spectral formulation and wkb approximation for rare event statistics in reaction systems we develop a spectral formulation and a stationary wkb approximation for calculating the probabilities of rare events large deviations from the mean in systems of reacting particles with infinite range interaction describable by a master equation we compare the stationary wkb approximation to a recent time dependent semiclassical approximation developed for the same class of problems by elgart and kamenev phys rev e 70 41106 2004 as a benchmark we use an exactly solvable problem of the binary annihilation reaction 2a 0

how colored environmental noise affects population extinction environmental noise can cause an exponential reduction in the mean time to extinction mte of an isolated population we study this effect on an example of a stochastic birth death process with rates modulated by a colored that is correlated gaussian noise a path integral formulation yields a transparent way of evaluating the mte and finding the optimal realization of the environmental noise that determines the most probable path to extinction the population size dependence of the mte changes from exponential in the absence of the environmental noise to a power law for a short correlated noise and to no dependence for long correlated noise we also establish the validity domains of the white noise limit and adiabatic limit

a new meta heuristic algorithm for continuous engineering optimization harmony search theory and practice most engineering optimization algorithms are based on numerical linear and nonlinear programming methods that require substantial gradient information and usually seek to improve the solution in the neighborhood of a starting point these algorithms however reveal a limited approach to complicated real world optimization problems if there is more than one local optimum in the problem the result may depend on the selection of an initial point and the obtained optimal solution may not necessarily be the global optimum this paper describes a new harmony search hs meta heuristic algorithm based approach for engineering optimization problems with continuous design variables this recently developed hs algorithm is conceptualized using the musical process of searching for a perfect state of harmony it uses a stochastic random search instead of a gradient search so that derivative information is unnecessary various engineering optimization problems including mathematical function minimization and structural engineering optimization problems are presented to demonstrate the effectiveness and robustness of the hs algorithm the results indicate that the proposed approach is a powerful search and optimization technique that may yield better solutions to engineering problems than those obtained using current algorithms 2004 elsevier b v all rights reserved

degree dispersion increases the rate of rare events in population networks there is great interest in predicting rare and extreme events in complex systems and in particular understanding the role of network topology in facilitating such events in this letter we show that degree dispersion the fact that the number of local connections in networks varies broadly increases the probability of large rare fluctuations in population networks generically we perform explicit calculations for two canonical and distinct classes of rare events network extinction and switching when the distance to threshold is held constant and hence stochastic effects are fairly compared among networks we show that there is a universal exponential increase in the rate of rare events proportional to the variance of a network s degree distribution over its mean squared

weak solution to the steady compressible flow of nematic liquid crystals abstract in this study three dimensional equations for the steady compressible flow of nematic liquid crystals are considered in a bounded domain for the adiabatic exponent 1 we establish the existence of a weak solution by three level approximation and adapting the weak convergence method

extinction rates for fluctuation induced metastabilities a real space wkb approach the extinction of a single species due to demographic stochasticity is analyzed the discrete nature of the individual agents and the poissonian noise related to the birth death processes result in local extinction of a metastable population as the system hits the absorbing state the fokker planck formulation of that problem fails to capture the statistics of large deviations from the metastable state while approximations appropriate close to the absorbing state become in general invalid as the population becomes large to connect these two regimes a real space wkb method based on the master equation is presented and is shown to yield an excellent approximation for the decay rate and the extreme events statistics all the way down to the absorbing state the details of the underlying microscopic process smeared out in a mean field treatment are shown to be crucial for an exact determination of the extinction exponent this general scheme is shown to reproduce the known results in the field to yield new corollaries and to fit quite precisely the numerical solutions moreover it allows for systematic improvement via a series expansion where the small parameter is the inverse of the number of individuals in the metastable state

the low mach number limit for the compressible flow of liquid crystals abstract in this paper we are concerned with the compressible flow of liquid crystals based on the convergence stability principle it is shown that for the mach number sufficiently small the cauchy problem of compressible liquid crystal flow has a unique smooth solution on the finite time interval where the incompressible liquid crystal flow exists furthermore it is justified that as the mach number tends to zero the smooth solutions converge rigorously to those of the incompressible equations and the sharp convergence orders are also obtained

maximizing influence in a social network improved results using a genetic algorithm abstract the influence maximization problem focuses on finding a small subset of nodes in a social network that maximizes the spread of influence while the greedy algorithm and some improvements to it have been applied to solve this problem the long solution time remains a problem stochastic optimization algorithms such as simulated annealing are other choices for solving this problem but they often become trapped in local optima we propose a genetic algorithm to solve the influence maximization problem through multi population competition using this algorithm we achieve an optimal result while maintaining diversity of the solution we tested our method with actual networks and our genetic algorithm performed slightly worse than the greedy algorithm but better than other algorithms

distinguished material surfaces and coherent structures in three dimensional fluid flows we prove analytic criteria for the existence of finite time attracting and repelling material surfaces and lines in three dimensional unsteady flows the longest lived such structures define coherent structures in a lagrangian sense our existence criteria involve the invariants of the velocity gradient tensor along fluid trajectories an alternative approach to coherent structures is shown to lead to their characterization as local maximizers of the largest finite time lyapunov exponent field computed directly from particle paths both approaches provide effective tools for extracting distinguished lagrangian structures from three dimensional velocity data we illustrate the results on steady and unsteady abc type flows

an iterative action minimizing method for computing optimal paths in stochastic dynamical systems abstract we present a numerical method for computing optimal transition pathways and transition rates in systems of stochastic differential equations sdes in particular we compute the most probable transition path of stochastic equations by minimizing the effective action in a corresponding deterministic hamiltonian system the numerical method presented here involves using an iterative scheme for solving a two point boundary value problem for the hamiltonian system we validate our method by applying it to both continuous stochastic systems such as nonlinear oscillators governed by the duffing equation and finite discrete systems such as epidemic problems which are governed by a set of master equations furthermore we demonstrate that this method is capable of dealing with stochastic systems of delay differential equations

nonparabolic dissipative systems modeling the flow of liquid crystals we study a simplified system which retains most of the interesting mathematical properties of the original ericksen leslie equations for the flow of liquid crystals this is a coupled nonparabolic dissipative dynamic system we derive several energy laws which enable us to prove the global existence of the weak solutions and the classical solutions we also discuss uniqueness and some stability properties of the system 1995 john wiley sons inc

evolution of a fluctuating population in a randomly switching environment environment plays a fundamental role in the competition for resources and hence in the evolution of populations here we study a well mixed finite population consisting of two strains competing for the limited resources provided by an environment that randomly switches between states of abundance and scarcity assuming that one strain grows slightly faster than the other we consider two scenarios one of pure resource competition and one in which one strain provides a public good and investigate how environmental randomness external noise coupled to demographic internal noise determines the population s fixation properties and size distribution by analytical means and simulations we show that these coupled sources of noise can significantly enhance the fixation probability of the slower growing species we also show that the population size distribution can be unimodal bimodal or multimodal and undergoes noise induced transitions between these regimes when the rate of switching matches the population s growth rate

nonlinear theory of defects in nematic liquid crystals phase transition and flow phenomena this is a summary of some recent mathematical advances in the theory of defects in nematic liquid crystals it also includes some new results concerning disclinations line defects which have not been published elsewhere

intrinsic noise in systems with switching environments we study individual based dynamics in finite populations subject to randomly switching environmental conditions these are inspired by models in which genes transition between on and off states regulating underlying protein dynamics similarly switches between environmental states are relevant in bacterial populations and in models of epidemic spread existing piecewise deterministic markov process approaches focus on the deterministic limit of the population dynamics while retaining the randomness of the switching here we go beyond this approximation and explicitly include effects of intrinsic stochasticity at the level of the linear noise approximation specifically we derive the stationary distributions of a number of model systems in good agreement with simulations this improves existing approaches which are limited to the regimes of fast and slow switching

taming the diffusion approximation through a controlling factor wkb method the diffusion approximation da is widely used in the analysis of stochastic population dynamics from population genetics to ecology and evolution the da is an uncontrolled approximation that assumes the smoothness of the calculated quantity over the relevant state space and fails when this property is not satisfied this failure becomes severe in situations where the direction of selection switches sign here we employ the wkb wentzel kramers brillouin large deviations method which requires only the logarithm of a given quantity to be smooth over its state space combining the wkb scheme with asymptotic matching techniques we show how to derive the diffusion approximation in a controlled manner and how to produce better approximations applicable for much wider regimes of parameters we also introduce a scalable independent of population size wkb based numerical technique the method is applied to a central problem in population genetics and evolution finding the chance of ultimate fixation in a zero sum two types competition

an improved harmony search algorithm for solving optimization problems this paper develops an improved harmony search ihs algorithm for solving optimization problems ihs employs a novel method for generating new solution vectors that enhances accuracy and convergence rate of harmony search hs algorithm in this paper the impacts of constant parameters on harmony search algorithm are discussed and a strategy for tuning these parameters is presented the ihs algorithm has been successfully applied to various benchmarking and standard engineering optimization problems numerical results reveal that the proposed algorithm can find better solutions when compared to hs and other heuristic or deterministic methods and is a powerful search algorithm for various engineering optimization problems

disease extinction in the presence of random vaccination we investigate disease extinction in an epidemic model described by a birth death process we show that in the absence of vaccination the effective entropic barrier for extinction displays scaling with the distance to the bifurcation point with an unusual critical exponent even a comparatively weak poisson distributed random vaccination leads to an exponential increase in the extinction rate with the exponent that strongly depends on the vaccination parameters

colonization of a territory by a stochastic population under a strong allee effect and a low immigration pressure we study the dynamics of colonization of a territory by a stochastic population at low immigration pressure we assume a sufficiently strong allee effect that introduces in deterministic theory a large critical population size for colonization at low immigration rates the average precolonization population size is small thus invalidating the wkb approximation to the master equation we circumvent this difficulty by deriving an exact zero flux solution of the master equation and matching it with an approximate nonzero flux solution of the pertinent fokker planck equation in a small region around the critical population size this procedure provides an accurate evaluation of the quasistationary probability distribution of population sizes in the precolonization state and of the mean time to colonization for a wide range of immigration rates at sufficiently high immigration rates our results agree with wkb results obtained previously at low immigration rates the results can be very different

population extinction risk in the aftermath of a catastrophic event we investigate how a catastrophic event modeled as a temporary fall of the reproduction rate increases the extinction probability of an isolated self regulated stochastic population using a variant of the verhulst logistic model as an example we combine the probability generating function technique with an eikonal approximation to evaluate the exponentially large increase in the extinction probability caused by the catastrophe this quantity is given by the eikonal action computed over the optimal path instanton of an effective classical hamiltonian system with a time dependent hamiltonian for a general catastrophe the eikonal equations can be solved numerically for simple models of catastrophic events analytic solutions can be obtained one such solution becomes quite simple close to the bifurcation point of the verhulst model the eikonal results for the increase in the extinction probability caused by a catastrophe agree well with numerical solutions of the master equation

extinction of an infectious disease a large fluctuation in a nonequilibrium system we develop a theory of first passage processes in stochastic nonequilibrium systems of birth death type using two closely related epidemiological models as examples our method employs the probability generating function technique in conjunction with the eikonal approximation in this way the problem is reduced to finding the optimal path to extinction a heteroclinic trajectory of an effective multidimensional classical hamiltonian system we compute this trajectory and mean extinction time of the disease numerically and uncover a nonmonotone spiral path to extinction of a disease we also obtain analytical results close to a bifurcation point where the problem is described by a hamiltonian previously identified in one species population models

rare event statistics in reaction diffusion systems we present an efficient method to calculate probabilities of large deviations from the typical behavior rare events in reaction diffusion systems this method is based on a semiclassical treatment of an underlying quantum hamiltonian encoding the system s evolution to this end we formulate the corresponding canonical dynamical system and investigate its phase portrait this method is presented for a number of pedagogical examples

large negative velocity gradients in burgers turbulence we consider one dimensional burgers equation driven by large scale white in time random force the tails of the velocity gradients probability distribution function pdf are analyzed by saddle point approximation in the path integral describing the velocity statistics the structure of the saddle point instanton that is the velocity field configuration realizing the maximum of probability is studied numerically in details the numerical results allow us to find analytical solution for the long time part of the instanton its careful analysis confirms the result of balkovsky et al phys rev lett 78 1452 1997 based on short time estimations that the left tail of pdf has the form mathrm ln mathcal p u x ensuremath propto ensuremath u x 3 2

global well posedness and decay of smooth solutions to the non isothermal model for compressible nematic liquid crystals abstract the cauchy problem for the three dimensional non isothermal model for compressible nematic liquid crystals is considered existence of global in time smooth solutions is established provided that the initial datum is close to a steady state 0 d by using the l q l p estimates and the fourier splitting method if the initial perturbation is small in h 3 norm and bounded in l q q 1 6 5 norm we obtain the optimal decay rates for the first and second order spatial derivatives of solutions in addition the third and fourth order spatial derivatives of director field d in l 2 norm are achieved

chemical langevin equation a path integral view of gillespie s derivation in 2000 gillespie rehabilitated the chemical langevin equation cle by describing two conditions that must be satisfied for it to yield a valid approximation of the chemical master equation cme in this work we construct an original path integral description of the cme and show how applying gillespie s two conditions to it directly leads to a path integral equivalent to the cle we compare this approach to the path integral equivalent of a large system size derivation and show that they are qualitatively different in particular both approaches involve converting many sums into many integrals and the difference between the two methods is essentially the difference between using the euler maclaurin formula and using riemann sums our results shed light on how path integrals can be used to conceptualize coarse graining biochemical systems and are readily generalizable

novel derivative of harmony search algorithm for discrete design variables calculus has widespread applications in science and engineering optimization is one of its major subjects where a problem can be mathematically formulated and its optimal solution is determined by using derivatives however this calculus based derivative technique can only be applied to real valued or continuous valued functions rather than discrete valued functions while there are many situations where design variables contain not continuous values but discrete values by nature in order to consider these realistic design situations this study proposes a novel derivative for discrete design variables based on a harmony search algorithm detailed analysis shows how this new stochastic derivative works in the bench mark function and fluid transport network design hopefully this new derivative as a fundamental technology will be utilized in various science and engineering problems

molecular evolution under fitness fluctuations molecular evolution is a stochastic process governed by fitness mutations and reproductive fluctuations in a population here we study evolution where fitness itself is stochastic with random switches in the direction of selection at individual genomic loci as the correlation time of these fluctuations becomes larger than the diffusion time of mutations within the population fitness changes from an annealed to a quenched random variable we show that the rate of evolution has its maximum in the crossover regime where both time scales are comparable adaptive evolution emerges in the quenched fitness regime evidence for such fitness fluctuations has recently been found in genomic data the joint statistical theory of reproductive and fitness fluctuations establishes a conceptual connection between evolutionary genetics and statistical physics of disordered systems

the geometric minimum action method a least action principle on the space of curves freidlin wentzell theory of large deviations for the description of the effect of small random perturbations on dynamical systems is exploited as a numerical tool specifically a numerical algorithm is proposed to compute the quasi potential in the theory which is the key object to quantify the dynamics on long time scales when the effect of the noise becomes ubiquitous the equilibrium distribution of the system the pathways of transition between metastable states and their rate etc can all be expressed in terms of the quasi potential we propose an algorithm to compute these quantities called the geometric minimum action method gmam which is a blend of the original minimum action method mam and the string method it is based on a reformulation of the large deviations action functional on the space of curves that allows one to easily perform the double minimization of the original action required to compute the quasi potential the theoretical background of the gmam in the context of large deviations theory is discussed in detail as well as the algorithmic aspects of the method the gmam is then illustrated on several examples a finite dimensional system displaying bistability and modeled by a nongradient stochastic ordinary differential equation an infinite dimensional analogue of this system modeled by a stochastic partial differential equation and an example of a bistable genetic switch modeled by a markov jump process

stability measures in metastable states with gaussian colored noise we present a study of the escape time from a metastable state of an overdamped brownian particle in the presence of colored noise generated by ornstein uhlenbeck process we analyze the role of the correlation time on the enhancement of the mean first passage time through a potential barrier and on the behavior of the mean growth rate coefficient as a function of the noise intensity we observe the noise enhanced stability effect for all the initial unstable states used and for all values of the correlation time tau c investigated we can distinguish two dynamical regimes characterized by weak and strong correlated noises depending on the value of tau c with respect to the relaxation time of the system

global best harmony search harmony search hs is a new meta heuristic optimization method imitating the music improvisation process where musicians improvise their instruments pitches searching for a perfect state of harmony a new variant of hs called global best harmony search ghs is proposed in this paper where concepts from swarm intelligence are borrowed to enhance the performance of hs the performance of the ghs is investigated and compared with hs and a recently developed variation of hs the experiments conducted show that the ghs generally outperformed the other approaches when applied to ten benchmark problems the effect of noise on the performance of the three hs variants is investigated and a scalability study is conducted the effect of the ghs parameters is analyzed finally the three hs variants are compared on several integer programming test problems the results show that the three approaches seem to be an efficient alternative for solving integer programming problems 2007 elsevier inc all rights reserved

a self adaptive global best harmony search algorithm for continuous optimization problems this paper presents a self adaptive global best harmony search sghs algorithm for solving continuous optimization problems in the proposed sghs algorithm a new improvisation scheme is developed so that the good information captured in the current global best solution can be well utilized to generate new harmonies the harmony memory consideration rate hmcr and pitch adjustment rate par are dynamically adapted by the learning mechanisms proposed the distance bandwidth bw is dynamically adjusted to favor exploration in the early stages and exploitation during the final stages of the search process extensive computational simulations and comparisons are carried out by employing a set of 16 benchmark problems from literature the computational results show that the proposed sghs algorithm is more effective in finding better solutions than the state of the art harmony search hs variants

classical solutions for the compressible liquid crystal flows with nonnegative initial densities abstract in this paper we study the cauchy problem of the simplified ericksen leslie system modeling compressible nematic liquid crystal flows in r 3 we first prove the local existence of the strong solutions provided that the data satisfies a natural compatibility condition then by deriving the smoothing effect of the solution in t 0 we conclude that it is indeed classical on some time interval 0 t 0 here we do not need the condition that initial density is bounded below away from zero

liquid crystal flows in two dimensions this paper is concerned with a simplified hydrodynamic equation proposed by ericksen and leslie modeling the flow of nematic liquid crystals in dimension two we establish both interior and boundary regularity theorems for such a flow under smallness conditions as a consequence we establish the existence of global in time weak solutions on a bounded smooth domain in mathbb r 2 which are smooth everywhere with possible exceptions of finitely many singular times

chaotic harmony search algorithms harmony search hs is one of the newest and the easiest to code music inspired heuristics for optimization problems like the use of chaos in adjusting note parameters such as pitch dynamic rhythm duration tempo instrument selection attack time etc in real music and in sound synthesis and timbre construction this paper proposes new hs algorithms that use chaotic maps for parameter adaptation in order to improve the convergence characteristics and to prevent the hs to get stuck on local solutions this has been done by using of chaotic number generators each time a random number is needed by the classical hs algorithm seven new chaotic hs algorithms have been proposed and different chaotic maps have been analyzed in the benchmark functions it has been detected that coupling emergent results in different areas like those of hs and complex dynamics can improve the quality of results in some optimization problems it has been also shown that some of the proposed methods have somewhat increased the solution quality that is in some cases they improved the global searching capability by escaping the local solutions

phase diagram for logistic systems under bounded stochasticity extinction is the ultimate absorbing state of any stochastic birth death process hence the time to extinction is an important characteristic of any natural population here we consider logistic and logisticlike systems under the combined effect of demographic and bounded environmental stochasticity three phases are identified an inactive phase where the mean time to extinction t increases logarithmically with the initial population size an active phase where t grows exponentially with the carrying capacity n and a temporal griffiths phase with a power law relationship between t and n the system supports an exponential phase only when the noise is bounded in which case the continuum diffusion approximation breaks down within the griffiths phase this breakdown is associated with a crossover between qualitatively different survival statistics and decline modes to study the power law phase we present a new wkb scheme which is applicable both in the diffusive and in the nondiffusive regime

hybridizing harmony search algorithm with sequential quadratic programming for engineering optimization problems this study presents a hybrid harmony search algorithm hhsa to solve engineering optimization problems with continuous design variables although the harmony search algorithm hsa has proven its ability of finding near global regions within a reasonable time it is comparatively inefficient in performing local search in this study sequential quadratic programming sqp is employed to speed up local search and improve precision of the hsa solutions moreover an empirical study is performed in order to determine the impact of various parameters of the hsa on convergence behavior various benchmark engineering optimization problems are used to illustrate the effectiveness and robustness of the proposed algorithm numerical results reveal that the proposed hybrid algorithm in most cases is more effective than the hsa and other meta heuristic or deterministic methods

population switching under a time varying environment we study the switching dynamics of a stochastic population subjected to a deterministically time varying environment our approach is demonstrated on a problem of population establishment which is important in ecology at the deterministic level the model we study gives rise to a critical population size beyond which the system experiences establishment notably the latter has been shown to be strongly influenced by the interplay between demographic and environmental variations here we consider two prototypical examples of a time varying environment a temporary change in the environment and a periodically varying environment by employing a semiclassical approximation we compute within exponential accuracy the change in the establishment probability and mean establishment time of the population due to the environmental variability our analytical results are verified by using a modified gillespie algorithm which accounts for explicitly time dependent reaction rates importantly our theoretical approach can also be useful in studying switching dynamics in gene regulatory networks under external variations

randomness as source for inspiring solution search methods music based approaches abstract as the world progresses towards industrialization engineering problems become increasingly complex and it becomes even more difficult to optimize these problems the reason for this is the increasing complexity of variables dimensions space complexity and time complexity in order to be able to cope with such a situation randomized intelligent optimization and search algorithms are proposed to optimize numerical benchmarking problems multi objective problems and solve difficult problems including a large number of variables dimensions constraints and objectives metaheuristic random search and optimization methods are widely used to search and find the most appropriate solutions for large scale optimization problems in an acceptable time they are general purposed methods that can be efficiently applied to optimization and search problems without too much modification to accommodate a specific probing metaheuristic optimization algorithms are generally categorized as physics music sociology biology swarm mathematics plant chemistry sports water and hybrid based although most of the intelligent metaheuristic methods are inspired by physics and biology concepts activities rules and processes in music can be an inspiration source of new intelligent optimization and search techniques that is why novel and efficient music inspired intelligent optimization and search methods having effective exploitation and exploration capabilities have been proposed in this paper music based metaheuristic optimization algorithms were gathered and analyzed for the first time harmony search and its versions melody search algorithm and method of musical composition have been examined in detail furthermore their performances have been compared within both unconstrained numerical benchmark functions and constrained problems and the obtained results from music based algorithms have been comparatively studied

long time behavior of solution for the compressible nematic liquid crystal flows in r 3 abstract in this paper we investigate the global existence and long time behavior of classical solution for the compressible nematic liquid crystal flows in three dimensional whole space first of all the global existence of classical solution is established under the condition that the initial data are close to the constant equilibrium state in h n r 3 n 3 framework then one establishes algebraic time decay for the classical solution by weighted energy method finally the algebraic decay rate of classical solution in l p r 3 norm with 2 p and optimal decay rate of their spatial derivative in l 2 r 3 norm are obtained if the initial perturbation belong to l 1 r 3 additionally

theory of time averaged neutral dynamics with environmental stochasticity competition is the main driver of population dynamics which shapes the genetic composition of populations and the assembly of ecological communities neutral models assume that all the individuals are equivalent and that the dynamics is governed by demographic shot noise with a steady state species abundance distribution sad that reflects a mutation extinction equilibrium recently many empirical and theoretical studies emphasized the importance of environmental variations that affect coherently the relative fitness of entire populations here we consider two generic time averaged neutral models in both the relative fitness of each species fluctuates independently in time but its mean is zero the first model a describes a system with local competition and linear fitness dependence of the birth death rates while in the second model b the competition is global and the fitness dependence is nonlinear due to this nonlinearity model b admits a noise induced stabilization mechanism that facilitates the invasion of new mutants a self consistent mean field approach is used to reduce the multispecies problem to two species dynamics and the large n asymptotics of the emerging set of fokker planck equations is presented and solved our analytic expressions are shown to fit the sads obtained from extensive monte carlo simulations and from numerical solutions of the corresponding master equations

definition and properties of lagrangian coherent structures from finite time lyapunov exponents in two dimensional aperiodic flows this paper develops the theory and computation of lagrangian coherent structures lcs which are defined as ridges of finite time lyapunov exponent ftle fields these ridges can be seen as finite time mixing templates such a framework is common in dynamical systems theory for autonomous and time periodic systems in which examples of lcs are stable and unstable manifolds of fixed points and periodic orbits the concepts defined in this paper remain applicable to flows with arbitrary time dependence and in particular to flows that are only defined computed or measured over a finite interval of time previous work has demonstrated the usefulness of ftle fields and the associated lcss for revealing the lagrangian behavior of systems with general time dependence however ridges of the ftle field need not be exactly advected with the flow the main result of this paper is an estimate for the flux across an lcs which shows that the flux is small and in most cases negligible for well defined lcss or those that rotate at a speed comparable to the local eulerian velocity field and are computed from ftle fields with a sufficiently long integration time under these hypotheses the structures represent nearly invariant manifolds even in systems with arbitrary time dependence the results are illustrated on three examples the first is a simplified dynamical model of a double gyre flow the second is surface current data collected by high frequency radar stations along the coast of florida and the third is unsteady separation over an airfoil in all cases the existence of lcss governs the transport and it is verified numerically that the flux of particles through these distinguished lines is indeed negligible

interfacial velocity corrections due to multiplicative noise the problem of velocity selection for reaction fronts has been intensively investigated leading to the successful marginal stability ms approach for propagation into an unstable state because the front velocity is controlled by the leading edge which perforce has low density it is interesting to study the role that finite particle number fluctuations have on this picture here we use the well known mapping of discrete markov processes to stochastic differential equations and focus on the front velocity in the simple a a ensuremath leftrightarrows a system our results are consistent with a recent heuristic proposal that v mathrm ms ensuremath v ensuremath sim 1 mathrm ln 2 n

dynamics of simple gene network motifs subject to extrinsic fluctuations cellular processes do not follow deterministic rules even in identical environments genetically identical cells can make random choices leading to different phenotypes this randomness originates from fluctuations present in the biomolecular interaction networks most previous work has been focused on the intrinsic noise in of these networks yet especially for high copy number biomolecules extrinsic or environmental noise en has been experimentally shown to dominate the variation here we develop an analytical formalism that allows for calculation of the effect of en on gene expression motifs we introduce a method for modeling bounded en as an auxiliary species in the master equation the method is fully generic and is not limited to systems with small en magnitudes we focus our study on motifs that can be viewed as the building blocks of genetic switches a nonregulated gene a self inhibiting gene and a self promoting gene the role of the en properties magnitude correlation time and distribution on the statistics of interest are systematically investigated and the effect of fluctuations in different reaction rates is compared due to its analytical nature our formalism can be used to quantify the effect of en on the dynamics of biochemical networks and can also be used to improve the interpretation of data from single cell gene expression experiments

enhancement of large fluctuations to extinction in adaptive networks during an epidemic individual nodes in a network may adapt their connections to reduce the chance of infection a common form of adaption is avoidance rewiring where a noninfected node breaks a connection to an infected neighbor and forms a new connection to another noninfected node here we explore the effects of such adaptivity on stochastic fluctuations in the susceptible infected susceptible model focusing on the largest fluctuations that result in extinction of infection using techniques from large deviation theory combined with a measurement of heterogeneity in the susceptible degree distribution at the endemic state we are able to predict and analyze large fluctuations and extinction in adaptive networks we find that in the limit of small rewiring there is a sharp exponential reduction in mean extinction times compared to the case of zero adaption furthermore we find an exponential enhancement in the probability of large fluctuations with increased rewiring rate even when holding the average number of infected nodes constant

strong solutions of the compressible nematic liquid crystal flow abstract we study strong solutions of the simplified ericksen leslie system modeling compressible nematic liquid crystal flows in a domain r 3 we first prove the local existence of a unique strong solution provided that the initial data 0 u 0 d 0 are sufficiently regular and satisfy a natural compatibility condition the initial density function 0 may vanish on an open subset i e an initial vacuum may exist we then prove a criterion for possible breakdown of such a local strong solution at finite time in terms of blow up of the quantities l t l x and d l t 3 l x

population extinction under bursty reproduction in a time modulated environment in recent years nondemographic variability has been shown to greatly affect dynamics of stochastic populations for example nondemographic noise in the form of a bursty reproduction process with an a priori unknown burst size or environmental variability in the form of time varying reaction rates have been separately found to dramatically impact the extinction risk of isolated populations in this work we investigate the extinction risk of an isolated population under the combined influence of these two types of nondemographic variation using the so called momentum space wentzel kramers brillouin wkb approach and accounting for the explicit time dependence in the reaction rates we arrive at a set of time dependent hamilton equations to this end we evaluate the population s extinction risk by finding the instanton of the time perturbed hamiltonian numerically whereas analytical expressions are presented in particular limits using various perturbation techniques we focus on two classes of time varying environments periodically varying rates corresponding to seasonal effects and a sudden decrease in the birth rate corresponding to a catastrophe all our theoretical results are tested against numerical monte carlo simulations with time dependent rates and also against a numerical solution of the corresponding time dependent hamilton equations

field theory of branching and annihilating random walks we develop a systematic analytic approach to the problem of branching and annihilating random walks equivalent to the diffusion limited reaction processes 2a and a m 1 a where m 1 starting from the master equation a field theoretic representation of the problem is derived and fluctuation effects are taken into account via diagrammatic and renormalization group methods for d 2 the mean field rate equation which predicts an active phase as soon as the branching process is switched on applies qualitatively for both even and odd m but the behavior in lower dimensions is shown to be quite different for these two cases for even m and d near 2 the active phase still appears immediately but with nontrivial crossover exponents which we compute in an expansion in 2 d and with logarithmic corrections in d 2 however there exists a second critical dimension d c 4 3 below which a nontrivial inactive phase emerges with asymptotic behavior characteristic of the pure annihilation process this is confirmed by an exact calculation in d 1 the subsequent transition to the active phase which represents a new nontrivial dynamic universality class is then investigated within a truncated loop expansion which appears to give a correct qualitative picture the model with m 2 is also generalized to n species of particles which provides yet another universality class and which is exactly solvable in the limit n for odd m we show that the fluctuations of the annihilation process are strong enough to create a nontrivial inactive phase for all d 2 in this case the transition to the active phase is in the directed percolation universality class finally we study the modification when the annihilation reaction is 3a when m 0 mod 3 the system is always in its active phase but with logarithmic crossover corrections for d 1 while the other cases should exhibit a directed percolation transition out of a fluctuation driven inactive phase