dynamic response optimization using an active set rqp algorithm a recently developed recursive quadratic programming rqp algorithm is applied to dynamic response design problems the algorithm incorporates updated hessians of the lagrange function and uses an active set strategy in which only a subset of the constraints is included in the direction finding qp subproblem hessian updating with dynamic response constraints presents some difficulties the primary difficulty is that the total number of constraints and the location of time points where they have to be imposed can change from iteration to iteration this can cause inconsistencies in hessian updating if proper numerical procedures are not used a numerical procedure to handle the situation is developed implemented and evaluated automatic restarting procedures are necessary for proper convergence of the algorithm the new algorithm is robust as well as more efficient than the purely linear algorithm the active set strategy plays an important role for application to dynamic response problems the rqp algorithms that do not use such a strategy are not applicable to this class of problems

short time critical dynamics of the ising model studied within the n fold algorithm abstract the short time behaviour of the critical two dimensional ising model is studied for the bortz kalos lebowitz n fold way algorithm bkl algorithm for square lattices of linear sizes l 110 128 140 170 and 200 we calculate the short time critical behaviour for the bkl algorithm and also for the heat bath algorithm comparison of these results shows that although power law scaling form emerges from the early times of the dynamics there are noticeable differences which do not produce negligible effects on the estimates of critical exponents the observed universality of short time critical behaviour supplements our fundamental knowledge of critical phenomena however short time dynamics seem to be related only approximately with equilibrium critical properties therefore any attempt to estimate equilibrium critical exponents from the short time regime would be superfluous except for the purpose of comparison because these exponents have been determined very precisely by different methods

role of noise in population dynamics cycles noise is an intrinsic feature of population dynamics and plays a crucial role in oscillations called phase forgetting quasicycles by converting damped into sustained oscillations this function of noise becomes evident when considering langevin equations whose deterministic part yields only damped oscillations we formulate here a consistent and systematic approach to population dynamics leading to a fokker planck equation and the associate langevin equations in accordance with this conceptual framework founded on stochastic lattice gas models that describe spatially structured predator prey systems langevin equations in the population densities and predator prey pair density are derived in two stages first a birth and death stochastic process in the space of prey and predator numbers and predator prey pair number is obtained by a contraction method that reduces the degrees of freedom second a van kampen expansion in the inverse of system size is then performed to get the fokker planck equation we also study the time correlation function the asymptotic behavior of which is used to characterize the transition from the cyclic coexistence of species to the ordinary coexistence

analysis of earlier times and flux of entropy on the majority voter model with diffusion we study the properties of nonequilibrium systems modelled as spin models without defined hamiltonian as the majority voter model this model has transition probabilities that do not satisfy the condition of detailed balance the lack of detailed balance leads to entropy production phenomena which are a hallmark of the irreversibility by considering that voters can diffuse on the lattice we analyze how the entropy production and how the critical properties are affected by this diffusion we also explore two important aspects of the diffusion effects on the majority voter model by studying entropy production and entropy flux via time dependent and steady state simulations this study is completed by calculating some critical exponents as function of the diffusion probability

spreading of damage in the domany kinzel cellular automaton a mean field approach abstract we present a detailed analytical formulation and a mean field approximation analysis of the spreading of damage in the domany kinzel cellular automaton our results show that the system exhibits a chaotic state besides the frozen and active these results are in agreement with recent numerical simulations also we study the conjugate fields associated to the order parameters of the active and chaotic phases

stochastic lattice gas model for a predator prey system we propose a stochastic lattice gas model to describe the dynamics of two animal species population one being a predator and the other a prey this model comprehends the mechanisms of the lotka volterra model our analysis was performed by using a dynamical mean field approximation and computer simulations our results show that the system exhibits an oscillatory behavior of the population densities of prey and predators for the sets of parameters used in our computer simulations these oscillations occur at a local level mean field results predict synchronized collective oscillations

monopole charges for arbitrary compact gauge groups and higgs fields in any representation the topological invariants of monopoles are described for an arbitrary compact gauge groupg and higgs field in any representation the results generalize those obtained recently for compact and simply connectedg and in the adjoint representation the cases when the residual symmetry group ish u 1 orh u 3 are worked out explicitly this latter is needed to accommodate fractional electric charge with monopoles having one dirac unit magnetic charge

design oriented identification of critical times in transient response on decrit 3 techniques de reduction de l effort de calcul implique dans l identification des temps critiques dans les problemes d optimisation des structures

topological charges in monopole theories let us consider a monopole theory with a compact simply connected gauge group and the higgs field in the adjoint representation using root theory we show that

optimum design of systems for dynamics and controls using sequentialquadratic programming this paper describes application of a sequential quadratic programming method for dynamic response optimization and optimal control problems several methods to treat time dependent constraints are described

structural optimization using equivalent static loads at all time intervals a quasi static structural optimization for elastic structures under dynamic loads is presented an equivalent static load esl set is defined as a static load set which generates the same displacement field as that from a dynamic load at a certain time multiple esl sets calculated at all the time intervals are employed to represent the various states of the structure under the dynamic load they can cover all the critical states that might happen at arbitrary times the continuous characteristics of a dynamic load are considered by multiple static load sets the calculated sets of esls are utilized as a multiple loading condition in the optimization process a design cycle is defined as a circulated process between an analysis domain and a design domain the analysis domain gives the loading condition needed in the design domain the design domain gives a new updated design to be verified by the analysis domain in the next design cycle the design cycles are iterated until the design converges structural optimization with dynamic loads is tangible by the proposed method standard example problems are solved to verify the validity of the method

critical behavior of nonequilibrium models in short time monte carlo simulations we analyze two alternative methods for determining the dynamic critical exponent z of the contact process and the domany kinzel cellular automaton in monte carlo simulations one method employs mixed initial conditions as proposed for magnetic models phys lett a 298 325 2002 the other is based on the growth of the moment ratio m t 2 starting with all sites occupied the methods provide reliable estimates for z using the short time dynamics of the process estimates of nu are obtained using a method suggested by grassberger

isotropic majority vote model on a square lattice the stationary critical properties of the isotropic majority vote model on a square lattice are calculated by monte carlo simulations and finite size analysis the critical exponents and are found to be the same as those of the ising model and the critical noise parameter is found to beqc 0 075 0 001

design sensitivity analysis and optimization of dynamic response abstract the paper presents methods of design sensitivity analysis and optimization of dynamic response of mechanical and structural systems a key feature of the paper is the development of procedures to handle point wise state variable constraints difficulties with a previous treatment where such constraints were transformed to equivalent integral constraints are noted and explained from theoretical as well as engineering standpoints an alternate treatment of such constraints is proposed developed and evaluated in this treatment each point wise state variable constraint is replaced by several constraints that are imposed at all the local max points for the original constraint function the differential equations of motion are formulated in the first order form so as to handle more general problems the direct differentiation and adjoint variable methods of design sensitivity analysis to deal with the point wise constraints are presented with the adjoint variable methods there are two ways of calculating design sensitivity coefficients the first approach uses an impulse load and the second approach uses a step load for the corresponding adjoint equation since the adjoint variable methods are better for a large class of problems an efficient computational algorithm with these methods is presented in detail optimum results for several problems are obtained and compared with those available in the literature the new formulation works extremely well as precise optimum designs are obtained

finite size scaling for first order transitions potts model the finite size scaling algorithm based on bulk and surface renormalization of de oliveira is tesed onq state potts models in dimensionsd 2 and 3 our monte carlo data clearly distinguish between first and second order phase transitions continuous q analytic calculations performed for small lattices show a clear tendency of the magnetic exponenty d v to reach a plateau for increasing values ofq which is consistent with the first order transition valuey d monte carlo data confirm this trend

a probabilistic automata network epidemic model with births and deaths exhibiting cyclic behaviour a probabilistic automata network model for the spread of an infectious disease in a population of moving individuals is studied the local rule consists of two subrules the first one applied synchronously models infection birth and death processes it is a probabilistic cellular automaton rule the second applied sequentially describes the motion of the individuals the model contains six parameters the probabilities p for a susceptible to become infected by contact with an infective the respective birth rates bs and bi of the susceptibles from either a susceptible or an infective parent the respective death rates ds and di of susceptibles and infectives and a parameter m characterizing the motion of the individuals the model has three fixed points the first is trivial it describes a stationary state with no living individuals the second corresponds to a disease free state with no infectives the third and last one characterizes an endemic state with non zero densities of susceptibles and infectives moreover the model may exhibit oscillatory behaviour of the susceptible and infective densities as functions of time through a hopf type bifurcation the influence of the different parameters on the stability of all these states is studied with a particular emphasis on the influence of motion which has been found to be a stabilizing factor of the cyclic behaviour

surface integrals and monopole charges in non abelian gauge theories we derive a formula which gives all the magnetic charges topological invariants of a monopole in the adjoint representation of a non abelian gauge theory in terms of surface integrals at infinity

the problem of global color in gauge theories the problem of global color which arose recently in monopole theory is generalized to arbitrary gauge theories a subgroup k of the unbroken gauge group g is implementable iff the gauge bundle reduces to the centralizer of k in g equivalent implementations correspond to equivalent reductions such an action is an internal symmetry for a given configuration iff the yang mills field reduces also the case of monopoles is worked out in detail

several simultaneous formulations for transient dynamic response optimization an evaluation several simultaneous formulations for transient dynamic response optimization are described analyzed and compared a key feature of the formulations is that the state variables in addition to the real design variables are treated as independent variables in the optimization process the state variables include different combinations of generalized displacements velocities and accelerations formulations based on different discretization techniques for first order and second order differential equations are presented finite difference newmark s method and methods based on collocation are all discussed similar to the simultaneous analysis and design approach used for the optimization of structures subjected to static loads and the direct collocation transcription method for optimal control the equations of motion are treated as equality constraints a major advantage of these formulations is that special design sensitivity analysis methods are no longer needed however the formulations have larger numbers of variables and constraints therefore sparsity of the problem functions must be exploited in all the calculations advantages and disadvantages of the formulations are discussed the numerical results for an example problem and performance features of the formulations are compared all the formulations converge to the optimum solution for the example problem they are quite efficient for a smaller number of time grid points however the computational times increase as the number of grid points is increased copyright 2009 john wiley sons ltd

stable oscillations of a predator prey probabilistic cellular automaton a mean field approach we analyze a probabilistic cellular automaton describing the dynamics of coexistence of a predator prey system the individuals of each species are localized over the sites of a lattice and the local stochastic updating rules are inspired by the processes of the lotka volterra model two levels of mean field approximations are set up the simple approximation is equivalent to an extended patch model a simple metapopulation model with patches colonized by prey patches colonized by predators and empty patches this approximation is capable of describing the limited available space for species occupancy the pair approximation is moreover able to describe two types of coexistence of prey and predators one where population densities are constant in time and another displaying self sustained time oscillations of the population densities the oscillations are associated with limit cycles and arise through a hopf bifurcation they are stable against changes in the initial conditions and in this sense they differ from the lotka volterra cycles which depend on initial conditions in this respect the present model is biologically more realistic than the lotka volterra model

majority vote on directed erdős renyi random graphs abstract through monte carlo simulation the well known majority vote model has been studied with noise on directed random graphs in order to characterize completely the observed order disorder phase transition the critical noise parameter q c as well as the critical exponents and 1 have been calculated as a function of the connectivity z of the random graph

alternative formulations for transient dynamic response optimization three alternative formulations for transient dynamic response optimization of mechanical systems are presented analyzed and evaluated the basic idea of these formulations is to treat various state variables as independent variables in the optimization process in addition to the real design variables that is generalized displacements velocities and accelerations because all functions of the optimization problem become explicit in terms of the variables in these formulations their gradients can be calculated easily as compared to the conventional approach where special design sensitivity analysis methods need to be used also the equations of motion are not integrated explicitly they are imposed as equality constraints for the alternative formulations the optimization problem is quite large in terms of the numbers of variables and constraints however the problem functions are quite sparse which is exploited in the optimization process advantages and disadvantages of the formulations are discussed several cases of two example problems are solved to study the performance of the formulations based on the extensive numerical experiments it is concluded that the proposed formulations work well for the example problems and have potential for further development for practical applications

the threshold of coexistence and critical behaviour of a predator prey cellular automaton we study a probabilistic cellular automaton to describe two population biology problems the threshold of species coexistence in a predator prey system and the spreading of an epidemic in a population by carrying out mean field approximations and numerical simulations we obtain the phase boundaries thresholds related to the transition between an active state where prey and predators present a stable coexistence and a prey absorbing state the numerical estimates for the critical exponents show that the transition belongs to the directed percolation universality class in the limit where the cellular automaton maps into a model for the spreading of an epidemic with immunization we observe a crossover from directed percolation class to the dynamic percolation class patterns of growing clusters related to species coexistence and spreading of epidemic are shown and discussed

probabilistic cellular automaton describing a biological immune system we have analyzed a probabilistic cellular automaton to describe the t helper cells response under parasitic infections the evolution rules are of totalistic type and possess up down symmetry the automaton displays a dynamical phase transition from a disordered state to an ordered one which takes place through a spontaneous symmetry breaking in the ordered phase one type of t helper cells predominates over the others the phase transition was studied both by a pair approximation and by monte carlo simulations in addition we were able to obtain some exact results for the densities of t helper cells

non equilibrium relaxation at a tricritical point we study the purely relaxational tricritical dynamics of a non conserved order parameter model a in the upper critical dimension dc 3 and in 3 epsilon dimensions we are especially interested in the relaxation starting from a macroscopically prepared initial state with a small correlation length using the methods of renormalized field theory we obtain the scaling behaviour of the correlation and response functions and study the nonlinear relaxation of the order parameter m t in three dimensions m t displays a crossover from the purely logarithmic short time behaviour m t approximately in t t0 a to a t 14 power law with logarithmic corrections for dimensions d 3 we obtain the exponents which govern the tricritical relaxation at lowest non trivial order in epsilon 3 d the dynamic scaling exponent z is calculated at second order in epsilon

very low thrust trajectory optimization using a direct sqp method abstract the direct transcription or collocation method has demonstrated notable success in the solution of trajectory optimization and optimal control problems this approach combines a sparse nonlinear programming algorithm with a discretization of the trajectory dynamics a challenging class of optimization problems occurs when the spacecraft trajectories are characterized by thrust levels that are very low relative to the vehicle weight low thrust trajectories are demanding because realistic forces due to oblateness aerodynamic drag and third body perturbions often dominate the thrust furthermore because the thrust is so low significant changes to the orbits require very long duration trajectories when a collocation method is applied to a problem of this type the resulting nonlinear program is very large because the trajectories are long and very nonlinear because of the perturbing forces this paper describes the application of the transcription method to the solution of very low thrust orbit transfers the vehicle dynamics are defined using a modified set of equinoctial coordinates and the trajectory modeling is described using these dynamics a solution is presented for a representative transfer using a spacecraft with a thrust acceleration of approximately 1 25 10 7 km s 2 this transfer requires over 578 revolutions and leads to a sparse optimization problem with 416 123 variables and 249 674 constraints issues related to the numerical conditioning and problem formulation are discussed

persistence and dynamics in the annni chain we investigate both the local and global persistence behaviour in the annni axial next nearest neighbour ising model we find that when the ratio of the second neighbour interaction to the first neighbour interaction is less than 1 p t the probability of a spin to remain in its original state up to time t shows a stretched exponential decay for 1 p t has an algebraic decay but the exponent is different from that of the nearest neighbour ising model the global persistence behaviour shows similar features we also conduct some deeper investigations in the dynamics of the annni model and conclude that it has a different dynamical behaviour compared to the nearest neighbour ising model

an alternative order parameter for the 4 state potts model abstract we have investigated the dynamic critical behavior of the two dimensional 4 state potts model using an alternative order parameter first used by vanderzande j phys a 20 1987 l549 in the study of the z 5 model we have estimated the global persistence exponent g by following the time evolution of the probability p t that the considered order parameter does not change its sign up to time t we have also obtained the critical exponents z and using this alternative definition of the order parameter and our results are in complete agreement with available values found in literature

high dimensional simulation of the shape space model for the immune system abstract for the reactions among the antibodies of the immune system fighting against a foreign antigen the recent model of de boer segel and perelson introduced a cellular automata approximation for the interaction of different types of b cells bone marrow derived lymphocytes in contrast to most physics models here each lattice site interacts mainly with its mirror image with respect to the lattice center in the opposite part of the lattice we simplify their model and then generalize it to include more than one or two shape space parameters thus instead of simulating a chain or square lattice we simulate a d dimensional hypercubic lattice with dimension d up to 10 in particular we check for the concentration of b cells and the stability against localized perturbations damage spreading

fixation in a cyclic lotka volterra model we study a cyclic lotka volterra model of n interacting species populating a d dimensional lattice in the realm of a kirkwood approximation a critical number of species nc d above which the system fixates is determined analytically we find nc d 5 14 23 in dimensionsdd 1 2 3 in remarkably good agreement with simulation results in two dimensions a cyclic variant of the lotka volterra model of interacting populations originally introduced by vito volterra for the description of the struggle for existence among species 1 2 has then appeared in a number of apparently unrelated fields ranging from plasma physics 3 to integrable systems 4 5 recently the cyclic lotka volterra model also known as the cyclic voter model has attracted considerable interest as it was realized that introduction of the spatial structure drastically enriches the dynamics 6 11 namely if species live on a one dimensional 1d lattice a homogeneous initial state evolves into a coarsening mosaic of interacting species this heterogeneous spatial structure spontaneously develops when the number of species is sufficiently small n nc fixation occurs i e the system approaches a frozen state little is known in higher dimensions not even the existence of nc has yet been established theoretically or numerically in simulations on two dimensional 2d lattices with n 6 10 species no sign of fixation has been found and instead a reactive steady state has been observed 6 11 in this letter we investigate the cyclic lotka volterra model in the framework of a kirkwood like approximation this approach predicts a finite nc in all spatial dimensions in the following we shall use the language of the voter model 12 consider the cyclic voter model with n possible opinions each site of a d dimensional cubic lattice is occupied by a voter which has an opinion labelled by with d 1 n voters can change their opinions in a cyclic manner 1 modulo n according to the opinions of their neighbourhood specifically the following sequential dynamics is implemented i we randomly choose a site of opinion say and one of its 2d nearest neighbours of opinion ii if d 1 then the chosen site changes its opinion from to d 1 and iii otherwise opinion does not change we set the timescale so that in unit time each site of the lattice is chosen once on average when nd 2 the cyclic voter model is

short time critical dynamics of the baxter wu model we study the early time behavior of the baxter wu model an ising model with three spin interactions on a triangular lattice our estimates for the dynamic exponent z are compatible with results recently obtained for two models which belong to the same universality class of the baxter wu model the two dimensional four state potts model and the ising model with three spin interactions in one direction however our estimates for the dynamic exponent ensuremath theta of the baxter wu model are completely different from the values obtained for those models this discrepancy could be related to the absence of a marginal operator in the baxter wu model

fluctuations and correlations in lattice models for predator prey interaction including spatial structure and stochastic noise invalidates the classical lotka volterra picture of stable regular population cycles emerging in models for predator prey interactions growth limiting terms for the prey induce a continuous extinction threshold for the predator population whose critical properties are in the directed percolation universality class we discuss the robustness of this scenario by considering an ecologically inspired stochastic lattice predator prey model variant where the predation process includes next nearest neighbor interactions we find that the corresponding stochastic model reproduces the above scenario in dimensions 1 d or 4 in contrast with the mean field theory which predicts a first order phase transition however the mean field features are recovered upon allowing for nearest neighbor particle exchange processes provided these are sufficiently fast

cumulants of the three state potts model and of nonequilibrium models with c3v symmetry the critical behaviour of two dimensional stochastic lattice gas models with c3v symmetry is analysed we study the cumulants of the order parameter for the three state equilibrium potts model and for two irreversible models whose dynamic rules are invariant under the symmetry operations of the point group c3v by means of extensive numerical analysis of the phase transition we show that irreversibility does not affect the critical behaviour of the systems in particular we find that the binder reduced fourth order cumulant takes a universal value u which is the same for the three state potts model and for the irreversible models the same universal behaviour is observed for the reduced third order cumulant

critical behavior of a probabilistic cellular automaton describing a biological system we study nonequilibrium phase transitions occurring in a probabilistic cellular automaton which describes one part of the immune system in this model each site can be occupied by three type of cells and the immune response under parasitic infections is described in terms of two parameters p and r the local rules governing the evolution of this automaton possess up down symmetry similar to ising models performing monte carlo simulations on square and cubic lattices we verify that the model displays continuous kinetic phase transitions with spontaneous symmetry breaking we present detailed simulations and analysis of the critical behavior our results indicate that the model belongs to the ising universality class supporting the up down conjecture c 1998 elsevier science b v all rights reserved

bulk and surface critical behaviour at the conformal invariant point in the z5 model the author determines the bulk thermal and magnetic exponents at the conformal invariant point in the z5 model with a monte carlo based finite size calculation the results are in good agreement with the predictions of zamolodchikov and fateev 1985 the author also argues that the n 1 surface magnetic exponents xh j in the zn model are given by j n j n j 1 n 1 this prediction is also verified in a monte carlo finite size calculation for the z5 model

self organized formulation of standard percolation phenomena abstract we consider standard percolation processes such as epidemic processes with or without immunization we show that their dynamics can be formulated so that they mimic self organized critical phenomena the wetting probability p needs not to be fine tuned to its critical value p c in order to arrive at criticality but it rather emerges as a singularity in some time dependent distribution on the one hand this casts doubts on the significance of self organized as opposed to ordinary criticality on the other hand it suggests very efficient algorithms where percolation problems are studied at several values of p in a single run as an example we apply such an algorithm to directed percolation in 2 1 dimensions where it allows a very precise determination of critical behavior

dynamic exponents of a probabilistic three state cellular automaton abstract in this work a three state cellular automaton proposed to describe part of a biological immune system is revisited we obtain the dynamic critical exponent z of the model by means of a recent technique that mixes different initial conditions moreover by using two distinct approaches we have also calculated the global persistence exponent g related to the probability that the order parameter of the model does not change its sign up to time t p t t g

sparse approach to simultaneous analysis and design of geometricallynonlinear structures this method to increase the efficiency of the opimization process for nonlinear structures considers the equilibrium equations as equality constraints of the nonlinear mathematical programming problem

generalized magnetic monopoles over contact manifolds a generalization of magnetic monopoles is given over an odd dimensional contact manifold and we discuss whether the yang mills higgs functional attains at generalized monopoles the absolute minimal value the topological invariant