particle swarm optimization in electromagnetics the particle swarm optimization pso new to the electromagnetics community is a robust stochastic evolutionary computation technique based on the movement and intelligence of swarms this paper introduces a conceptual overview and detailed explanation of the pso algorithm as well as how it can be used for electromagnetic optimizations this paper also presents several results illustrating the swarm behavior in a pso algorithm developed by the authors at ucla specifically for engineering optimizations ucla pso also discussed is recent progress in the development of the pso and the special considerations needed for engineering implementation including suggestions for the selection of parameter values additionally a study of boundary conditions is presented indicating the invisible wall technique outperforms absorbing and reflecting wall techniques these concepts are then integrated into a representative example of optimization of a profiled corrugated horn antenna

fractal design of multiband and low side lobe arrays most array factor design techniques are highly dependent on the operating wavelength in this paper a novel technique based on fractal structures is described for multiband operation the analysis is focused in two different approaches the fractal spatial arrangement of array elements and the fractal design of array factors although the patterns of fractal arrays show some interesting similarity properties at several bands the directivity is not held constant through the bands nevertheless such structures have been shown to be useful for designing low side lobe arrays with equally weighted current elements on the other hand the fractal array factors presented do keep the same shape at several bands because they are designed as selfsimilar curves the arrays that would synthesize such patterns present a characteristic power law current distribution analogous to the spectral distribution of the bandlimited fractal weierstrass function

effective beam forming networks for large arbitrary array of antennas a deterministic and effective strategy to reduce as much as possible the number of amplitude controls points in large arrays is herein proposed and applied to cases of practical interest the proposed strategy exploits two important concepts the first one coming from a special class of aperiodic tiling and the second one based on nufft non uniform fast fourier transform techniques the first one allows designing innovative front end architectures made of a reduced number of control points while nufft algorithms lead to computationally effective synthesis procedures the overall results and design guidelines allow to achieve simplified beamforming networks derived from aperiodic tilings and to know the performances that can be achieved using this approach particularly in case of low sidelobe requirements to confirm the usefulness of the proposed tools numerical examples are discussed conclusion follows

irregular phased array tiling by means of analytic schemata driven optimization the design of subarrayed planar phased arrays characterized by an irregular organization of domino shaped tiles is addressed starting from optimal tiling theorems drawn from mathematical theory an enumerative approach able to retrieve the optimal clustering providing the maximum aperture coverage and the best radiation performance is proposed to deal with the synthesis of low medium size rectangular arrays based on the same optimal theorems and still exploiting the algorithmic procedures at the basis of the enumerative approach an innovative schemata based optimization method is introduced for designing large arrays as well a set of representative results concerned with ideal as well as real radiating elements is reported and discussed to highlight the features and the potentialities of the proposed analytically based design framework

investigation of scattering properties of large scale aperiodic tilings using a combination of the characteristic basis function and adaptive integral methods this paper presents a hybrid approach for efficient analysis of electromagnetic em scattering from large scale aperiodic structures e g aperiodic penrose and danzer tilings which integrates the characteristic basis function method cbfm and the adaptive integral method aim by performing a domain decomposition a series of characteristic basis functions cbfs that are defined on a macro block and comprised of a relatively large number of sub domain basis functions facilitate a substantial reduction in the method of moments mom matrix size enabling the use of a direct solver for large problems the aim is applied to accelerate the calculation of cbfm reduced mom matrices significantly decreasing the cpu time and memory required for solving large scale problems as the size of one block becomes electrically large the original cbfm combined with the aim is employed to generate the initial cbfs by solving a large problem with multiple excitations which results in efficiently constructing the final cbfs afforded by the singular value decomposition svd procedure this methodology produces a two level cbfm aim hybrid algorithm for efficiently characterizing large scale objects the numerical results presented demonstrate the accuracy and efficiency of the proposed hybrid algorithm then the developed solver is applied to investigate em scattering properties of large scale aperiodic tilings the numerical results show that penrose danzer tilings exhibit significantly improved grating lobe suppression as compared to their periodic counterparts

aperiodic array layout optimization by the constraint relaxation approach an optimization procedure for the layout assessment of electrically large but finite planar arrays is presented the synthesis takes into account the desired directivity pattern that is prescribed employing bound constraints moreover the size of the radiators is taken into account which results in a hard nonoverlapping between the elements constraint the latter should not be violated if we want the attained solution not only to obey the far field mask but also to be physically realizable as stated the optimization problem is twofold an antenna design is associated with a packing problem in order to take the constraints on the layout into account and solve the whole problem we propose the constraint relaxation approach which is equipped with a packing algorithm our study is applied to various initial geometries and the resulting arrays appear to comply with the desired pattern and the nonoverlapping constraint several examples for different cases including symmetric arrays and a study on maximally sparse arrays are presented which show the applicability and merit of the method

interpolatory macro basis functions analysis of non periodic arrays an efficient method of moments mom technique for analyzing non periodic antenna arrays of identical elements with fixed orientation is presented the proposed method which uses macro basis functions mbfs is based on a compact representation of the interactions between mbfs these interactions are expressed via a low order harmonic polynomial function after an explicit pre computation of the reaction integrals in a very limited set of relative positions this is possible for arrays of arbitrary size thanks to three transformations subtraction of the far field expression for the interactions phase correction and modified radial distance applied successively to the pre computed interactions after obtaining the harmonic polynomial expressions the computation time for the reaction integral between two mbfs is independent from the complexity of the antenna array element

design of planar arrays with reduced nonuniform excitation subject to constraints on the resulting pattern and the directivity a design procedure for the synthesis of planar arrays is presented synthesis takes into account the desired pattern and the constraint on the directivity index it makes use of the perturbation method in conjunction with the lagrange multiplier theory starting from an initial array we perturb the element positions by employing an iterative technique in the iteration by setting the first variation of the lagrangian cost function equal to zero we derive the perturbed positions perturbation is applied simultaneously along two independent variables element coordinates x and y the final position of the elements results from the last iteration where the stopping criteria are met the choice of the initial array takes into account the number of elements and the reduction need of nonuniformity in the excitation our study is used for various initial geometries and the resulting arrays are shown to comply with the desired pattern and the directivity index

bayesian compressive sampling for pattern synthesis with maximally sparse non uniform linear arrays a numerically efficient technique based on the bayesian compressive sampling bcs for the design of maximally sparse linear arrays is introduced the method is based on a probabilistic formulation of the array synthesis and it exploits a fast relevance vector machine rvm for the problem solution the proposed approach allows the design of linear arrangements fitting desired power patterns with a reduced number of non uniformly spaced active elements the numerical validation assesses the effectiveness and computational efficiency of the proposed approach as a suitable complement to existing state of the art techniques for the design of sparse arrays

modular broadband phased arrays based on a nonuniform distribution of elements along the peano gosper space filling curve the peano gosper space filling curve provides an excellent framework for designing broadband planar antenna arrays with highly modular architectures uniformly distributing elements along the curve leads to an element distribution with a triangular lattice that has an irregular fractal boundary contour this boundary contour allows for a modular subarray configuration and better sidelobe suppression than conventional triangular lattice arrays with a regular boundary contour while they have a greater bandwidth than square lattice distributions arrays based on a triangular lattice still possess a rather limited bandwidth for beam steering applications due to the formation of grating lobes in this communication it will be shown that the beam steering capabilities of the peano gosper array can be enhanced by introducing perturbations into the basic recursive array generation scheme with the proper implementation the perturbed arrays retain the attractive features of modularity and recursive beamforming that are associated with the standard peano gosper array examples will be presented for several stages of peano gosper arrays that were designed for 2 1 broadband performance while scanning within a 30 conical volume full wave simulations will be used to examine the effects of mutual coupling on these aperiodic array layouts

non periodic tessellations with unit and non unit pisot inflation factors non periodic planar patterns generated by deterministic inflation rules are described several types of patterns with both unit and non unit pisot numbers as inflation factors are formed by triangular prototiles when the inflation factor is the silver mean the patterns can be obtained by superimposing two subpatterns and some of them can be converted into face to face patterns the geometric constructions corresponding to 12 fold symmetry are also studied the fourier transform of point masses placed in vertex positions of the transformed subpatterns exhibit two fold four fold and six fold symmetries although the peaks with highest intensities are situated in rings with apparent octagonal and dodecagonal symmetries

an efficient recursive procedure for evaluating the impedance matrix of linear and planar fractal arrays the self similar geometrical properties of fractal arrays are exploited in this paper to develop fast recursive algorithms for efficient evaluation of the associated impedance matrices as well as driving point impedances the methodology is demonstrated by considering two types of uniformly excited fractal arrays consisting of side by side half wave dipole antenna elements these examples include a triadic cantor linear fractal array and a sierpinski carpet planar fractal array this class of self similar antenna arrays become significantly large at higher order stages of growth and utilization of fractal analysis allows the impedance matrix and hence the driving point impedances to be obtained much more efficiently than would be possible using conventional analysis techniques

quaquaversal tilings and rotations we construct a hierarchical tiling of 3 dimensional euclidean space based on a triangular prism using repeated rotations about orthogonal axes by angles 2 m and 2 n to analyze the structure of the tiling we are led to determine the group g m n generated by such a pair of rotations for m n 3 and for m 3 n 4

a hierarchical strongly aperiodic set of tiles in the hyperbolic plane we give a new construction of strongly aperiodic set of tiles in h 2 exhibiting a kind of hierarchical structure simplifying the central framework of margenstern s proof that the domino problem is undecidable in the hyperbolic plane margenstern 2008 16

design of broadband planar arrays based on the optimization of aperiodic tilings antenna arrays based on aperiodic tilings have been shown to exhibit low sidelobe levels and modest bandwidths over which grating lobes are suppressed in addition compared to conventional periodic arrays these arrays are naturally thinned i e mean inter element spacing is greater than the generation of these arrays involves placing array elements at the locations of the vertices of an aperiodic tiling to obtain a realizable design the entire array is then scaled and truncated to achieve a desired minimum element spacing and aperture size this paper demonstrates that it is possible to greatly extend the bandwidth of these arrays by incorporating a simple perturbation scheme into the basic array generation process the implementation of this perturbation scheme is straightforward and it lends itself well to being combined with an optimization technique such as the genetic algorithm it is successfully used to generate arrays that have large bandwidths peak sidelobe level db with no grating lobes of up to a minimum element spacing of moreover the flexibility of this technique will be further demonstrated by introducing a slight variation of the basic scheme that is capable of generating arrays with extremely wide bandwidths an example will be presented for an array design that has a bandwidth corresponding to a minimum element spacing of up to

consensus problem in multi agent systems with physical position neighbourhood evolving network abstract in multi agent system mas the communication topology of agent network plays a very important role in its consensus problem to describe the communication topologies of mas a class of evolving network models with the concept of physical position neighbourhood connectivity are proposed and studied in this paper the analysis and simulation results for network parameters such as the first nonzero eigenvalue and maximal eigenvalue of graph laplacian matrix clustering coefficients average distances and degree distributions for different evolving parameters of these models are presented the dynamical behaviour of each node on the consensus problem is also studied it was found that the time to reach consensus becomes shorter sharply with the increasing of neighbourhood depth of the nodes in these models and it was also found that for the maximal distance preferential attachment model model 3 the synthetic characteristic such as robustness to communication delay as well as convergence speed in consensus problem is the best in all these models

decentralized formation control of mobile agents a unified framework abstract this paper studies the formation control problem for systems consisting of multiple mobile agents that are described by first order differential equations and second order differential equations respectively the following issues are investigated bounded input disturbance and time delay in derivation of the main results a blend of graph theoretic and system theoretic tools is employed where local potential functions and lasalle s invariant principle play central roles finally numerical examples which support the analytical results very well are also included

constrained pareto optimization of wide band and steerable concentric ring arrays a multi objective evolutionary algorithm that explicitly introduces the management of a single or multiple constraints on the solutions of an electromagnetic problem is presented in this paper the proposed strategy is based upon a modified genetic algorithm which evaluates the strength of a solution by considering both the match to the desired performance objectives as well as the satisfaction of specific requirements imposed to the design constraints the key issue is represented by the adaptive constraints management and its influence on the selective pressure of the genetic algorithm the procedure is applied to the optimization of concentric ring arrays several design examples of steerable and wideband arrays are provided to prove the flexibility and reliability of the approach a particular emphasis is given to the changes in array performance when the same objectives are requested but different kinds of constraints are forced

compact self dual hermitian surfaces in this paper we obtain a classification up to conformal equivalence of the compact self dual hermitian surfaces as an application we prove that every compact hermitian surface of pointwise constant holomorphic sectional curvature with respect to either the riemannian or the hermitian connection is kahler

the pinwheel tilings of the plane prototiles in euclidean n space en for n 2 the prototiles are usually required to be rather nice topologically at least homeomorphs of the closed unit ball one then makes arbitrarily many congruent copies called tiles of these prototiles and considers all ways called tilings that such tiles may provide a simultaneous covering and packing of en a tiling is thus an unordered collection of tiles for which the union is all of en but such that the interiors of each pair of tiles do not intersect wang s original problem was to determine if it was possible to have a finite set of prototiles with associated tilings of space for which all the tilings were nonperiodic a tiling is nonperiodic if it is not invariant under any single simultaneous translation of its tiles this was settled in the affirmative in the thesis of wang s student robert berger 1

generalized space filling gosper curves and their application to the design of wideband modular planar antenna arrays the peano gosper space filling curve provides an excellent framework for designing planar antenna array distributions with modular architectures and suppressed sidelobes over a relatively wide bandwidth the curve consists of a self avoiding path that intersects a triangular lattice and its construction is based on the iterative application of a generating curve there exist a number of other recently discovered curves coined generalized gosper curves that possess properties similar to those of the peano gosper curve but are based on larger and more complex generating curves in this paper these generalized curves will be examined as the framework for antenna array layouts it will be shown that arrays based on these curves have a number of excellent characteristics while offering modular array configurations and sizes that are not inherent to peano gosper arrays moreover when combined with a simple recursive perturbation technique the element distributions of these arrays can be efficiently adjusted to generate designs with bandwidths that far exceed that of standard periodic and triangular lattice arrays the efficacy of this technique will be demonstrated through design examples including one that has more than a 10 1 bandwidth full wave simulations of a wideband patch array will also be used to investigate the effects of mutual coupling on these array distributions

symmetries of quasicrystals we consider tiling models of round quasicrystals which would have diffraction patterns which are fully rotation invariant rings instead of bragg peaks they can be distinguished from glasses by self similarity of the pattern of radii of the rings

on the sum of the hermitian scalar curvatures of a compact hermitian manifold soit m une variete hermitienne compacte alors a u v 0 p m 0 m 0 b u v 0 p m 0 1 m 0 ou u et v sont les deux courbures scalaires de geometrie hermitienne et p m et q m sont les miemes plurigenres et le mieme plurigenre dual de m

the peano gosper fractal array this paper investigates the radiation characteristics of a new type of array that is based on the family of space filling and self avoiding fractals known as peano gosper curves the elements of the fractal array are uniformly distributed along a peano gosper curve which leads to a planar array configuration with parallelogram cells that is bounded by a closed koch curve these unique properties are exploited in order to develop a design methodology for deterministic arrays that have no grating lobes even when the minimum spacing between elements is increased to at least one wavelength this leads to a class of arrays that are relatively broad band when compared to more conventional periodic planar arrays with square or rectangular cells and regular boundary contours an efficient iterative procedure for calculating the radiation patterns of these peano gosper fractal arrays to arbitrary stage of growth p is also introduced in this paper

the evolution of optimal linear polyfractal arrays using genetic algorithms recently in order to successfully combine the positive attributes of both periodic and random arrays into one design a novel class of arrays known as fractal random arrays has been introduced in addition several researchers have successfully used genetic algorithms robust global optimization techniques based on natural selection to find solutions to complex array layout problems this paper introduces a type of nature based design process that applies a specially formulated genetic algorithm to evolve optimal layouts of an important subset of fractal random arrays which we call polyfractal arrays also this paper discusses how the underlying self similar properties of polyfractal arrays can be exploited to increase the speed of the associated array factor calculations this speed increase dramatically reduces the time required for the genetic algorithm to converge thereby making it possible to effectively evolve optimal array configurations which are much larger than has been previously possible moreover the fractal random properties of these polyfractal arrays are shown to provide substantially wider bandwidth performance than their conventional counterparts finally several design examples of genetically optimized linear polyfractal arrays with narrow beamwidths improved sidelobe suppression and wide bandwidths are presented

fractile arrays a new class of tiled arrays with fractal boundaries in this paper a new class of antenna arrays are introduced which we call fractile arrays a fractile array is defined as any array with a fractal boundary contour that tiles the plane without gaps or overlaps it will be shown that the unique geometrical features of fractiles may be exploited in order to make available a family of deterministic arrays that offer several highly desirable performance advantages over their conventional periodic planar array counterparts most notably fractile arrays have no grating lobes even when the minimum spacing between elements is increased to at least one wavelength this has led to the development of a new design methodology for modular broadband low sidelobe arrays that is based on fractal tilings several examples of fractile arrays will be considered including peano gosper terdragon 6 terdragon and fudgeflake arrays efficient iterative procedures for calculating the radiation patterns of these fractile arrays to arbitrary stage of growth p are also introduced in this paper

a self similar fractal radiation pattern synthesis technique for reconfigurable multiband arrays a novel method for designing reconfigurable multiband linear and planar antenna arrays is presented the technique is based on a generalized fourier series synthesis approach that exploits the self similarity of a specified fractal radiation pattern in order to achieve the desired multiband performance the fractal radiation patterns are composed of scaled and shifted copies of an appropriately chosen generating window function that exhibits low sidelobe levels and rapid spectral rolloffs in the transform domain a newly developed thinning algorithm is presented which may be employed to reduce considerably both the overall physical size and the total number of elements in a synthesized multiband array finally a band switching scheme is introduced that is well suited for implementation in the form of a reconfigurable common aperture array

conjugacies for tiling dynamical systems we consider tiling dynamical systems and topological conjugacies between them we prove that the criterion of being of finite type is invariant under topological conjugacy for substitution tiling systems under rather general conditions including the penrose and pinwheel systems we show that substitutions are invertible and that conjugacies are generalized sliding block codes

mean field theory for scale free random networks random networks with complex topology are common in nature describing systems as diverse as the world wide web or social and business networks recently it has been demonstrated that most large networks for which topological information is available display scale free features here we study the scaling properties of the recently introduced scale free model that can account for the observed power law distribution of the connectivities we develop a mean eld method to predict the growth dynamics of the individual vertices and use this to calculate analytically the connectivity distribution and the scaling exponents the mean eld method can be used to address the properties of two variants of the scale free model that do not display power law scaling c 1999 elsevier science b v all rights reserved

stability of multiagent systems with time dependent communication links we study a simple but compelling model of network of agents interacting via time dependent communication links the model finds application in a variety of fields including synchronization swarming and distributed decision making in the model each agent updates his current state based upon the current information received from neighboring agents necessary and or sufficient conditions for the convergence of the individual agents states to a common value are presented thereby extending recent results reported in the literature the stability analysis is based upon a blend of graph theoretic and system theoretic tools with the notion of convexity playing a central role the analysis is integrated within a formal framework of set valued lyapunov theory which may be of independent interest among others it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence even for the simple models discussed in the present paper

canonical substitutions tilings of ammann beenker type we present a large class of parallelogram tilings that have two important features in common with the ammann beenker tiling they can be constructed by canonical projection from z4 r4 to a plane and they admit substitution rules