a greedy randomized adaptive search procedure for maximum independent set an efficient randomized heuristic for a maximum independent set is presented the procedure is tested on randomly generated graphs having from 400 to 3 500 vertices and edge probabilities from 0 2 to 0 9 the heuristic can be implemented trivially in parallel and is tested on an mimd computer with 1 2 4 and 8 processors computational results indicate that the heuristic frequently finds the optimal or expected optimal solution in a fraction of the time required by implementations of simulated annealing tabu search and an exact partial enumeration method

similarity solutions for unsteady free convection flow from a continuous moving vertical surface the transformation group theoretic approach is applied to present an analysis of the problem of unsteady free convection flow over a continuous moving vertical sheet in an ambient fluid the thermal boundary layer induced within a vertical semi infinite layer of boussinseq fluid by a constant heated bounding plate the application of two parameter groups reduces the number of independent variables by two and consequently the system of governing partial differential equations with the boundary conditions reduces to a system of ordinary differential equations with appropriate boundary conditions the obtained ordinary differential equations are solved analytically for the temperature and numerically for the velocity using the shooting method effect of prandtl number on the thermal boundary layer and velocity boundary layer are studied and plotted in curves

intraband discrete breathers in disordered nonlinear systems ii localization abstract we find spatially localized time periodic solutions discrete breathers or dbs in disordered nonlinear systems with frequency inside the linear phonon spectrum under conditions that strictly prohibit their existence in their periodic counterparts for that purpose we develop a new in situ method for the accurate calculation of these solutions which does not make use of any continuation from an anticontinuous limit using this method we demonstrate that intraband localized modes intraband discrete breathers or idbs at a given site with frequencies inside the discrete linear spectrum do exist provided these frequencies do not belong to forbidden resonance gaps since there is a dense set of resonant frequencies we illustrate numerically in agreement with a theorem by albanese and frohlich that the localized dbs exist provided that their frequencies belong to fat cantor sets i e with finite measure such a set contains as accumulation points the linear frequency of the normal mode at the occupied site we check that many of these solutions are linearly stable and conjecture that their frequency belongs to another smaller fat cantor set our numerical methods provide a much wider set of exact solutions which are multisite breathers and suggest conjectures extending the existing theorems the physical implications of the existence of idbs and possible applications for glasses and the persistent spectral hole burning are discussed

group similarity solutions of the lax pair for a generalized hirota satsuma equation a modified version of generalized hirota satsuma is here analytically solved using a two parameter group transformation method we here through a group symmetry transformation reduce its lax pair to a system of ordinary equations and find new solutions three similarity transformation variables are investigated for each case an analytical solution is obtained through a homogenous balance of terms in the reduced lax pair the obtained results are plotted and show a profile proper to deflagration processes well described by degasperis procesi equation

subdiffusion in the nonlinear schrodinger equation with disorder the nonlinear schrodinger equation in the presence of disorder is considered the dynamics of an initially localized wave packet is studied a subdiffusive spreading of the wave packet is explained in the framework of a continuous time random walk a probabilistic description of subdiffusion is suggested and a transport exponent of subdiffusion is obtained to be 2 5

intrinsic localized modes discrete breathers existence and linear stability we present some examples of detailed analysis of intrinsic localized modes in lattices using the accurate numerical methods derived from the proof of existence of mackay aubry we report on some improvements on the methods which are then used to the fullest to obtain the floquet analysis of the breather solutions such calculations are possible taking into account the whole lattice without any approximations this yields an unprecedented detail of the mechanisms that govern instabilities in discrete breathers giving a complete picture of the interplay between localized internal and extended phonon like instabilities copyright 1998 elsevier science b v

localization length of stationary states in the nonlinear schrodinger equation for the nonlinear schrodinger equation nlse in the presence of disorder exponentially localized stationary states are found we demonstrate analytically that the localization length is typically independent of the strength of the nonlinearity and is identical to the one found for the corresponding linear equation the analysis makes use of the correspondence between the stationary nlse and the langevin equation as well as of the resulting fokker planck equation the calculations are performed for the white noise random potential and an exact expression for the exponential growth of the eigenstates is obtained analytically it is argued that the main conclusions are robust

analysis of 3 1 dimensional boitileonmannapempinelli equation via lax pair investigation and group transformation method singular manifolds method smm is utilized to detect the lax pair and bcklund transformation of 3 1 dimensional boitileonmannapempinelli blmp equation an extension of group transformation method with three parameters is exploited in transforming the lax pair directly to a system of ordinary differential equations odes two cases of similarity variables are considered resulting in solvable systems of odes new analytical solutions are attained and graphed containing some soliton waves some of these solutions are applicable of plasma explosions and fluid dynamics both of investigation of lax pair of 3 1 dimensional evolution equations and three parameters group method are seldom utilized in this kind of evolution equations

an analysis of network location problems with distance constraints this paper concerns a class of network location problems with minimum or maximum separation requirements between uncapacitated facilities or between demand points and the facilities or both its purpose is three fold first it is to recognize distance constraints as increasing real life restrictions through various motivating illustrations using a new classification scheme the paper introduces a variety of distance constrained problems defined in a unified manner these include a number of new problems second it is to survey existing solution techniques available only for a few of such constrained problems finally it is to shed some light on yet unstudied problems by exploring possible extensions of some of the known solution techniques or discussing varying degrees of difficulties involved in particular the paper presents integer programming formulations of several new problems along with the results of applying linear programming relaxation methods although the computational experience is somewhat disappointing for some of these problems the results provide greater insight into the problems with the stated purpose it is hoped that this paper will stimulate future research in this important problem area

the equitable dispersion problem most optimization problems focus on efficiency based objectives given the increasing awareness of system inequity resulting from solely pursuing efficiency we conceptualize a number of new element based equity oriented measures in the dispersion context we propose the equitable dispersion problem that maximizes the equity among elements based on the introduced measures in a system defined by inter element distances given the proposed optimization framework we develop corresponding mathematical programming formulations as well as their mixed integer linear reformulations we also discuss computational complexity issues related graph theoretic interpretations and provide some preliminary computational results

on the unified dispersion problem efficient formulations and exact algorithms abstract facility dispersion problems involve placing a number of facilities as far apart from each other as possible four different criteria of facility dispersal have been proposed in the literature erkut neuman 1991 despite their formal differences these four classic dispersion objectives can be expressed in a unified model called the partial sum dispersion model lei church 2013 in this paper we focus on the unweighted partial sum dispersion problem and introduce an efficient formulation for this generalized dispersion problem based on a construct by ogryczak and tamir 2003 we also present a fast branch and bound based exact algorithm

nonlinearity effects on conductance statistics in one dimensional disordered systems abstract we investigate numerically the effect of non linear interaction on conductance statistics in one dimensional disordered systems with peak potentials it is shown that the non linearity can either localize or delocalize the electronic states depending on its sign for an attractive nonlinear interaction we found that the mean conductance decays as g l the exponent is found to be sensitive to the kind of the potential it seems to be independent of the strength of the non linearity in the case of disordered barrier potentials while it varies with this strength for well and mixed potentials the conductance probability distribution shows a deviation from its log normal form linear case when the nonlinearity is increased and the fluctuations of conductance decrease indicating the delocalization of the eigenstates

subdiffusion in classical and quantum nonlinear schrdinger equations with disorder the review is concerned with the nonlinear schrdinger equation nlse in the presence of disorder disorder leads to localization in the form of the localized anderson modes am while nonlinearity is responsible for the interaction between the ams and transport the dynamics of an initially localized wave packets are concerned in both classical and quantum cases in both cases there is a subdiffusive spreading which is explained in the framework of a continuous time random walk ctrw and it is shown that subdiffusion is due to the transitions between those ams which are strongly overlapped this overlapping being a common feature of both classical and quantum dynamics leads to the clustering with an effective trapping of the wave packet inside each cluster therefore the dynamics of the wave packet corresponds to the ctrw where the basic mechanism of subdiffusion is an entrapping of the wave packet with delay or waiting times distributed by the power law w t 1 t1 where is the transport exponent it is obtained that 1 3 for the classical nlse and 1 2 for the quantum nlse

dynamics of wave packets for the nonlinear schrodinger equation with a random potential the dynamics of an initially localized anderson mode is studied in the framework of the nonlinear schrodinger equation in the presence of disorder it is shown that the dynamics can be described in the framework of the liouville operator an analytical expression for a wave function of the initial time dynamics is found by a perturbation approach as follows from a perturbative solution the initially localized wave function remains localized at asymptotically large times the dynamics can be described qualitatively in the framework of a phenomenological probabilistic approach by means of a probability distribution function it is shown that the probability distribution function may be governed by the fractional fokker planck equation and corresponds to subdiffusion

breathers in nonlinear lattices existence linear stability and quantization abstract it has been proved by the principle of anti integrable limit renamed here anti continuous limit and the implicit function theorem that under rather weak hypotheses there exist spatially localized and time periodic solutions breathers in arrays of nonlinear coupled classical oscillators provided the coupling is not too strong the models can be translationally invariant or not and be of any dimension there are also time periodic solutions corresponding to arbitrary distributions on the lattice of such solutions multibreathers the whole set of these solutions can be labeled by a discrete coding sequence the condition that the frequency of the breather or multibreather solution has no harmonics in the phonon spectrum can be discarded for a large subset of spatially extended time periodic solutions called phonobreather which correspond to special codes which can be also spatially chaotic and where no oscillator is at rest these results extend almost without change to models with coupled rotors the existence of rotobreathers which are exact solutions consisting of a single rotor rotating while the other rotors oscillate is proved there are also multirotobreather solutions and phono rotobreathers etc it is also shown that the phase of the single breathers constituting a multibreather or multirotobreather solution can be submitted to a phase torsion these new dynamical structures carry a nonzero energy flow in models with two dimensions and more the phase torsion of multibreather solutions can generate new dynamical solutions with vortices in the energy flow the dynamics of a quantum electron coupled to a classical lattice is also studied within the same approach from the anti continuous limit the existence of two kinds of polarobreathers which are spatially exponentially localized dynamical solutions is proved for a small enough electronic transfer integral the polarobreathers of the first kind include the standard static polaron the lattice configuration is static time independent when the electron is in an excited state i e the electronic oscillator oscillates periodically they can be spatially chaotic a polarobreather of the second kind corresponds to a localized periodic lattice oscillation associated with a localized quasiperiodic electronic oscillation the most simple of these solutions are those for which both the lattice oscillation and the electron wave function are mostly concentrated close to the same single site the standard floquet analysis of the linear stability of the breather and multibreather solutions is shown to be related with the band spectrum property of the newton operator involved in the implicit function theorem the krein theory of bifurcations is reinterpreted from this point of view the linear stability of the single breather and rotobreather solutions is then proved at least at small enough coupling finally it is shown that in the quantum version of translationally invariant classical models where there cannot exist in principle any strictly localized excitation there are narrow bands of excitations consisting of bound states of many bosons which are the quantum counterpart of the classical breathers the bandwidth of these excitations goes exponentially to zero with the number of bound phonons this theory provides simultaneously existence theorems and a new powerful and accurate numerical method for calculating practically any of the solutions which has been formally predicted to exist these numerical applications are currently written elsewhere

numerical study of two dimensional disordered klein gordon lattices with cubic soft anharmonicity localized oscillations appear both in ordered nonlinear lattices breathers and in disordered linear lattices anderson modes numerical studies on a class of two dimensional systems of the klein gordon type show that there exist two different types of bifurcation in the path from nonlinearity order to linearity disorder inverse pitchforks with or without period doubling and saddle nodes this was discovered for a one dimensional system in a previous work of archilla mackay and marin the appearance of a saddle node bifurcation indicates that nonlinearity and disorder begin to interfere destructively and localization is not possible in contrast the appearance of a pitchfork bifurcation indicates that localization persists

discrete breathers localization and transfer of energy in discrete hamiltonian nonlinear systems we present a partial review of results concerning the theory of discrete breathers in nonlinear hamiltonian and discrete systems these special time periodic solutions gained much interest during the last decade because they may be involved in numerous and various phenomena in physics and biophysics where they could produce nontrivial effects of energy focusing and transfer we first review the principles which govern their existence and which are used in the existence proofs available up to now next we discuss their linear stability and the interaction of discrete breathers with small amplitude waves showing also how they could grow or decay we also briefly discuss the existence of intraband dbs in systems with a linear discrete spectrum which are not spatially periodic random or otherwise and where linear waves cannot propagate we also show that nonlinearity may restore the existence of solutions that propagate energy we review some results concerning energy transportation by dbs and especially the main features associated with their mobility we briefly discuss new perspectives opened up by the theory for applications that in particular look especially interesting for biophysics

discrete breathers classical and quantum abstract discrete breathers are time periodic spatially localised motions in networks of oscillators their occurrence in three principal contexts is reviewed i autonomous hamiltonian or reversible systems ii autonomous forced damped systems and iii time periodically forced systems the main proposed area of application however is to molecular crystals where quantum effects must be taken into account thus an idea for a theory of quantum discrete breathers is also presented though some details remain to be worked out

on the problem of dynamical localization in the nonlinear schrodinger equation with a random potential we prove a dynamical localization in the nonlinear schrodinger equation with a random potential for times of the order of o 2 w here is the strength of the nonlinear ity

group solution of a time dependent chemical convective process the time dependent progress of a chemical reaction over a flat vertical plate is here considered the problem is solved using the two parameter group method which reduces the number of independent by one and leads to a set of nonlinear ordinary differential equation the behavior of the process is numerically investigated for the chemical reaction order n 1 and different schmidt numbers as the problem shows a singularity at n 1 the nonlinear system of ordinary differential equation resulting from the transformation of the problem are analytically solved through the perturbation method the velocity and concentration of chemicals based on the analytical and numerical solutions are presented compared and discussed

potential method applied to boussinesq equation in this paper a solution of the nonlinear boussinesq equation is presented using the potential similarity transformation method the equation is first written in a conserved form a potential function is then assumed reducing it to a system of equations which is further solved through the group transformation method new transformations are found

targeted energy transfer between a rotor and a morse oscillator a model for selective chemical dissociation abstract standard kramers theory of chemical reactions involves a coupling with a langevin thermal bath which intrinsically forbids the possible existence of discrete breathers dbs i e local modes however it is now known that in complex systems that energy may focus for long time as discrete breathers local mode in very special systems targeted energy transfer may occur subsequently to another selected site and induces an ultraselective chemical reaction operating at low temperature the dynamics of the reaction is non brownian but highly coherent along a specific path in the phase space where the system is nearly integrable chemical expressway a simple toy model illustrating this idea is reduced to a rotor weakly coupled to a morse oscillator supposed to represent two specific local modes in a complex system which are appropriately tuned for targeted energy transfer when the rotor is initially rotating with a frequency resonant with those of the morse oscillator at rest the energy of the rotor is almost completely transferred to the morse oscillator and induces chemical dissociation the periodic oscillations of the rotor and morse oscillator remain coherent and their frequencies simultaneously vary but always remain resonant this process is analytically described within an integrable approximation numerical investigations of this model confirm that in the appropriate conditions the particle in the morse oscillator is indeed promptly ejected at infinity with a finite velocity chemical dissociation despite some chaotic transient manifesting imperfect integrability

perturbation theory for periodic orbits in a class of infinite dimensional hamiltonian systems we consider a class of hamiltonian systems describing an infinite array of coupled anharmonic oscillators and we study the bifurcation of periodic orbits off the equilibrium point the family of orbits we construct can be parametrized by their periods which belong to cantor sets of large measure containing certain periods of the linearized problem as accumulation points the infinitely many holes forming a dense set on which the existence of a periodic orbit cannot be proven originate from a dense set of resonances that are present in the system we also have a result concerning the existence of solutions of arbitrarily large amplitude

demonstration of the stability or instability of multibreathers at low coupling abstract whereas there exists a mathematical proof for one site breathers stability and an unpublished one for two site breathers the methods for determining the stability properties of multibreathers rely on numerical computation of the floquet multipliers or on the weak nonlinearity approximation leading to discrete nonlinear schrodinger equations here we present a set of multibreather stability theorems mst that provides a simple method to determine multibreathers stability in klein gordon systems these theorems are based in the application of degenerate perturbation theory to aubry s band theory we illustrate them with several examples

heuristic concentration two stage solution construction abstract by utilizing information from multiple runs of an interchange heuristic we construct a new solution that is generally better than the best local optimum previously found this new two stage approach to combinatorial optimization is demonstrated in the context of the p median problem two layers of optimization are superimposed the first layer is a conventional heuristic the second is a heuristic or exact procedure which draws on the concentrated solution set generated by the initial heuristic the intention is to provide an alternative heuristic procedure which when dealing with large problems has a higher probability of producing optimal solutions than existing methods the procedure is fairly general and appears to be applicable to combinatorial problems in a number of contexts

the gravity p median model abstract in this paper we propose a new model for the p median problem in the standard p median problem it is assumed that each demand point is served by the closest facility in many situations for example when demand points are communities of customers and each customer makes his own selection of the facility demand is divided among the facilities each customer selects a facility which is not necessarily the closest one in the gravity p median problem it is assumed that customers divide their patronage among the facilities with the probability that a customer patronizes a facility being proportional to the attractiveness of that facility and to a decreasing utility function of the distance to the facility the model is analyzed and heuristic solution procedures are proposed computational experiments using a set of test problems provide excellent results

supratransmission in a disordered nonlinear periodic structure abstract we study the interaction among dispersion nonlinearity and disorder effects in the context of wave transmission through a discrete periodic structure subjected to continuous harmonic excitation in its stop band we consider a damped nonlinear periodic structure of finite length with disorder disorder is introduced throughout the structure by small changes in the stiffness parameters drawn from a uniform statistical distribution dispersion effects forbid wave transmission within the stop band of the linear periodic structure however nonlinearity leads to supratransmission phenomenon by which enhanced wave transmission occurs within the stop band of the periodic structure when forced at an amplitude exceeding a certain threshold the frequency components of the transmitted waves lie within the pass band of the linear structure where disorder is known to cause anderson localization there is therefore a competition between dispersion nonlinearity and disorder in the context of supratransmission we show that supratransmission persists in the presence of disorder the influence of disorder decreases in general as the forcing frequency moves away from the pass band edge reminiscent of dispersion effects subsuming disorder effects in linear periodic structures we compute the dependence of the supratransmission force threshold on nonlinearity and strength of coupling between units we observe that nonlinear forces are confined to the driven unit for weakly coupled systems this observation together with the truncation of higher order nonlinear terms permits us to develop closed form expressions for the supratransmission force threshold in sum in the frequency range studied here disorder does not influence the supratransmission force threshold in the ensemble average sense but it does reduce the average transmitted wave energy

asymptotic localization of stationary states in the nonlinear schrodinger equation the mapping of the nonlinear schrodinger equation with a random potential on the fokker planck equation is used to calculate the localization length of its stationary states the asymptotic growth rates of the moments of the wave function and its derivative for the linear schrodinger equation in a random potential are computed analytically and resummation is used to obtain the corresponding growth rate for the nonlinear schrodinger equation and the localization length of the stationary states

anderson localization for one and quasi one dimensional systems we prove almost sure exponential localization of all the eigenfunctions and nondegeneracy of the spectrum for random discrete schrodinger operators on one and quasi one dimensional lattices this paper provides a much simpler proof of these results than previous approaches and extends to a much wider class of systems we remark in particular that the singular continuous spectrum observed in some quasiperiodic systems disappears under arbitrarily small local perturbations of the potential our results allow us to prove that e g for strong disorder the smallest positive lyapunov exponent of some products of random matrices does not vanish as the size of the matrices increases to infinity

the discrete p dispersion problem considered is the problem of selecting p out of n given points in some space such that the minimum distance between pairs of selected points is maximized this objective may be appropriate if the selected points correspond to facility sites and the objective is to have as dispersed a set as possible this problem is np complete related graph theoretical problems are discussed integer programming models are proposed and an outline is given on a line search procedure to solve this problem optimally using a branch and bound procedure problems with n 40 and p 16 can be solved on a microcomputer the heuristic developed to get an initial lower bound finds an optimal solution for most of our random test problems also described is an extension to the basic problem that allows for preselected points which may correspond to existing facility locations this more general version can be solved by slight modifications of the algorithms

group solution for unsteady free convection flow from a vertical moving plate subjected to constant heat flux the problem of heat and mass transfer in an unsteady free convection flow over a continuous moving vertical sheet in an ambient fluid is investigated for constant heat flux using the group theoretical method the nonlinear coupled partial differential equation governing the flow and the boundary conditions are transformed to a system of ordinary differential equations with appropriate boundary conditions the obtained ordinary differential equations are solved numerically using the shooting method the effect of prandlt number on the velocity and temperature of the boundary layer is plotted in curves a comparison with previous work is presented

group analysis for natural convection from a vertical plate the steady laminar natural convection of a fluid having chemical reaction of order n past a semi infinite vertical plate is considered the solution of the problem by means of one parameter group method reduces the number of independent variables by one leading to a system of nonlinear ordinary differential equations two different similarity transformations are found in each case the set of differential equations are solved numerically using runge kutta and the shooting method for each transformation different schmidt numbers and chemical reaction orders are tested

discrete breathers in disordered media abstract we describe some simple physical models where discrete breathers nonlinear localised modes in a lattice exist together with spatial disorder as the models are translation invariant both spatial localisation and spatial disorder are only due to the interplay of nonlinearity and discreteness this result is obtained as a straightforward application of a general result of existence of discrete breathers j a sepulchre r s mackay localised oscillations in conservative or dissipative networks of weakly coupled autonomous oscillators nonlinearity 10 1997 1 35

heuristic and special case algorithms for dispersion problems the dispersion problem arises in selecting facilities to maximize some function of the distances between the facilities the problem also arises in selecting nondominated solutions for multiobjective decision making it is known to be np hard under two objectives maximizing the minimum distance max min between any pair of facilities and maximizing the average distance max avg we consider the question of obtaining near optimal solutions for max min we show that if the distances do not satisfy the triangle inequality there is no polynomial time relative approximation algorithm unless p np when the distances satisfy the triangle inequality we analyze an efficient heuristic and show that it provides a performance guarantee of two we also prove that obtaining a performance guarantee of less than two is np hard for max avg we analyze an efficient heuristic and show that it provides a performance guarantee of four when the distances satisfy the triangle inequality we also present a polynomial ti

finite size effects on instabilities of discrete breathers abstract when the two arcs of the continuous phonon spectrum of the floquet matrix of a discrete breather overlap on the unit circle the breather solution in the infinite lattice might be stable while the corresponding solutions in finite systems appear to be unstable more precisely when the model parameters vary the breather in the finite system exhibits a large number of collisions between the floquet eigenvalues belonging to the phonon spectrum these collisions correspond to complex cascades of instability thresholds followed near after by re entrant stability thresholds we interpret this complex structure on the basis of the band analysis of the matrix of the second variation of the action then we can predict that in the limit of an infinite system the number of instability and stability thresholds in the cascade diverges but simultaneously the maximum amplitude of the instabilities vanishes so that the breather in the infinite system recovers its linear stability as long as all its other localized modes remain stable this is the situation which is required in cretegny et al physica d 119 1998 73 87 for having inelastic phonon scattering with two channels we also analyze the size effects when a floquet eigenvalue associated with a localized mode collides with the floquet continuous phonon spectrum with different krein signature in contrast to the previous case the infinite system is unstable after the collision

solitons in triangular and honeycomb dynamical lattices with the cubic nonlinearity we study the existence and stability of localized states in the discrete nonlinear schrodinger equation on two dimensional nonsquare lattices the model includes both the nearest neighbor and long range interactions for the fundamental strongly localized soliton the results depend on the coordination number i e on the particular type of lattice the long range interactions additionally destabilize the discrete soliton or make it more stable if the sign of the interaction is respectively the same as or opposite to the sign of the short range interaction we also explore more complicated solutions such as twisted localized modes and solutions carrying multiple topological charge vortices that are specific to the triangular and honeycomb lattices in the cases when such vortices are unstable direct simulations demonstrate that they typically turn into zero vorticity fundamental solitons