bandt pompe approach to the classical quantum transition abstract by regarding the celebrated classical quantum transition problem as one pertaining to the domain of dynamic systems theory we present a discussion that exhibits the superiority of the bandt pompe approach to the extraction of a probability distribution from time series values

pinning of a rough interface by an external potential abstract an analysis is given of the behavior of an interface between two phases in the presence of an external pinning potential in the solid on solid limit of the two dimensional ising model it is found that the potential turns a rough interface into a smooth one except in the case of a boundary potential where a minimum potential strength is required the connection with the roughening transition found by abraham is discussed the interface width is calculated as a function of the potential parameters in the limit of a weak pining potential

constructing and predicting solitary pattern solutions for nonlinear time fractional dispersive partial differential equations building fractional mathematical models for specific phenomena and developing numerical or analytical solutions for these fractional mathematical models are crucial issues in mathematics physics and engineering in this work a new analytical technique for constructing and predicting solitary pattern solutions of time fractional dispersive partial differential equations is proposed based on the generalized taylor series formula and residual error function the new approach provides solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software for method evaluation and validation the proposed technique was applied to three different models and compared with some of the well known methods the resultant simulations clearly demonstrate the superiority and potentiality of the proposed technique in terms of the quality performance and accuracy of substructure preservation in the construct as well as the prediction of solitary pattern solutions for time fractional dispersive partial differential equations

growth of order in vector spin systems scaling and universality the growth of order in vector spin systems with nonconserved order parameter model a is considered following an instantaneous quench from infinite to zero temperature the results of numerical simulations in spatial dimension d 2 and spin dimension 2n5 are presented for n4 a scaling regime where a characteristic length scale l t emerges is entered for sufficiently long times with l t t12 the autocorrelation function a t decays with time as a t t d lambda 2 and the exponent lambda n agrees well with the predictions of the 1 n expansion the cases n 2 and 3 are more complicated due to the non trivial role played by topological singularities i e vortices n 2 and polyakov solitons n 3 for n4 universal amplitudes and scaling functions characterizing the energy relaxation and the equal time correlation function are identified it is argued that for d3 where an ordered phase exists at low temperature such universal quantities characterize the entire ordered phase

extinction in population dynamics we study a generic reaction diffusion model for single species population dynamics that includes reproduction death and competition the population is assumed to be confined in a refuge beyond which conditions are so harsh that they lead to certain extinction standard continuum mean field models in one dimension yield a critical refuge length l c such that a population in a refuge larger than this is assured survival herein we extend the model to take into account the discreteness and finiteness of the population which leads us to a stochastic description we present a particular critical criterion for likely extinction namely that the standard deviation of the population be equal to the mean according to this criterion we find that while survival can no longer be guaranteed for any refuge size for sufficiently weak competition one can make the refuge large enough certainly larger than l c to cause extinction to be unlikely however beyond a certain value of the competition rate parameter it is no longer possible to escape a likelihood of extinction even in an infinite refuge these unavoidable fluctuations therefore have a severe impact on refuge design issues

analytic solutions of a nonlinear convective equation in population dynamics analytic solutions are presented for a simple nonlinear convective equation of use in population dynamics in spite of its simplicity the equation predicts rich behavior including a velocity inversion transition stability considerations are also presented

modeling of biological population problems using the element free kp ritz method a degenerate parabolic equation arising in the spatial diffusion of biological population is analyzed using the mesh free kp ritz method the mesh free kernel particle estimate is employed to approximate the 2d displacement field a system of discrete equations is obtained through application of the ritz minimization procedure to the energy expressions to validate the accuracy of the results and stability of the present method convergence studies were carried out based on influences of support size and number of nodes effectiveness of the mesh free kp ritz method for biological population model is investigated by numerical examples in this paper the present results were compared with results reported in extant literature and were found to be in good agreement with the literature

thermostats for slow configurational modes thermostats are dynamical equations used to model thermodynamic variables such as temperature and pressure in molecular simulations for computationally intensive problems such as the simulation of biomolecules we propose to average over fast mo mentum degrees of freedom and construct thermostat equations in configuration space the equations of motion are deterministic analogues of the smoluchowski dynamics in the method of stochastic differential equations

exact evaluation of the collapse phase boundary for two dimensional directed polymers the phase boundary of the collapsed phase for a directed polymer on a square lattice in the presence of an attractive wall and monomer monomer interactions is calculated exactly using transfer matrix techniques the position of the multicritical point is also identified

nonlinear diffusion effects on biological population spatial patterns motivated by the observation that anomalous diffusion is a realistic feature in the dynamics of biological populations we investigate its implications in a paradigmatic model for the evolution of a single species density u x t the standard model includes growth and competition in a logistic expression and spreading is modeled through normal diffusion moreover the competition term is nonlocal which has been shown to give rise to spatial patterns we generalize the diffusion term through the nonlinear form tu x t d xxu x t with d 0 encompassing the cases where the state dependent diffusion coefficient either increases 1 or decreases 1 with the density yielding subdiffusion or superdiffusion respectively by means of numerical simulations and analytical considerations we display how that nonlinearity alters the phase diagram the type of diffusion imposes critical values of the model parameters for the onset of patterns and strongly influences their shape inducing fragmentation in the subdiffusive case the detection of the main persistent mode allows analytical prediction of the critical thresholds

fast approximations of shift variant blur image deblurring is essential in high resolution imaging e g astronomy microscopy or computational photography shift invariant blur is fully characterized by a single point spread function psf blurring is then modeled by a convolution leading to efficient algorithms for blur simulation and removal that rely on fast fourier transforms however in many different contexts blur cannot be considered constant throughout the field of view and thus necessitates to model variations of the psf with the location these models must achieve a trade off between the accuracy that can be reached with their flexibility and their computational efficiency several fast approximations of blur have been proposed in the literature we give a unified presentation of these methods in the light of matrix decompositions of the blurring operator we establish the connection between different computational tricks that can be found in the literature and the physical sense of corresponding approximations in terms of equivalent psfs physically based approximations being preferable we derive an improved approximation that preserves the same desirable low complexity as other fast algorithms while reaching a minimal approximation error comparison of theoretical properties and empirical performances of each blur approximation suggests that the proposed general model is preferable for approximation and inversion of a known shift variant blur

a collapse transition in a directed walk model the authors consider a directed walk model of linear polymers in dilute solution with an energy associated with the number of near neighbour contacts in the walk for this model they can derive an exact expression for the generating function in two variables conjugate to the number of steps and the number of contacts they discuss the analytic structure of this generating function and identify the transition corresponding to collapse

asymptotics semiclassically concentrated on curves for the nonlocal fisher kolmogorov petrovskii piskunov equation in this paper we construct asymptotic solutions for the nonlocal multidimensional fisher kolmogorov petrovskii piskunov equation in the class of functions concentrated on a one dimensional manifold curve using a semiclassical approximation technique we show that the construction of these solutions can be reduced to solving a similar problem for the nonlocal fisher kolmogorov petrovskii piskunov in the class of functions concentrated at a point zero dimensional manifold together with an additional operator condition the general approach is exemplified by constructing a two dimensional two parametric solution which describes quasi steady state patterns on a circumference

transfer matrix study of the adsorption of a flexible self avoiding polymer chain in two dimensions the authors model the polymer as a self avoiding walk on a semi infinite square lattice with an energy contribution in from each step along the lattice boundary the critical adsorption temperature ta and the ordinary and special surface exponents of the walk above and at the adsorption temperature respectively are estimated with transfer matrix finite size scaling methods for the adsorption temperature they obtain exp in kta 2 041 or 0 002 and for the crossover and susceptibility exponents of the special transition phi sp 0 501 or 0 003 and gamma 1sp 1 454 or 0 004

any l state solutions of the hulthen potential in arbitrary dimensions the energy spectra of the hulthen effective potential in d dimensions are obtained within the new quantization rule approach for any l states the interdimensional degeneracies among states are also presented in the case of d 3 the agreement between our results and those obtained by other methods is excellent

analytic solutions for nonlinear waves in coupled reacting systems abstract we analyze a system of reacting elements harmonically coupled to nearest neighbors in the continuum limit an analytic solution is found for traveling waves the procedure is used to find oscillatory as well as solitary waves a comparison is made between exact solutions and solutions of the piecewise linearized system showing how the linearization affects the amplitude and frequency of the solutions

global analysis of pattern selection and bifurcations in monostable reaction diffusion systems we study a piecewise linear version of a one component monostable reaction diffusion model in a bounded domain subjected to partially reflecting boundary conditions albedo b c we analyze the local and the global stability of the merging patterns and detect a bifurcation of the uniform solution induced by changes in the reflectivity of the boundaries

approximate analytical solution of the nonlinear fractional kdv burgers equation in this paper explicit and approximate solutions of the nonlinear fractional kdv burgers equation with time space fractional derivatives are presented and discussed the solutions of our equation are calculated in the form of rabidly convergent series with easily computable components the utilized method is a numerical technique based on the generalized taylor series formula which constructs an analytical solution in the form of a convergent series five illustrative applications are given to demonstrate the effectiveness and the leverage of the present method graphical results and series formulas are utilized and discussed quantitatively to illustrate the solution the results reveal that the method is very effective and simple in determination of solution of the fractional kdv burgers equation

melting and wetting transitions in the three state chiral clock model abstract the melting transition of the two dimensional three state asymmetric or chiral clock model is examined evidence from scaling arguments and analysis of perturbation series is presented indicating that the chiral symmetry breaking operator is relevant at the symmetric or pure potts critical point with a crossover exponent of o 0 2 the remainder of the commensurate disordered phase boundary therefore appears to be in a new universality class distinct from the pure three state potts transition an interfacial wetting transition that plays an important role in the crossover between the two types of critical behavior is discussed the location and exponents of this wetting transition are obtained both in a low temperature limit using generating function techniques and in a systematic low temperature expansion of the transfer matrix

paradox of enrichment a fractional differential approach with memory abstract the paradox of enrichment poe proposed by rosenzweig m rosenzweig the paradox of enrichment science 171 1971 385 387 is still a fundamental problem in ecology most of the solutions have been proposed at an individual species level of organization and solutions at community level are lacking knowledge of how learning and memory modify behavioral responses to species is a key factor in making a crucial link between species and community levels poe resolution via these two organizational levels can be interpreted as a microscopic and macroscopic level solution fractional derivatives provide an excellent tool for describing this memory and the hereditary properties of various materials and processes the derivatives can be physically interpreted via two time scales that are considered simultaneously the ideal equably flowing homogeneous local time and the cosmic inhomogeneous non local time several mechanisms and theories have been proposed to resolve the poe problem but a universally accepted theory is still lacking because most studies have focused on local effects and ignored non local effects which capture memory here we formulate the fractional counterpart of the rosenzweig model and analyze the stability behavior of a system we conclude that there is a threshold for the memory effect parameter beyond which the rosenzweig model is stable and may be used as a potential agent to resolve poe from a new perspective via fractional differential equations

hurst exponents for interacting random walkers obeying nonlinear fokker planck equations abstract anomalous diffusion of random walks has been extensively studied for the case of non interacting particles here we study the evolution of nonlinear partial differential equations by interpreting them as fokker planck equations arising from interactions among random walkers we extend the formalism of generalized hurst exponents to the study of nonlinear evolution equations and apply it to several illustrative examples they include an analytically solvable case of a nonlinear diffusion constant and three nonlinear equations which are not analytically solvable the usual fisher equation which contains a quadratic nonlinearity a generalization of the fisher equation with density dependent diffusion constant and the nagumo equation which incorporates a cubic rather than a quadratic nonlinearity we estimate the generalized hurst exponents

statistical mechanical considerations in the theory of the spread of the hantavirus abstract calculations in the theory of the spread of epidemics are described with particular focus on the estimation of motion parameters describing rodents that are the carriers of the hantavirus epidemic the data considered are of the mark recapture kind i e those collected by capturing tagging and recapturing the animals in a prescribed finite region of space the theoretical tool used is the fokker planck equation its characteristic quantities being the diffusion constant which describes the motion of the rodents and the attractive potential which addresses their tendency to live near their burrows the measurements are addressed through simple analytical calculations of the mean squared displacement of the animals relevant to the specific probing window in space corresponding to the trapping region a fourier prescription is provided to extract the home range of the animals from the observations applications of the theory to rodent movement in panama and new mexico are mentioned and several on going generalizations of current models of hantavirus epidemic spread are introduced

on the new fractional derivative and application to nonlinear fisher s reaction diffusion equation recently caputo and fabrizio introduced a new derivative with fractional order in this paper we presented useful tools about the new derivative and applied it to the nonlinear fisher s reaction diffusion equation we presented the solution of the modified equation using the notion of iterative method using the theory of fixed point we presented the stability of the used method some numerical simulations were presented for different values of fractional order

the embedding e0 and the spectrum dependent r matrix for q f4 the explicit embedding forms of e0 for the minimal representations of the quantum f4 e6 and e7 are obtained in this paper in terms of jimbo s method the spectrum dependent r matrices both trigonometric and rational for those representations are computed

numerical solution of a biological population model using he s variational iteration method this paper presents numerical solution of a degenerate parabolic equation arising in the spatial diffusion of biological populations the variational iteration method and adomian decomposition method are used for solving this equation and then numerical results are compared with each other showing that the variational iteration method leads to more accurate results furthermore variational iteration method overcomes the difficulty arising in calculating the adomian s polynomials which is an important advantage over the adomian decomposition method

results from variants of the fisher equation in the study of epidemics and bacteria the fisher equation which combines di usive motion of individuals with nonlinearities arising from their growth and competition processes is analyzed generalized and applied to the dynamics of bacteria pattern formation and the spread of epidemics analytic solutions are also presented for some exactly soluble and physically relevant variants of the equation c

collapsing and adsorbing polygons the adsorption transition in the phase diagram of a self interacting lattice polygon is examined the polygon has a nearest neighbour contact fugacity and the interaction between the polygon and an impenetrable wall is modelled by a visit fugacity which is conjugate to the number of vertices of the polygon incident with the wall the partition function of this model is z c y z d p v cp c v c y v z c where p c v c is the number of polygons with c nearest neighbour contacts v visits to the wall and n edges and counted up to translations parallel to the wall the limiting free energy of this model is f c y z d limn 1 1 logz c y z and it is known to be a non analytic function of y for each z 1 for all z2 0 1

canonically modified nose hoover equation with explicit inclusion of the virial the nos e hoover equation has recently been introduced to simulate in a deterministic and reversible way the equilibrium properties of a system at constant temperature however for many one dimensional potentials such as the harmonic oscillator the nos e hoover scheme is not adequate since the dynamics is not sufficiently ergodic we present modifications of the nos e hoover equation in which the kinetic energy and the virial are treated in an equivalent manner and which explicitly include the virial within a canonical framework we show that these modifications can yield an adequate statistical description for one dimensional potentials such as the double well and harmonic oscillator

local magnetization of the two dimensional ising model near the phase boundary abstract we study the two dimensional ising model on a square lattice with bonds which differ on the two sides of the column of the defect vertical couplings we compute exactly the local magnetization near the defect column we also show explicitly that near the critical point the magnetization has the scaling form we calculate the asymptotic behaviour of the scaling function in the different special cases

nonlocal competition and logistic growth patterns defects and fronts logistic growth of diffusing reactants on spatial domains with long range competition is studied the bifurcations cascade involved in the transition from the homogeneous state to a spatially modulated stable solution is presented and a distinction is made between a modulated phase dominated by single or few wave numbers and the spiky phase where localized colonies are separated by depleted region the characteristic defects in the periodic structure are presented for each phase together with the invasion dynamics in the case of local initiation it is shown that the basic length scale that controls the bifurcation is the width of the fisher front and that the total population grows as this width decreases a mix of analytic results and extensive numerical simulations yields a comprehensive examination of the possible phases for logistic growth in the presence of nonlocal competition

effects of transport memory and nonlinear damping in a generalized fisher s equation memory effects in transport require for their incorporation into reaction diffusion investigations a generalization of traditional equations the well known fisher s equation which combines diffusion with a logistic nonlinearity is generalized to include memory effects and traveling wave solutions of the equation are found comparison is made with alternative generalization procedures

pseudospectral method for fisher equation in a disk abstract in this paper we develop a mixed jacobi fourier pseudospectral method for solving the fisher equation in a disc fisher s equation always plays a large role in many fields such as logistic population growth models tissue engineering nuclear reactions and neurophysiology etc it is very important to study how to solve these equations numerically in this work we employ the generalized jacobi approximation to simulate the singularity of solutions at the regional center some mixed jacobi fourier interpolation approximation results are established which play important roles in numerical simulation of various problems defined in a disc as an application the mixed jacobi fourier pseudospectral scheme is provided for the fisher equation in a disk the generalized stability and convergence of the proposed scheme are proved some numerical results are presented to demonstrate the efficiency of this new algorithm

finite difference spectral approximations for the time fractional diffusion equation in this paper we consider the numerical resolution of a time fractional diffusion equation which is obtained from the standard diffusion equation by replacing the first order time derivative with a fractional derivative of order a with 0 a 1 the main purpose of this work is to construct and analyze stable and high order scheme to efficiently solve the time fractional diffusion equation the proposed method is based on a finite difference scheme in time and legendre spectral methods in space stability and convergence of the method are rigourously established we prove that the full discretization is unconditionally stable and the numerical solution converges to the exact one with order o dt 2 a n m where dt n and m are the time step size polynomial degree and regularity of the exact solution respectively numerical experiments are carried out to support the theoretical claims

theory of nonstationary linear filtering in the fourier domain with application to time variant filtering a general linear theory describes the extension of the convolutional method to nonstationary processes this theory can apply any linear nonstationary filter with arbitrary time and frequency variation in the time fourier or mixed domains the filter application equations and the expressions to move the filter between domains are all ordinary fourier transforms or generalized convolutional integrals nonstationary transforms such as the wavelet transform are not required there are many possible applications of this theory including the one way propagation of waves through complex media time migration normal moveout removal time variant filtering and forward and inverse q filtering two complementary nonstationary filters are developed by generalizing the stationary convolution integral the first called nonstationary convolution corresponds to the linear superposition of scaled impulse responses of a nonstationary filter the second called nonstationary combination does not correspond to such a superposition but is shown to be a linear process capable of achieving arbitrarily abrupt temporal variations in the output frequency spectrum both extensions have stationary convolution as a limiting form and in the discrete case can be formulated as matrix operations fourier transformation shows that both filter types are nonstationary filter integrals in the fourier domain as well this result is a generalization of the convolution theorem for stationary signals because as the filter becomes stationary in one domain the integral in the other domain collapses to a scalar multiplication for discrete signals stationary filters are a matrix multiplication of the input signal spectrum by a diagonal spectral matrix while nonstationary filters require off diagonal terms for quasi stationary filters a computational advantage is obtained by computing only the significant terms near the diagonal unlike stationary theory a mixed domain of time and frequency is also possible in this context the nonstationary filter is applied simultaneously with the transform from time to frequency or the reverse nonstationary convolution becomes a generalized forward fourier integral and nonstationary combination is a generalized inverse fourier integral

a novel expansion iterative method for solving linear partial differential equations of fractional order in this manuscript we implement a relatively new analytic iterative technique for solving time space fractional linear partial differential equations subject to given constraints conditions based on the generalized taylor series formula the solution methodology is based on generating the multiple fractional power series expansion solution in the form of a rapidly convergent series with minimum size of calculations this method can be used as an alternative to obtain analytic solutions of different types of fractional linear partial differential equations applied in mathematics physics and engineering some numerical test applications were analyzed to illustrate the procedure and to confirm the performance of the proposed method in order to show its potentiality generality and accuracy for solving such equations with different constraints conditions numerical results coupled with graphical representations explicitly reveal the complete reliability and efficiency of the suggested algorithm

memory controlled diffusion memory effects require for their incorporation into random walk models an extension of the conventional equations the linear fokker planck equation for the probability density p stackrel p vec r t is generalized by including nonlinear and nonlocal spatial temporal memory effects the realization of the memory kernel is restricted due the conservation of the basic quantity p a general criteria is given for the existence of stationary solutions in case the memory kernel depends on p polynomially transport may be prevented owing to the delay effects a finite amount of particles remains localized and the further transport is terminated for diffusion with nonlinear memory effects we find an exact solution in the long time limit although the mean square displacement exhibits diffusive behavior higher order cumulants offer differences to diffusion and they depend on the memory strength

revisited fisher s equation in a new outlook a fractional derivative approach abstract the well known fisher equation with fractional derivative is considered to provide some characteristics of memory embedded into the system the modified model is analyzed both analytically and numerically a comparatively new technique residual power series method is used for finding approximate solutions of the modified fisher model a new technique combining sinc collocation and finite difference method is used for numerical study the abundance of the bird species phalacrocorax carbois considered as a test bed to validate the model outcome using estimated parameters we conjecture non diffusive and diffusive fractional fisher equation represents the same dynamics in the interval memory index 0 8384 0 9986 we also observe that when the value of memory index is close to zero the solutions bifurcate and produce a wave like pattern we conclude that the survivability of the species increases for long range memory index these findings are similar to fisher observation and act in a similar fashion that advantageous genes do

an electrothermal instability the influence of albedo boundary conditions on the stationary states of an exactly solvable model abstract in order to study the effect of partially reflective albedo boundary conditions on pattern formation and stability in reaction diffusion systems we have analyzed an exactly soluble model of an electrothermal instability the ballast resistor the present results allow a continuous interpolation between the results corresponding to neumann and dirichlet boundary conditions and they allow qualitative changes in the patterns to be followed

higher dimensional localized patterns in excitable media abstract the excitable reaction diffusion equation model of the form e u t e 2 2 u u v v t 2 v u v is considered when u is assumed to be of mckean s piecewise linear type the interfacial approach can be applied to the stability of various localized patterns in higher dimensional spaces it is shown that a band shaped localized pattern is destabilized into a zig zag mode or a varicose mode and that a disk shaped localized pattern is destabilized into static modes and when is small into an oscillatory mode like a breather motion numerical simulations are performed to confirm such destabilizations for more general nonlinear functions u

non hermitian localization and population biology the time evolution of spatial fluctuations in inhomogeneous d dimensional biological systems is analyzed a single species continuous growth model in which the population disperses via diffusion and convection is considered time independent environmental heterogeneities such as a random distribution of nutrients or sunlight are modeled by quenched disorder in the growth rate linearization of this model of population dynamics shows that the fastest growing localized state dominates in a time proportional to a power of the logarithm of the system size using an analogy with a schr odinger equation subject to a constant imaginary vector potential we propose a delocalization transition for the steady state of the nonlinear problem at a critical convection threshold separating localized and extended states in the limit of high convection velocity the linearized growth problem in d dimensions exhibits singular scaling behavior described by a d ensuremath 1 dimensional generalization of the noisy burgers equation with universal singularities in the density of states associated with disorder averaged eigenvalues near the band edge in the complex plane the burgers mapping leads to unusual transverse spreading of convecting delocalized populations

fast space varying convolution using matrix source coding with applications to camera stray light reduction many imaging applications require the implementation of space varying convolution for accurate restoration and reconstruction of images here we use the term space varying convolution to refer to linear operators whose impulse response has slow spatial variation in addition these space varying convolution operators are often dense so direct implementation of the convolution operator is typically computationally impractical one such example is the problem of stray light reduction in digital cameras which requires the implementation of a dense space varying deconvolution operator however other inverse problems such as iterative tomographic reconstruction can also depend on the implementation of dense space varying convolution while space invariant convolution can be efficiently implemented with the fast fourier transform this approach does not work for space varying operators so direct convolution is often the only option for implementing space varying convolution in this paper we develop a general approach to the efficient implementation of space varying convolution and demonstrate its use in the application of stray light reduction our approach which we call matrix source coding is based on lossy source coding of the dense space varying convolution matrix importantly by coding the transformation matrix we not only reduce the memory required to store it we also dramatically reduce the computation required to implement matrix vector products our algorithm is able to reduce computation by approximately factoring the dense space varying convolution operator into a product of sparse transforms experimental results show that our method can dramatically reduce the computation required for stray light reduction while maintaining high accuracy

difference equations in statistical mechanics ii solid on solid models in two dimensions a review and some new results are presented for the solid on solid models of wetting in two dimensions i e line interfaces with an emphasis on the difference equations arising in the transfer matrix calculations for these models methods for solving the appropriate difference equations exactly or approximately are surveyed including specific results for short range long range power law and applied field like binding external potentials

finite length scaling of collapsing directed walks we study the finite length scaling of self interacting partially directed self avoiding walks utilising enumeration data up to a total length of 6000 steps this facilitates the evaluation of the numerical techniques available for calculating exponents at the point and in the collapsed phase of walk type models another consequence is the conjecture of a new scaling theory for the collapsed region of the phase diagram and the suggestion that this should be applicable to the wider range of undirected problems including interacting saw we provide a phenomenological picture of the phase transition in terms of the condensation of droplets that allows us to understand the various length scales involved in the problem pacs numbers 05 50 q 05 70 fh 61 41 e email prel aleks brak tonyg mundoe maths mu oz au

exact solutions for heat like and wave like equations with variable coefficients in this paper adomian decomposition method is presented for solving heat like and wave like models with variable coefficients the method is demonstrated for a variety of problems in one and higher dimensional spaces where exact solutions are obtained the results obtained in all cases show the reliability and the efficiency of this method

necklace solid on solid models of interfaces and surfaces using the exact generating functions for solid on solid models the authors construct necklace partition functions for wetting and prewetting at a sticky wall in two bulk dimensions three component generalisations of these models constructed to study interfacial wetting are introduced and solved based on these models they discuss the types of interfacial critical behaviour to be expected in three component systems in two dimensions

exact solution of the discrete 1 1 dimensional sos model with field and surface interactions we present the solution of a linear solid on solid sos model configurations are partially directed walks on a two dimensional square lattice and we include a linear surface tension a magnetic field and surface interaction terms in the hamiltonian there is a wetting transition at zero field and as expected the behavior is similar to a continuous model solved previously the solution is in terms ofq series most closely related to theq hypergeometric functions1 1

population persistence in weakly coupled sinks abstract we consider a single species population obeying a saturated growth model with spatial diffusion taken into account explicitly strong spatial heterogeneity is considered represented by a position dependent reproduction rate the geometry of the problem is that of two patches where the reproductive rate is positive surrounded by unfavorable patches where it is negative we focus on the particular case where the population would not persist in the single patches sinks we find by means of an analytical derivation supplemented by a numerical calculation the conditions for the persistence of the population in the compound system of weakly connected patches we show that persistence is possible even if each individual patch is a sink where the population would go extinct the results are of particular relevance for ecological management at the landscape level showing that small patches may harbor populations as long as the connectivity with adjacent patches is maintained microcosmos experiences with bacteria could be performed for experimental verification of the predictions

delay asymptotic solutions for the time fractional delay type wave equation abstract a new version of the wave equation endowed with time fractional derivative and multiple time delays is considered a new form of the generalized maclaurin fractional series is suggested to extract analytical solution of the model graphical investigations on the relation between the fractional derivative and the time delay are established finally we reported some remarks regarding the new model

pattern formation in terms of semiclassically limited distribution on lower dimensional manifolds for the nonlocal fisher kolmogorov petrovskii piskunov equation we have investigated the pattern formation in systems described by the nonlocal fisher kolmogorov petrovskii piskunov equation for the cases where the dimension of the pattern concentration domain is lower than that of the domain of independent variables we have obtained a system of integro differential equations which describe the dynamics of the concentration domain and the semiclassically limited density distribution for a pattern in the class of trajectory concentrated functions also asymptotic large time solutions have been obtained that describe the semiclassically limited distribution for a quasi steady state pattern on the concentration manifold the approach is illustrated by an example for which the analytical solution is in good agreement with the results of numerical calculations

isolation effects in a system of two mutually communicating identical patches abstract starting from the fisher kolmogorov petrovskii piskunov equation fkpp we model the dynamic of a diffusive system with two mutually communicating identical patches and isolated of the remaining matrix for this system we find the minimal size of each fragment in the explicit form and compare with the explicit results for similar problems found in the literature from this comparison emerges an unexpected result that for a same set of the parameters the isolated system studied in this work with size l can be better or worst than the non isolated systems with the same size l uniquely depending on the parameter a 0 internal conditions of the patches due to the fact that this result is unexpected we propose an experimental verification

infinitely many symmetries of the davey stewartson equation using a formal series symmetry method for the davey stewartson equation dse we find that there exist two sets of infinitely many formal series symmetries of the dse however different from the kadomtsev petviashvili equation kpe we failed to get infinitely many truncated symmetries only six truncated symmetries can be obtained simply from the formal series symmetries

the yukawa and hulthen potentials in quantum mechanics the concept of kinetic potentials is used to construct a global geometrical approximation theory for the spectra of schrodinger operators h delta vy in which the potential shape y is either i a transformation y r g h r of a soluble potential h r or ii a continuous mixture y r integral rho t h rt dt the case in which y is the yukawa potential and h er 1 1 is the hulthen potential is discussed in detail simple formulae are derived for eigenvalue bounds which are compared to accurate data obtained by the direct numerical integration of schrodinger s equation

arbitrary nonlinearities in convective population dynamics with small diffusion convective counterparts of variants of the nonlinear fisher equation which describes reaction diffusion systems in population dynamics are studied with the help of an analytic prescription and shown to lead to interesting consequences for the evolution of population densities the initial value problem is solved explicitly for some cases and for others it is shown how to find traveling wave solutions analytically the effect of adding diffusion to the convective equations is first studied through exact analysis through a piecewise linear representation of the nonlinearity using an appropriate small parameter suggested by that analysis a perturbative treatment is developed to treat the case in which the convective evolution is augmented by a small amount of diffusion

a geometrical theory of energy trajectories in quantum mechanics suppose f r is an attractive central potential of the form f r ki 1 g i f i r where f i is a set of basis potentials powers log hulthen sech2 and g i is a set of smooth increasing transformations which for a given f are either all convex or all concave formulas are derived for bounds on the energy trajectories enl fnl v of the hamiltonian h vf r where v is a coupling constant the transform f f is carried out in two steps f f f where f s is called the kinetic potential of f and is defined by f s inf f subject to d l2 r3 where d is the domain of h 1 and s a table is presented of the basis kinetic potentials f i s the general trajectory bounds f v are then shown to be given by a legendre transformation of the form s f s v f v where f s ki 1g i f i s and f v mins 0 s v f s with the aid of this potential construction set a kind of schrodinger lego ground state trajectory bounds are derived for a vari

kinetic potentials in quantum mechanics suppose that the hamiltonian h vf r represents the energy of a particle which moves in an attractive central potential and obeys nonrelativistic quantum mechanics the discrete eigenvalues enl fnl v of h may be expressed as a legendre transformation fnl v mins 0 s vfnl s n 1 2 3 l 0 1 2 where the kinetic potentials fnl s associated with f r are defined by fnl s infdnl sup dnl 1 r f s 1 2r r d3r and dnl is an n dimensional subspace of l2 r3 labeled by ylm m 0 and contained in the domain d h of h if the potential has the form f r ni 1 g i f i r then in many interesting cases it turns out that the corresponding kinetic potentials can be closely approximated by ni 1 g i fnl i s this nice behavior of the kinetic potentials leads to a constructive global approximation theory for schrodinger eigenvalues as an illustration detailed recipes are provided for arbitrary linear combinations of power law potentials and the log potential fo

stochastic skellam model abstract we consider the dynamics of a biological population described by the fisher kolmogorov petrovskii piskunov fkpp equation in the case where the spatial domain consists of alternating favorable and adverse patches whose sizes are distributed randomly for the one dimensional case we define a stochastic analogue of the classical critical patch size we address the issue of persistence of a population and we show that the minimum fraction of the length of favorable segments to the total length is always smaller in the stochastic case than in a periodic arrangement in this sense spatial stochasticity favors viability of a population

renormalization group solutions for yukawa potential the self similar renormalization group is used to obtain expressions for the spectrum of the hamiltonian with the yukawa potential the critical screening parameter above which there are no bound states is also obtained by this method the approach presented illustrates that one can achieve good accuracy without involving extensive numerical calculations but invoking instead the renormalization group techniques

phenomenological renormalisation of the self avoiding walk in two dimensions phenomenological renormalisation is used to calculate the exponent v and the connective constant of the self avoiding walk problem on a square lattice a transfer matrix technique is developed for the polymer problem the results indicate that flory s value v 0 75 is true in two dimensions to extremely high accuracy

berry phases for the nonlocal gross pitaevskii equation with a quadratic potential a countable set of asymptotic space localized solutions is constructed by the complex germ method in the adiabatic approximation for the nonstationary gross pitaevskii equation with nonlocal nonlinearity and a quadratic potential the asymptotic parameter is 1 t where t 1 is the adiabatic evolution time a generalization of the berry phase of the linear schrodinger equation is formulated for the gross pitaevskii equation for the solutions constructed the berry phases are found in explicit form

spatial organization of vegetation arising from non local excitation with local inhibition in tropical rainforests abstract the janzen connell jc effect which hypothesizes that recruitment and growth of seedlings is positively correlated to the distance from the parent tree is shown to generate highly organized vegetation biomass spatial patterns when coupled to a revised fisher kolmogorov fk equation spatial organization arises through a novel mechanism of non local activation and local inhibition over a single generation the revised fk model calculations predict a hen and chicks dynamic pattern with mature trees surrounded by new seedlings growing at characteristic spatial distances in agreement with field data over longer timescales the importance of stochastic dynamics such as those associated with randomly occurring light gaps increase thereby causing a substantial deviation between predictions from the deterministic fk model and its stochastic counterpart derived to account for such random disturbances at still longer timescales however statistical measures of the spatial organization specifically the spatial density of mature trees and their minimum spacing converge between these two model representations

asymptotic properties of eigenvalues in variational calculations for double well oscillators simple and accurate formulae for the eigenvalues of the hamiltonian with an anharmonic double well potential are presented special attention is paid to the following three regions of coupling parameters where difficulties arise i in the weak coupling limit the eigenvalues depend on the coupling parameter nonanalytically to obtain accurate explicit expressions in this limit a composite asymptotic expansion is applied ii in the strong coupling limit the derivation of asymptotic expansions is obstructed by the nonuniqueness of solutions to variational equations to overcome this obstacle a restricted variational procedure is suggested iii there exist also critical values of the coupling parameter at which eigenvalues cross zero in the regions around these critical values a dramatic increase of the percentage error occurs a remedy against this critical behaviour is the positive definite shift removing the critical regions the formulae obtained for the eigenvalues provide an accuracy within the errors not exceeding 3 for all values of the coupling parameter from zero to infinity

a fast algorithm for convolution integrals with space and time variant kernels mathematical models in many fields of the physical sciences involve nonlocal terms which are formally similar to convolution integrals we show that it is possible to approximate a particular class of such integrals which by themselves are not convolutions as a linear combination of convolution integrals allowing for their efficient numerical computation as an o n log n process

refining the comparison theorem of quantum mechanics if two potentials v1 x and v2 x are ordered v1 v2 then the comparison theorem tells the author that the corresponding schrodinger eigenvalues are ordered e1 e2 he presents some simple conditions which allow him to predict such spectral ordering for the ground state even when the graphs of the potentials cross over as illustrations the truncated quartic oscillator and the yukawa potential are studied by allowing coulomb tangents to cross over the yukawa in various ways he is able to improve earlier energy upper bounds which he had obtained by representing the yukawa potential as a smooth transformation of the coulomb potential and also to augment these results with lower bounds

periodic solutions of nonlocal semilinear fourth order differential equations abstract in this paper we study the existence of periodic solutions with prescribed wavelength for two classes of nonlocal fourth order nonautonomous differential equations existence of nontrivial solutions for the first equation is proved using clark s theorem existence of nontrivial solutions for the second equation is proved using the symmetric mountain pass theorem

on quantum deformations of the simplest lie parasuperalgebra quantum deformations of the simplest lie parasuperalgebra psqm 2 are constructed by taking advantage of the well known representations of suq 2 c as a particular result the authors show that the fundamental witten superalgebra sqm 2 cannot be deformed

self consistent screening approximation for critical dynamics we generalize bray s self consistent screening approximation to describe the critical dynamics of the theory in order to obtain the dynamical exponent z we have to make an ansatz for the form of the scaling functions which fortunately can be restricted by general arguments numerical values of z for d 3 and n 1 10 are obtained using two different ansatz and differ by a very small amount in particular the value of obtained for the three dimensional ising model agrees well with recent monte carlo simulations

two dimensional self avoiding walk with hydrogen like bonding phase diagram and critical behaviour the phase diagram for a two dimensional self avoiding walk model on the square lattice incorporating attractive short ranged interactions between parallel sections of walk is derived using numerical transfer matrix techniques the model displays a collapse transition in contrast to the standard point model the transition is first order the phase diagram in the full fugacity temperature plane displays an additional transition line when compared to the point model as well as a critical transition at finite temperature in the hamiltonian walk limit

applicability of the fisher equation to bacterial population dynamics the applicability of the fisher equation which combines diffusion with logistic nonlinearity to population dynamics of bacterial colonies is studied with the help of explicit analytic solutions for the spatial distribution of a stationary bacterial population under a static mask the mask protects bacteria from ultraviolet light the solution which is in terms of jacobian elliptic functions is used to provide a practical prescription to extract fisher equation parameters from observations and to decide on the validity of the fisher equation

interface properties of the two dimensional blume emery griffiths model the authors study the interface behaviour of the two dimensional blume emery griffiths model 1971 which is described by the hamiltonian h j sigma ij sisj k sigma ij si2sj 2 d sigma isi2 si 1 0 1 an interface is introduced into the system by fixing the spins on opposite boundaries in two different states 1 and 1 they pay particular attention to the appearance of an excess of the third state 0 in the vicinity of the interface the net adsorption of the non boundary state is studied near critical first order and tricritical transitions two methods have been used to attack this problem the monte carlo technique and a modified version of the interface free energy approximation of muller hartmann and zittartz 1977 which is seen to give a surprisingly good description of interface properties in three state systems

swarming patterns in a two dimensional kinematic model for biological groups we construct a continuum model for the motion of biological organisms experiencing social interactions and study its pattern forming behavior the model takes the form of a conservation law in two spatial dimensions the social interactions are modeled in the velocity term which is nonlocal in the population density and includes a parameter that controls the interaction length scale the dynamics of the resulting partial integrodifferential equation may be uniquely decomposed into incompressible motion and potential motion for the purely incompressible case the model resembles one for fluid dynamical vortex patches there exist solutions which have constant population density and compact support for all time numerical simulations produce rotating structures which have circular cores and spiral arms and are reminiscent of naturally observed phenomena such as ant mills the sign of the social interaction term determines the direction of the rotation and the interaction length scale affects the degree o

the monge metric on the sphere and geometry of quantum states topological and geometrical properties of the set of mixed quantum states in the n dimensional hilbert space are analysed assuming that the corresponding classical dynamics takes place on the sphere we use the vector su 2 coherent states and the generalized husimi distributions to define the monge distance between two arbitrary density matrices the monge metric has a simple semiclassical interpretation and induces a non trivial geometry among all pure states the distance from the maximally mixed state proportional to the identity matrix admits the largest value for the coherent states while the delocalized chaotic states are close to this contrasts the geometry induced by the standard trace hilbert schmidt or bures metrics for which the distance from is the same for all pure states we discuss possible physical consequences including unitary time evolution and the process of decoherence we introduce also a simplified monge metric defined in the space of pure quantum states and more suitable for numerical computation

recursive formulae for the analytic solution of the nonlinear spatial conformable fractional evolution equation abstract nonlinear evolution equations nees are very important partial differential equations in nonlinear physics optics and engineering in this article we apply the residual power series rps method to the initial value problem of the nonlinear spatial conformable fractional evolution equations coefficients of the analytic solution are computed by recursive formulae and the famous nonlinear spatial conformable fractional fisher equation is taken as an example to verify this method direct computations demonstrate the correctness of the recursive formulae meanwhile the recursive formulae can be easily implemented by mathematical software

interacting partially directed walks a model of polymer collapse abstract a survey of the results that have been obtained to date on the partially directed walk model of the polymer collapse transition is presented

species survival and scaling laws in hostile and disordered environments in this work we study the likelihood of survival of single species in the context of hostile and disordered environments population dynamics in this environment as modeled by the fisher equation is characterized by negative average growth rate except in some random spatially distributed patches that may support life in particular we are interested in the phase diagram of the survival probability and in the critical size problem i e the minimum patch size required for surviving in the long time dynamics we propose a measure for the critical patch size as being proportional to the participation ratio of the eigenvector corresponding to the largest eigenvalue of the linearized fisher dynamics we obtain the extinction survival phase diagram and the probability distribution function pdf of the critical patch sizes for two topologies namely the one dimensional system and the fractal peano basin we show that both topologies share the same qualitative features but the fractal topology requires higher spatial fluctuations to guarantee species survival we perform a finite size scaling and we obtain the associated scaling exponents in addition we show that the pdf of the critical patch sizes has an universal shape for the 1d case in terms of the model parameters diffusion growth rate etc in contrast the diffusion coefficient has a drastic effect on the pdf of the critical patch sizes of the fractal peano basin and it does not obey the same scaling law of the 1d case