non fock representations when g is taken to be the space time translation group together with rotations or space time translations together with boosts in one direction and rotations about it and the fermion mass is zero in two space time dimensions some new fully poincare covariant representations for free massless fermions are constructed

quasi free photon states and the poincare group it is proven that every projectively poincare covariant representation of the free photon field defined by a pure quasi free state is unixarily equivalent to the fock representation of that field

some covariant representations of massless boson fields considers the c algebra of the canonical commutation relations ccr acted on by a group g of one particle symmetry transformations v a symplectic operator t defines a representation pi t pi f omicron t where pi f is the fock representation the automorphisms of the ccr algebra that are induced by g are shown to be continuously implemented in pi t if and only if a v g av g is a continuous hilbert schmidt 1 cocycle of g here a is related to t by t exp a a being a suitable bounded antilinear self adjoint operator some new examples of fully poincare covariant representations of massless fields in 1 1 dimensions are constructed

a note on the boson fermion correspondence and infinite dimensional groups we show how to construct irreducible projective representations of the infinite dimensional lie group map s1 mathbb t by embedding it into the group of bogoliubov automorphisms of the car using techniques of g segal for extending certain representations of map s1 su 2 we show that our representations extend to give representations of a certain infinite dimensional superalgebra we relate our work to the well known boson fermion correspondence which exists in 1 1 dimensions

renormalization group for strongly coupled maps systems of strongly coupled chaotic maps generically exhibit collective behavior emerging out of extensive chaos we show how the well known renormalization group rg of unimodal maps can be extended to the coupled systems and in particular to coupled map lattices cmls with local diffusive coupling the rg relation derived for cmls is nonperturbative i e not restricted to a particular class of configurations nor to some vanishingly small region of parameter space after defining the strong coupling limit in which the rg applies to almost all asymptotic solutions we first present the simple case of coupled tent maps we then turn to the general case of unimodal maps coupled by diffusive coupling operators satisfying basic properties extending the formal approach developed by collet and eckmann for single maps we finally discuss and illustrate the general consequences of the rg cmls are shown to share universal properties in the space continuous limit which emerges naturally as the group is iterated we prove that the scaling properly ties of the local map carry to the coupled systems with an additional scaling factor of length scales implied by the synchronous updating of these dynamical systems this explains various scaling laws and self similar features previously observed numerically

the hilbert schmidt cohomology for the poincare group we consider cocycles for the poincart group pi satisfying gk v k v g where v is an irreducible strongly continuous representation of pi and g e b y the hilbert schmidt operators on the representation space 3 of v it is shown that i ii must be of the form g v av a with a e b x the method can be extended to analyse the cocycles of products of arbitrary irreducible representations of pi providing neither representation belongs to the little group of vanishing four momentum

a transformation media based approach for efficient monte carlo analysis of scattering from rough surfaces with objects this paper presents a computational model that utilizes transformation based metamaterials to enhance the performance of numerical modeling methods for achieving the statistical characterization of two dimensional electromagnetic scattering from objects on or above one dimensional rough sea surfaces monte carlo simulation of the rough surface scattering problem by means of differential equation based finite methods such as finite element or finite difference methods usually places a heavy burden on computational resources because at each realization of the monte carlo technique a mesh must be generated anew for each surface realization the main purpose of the proposed approach in this paper is to create a single mesh without repeating mesh generation at each step by introducing a transformation medium above the rough surface in the computational domain of the finite methods material parameters of the medium are obtained by the coordinate transformation technique which is based on the form invariance property of maxwell s equations at each realization only the material parameters are modified with respect to the geometry of surface without changing the mesh in this manner a great reduction in cpu time is achieved the proposed technique is analyzed and validated via various finite element simulations

implementability of gauge transformations and quantization of fermions in external fields quantization of fermions in an external soliton field leading to a representation of the canonical anticommutation relation car which is inequivalent to the representation connected to the massive dirac operator is studied classes of gauge and axial gauge transformations that can be unitarily implemented are determined in the latter case quantization conditions for gauge functions are obtained integers entering can be interpreted as winding numbers

universality and scaling of period doubling bifurcations in a dissipative distributed medium abstract a homogeneous medium consisting of nonlinear elements demonstrating transition to chaos via period doubling bifurcations is considered the coupling between the elements is supposed to be of a dissipative type i e it tends to equalize their instantaneous states using the renormalization group approach the following scaling law for weakly inhomogeneous states near the critical point is obtained at each period doubling the spatial scale increases by 2 on the basis of this law the scaling hypotheses for the transition to chaos in the semi infinite and finite systems are proposed the scaling properties are verified by the numerical calculations with a simple model