numerical simulation of unsteady viscous free surface flow abstract a finite element method is presented for the numerical simulation of time dependent incompressible viscous free surface flows the time dependent primitive equations are solved sequentially using explicit time marching procedure the method is based on a velocity correction approach to the time integration of the navier stokes equations in which only the incompressibility condition is treated implicitly a special arbitrary mixed lagrangian eulerian description has been used to avoid the typical problems encountered in a purely lagrangian description the method appears applicable for small computers problems requiring several thousand nodes can be solved on personal computers numerical experiments have been performed that show that this approach is reasonably efficient and robust for a range of complicated highly nonlinear problems

numerical simulation of 3d viscoelastic flows with free surfaces a numerical model is presented for the simulation of viscoelastic flows with complex free surfaces in three space dimensions the mathematical formulation of the model is similar to that of the volume of fluid vof method but the numerical procedures are different a splitting method is used for the time discretization the prediction step consists in solving three advection problems one for the volume fraction of liquid which allows the new liquid domain to be obtained one for the velocity field one for the extra stress the correction step corresponds to solving an oldroyd b fluid flow problem without advection in the new liquid domain two different grids are used for the space discretization the three advection problems are solved on a fixed structured grid made out of small cubic cells using a forward characteristics method the oldroyd b problem without advection is solved using continuous piecewise linear stabilized finite elements on a fixed unstructured mesh of tetrahedrons efficient post processing algorithms enhance the quality of the numerical solution a hierarchical data structure reduces the memory requirements convergence of the numerical method is checked for the pure extensional flow and the filling of a tube numerical results are presented for the stretching of a filament fingering instabilities are obtained when the aspect ratio is large also results pertaining to jet buckling are reported

computations of multi fluid flows abstract full numerical simulations of three dimensional flows of two or more immiscible fluids of different densities and viscosities separated by a sharp interface with finite surface tension are discussed the method used is based on a finite difference approximation of the full navier stokes equations and explicit tracking of the interface between the fluids preliminary simulations of the rayleigh taylor instability and the motion of bubbles are shown

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

shift orthogonal space time block codes in this paper we present a new class of spacetime block code called shift orthogonal space time block codes sostbc which can maintain orthogonality hence symbolwise linear decoding in asynchronous wireless relay networks under both amplify and forward af and decode and forward df relaying schemes the definitions systematic constructions and properties of sostbc are presented we also present some simulation results to illustrate its effectiveness in achieving full asynchronous cooperative diversity

a family of distributed space time trellis codes with asynchronous cooperative diversity in current cooperative communication schemes to achieve cooperative diversity synchronization between terminals is usually assumed which may not be practical since each terminal has its own local oscillator in this paper based on the stack construction proposed by hammons and el gamal we first construct a family of space time trellis codes for bpsk modulation scheme that is characterized to possess the full cooperative diversity order without the synchronization assumption we then generalize this family of the space time trellis codes from bpsk to higher order qam and psk modulation schemes based on the unified construction proposed by lu and kumar some diversity product properties of space time trellis codes are studied and simplified decoding methods are discussed simulation results are given to illustrate the performance of the newly proposed codes

shift full rank matrices and applications in space time trellis codes for relay networks with asynchronous cooperative diversity to achieve full cooperative diversity in a relay network most of the existing space time coding schemes require the synchronization between terminals a family of space time trellis codes that achieve full cooperative diversity order without the assumption of synchronization has been recently proposed the family is based on the stack construction by hammons and el gamal and its generalizations by lu and kumar it has been shown that the construction of such a family is equivalent to the construction of binary matrices that have full row rank no matter how their rows are shifted where a row corresponds to a terminal or transmit antenna and its length corresponds to the memory size of the trellis code on that terminal we call such matrices as shift full rank sfr matrices a family of sfr matrices has been also constructed but the memory sizes of the corresponding space time trellis codes the number of columns of sfr matrices grow exponentially in terms of the number of terminals the number of rows of sfr matrices which may cause a high decoding complexity when the number of terminals is not small in this paper we systematically study and construct sfr matrices of any sizes for any number of terminals furthermore we construct shortest square sfr ssfr matrices that correspond to space time trellis codes with the smallest memory sizes and asynchronous full cooperative diversity we also present some simulation results to illustrate the performances of the space time trellis codes associated with sfr matrices in asynchronous cooperative communications

a unified construction of space time codes with optimal rate diversity tradeoff the problem of constructing space time st block codes over a fixed desired signal constellation is considered in this situation there is a tradeoff between the transmission rate as measured in constellation symbols per channel use and the transmit diversity gain achieved by the code the transmit diversity is a measure of the rate of polynomial decay of pairwise error probability of the code with increase in the signal to noise ratio snr in the setting of a quasi static channel model let n sub t denote the number of transmit antennas and t the block interval for any n sub t spl les t a unified construction of n sub t spl times t st codes is provided here for a class of signal constellations that includes the familiar pulse amplitude pam quadrature amplitude qam and 2 sup k ary phase shift keying psk modulations as special cases the construction is optimal as measured by the rate diversity tradeoff and can achieve any given integer point on the rate diversity tradeoff curve an estimate of the coding gain realized is given other results presented here include i an extension of the optimal unified construction to the multiple fading block case ii a version of the optimal unified construction in which the underlying binary block codes are replaced by trellis codes iii the providing of a linear dispersion form for the underlying binary block codes iv a gray mapped version of the unified construction and v a generalization of construction of the ary case corresponding to constellations of size sup k items ii and iii are aimed at simplifying the decoding of this class of st codes

distribution of sizes of erased loops for loop erased random walks the loop erased random walk lerw is a simpler variant of the well known self avoiding walk saw problem which retains the no self intersection property of saws but is closer to the ordinary random walk problem in this paper we study the distribution of sizes of erased loops for lerws on arbitrary graphs and relate it to the distribution of sizes of loops formed when a bond is added to a random spanning tree on the same graph in the themodynamic limit this distribution has a power law tail and we express the exponent in terms of the fractal dimension of the chemical paths on spanning trees we show also how this relation is modified for deterministic fractals in spite of the fact that the lerw model is somewhat more tractable analytically than the saw problem the number of papers devoted to this problem has remained rather small the model was defined by lawler 1 who called it the loop erased self avoiding walk lesaw this terminology is somewhat inappropriate and

convergence analyses of galerkin least squares methods for symmetric advective diffusive forms of the stokes and incompressible navier stokes equations abstract symmetric advective diffusive forms of the stokes and incompressible navier stokes equations are presented the galerkin least squares method for advective diffusive equations is used for both systems and is related to other stabilized methods previously studied the presentation reveals that the convergence analysis for advective diffusive equations as applied before to a linearized form of the compressible navier stokes equations carries over in a straightforward manner to the stokes problem and to a linearized form of the incompressible navier stokes equations

analytical enumeration of hamiltonian walks on a fractal the connectivity constant omega for hamiltonian walks on dhar s 4 simplex 1978 is found using an exact set of recursion relations the result omega 1 399710 differs from the value of omega for hamiltonian walks on the square lattice as a consequence omega must depend on other lattice characteristics besides the coordination number and the fractal dimension the first correction to the leading order asymptotic behaviour is also obtained

asymptotic behavior of the gyration radius for long range self avoiding walk and long range oriented percolation let 0 and l 2 1 1 and suppose that the 1 step distribution d for random walk on z d decays as d x jx lj d for large jxjsuch that

diversity embedded space time codes rate and diversity impose a fundamental tradeoff in wireless communication high rate space time codes come at a cost of lower reliability diversity and high reliability diversity implies a lower rate however wireless networks need to support applications with very different quality of service qos requirements and it is natural to ask what characteristics should be built into the physical layer link in order to accommodate them in this paper we design high rate space time codes that have a high diversity code embedded within them this allows a form of communication where the high rate code opportunistically takes advantage of good channel realizations while the embedded high diversity code provides guarantees that at least part of the information is received reliably we provide constructions of linear and nonlinear codes for a fixed transmit alphabet constraint the nonlinear constructions are a natural generalization to wireless channels of multilevel codes developed for the additive white gaussian noise awgn channel that are matched to binary partitions of quadrature amplitude modulation qam and phase shift keying psk constellations the importance of set partitioning to code design for the wireless channel is that it provides a mechanism for translating constraints in the binary domain into lower bounds on diversity protection in the complex domain we investigate the systems implications of embedded diversity codes by examining value to unequal error protection rate opportunism and packet delay optimization these applications demonstrate that diversity embedded codes have the potential to outperform traditional single layer codes in moderate signal to noise snr regimes

self repelling walk on the sierpinski gasket we construct a one parameter family of self repelling processes on the sierpinski gasket by taking continuum limits of self repelling walks on the pre sierpinski gaskets we prove that our model interpolates between the brownian motion and the self avoiding process on the sierpinski gasket namely we prove that the process is continuous in the parameter in the sense of convergence in law and that the order of holder continuity of the sample paths is also continuous in the parameter we also establish a law of the iterated logarithm for the self repelling process finally we show that this approach yields a new class of one dimensional self repelling processes

critical exponents of manhattan hamiltonian walks in two dimensions from potts and o n models we consider a set of hamiltonian circuits filling a manhattan lattice i e a square lattice with alternating traffic regulation we show that the generating function with fugacityz of this set is identical to the critical partition function of aq state potts model on an unoriented square lattice withq1 2 z the set of critical exponents governing correlations of hamiltonian circuits is derived using a coulomb gas technique these exponents are also found to be those of an o n vector model in the low temperature phase withn q1 2 z the critical exponents in the limitz 0 are then those of spanning trees q 0 and of dense polymers n 0 t tc corresponding to a conformal theory with central chargec 2 this shows that the manhattan orientation and the hamiltonian constraint of filling all the lattice are irrelevant for the infrared critical properties of hamiltonian walks

a unified framework for tree search decoding rediscovering the sequential decoder we consider receiver design for coded transmission over linear gaussian channels we restrict ourselves to the class of lattice codes and formulate the joint detection and decoding problem as a closest lattice point search clps here a tree search framework for solving the clps is adopted in our framework the clps algorithm is decomposed into the preprocessing and tree search stages the role of the preprocessing stage is to expose the tree structure in a form matched to the search stage we argue that the forward and feedback matrix filters of the minimum mean square error decision feedback equalizer mmse dfe are instrumental for solving the joint detection and decoding problem in a single search stage it is further shown that mmse dfe filtering allows for solving underdetermined linear systems and using lattice reduction methods to diminish complexity at the expense of a marginal performance loss for the search stage we present a generic method based on the branch and bound bb algorithm and show that it encompasses all existing sphere decoders as special cases the proposed generic algorithm further allows for an interesting classification of tree search decoders sheds more light on the structural properties of all known sphere decoders and inspires the design of more efficient decoders in particular an efficient decoding algorithm that resembles the well known fano sequential decoder is identified the excellent performance complexity tradeoff achieved by the proposed mmse dfe fano decoder is established via simulation results and analytical arguments in several multiple input multiple output mimo and intersymbol interference isi scenarios

a two grids projection algorithm for obstacle problems in order to emphasize the possible relation between discontinuous and continuous approximations on different meshes a two grids method for the resolution of parabolic variational inequality problems is presented the numerical methodology combines a time splitting algorithm to decouple a diffusion phenomenon from an obstacle problem the diffusion problem is solved by using finite differences while piecewise linear finite element techniques are used together with a newton method for the obstacle problem projections are used to interpolate the solution from one grid to the other numerical experiments show that the resulting method has good accuracy properties

a simple orthogonal space time coding scheme for asynchronous cooperative systems for frequency selective fading channels in this paper we propose a simple orthogonal space time transmission scheme for asynchronous cooperative systems in the proposed scheme ofdm is implemented at the source node some very simple operations namely time reversion and complex conjugation are implemented at the relay nodes and a two step of cyclic prefix cp removal is performed at the destination the cp at the source node is used for combating the frequency selective fading channels and the timing errors in this scheme the received signals at the destination node have the orthogonal code structure on each subcarrier and thus it has the fast symbol wise ml decoding and can achieve full spatial diversity when snr is large without the requirement of symbol level synchronization it should be emphasized that since no add remove cp or ifft fft operation is needed at the relay nodes the relay nodes do not have to know any information about the channels and the timing errors and the complexity of the relay nodes is very low

the ice model and the eight vertex model on the two dimensional sierpinski gasket abstract we present the numbers of ice model configurations with boltzmann factors equal to one i n on the two dimensional sierpinski gasket s g n at stage n the upper and lower bounds for the entropy per site defined as lim v ln i n v where v is the number of vertices on s g n are derived in terms of the results at a certain stage as the difference between these bounds converges quickly to zero as the calculated stage increases the numerical value of the entropy can be evaluated with more than a hundred significant figures accuracy the corresponding result of the ice model on the generalized two dimensional sierpinski gasket s g b n with b 3 is also obtained and the general upper and lower bounds for the entropy per site for arbitrary b are conjectured we also consider the number of eight vertex model configurations on s g n and the number of generalized vertex models e b n on s g b n and obtain exactly e b n 2 2 b 1 b b 1 2 n b 4 b 2 it follows that the entropy per site is lim v ln e b n v 2 b 1 b 4 ln 2

the art of signaling fifty years of coding theory in 1948 shannon developed fundamental limits on the efficiency of communication over noisy channels the coding theorem asserts that there are block codes with code rates arbitrarily close to channel capacity and probabilities of error arbitrarily close to zero fifty years later codes for the gaussian channel have been discovered that come close to these fundamental limits there is now a substantial algebraic theory of error correcting codes with as many connections to mathematics as to engineering practice and the last 20 years have seen the construction of algebraic geometry codes that can be encoded and decoded in polynomial time and that beat the gilbert varshamov bound given the size of coding theory as a subject this review is of necessity a personal perspective and the focus is reliable communication and not source coding or cryptography the emphasis is on connecting coding theories for hamming and euclidean space and on future challenges specifically in data networking wireless communication and quantum information theory

rate diversity tradeoff of space time codes with fixed alphabet and optimal constructions for psk modulation we show that for any q spl times m space time code s having a fixed finite signal constellation there is a tradeoff between the transmission rate r and the transmit diversity gain spl nu achieved by the code the tradeoff is characterized by r spl les q spl nu 1 where q is the number of transmit antennas when either binary phase shift keying bpsk or quaternary phase shift keying qpsk is used as the signal constellation a systematic construction is presented to achieve the maximum possible rate for every possible value of transmit diversity gain

the exponent for the mean square displacement of self avoiding random walk on the sierpinski gasket the authors rigorously prove that the exponent for the mean square displacement of self avoiding random walk on the sierpinski gasket is log 2 log left frac 7 sqrt 5 2 right 0 79862 0 5 log 2 log 5

achieving full diversity and fast ml decoding via simple analog network coding for asynchronous two way relay networks in this paper we propose a simple analog network coding anc scheme for asynchronous two way relay networks where two sources exchange information through the relay nodes in our proposed scheme we consider a wireless scenario with frequency selective fading channels orthogonal frequency division multiplexing ofdm is implemented at the two sources and then the ofdm blocks are transmitted to the relay nodes in the first time slot in the second time slot at the relay nodes the anc that has a few simple operations are implemented on the received mixed signals and then the processed signals are broadcasted to the two sources to finish the information exchange in this scheme at each source when recovering the designed information transmitted from another source the received signals have the orthogonal space time block code ostbc structure or the quasi orthogonal space time block code qostbc structure on each subcarrier by a proper power allocation the two sources can achieve full spatial diversity and fast ml decoding without the requirement of symbol level synchronization by the repetition across the subcarriers multi path diversity available in frequency selective fading channels can be also exploited moreover the proposed anc scheme is also valid for multi way relay networks where multiple sources exchange information

construction of new delay tolerant space time codes perfect space time codes stc are optimal codes in their original construction for multiple input multiple output mimo systems based on cyclic division algebras cda they are full rate full diversity codes have non vanishing determinants nvd and hence achieve diversity multiplexing tradeoff dmt in addition these codes have led to optimal distributed space time codes when applied in cooperative networks under the assumption of perfect synchronization between relays however they lose their diversity when delays are introduced and thus are not delay tolerant in this paper using the cyclic division algebras of perfect codes we construct new codes that maintain the same properties as perfect codes in the synchronous case moreover these codes preserve their full diversity in asynchronous transmission

self avoiding paths on the pre sierpinski gasket we study a statistical mechanics of self avoiding paths on the pre sierpinski gasket we first show the existence of the thermodynamic limit of the appropriately scaled free energy then we show that there are two domains in the weight parameters i e two phases between which the scaling differs i e there is a certain kind of phase transition in our model and we find the critical exponents of the free energy at the phase transition point we also show the convergence of the distribution of the scaled length of the paths at thermodynamic limit

hamiltonian walks on the sierpinski gasket we derive the exact number of hamiltonian walks h n on the two dimensional sierpinski gasket sg n at stage n whose asymptotic behavior is given by 3 23 3n 13 52 72 172212 35 13 16 n we also obtain the number of hamiltonian walks with one end at a specific outmost vertex of sg n with asymptotic behavior 3 23 3n 13 7 1724 33 4n the distribution of hamiltonian walks on sg n with one end at a specific outmost vertex and the other at an arbitrary vertex of sg n is investigated we rigorously prove that the exponent for the mean l displacement between the two end vertices of such hamiltonian walks on sg n is lln 2 ln 3 for l 0

scaling of hamiltonian walks on fractal lattices we investigate asymptotical behavior of numbers of long hamiltonian walks hws i e self avoiding random walks that visit every site of a lattice on various fractal lattices by applying an exact recursive technique we obtain scaling forms for open hws on three simplex lattice sierpinski gasket and their generalizations given mandelbrot gm modified sierpinski gasket msg and n simplex fractal families for gm msg and n simplex lattices with odd values of n the number of open hws z n for the lattice with n 1 sites varies as omega n n gamma we explicitly calculate the exponent gamma for several members of gm and msg families as well as for n simplices with n 3 5 and 7 for n simplex fractals with even n we find different scaling form z n approximately omega n mu n1 d f where d f is the fractal dimension of the lattice which also differs from the formula expected for homogeneous lattices we discuss possible implications of our results on studies of real compact polymers

compact self avoiding circuits on two dimensional lattices close packed self avoiding walks and circuits as models for condensed polymer phases are studied on the square planar and honeycomb lattices exact solutions for strips from these lattices are obtained via transfer matrix methods extrapolations are made for the leading asymptotic terms in the count of compact conformations on the square planar lattice the leading asymptotic term for each lattice is bounded from below and it is noted that boundary effects can be important

constellation design for trellis coded unitary space time modulation systems we consider the problem of creating signal constellations for trellis coded unitary space time communication links where neither the transmitter nor the receiver knows the fading gains of the channel our study includes constellation design techniques for trellis coded schemes with and without parallel paths which allows us to find a tradeoff between low complexity and high performance we present a new formulation of the constellation design problem for trellis coded unitary space time modulation tcustm schemes the two key differences in our approach against those of other authors are that we not only combine the constellation design and mapping by set partitioning into one step but we also use directly the chernoff bound of the pairwise error probability as a design metric by novelly employing a theorem for the clarke subdifferential of the sum of the k largest singular values of the unitary matrix we also present a numerical optimization procedure for finding signal constellations resulting in high performance communications systems to demonstrate the advantages of our new design method we report the best constellations found for tcustm systems simulation results show that these constellations achieve a 1 db coding gain at a bit error rate of 10 4 against usually used constellations

regular article numerical simulation of free surface flows a numerical model is presented for the simulation of complex fluid flows with free surfaces the unknowns are the velocity and pressure fields in the liquid region together with a function defining the volume fraction of liquid although the mathematical formulation of the model is similar to the volume of fluid vof method the numerical schemes used to solve the problem are different a splitting method is used for the time discretization at each time step two advection problems and a generalized stokes problem are to be solved two different grids are used for the space discretization the two advection problems are solved on a fixed structured grid made out of small rectangular cells using a forward characteristic method the generalized stokes problem is solved using a finite element method on a fixed unstructured mesh numerical results are presented for several test cases the filling of an s shaped channel the filling of a disk with core the broken dam in a confined domain

multigroup ml decodable collocated and distributed space time block codes in this paper collocated and distributed space time block codes dstbcs which admit multigroup maximum likelihood ml decoding are studied first the collocated case is considered and the problem of constructing space time block codes stbcs which optimally tradeoff rate and ml decoding complexity is posed recently sufficient conditions for multigroup ml decodability have been provided in the literature and codes meeting these sufficient conditions were called clifford unitary weight cuw stbcs an algebraic framework based on extended clifford algebras ecas is proposed to study cuw stbcs and using this framework the optimal tradeoff between rate and ml decoding complexity of cuw stbcs is obtained for few specific cases code constructions meeting this tradeoff optimally are also provided the paper then focuses on multigroup ml decodable dstbcs for application in synchronous wireless relay networks and three constructions of four group ml decodable dstbcs are provided finally the orthogonal frequency division multiplexing ofdm based alamouti space time coded scheme proposed by li xia for a 2 relay asynchronous relay network is extended to a more general transmission scheme that can achieve full asynchronous cooperative diversity for arbitrary number of relays it is then shown how differential encoding at the source can be combined with the proposed transmission scheme to arrive at a new transmission scheme that can achieve full cooperative diversity in asynchronous wireless relay networks with no channel information and also no timing error knowledge at the destination node four group decodable dstbcs applicable in the proposed ofdm based transmission scheme are also given

delay tolerant distributed tast codes for cooperative diversity in cooperative networks using a decode and forward strategy the multiple relays effectively transmit a distributed space time code the performance of which can be severely degraded when timing synchronization among the relays is not assured e g in cases of broadcast to dispersed recipients or in networks without a shared high quality timing reference recent work by xia and hammons have investigated the design of distributed space time codes that are delay tolerant in the sense that full spatial diversity is achieved regardless of timing offsets in general the previously known space time block codes belonging to the class of c linear codes however which are important because they achieve full spatial diversity and admit near optimal lattice decoding algorithms are not delay tolerant in this paper we present a new family of such codes that are fully delay tolerant the new codes generalize the threaded algebraic space time tast codes introduced by el gamal and damen like their brethren the new distributed tast codes are effective and flexible enabling use of different signaling constellations transmission rates numbers of transmit and receive antennas and decoders of varying levels of complexity

numerical simulation of free surface incompressible liquid flows surrounded by compressible gas a numerical model for the three dimensional simulation of liquid gas flows with free surfaces is presented the incompressible navier stokes equations are assumed to hold in the liquid domain in the gas domain the velocity is disregarded the pressure is supposed to be constant in each connected component of the gas domain and follows the ideal gas law the gas pressure is imposed as a normal force on the liquid gas interface an implicit splitting scheme is used to decouple the physical phenomena given the gas pressure on the interface the method described in j comput phys 155 1999 439 int j numer meth fluids 42 7 2003 697 is used to track the liquid domain and to compute the velocity and pressure fields in the liquid then the connected components of the gas domain are found using an original numbering algorithm finally the gas pressure is updated from the ideal gas law in each connected component of gas the implementation is validated in the frame of mould filling numerical results in two and three space dimensions show that the effect of pressure in the bubbles of gas trapped by the liquid cannot be neglected

analysis of a one dimensional free boundary flow problem a one dimensional free surface problem is considered it consists in burgers equation with an additional diffusion term on a moving interval the well posedness of the problem is investigated and existence and uniqueness results are obtained locally in time a semi discretization in space with a piecewise linear finite element method is considered a priori and a posteriori error estimates are given for the semi discretization in space a time splitting scheme allows to obtain numerical results in agreement with the theoretical investigations

multilevel codes and multistage decoding h imai and s hirakawa have proposed 1977 a multilevel coding method based on binary block codes that admits a staged decoding procedure the author extends the coding method to coset codes and shows how to calculate minimum squared distance and path multiplicity in terms of the norms and multiplicities of the different cosets the multilevel structure allows the redundancy in the coset selection procedure to be allocated efficiently among the different levels it also allows the use of suboptimal multistage decoding procedures that have performance complexity advantages over maximum likelihood decoding

pragmatic space time trellis codes gtf based design for block fading channels the pragmatic approach for the construction of space time codes over block fading channels leads to low complexity encoders decoders making them suitable for various applications including cooperative communications we propose a design methodology for pragmatic space time codes which is based on an extension of the concept of generalized transfer function our search algorithm provides code generators for arbitrary number of states antennas and fading rates numerical results show that the performance of the pragmatic space time codes obtained by our design methodology is generally better than that of previously known space time trellis codes in block fading channels

a space time galerkin least squares finite element formulation of the navier stokes equations for moving domain problems a space time galerkin least squares finite element formulation of the navier stokes equations is presented for the analysis of free surface flows moving spatial configurations and deforming fluid structure interfaces the variational equation is based on the time discontinuous galerkin method employing the physical entropy variables the space time elements are oriented in time to accommodate the spatial deformations if the elements are oriented along the particle paths the formulation is lagrangian and if they are fixed in time it is eulerian consequently this formulation is analogous to the arbitrary lagrangian eulerian ale technique a novel mesh rezoning strategy is presented to orient the elements in time and adapt the fluid mesh to the changing spatial configuration numerical results are presented to show the performance of the method

diagonal block space time code design for diversity and coding advantage over flat fading channels the potential promised by multiple transmit antennas has raised considerable interest in space time coding for wireless communications in this paper we propose a systematic approach for designing space time trellis codes over flat fading channels with full antenna diversity and good coding advantage it is suitable for an arbitrary number of transmit antennas with arbitrary signal constellations the key to this approach is to separate the traditional space time trellis code design into two parts it first encodes the information symbols using a one dimensional m 1 nonbinary block code with m being the number of transmit antennas and then transmits the coded symbols diagonally across the space time grid we show that regardless of channel time selectivity this new class of space time codes always achieves a transmit diversity of order m with a minimum number of trellis states and a coding advantage equal to the minimum product distance of the employed block code traditional delay diversity codes can be viewed as a special case of this coding scheme in which the repetition block code is employed to maximize the coding advantage we introduce an optimal construction of the nonbinary block code for a given modulation scheme in particular an efficient suboptimal solution for multilevel phase shift keying psk modulation is proposed some code examples with 2 6 bits s hz and two to six transmit antennas are provided and they demonstrate excellent performance via computer simulations although it is proposed for flat fading channels this coding scheme can be easily extended to frequency selective fading channels

hamiltonian walks on sierpinski and n simplex fractals we study hamiltonian walks hws on sierpinski and n simplex fractals via numerical analysis of exact recursion relations for the number of hws we calculate the connectivity constant and find the asymptotic behaviour of the number of hws depending on whether or not the polymer collapse transition is possible on a studied lattice different scaling relations for the number of hws are obtained these relations are in general different from the well known form characteristic of homogeneous lattices which has thus far been assumed to also hold for fractal lattices

on the theory of space time codes for psk modulation the design of space time codes to achieve full spatial diversity over fading channels has largely been addressed by handcrafting example codes using computer search methods and only for small numbers of antennas the lack of more general designs is in part due to the fact that the diversity advantage of a code is the minimum rank among the complex baseband differences between modulated codewords which is difficult to relate to traditional code designs over finite fields and rings we present general binary design criteria for psk modulated space time codes for linear bpsk qpsk codes the rank of binary projections of the unmodulated codewords as binary matrices over the binary field is a sufficient design criterion full binary rank guarantees full spatial diversity this criterion accounts for much of what is currently known about psk modulated space time codes we develop new fundamental code constructions for both quasi static and time varying channels these are perhaps the first general constructions other than delay diversity schemes that guarantee full spatial diversity for an arbitrary number of transmit antennas

self avoiding walk in five or more dimensions i the critical behaviour we use the lace expansion to study the standard self avoiding walk in thed dimensional hypercubic lattice ford 5 we prove that the numbercn ofn step self avoiding walks satisfiescn a n where is the connective constant i e 1 and that the mean square displacement is asymptotically linear in the number of steps i e v 1 2 a bound is obtained forcn x the number ofn step self avoiding walks ending atx the correlation length is shown to diverge asymptotically like z 1 2 the critical two point function is shown to decay at least as fast as x 2 and its fourier transform is shown to be asymptotic to a multiple ofk 2 ask 0 i e 0 we also prove that the scaling limit is gaussian in the sense of convergence in distribution to brownian motion the infinite self avoiding walk is constructed in this paper we prove these results assuming convergence of the lace expansion the convergence of the lace expansion is proved in a companion paper

on the design and performance of algebraic space time codes for bpsk and qpsk modulation the authors previously developed an algebraic approach to space time code design that unifies most of the known results on trellis space time codes and opens the door for more sophisticated space time code constructions we present algebraic constructions for trellis and block space time codes for bpsk and qpsk modulated systems the new designs benefit from the algebraic approach and are general for arbitrary number of transmit antennas in quasistatic fading channels we also provide simulation results comparing the frame error rate performance of various constructions these simulation results establish the performance advantage achieved by algebraic space time codes compared to previously known codes in various scenarios