critical behaviour of ab percolation in two dimensions monte carlo simulation of the ab percolation model on large triangular lattices gives indications that this problem has the same set of critical exponents as ordinary percolation although a critical amplitude ratio which is thought to be universal appears to be significantly different from accepted values for two dimensional percolation in addition finite size scaling functions for both the percolation probability and susceptibility seem to be significantly different from those for ordinary percolation in two dimensions the author also shows that this problem is closely connected to that of the percolation hull and in fact is dual to the complement of the hull problem

efficient calculation of large finite periodic structures based on surface wave analysis the electromagnetic modeling of practical finite periodic structures is a topic of growing interest due to the truncation of infinite periodic structures surface waves will be excited and localized near discontinuous interfaces leading to the edge effect in this work surface waves are numerically extracted and their magnitudes and decay rates are analyzed for different materials and geometries based on the exponential decay of the surface wave a novel method is developed by connecting the solution to the large finite array problem with that to a relatively small one to achieve low complexity and memory consumption the method numerically reconstructs propagating bloch waves and surface waves according to the bloch floquet theorem of periodic structures and translation invariant properties of semi infinite periodic structures respectively numerical examples are shown for near field distributions and far field radiation patterns the results obtained from small finite periodic structures capture the edge effect and agree well with the results by the rigorous element by element approach

the thermodynamic limit on bethe lattices the author emphasises the fact that to obtain the exact solution of hamiltonian models on bethe lattices one can apply explicitly the formal method of rigorous statistical mechanics i e the thermodynamic limit of probability measures this approach solves the well known dichotomy between clashing alternative solutions and provides a very simple analytic solution for a large class of hamiltonian models

efficient calculation of the green s function for multilayered planar periodic structures an efficient calculation scheme is presented for the periodic green s function in planar multilayered structures the proposed method is based on the static complex image conversion and the ewald sum technique and it converts the slowly convergent green s function into the sum of two rapidly convergent series

structure and perimeters of percolation clusters site percolation clusters are simulated at the percolation threshold on the square lattice an algorithm for walks around each cluster is used to obtain information on its fractal geometry the fractal dimensionality of the external perimeter is found to depend on the size of adsorbent particles used to measure it if the vacant perimeter sites have only nearest neighbour connectivity then the perimeter has dimension de 1 37 or 0 03 instead of that of the hull dh 1 75 the authors also measured the mass of internal dangling sites surrounded by the backbone s blobs singly and doubly connected sites the number of blobs and the average linear distance between entry into the exit from a blob

a percolation model for venereal epidemics i mean field theory a percolation model which the authors call bond percolation on antipercolation clusters is introduced for venereal epidemics in a heterosexual population a spin model which is equivalent to this model is found and solved in the bethe cluster approximation they obtain the static critical exponents beta 1 and gamma 1 using this approximation and these are the same as the mean field exponents for regular percolation the approximate phase diagram for arbitrary coordination number z is also constructed finally the probability that an infected individual belongs to an infected group with s individuals is obtained analytically in the limit z to infinity

efficient computation of the 2 d green s function for 1 d periodic structures using the ewald method the ewald method is applied to accelerate the evaluation of the green s function of an infinite periodic phased array of line sources the ewald representation for a cylindrical wave is obtained from the known representation for the spherical wave and a systematic general procedure is applied to extend previous results only a few terms are needed to evaluate ewald sums which are cast in terms of error functions and exponential integrals to high accuracy singularities and convergence rates are analyzed and a recipe for selecting the ewald splitting parameter spl epsiv is given to handle both low and high frequency ranges indeed it is shown analytically that the choice of the standard optimal splitting parameter spl epsiv sub 0 will cause overflow errors at high frequencies numerical examples illustrate the results and the sensitivity of the ewald representation to the splitting parameter spl epsiv

global positioning of robot manipulators via pd control plus a class of nonlinear integral actions deals with the position control of robot manipulators proposed is a simple class of robot regulators consisting of a linear proportional derivative pd feedback plus an integral action of a nonlinear function of position errors by using lyapunov s direct method and lasalle s invariance principle the authors characterize a class of such nonlinear functions and they provide explicit conditions on the regulator gains to ensure global asymptotic stability these regulators offer an attractive alternative to global regulation compared with the well known partially model based pd control with gravity compensation and pd control with desired gravity compensation

a comparison of acceleration procedures for the two dimensional periodic green s function alternate acceleration procedures are evaluated for the two dimensional free space periodic green s function two of these techniques yield exponential convergence rates and are preferable if high accuracies are required numerical aspects of these procedures are described

an efficient approach for the computation of 2 d green s functions with 1 d and 2 d periodicities in homogeneous media this paper presents an algorithm for the acceleration of the series involved in the computation of 2 d homogeneous green s functions with 1 d and 2 d periodicities the algorithm is based on an original implementation of the spectral kummer poisson s method and it can be applied to the efficient computation of a wide class of infinite series in the algorithm the number of asymptotic terms retained in kummer s transformation is externally controlled so that any of the series that has to be accelerated is split into one series with exponential convergence and another series with algebraic convergence of arbitrarily large order numerical simulations have shown that there is an ldquooptimumrdquo number of asymptotic terms retained in kummer s transformation for which the cpu time needed in the summation of the series is minimized the cpu times required by ewald s method for the evaluation of 2 d green s functions with 1 d and 2 d periodicities have been compared with those required by the present algorithm and the algorithm has been found to be between 1 2 and 3 times faster than ewald s method when working in ldquooptimumrdquo operation conditions

on the absence of infinite ab percolation clusters in bipartite graphs the authors give a rigorous proof that infinite ab percolation does not occur for any parameter value in a certain class of bipartite planar graphs in particular infinite ab percolation cannot occur on the square lattice

an efficient numerical evaluation of the green s function for the helmholtz operator on periodic structures abstract numerical methods which are based on boundary integral formulations require the numerical evaluation of the green s function associated with the problem in the case of periodic structures the green s function is often an infinite series this infinite series may converge slowly making numerical evaluation expensive here we present a practical computer implementation of a technique which dramatically speeds up the convergence of the infinite series green s function associated with the helmholtz operator to show the consequences of using this technique we include some numerical examples

efficient computation of the 3d green s function for the helmholtz operator for a linear array of point sources using the ewald method the ewald method is applied to accelerate the evaluation of the green s function gf of an infinite equispaced linear array of point sources with linear phasing only a few terms are needed to evaluate ewald sums which are cast in terms of error functions and exponential integrals to high accuracy it is shown analytically that the choice of the standard optimal ewald splitting parameter e0 causes overflow errors at high frequencies period large compared to the wavelength and convergence rates are analyzed a recipe for selecting the ewald splitting parameter is provided

rapidly convergent representations for 2d and 3d green s functions for a linear periodic array of dipole sources hybrid spectral spatial representations are introduced to rapidly calculate periodic scalar and dyadic green s functions of the helmholtz equation for 2d and 3d configurations with a 1d linear periodicity the presented schemes work seamlessly for any observation location near the array and for any practical array periodicities including electrically small and large periodicities the representations are based on the expansion of the periodic green s functions in terms of the continuous spectral integrals over the transverse to the array spectral parameters to achieve high convergence and numerical efficiency the introduced integral representations are cast in a hybrid form in terms of i a small number of contributions due to sources located around the unit cell of interest ii a small number of symmetric combinations of the floquet modes and iii an integral evaluated along the steepest descent path sdp the sdp integral is regularized by extracting the singular behavior near the saddle point of the integrand and integrating the extracted components in closed form efficient quadrature rules are established to evaluate this integral using a small number of quadrature nodes with arbitrary small error for a wide range of structure parameters strengths of the introduced approach are demonstrated via extensive numerical examples

counterexamples in ab percolation halley 1983 conjectured that the ab percolation probability function attains its maximum at p 1 2 and that consequently infinite ab percolation is impossible on a bipartite graph whose standard site percolation critical probability is greater than 1 2 the authors produce counterexamples that demonstrate that both conjectures are false in fact for any positive integer n a graph may be constructed which has at least n ab percolation transitions

some ab percolation problems in the antiferromagnetic potts model abstract the ab correlated site random bond percolation problem in a q state antiferromagnetic potts model on bethe lattices is solved we find the analytic expression of the ab percolation characteristic functions in terms of the temperature the external field and the active bond concentration p b the ab threshold and the phase boundary of the system coincide at zero temperature and at most in two other points for every constant p b 1 the properties of the bethe lattice allow us to find the temperature dependent p b which defines the ab droplets i e those special ab clusters which diverge with thermal exponents along the phase boundary

some remarks on ab percolation in high dimensions in this paper we consider the ab percolation model on z d and zd let phalt zd be the critical probability for ab percolation on zd we show that phalt zd 1 2d2 if the probability of a site to be in state a is 2d2 for some fixed 1 then the probability that ab percolation occurs converges as d to the unique strictly positive solution y of the equation y 1 exp y we also find the limit for the analogous quantities for oriented ab percolation on z d in particular phalt z d 2 d2 we further obtain a small extension to the two parameter problem in which even vertices of zd have probability pa of being in state a and odd vertices have probability pb of being in state b but without relation between pa and pb the principal tools in the proofs are a method of penrose 1993 for asymptotics of percolation on graphs with vertices of high degree and the second moment method

computations of the complex error function rational expansions for computing the complex error function w z e z 2 text erfc iz are presented these expansions have the following attractive properties 1 they can be evaluated using a polynomial evaluation routine such as homer s method 2 the polynomial coefficients can be computed once and for all by a single fast fourier transform fft and 3 high accuracy is achieved uniformly in the complex plane with only a small number of terms comparisons reveal that in some parts of the complex plane certain competitors may be more efficient however the difference in efficiency is never great and the new algorithms are simpler than existing ones a complete program takes eight lines of matlab code

1 d periodic green s function for leaky and complex waves using the ewald method the ewald method for evaluating the free space 1 d periodic green s function is extended to leaky waves by allowing for complex wavenumbers it is shown that care must be taken when choosing the path of integration in the complex plane in the derivation of the ewald method in order to obtain solutions that correspond to physical leaky wave solutions the use of different paths results in an evaluation of the ewald method using an analytical continuation of the exponential integral function previously used when the wavenumber is real the extension of the ewald method to complex wavenumbers allows for the treatment of practical periodic leaky wave antennas and periodic guiding structures with losses as well as metamaterials including 1 d chains of plasmonic nanoparticles

infinite ab percolation clusters exist on the triangular lattice infinite ab percolation clusters are shown to exist almost surely on the triangular lattice for an interval of parameter values it was not previously known that infinite ab percolation occurred with positive probability on any planar lattice

dynamics modeling and tracking control of robot manipulators in random vibration environment in this technical brief the problem of modeling and tracking control for the manipulator with multi revolute joints in random vibration environment is considered by analyzing the effect of environment to the mass points and introducing an equivalent stochastic noise process a stochastic hamiltonian dynamic model is constructed to describe the motion of the manipulator based on the constructed model a state feedback backstepping controller in vector form is designed such that the unique solution of the closed loop system is bounded in probability and the mean square of the tracking error converges to an arbitrarily small neighborhood of zero

critical distance for grating lobe series estimating a transition or critical distance above a planar periodic array of point sources radiating into an unbounded medium is considered it is shown that as an observation point approaches a periodic planar phased array of point sources the corresponding spectral domain green s function or grating lobe series converges much more slowly than an equivalent mixed domain representation exhibiting gaussian convergence for a given argument of the green s function the critical transition distance above the array for which both representations take the same time to compute can be estimated numerically since phased array antenna structures with cavity or waveguide type backings often have dimensions that fall well below the critical distance investigations of such structures would seem to benefit significantly from formulations incorporating such hybrid green s functions

eigenvalues of schrodinger operators with definite and indefinite weights in this paper computational algorithms are presented to compute the eigenvalues of schrodinger operators with definite and indefinite weights the algorithms are based on titchmarsh weyl s theory and can be applied to solve a wide class of problems in quantum mechanics explicit examples are presented some of which recover the known exact solutions finally some analytical bounds have been reviewed for definite and indefinite singular problems weyl s spectral bisection algorithm has been proposed to solve definite problems as algebraic problems open problems have been presented based on the results of the presented algorithms

phase diagrams of the q state potts model on bethe lattices abstract we use a rigorous recently developed method of solution of spin models on bethe lattices cayley trees it allows us to detect all the phases of the ferromagnetic and antiferromagnetic q state potts models in a field fpm and apm respectively the phase diagrams of the fpm are characterized by three critical lines of first order transitions in the apm the ordered phases which appear always for h 0 and under certain conditions for h 0 and or h

hull generating walks abstract a hull generating walk hgw is a type of kinetic random walk that generates the hull or perimeter of a percolation cluster and thus has a fractal dimension of 1 75 some examples of hgws for site and bond percolation on a square lattice are described

application of kummer s transformation to the efficient computation of the 3 d green s function with 1 d periodicity the 3 d homogeneous green s function with 1 d periodicity is commonly expressed as spatial and spectral infinite series that may show very slow convergence in this work kummer s transformation is applied to the spatial series in order to accelerate its convergence by retaining a sufficiently large number of asymptotic terms in the application of kummer s transformation the spatial series is split into a set of series which can be accurately obtained with very low computational effort the numerical results obtained show that when the number of asymptotic terms retained in kummer s transformation is large enough the convergence acceleration method proposed in this work is always faster than existing acceleration methods such as the spectral kummer poisson s method and ewald s method

lattice sums for the helmholtz equation a survey of different representations for lattice sums for the helmholtz equation is made these sums arise naturally when dealing with wave scattering by periodic structures one of the main objectives is to show how the various forms depend on the dimension d of the underlying space and the lattice dimension d lambda lattice sums are related to and can be calculated from the quasi periodic green s function and this object serves as the starting point of the analysis

percolation and self avoiding random loops presents simulations supporting the conjecture that properly defined exterior perimeters of 2d critical percolation clusters have the same fractal dimension d 4 3 as self avoiding random walks in addition the authors discuss possible generalizations

fragmentation of percolation cluster perimeters we introduce a model for the fragmentation of porous random solids under the action of an external agent in our model the solid is represented by a bond percolation cluster on the square lattice and bonds are removed only at the external perimeter or hull of the cluster this model is shown to be related to the self avoiding walk on the manhattan lattice and to the disconnection events at a diffusion front these correspondences are used to predict the leading and the first correction to scaling exponents for several quantities defined for hull fragmentation our numerical results support these predictions in addition the algorithm used to construct the perimeters reveals itself to be a very efficient tool for detecting subtle correlations in the pseudo random number generator used we present a quantitative test of two generators which supports recent results reported in more systematic studies

rapidly convergent representations for periodic green s functions of a linear array in layered media green s function representations are presented to rapidly compute the fields resulting from a linear 1d periodic array of dipole current sources on or near a planarly layered medium in 2d and 3d space the representation is formulated as spectral integral which accounts for the reflected continuous spectrum of fields and a series that accounts for the discrete spectrum of guided modes it is exponentially convergent for observation points on and near the array axis and surface and for complex phase shifts between periodic unit cells it can be defined on alternate riemann sheets with respect to any of the diffraction modes characterizing the array a complete dyadic green s function is derived to fully account for the reflected fields for all source current orientations this green s function representation can greatly accelerate the simulation of printed 1d periodic structures in optics and microwave engineering

acceleration of mixed potentials from vertical currents in layered media for 2 d structures with 1 d periodicity an original acceleration procedure is proposed for the efficient calculation of the vertical components of the dyadic and scalar mixed potential layered media periodic green s functions the extraction of suitable asymptotic terms i e quasi static images is performed in order to speed up the convergence of the relevant spectral series this procedure well known for planar green s functions is here generalized to treat the off diagonal dyadic components and the corrective scalar potential arising from the vertical currents the extracted terms are homogeneous medium green s functions due to a periodic phased array of half plane currents computed through a modified ewald method leading to a pair of gaussian convergent series the highly improved convergence rate of the relevant series is shown and the reduction of the computation time is numerically tested and discussed the algorithm is implemented in eiger an open source code based on the method of moments several periodic structures are analyzed and fully validated through numerical comparisons the proposed formulation has been proven very efficient accurate and stable

on ab percolation on bipartite graphs a method is presented for determining lower bounds for the ab percolation critical probability of bipartite graphs for some graphs the method shows that ab percolation is impossible in an interval containing p 1 2 the results improve those of appel and wierman 1987 by removing symmetry and periodicity restrictions and lend support to a conjecture of halley 1983

finite size scaling for branched polymers on a bethe lattice an analytical result the application of finite size scaling arguments to problems defined on a bethe lattice is discussed for the case of isolated branched polymers fugacities p lambda and h are assigned respectively to monomers branching points and end points for coordination numbers sigma 1 3 and 4 analytical expressions are found for the pseudo critical monomer fugacity on a finite n generation tree which satisfy pc n pc approximately n 2 thus constituting an analytical verification of finite size scaling predictions and implying that the correlation length exponent nu 1 2 the relationship between chemical and euclidean distance is invoked in order to show that the mean field value of 1 4 can be obtained through an appropriate exponent renormalisation for fixed h the crossover variable z is n lambda 1 2 for sigma 2 and n lambda 1 3 for sigma 3 such that the n 2 behaviour of pc n pc sets in for z 1 at lambda 0 there is no pseudo critical behaviour

a novel efficient technique for the calculation of the green s functions in rectangular waveguides based on accelerated series decomposition a new efficient technique for computing the green s functions inside rectangular waveguides is presented after a summary of the classical approaches and their difficulties a new strategy is proposed based on the decomposition of the main spectral series into simpler terms although the resulting series present better convergence rate several acceleration techniques are combined to further improve the efficiency several results are presented to demonstrate the improvements in convergence rates obtained using the new decomposition

antipercolation on bethe and triangular lattices the antipercolation problem is solved on the bethe lattice the critical exponents are identical to the percolation exponents when the coordination number z is greater than a critical value zc 3 for which the problem has new exponents satisfying extended universality and below which there is no transition for alternate lattices the problem may be transformed into a percolation problem with different occupation probabilities on the two sublattices this allows a connection with an s state potts model with different z spin interactions on the two sublattices in two dimensions there is no transition on the alternate square and honeycomb lattices whereas a transition exists on the triangular lattice using the phenomenological renormalisation group method the critical concentration is found to be pc a 0 21 whereas the correlation length exponent nu a seems to converge towards the accepted percolation value nu p 1 333

spreading of percolation in three and four dimensions the authors present monte carlo simulations of the spreading of bond percolation on three and four dimensional simple hyper cubic lattices the algorithm is the same as that applied previously in two dimensions with the spreading proceeding from a hyperplane they find the spreading dimension to be d 1 82 or 0 02 three dimensional and d 1 88 or 0 03 four dimensional also they obtain values of the percolation probability and of the static exponents with errors at least comparable to the best values from the literature

dilute potts model duality and site bond percolation a number of results are obtained for potts models on an arbitrary planar lattice it is shown that the dual of a dilute potts model is a graph generating function and that the dual of a constrained dilute potts model is an undiluted potts model it is also shown that the dilute potts model generates a correlated site bond percolation for uncorrelated site bond percolations the analysis determines the percolation threshold from a knowledge of the critical point of a potts model this generalises a recent result of kondor 1980 who uses a star triangle transformation to derive this relationship for the honeycomb and triangle lattices

ab percolation on close packed graphs for a class of close packed graphs the ab percolation critical probability is equal to the classical site percolation critical probability of the related graph obtained by inserting next nearest neighbour bonds as a consequence infinite ab percolation occurs for many fully triangulated graphs

scaling properties of antipercolation hulls on the triangular lattice the critical properties of the perimeters or hulls of antipercolation clusters are studied in two dimensions by monte carlo simulations on the triangular lattice two different types of hulls are constructed with the help of two kinetic walk algorithms for the standard hull the authors very accurately determine the size distribution exponent tau 2 14250 0003 as well as the fractal dimension dfs 1 7500 001 the corresponding exponents for regular percolation hulls 15 7 and 7 4 respectively are within the error bars of their results for antipercolation for the reduced hull they obtain the estimate dfr 1 3340 004 for the fractal dimension a result which is again close to that found for regular percolation

bi partite percolation and gelation bi partite percolation is discussed in the context of gelation the partial generating function method is used to derive expansions for the mean number of clusters and for the weight average molecular weight in terms of the reactant concentrations a and b renormalisation group and other arguments imply that the critical behaviour in bi partite percolation is determined by the ordinary percolation fixed point at a b pc

enhanced mom analysis of the scattering by periodic strip gratings in multilayered substrates the method of moments mom is applied to the analysis of the scattering of a multilayered periodic strip grating by a plane wave with oblique incidence and arbitrary polarization although this problem has been traditionally solved by means of the mom in the spectral domain this is an approach which leads to the computation of slowly convergent infinite summations in this paper the problem is solved by means of the mixed potential integral equation mpie formulation of the mom in the spatial domain while applying the mom in the spatial domain two improvements are introduced which lead to important cpu time savings first the multilayered periodic green s functions are accurately interpolated in terms of chebyshev polynomials second half the integrals involved in the computation of the mom matrix entries are obtained in closed form as a consequence of these two improvements the spatial domain version of the mom presented in this paper turns out to be between one and two orders of magnitude faster than the conventional spectral domain version when basis functions that account for edge singularities are used in the modeling of the current density on the metallizations

probability measures and hamiltonian models on bethe lattices i properties and construction of mrt probability measures the properties of one step markov rotationally and m step m 1 or 2 translationally invariant mrt probability measures on q state site qss bethe lattices are studied a theorem is proven which completely defines such measures in terms of m q2 q fundamental probabilities these are explicitly calculated for any mrt qss hamiltonian model as a consequence of our approach the dychotomy between alternative solutions of hamiltonian models on bethe lattices is solved

a modification of the kummer s method for efficient computation of the 2 d and 3 d green s functions for 1 d periodic structures an auxiliary function in the form of standing spherical waves with attenuation is proposed in the kummer s method for accelerating the convergence of the spectral series representing the green s function of doubly periodic structures in free space expressions for the amplitude and phase constants of the auxiliary waves versus their attenuation constant are derived at which the spectral difference series formed as a result of the kummer s transformation converges in the worst case as the floquet mode propagation constant in the power of minus 5 9 and 13 for the cases of using one two and three auxiliary waves respectively while the spatial series formed by the auxiliary waves converges exponentially some examples allowing determination of optimum values for the attenuation constant are considered and some comparative results characterizing the effectiveness of the technique proposed are presented and discussed

comparative analysis of acceleration techniques for 2 d and 3 d green s functions in periodic structures along one and two directions the problem of accelerating the calculation of the periodic green s function is addressed here for both 3 d and 2 d free space configurations in the 3 d case periodicity is considered both along one axis and along two generally skew axes a comprehensive review of the existing methods is first presented and some extensions are developed the possibility of treating the case of complex phase shifts between unit cells necessary for the study of complex modes in periodic structures is also investigated comparisons among the various acceleration methods are performed thus providing fundamental information on their actual efficiency in typical problems

some general relations between dressed self avoiding walks and percolation perimeters on lattices the author shows for some simple examples the relations between some recently proposed dressed self avoiding walks and site percolation connection between matching pairs and dressed walk generators is specified and some features of the corresponding bond percolation problem are given the case of surface generators for dressed self avoiding surfaces is briefly examined

some exact results from the mean field renormalization group abstract the mean field renormalization group is applied to the study of the directed self avoiding random walk in d dimensions and to the spin ferromagnetic ising model on the bethe lattice in both cases the known exact results are obtained

stable and efficient evaluation of periodized green s functions for the helmholtz equation at high frequencies a difficulty that arises in the context of infinite d periodic rough surface scattering relates to the effective numerical evaluation of the corresponding quasi periodic green function g q p due to its relevance in a variety of applications this problem has generated significant interest over the last 40 years and a variety of numerical methods have been devised for this purpose none of these methods to evaluate g q p however were designed for high frequency calculations as a result in this regime these methods become prohibitively expensive and or unstable here we present a novel scheme that can be shown to outperform every alternative numerical evaluation procedure and is especially effective for high frequency calculations our new algorithm is based on the use of some exact integrals that arise on judicious manipulation of the integral representation of g q p and which reduce the overall problem to that of evaluation of a sequence of simpler integrals that can be effectively handled by standard quadrature formulas we include a variety of numerical results that confirm that indeed our algorithm compares favorably with alternative methods

regularization of mixed potential layered media green s functions for efficient interpolation procedures in planar periodic structures the problem of improving the computational efficiency in the numerical analysis of planar periodic structures is investigated here using the mixed potential integral equation mpie approach a new regularization of the periodic green s functions pgfs that are involved in the analysis of multilayered structures is introduced based on the effective medium concept this regularization involves extracting the singularities of the pgfs up to second order terms the resulting regularized pgf is very smooth and amenable to interpolation thus optimized interpolation procedures for the pgfs can be applied resulting in a considerable reduction of computation time without any significant effect on the accuracy another benefit of the regularization is that it significantly enhances the convergence of the series for both the vector and scalar potential pgfs the theoretical formulation is fully validated with various numerical results for both two dimensional 2 d and one dimensional 1 d layered media periodic structures

first order transitions in percolation models abstract we describe the analytic solution of a potts correlated site random bond percolation model which exhibits a first order percolative transition at the potts critical point the subject is discussed in connection with the droplet theory in lattice spin models

on ab bond percolation on the square lattice and ab site percolation on its line graph we prove that ab site percolation occurs on the line graph of the square lattice when p in 1 sqrt 1 p c sqrt 1 p c where p c is the critical probability for site percolation in mathbb z 2 also we prove that ab bond percolation does not occur on mathbb z 2 for p frac 1 2

accessible external perimeters of percolation clusters the authors introduce a new definition of a cluster s accessible external perimeter which is different from the usual definition of the hull this external perimeter can be measured by probing adsorbent particles coming from the cluster s exterior the size of these particles determines which perimeter sites are accessible from the outside and hence one can define different external or accessible perimeters according to this size using a monte carlo simulation they measured the fractal dimensions of these accessible perimeters de for percolation clusters at the threshold on the square and the triangular lattices the fractal dimension of the accessible perimeter is found to depend on the size of the probing particles for several sizes which are larger than some lattice dependent threshold they find de approximately 4 3 which is significantly smaller than the hull dimension dh 7 4 found with smaller probing particles

task space adaptive control of robotic manipulators with uncertainties in gravity regressor matrix and kinematics thus far most research in adaptive control of robotic manipulators has assumed that models of regressor matrix and kinematics are known exactly to overcome these drawbacks we propose in this paper a task space adaptive law for setpoint control of robots with uncertainties in gravity regressor matrix and kinematics in addition we investigate the stability problem when an estimated task space velocity is used in the feedback loop sufficient conditions for choosing the feedback gains gravity regressor and jacobian matrix are presented to guarantee the stability

generation of percolation cluster perimeters by a random walk a type of self avoiding random walk whish generates the perimeter of two dimensional lattice percolation clusters is given the algorithm has been simulated on a computer yielding the mean perimeter length as a function of occupation probability

approximate jacobian control with task space damping for robot manipulators in this note we propose two new approximate jacobian control laws with task space damping for setpoint control of robot manipulators the proposed controllers do not require exact knowledge of the jacobian matrix and dynamics of the robots we will show that the end effector s position converges to a desired position in a finite task space even when the kinematics and jacobian matrix are uncertain experimental results are presented to illustrate the performance of the proposed controllers

stabilization of uncertain nonholonomic systems via time varying sliding mode control this note addresses the robust stabilization problem for a general class of nonholonomic systems in the presence of drift uncertainties the control approach developed is based on the combined applications of the sliding mode control technique and nonlinear time varying systems theory first some properties of nonlinear time varying systems are introduced for the purpose of designing sliding mode controller an explicit time varying feedback form is provided to guarantee the existence and uniqueness of periodic time varying solution for the corresponding linear periodic partial differential equation second an explicit discontinuous feedback control law is presented to guarantee the existence of sliding mode the first integrals obtained by the previous periodic partial differential equation are then directly used to determine the switching function the uniform asymptotic stability of the closed loop system is proved via the invariance principle of nonlinear time varying systems finally an example is given to illustrate the proposed approach

concentration gradient approach to continuum percolation in two dimensions the author has investigated percolation properties of a system of overlapping discs randomly distributed with a gradient of concentration fractal properties and critical exponents of this system appear to be identical to their counterparts on a lattice this is in agreement with the universality of critical exponents of percolation the concentration gradient approach permits a precise calculation of the percolation threshold corresponding to a critical area fraction of 0 6766 or 0 0005 he has investigated the part of the external perimeter of the percolation cluster which is accessible to discs of various sizes the fractal dimension of this accessible perimeter is found to decrease abruptly as a function of the radius of invading discs from 1 75 or 0 02 to 1 35 or 0 02

calculation of the free space periodic green s function using equivalent finite array we present a novel method for the calculation of the 2d and 3d free space periodic green s function pgf especially efficient when observation points are in the vicinity of the array plane a case for which both spatial and spectral domain forms of pgf are known to be slowly convergent the pgf is approximated by a truncation of the original array and the assignment of new fictitious amplitudes to maintained sources both 2d and 3d numerical tests show that a highly accurate approximation of the pgf can be obtained with such an equivalent finite array composed of a few sources making the method especially relevant for fast electromagnetic computation of periodic structures with the method of moments mom for example

conformations of randomly linked polymers we consider polymers in which m randomly selected pairs of monomers are restricted to be in contact analytical arguments and numerical simulations show that an ideal gaussian chain of n monomers remains expanded as long as m n m nu the number of links needed to collapse a polymer in three dimensions thus scales as n phi with phi 0 43

a unified design method for adaptive visual tracking control of robots with eye in hand fixed camera configuration a unified design method is proposed in this paper to handle adaptive visual tracking control problem of robots in the proposed scheme the robot dynamic parameters camera intrinsic and extrinsic parameters and position parameters of feature points are assumed to be uncertain a unified kinematics model is presented to simultaneously cope with kinematics modeling problem of robots with the eye in hand or fixed camera configuration based on the unified kinematics a unified design method is proposed to solve the visual tracking control problem of robots with the eye in hand or fixed camera configuration by using the depth independent interaction matrix framework adaptive laws are derived to handle the unknown parameters lyapunov stability analysis is provided to show asymptotical convergence of image position and velocity tracking errors to show the effectiveness of the proposed unified design method experimental results for both camera configurations are also given

on scaling relations in growth models for percolating clusters and diffusion fronts employing analogies between the growth of the incipient percolating cluster and the growth of a diffusion front the authors develop a scaling theory for this latter model their scaling assumptions support the sapoval rosso gouyet conjecture dh 1 1 nu which relates in two dimensions the fractal dimension dh of the hull of the incipient percolating cluster to the correlation length exponent nu in percolation and yield relations between the static and dynamic exponents of the growth of a diffusion front

clusters and droplets in the q state potts model a potts correlated polychromatic percolation is studied the clusters are made of sites corresponding to a given value of the q state potts variables connected by bonds being active with probability pb to treat this problem an s state potts hamiltonian diluted with q state potts variables instead of lattice gas variables is introduced to which the the migdal kadanoff renormalisation group is applied it is found for a particular choice of pb 1 e k where k is the potts coupling constant divided by the boltzmann factor that these clusters called droplets diverge at the potts critical point with potts exponents

probability measures and hamiltonian models on bethe lattices ii the solution of thermal and configurational problems in a previous paper we introduced a method for the construction of rotationally and translationally invariant probability measures generated by one step markov hamiltonian models on q state site bethe lattices here the corresponding thermal problems are solved by finding the relative free energy which gives complete information on the properties of the models under study configurational problems also can be solved with the present tools as an example the solution of polychromatic correlated site random bond percolation models is found