internal stabilization of semilinear parabolic systems this work is concerned with the internal stabilization of the steady state solutions to semilinear parabolic systems via finite dimensional feedback controllers the internal controller is active on a nonempty open subset and in one equation only

space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

profiles of tries tries from retrieval are one of the most popular data structures on words they are pertinent to the internal structure of stored words and several splitting procedures used in diverse contexts the profile of a trie is a parameter that represents the number of nodes either internal or external with the same distance from the root it is a function of the number of strings stored in a trie and the distance from the root several if not all trie parameters such as height size depth shortest path and fill up level can be uniformly analyzed through the external and internal profiles although profiles represent one of the most fundamental parameters of tries they have hardly been studied in the past the analysis of profiles is surprisingly arduous but once it is carried out it reveals unusually intriguing and interesting behavior we present a detailed study of the distribution of the profiles in a trie built over random strings generated by a memoryless source we first derive recurrences satisfied by the expected profiles and solve them asymptotically for all possible ranges of the distance from the root it appears that profiles of tries exhibit several fascinating phenomena when moving from the root to the leaves of a trie the growth of the expected profiles varies near the root the external profiles tend to zero at an exponential rate and then the rate gradually rises to being logarithmic the external profiles then abruptly tend to infinity first logarithmically and then polynomially they then tend polynomially to zero again furthermore the expected profiles of asymmetric tries are oscillating in a range where profiles grow polynomially while symmetric tries are nonoscillating in contrast to most shape parameters of random tries studied previously such a periodic behavior for asymmetric tries implies that the depth satisfies a central limit theorem but not a local limit theorem of the usual form also the widest levels in symmetric tries contain a linear number of nodes differing from the order n sqrt log n for asymmetric tries n being the size of the trees finally it is observed that profiles satisfy central limit theorems when the variance goes unbounded while near the height they are distributed according to poisson laws as a consequence of these results we find typical behaviors of the height shortest path fill up level and depth these results are derived here by methods of analytic algorithmics such as generating functions mellin transform poissonization and de poissonization the saddle point method singularity analysis and uniform asymptotic analysis

analytical depoissonization and its applications in combinatorics and analysis of algorithms a poisson version of a problem henceforth called a poisson model or poissonization is often easier to solve than the original one which we name here the bernoulli model poissonization is a technique that replaces the original input e g think of balls thrown into urns by a poisson process e g think of balls arriving according to a poisson process into urns more precisely analytical poisson transform maps a sequence e g characterizing the bernoulli model into a generating function of a complex variable however after poissonization one must depoissonize in order to translate the results of the poisson model into the original i e bernoulli model we present in this paper several analytical depoissonization results that fall into the following general scheme if the poisson transform has an appropriate growth in the complex plane then an asymptotic expansion of the sequence can be expressed in terms of the poisson transform and its derivatives evaluated on the real line not surprisingly actual formulations of depoissonization results depend on the nature of the growth of the poisson transform and thus we have polynomial and exponential depoissonization theorems normalization e g as in the central limit theorem introduces another twist that led us to formulate the so called diagonal depoissonization theorems finally we illustrate our results on numerous examples from combinatorics and the analysis of algorithms and data structures e g combinatorial assemblies digital trees multiaccess protocols probabilistic counting selecting a leader data compression etc authors abstract

asymptotic behaviour of a phase field model with three coupled equations without uniqueness abstract we prove the existence of weak solutions for a phase field model with three coupled equations with unknown uniqueness and state several dynamical systems depending on the regularity of the initial data then the existence of families of global attractors level set depending for the corresponding multi valued semiflows is established applying an energy method finally using the regularizing effect of the problem we prove that these attractors are in fact the same

analysis of hybrid selection maximal ratio combining in correlated nakagami fading we present an analysis of a hybrid selection maximal ratio combining diversity system over an evenly correlated slow frequency nonselective nakagami fading channel where the correlation coefficient between any pair of the diversity branch gain amplitudes is the same and all average branch signal to noise ratios snrs are equal in this system the l branches with the largest instantaneous snr out of n available branches are selected and combined using maximal ratio combining from the joint characteristic function cf of the instantaneous branch snrs we obtain an expression for the cf of the combiner output snr as a series of elementary cfs the expression can be conveniently used to obtain the symbol error probability of coherent detection of different m ary modulation schemes we illustrate our methodology using m ary phase shift keying as an example

asymptotic behavior of the lempel ziv parsing scheme and digital search trees the lempel ziv parsing scheme finds a wide range of applications most notably in data compression and algorithms on words it partitions a sequence of length n into variable phrases such that a new phrase is the shortest substring not seen in the past as a phase the parameter of interest is the number mn of phrases that one can construct from a sequence of length n in this paper for the memoryless source with unequal probabilities of symbols generation we derive the limiting distribution of mn which turns out to be normal this proves a long standing open problem in fact to obtain this result we solved another open problem namely that of establishing the limiting distribution of the internal path length in a digital search tree the latter is a consequence of an asymptotic solution of a multiplicative differential functional equation often arising in the analysis of algorithms on words interestingly enough our findings are proved by a combination of probabilistic techniques such as renewal equation and uniform integrability and analytical techniques such as mellin transform differential functional equations de poissonization and so forth in concluding remarks we indicate a possibility of extending our results to markovian models

retrieving topological information for phase field models the phase field approach has become a popular tool in modeling interface motion microstructure evolution and more recently the shape transformation of vesicle membranes under elastic bending energy while it is advantageous to employ phase field models in numerical simu lations to automatically handle topological changes to the microstructures or the configurations of vesicle membranes detecting topological events may also become important for many applications such as those in the simulation of blood cells motivated by such considerations a new quantity is formulated to retrieve some topological information based on the phase field formulation and to capture the occurrence of topological events it can also be used as a control method to avoid unphys ical changes of topology due to the numerical methods should it become necessary for particular practical applications through numerical experiments we demonstrate the effectiveness and the robustness of the new quantity in detecting the topology of fluid bubbles and vesicle membranes

well posedness results and asymptotic behaviour for a phase transition model taking into account microscopic accelerations we obtain an existence and uniqueness result to fremond s phase transition model which take into account microscopic movements and accelerations moreover the irreversible evolution of the phase variable is considered next we perform an asymptotic analysis on the solution to the above problem as the power of the microscopic acceleration forces goes to zero

error estimates for a finite element discretization of a phase field model for mixtures we derive error estimates for finite element discretizations of phase field models that describe phase transitions in nonisothermal mixtures special attention is paid to the applicability of the result for a large class of models with nonlinear constitutive relations and to an approach that avoids an exponential dependence of the constants in the error estimate on the approximation parameter that models the thickness of the diffuse phase transition region the main assumptions on the model are a convexity condition for a function that can be interpreted as the negative local part of the entropy of the system a suitable regularity of the exact solutions and a spectrum estimate for the operator of the allen cahn equation the spectrum estimate is crucial to avoid the exponential dependence of error constants on the approximation parameters in the model this is done by a technique introduced in x feng and a prohl math comp 73 2004 pp 541 567 for phase transitions of pure materials with linear constitutive relations

entropy computations via analytic depoissonization we investigate the basic question of information theory namely evaluation of shannon entropy and a more general renyi 1961 entropy for some discrete distributions e g binomial negative binomial etc we aim at establishing analytic methods i e those in which complex analysis plays a pivotal role for such computations which often yield estimates of unparalleled precision the main analytic tool used here is that of analytic poissonization and depoissonization we illustrate our approach on the entropy evaluation of the binomial distribution that is we prove that for binomial n p distribution shannon s h sub n becomes h sub n spl ap 1 2 ln n 1 2 ln spl radic 2 spl pi p 1 p spl sigma sub k spl ges 1 a sub k n sup k where a sub k are explicitly computable constants moreover we argue that analytic methods e g complex asymptotics such as rice s method and singularity analysis mellin transforms poissonization and depoissonization can offer new tools for information theory especially for studying second order asymptotics e g redundancy in fact there has been a resurgence of interest and a few successful applications of analytic methods to a variety of problems of information theory therefore we propose to name such investigations as analytic information theory

continuity of the temperature in the two phase stefan problem the classical two phase stefan problem a model for ice water melting gives rise to a singular nonlinear partial differential equation which admits a unique weak solution here we prove that this solution and therefore the temperature in the stefan problem are continuous

limit theorems for recursive algorithms abstract we study random algorithms arising in multiple access communication problems we prove asymptotic stability and normality numerical analysis of the performance of the algorithms is provided the general convergence theorems in the paper are based on contraction properties of suitably chosen ideal metrics the approach allows us to prove asymptotic normality under very weak conditions superseding the results of other authors stable and multivariate extensions seem to be analysed for the first time in the literature our numerical results show that the capetanakis tsybakov mikhailov ctm algorithm and the trinomial algorithm have a similar asymptotic behaviour for a small number of users there are some differences concerning the quality of the normal approximation

virtual branch analysis of symbol error probability for hybrid selection maximal ratio combining in rayleigh fading we derive analytical expressions for the symbol error probability sep for a hybrid selection maximal ratio combining h s mrc diversity system in multipath fading wireless environments with h s mrc l out of n diversity branches are selected and combined using maximal ratio combining mrc we consider coherent detection of m ary phase shift keying mpsk and quadrature amplitude modulation mqam using h s mrc for the case of independent rayleigh fading with equal signal to noise ratio averaged over the fading the proposed problem is made analytically tractable by transforming the ordered physical diversity branches which are correlated into independent and identically distributed i i d virtual branches which results in a simple derivation of the sep for arbitrary l and n we further obtain a canonical structure for the sep of h s mrc as a weighted sum of the elementary seps which are the seps using mrc with i i d diversity branches in rayleigh fading or equivalently the seps of the nondiversity single branch system in nakagami fading whose closed form expressions are well known we present numerical examples illustrating that h s mrc even with l spl lt n can achieve a performance close to that of n branch mrc

on a navier stokes allen cahn model with inertial effects abstract a mathematical model describing the flow of two phase fluids in a bounded container is considered under the assumption that the phase transition is influenced by inertial effects the model couples a variant of the navier stokes system for the velocity u with an allen cahn type equation for the order parameter relaxed in time in order to introduce inertia at the microscopic level the resulting model is characterized by second order material derivatives which constitute the main difficulty in the mathematical analysis in order to obtain a tractable problem a viscous relaxation term is then included in the phase equation the mathematical results consist in existence of weak solutions in 3d and under additional assumptions existence and uniqueness of strong solutions in 2d a partial characterization of the long time behavior of solutions is also given and in particular some issues related to dissipation of energy are discussed

new results on the size of tries a precise asymptotic expansion of the variance of the size of a trie built on random binary strings is presented this data structure appears in some hashing schemes and communications protocols the variance is asymptotically linear and numerical results are given the reader is referred to an earlier work for formal proofs

renewal theory in the analysis of tries and strings we give a survey of a number of simple applications of renewal theory to problems on random strings and tries insertion depth size insertion mode and imbalance of tries variations for b tries and patricia tries khodak and tunstall codes

thermodynamically consistent models of phase field type for the kinetics of phase transitions abstract a general framework is given for the phenomenological kinetics of phase transitions in which not only the order parameter but also the temperature may vary in time and space instead of a ginzburg landau free energy functional as used in formulating the cahn hilliard equation we use the analogous entropy functional model entropy functionals and the kinetic equations resulting from them are constructed for various cases phase transitions with and without a critical point and in the former case with or without a latent heat the class considered is general enough to include the entropy functionals for the ising model in mean field approximation the van der waals fluid and a simplified version of the density functional theory of freezing a case without critical point for which the energy is conserved but the order parameter is not provides a thermodynamically consistent derivation of the phase field equations studied by caginalp fix and others and also leads in a natural way to the lyapunov functional given by langer for these equations but the treatment also suggests that a modified version of the phase field equations might provide a more realistic model of freezing

weak solution of a stochastic 3d cahn hilliard navier stokes model driven by jump noise abstract we investigate a stochastic 2d and 3d cahn hilliard navier stokes system with a multiplicative noise of levy type the model consists of the navier stokes equations for the velocity coupled with a cahn hilliard system for the order phase parameter we prove that the system the existence of weak martingale solution for both 2d and 3d cases the proof of the existence is based on a classical galerkin approximation as well as some compactness methods in the 2d case we prove the pathwise uniqueness of the weak solution

existence of global solutions to the caginalp phase field system with dynamic boundary conditions and singular potentials our aim in this article is to prove the global in time existence of solutions to a caginalp phase field system with dynamic boundary conditions and a singular potential the main difficulty is to prove that the solutions are strictly separated from the singular values of the potential this is achieved by studying an auxiliary elliptic problem

the phase field method in the sharp interface limit the phase field pf method for solidification phenomena is an open formulation based on a free energy functional two common choices for the pf potential here referred to briefly as the caginalp and kobayashi models are compared with respect to their numeric results within the classical sharp interface limit both qualitative and quantitative behavior are addressed and an assessment of the computational effort required to approximate a sharp interface problem is made it is shown that the specific form of the free energy potential does have a strong influence on the convergence of the pf results to their sharp interface limit compliance of the pf solutions with the linear kinetic model for the interface temperature is also investigated a simple one dimensional solidification problem in the presence of kinetic undercooling is solved by the pf model and also by a deforming grid method our results support the view that if care is exercised in formulating the phase temperature coupling there is a high degree of confidence in using the pf method for the numerical modeling of general solidification phenomena

an analysis of a phase field model of a free boundary a mathematical analysis of a new approach to solidification problems is presented a free boundary arising from a phase transition is assumed to have finite thickness the physics leads to a system of nonlinear parabolic differential equations existence and regularity of solutions are proved invariant regions of the solution space lead to physical interpretations of the interface a rigorous asymptotic analysis leads to the gibbs thompson condition which relates the temperature at the interface to the surface tension and curvature

the gibbs thompson relation within the gradient theory of phase transitions this paper discusses the asymptotic behavior as 0 of the chemical potentials associated with solutions of variational problems within the van der waals cahn hilliard theory of phase transitions in a fluid with free energy per unit volume given by 2 2 w where is the density the main result is that is asymptotically equal to e d o with e the interfacial energy per unit surface area of the interface between phases the constant sum of principal curvatures of the interface and d the density jump across the interface this result is in agreement with a formula conjectured by m gurtin and corresponds to the gibbs thompson relation for surface tension proved by g caginalp within the context of the phase field model of free boundaries arising from phase transitions

the quasistationary phase field equations with neumann boundary conditions abstract we prove that the quasistationary phase field equations t u u f 2e 1 e w u where w t t 2 1 2 is a double well potential admit a solution when the space dimension n 3 and that the solutions converge for e 0 to solutions of the stefan problem with gibbs thomson law

mimo antenna subset selection with space time coding this paper treats multiple input multiple output mimo antenna subset selection employing space time coding we consider two cases differentiated based on the type of channel knowledge used in the selection process we address both the selection algorithms and the performance analysis we first consider the case when the antenna subsets are selected based on exact channel knowledge eck our results assume the transmission of orthogonal space time block codes with emphasis on the alamouti see ieee j select areas commun vol 16 p 1451 68 oct 1998 code next we treat the case of antenna subset selection when statistical channel knowledge sck is employed by the selection algorithm this analysis is applicable to general space time coding schemes when eck is available we show that the selection algorithm chooses the antenna set that maximizes the channel frobenius norm leading to both coding and diversity gain when sck is available the selection algorithm chooses the antenna set that maximizes the determinant of the covariance of the vectorized channel leading mostly to a coding gain in case of eck based selection we provide analytical expressions for average snr and outage probability improvement for the case when sck based selection is used we derive expressions for coding gain we also present extensive simulation studies validating our results

stabilization by sparse controls for a class of semilinear parabolic equations stabilization problems for parabolic equations with polynomial nonlinearities are investigated in the context of an optimal control formulation with a sparsity enhancing cost functional this formulation allows that the optimal control completely shuts down once the trajectory is sufficiently close to a stable steady state such a property is not present for commonly chosen control mechanisms to establish these results it is necessary to develop a function space framework for a class of optimal control problems posed on infinite time horizons which is otherwise not available

shape instabilities and pattern formation in solidification a new method for numerical solution of the moving boundary problem abstract when a solidification front is advancing into a region of supercooled liquid its shape is subject to instabilities which can lead to complex modes of growth the evaluation of the growth pattern is determined by the interaction of the driving force of the instability due to heat diffusion with the restabilizing force due to surface tension and its full development is a highly nonlinear process a new method for solving the two phase heat diffusion problem under these conditions is described the method is based on a single domain treatment weak formulation of the moving boundary problem with the temperature field near the interface approximated by a piecewise linear function in the spirit of the finite element technique calculated results for a model problem are in excellent agreement with the predictions of an analytical approximation

reconstruction of two time independent coefficients in an inverse problem for a phase field system abstract in this paper we present stability results concerning the inverse problem of determining two time independent coefficients for a phase field system in a bounded domain r n for the dimension n 3 with a single observation on a subdomain and the sobolev norm of certain partial derivatives of the solutions at a fixed positive time 0 t over the whole spatial domain the proof of these results relies on an appropriate carleman estimate for the phase field system

maximum likelihood analysis of algorithms and data structures we present a new approach for an average case analysis of algorithms and data structures that supports a non uniform distribution of the inputs and is based on the maximum likelihood training of stochastic grammars the approach is exemplified by an analysis of the expected size of binary tries as well as by three sorting algorithms and it is compared to the known results that were obtained by traditional techniques investigating traditional settings like the random permutation model we rediscover well known results formerly derived by pure analytic methods changing to biased data yields original results all but one step of our analysis can be automated on top of a computer algebra system thus our new approach can reduce the effort required for an average case analysis allowing for the consideration of realistic input distributions with unknown distribution functions at the same time as a by product our approach yields an easy way to generate random combinatorial objects according to various probability distributions

quasilinear systems with memory kernels we consider a quasilinear integrodifferential system in non normal form such a system is a generalization of a phase field model with memory and includes as a particular case the system describing the combustion of a material with memory in this paper we study both the direct and the inverse problems our fundamental tools are the theory of analytic semigroups optimal regularity results and fixed point arguments

exponential attractors for a conserved phase field system with memory we consider a conserved phase field system of caginalp type characterized by the assumption that both the internal energy and the heat flux depend on the past history of the temperature and its gradient respectively the model consists of a parabolic integrodifferential equation coupled with a fourth order evolution equation for the phase field this system supplemented with suitable boundary conditions can be interpreted as a dissipative dynamical system in a proper phase space in a previous joint work the last two authors have proved the existence of a global attractor of finite fractal dimension here we show the existence of an exponential attractor by means of the techniques we developed for nonconserved phase field systems with memory

performance bounds for space time block codes with receive antenna selection in this correspondence we present a comprehensive performance analysis of orthogonal space time block codes stbcs with receive antenna selection for a given number of receive antennas m we assume that the receiver uses the best l of the available m antennas where typically l spl les m the selected antennas are those that maximize the instantaneous received signal to noise ratio snr we derive explicit upper bounds on the bit error rate ber performance of the above system for any m and l and for any number of transmit antennas we show that the diversity order with antenna selection is maintained as that of the full complexity system whereas the deterioration in snr is upper bounded by 10log sub 10 m l decibels furthermore we derive a tighter upper bound for the ber performance for any n and m when l 1 and derive an expression for the exact ber performance for the alamouti scheme when l 1 we also present simulation results that validate our analysis

on the variance of a class of inductive valuations of data structures for digital search let an inductive valuation l on the family of binary tries or patricia tries or digital search trees be defined in the following way l t l tl l tr r t where tl and tr denote the left and right subtrees of t and r depends only on the size the number of records t of t let ln denote l restricted to the trees of size n in theorem 1 we give sufficient conditions on the sequence r t r t for the variance var ln to be of exact order n if the family of tries resp patricia tries resp digital search trees is equipped with the bernoulli model for the symmetric bernoulli model we prove the existence of a continuous periodic function with period 1 such that var ln log2 n n holds

the numerical computation of heteroclinic connections in systems of gradient partial differential equations the numerical computation of heteroclinic connections in partial differential equations pdes with a gradient structure such as those arising in the modeling of phase transitions is considered initially a scalar reaction diffusion equation is studied structural assumptions are made on the problem to ensure the existence of absorbing sets and consequently a global attractor as a result of the gradient structure it is known that if all equilibria are hyperbolic the global attractor comprises the set of equilibria and heteroclinic orbits connecting equilibria to one another thus it is natural to consider direct approximation of the set of equilibria and the connecting orbits results are proved about the fourier spanning basis for branches of equilibria and also for certain heteroclinic connections these results exploit the oddness of the nonlinearity the reaction diffusion equation is then approximated by a galerkin spectral discretization to produce a system of ordinary differential equations

abstract approach to evolution equations of phase field type and applications a general system of abstract nonlinear parabolic equations deriving from phase field models of heat transfer in anisotropic fluids with phase transitions is studied through a backward finite differences approximation scheme and existence and uniqueness theorems are proved then applications are presented to two physical situations first a standard heat diffusion problem is briefly discussed mainly as a justification of the choices of the abstract setting second a more interesting transmission problem between two different adjoining fluids is studied under very general compatibility hypotheses and the abstract results are adapted to provide an existence and uniqueness theorem also in this case moreover through convex analysis techniques it is performed a mathematical study of the subdifferential type relations linking the phase fields and the temperatures to the internal energies of the fluids email schimper dragon ian pv cnr it keywords phase field models subdifferential operators abstract evolution equations

global existence and asymptotic behavior for the radially symmetric case of a two phase stefan problem with interfacial energy abstract this paper is concerned with global existence in time and asymptotic behavior for the radially symmetric case of a stefan problem with surface tension effects on the interface according to the static gibbs thomson law these problems arise in phase change theory

local minimisers and singular perturbations we construct local minimisers to certain variational problems the method is quite general and relies on the theory of convergence the approach is demonstrated through the model problem it is shown that in certain nonconvex domains n and for e small there exist nonconstant local minimisers u e satisfying u e 1 except in a thin transition layer the location of the layer is determined through the requirement that in the limit u e u 0 the hypersurface separating the states u 0 1 and u 0 1 locally minimises surface area generalisations are discussed with for example vector valued u and anisotropic perturbations replacing u 2

an analytic approach to the asymptotic variance of trie statistics and related structures we develop analytic tools for the asymptotics of general trie statistics which are particularly advantageous for clarifying the asymptotic variance many concrete examples are discussed for which new fourier expansions are given the tools are also useful for other splitting processes with an underlying binomial distribution we specially highlight philippe flajolet s contribution in the analysis of these random structures

front tracking finite element method for dendritic solidification 765 abstract a two dimensional finite element method capable of tracking sharp interfaces is developed the method is based on a fixed mesh of bilinear isoparametric elements and is extremely simple and easy to use the interfaces are tracked with a set of marker points that define their position at all times several different approaches to finding the interface position and velocity are discussed and their effect on the convergence rate is examined it is shown through numerical examples that the approximation to the interface position converges with second order accuracy in two dimensional problems as opposed to previously developed finite difference algorithms that are only first order accurate the approximation to the interface velocity is shown to be of first order a number of examples are examined including several that provide a careful comparison with previously published results

phase field method to optimize dielectric devices for electromagnetic wave propagation we discuss a phase field method for shape optimization in the context of electromagnetic wave propagation the proposed method has the same functional capabilities as the level set method for shape optimization the first advantage of the method is the simplicity of computation since extra operations such as re initialization of functions are not required the second is compatibility with the topology optimization method due to the similar domain representation and the sensitivity analysis structural shapes are represented by the phase field function defined in the design domain and this function is optimized by solving a time dependent reaction diffusion equation the artificial double well potential function used in the equation is derived from sensitivity analysis we study four types of 2d or 2 5d axisymmetric optimization problems two are the classical problems of photonic crystal design based on the bloch theory and photonic crystal wave guide design and two are the recent topics of designing dielectric left handed metamaterials and dielectric ring resonators

phase transitions with semi diffuse interfaces in this paper we examine new phase field models with semi diffuse interfaces these models have the property that the 1 1 planar phase transitions take place over a finite interval the models also support multiple interface solutions with interfaces centered at arbitrary points l sub 1 l sub 2 l sub n these solutions correspond to local minima of an entropy functional rather than saddle points and are dynamically stable the classical models have no such exact solutions but they do support solutions with n equally spaced transition points where the order parameter transitions between valves p sub min n and p sub max n satisfying 1 p sub min n 0 p sub max n 1 these solutions of the classical model are saddle points of the entropy functional associated with those models and are not dynamically stable

hypersurfaces with mean curvature given by an ambient sobolev function we consider n hypersurfaces j with interior ej whose mean curvature are given by the trace of an ambient sobolev function uj w 1 p r h j uj ej on j 0 1 where ej denotes the inner normal of j we investigate 0 1 when j weakly as varifolds and prove that is an integral n varifold with bounded first variation which still satisfies 0 1 for uj u ej e p has to satisfy

phase field models for hypercooled solidification abstract properties of the solidification front in a hypercooled liquid so called because the temperature of the resulting solid is below the melting temperature are derived using a phase field diffuse interface model certain known properties for hypercooled fronts in specific materials are reflected within our theories such as the presence of thin thermal layers and the trend towards smoother fronts with less pronounced dendrites when the undercooling is increased within the hypercooled regime both an asymptotic analysis to derive the relevant free boundary problems and a rigorous determination of the inner profile of the diffusive interface are given of particular interest is the incorporation of anisotropy and general microscale interactions leading to higher order differential operators these features necessitate a much richer mathematical analysis than previous theories anisotropic free boundary problems are derived from our models the simplest of which involves determining the evolution of a set a solid particle whose boundary moves with velocity depending on its normal vector considerable attention is given to the identification of surface tension to comparison with previous theories and to questions of stability

riccati based feedback control of the monodomain equations with the fitzhugh nagumo model feedback control for the monodomain equations is studied the dynamics of interest are governed by a coupled pde ode reaction diffusion system with nonmonotone nonlinearity of fitzhugh nagumo type a localized distributed control is used to locally stabilize the nonlinear system this is achieved by a riccati based feedback law determined by the linearized system it is shown that the riccati equation corresponding to the pde variable suffices for exponential stabilization of the linearized pde ode system the theoretical findings are underlined by several numerical examples

hyperbolic phase field dynamics with memory abstract we consider a non conserved phase field system which consists of two nonlinearly coupled hyperbolic integrodifferential equations this model is derived from two basic assumptions the heat flux law is of gurtin pipkin type and the response of the order parameter to the variation of the free energy functional is delayed these hypotheses might be a reasonable attempt to describe for instance the melt of he 4 crystals a suitable initial and boundary value problem is then associated with the system and its well posedness is analyzed in detail

regularity of solutions of evolution integrodifferential equations with deviating argument abstract in this paper we prove the existence of mild and classical solutions of delay integrodifferential equation and delay integrodifferential evolution equations with nonlocal condition in banach spaces the regularity solutions of integrodifferential evolution equations interconnected with viscoelastic material is derived to guarantee the stabilization the results are established by using the resolvent operators and the fixed point principles finally an example is given to show the potential of the proposed techniques

computation of sharp phase boundaries by spreading the planar and spherically symmetric cases abstract the sharp interface that arises from any of the major transition problems classical or modified stefan etc can be smoothed using the phase field approach as a numerical tool the basic idea is that the thickness of the interface can be regarded as a mathematical free parameter which can be stretched beyond its physical value for computational convenience the computations in one dimensional space and n dimensions with radial symmetry indicate that this is an efficient method for dealing with stiff equations and results in a very accurate interface determination without explicit tracking the question of optimizing the interfacial thickness with respect to grid size is also considered empirically the technique also provides a numerical verification of the concept of an unstable critical radius of solidification

finite dimensional controller design for semilinear parabolic systems this paper considers the stabilization of steady state solutions of a semilinear parabolic system using finite dimensional feedback controllers with support in an arbitrary open subset and which are active in one equation only it is shown that such a controller with dimension given by the largest algebraic multiplicity of the unstable eigenvalues of the linearized system exponentially stabilizes the steady state solution an optimal design methodology for these types of controllers which is based on the finite element approximation of the semilinear parabolic system is introduced and illustrated by numerical simulation examples

feedback stabilization of the cahn hilliard type system for phase separation abstract this article is concerned with the internal feedback stabilization of the phase field system of cahn hilliard type modeling the phase separation in a binary mixture under suitable assumptions on an arbitrarily fixed stationary solution we construct via spectral separation arguments a feedback controller having its support in an arbitrary open subset of the space domain such that the closed loop nonlinear system exponentially reaches the prescribed stationary solution this feedback controller has a finite dimensional structure in the state space of solutions in particular every constant stationary solution is admissible

receive antenna selection for mimo spatial multiplexing theory and algorithms this paper discusses the problem of receive antenna subset selection in multiple input multiple output spatial multiplexing mimo sm systems we develop selection algorithms for maximizing the channel capacity one algorithm in particular allows tractable statistical analysis of performance we leverage this to prove that the capacity of the system through receive antenna selection is statistically lower bounded by the capacity of a set of parallel independent single input multiple output simo channels each with selection diversity this provides the crucial step in proving the next main result the diversity order achievable through antenna selection is the same as that of the full system the result sets up strong motivation for introducing receive selection in mimo sm systems the remainder of the paper discusses selection algorithms for two popular mimo sm systems namely ordered successive interference cancellation with independently encoded layers and minimum mean square error mmse receiver with joint encoding of data streams extensive monte carlo simulations are presented to validate and demonstrate performance

analysis of digital tries with markovian dependency a complete characterization of a digital tree also called a trie is presented from the depth viewpoint in a markovian framework that is under the assumption that symbols in a key are markov dependent the main findings show that asymptotically as the number of keys n tends to infinity the average depth becomes ed sub n approximately 1 h sub 1 log n c and the variance is var d sub n approximately alpha log n c where h sub 1 is the entropy of the markovian dependent alphabet alpha is a parameter of the probabilistic model and c and c are constants the symmetric independent model has alpha 0 hence in this case var d sub n o 1 limiting distribution is also derived for the depth d sub n and in particular it is shown that d sub n tends to the normal distribution in all cases except the symmetric independent model these results extend all previous analyses since most of them have been limited to independent models

antenna selection for unitary space time modulation this correspondence studies receive antenna selection as for multiple antenna systems that employ unitary space time st signals where the channel state information csi is known neither at the transmitter nor at the receiver without csi at the receiver we perform as only at the receiver and the selection is based on a maximum norm criterion i e a subset of receive antennas that have the largest received signal power is chosen using a chernoff bound approach we present theoretical performance analysis based on the pairwise error probability pep and quantify the asymptotic performance at high signal to noise ratio snr by giving the diversity and coding gain expressions we prove that with no csi at the receiver the diversity gain with as is preserved for unitary st codes with full spatial diversity the same as the case with known csi as a concrete example for differential unitary st modulation with m 2 transmit antennas and n 2 receive antennas we have devised new excellent performing parametric codes based on the derived pep bound the new codes which are specifically designed for differential as systems outperform known differential codes when as is employed corroborating simulations validate our analysis and code design

optimal control of semilinear parabolic systems with state constraint abstract the aim of this work is to obtain the existence of optimal solution and maximum principle for optimal control problem with pointwise type state constraint governed by semilinear parabolic systems with certain polynomial like nonlinearity application to optimal control problems of the phase transition system is given

null controllability of some reaction diffusion systems with one control force this work is concerned with the null controllability of semilinear parabolic systems by a single control force acting on a subdomain

on a nonlocal phase field system abstract we study the existence uniqueness and continuous dependence on initial data of the solution to a nonlocal phase field system on a bounded domain the system is a gradient flow for a free energy functional with nonlocal interaction also we study the asymptotic behavior of the solution and show the existence of an absorbing set in some metric space