the duality relation between glauber dynamics and the diffusion annihilation model as a similarity transformation in this paper we address the relationship between zero temperature glauber dynamics and the diffusion annihilation problem in the free fermion case we show that the well known duality transformation between the two problems can be formulated as a similarity transformation if one uses appropriate toroidal boundary conditions this allows us to establish and clarify the precise nature of the relationship between the two models in this way we obtain a one to one correspondence between observables and initial states in the two problems a random initial state in glauber dynamics is related to a short range correlated state in the annihilation problem in particular the long time behaviour of the density in this state is seen to depend on the initial conditions hence we show that the presence of correlations in the initial state determine the dependence of the long time behaviour of the density on the initial conditions even if such correlations are short ranged we also apply a field theoretical method to the calculation of multi time correlation functions in this initial state

exact solution of a reaction diffusion process with three site interactions the one dimensional reaction diffusion process aa a and a a aaa is exactly solvable through the empty interval method if the diffusion rate equals the coagulation rate independently of the particle production rate the model is always in the universality class of diffusion annihilation this allows us to check analytically the universality of finite size scaling in a non equilibrium critical point

a progressive simultaneous iteration solution for dynamic element vibration analysis development and employment of dynamic elements can result in substantial gain in solution convergence for vibration analysis when compared with the usual finite element discretization efficient solution of the associated quadratic matrix eigenproblem is crucial in achieving a superior and relatively economical solution this paper first describes a novel eigensolution of the quadratic matrix equation by a progressive simultaneous iteration method free vibration analysis results of a rectangular prestressed membrane are next presented in detail that provides an assessment of relative solution convergence and computing expenses of the two idealization procedures

improving the speed of parallel decimal multiplication hardware support for decimal computer arithmetic is regaining popularity one reason is the recent growth of decimal computations in commercial scientific financial and internet based computer applications newly commercialized decimal arithmetic hardware units use radix 10 sequential multipliers that are rather slow for multiplication intensive applications therefore the future relevant processors are likely to host fast parallel decimal multiplication circuits the corresponding hardware algorithms are normally composed of three steps partial product generation ppg partial product reduction ppr and final carry propagating addition the state of the art is represented by two recent full solutions with alternative designs for all the three aforementioned steps in addition ppr by itself has been the focus of other recent studies in this paper we examine both of the full solutions and the impact of a ppr only design on the appropriate one in order to improve the speed of parallel decimal multiplication we present a new ppg method fine tune the ppr method of one of the full solutions and the final addition scheme of the other thus assembling a new full solution logical effort analysis and 0 13 mum synthesis show at least 13 percent speed advantage but at a cost of at most 36 percent additional area consumption

static and dynamic phase transitions in multidimensional voting models on continua a voting model or a generalization of the glauber model at zero temperature on a multidimensional lattice is defined as a system composed of a lattice each site of which is either empty or occupied by a single particle the reactions of the system are such that two adjacent sites one empty the other occupied may evolve to a state where both of these sites are either empty or occupied the continuum version of this model in a d dimensional region with a boundary is studied and two general behaviors of such systems are investigated the stationary behavior of the system and the dominant way of relaxation of the system toward its stationary state based on the first behavior a static phase transition discontinuous changes in the stationary profiles of the system is studied based on the second behavior a dynamical phase transition discontinuous changes in the relaxation times of the system is studied it is shown that the static phase transition is induced by the bulk reactions only while the dynamical phase transition is a result of both bulk reactions and boundary conditions

structural vibration analysis by a progressive simultaneous iteration method this paper provides details of a newly developed structural eigenproblem solution technique that effects simultaneous convergence of a set of desired roots and associated vectors in an accurate and efficient fashion the procedure is based on a progressive simultaneous iteration method that enables effective computation of either the first few or a specified number of intermediate roots and associated vectors without having to compute any other numerical results pertaining to some practical problems are also presented that testify to the superior convergence characteristics of the present procedure when compared with other existing ones

lanczos algorithm for the quadratic eigenvalue problem in engineering applications abstract a new approach of employing the lanczos two sided recursion to solve the quadratic eigenvalue problem is presented the methodology employed retains the n order quadratic problems as posed without the need to use the method of matrix augmentation traditionally used to cast the problem as a linear eigenvalue problem of order 2n pursuing the concept of finding a characteristic matrix to yield an eigenvalue square matrix the lanczos recursion has been devised to solve the quadratic eigenvalue problem appropriate proofs showing the lanczos biorthogonal transformation are included the example problems presented validate the algorithm and show the effectiveness of the method for large quadratic eigenproblems

area efficient and fast combined binary decimal floating point fused multiply add unit in this work we present a new 64 bit floating point fused multiply add fma unit that can perform both binary and decimal addition multiplication and fused multiply add operations the presented fma has 6 percent less delay than the fastest stand alone decimal unit and 23 percent less area than both binary and decimal units together these results were achieved by the use of 1 column by column reduction to reduce the partial products in the multiplier tree 2 a new leading zeros detector that produces its output in base 3 to simplify the normalization shifting in the binary datapath 3 the use of a redundant adder to perform the final addition 4 using a new rounding while redundant technique to hide the rounding delay and remove it from the critical path and 5 using a new simple conversion technique from redundant to binary decimal

improved design of high performance parallel decimal multipliers the new generation of high performance decimal floating point units dfus is demanding efficient implementations of parallel decimal multipliers in this paper we describe the architectures of two parallel decimal multipliers the parallel generation of partial products is performed using signed digit radix 10 or radix 5 recodings of the multiplier and a simplified set of multiplicand multiples the reduction of partial products is implemented in a tree structure based on a decimal multioperand carry save addition algorithm that uses unconventional non bcd decimal coded number systems we further detail these techniques and present the new improvements to reduce the latency of the previous designs which include optimized digit recoders for the generation of 2n tuples and 5 tuples decimal carry save adders csas combining different decimal coded operands and carry free adders implemented by special designed bit counters moreover we detail a design methodology that combines all these techniques to obtain efficient reduction trees with different area and delay trade offs for any number of partial products generated evaluation results for 16 digit operands show that the proposed architectures have interesting area delay figures compared to conventional booth radix 4 and radix 8 parallel binary multipliers and outperform the figures of previous alternatives for decimal multiplication

high speed multioperand decimal adders there is increasing interest in hardware support for decimal arithmetic as a result of recent growth in commercial financial and internet based applications consequently new specifications for decimal floating point arithmetic have been added to the draft revision of the ieee 754 standard for floating point arithmetic this paper introduces and analyzes three techniques for performing fast decimal addition on multiple binary coded decimal bcd operands two of the techniques speculate bcd correction values and correct intermediate results while adding the input operands the first speculates over one addition the second speculates over two additions the third technique uses a binary carry save adder tree and produces a binary sum combinational logic is then used to correct the sum and determine the carry into the next more significant digit multioperand adder designs are constructed and synthesized for four to 16 input operands analyses are performed on the synthesis results and the merits of each technique are discussed finally these techniques are compared to several previous techniques for high speed decimal addition

a lanczos based technique for exact vibration analysis of skeletal structures this paper presents and discusses a lanczos based eigensolution technique for evaluating the natural frequencies and modes from frequency dependent eigenproblems in structural dynamics the new solution technique is used in conjunction with a mixed finite element modelling procedure which utilizes both the polynomial and frequency dependent displacement fields in formulating the system matrices the method is well suited to the solution of large scale problems the new solution methodology presented here is based on the ability to evaluate a specific set of parameterized non linear eigenvalue curves at given values of the parameter through an implicitly restarted lanczos technique numerical examples illustrate that the implicitly restarted lanczos method with secant interpolation accurately evaluates the exact natural frequencies and modes of the non linear eigenproblem and verifies that the new eigensolution technique coupled with the mixed finite element modelling procedure is more accurate than the conventional finite element models in addition the eigenvalue technique presented here is shown to be far more computationally efficient on large scale problems than the determinant search techniques traditionally employed for solving exact vibration problems

renormalization group approach to simple reaction diffusion phenomena a field theoretical model describing simple one species reaction diffusion systems a a ensuremath rightarrow o inert or a a ensuremath rightarrow a with an external source is analyzed from a renormalization group point of view it is shown that when the dimension of the system is larger than the upper critical dimension mathit d mathit u 2 the behavior of the system is governed by a trivial fixed point dominated by diffusion below the upper critical dimension a line of fixed points governs the behavior reaction and diffusion processes play an equally important role resulting in a so called anomalous kinetic behavior this approach confirms previous scaling arguments possible generalizations to more complicated models are discussed

decimal floating point multiplication decimal multiplication is important in many commercial applications including financial analysis banking tax calculation currency conversion insurance and accounting this paper presents the design of two decimal floating point multipliers one whose partial product accumulation strategy employs decimal carry save addition and one that employs binary carry save addition the multiplier based on decimal carry save addition favors a nonpipelined iterative implementation the multiplier utilizing binary carry save addition allows for an efficient pipelined implementation when latency and throughput are considered more important than area both designs comply with specifications for decimal multiplication given in the ieee 754 standard for floating point arithmetic ieee 754 2008 the multipliers extend previously published decimal fixed point multipliers by adding several features including exponent generation sticky bit generation shifting of the intermediate product rounding and exception detection and handling novel features of the multipliers include support for decimal floating point numbers on the fly generation of the sticky bit in the iterative design early estimation of the shift amount and efficient decimal rounding iterative and parallel decimal fixed point and floating point multipliers are compared in terms of their area delay latency and throughput based on verified verilog register transfer level models

ageing in one dimensional coagulation diffusion processes and the fredrickson andersen model we analyse the ageing dynamics of the one dimensional fredrickson andersen fa model in the nonequilibrium regime following a low temperature quench relaxation then effectively proceeds via diffusion limited pair coagulation dlpc of mobility excitations by employing a familiar stochastic similarity transformation we map exact results from the free fermion case of diffusion limited pair annihilation to dlpc crucially we are able to adapt the mapping technique to averages involving multiple time quantities this relies on knowledge of the explicit form of the evolution operators involved exact results are obtained for two time correlation and response functions in the free fermion dlpc process the corresponding long time scaling forms apply to a wider class of dlpc processes including the fa model we are thus able to exactly characterize the violations of the fluctuation dissipation theorem fdt in the ageing regime of the fa model we find nontrivial scaling forms for the fluctuation dissipation ratio fdr x x tw t but with a negative asymptotic value x 3 6 16 3 307 while this prevents a thermodynamic interpretation in terms of an effective temperature it is a direct consequence of probing fdt with observables that couple to activated dynamics the existence of negative fdrs should therefore be a widespread feature in non mean field systems

monte carlo studies on three species two particle diffusion limited reactions abstract we studied two models of three species two particle diffusion limited reactions with and without a drift model a involves annihilations a b 0 b c 0 and c a 0 with hard core interactions between like species and assumes equal initial densities of the species the density decays according to a power law c t t the critical exponent was estimated as 0 353 6 without the drift and 0 390 4 with the maximum drift model b is a coagulation model as a b c b c a and c a b in this model we observed the critical exponent 1 2 regardless of the drift we argue that model b belongs to the same universality class as single species annihilation or coagulation diffusion limited reactions we also studied the average distance of the nearest neighbor species the average domain size and the average number of the species pairs

multioperand parallel decimal adder a mixed binary and bcd approach decimal arithmetic has been revived in recent years due to the large amount of data in commercial applications we consider the problem of multioperand parallel decimal addition with an approach that uses binary arithmetic suggested by the adoption of binary coded decimal bcd numbers this involves corrections in order to obtain the bcd result or a binary to decimal bd conversion we adopt the latter approach which is particularly efficient for a large number of addends conversion requires a relatively small area and can afford fast operation the bd conversion moreover allows an easy alignment of the sums of adjacent columns we treat the design of bcd digit adders using fast carry free adders and the conversion problem through a known parallel scheme using elementary conversion cells spreadsheets have been developed for adding several bcd digits and for simulating the bd conversion as a design tool

high speed parallel decimal multiplication with redundant internal encodings the decimal multiplication is one of the most important decimal arithmetic operations which have a growing demand in the area of commercial financial and scientific computing in this paper we propose a parallel decimal multiplication algorithm with three components which are a partial product generation a partial product reduction and a final digit set conversion first a redundant number system is applied to recode not only the multiplier but also multiples of the multiplicand in signed digit sd numbers furthermore we present a multioperand sd addition algorithm to reduce the partial product array finally a digit set conversion algorithm with a hybrid prefix network to decrease the number of the logic gates on the critical path is discussed an analysis of the timing delay and an hdl model synthesized under 90 nm technology show that by considering the tradeoff of designs among three components the overall delay of the proposed 16 16 digit multiplier takes about 11 percent less timing delay with 2 percent less area compared to the current fastest design

fast diffusion mean field theory for k body reactions in one dimension the authors derive an improved mean field approximation for k body annihilation reactions ka to inert for hard core diffusing particles on a line annihilating in groups of k neighbours with probability 0 q or 1 the hopping and annihilation processes are correlated to mimic chemical reactions their new mean field theory accounts for hard core particle properties and has a larger region of applicability than the standard chemical rate equation especially for large k values criteria for validity of the mean field theory and its use in phenomenological data fits are derived numerical tests are reported for k 3 4 5 6

development of a block lanczos algorithm for free vibration analysis of spinning structures this paper is concerned with the development of an efficient eigenproblem solution algorithm and an associated computer program for the economical solution of the free vibration problem of complex practical spinning structural systems thus a detailed description of a newly developed block lanczos procedure is presented in this paper that employs only real numbers in all relevant computations and also fully exploits sparsity of associated matrices the procedure is capable of computing multiple roots and proves to be most efficient compared to other existing similar techniques

on the free vibration analysis of spinning structures by using discrete or distributed mass models abstract the analysis of the natural frequencies and modes of vibration of a spinning structure is in general complicated by the presence of gyroscopic or coriolis forces leading to a complex hermitian dynamic stiffness or impedance matrix it is shown that if the analysis is performed by using a discrete model with n degrees of freedom the leading principal minors of the n th order dynamic stiffness matrix exhibit a type of sturm sequence property this leads to a theorem which can be used for the systematic calculation of the natural frequencies of either a discrete system which is assembled from sub structures or an assembly of distributed mass members in both of these cases the order n of the matrix is less than the number of degrees of freedom and its determinant possesses poles as well as zeros the theorem is identical with a corresponding one for non spinning structures previously derived by the authors the application of the theorem to a spinning two dimensional frame with distributed mass members is discussed in some detail

on the relation between one species diffusion limited coalescence and annihilation in one dimension the close similarity between the hierarchies of multiple point correlation functions for the diffusion limited coalescence and annihilation processes has caused some recent confusion raising doubts as to whether such hierarchies uniquely determine an infinite particle system we elucidate the precise relations between the two processes arriving at the conclusion that the hierarchy of correlation functions does provide a complete representation of a particle system on the line we also introduce a new hierarchy of probability density functions for finding particles at specified locations and none in between this hierarchy is computable for coalescence through the method of empty intervals and is naturally suited for questions concerning the ordering of particles on the line

a subspace forward iteration method for solving the quadratic eigenproblem associated with the fde formulation this paper presents the development of an efficient and numerically stable algorithm for accurately computing the eigensolutions of the quadratic real symmetric eigenproblem arising in the finite dynamic element fde formulation closely related to the subspace forward iteration method the proposed scheme is well suited to extracting the lowest natural frequencies and associated mode shapes of large practical eigenproblems takes full advantage of the banded configuration of the stiffness inertia and dynamic correction matrices involved in the eigenproblem and ensures a monotonic convergence from above to the required eigenpairs a shifting technique for convergence acceleration and an eigenpair verification scheme are also presented numerical examples are shown demonstrating the excellent performance of the solution procedure

free vibration behavior of spinning shear deformable plates composedof composite materials the theory accounts for geometric nonlinearity in the form of the von karman strains and the effects of rotatory inertia the plate is permitted to have an arbitrary orientation offset from the axis of rotation a finite element model is developed the mode shapes as functions of angular velocity pitch angle and sweep angle are presented

a solution of the eigenproblem for undamped gyroscopic systems with the lanczos algorithm this paper presents an efficient numerical solution of the quadratic eigenproblem arising in the analysis of gyroscopic systems such problems are known to reduce to a generalized linear eigenproblem defined by two real non singular matrices one symmetric and one skew symmetric for this class of problems the general lanczos algorithm for unsymmetric matrices is shown to simplify considerably and yields an efficient solution of the problem full advantage can be taken of the sparsity of the matrices and of the specific nature of gyroscopic systems numerical examples are presented which demonstrate the efficiency and accuracy of the solution procedure

exact results for diffusion limited reactions with synchronous dynamics a method is introduced allowing one to solve exactly the reactions a a ensuremath rightarrow inert and a a ensuremath rightarrow a on the one dimensional lattice with synchronous diffusional dynamics simultaneous hopping of all particles exact connections are found relating densities and certain correlation properties of these two reactions at all times asymptotic behavior at large times as well as scaling form describing the regime of low initial density are derived explicitly

finite size scaling studies of one dimensional reaction diffusion systems part i analytical results we consider two single species reaction diffusion models on one dimensional lattices of lengthl the coagulation decoagulation model and the annihilation model for the coagulation model the system of differential equations describing the time evolution of the empty interval probabilities is derived for periodic as well as for open boundary conditions this system of differential equations grows quadratically withl in the latter case the equations are solved analytically and exact expressions for the concentration are derived we investigate the finite size behavior of the concentration and calculate the corresponding scaling functions and the leading corrections for both types of boundary conditions we show that the scaling functions are independent of the initial conditions but do depend on the boundary conditions a similarity transformation between the two models is derived and used to connect the corresponding scaling functions

model of cluster growth and phase separation exact results in one dimension we present exact results for a lattice model of cluster growth in one dimension the growth mechanism involves interface hopping and pairwise annihilation supplemented by spontaneous creation of the stable phase 1 regions by overturning the unstable phase 1 spins with probabilityp for cluster coarsening at phase coexistence p 0 the conventional structure factor scaling applies in this limit our model falls in the class of diffusion limited reactions a a inert the 1 cluster size grows diffusively t and the two point correlation function obeys scaling however forp 0 i e for the dynamics of formation of stable phase from unstable phase we find that structure factor scaling breaks down the length scale associated with the size of the growing 1 clusters reflects only the short distance properties of the two point correlations

exact exponent for the number of persistent spins in the zero temperature dynamics of the one dimensional potts model for the zero temperature glauber dynamics of theq state potts model the fractionr q t of spins which never flip up to timet decays like a power lawr q t t q when the initial condition is random by mapping the problem onto an exactly soluble one species coagulation model a a a or alternatively by transforming the problem into a free fermion model we obtain the exact expression of q for all values ofq the exponent q is in general irrational 3 0 53795082 4 0 63151575 with the exception ofq 2 andq for which 2 3 8 and 1

on development of a finite dynamic element and solution of associated eigenproblem by a block lanczos procedure the paper first presents the details of the development of a new six noded plane triangular finite dynamic element a block lanczos algorithm is developed next for the accurate and efficient solution of the quadratic matrix eigenvalue problem associated with the finite dynamic element formulation the resulting computer program fully exploits matrix sparsity inherent in such a discretization and proves to be most efficient for the extraction of the usually required first few roots and vectors including repeated ones most importantly the present eigenproblem solution effort is shown to be comparable to that of the corresponding finite element analysis thereby rendering the associated dynamic element method rather attractive owing to superior convergence characteristics of such elements presented herein

general solutions for multispin two time correlation and response functions in the glauber ising chain the kinetic glauber ising spin chain is one of the very few exactly solvable models of non equilibrium statistical mechanics nevertheless existing solutions do not yield tractable expressions for two time correlation and response functions of observables involving products of more than one or two spins we use a new approach to solve explicitly the full hierarchy of differential equations for the correlation and response functions from this general solution follow closed expressions for arbitrary multispin two time correlation and response functions for the case where the system is quenched from equilibrium at ti 0 to some arbitrary t 0 by way of application we give the results for two and four spin two time correlation and response functions from the standard mapping these also imply new exact results for two time particle correlation and response functions in one dimensional diffusion limited annihilation

lanczos versus subspace iteration for solution of eigenvalue problems in this paper we consider solution of the eigen problem in structural analysis using a recent version of the lanczos method and the subspace method the two methods are applied to examples and we conclude that the lanczos method has advantages which are too good to overlook

smoluchowski approach for three body reactions in one dimension we present an extension of the smoluchowski approach for the analysis of diffusion limited three body reactions in one dimensional systems in terms of this approach we define the evolution of the particles mean concentration over the entire time domain c 1995 the american physical society

the spectral gap and the dynamical critical exponent of an exact solvable probabilistic cellular automaton abstract we obtained the exact solution of a probabilistic cellular automaton related to the diagonal to diagonal transfer matrix of the six vertex model on a square lattice the model describes the flow of ants or particles traveling on a one dimensional lattice whose sites are small craters containing sleeping or awake ants two kinds of particles we found the bethe ansatz equations and the spectral gap for the time evolution operator of the cellular automaton from the spectral gap we show that in the asymmetric case it belongs to the kardar parisi zhang kpz universality class exhibiting a dynamical critical exponent value z 3 2 this result is also obtained from a direct monte carlo simulation by evaluating the lattice size dependence of the decay time to the stationary state

free and forced vibration analysis using the smoothed finite element method sfem abstract smoothed finite element method sfem was recently proposed by the authors to improve the accuracy and convergence rate of the existing standard four node isoparametric finite element method fem by 2 2 quadrature in the static analysis in this work it is further extended to the free and forced analysis of two dimensional 2d dynamic problems it is found that sfem achieves more accurate results and higher convergence rates as compared with the corresponding finite elements in solving dynamic problems without increasing the computational cost as only shape function itself is involved in computing the field gradients and no coordinate transformation is required the method is very easy to implement nonlinear elastic forced vibration problem is also examined by using smoothed deformation gradients on each cell

fast radix 10 multiplication using redundant bcd codes we present the algorithm and architecture of a bcd parallel multiplier that exploits some properties of two different redundant bcd codes to speedup its computation the redundant bcd excess 3 code xs 3 and the overloaded bcd representation odds in addition new techniques are developed to reduce significantly the latency and area of previous representative high performance implementations partial products are generated in parallel using a signed digit radix 10 recoding of the bcd multiplier with the digit set 5 5 and a set of positive multiplicand multiples 0x 1x 2x 3x 4x 5x coded in xs 3 this encoding has several advantages first it is a self complementing code so that a negative multiplicand multiple can be obtained by just inverting the bits of the corresponding positive one also the available redundancy allows a fast and simple generation of multiplicand multiples in a carry free way finally the partial products can be recoded to the odds representation by just adding a constant factor into the partial product reduction tree since the odds uses a similar 4 bit binary encoding as non redundant bcd conventional binary vlsi circuit techniques such as binary carry save adders and compressor trees can be adapted efficiently to perform decimal operations to show the advantages of our architecture we have synthesized a rtl model for 16 times 16 digit and 34 times 34 digit multiplications and performed a comparative survey of the previous most representative designs we show that the proposed decimal multiplier has an area improvement roughly in the range 20 35 percent for similar target delays with respect to the fastest implementation

anomalous coalescence phenomena under stationary regime condition through thompson s method abstract in this work anomalous coalescence phenomena of type a a a 0 are considered in the case of stationary regime namely the case of an external homogeneous source h of single particles a in the limit of zero external field rate the main purpose here is to pick up new critical exponents in the stationary regime for the phenomenon of anomalous coalescence of bubbles found in one dimension by josserand and rica jr phys rev lett 78 1997 1215 the critical exponents of statical concentration relaxation time and the exponent for concentration decay are evaluated in the limit h 0 zero field rate we show that such critical exponents depend on the parameter physica a 334 2004 335 which characterizes the anomalous diffusion condition in order to explain the anomalous coalescence of jr s work as already made before by the present author physica a 334 2004 335 the parameter must display an explicit dependence on the dimensionality d 4 d for d 2 we use such a result d in order to pick up new critical exponents for the special case of anomalous coalescence found by jr we find 5 4 5 and 1 4 in 1 d we also verify that the known scaling relations among such critical indexes phys rev a 32 2 1985 1129 are obeyed so that in the special case of 2 brownian diffusion condition given to mean field regime we naturally recover those results previously obtained by racz phys rev a 32 2 1985 1129 we go further to give a better explanation for such new results taking into account another exponent physica a 334 2004 335 to explain the behavior of diffusion constant which depends on concentration d d 0 n that is to say we obtain analytically new critical indexes which controll the diffusion behavior d for long time regime in the presence of an external homogeneous source

three species diffusion limited reaction with continuous density decay exponents we introduce a model of three species two particle diffusion limited reactions or b or c and or a with three persistence parameters survival probabilities in reaction of the hopping particle we consider isotropic and anisotropic diffusion hopping with a drift in one dimension we find that the particle density decays as a power law for certain choices of the persistence parameter values in the anisotropic case on one symmetric line in the parameter space the decay exponent is monotonically varying between the values close to 1 3 and 1 2 on another less symmetric line the exponent is constant for most parameter values the density does not follow a power law we also calculated various characteristic exponents for the distance of nearest particles and domain structure our results support the recently proposed possibility that one dimensional diffusion limited reactions with a drift do not fall within a limited number of distinct universality classes

asymptotic behavior of densities for two particle annihilating random walks consider the system of particles on d where particles are of two types a andb and execute simple random walks in continuous time particles do not interact with their own type but when ana particle meets ab particle both disappear i e are annihilated this system serves as a model for the chemical reactiona b inert we analyze the limiting behavior of the densities a t and b t when the initial state is given by homogeneous poisson random fields we prove that for equal initial densities a 0 b 0 there is a change in behavior fromd 4 where a t b t c t d 4 tod 4 where a t b t c tast for unequal initial densities a 0 b 0 a t e c l ind 1 a t e ct logt ind 2 and a t e ct ind 3 the termc depends on the initial densities and changes withd techniques are from interacting particle systems the behavior for this two particle annihilation process has similarities to those for coalescing random walks a a a and annihilating random walks a a inert the analysis of the present process is made considerably more difficult by the lack of comparison with an attractive particle system

renormalisation of fluctuation effects in the a a to a reaction the field theoretical description of the a a to a reaction is exactly renormalised to all orders in perturbation theory it is confirmed that it belong to the same universality class as the a a to oe reaction and that the concentration decay like t d 2 for space dimensionality d smaller than two and like ln t t for d 2 are exact results

lattice models solvable through the full interval method on links a two state model on a one dimensional lattice is considered where the evolution of the state of each site is determined by the states of that site and its neighboring sites corresponding to this original lattice a derived lattice is introduced the sites of which are the links of the original lattice it is shown that there is only one reaction on the original lattice which results in the derived lattice being solvable through the full interval method and that reaction corresponds to the one dimensional stochastic non consensus opinion model a one dimensional non consensus opinion model with deterministic evolution has already been introduced here this is extended to be a model which has a stochastic evolution discrete time evolution of such a model is investigated including the two limiting cases of small probabilities for evolution resulting to an effectively continuous time evolution and deterministic evolution the formal solution to the evolution equation is obtained and the large time behavior of the system is investigated some special cases are studied in more detail

a radix 10 digit recurrence division unit algorithm and architecture in this work we present a radix 10 division unit that is based on the digit recurrence algorithm the previous decimal division designs do not include recent developments in the theory and practice of this type of algorithm which were developed for radix 2k dividers in addition to the adaptation of these features the radix 10 quotient digit is decomposed into a radix 2 digit and a radix 5 digit in such a way that only five and two times the divisor are required in the recurrence moreover the most significant slice of the recurrence which includes the selection function is implemented in radix 2 avoiding the additional delay introduced by the radix 10 carry save additions and allowing the balancing of the paths to reduce the cycle delay the results of the implementation of the proposed radix 10 division unit show that its latency is close to that of radix 16 division units comparable dynamic range of significant and it has a shorter latency than a radix 10 unit based on the newton raphson approximation

reviewing high radix signed digit adders higher radix values of the form beta 2 r have been employed traditionally for recoding of multipliers and for determining quotient and root digits in iterative division and square root algorithms usually only for quite moderate values of r like 2 or 3 for fast additions in particular for the accumulation of many terms generally redundant representations are employed most often binary carry save or borrow save but in a number of publications it has been suggested to recode the addends into a higher radix it is shown that there are no speed advantages in doing so if the radix is a power of 2 on the contrary there are significant savings in using standard 4 to 2 adders even saving half of the operations in multi operand addition

equivalences between stochastic systems time dependent correlation functions of unstable particles undergoing biased or unbiased diffusion coagulation and annihilation are studied this is achieved by similarity transformations between different stochastic models and between stochastic and soluble nonstochastic models for special cases we obtain exact results which are in good agreement with experiments on one dimensional annihilation coagulation processes

continuously varying exponents in reaction diffusion systems we propose a simple reaction diffusion model describing a class of competitive multi species reactions the model is exactly solvable at its upper critical dimension du 2 the local moments of the component concentrations follow a power law decay with exponents which vary continuously with system parameters the exponents also have an underlying multifractal spectrum the main results are supported by results from a numerical integration of the model

the lanczos algorithm applied to unsymmetric generalized eigenvalue problem application of the two sided lanczos recursion to the unsymmetric generalized eigenvalue problem is presented the system matrices are real and unsymmetric therefore the recursions are performed in real arithmetic and complex arithmetic is employed in the qr algorithm used to extract the eigenvalues of the transformed tridiagonal matrix the biorthonormal transformation of the unsymmetric generalized eigenvalue problem is considered in detail with appropriate proofs presented in appendices issues relating to the computer implementation of the unsymmetric generalized eigenvalue problem are discussed the example problems solved demonstrate the working of the algorithm in extracting the complex and or real eignevalues of an unsymmetric system of matrices also the algorithm is applied to extract a few of the eigenvalues of a large fluid structure interaction problem and the results are compared with the eigenfrequencies extracted by an unsymmetric subspace iteration procedure presented in the literature

smooth finite element methods convergence accuracy and properties a stabilized conforming nodal integration finite element method based on strain smoothing stabilization is presented the integration of the stiffness matrix is performed on the boundaries of the finite elements a rigorous variational framework based on the hu washizu assumed strain variational form is developed we prove that solutions yielded by the proposed method are in a space bounded by the standard finite element solution infinite number of subcells and a quasi equilibrium finite element solution a single subcell we show elsewhere the equivalence of the one subcell element with a quasi equilibrium finite element leading to a global a posteriori error estimate we apply the method to compressible and incompressible linear elasticity problems the method can always achieve higher accuracy and convergence rates than the standard finite element method especially in the presence of incompressibility singularities or distorted meshes for a slightly smaller computational cost it is shown numerically that the one cell smoothed four noded quadrilateral finite element has a convergence rate of 2 0 in the energy norm for problems with smooth solutions which is remarkable for problems with rough solutions this element always converges faster than the standard finite element and is free of volumetric locking without any modification of integration scheme copyright 2007 john wiley sons ltd

on matrix product ground states for reaction diffusion models we discuss a new mechanism leading to a matrix product form for the stationary state of one dimensional stochastic models the corresponding algebra is quadratic and involves four different matrices for the example of a coagulation decoagulation model explicit four dimensional representations are given and exact expressions for various physical quantities are recovered we also find the general structure of n point correlation functions at the phase transition

finite size scaling of the time dependent structure factor in the one dimensional glauber model abstract we study the time dependent structure factor of the one dimensional glauber model upon instantaneous cooling results obtained earlier by reiss mazenko and widom and bray are linked together next finite size scaling in the limit of zero temperature long times small wave vectors and large systems is established the scaling function is compared with numerical simulation results obtained by vinals and jasnow in the case of a two dimensional glauber model quenched into the region of phase separation