electromagnetic multiple pec object scattering using equivalence principle and addition theorem for spherical wave harmonics a novel domain decomposition procedure is presented to analyze the electromagnetic wave multiple scattering among separate pec objects the method is based on the equivalence principle algorithm epa that transfers the primary unknowns on the objects to the unknowns on the equivalence surfaces each equivalence surface is considered to be a spherical surface encompassing a pec object inside the equivalence spheres the analysis is performed based on the rao wilton glisson rwg basis functions where the electromagnetic interactions outside them are considered by means of the addition theorem for spherical wave harmonics swhs the translation procedures are presented to translate the rwg basis functions to swhs and vice versa the reduction of unknowns in the presented method versus the conventional epa which uses translation operators among equivalence surfaces shows its efficiency some numerical examples are presented to evaluate the efficacy of the proposed approach the acceptable consistency among the results of the proposed method and the conventional epa as well as the direct method of moments validates the proposed method

fuzzy completely irresolute and fuzzy weakly completely irresolute functions abstract the aim of this paper is to introduce two new classes of functions called fuzzy completely irresolute and fuzzy weakly completely irresolute functions their characterizations examples compositions of these functions their relationships with other functions and preservations of some fuzzy spaces under these functions are studied

rate of quantum ergodicity in euclidean billiards for a large class of quantized ergodic flows the quantum ergodicity theorem states that almost all eigenfunctions become equidistributed in the semiclassical limit in this work we give a short introduction to the formulation of the quantum ergodicity theorem for general observables in terms of pseudodifferential operators and show that it is equivalent to the semiclassical eigenfunction hypothesis for the wigner function in the case of ergodic systems of great importance is the rate by which the quantum mechanical expectation values of an observable tend to their mean value this is studied numerically for three euclidean billiards stadium cosine and cardioid billiard using up to 6000 eigenfunctions we find that in configuration space the rate of quantum ergodicity is strongly influenced by localized eigenfunctions such as bouncing ball modes or scarred eigenfunctions we give a detailed discussion and explanation of these effects using a simple but powerful model for the rate of quantum ergodicity in momentum space we observe a slower decay we also study the suitably normalized fluctuations of the expectation values around their mean and find good agreement with a gaussian distribution

h measures a new approach for studying homogenisation oscillations and concentration effects in partial differential equations new mathematical objects called h measures are introduced for studying oscillations and concentration effects in partial differential equations applications to transport properties and to homogenisation are given as an example of the new results which can be obtained by this approach

equipartition of the eigenfunctions of quantized ergodic maps on the torus we give a simple proof of the equipartition of the eigenfunctions of a class of quantized ergodic area preserving maps on the torus examples are the irrational translations the skew translations the hyperbolic automorphisms and some of their perturbations

separating the regular and irregular energy levels and their statistics in a hamiltonian system with mixed classical dynamics we look at the high lying eigenstates from the 10001 to the 13000 in the robnik billiard defined as a quadratic conformal map of the unit disk with the shape parameter lambda 0 15 all the 3000 eigenstates have been numerically calculated and examined in the configuration space and in the phase space which in comparison with the classical phase space enabled a clear cut classification of energy levels into regular and irregular this is the first successful separation of energy levels based on purely dynamical rather than special geometrical symmetry properties we calculate the fractional measure of regular levels as rho 1 0 365 or 0 01 which is in remarkable agreement with the classical estimate rho 1 0 360 or 0 001 this finding confirms the percival s 1973 classification scheme the assumption in berry robnik 1984 theory and the rigorous result by lazutkin 1981 1991 the regular levels obey the poissonian statistics quite well whereas the irregular sequence exhibits the fractional power law level repulsion and globally brody like statistics with beta 0 286 or 0 001 this is due to the strong localization of irregular eigenstates in the classically chaotic regions therefore in the entire spectrum we see that the berry robnik regime is not yet fully established so that the level spacing distribution is correctly captured by the berry robnik brody distribution

ergodicity of eigenfunctions for ergodic billiards we give a simple proof of ergodicity of eigenfunctions of the laplacian with dirichlet boundary conditions on compact riemannian manifolds with piecewise smooth boundaries and ergodic billiards examples include the bunimovich stadium the sinai billiard and the generic polygonal billiard tables of kerckhoff masur and smillie

wigner measures and codimension two crossings this article gives a semiclassical description of nucleonic propagation through codimension two crossings of electronic energy levels codimension two crossings are the simplest energy level crossings which affect the born oppenheimer approximation in the zeroth order term the model we study is a two level schrodinger equation with a laplacian as kinetic operator and a matrix valued linear potential whose eigenvalues cross if the two nucleonic coordinates equal zero we discuss the case of well localized initial data and obtain a description of the wavefunction s two scaled wigner measure and of the weak limit of its position density which is valid globally in time

ergodicite et limite semi classique consider a self adjoint quantic hamiltonian p h p x hdx whereh 0 is the planck s constant andp some smooth classical observable on the phase space r2n when the classical flow on a compact energy shell p is ergodic we prove that in the limith 0 almost all the eigenfunctions ofp h whose energy is near of are distributed according to the liouville measure on p

nodal domain distributions for quantum maps the statistics of the nodal lines and nodal domains of the eigenfunctions of quantum billiards have recently been observed to be fingerprints of the chaoticity of the underlying classical motion by blum et al 2002 phys rev lett 88 114101 and by bogomolny and schmit 2002 phys rev lett 88 114102 these statistics were shown to be computable from the random wave model of the eigenfunctions we here study the analogous problem for chaotic maps whose phase space is the two torus we show that the distributions of the numbers of nodal points and nodal domains of the eigenvectors of the corresponding quantum maps can be computed straightforwardly and exactly using random matrix theory we compare the predictions with the results of numerical computations involving quantum perturbed cat maps

integral equation based domain decomposition method for solving electromagnetic wave scattering from non penetrable objects the integral equation ie method is commonly utilized to model time harmonic electromagnetic em problems one of the greatest challenges in its applications arises in the solution of the resulting ill conditioned matrix equation we introduce a new domain decomposition method ddm for the ie solution of em wave scattering from non penetrable objects the proposed method is a non overlapping non conformal ddm and it provides a computationally efficient and effective preconditioner for the ie matrix equations moreover the proposed approach is very suitable for dealing with multi scale electromagnetic problems since each sub domain has its own characteristics length and will be meshed independently furthermore for each sub domain we are free to choose the most effective ie sub domain solver based on its local geometrical features and electromagnetic characteristics additionally the multilevel fast multi pole algorithm mlfma is utilized to accelerate the computations of couplings between sub domains numerical results demonstrate that the proposed method yields rapid convergence in the outer krylov iterative solution process finally simulations of several large scale examples testify to the effectiveness and robustness of the proposed ie based ddm

a domain decomposition method for the vector wave equation a nonoverlapping domain decomposition method ddm is presented for the finite element fe solution of electromagnetic scattering problems by inhomogeneous three dimensional 3 d bodies the computational domain is partitioned into concentric subdomains on the interfaces of which conformal vector transmission conditions are prescribed and that can be implemented in the inhomogeneous part the ddm is numerically implemented when a conformal vector absorbing boundary condition abc is utilized on the outer boundary terminating the fe mesh while employing the standard edge based fe formulation then numerical experiments are performed on a sphere and a cone sphere that emphasize the advantages of this technique in terms of memory storage and computing times especially when the total number of unknowns is very large also these numerical experiments serve as a severe test for the performances of the abc

a generalized surface integral equation formulation for analysis of complex electromagnetic systems a novel method is presented to analyze the electromagnetic characteristics of systems consisting of a large number of scatterers with different shapes and materials in the method nearly located scatterers are grouped together while large bulk materials are divided into subblocks with adequate sizes a scatterer group or a subblock forms a basic block of the system and each block is contained with a virtual reference surface a generalized transition matrix defined on the reference surface is used to characterize the electromagnetic characteristics of the block the generalized transition matrix relates the rotated tangential components of the scattered fields or the equivalence sources to the rotated tangential components of the incident fields directly the generalized transition matrix can be calculated for each block independently using proper methods according to its structure and material surface integral equations are established on all the virtual reference surfaces which can be solved by moment method to get the electromagnetic characteristics of the whole system characteristic basis functions and synthetic basis functions can be applied to further reduce the unknown number while fast multipole method can be used to accelerate the evaluation of interactions two dimensional examples are provided to verify the method

fuzzy weak totally semicontinuous and fuzzy weak totally precontinuous mappings abstract the aim of this paper is to introduce some new classes of mappings called fuzzy weak totally continuous fuzzy totally precontinuous fuzzy weak totally semicontinuous fuzzy totally m precontinuous fuzzy totally m precontinuous and fuzzy totally irresolute mappings their compositions their relationships with other mappings preservations of some fuzzy spaces under these mappings and some examples are studied we also prove that the property that the mapping is fuzzy totally semicontinuous and fuzzy totally precontinuous is equivalent to the property that the mapping is fuzzy totally continuous

on fuzzy semi irresolute and strongly irresolute functions abstract in this paper two classes of functions between fuzzy topological spaces are introduced under the terminologies fuzzy semi irresolute and strongly irresolute functions each of which is independent of the fuzzy continuity of chang 1968 the class of fuzzy irresolute functions as recently introduced by mukherjee and sinha 1989 is seen to lie strictly between these two classes several characterizations of these functions along with their relationships with certain other types of functions are investigated

fuzzy totally continuous and totally semi continuous functions abstract the aim of this paper is to introduce two new classes of functions called fuzzy totally continuous and fuzzy totally semicontinuous functions their characterizations examples composition of these functions their relationships with other fuzzy functions and preservation of some fuzzy spaces under these functions are studied

survey of the eigenfunctions of a billiard system between integrability and chaos we study numerically the eigenfunctions and their wigner phase space distributions of the two dimensional billiard system defined by the quadratic conformal image of the unit disk as introduced by robnik 1983 this system is a generic kam system and displays a transition from integrability to almost ergodicity as the billiard shape changes we clearly identify two classes of states the regular ones associated with integrable regions and the irregular states supported on classically chaotic regions whilst the mixed type states were not found in support of percival s conjecture 1973 we confirm the existence of extremely intense scars in the classically chaotic regions and demonstrate their association with classical periodic orbits three classes of scars are revealed one orbit scars many orbit one family scars of statistically similar orbits in the homoclinic neighbourhood and many orbit many family scars we argue that it is impossible to find an a priori semiclassical theory of individual eigenstates but do not deny the usefulness of general semiclassical arguments in analysing the collective and statistical properties of eigenstates

comparable upper and lower bounds for boundary values of neumann eigenfunctions and tight inclusion of eigenvalues for smooth bounded domains in rn we prove upper and lower l2 bounds on the boundary data of neumann eigenfunctions and we prove quasiorthogonality of this boundary data in a spectral window the bounds are tight in the sense that both are independent of the eigenvalues this is achieved by working with an appropriate norm for boundary functions which includes a spectral weight that is a function of the boundary laplacian this spectral weight is chosen to cancel concentration at the boundary that can happen for whispering gallery type eigenfunctions these bounds are closely related to wave equation estimates due to tataru using this we bound the distance from an arbitrary helmholtz parameter e 0 to the nearest neumann eigenvalue in terms of boundary normal derivative data of a trial function u solving the helmholtz equation e u 0 this inclusion bound improves over previously known bounds by a factor of e5 6 analogously to a recently improved inclusion bound in the dirichlet case due to the first two authors finally we apply our theory to present an improved numerical implementation of the method of particular solutions for computation of neumann eigenpairs on smooth planar domains we show that the new inclusion bound improves the relative accuracy in a computed neumann eigenvalue around the 42000th from nine to fourteen digits with negligible extra numerical effort

irresolute and lmost open functions between fuzzy topological spaces abstract the aim of this paper is to introduce and characterize the concept of fuzzy irresolute functions which is strictly stronger than the concept of fuzzy semi continuous functions and independent of the concept of fuzzy continuous functions the independence of the two definitions of fuzzy almost open functions as introduced in 5 and 3 and some of their characterizations are also established

semi continous and semi closed mappings and semi connectedness in fuzzy setting abstract the aim of the paper is mainly to study and to find different characterizations of semi continuous and semi closed mappings between fuzzy topological spaces the notion of fuzzy semi open sets is used to define fuzzy ti spaces i 0 1 2 and these spaces are investigated under fuzzy semi continuity finally fuzzy semi connectedness is introduced and studied to some extent

linear embedding via green s operators a modeling technique for finite electromagnetic band gap structures we propose a modular electromagnetic modeling procedure for large finite electromagnetic band gap ebg structures called linear embedding via green s operators it is a diakoptic method based on the huygens schelkunoff principle involving equivalent boundary current sources that electromagnetically characterize the enclosed domain of arbitrary shapes as if it were a multiport system in a cascade of embedding steps separate reusable domains are combined to form larger domains device design often involves tuning local medium properties in a compact designated domain with a large environment through an additional embedding step the equivalent sources describing the environment can be transferred to the boundary of the designated domain rendering subsequent design steps very fast this two stage optimization process is applied in the design of an ebg power splitter

coupling of bouncing ball modes to the chaotic sea and their counting function we study the coupling of bouncing ball modes to chaotic modes in two dimensional billiards with two parallel boundary segments analytically we predict the corresponding decay rates using the fictitious integrable system approach agreement with numerically determined rates is found for the stadium and the cosine billiard we use this result to predict the asymptotic behavior of the counting function n text bb e ensuremath sim e ensuremath delta for the stadium billiard we find agreement with the previous result ensuremath delta 3 4 for the cosine billiard we derive ensuremath delta 5 8 which is confirmed numerically and is well below the previously predicted upper bound ensuremath delta 9 10

consequences of flooding on spectral statistics we study spectral statistics in systems with a mixed phase space in which regions of regular and chaotic motion coexist increasing their density of states we observe a transition of the level spacing distribution p s from berry robnik to wigner statistics although the underlying classical phase space structure and the effective planck constant h eff remain unchanged this transition is induced by flooding i e the disappearance of regular states due to increasing regular to chaotic couplings we account for this effect by a flooding improved berry robnik distribution in which an effectively reduced size of the regular island enters to additionally describe power law level repulsion at small spacings we extend this prediction by explicitly considering the tunneling couplings between regular and chaotic states this results in a flooding and tunneling improved berry robnik distribution which is in excellent agreement with numerical data

an eigencurrent approach to the analysis of electrically large 3 d structures using linear embedding via green s operators we present an extension of the linear embedding via green s operators lego procedure for efficiently dealing with 3 d electromagnetic composite structures in lego s notion we enclose the objects forming a structure within arbitrarily shaped domains bricks which by invoking the equivalence principle we characterize through scattering operators in the 2 d instance we then combined the bricks numerically in a cascade of successive embedding steps to build increasingly larger domains and obtain the scattering operator of the whole aggregate of objects in the 3 d case however this process becomes quite soon impracticable in that the resulting scattering matrices are too big to be stored and handled on most computers to circumvent this hurdle we propose a novel formulation of the electromagnetic problem based on an integral equation involving the total inverse scattering operator of the structure which can be written analytically in terms of scattering operators of the bricks and transfer operators among them we then solve this equation by the method of moments combined with the eigencurrent expansion method which allows for a considerable reduction in size of the system matrix and thereby enables us to study very large structures

efficient solution of integral equation based electromagnetic problems with the use of macromodels the idea of so called macromodels is applied to problems of computational electromagnetics involving integral equation method of moments formulations it is shown that with the use of equivalence principles it is possible to exclude a part of the problem calculate its wideband response without an a priori knowledge of the excitations and then efficiently combine the result into the original situation the idea is validated using examples involving slot excited dielectric resonator antennas

on the convergence of the eigencurrent expansion method applied to linear embedding via green s operators lego the scattering from a large complex structure comprised of many objects may be efficiently tackled by embedding each object within a bounded domain brick which is described through a scattering operator upon electromagnetically combining the scattering operators we arrive at an equation which involves the total inverse scattering operator s 1 of the structure we call this procedure linear embedding via green s operators lego to solve the relevant equation we then employ the eigencurrent expansion method eem essentially the method of moments with a set of basis and test functions that are approximations to the eigenfunctions of s 1 termed eigencurrents we have investigated the convergence of the eem applied to lego in cases when all the bricks are identical our findings lead us to formulate a simple and practical criterion for controlling the error of the computed solution a priori

a generalized transition matrix model for open ended cavity with complex internal structures in this paper a novel generalized transition matrix gtm algorithm is proposed to analyze the electromagnetic problems of open ended cavity structures an artificial reference surface is applied to seal the slots and or apertures to reshape the target cavity into an interior domain containing inner metallic surface and internal structures and an exterior domain containing the outer surface of the cavity special junctions at the transitional connection of the two domains are applied to guarantee the current continuity on the metallic surface based on the huygens principle an associated gtm is constructed on the reference surface and the special junctions to extract the characteristics of the interior region of the cavity the gtm is independent of the outer shape of the cavity and the exterior electromagnetic environment the computational complexity can be effectively reduced especially when the interior region is with fine structures and internal sources to investigate the feasibility and effectiveness of the proposed approach several numerical examples are presented

equivalence principle algorithm with body of revolution equivalence surface for the modeling of large multiscale structures we propose a multiscale solver of equivalence principle algorithm with a body of revolution bor equivalence surface es first the whole object is decomposed into subdomains the ess are defined as proper bors e g spheres in this work to enclose each subdomain the rao wilton glisson rwg and bor basis functions are defined on each sphere respectively second the octree is constructed in each nonzero subdomain the multilevel fast multipole algorithm mlfma is employed to solve the equivalent currents on the es individually and then the equivalent currents are projected from rwg onto the bor basis functions the couplings between neighboring subdomains are evaluated directly using mlfma and the separated subdomains are substituted by the es to es couplings and are evaluated efficiently by the bor method of moments bor mom to solve the equation system a hybrid inner and outer iterative solver is employed where the inner iteration is used to solve each local subdomains and the outer iteration is used to update the global solutions by collecting all the local solutions numerical results and discussions demonstrate the validity of the proposed work

application of the characteristic basis function method utilizing a class of basis and testing functions defined on nurbs patches a novel implementation of the characteristic basis function method cbfm is given in which the high level basis functions called characteristic basis functions cbfs are represented in terms of curved rooftops generated from nonuniform rational b splines nurbs in the parametric u v domain the associated macro testing functions are defined by using curved razor blade functions corresponding to each rooftop the underlying objective of the cbfm is the reduction of the number of unknowns that arise from the discretization process when applying the conventional method of moments mom the result is therefore an approach which can handle many complex cases via direct solvers without suffering from convergence problems as many of the iterative techniques are known to do when dealing with ill conditioned matrices as a result of the combination of the cbfm with the special class of low level basis and testing functions directly located over nurbs surfaces complex and realistic geometries can be efficiently analyzed to yield accurate results while reducing the cpu time as well as required memory resources

a recursive green s function method for boundary integral analysis of inhomogeneous domains the recursive green s function method rgfm for computation of fields scattered by two dimensional 2 d inhomogeneous dielectric bodies is presented the algorithm efficiently constructs the green s function for the inhomogeneous region by recursively combining known green s functions from smaller subdomains the fields on the scatterer surface are then computed using a boundary integral formulation proper implementation of the rgfm results in computational and storage complexities which scale as n sup 1 5 and n respectively where n is the total number of discrete cells in a domain comparisons of results obtained using the rgfm with those computed from moment method and exact solutions show the efficiency and accuracy of the technique

integral equation analysis of scattering from multilayered periodic array using equivalence principle and connection scheme an integral equation approach is presented to analyze the two dimensional 2 d scattering from multilayered periodic array the proposed approach is capable of handling scattering from the array filled with different media in different layers combining the equivalence principle algorithm epa and connection scheme epacs it can be avoided to find and evaluate the multilayered periodic green s functions for 2n identical layers the elimination of the unknowns between top and bottom surfaces can be accelerated using the logarithm algorithm more importantly based on epacs an approach is proposed to effectively handle the semi infinitely layered case in which a unit consisting of several layers is repeated infinitely in one direction

mixed fuzzy ideal topological spaces the aim of this paper is to introduce a new concept of mixed fuzzy ideal topological spaces and investigate some properties of this space

study of regular and irregular states in generic systems in this work we present the results of a numerical and semiclassical analysis of high lying states in a hamiltonian system whose classical mechanics is of a generic mixed type where the energy surface is split into regions of regular and chaotic motion as predicted by the principle of uniform semiclassical condensation when the effective tends to zero each state can be classified as regular or irregular we were able to semiclassically reproduce individual regular states by the einstein brillouin keller torus quantization for which we devise a new approach while for the irregular ones we found the semiclassical prediction of their autocorrelation function in a good agreement with numerics we also looked at the low lying states to get a better understanding of the onset of semiclassical behaviour

temporal flooding of regular islands by chaotic wave packets we investigate the time evolution of wave packets in systems with a mixed phase space where regular islands and chaotic motion coexist for wave packets started in the chaotic sea on average the weight on a quantized torus of the regular island increases due to dynamical tunneling this flooding weight initially increases linearly and saturates to a value which varies from torus to torus we demonstrate for the asymptotic flooding weight universal scaling with an effective tunneling coupling for quantum maps and the mushroom billiard this universality is reproduced by a suitable random matrix model

wigner measures and observability for the schrodinger equation on the disk we analyse the structure of semiclassical and microlocal wigner measures for solutions to the linear schrodinger equation on the disk with dirichlet boundary conditions our approach links the propagation of singularities beyond geometric optics with the completely integrable nature of the billiard in the disk we prove a structure theorem expressing the restriction of the wigner measures on each invariant torus in terms of second microlocal measures they are obtained by performing a finer localization in phase space around each of these tori at the limit of the uncertainty principle and are shown to propagate according to heisenberg equations on the circle our construction yields as corollaries a that the disintegration of the wigner measures is absolutely continuous in the angular variable which is an expression of the dispersive properties of the equation b an observability inequality saying that the l 2 norm of a solution on any open subset intersecting the boundary resp the l 2 norm of the neumann trace on any nonempty open set of the boundary controls its full l 2 norm resp h 1 norm these results show in particular that the energy of solutions cannot concentrate on periodic trajectories of the billiard flow other than the boundary

marching on in degree solution of the transient scattering from multiple bodies of revolution an efficient marching on in degree mod scheme is proposed to analyze the transient em scattering from multiple conducting bodies of revolution mbors with arbitrary axis using the equivalence principle algorithm epa the self acting of each bor is calculated by taking advantage of the rotationally symmetrical property in its local bor coordinate system the interaction between any two bors is replaced by the one between their equivalence spheres which enclose corresponding bor with epa in this way the transient scattering properties of the randomly distributed mbors can be obtained with high efficiency by the use of the bor basis functions and the weighted laguerre polynomial numerical results are presented to demonstrate the accuracy and efficiency of proposed algorithm

integral equation based nonoverlapping ddm using the explicit boundary condition a new integral equation based nonoverlapping domain decomposition method nddm is proposed for analyzing electromagnetic em scattering from electrically large pec objects whose mlfma models are too large for the user s computer to accommodate the integral equation is first built on the entire pec surface and the entire surface is partitioned into some nonoverlapping subsurfaces the rwg functions are used to expand the surface current on the entire surface then each full rwg function across some boundary curve is split into two half rwg functions whose unknown coefficients are constrained by the boundary current continuity using the explicit boundary condition the convergence of the outer iterative scheme of the proposed nddm is investigated theoretically and demonstrated to be very good and hence a very large problem can be effectively solved in an ordinary computer some numerical examples are provided to demonstrate the correctness and robustness of the proposed method and to compare the proposed method with the existing overlapping ddms having similar attributes

a class of strong forms of fuzzy complete continuity abstract the aim of this paper is devoted to make use of operations on ix of a fuzzy topological space x to unify and generalize classes of strong forms of fuzzy complete continuity furthermore we add more types of strong forms of fuzzy completely continuous functions by choosing special operations a comparison between these types of functions is of interest preservations of some fuzzy aspects under these functions are studied

a domain decomposition method for boundary integral equations using a transmission condition based on the near zone couplings a domain decomposition method ddm for the solution of boundary integral equations for impenetrable objects is presented the approach uses a transmission condition which is based on the near range couplings in order to obtain close approximations of the global solution on the subdomains the comparatively strong near zone interactions are taken into account to avoid unphysical reflections from the domain interfaces the algorithm can be accelerated by fast integral solvers such as the multilevel fast multipole method mlfmm by creating local subtrees which coincide with the different computing domains this concept is embedded in an inner outer iterative solution algorithm in which the ddm acts as a preconditioner in the inner iterations by introducing small overlap regions the convergence of the iterative solver is further improved this results in a very robust ddm which can be integrated into existing codes with reasonable effort and which is suited for parallelization numerical results for various open and closed objects demonstrate the effectiveness and the excellent performance of the proposed ddm for the solution of electromagnetic radiation and scattering problems

uniform distribution of eigenfunctions on compact hyperbolic surfaces on demontre que les fonctions propres k du laplacien sur une surface hyperbolique compacte x devient uniformement distribuee sur x quand k

an iterative solution for electrically large problems combining the characteristic basis function method and the multilevel fast multipole algorithm an iterative scheme for the rigorous computation of electrically large problems is presented the approach is based on a combination of the characteristic basis function method cbfm and the multilevel fast multipole algorithm mlfma that can deal with very large problems that require an iterative solution process even considering that the application of the cbfm entails an important reduction of the number of unknowns when compared to method of moments approaches based on subdomain functions this reduction is due to the fact that the number of macro basis functions called characteristic basis functions cbfs is lesser than the number of low level subsectional functions used to sample the geometry in addition the use of the mlfma avoids the need to calculate and store the coupling terms in the reduced matrix that are not on or close to the diagonal thereby optimizing the cpu time and the memory storage requirements non uniform rational b splines nurbs surfaces are employed for the representation of the geometry and the cbfs are described in terms of curved rooftops generated in the parametric space the associated macro testing functions are defined as aggregations of curved razor blade functions

universality of eigenvector statistics of kicked tops of different symmetries the authors show that the eigenvectors of the floquet operators of periodically kicked tops with orthogonal unitary and symplectic canonical transformations conform to the predictions of the respective circular ensembles of random matrices

fuzzy less strongly semiopen sets and fuzzy less strong semicontinuity abstract in this paper we first introduce the concepts of a fuzzy less strongly semiopen set a fuzzy less strongly semiclosed set fuzzy less strong semi interior and fuzzy less strong semiclosure we study their properties and discuss the relationships between these concepts and relevant concepts in fuzzy topological space finally we introduce the fuzzy less strongly continuous fuzzy less strongly semiopen and fuzzy less strongly semiclosed mappings on fuzzy topological space and establish their various characteristic properties

efficient electromagnetic scattering computation using the random auxiliary sources method for multiple composite 3 d arbitrary objects the electromagnetic em scattering problem from three dimensional 3 d arbitrary composite objects is proposed using the random auxiliary sources ras method based on direct application of the boundary conditions with the uniqueness theorem and the use of random equivalent problems concept more degrees of freedom to the sources positions are added resulting in significantly efficient solutions with lower memory requirements the technique does not require any singularity treatment due to placing the equivalent sources away from the boundaries while boundary conditions are not enforced exactly an iterative framework is introduced that can achieve an acceptable level of error in their satisfaction for an arbitrary randomly generated set of equivalent sources the presented technique promises a significant reduction in the execution time and memory requirements compared to the surface equivalent based method of moments mom the solution stability repeatability and numerical noise susceptibility are investigated thoroughly through this work also a novel edge correction scheme has been implemented to extend the capabilities of this procedure to structures with sharp edges the results of the presented technique are compared to series solutions for conducting spheres and a commercially available mom code for arbitrarily shaped objects and combinations of different materials

beyond the berry robnik regime a random matrix study of tunneling effects we consider the energy spectra of quantum hamilton systems whose classical dynamics is of mixed type i e regular for some initial conditions in the classical phase space and chaotic for the complementary initial conditions in the strict semiclassical limit when the effective planck constant eff is sufficiently small the berry robnik br statistics applies while at larger values of eff or smaller energies one sees deviations from br due to localization and tunneling effects we derive a two level random matrix model which describes these effects and can be treated analytically in a closed form the coupling between the regular and chaotic levels due to tunneling is assumed to be gaussian distributed this two level model describes most of the features of matrices of large dimensions here n 1000 which we treat numerically and is predicted to apply in mixed type systems at low energies the proposed analytical level spacing distribution function has two parameters the br parameter characterizing the classical phase space and the coupling antenna distortion or tunneling parameter between states localization effects so far are not included in our analysis except in the special case where can be replaced by some effective eff

electromagnetic scattering for multiple pec bodies of revolution using equivalence principle algorithm an equivalence principle algorithm epa method is extended to analyze the electromagnetic scattering from multiple bodies of revolution mbor with the axes arbitrarily oriented equivalence spheres are used to enclose each bor and the equivalence currents are expanded by the basis functions of bodies of revolution bor to obtain the scattering operators and translation operators of epa for fourier modes independently the rotational symmetry systems are established in local bor coordinate systems the origin of the local bor coordinate system is located at the center of the equivalence sphere and the z axis coincides with the axis of the enclosed bor to obtain the scattering operator of each equivalence sphere whereas the origin is located at the observation sphere and z axis passes through the center of the source sphere to obtain the translation operator of each pair of equivalence spheres the current coefficient transformation algorithm is used to transform the equivalence currents among local bor coordinate systems the total equation is iteratively solved in the global coordinate system the proposed scheme is especially efficient for the analysis of scattering from mbor randomly distributed in electrically large scale region numerical results are given to demonstrate the efficiency

the level splitting distribution in chaos assisted tunnelling a compound tunneling mechanism from one integrable region to another mediated by a delocalized state in an intermediate chaotic region of phase space was recently introduced to explain peculiar features of tunneling in certain two dimensional systems this mechanism is known as chaos assisted tunneling we study its consequences for the distribution of the level splittings and obtain a general analytical form for this distribution under the assumption that chaos assisted tunneling is the only operative mechanism we have checked that the analytical form we obtain agrees with splitting distributions calculated numerically for a model system in which chaos assisted tunneling is known to be the dominant mechanism the distribution depends on two parameters the first gives the scale of the splittings and is related to the magnitude of the classically forbidden processes the second gives a measure of the efficiency of possible barriers to classical transportwhich may exist in the chaotic region if these are weak this latter parameter is irrelevant otherwise it sets an energy scale at which the splitting distribution crosses over from one type of behavior to another the detailed form of the crossover is also obtained and found to be in good agreement with numerical results for models for chaos assisted tunneling

universality in the flooding of regular islands by chaotic states we investigate the structure of eigenstates in systems with a mixed phase space in terms of their projection onto individual regular tori depending on dynamical tunneling rates and the heisenberg time regular states disappear and chaotic states flood the regular tori for a quantitative understanding we introduce a random matrix model the resulting statistical properties of eigenstates as a function of an effective coupling strength are in very good agreement with numerical results for a kicked system we discuss the implications of these results for the applicability of the semiclassical eigenfunction hypothesis

connected patch array analysis using the characteristic basis function method the characteristic basis function method cbfm is extended to apply to efficient analysis of dual polarized connected patch arrays where neighboring patches are connected via two wire transmission lines and a groundplane comparison with a reference solution shows that the use of tertiary basis functions can significantly improve the cbfm approximation to the array currents and radiation patterns a simple procedure for estimating the error in the cbfm current is shown to produce good approximations to the true error and therefore may be useful more generally in determining suitable parameters of the cbfm basis the technique is applied to a prototype phased array feed for a next generation radio telescope a thin dielectric supporting the array patches is shown to produce a loading effect that modifies the radiation patterns good agreement with the results of other techniques and measured data has been obtained

a domain decomposition finite difference method for parallel numerical implementation of time dependent maxwell s equations a domain decomposition technique together with an implicit finite difference scheme is used to design a parallel algorithm to solve for electromagnetic scattering in the time domain by an infinite square metallic cylinder the implicit difference scheme yields second order accuracy unconditional stability and at each time step a large system of linear equations the domain decomposition technique reduces the solution of this large system to that of many independent smaller subsystems the present algorithm can be easily implemented on coarse grain parallel vector supercomputers to obtain a speedup close to the number of available central processing units cpus

wave field interaction with complex structures using equivalence principle algorithm a domain decomposition scheme based on the equivalence principle similar to huygens principle for integral equation solvers and the method of moments is introduced the equivalence principle allows the replacement of unknown currents distributed in a volume in space by equivalence currents residing on the surface that bounds the volume it also allows the dissociation of the solution of one region from that of another region in this manner problems of high complexity can be encapsulated by surfaces of simpler shapes using less unknowns it can aid in parallel algorithms reusability of solutions as well as improving the condition number of a matrix system when disparate mesh or adaptive mesh are needed the challenge arises when an equivalence surface intercepts a current carrying conductor because the breakup of the current into separate pieces gives rise to charge singularity a junction basis can be used to mitigate this singularity however a better solution is to introduce a tap basis to model the current that intercepts with the equivalence surfaces using this scheme the current continuity is conserved and the singularity of the charges is avoided the solution is shown to be accurate