ballot number representation of the percolation probability series for the directed square lattice series expansion data are matters of increasing importance for studying the directed percolation problem and others which are not yet solved in order to extrapolate series for the percolation probability on the directed square lattice baxter and guttmann proposed a numerical method based on an assumption that the so called correction terms are expressed as rational functions of the catalan numbers we give a theorem that the coefficients of the series are generally given as finite series of the ballot numbers which proves the assumption by baxter and guttmann as a corollary the proof of the theorem gives a method to calculate correction terms exactly as demonstrated by calculating the first three correction terms explicitly although the present work provides a mathematical basis for the extrapolation procedure there are still open problems concerning this procedure

catalan numbers in a series expansion of the directed percolation probability on a square lattice we regard the bond directed percolation on a square lattice as a discrete time markov process of a one dimensional interacting particle system the coefficients in series expansion of the probability of having m particles at time n 1 are studied we derive the difference equations for the first and the second series of coefficients and prove that these coefficients are expressed using the ballot numbers whose special cases are known as the catalan numbers as a corollary of our results we prove a part of the conjecture by baxter and guttmann that the correction terms are expressed as rational functions of the catalan numbers we also give approximations for the percolation probability using the present formula

evolutionary subgradient inclusions with nonlinear weakly continuous operators and applications abstract in this paper we consider the first order evolutionary inclusions with nonlinear weakly continuous operators and a multivalued term which involves the clarke subgradient of a locally lipschitz function first we provide a surjectivity result for stationary inclusion with weakly weakly upper semicontinuous multifunction then we use this result to prove the existence of solutions to the rothe sequence and the evolutionary subgradient inclusion finally we apply our results to the non stationary navier stokes equation with nonmonotone and multivalued frictional boundary conditions

low density series expansions for directed percolation on square and triangular lattices greatly extended series have been derived for moments of the pair connectedness for bond and site percolation on the directed square and triangular lattices the length of the various series has been at least doubled to more than 110 100 terms for the square lattice bond site problem and more than 55 terms for the bond and site problems on the triangular lattice analysis of the series leads to very accurate estimates for the critical parameters and generally seems to rule out simple rational values for the critical exponents the values of the critical exponents for the average cluster size parallel and perpendicular connectedness lengths are estimated by d 2 277 69 4 k d 1 733 825 25 and d 1 096 844 14 respectively an improved estimate for the percolation probability exponent is obtained from the scaling relation d k c 2 d 0 276 49 4 in all cases the leading correction to scaling term is analytic

efficient determination of the poles and residues of spectral domain multilayered green s functions that are relevant in far field calculations in this work the total least squares algorithm tlsa is applied to the determination of the proper and improper poles of spectral domain multilayered green s functions that are closer to the branch point and to the determination of the residues at these poles the introduction of an adequate transformation in the spectral domain permits that the tlsa provides accurate values of the poles and residues regardless of the proximity of the poles to the branch point it is shown that the poles and residues supplied by the tlsa can be used to write the far field of the spatial domain green s functions in terms of closed form expressions that are reliable in a wide variety of scenarios

closed form uniform asymptotic expansions of green s functions in layered media far field closed form expressions are derived for spatial domain multilayered green s functions gf for the derivation of these far field expressions the spectral domain multilayered gf are approximated by means of the total least square algorithm tlsa in terms of the spectral variable u0 k 2 k02 1 2 and uniform asymptotic expansions are determined for the sommerfeld integrals of the resulting tlsa approximations numerical results show that the far field asymptotic expressions are accurate within 0 1 for distances between source and field points larger than one free space wavelength also it is shown that the hybrid use of the discrete complex image method and the tlsa in terms of the spectral variable k leads to near field closed form expressions of multilayered gf that are typically accurate within 0 1 for distances between source and field points smaller than one free space wavelength therefore the combination of the novel far field asymptotic expressions and the well known near field expressions makes it possible to compute multilayered gf with a great accuracy in the whole range of distances between source and field points and in a wide range of frequencies

two neighbour stochastic cellular automata and their planar lattice duals two neighbour stochastic cellular automata sca are the set of one dimensional discrete time interacting particle systems with two parameters which show non equilibrium phase transitions from the extinction phase to the survival phase the phase diagram was first studied by kinzel using a numerical method called transfer matrix scaling for some parameter region the processes can be defined as directed percolation models on the spatio temporal plane and the bond and site directed percolation models are included as special cases extending the argument of dhar barma and phani 1981 originally given for bond directed percolation we introduce diode resistor percolation models which are the planar lattice duals of the sca and give rigorous lower bounds for the critical line in special cases our results give 0 6885 or alpha c and 0 6261 or beta c where alpha c and beta c denote the critical probabilities of the site and bond directed percolation models on the square lattice respectively combining the upper bound for the critical line recently proved by liggett 1994 we summarize the rigorous results for the phase diagram of the systems results of computer simulation are also shown

time dependent perturbation theory for nonequilibrium lattice models we develop a time dependent perturbation theory for nonequilibrium interacting particle systems we focus on models such as the contact process which evolve via destruction and autocatalytic creation of particles at a critical value of the destruction rate there is a continuous phase transition between an active steady state and the vacuum state which is absorbing we present several methods for deriving series for the evolution starting from a single seed particle including expansions for the ultimate survival probability in the super and subcritical regions expansions for the average number of particles in the subcritical region and short time expansions algorithms for computer generation of the various expansions are presented rather long series 24 terms or more and precise estimates of critical parameters are presented

numerical analysis of elliptic hemivariational inequalities this paper is devoted to a study of the numerical solution of elliptic hemivariational inequalities with or without convex constraints by the finite element method for a general family of elliptic

directed percolation fractal roots and the lee yang theorem abstract in the directed percolation model we consider the probability p of having an open bond as a complex parameter we show that the roots of the survival probability p n p for a square lattice of n rows distribute themselves in a fractal manner in the complex p plane these roots have an accumulation point on the real axis which coincides with the critical probability p c 0 6447

low density series expansions for directed percolation i a new efficient algorithm with applications to the square lattice a new algorithm for the derivation of low density series for percolation on directed lattices is introduced and applied to the square lattice bond and site problems numerical evidence shows that the computational complexity grows exponentially but with a growth factor which is much smaller than the growth factor of the previous best algorithm for bond site percolation on the directed square lattice the series has been extended to order 171 158 analysis of the series yields sharper estimates of the critical points and exponents

an asymptotic closed form microstrip surface green s function for the efficient moment method analysis of mutual coupling in microstrip antennas a relatively simple closed form asymptotic representation for the single layer microstrip dyadic surface green s function is developed the large parameter in this asymptotic development is proportional to the lateral separation between the source and field points along the air dielectric interface this asymptotic solution remains surprisingly accurate even for very small a few tenths of a free space wavelength lateral separation of the source and field points thus using the present asymptotic approximation of the green s function can lead to a very efficient moment method mm solution for the currents on an array of microstrip antenna patches and feed lines numerical results based on the efficient mm analysis using the present closed form asymptotic approximation to the microstrip surface green s function are given for the mutual coupling between a pair of printed dipoles on a single layer grounded dielectric slab the accuracy of the latter calculation is confirmed by comparison with numerical results based on a mm analysis which employs an exact integral representation for the microstrip green s function

accurate approximation of green s functions in planar stratified media in terms of a finite sum of spherical and cylindrical waves a robust and computationally expedient methodology is presented for accurate closed form approximation of the green s functions used in the mixed potential integral equation statement of the electromagnetic boundary value problem in planar stratified media the proposed methodology is based on the fitting of the spectrum of the green s function after the extraction of the quasistatic part making use of rational functions the effectiveness and robustness of the proposed methodology rely upon the proper sampling of the spectrum in order to improve the accuracy of the rational function fit the resulting closed form approximation is in terms of both spherical and cylindrical waves thus high accuracy is obtained in the approximation of the green s function irrespective of the distance of the observation point from the source the methodology is validated through its application to the approximation of the green s function for a multi layered planar dielectric stack

directed compact lattice animals exact results the partially directed compact lattice animal model on the square lattice is solved exactly for the cluster number and average cluster radius along the directed axis in terms of the appropriate generating functions for the critical exponents we find 0 and 1 caliper size distribution along the directed axis is also calculated analytically it is used to confirm 1 and to study some finite size scaling properties for this model for the perpendicular cluster radius distribution a combination of analytic arguments and computer results leads to a conjecture on the exact form of the appropriate generating function and to the result 1 2 some calculations are reported for the triangular lattice and for hypercubic lattices ind 2

series expansions of the percolation probability for directed square and honeycomb lattices we have derived long series expansions of the percolation probability for site and bond percolation on directed square and honeycomb lattices for the square bond problem we have extended the series from 41 terms to 54 for the square site problem from 16 terms to 37 and for the honeycomb bond problem from 13 terms to 36 analysis of the series clearly shows that the critical exponent beta is the same for all the problems confirming expectations of universality for the critical probability and exponent we find in the square bond case qc 0 3552994 or 0 0000010 beta 0 27643 or 0 00010 in the square site case qc 0 294515 or 0 000005 beta 0 2763 or 0 0003 and in the honeycomb bond case qc 0 177143 or 0 000002 beta 0 2763 or 0 0002 in addition we have obtained accurate estimates for the critical amplitudes in all cases we find that the leading correction to scaling term is analytic i e the confluent exponent delta 1

series expansion of the directed percolation probability using a transfer matrix technique the authors obtain extended series expansion of the percolation probability for the directed site percolation problem on the square lattice their approach reveals a previously unsuspected connection between his problem and the enumeration of the number of ways of dissecting a ball they show that the method can also be used to determine a series expansion for the mean cluster size an analysis based on pade approximants gives estimates of the critical threshold and also of the critical exponent beta

phase transition in an elementary probabilistic cellular automaton abstract cellular automata exhibit a large variety of dynamical behaviors from fixed point convergence and periodic motion to spatio temporal chaos by introducing probabilistic interactions and regarding the asymptotic density of non quiescent cell states as an order parameter phase transitions may be identified from a quiescent phase with 0 to a chaotic phase with non zero we consider an elementary one dimensional probabilistic cellular automaton pca with deterministic limits given by the quiescent rule 0 the rule 72 that evolves into a non trivial fixed point and the chaotic rules 18 and 90 despite the simplicity of the rules the pca shows a surprising number of transition phenomena we identify second order phase transitions from 0 to 0 with static and dynamic exponents that differ from those of directed percolation moreover we find that the non trivial fixed point rule 72 is a singular point in pca space

series expansions of the percolation probability on the directed triangular lattice we have derived long series expansions of the percolation probability for site bond and site bond percolation on the directed triangular lattice for the bond problem we have extended the series from order 12 to 51 and for the site problem from order 12 to 35 for the site bond problem which has not been studied before we have derived the series to order 32 our estimates of the critical exponent are in full agreement with results for similar problems on the square lattice confirming expectations of universality for the critical probability and exponent we find in the site case qc d 0 404 352 8 0 000 001 0 and d 0 276 45 0 000 10 in the bond case qc d 0 521 98 0 000 01 and d 0 2769 0 0010 and in the site bond case qc d 0 264 173 0 000 003 and d 0 2766 0 0003 in addition we have obtained accurate estimates for the critical amplitudes in all cases we find that the leading correction to scaling term is analytic i e the confluent exponent 1 d 1 in an earlier paper jensen and guttmann 1995 we reported on the derivation and analysis of long series for the percolation probability of site and bond percolation on the directed square and hexagonal lattices in this paper we extend this work to site bond and site bond percolation on the directed triangular lattice we refer to our earlier paper for a more general introduction to directed percolation and its role in the modelling of physical systems in directed site percolation each site is either present with probability p or absent with probability q d 1 p independent of all other sites on the lattice similarly for bond percolation each bond is absent or present independently of other bonds finally in site bond percolation both sites and bonds may be absent or present with equal probability but again with no dependency on any other sites or bonds two sites in the various models are connected if one can find a path respecting the directions indicated in figure 1 through occupied sites bonds or sites and bonds respectively from one to the other when p is smaller than a critical value pc all clusters of connected sites remain finite while for p pc there is an infinite cluster spanning the lattice in the preferred direction the order parameter of the system is the percolation probability p p that a given site belongs to the infinite cluster this quantity is strictly zero when p p c the behaviour of p p in the vicinity of pc may be described by a critical exponent p p p pc p p c c 1

boundary hemivariational inequality of parabolic type abstract in this paper we consider a parabolic hemivariational inequality with a nonmonotone multivalued boundary condition and with a time dependent pseudomonotone operator we establish the existence of solutions for such inequality our proof is based on a known surjectivity result for operators of pseudomonotone type we present an example of semipermeability heat conduction problem to which the result applies

directed bond percolation on a square lattice i analytical results a rigorous mathematical formulation of directed percolation is given in terms of matrix recursion equations the domany kinzel limit is rederived in a very simple way expansion around this limit yields surprisingly good results for the percolation probabilities already to first order

green s functions in lossy layered media integration along the imaginary axis and asymptotic behavior this paper presents an efficient technique for evaluating green s functions associated to layered media when formulated as sommerfeld integrals in the space domain the key step in the formulation is that sommerfeld integrals are computed choosing a suitable integration path which is closed through the imaginary axis of the complex spectral plane it is shown that with this original choice of the integration contour the numerical effort usually involved in the evaluation of sommerfeld integrals can be greatly reduced specially when large source observer distances are involved one asset of this technique is that it can be easily incorporated into integral equation based cad packages for the efficient analysis of complex printed microwave circuit and antennas in addition the theoretical developments needed to set up the numerical algorithm throw a new light on the asymptotic behavior of the layered media green s functions for large source observer distances

on a point of order a method of using algebraic curves to obtain estimates of critical points accurate enough to identify them as simple algebraic numbers if that is what they are is discussed and illustrated with an application to the q state potts model on the triangular lattice for cases of pure two site interactions and pure three site interactions in the latter case the critical point is conjectured to be z c 2 tfrac 1 2 sqrt 3 q 2 2 q q geqslant in a similar conjecture for the critical percolation probability on thedirected square lattice q 1 2 q c 3 2 q c p c 1

distribution of poles in a series expansion of the asymmetric directed bond percolation probability on the square lattice we investigate numerically the percolation probability of the asymmetric directed bond percolation on the square lattice with two parameters p and q based on guttmann and enting s procedure 1996 phys rev lett 76 344 a series in the form of p n hn q p n is derived by using the finite transfer matrix method the denominator of hn q is directly calculated from the determinant of the transfer matrix and it leads to a proof that poles all lies on the unit circle in the complex q plane the solvability of the bond directed percolation is also discussed

series expansion of the percolation probability for the directed square lattice by extrapolation from finite lattices the authors extend the known series for the percolation probability on the directed square lattice from eight terms to 41 analysing the series they obtain the estimates qc 0 355 299 or 0 000 001 beta 0 2764 or 0 0001 for the critical probability and the critical exponent from this together with scaling relations and previous results on the moments of the pair connectedness function the authors conjecture that beta may be exactly 199 720

longitudinal size exponent for two dimensional directed animals using phenomenological renormalisation with strip widths up to size 23 the author has numerically estimated the longitudinal size exponent nu sub for two dimensional directed animals he gets nu sub 0 817 33 or 0 000 05 this rules out the simple fraction 9 11 suggested by earlier numerical data the effective correction to the scaling exponent in the continuous time version of the problem is 1 5 or 0 1

directed percolation near a wall series expansion methods are used to study directed bond percolation clusters on the square lattice whose lateral growth is restricted by a wall parallel to the growth direction the percolation threshold is found to be the same as that for the bulk however the values of the critical exponents for the percolation probability and mean cluster size are quite different from those for the bulk and are estimated by and respectively on the other hand the exponent characterizing the scale of the cluster size distribution is found to be unchanged by the presence of the wall the parallel connectedness length which is the scale for the cluster length distribution has an exponent which we estimate to be and is also unchanged the exponent of the mean cluster length is related to and by the scaling relation and using the above estimates yields to within the accuracy of our results we conjecture that this value of is exact and further support for the conjecture is provided by the direct series expansion estimate

existence and regularity results for doubly nonlinear inclusions with nonmonotone perturbation abstract this paper deals with a class of nonlinear evolution inclusions arising from enthalpy formulation of heat conduction problems with phase change and nonmonotone source using time discretization technique and monotone operators theory we show the existence of weak solutions then we prove strong convergence of approximate solutions and lift regularity of the weak solutions under appropriate conditions moreover application to physical model described by hemivariational inequality is given

a frictionless viscoelastodynamic contact problem with energy consistent properties numerical analysis and computational aspects a dynamic frictionless contact problem between a viscoelastic body and a rigid obstacle is numerically studied in this paper the contact is modelled using an adapted unilateral contact law in terms of velocities in order to obtain some energy conservation properties the variational formulation is briefly recalled then a fully discrete scheme is introduced based on the finite element method to approximate the spatial variable and the midpoint scheme to discretize the time derivatives error estimates are derived on the approximative solutions from which the linear convergence of the algorithm is deduced under suitable regularity conditions furthermore we focus our interest on the analysis of the discrete energy evolution and the presentation of an adapted numerical algorithm finally a representative two dimensional example is presented to demonstrate the accuracy and the energy consistent properties of the numerical scheme

nonequilibrium stationary states and equilibrium models with long range interactions it was recently suggested by blythe and evans that a properly defined steady state normalization factor can be seen as a partition function of a fictitious statistical ensemble in which the transition rates of the stochastic process play the role of fugacities in analogy with the lee yang description of phase transition of equilibrium systems they studied the zeros in the complex plane of the normalization factor in order to find phase transitions in nonequilibrium steady states we show that like for equilibrium systems the densities associated with the rates are nondecreasing functions of the rates and therefore one can obtain the location and nature of phase transitions directly from the analytical properties of the densities we illustrate this phenomenon for the asymmetric exclusion process we actually show that its normalization factor coincides with an equilibrium partition function of a walk model in which the densities have a simple physical interpretation

some exact results for moments of 2d directed animals using computer enumerations and the algebraic approximant method of series analysis several new exact results have been found for moments of width perimeter and loops for directed animals on the square and triangular lattices a proof using q series is given for exact solutions for widths on both the square and triangular lattices

weak solvability of a fractional viscoelastic frictionless contact problem abstract the goal of this paper is to study a quasistatic frictionless contact problem for a viscoelastic body in which the constitutive equation is modeled with the fractional kelvin voigt law and the contact condition is described by the clarke subdifferential of a nonconvex and nonsmooth functional the variational formulation of this problem is provided in the form of a fractional hemivariational inequality in order to solve this inequality we apply the rothe method and prove that the associated abstract volterra inclusion has at least one solution

estimates of the site percolation probability exponents for some directed lattices series expansion analysis has been used to obtain estimates of the percolation probability exponent beta for directed site percolation on the square triangular simple cubic and body centred cubic lattices these estimates are consistent with those obtained by please 1977 for the corresponding bond problems and the results for site and bond problems on all lattices considered are summarised by beta 0 28 or 0 01 d 2 and beta 0 59 or 0 02 d 3

enumeration of directed compact site animals in two dimensions the authors study the problem of directed compact site animals in two dimensions using exact enumeration methods the numerical analysis of the animal number series strongly indicates that the critical exponent theta equals zero they also estimate the non universal growth parameter lambda 2 66185 or 0 00050

clarification of issues on the closed form green s functions in stratified media the closed form green s functions cfgf derived for the vector and scalar potentials in planar multilayer media have been revisited to clarify some issues and misunderstandings on the derivation of these green s functions in addition the range of validity of these green s functions is assessed with and without explicit evaluation of the surface wave contributions as it is well known the derivation of the cfgf begins with the approximation of the spectral domain green s functions by complex exponentials and continues with applying the sommerfeld identity to cast these approximated spectral domain green s functions into the space domain in closed forms questions and misunderstandings of this derivation which have mainly originated from the approximation process of the spectral domain green s functions in terms of complex exponentials can be categorized and discussed under the topics of 1 branch point contributions 2 surface wave pole contributions and 3 the accuracy of the obtained cfgf when these issues are clarified the region of validity of the cfgf so obtained may be defined better therefore in this paper these issues will be addressed first and then their origins and possible remedies will be provided with solid analysis and numerical demonstrations

on existence of solutions for parabolic hemivariational inequalities abstract a class of parabolic hemivariational inequalities is considered in which the energy function is locally lipschitz not necessarily convex or differentiable and the nonlinear evolution operator is multivalued and generalized pseudomonotone using techniques of multivalued analysis and a surjectivity result for l generalized pseudomonotone operators we prove the existence for a cauchy problem and a periodic problem some applications to nonsmooth mechanics are also indicated

multilayered media green s functions in integral equation formulations a compact representation is given of the electric and magnetic type dyadic green s functions for plane stratified multilayered uniaxial media based on the transmission line network analog along the aids normal to the stratification furthermore mixed potential integral equations are derived within the framework of this transmission line formalism for arbitrarily shaped conducting or penetrable objects embedded in the multilayered medium the development emphasizes laterally unbounded environments but an extension to the case of a medium enclosed by a rectangular shield is also included

novel position space renormalization group for bond directed percolation in two dimensions abstract a new position space renormalization group approach is investigated for bond directed percolation in two dimensions the threshold value for the bond occupation probabilities is found to be p c 0 6443 correlation length exponents on time parallel and space transverse directions are found to be 1 719 and 1 076 respectively which are in very good agreement with the best known series expansion results

error analysis for implicit approximations to solutions to cauchy problems exact error analyses for two implicit approximation schemes to the cauchy problem du t dt mathcal a u t mathrel backepsilon 0 u 0 u 0 in d mathcal a are presented the operator mathcal a is required to be maximal monotone on a hilbert space mathcal h the approximations considered are u h kh i h mathcal a k u 0 and solutions u lambda to the approximating problems du lambda t dt mathcal a lambda u lambda 0 u lambda 0 u 0 where a lambda is the yosida approximation of mathcal a the special case of a being a subgradient is considered and tight estimates of the convergence of both u h and mathcal a h u h or u h and a h u h are given the new results in this case are the linear rates of convergence of u h in l infty 0 infty mathcal h and in the energy norm and the sublinear rate of convergence of a h u h in l 2 0 infty mathcal h applications to both linear and

efficient formulation of closed form green s functions for general electric and magnetic sources in multilayered media a complete set of closed form multilayered media green s functions with general electric and magnetic sources is presented the green s functions are written in the mixed potential integral equation formulation which is consistent with the michalski zheng 1990 c formulation in addition the differentiations of the curl operator are taken in the spectral domain this leads to calculation of the first and second order sommerfeld integrals and differentiation with respect to z traditionally only the zeroth order sommerfeld integrals are expressed in the closed form by the discrete complex image method with sommerfeld identity here we present a generalized sommerfeld identity by which also the higher order sommerfeld integrals can be expressed in closed form the closed form expressions are derived so that all required differentiations are obtained in closed form and numerical differentiation can be avoided in addition the number of required closed form green s functions is minimized in the source layer only three and in other layers four spectral domain functions have to be considered in writing the mixed potential green s functions with general electric and magnetic source in closed form in the source layer the derived closed form green s expressions are valid for all field and source points and in the other layers they are valid for a fixed z coordinate of a field point the power of the formulation becomes evident when both the electric and magnetic sources are present e g in the electromagnetic scattering by dielectric buried objects

hypergeometric series in a series expansion of the directed bond percolation probability on the square lattice the asymmetric directed bond percolation adbp problem with an asymmetry parameterk is introduced and some rigorous results are given concerning a series expansion of the percolation probability on the square lattice it is shown that the first correction term dn 1 k is expressed by gauss hypergeometric series with a variablek since the adbp includes the ordinary directed bond percolation as a special case withk 1 our results give another proof for the baxter guttmann s conjecture thatdn 1 1 is given by the catalan number which was recently proved by bousquet melou direct calculations on finite lattices are performed and combining them with the present results determines the first 14 terms of the series expansion for percolation probability of the adbp on the square lattice the analysis bydlog pade approximations suggests that the critical value depends onk while asymmetry does not change the critical exponent of percolation probability

on two dimensional directed percolation extended series expansions for the mean size and the first and second moments of the pair connectedness for both bond and site percolation on the directed square and triangular lattices have been obtained analysis based on differential approximants allows the critical percolation probabilities and exponents to be estimated and as a result the critical exponents are conjectured to be gamma 41 18 nu perpendicular to 79 72 and nu sub 26 15 scaling then gives beta 199 720 alpha 299 360 and delta 1839 199

regularity and rothe method error estimates for parabolic hemivariational inequality this paper deals with regularity of solutions to the abstract operator version of parabolic partial differential inclusion of the form u t au t j u t f t with the multivalued term given in the form of clarke subdifferential of a locally lipschitz functional j using the rothe method it is shown that under appropriate assumptions on the data the solution has the increased regularity three regularity theorems are given the first one concerns the regularity of solution in the besov space b2 1 2 0 t h the second theorem provides assumption under which the solution lies in the space h1 0 t h l 0 t v c 0 t vweak the last one shows that if the operator a is strongly monotone and the multivalued term satisfies the relaxed monotonicity assumption then the unique solution also belongs to h1 0 t v w1 0 t h in the last case the error estimates on the rothe method are also proved

comparison between two asymptotic methods two complete asymptotic expansions of an integral with many simple pole singularities and a first order isolated saddle point evaluated by two different methods are compared it is shown that both expansions are exactly the same term by term inside and outside the transition regions

evolutionary variational hemivariational inequalities existence and comparison results we consider an evolutionary quasilinear hemivariational inequality under constraints represented by some closed and convex subset our main goal is to systematically develop the method of sub supersolution on the basis of which we then prove existence comparison compactness and extremality results the obtained results are applied to a general obstacle problem we improve the corresponding results in the recent monograph s carl v k le d motreanu nonsmooth variational problems and their inequalities comparison principles and applications springer monogr math springer new york 2007

chromatic polynomials of large triangular lattices evaluating the q colourings of a lattice is equivalent to solving the q state zero temperature antiferromagnetic potts model this has recently been done exactly for an infinite triangular lattice with q real here the results are extended to the full complex q plane giving the limiting distribution of the zeros of the chromatic polynomial the results are compared with finite lattice calculations and the occurrence of isolated real zeros converging on the beraha numbers is noted

fixed scale transformation approach to critical fluctuations and fractal growth abstract a geometrical approach to the study of critical phenomena calls for a fractal description of critical fluctuations the fixed scale transformation fst approach introduces such a description incorporating both the scale and translational invariance properties of the critical state besides providing a theoretical understanding of the genesis of fractal structures it enables one to compute the fractal dimension of the critical clusters to a high degree of accuracy in terms of the critical statistics of the underlying model laplacian models of irreversible fractal growth to which the fst approach was first applied are presented within the general framework of critical phenomena this geometrical approach links the growth rules which are fully nonlocal in both space and time measured in number of particles added to the morphology of the grown cluster and its scaling behaviour possible directions towards a more comprehensive theory of fractal growth are discussed

series analysis of the generalized contact process abstract we study critical behavior in a one parameter family of generalized contact processes using series expansions our results show that the entire family belongs to a single universality class and permit a more accurate assessment of exponent uncertainties

series expansions for the percolation probability of a generalized domany kinzel cellular automaton series expansions have been derived for the percolation probability of a generalized domany kinzel cellular automaton with two equivalent absorbing states the analysis of the series generally yields estimates of the critical exponent consistent with earlier monte carlo studies thus confirming that the model belongs to the same universality class as branching annihilating random walks with an even number of offspring there is evidence to suggest that when the probability of spreading from two active sites becomes small a new critical behaviour emerges

a robust method for the computation of green s functions in stratified media closed form green s functions for unbounded planar stratified media are derived in terms of cylindrical and spherical waves the methodology is based on a two level approximation of the spectral domain representation of green s functions this robust efficient and fully numerical approach does not call for an analytical extraction of ldquoproblematicrdquo behaviors such as the quasi static terms and the surface wave poles prior to the spectrum fitting instead the spatial domain green s functions derived in this paper provide an accurate description of both the near field singularity in the vicinity of the source and the far field dominant behavior of the surface waves

existence and comparison results for noncoercive and nonmonotone multivalued elliptic problems abstract we consider noncoercive quasilinear elliptic inclusions under multivalued flux boundary conditions involving multifunctions of clarke s generalized gradient our main goal is to provide existence and comparison results which are based on an appropriate generalization of the notions of subsolutions and supersolutions furthermore compactness and extremality results of the solution set enclosed by an ordered pair of sub supersolutions will be proved

a posteriori error estimates for variable time step discretizations of nonlinear evolution equations we study the backward euler method with variable time steps for abstract evolution equations in hilbert spaces exploiting convexity of the underlying potential or the angle bounded condition thereby assuming no further regularity we derive novel a posteriori estimates of the discretization error in terms of computable quantities related to the amount of energy dissipation or monotonicity residual these estimators depend solely on the discrete solution and data and impose no constraints between consecutive time steps we also prove that they converge to zero with an optimal rate with respect to the regularity of the solution we apply the abstract results to a number of concrete strongly nonlinear problems of parabolic type with degenerate or singular character 2000 john wiley sons inc

extremal solutions of quasilinear parabolic inclusions with generalized clarke s gradient abstract in this paper we consider an initial boundary value problem for a parabolic inclusion whose multivalued nonlinearity is characterized by clarke s generalized gradient of some locally lipschitz function and whose elliptic operator may be a general quasilinear operator of leray lions type recently extremality results have been obtained in case that the governing multivalued term is of special structure such as multifunctions given by the usual subdifferential of convex functions or subgradients of so called dc functions the main goal of this paper is to prove the existence of extremal solutions within a sector of appropriately defined upper and lower solutions for quasilinear parabolic inclusions with general clarke s gradient the main tools used in the proof are abstract results on nonlinear evolution equations regularization comparison truncation and special test function techniques as well as tools from nonsmooth analysis

directed bond percolation on the honeycomb lattice using a transfer matrix method the authors derive a series expansion for the percolation probability on the directed honeycomb lattice the high density series is obtained to order q13 a pade approximant analysis of the series has been used to estimate the percolation threshold qc and the critical exponent beta

extrapolation procedure for low temperature series for the square lattice spin 1 ising model the finite lattice method of series expansions has been combined with a new extrapolation procedure to extend the low temperature series for the specific heat spontaneous magnetization and susceptibility of the spin 1 ising model on the square lattice the extended series were derived by directly calculating the series to order 99 in the variable and using the new extrapolation procedure to calculate an additional 13 14 terms

are damage spreading transitions generically in the universality class of directed percolation we present numerical evidence for the fact that the damage spreading transition in the domany kinzel automaton found by martinset al is in the same universality class as directed percolation we conjecture that also other damage spreading transitions should be in this universality class unless they coincide with other transitions as in the ising model with glauber dynamics and provided the probability for a locally damaged state to become healed is not zero

a new technique for the derivation of closed form electromagnetic green s functions for unbounded planar layered media a closed form electromagnetic green s function for unbounded planar layered media is derived in terms of a finite sum of hankel functions the derivation is based on the direct inverse hankel transform of a pole residue representation of the spectral domain form of the green s function such a pole residue form is obtained through the solution of the spectral domain form of the governing green s function equation numerically through a finite difference approximation rather than analytically the proposed methodology can handle any number of layers including the general case where the planar media exhibit arbitrary variation in their electrical properties in the vertical direction the numerical implementation of the proposed methodology is straightforward and robust and does not require any preprocessing of the spectrum of the green s function for the extraction of surface wave poles or its quasi static part the number of terms in the derived closed form expression is chosen adaptively with the distance between source and observation point as parameter the development of the closed form green s function is presented for both vertical and horizontal dipoles its accuracy is verified through a series of numerical examples and comparisons with results from other established methods

crossover from isotropic to directed percolation we generalize the directed percolation dp model by relaxing the strict directionality of dp such that propagation can occur in either direction but with anisotropic probabilities we denote the probabilities as p p pd and p p 1 pd with p representing the average occupation probability and pd controlling the anisotropy the leath alexandrowicz method is used to grow a cluster from an active seed site we call this model with two main growth directions biased directed percolation bdp standard isotropic percolation ip and dp are the two limiting cases of the bdp model corresponding to pd 1 2 and pd 0 1 respectively in this work besides ip and dp we also consider the 1 2 pd 1 region extensive monte carlo simulations are carried out on the square and the simple cubic lattices and the numerical data are analyzed by finite size scaling we locate the percolation thresholds of the bdp model for pd 0 6 and 0 8 and determine various critical exponents these exponents are found to be consistent with those for standard dp we also determine the renormalization exponent associated with the asymmetric perturbation due to pd 1 2 6 0 near ip and confirm that such an asymmetric scaling field is relevant at ip