disordered one dimensional contact process new theoretical and numerical analysis of the one dimensional contact process with quenched disorder are presented we derive new scaling relations different from their counterparts in the pure model which are valid not only at the critical point but also away from it due to the presence of generic scale invariance all the proposed scaling laws are verified in numerical simulations in addition we map the disordered contact process into a non markovian contact process by using the so called run time statistic and write down the associated field theory this turns out to be in the same universality class as one derived by janssen for the quenched system with a gaussian distribution of impurities our findings here support the lack of universality suggested by the field theoretical analysis generic power law behaviors are obtained evidence is shown of the absence of a characteristic time away from the critical point and the absence of universality is put forward the intermediate sublinear regime predicted by bramsom et al is also found

einstein maxwell solitons the application of the inverse scattering method to the einstein maxwell equations for stationary axisymmetric exterior fields leads the authors to an explicit formula for the ernst and electromagnetic potentials of new exact solutions generated from an arbitrary seed solution

applications of partial differential approximants test functions and dimensional crossover in the ising model the method of partial differential approximants pda has been introduced for approximating functions of two or more variables given a finite number of coefficients of their power series it is supposed to be effective close to the multicritical points where the thermodynamic functions are expected to behave according to the scaling hypothesis in order to assess the performance of the method the authors have undertaken the construction of pdas for several test functions of two variables for some simple functions which are represented exactly by pdas and which exhibit an analogue of a multicritical point the numerical estimates yielded very good results even at lower orders for other functions the estimates tended to improve as the order of the approximants is increased for the best pdas they constructed flow diagrams and estimated the scaling functions also they have analysed the dimensional crossover from d 3 to d 2 of the sign 1 2 axial anisotropic ising model on the fcc lattice they considered series expansions for the direct susceptibility and also for the sum of the direct and the staggered susceptibilities

equivalence of various pseudopotential approaches for einstein maxwell fields in the literature various systems of liner eigenvalue equations from which the einstein maxwell equations for stationary axisymmetric exterior fields follow as the integrability conditions were derived in the present paper these linear systems are shown to be equivalent the explicit transformations mapping one form to another are given

absorbing state phase transitions with quenched disorder quenched disorder in the sense of the harris criterion is generally a relevant perturbation at an absorbing state phase transition point here using a strong disorder renormalization group framework and effective numerical methods we study the properties of random fixed points for systems in the directed percolation universality class for strong enough disorder the critical behavior is found to be controlled by a strong disorder fixed point which is isomorph with the fixed point of random quantum ising systems in this fixed point dynamical correlations are logarithmically slow and the static critical exponents are conjecturedly exact for one dimensional systems the renormalization group scenario is confronted with numerical results on the random contact process in one and two dimensions and satisfactory agreement is found for weaker disorder the numerical results indicate static critical exponents which vary with the strength of disorder whereas the dynamical correlations are compatible with two possible scenarios either they follow a power law decay with a varying dynamical exponent like in random quantum systems or the dynamical correlations are logarithmically slow even for a weak disorder for models in the parity conserving universality class there is no strong disorder fixed point according to our renormalization group analysis

an efficient finite element method for simulation of droplet spreading on a topologically rough surface abstract we study numerically the dynamics of a three dimensional droplet spreading on a rough solid surface using a phase field model consisting of the coupled cahn hilliard and navier stokes equations with a generalized navier boundary condition gnbc an efficient finite element method on unstructured meshes is introduced to cope with the complex geometry of the solid surfaces we extend the gnbc to surfaces with complex geometry by including its weak form along different normal and tangential directions in the finite element formulation the semi implicit time discretization scheme results in a decoupled system for the phase function the velocity and the pressure in addition a mass compensation algorithm is introduced to preserve the mass of the droplet to efficiently solve the decoupled systems we present a highly parallel solution strategy based on domain decomposition techniques we validate the newly developed solution method through extensive numerical experiments particularly for those phenomena that can not be achieved by two dimensional simulations on a surface with circular posts we study how wettability of the rough surface depends on the geometry of the posts the contact line motion for a droplet spreading over some periodic rough surfaces are also efficiently computed moreover we study the spreading process of an impacting droplet on a microstructured surface a qualitative agreement is achieved between the numerical and experimental results the parallel performance suggests that the proposed solution algorithm is scalable with over 4 000 processors cores with tens of millions of unknowns

collocation solution for rlw equation with septic spline a collocation solution using the septic splines as a shape function for the regularized long wave rlw equation is presented here a linear stability analysis shows the scheme to be unconditionally stable test problems which migration and interaction of solitary waves are used to validate our scheme by calculate l 2 norm and l norm and three invariants of motion are evaluates to determine the conservation properties of the algorithm the numerical scheme is compared with other published methods and shown to be accurate and efficient

multiple travelling wave solutions of nonlinear evolution equations using a unified algebraic method a new direct and unified algebraic method for constructing multiple travelling wave solutions of general nonlinear evolution equations is presented and implemented in a computer algebraic system compared with most of the existing tanh methods the jacobi elliptic function method or other sophisticated methods the proposed method not only gives new and more general solutions but also provides a guideline to classify the various types of the travelling wave solutions according to the values of some parameters the solutions obtained in this paper include a kink shaped and bell shaped soliton solutions b rational solutions c triangular periodic solutions and d jacobi and weierstrass doubly periodic wave solutions among them the jacobi elliptic periodic wave solutions exactly degenerate to the soliton solutions at a certain limit condition the efficiency of the method can be demonstrated on a large variety of nonlinear evolution equations such as those considered in this paper kdv mkdv ito s fifth mkdv hirota nizhnik novikov veselov broer kaup generalized coupled hirota satsuma coupled schrodinger kdv 2 1 dimensional dispersive long wave 2 1 dimensional davey stewartson equations in addition as an illustrative sample the properties of the soliton solutions and jacobi doubly periodic solutions for the hirota equation are shown by some figures the links among our proposed method the tanh method extended tanh method and the jacobi elliptic function method are clarified generally

darboux transforms deep reductions and solitons explicit formalisms for deep reductions of matrix differential equations and darboux covariance properties are presented the matrix 2 2 spectral problem of the second order is considered this problem with the reduction constraints being imposed on the potentials is the first equation of the lax representation of the hirota satsuma system 1981 the two reduction cases are treated with the help of the bilinear delta forms the covariance of these forms with respect to the darboux transforms under restrictions gives rise to explicit formulas of n soliton solutions in particular the two parameter soliton solutions of the hirota satsuma system are obtained the specific feature of such solutions evolution is that the singularity appears in some parameter region the yajima oikawa system 1976 is given as an example of the technique application to a 3 3 spectral problem

time dependent perturbation theory for nonequilibrium lattice models we develop a time dependent perturbation theory for nonequilibrium interacting particle systems we focus on models such as the contact process which evolve via destruction and autocatalytic creation of particles at a critical value of the destruction rate there is a continuous phase transition between an active steady state and the vacuum state which is absorbing we present several methods for deriving series for the evolution starting from a single seed particle including expansions for the ultimate survival probability in the super and subcritical regions expansions for the average number of particles in the subcritical region and short time expansions algorithms for computer generation of the various expansions are presented rather long series 24 terms or more and precise estimates of critical parameters are presented

a splitting method for incompressible flows with variable density based on a pressure poisson equation a new fractional time stepping technique for solving incompressible flows with variable density is proposed the main feature of this method is that as opposed to other known algorithms the pressure is determined by just solving one poisson equation per time step which greatly reduces the computational cost the stability of the method is proved and the performance of the method is numerically illustrated

an efficient scheme for a phase field model for the moving contact line problem with variable density and viscosity abstract in this paper we develop an efficient numerical method for the two phase moving contact line problem with variable density viscosity and slip length the physical model is based on a phase field approach which consists of a coupled system of the cahn hilliard and navier stokes equations with the generalized navier boundary condition 1 2 5 to overcome the difficulties due to large density and viscosity ratio the navier stokes equations are solved by a splitting method based on a pressure poisson equation 11 while the cahn hilliard equation is solved by a convex splitting method we show that the method is stable under certain conditions the linearized schemes are easy to implement and introduce only mild cfl time constraint numerical tests are carried out to verify the accuracy stability and efficiency of the schemes the method allows us to simulate the interface problems with extremely small interface thickness three dimensional simulations are included to validate the efficiency of the method

solitary wave and periodic wave solutions for the thermally forced gravity waves in atmosphere by introducing a new transformation a new direct and unified algebraic method for constructing multiple travelling wave solutions of general nonlinear evolution equations is presented and implemented in a computer algebraic system which extends fan s direct algebraic method to the case when r 4 the solutions of a first order nonlinear ordinary differential equation with a higher degree nonlinear term and fan s direct algebraic method of obtaining exact solutions to nonlinear partial differential equations are applied to the combined kdv mkdv gkdv equation which is derived from a simple incompressible non hydrostatic boussinesq equation with the influence of thermal forcing and is applied to investigate internal gravity waves in the atmosphere as a result by taking advantage of the new first order nonlinear ordinary differential equation with a fifth degree nonlinear term and an eighth degree nonlinear term periodic wave solutions associated with the jacobin elliptic function and the bell and kink profile solitary wave solutions are obtained under the effect of thermal forcing most importantly the mechanism of propagation and generation of the periodic waves and the solitary waves is analysed in detail according to the values of the heating parameter which show that the effect of heating in atmosphere helps to excite westerly or easterly propagating periodic internal gravity waves and internal solitary waves in atmosphere which are affected by the local excitation structures in atmosphere in addition as an illustrative sample the properties of the solitary wave solution and jacobin periodic solution are shown by some figures under the consideration of heating interaction

derivation of the wenzel and cassie equations from a phase field model for two phase flow on rough surface in this paper the equilibrium behavior of an immiscible two phase fluid on a rough surface is studied from a phase field equation derived from minimizing the total free energy of the system when the size of the roughness becomes small we derive the effective boundary condition for the equation by the multiple scale expansion homogenization technique the wenzel and cassie equations for the apparent contact angles on the rough surfaces are then derived from the effective boundary condition the homogenization results are proved rigorously by the convergence theory

reduction of dispersionless coupled korteweg de vries equations to the euler darboux equation a quasilinear hyperbolic system of two first order equations is introduced the system is linearized by means of the hodograph transformation combined with riemann s method of characteristics in the process of linearization the main step is to explicitly express the characteristic velocities in terms of the riemann invariants the procedure is shown to be performed by quadrature only for specific combinations of the parameters in the system we then apply the method developed here to the dispersionless versions of the typical coupled korteweg de vries ckdv equations including the broer kaup ito hirota satsuma and bogoyavlenskii equations and show that these equations are transformed into the classical euler darboux equation a more general quasilinear system of equations is also considered with application to the dispersionless ckdv equations for the jaulent miodek and nutku oguz equations

variational iteration method for solving burger s and coupled burger s equations by means of variational iteration method the solutions of burger s equation and coupled burger s equations are exactly obtained comparison with the adomian decomposition method is made showing that the former is more effective than the later in this paper he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomials

binormal motion of curves of constant curvature and torsion generation of soliton surfaces the purely binormal motion of curves of constant curvature or torsion respectively is shown to lead to integrable extensions of the dym and classical sine gordon equations in the case of the extended dym equation a reciprocal invariance is used to establish the existence of novel dual soliton surfaces associated with a given soliton surface a cc ideal formulation is adduced to obtain a matrix darboux invariance for the extended dym and reciprocally linked m 2 kdv equations a backlund transformation with a classical constant length property is thereby constructed which allows the generation of associated soliton surfaces analogues of both backlund9s and bianchi9s classical transformations are derived for the extended sine gordon system

on series expansions giving closed form solutions of korteweg de vries like equations korteweg devries kdv like equations with higher degree nonlinearity are solved by a direct algebraic technique due to hereman et al j phys a 19 1986 pp 607 628 for two kdv like equations one with fifth degree nonlinearity the other a combined kdv and mkdv equation for particular choices of the coefficients of the nonlinear terms the kink and antikink solutions found by dey are recovered furthermore soliton solutions of the combined kdv and mkdv equation are found for all values of the coefficients closed form solutions for the calogero degasperis fokas modified mkdv equation are also developed applications of the solutions of these equations in quantum field theory plasma physics and solid state physics are mentioned the hereman et al method is illustrated and slightly extended and this direct series method is briefly compared to hirota s method

prolongation structures for harry dym type equations and backlund transformations of cc ideals the authors examine the prolongation structures for a certain class of differential equations the interrelation between the incomplete set of commutator relations and the defining relations for kac moody algebras is discussed constant coefficient ideals are introduced for which backlund transformations are found in a purely algebraic manner

a conservative phase field method for solving incompressible two phase flows in this paper a conservative phase field method based on the work of sun and beckermann y sun c beckermann sharp interface tracking using the phase field equation j comput phys 220 2007 626 653 for solving the two and three dimensional two phase incompressible navier stokes equations is proposed the present method can preserve the total mass as the cahn hilliard equation but the calculation and implementation are much simpler than that the dispersion relation preserving schemes are utilized for the advection terms while the helmholtz smoother is applied to compute the surface tension force term to verify the proposed method several benchmarks are examined and shown to have good agreements with previous results it also shows that the satisfactions of mass conservations are guaranteed

backlund transformations for the un pumped maxwell bloch system and the fifth painleve equation a backlund transformation for the un pumped maxwell bloch system governing phenomena in nonlinear optics is derived the approach is based on the use of constant coefficient ideals cc ideals since the maxwell bloch system in a certain one dimensional reduction is connected to the fifth painleve equation via a contact transformation chains of solutions for the latter equation are obtained as illustration some rational solutions are explicitly given

darboux transformation and solutions for an equation in 2 1 dimensions painleve analysis and the singular manifold method are the tools used in this paper to perform a complete study of an equation in 2 1 dimensions this procedure has allowed us to obtain the lax pair darboux transformation and functions in such a way that a plethora of different solutions with solitonic behavior can be constructed iteratively

violation of scaling in the contact process with quenched disorder we study the two dimensional contact process cp with quenched disorder dcp and determine the static critical exponents beta and nu perp the dynamic behavior is incompatible with scaling as applied to models such as the pure cp that have a continuous phase transition to an absorbing state we find that the survival probability starting with all sites occupied for a finite size system at critical decays according to a power law as does the off critical density autocorrelation function thus the critical exponent nu parallle which governs the relaxation time is undefined since the characteristic relaxation time is itself undefined the logarithmic time dependence found in recent simulations of the critical dcp moreira and dickman phys rev e54 r3090 1996 is further evidence of violation of scaling a simple argument based on percolation cluster statistics yields a similar logarithmic evolution

effective contact angle for rough boundary abstract we provide rigorous justification for the classical wenzel equation for the roughness enhanced effective contact angle the minimization of the total surface energy is reformulated into a variational problem as the size of the roughness becomes small we show convergence of the minimizer the limiting minimizer and effective contact angle are explicitly calculated to verify the wenzel equation

similarity solutions of the deformed maxwell bloch system the authors have found similarity reductions for the deformed maxwell bloch system to the fifth and second painleve equations asymptotics of the solutions of these equations which are relevant to two level atomic systems with pumping have also been derived

prolongation structure and linear eigenvalue equations for einstein maxwell fields the einstein maxwell equations for stationary axisymmetric exterior fields are shown to be the integrability conditions of a set of linear eigenvalue equations for pseudopotentials the prolongation structure in the spirit of wahlquist and estabrook 1975 of the einstein maxwell equations contains the su 2 1 lie algebra a new mapping of known solutions to other solutions has been found

an algebraic method for finding a series of exact solutions to integrable and nonintegrable nonlinear evolution equations an algebraic method is devised to uniformly construct a series of exact solutions for general integrable and nonintegrable nonlinear evolution equations compared with most existing tanh methods the jacobi function expansion method or other sophisticated methods the proposed method not only gives new and more general solutions but also provides a guideline to classify the various types of the solutions according to the values of some parameters the solutions obtained in this paper include a polynomial solutions b exponential solutions c rational solutions d triangular periodic wave solutions e hyperbolic and solitary wave solutions and f jacobi and weierstrass doubly periodic wave solutions the efficiency of the method can be demonstrated on a large variety of nonlinear equations such as those considered in this paper new 2 1 dimensional calogero kdv equation 3 1 dimensional jimbo miwa equation symmetric regular long wave equation drinfel d sokolov wilson equation 2 1 dimensional generalized dispersive long wave equation double sine gordon equation calogero degasperis fokas equation and coupled schrodinger boussinesq equation in addition the links among our proposed method the tanh method the extended method and the jacobi function expansion method are also clarified generally

integrable evolution systems based on gerdjikov ivanov equations bi hamiltonian structure finite dimensional integrable systems and n fold darboux transformation a spectral problem and the associated gerdjikov ivanov gi hierarchy of nonlinear evolution equations is presented as a reduction the well known gi equation of derivative nonlinear schrodinger equations is obtained it is shown that the gi hierarchy is integrable in a liouville sense and possesses bi hamiltonian structure moreover the spectral problem can be nonlinearized as a finite dimensional completely integrable system under the bargmann constraint between the potentials and the eigenfunctions in particular an explicit n fold darboux transformation for the gi equation is constructed with the help of a gauge transformation of spectral problems and a reduction technique some explicit solitonlike solutions of the gi equation are given by applying its darboux transformation

backlund transforms of chiral fields the action of the backlund transformations on the axisymmetric chiral fields is investigated in particular it is calculated how the superpotential associated with any chiral field is affected by the backlund transformations

an algebraic method to construct the darboux matrix we present an effective procedure to construct the 1 soliton darboux matrix our approach based on the zakharov shabat mikhailov s dressing method is especially useful in the case of non canonical normalization and for non isospectral linear problems the construction is divided into two steps first we represent a given linear problem as a system of some algebraic constraints on two matrices in this context we introduce and discuss invariants of the darboux matrix second we derive the darboux matrix demanding that it preserves the algebraic constraints in particular we consider in details the restrictions imposed by various reduction groups on the form of the darboux matrix

algebraic construction of the darboux matrix revisited we present algebraic construction of darboux matrices for 1 1 dimensional integrable systems of nonlinear partial differential equations with a special stress on the nonisospectral case we discuss different approaches to the darboux backlund transformation based on different dependences of the darboux matrix polynomial sum of partial fractions or the transfer matrix form we derive symmetric n soliton formulae in the general case the matrix spectral parameter and dressing actions in loop groups are also discussed we describe reductions to twisted loop groups unitary reductions the matrix lax pair for the kdv equation and reductions of chiral models harmonic maps to su n and to grassmann spaces we show that in the kdv case the nilpotent darboux matrix generates the binary darboux transformation the paper is intended as a review of known results usually presented in a novel context but some new results are included as well e g general compact formulae for n soliton surfaces and linear and bilinear constraints on the nonisospectral lax pair matrices which are preserved by darboux transformations

the structure function method for asymmetric solitary waves we present a method for the reconstruction of the waveform of asymmetric solitary waves which are observed in weakly dispersive nonlinear media starting from the morphology of the waveform we first give local differential laws which govern the waveform about its extrema and at infinity then we analytically extend these laws to find a differential equation of the generalized korteweg de vries family for the waveform holding over the whole real axis a multi valued singular functional dependence of the nonlinear term of this equation on the amplitude of the solitary wave results which was not considered before and which is intimately connected with the asymmetric nature of the solitary wave if cast in terms of a suitable combination of the wave amplitude a combination which we call the structure function of the solitary wave the differential equation reduces to a modified korteweg de vries equation with a polynomial nonlinear term which we solve by quadrature including up to sixth order nonlinearities in particular the fourth order accurate waveforms are given in terms of elementary functions and they are in excellent agreement with observations for a given maximum wave amplitude several waveforms are found each having a different width this width decreases as the maximum wave amplitude increases

symmetry algebras of the potential nizhnik novikov veselov model two sets of generalized symmetries of the potential nizhnik novikov veselov equation are given in a simple formula by developing a generalized formal series method for searching symmetries of one type of generalized partial differential equations these two sets of symmetries constitute an infinite dimensional lie algebra which contains three types of virasoro algebras and three w type algebras as its special cases

constructing of new exact solutions to the gkdv mkdv equation with any order nonlinear terms by g g expansion method abstract the g g expansion method is introduced to construct more general exact travelling wave solutions to the generalized kdv mkdv equation with any order nonlinear terms as a result hyperbolic function solution trigonometric function solution and rational solution with parameters are obtained when the parameters take up special values the solitary waves are also derived from the travelling wave solutions the g g expansion method presents a wider applicability for handling nonlinear wave equations

critical behavior and griffiths effects in the disordered contact process we study the nonequilibrium phase transition in the one dimensional contact process with quenched spatial disorder by means of large scale monte carlo simulations for times up to 10 9 and system sizes up to 10 7 sites in agreement with recent predictions of an infinite randomness fixed point our simulations demonstrate activated exponential dynamical scaling at the critical point the critical behavior turns out to be universal even for weak disorder however the approach to this asymptotic behavior is extremely slow with crossover times of the order of 10 4 or larger in the griffiths region between the clean and the dirty critical points we find power law dynamical behavior with continuously varying exponents we discuss the generality of our findings and relate them to a broader theory of rare region effects at phase transitions with quenched disorder

nested multivariate pade approximants abstract a new class of multivariate pade approximants is introduced when dealing with two variables x and y the approach consists in applying the pade approximation with respect to y to the coefficients of the pade approximation with respect to x this technique has a natural extension to n variables and is well adapted to programming in any usual language the advantage of the method is that the algorithm uses only univariate pade approximation as a consequence only small systems need to be solved and the computation of the approximant is much faster if m is the number of derivatives with respect to x and y the algorithm requires o m 4 operations instead of o m 6 when matrix methods are used for solving the coefficients problem or o m 3 operations instead of o m 4 if staircase methods are used another important feature is that the reliable methods which have been developed for choosing the degrees of the numerator and the denominator in the univariate case can be straightforwardly used in the multivariate case

efficient energy stable numerical schemes for a phase field moving contact line model in this paper we present two efficient energy stable schemes to solve a phase field model incorporating moving contact line the model is a coupled system that consists of incompressible navier stokes equations with a generalized navier boundary condition and cahn hilliard equation in conserved form in both schemes the projection method is used to deal with the navier stokes equations and stabilization approach is used for the non convex ginzburg landau bulk potential by some subtle explicit implicit treatments we obtain a linear coupled energy stable scheme for systems with dynamic contact line conditions and a linear decoupled energy stable scheme for systems with static contact line conditions an efficient spectral galerkin spatial discretization method is implemented to verify the accuracy and efficiency of proposed schemes numerical results show that the proposed schemes are very efficient and accurate we proposed two linear energy stable numerical schemes for a phase field moving contact line model discrete energy laws that are consistent to the continuous ones are proved the efficiency and fast convergence of the proposed schemes with spectral spatial approximations are numerically verified

delta dressing and exact solutions for the 2 1 dimensional harry dym equation exact implicit solutions with functional parameters of the 2 1 dimensional harry dym hd equation are constructed by the delta dressing method the interrelation between the hd and modified kadomtsev petviashvili mkp equations is established within the framework of the delta dressing method knowledge of the mkp eigenfunctions allows the solutions of the 2 1 dimensional hd equation to be represented in a simple parametric form

on a 2 1 dimensional integrable ernst type equation a strong 2 1 dimensional integrable extension of ernst s equation of general relativity is proposed its richness is demonstrated by means of various canonical dimensional reductions and specializations which lead to formal analogues of well known 1 1 and 2 1 dimensional integrable systems such as the self induced transparency equations the konopelchenko rogers equations a 2 1 dimensional darboux system descriptive of conjugate coordinate systems a single 2 1 dimensional sine gordon equation and the equations representing its backlund transformation a darboux levi type transformation is given and its compatibility with the above mentioned reductions is shown

new applications of variational iteration method abstract the variational iteration method is used for solving three types of nonlinear partial differential equations such as coupled schrodinger kdv generalized kdv and shallow water equations the exact and numerical solutions obtained by variational iteration method are compared with that obtained using adomian decomposition method the comparison shows that the two solutions obtained are excellent agreement the method is made showing that the former is more effective than the latter in this paper he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomials

study of universality crossover in the contact process we consider a generalization of the contact process stochastic model including an additional autocatalitic process the phase diagram of this model in the proper 2 parameter space displays a line of transitions between an active and an absorbing phase which starts at the critical point of the contact process and ends at the transition point of the voter model thus a crossover between the directed percolation and the compact percolation universality classes is observed at this latter point we study this crossover by a variety of techniques using supercritical series expansions analysed with partial differential approximants we obtain precise estimates of the crossover behaviour of the model in particular we find an estimate for the crossover exponent 2 00 0 02 we also show arguments that support the conjecture 2

critical dynamics of the contact process with quenched disorder we study critical spreading in monte carlo simulations of the two dimensional contact process cp with quenched disorder in the form of random dilution in the pure model spreading from a single particle at the critical point ensuremath lambda c follows power laws with the critical exponents of directed percolation with disorder critical spreading is logarithmic not power law below ensuremath lambda c there is a griffiths phase in which the time dependence is governed by nonuniversal power laws the effects of disorder are also apparent above ensuremath lambda c in the active phase where the relaxation of the survival probability is algebraic rather than exponential as in the pure model our results support the conjecture by bramson durrett and schonmann ann prob 19 960 1991 that in two or more dimensions the disordered cp has only a single phase transition

regular article calculation of two phase navier stokes flows using phase field modeling phase field models provide a way to model fluid interfaces as having finite thickness this can allow the computation of interface movement and deformation on fixed grids this paper applies phase field modeling to the computation of two phase incompressible navier stokes flows the navier stokes equations are modified by the addition of the continuum forcing email protected f where c is the composition variable and f is c s chemical potential the equation for interface advection is replaced by a continuum advective diffusion equation with diffusion driven by c s chemical potential gradients the paper discusses how solutions to these equations approach those of the original sharp interface navier stokes equations as the interface thickness e and the diffusivity both go to zero the basic flow physics of phase field interfaces is discussed straining flows can thin or thicken an interface and this must be resisted by a high enough diffusion on the other hand too large a diffusion will overly damp the flow these two constraints result in an upper bound for the diffusivity of o e and a lower bound of o e 2 within these two bounds the phase field navier stokes equations appear to generate an o e error relative to the exact sharp interface equations an o h 2 e 2 numerical method is introduced that is energy conserving in the sense that creation of interface energy by convection is always balanced by an equal decrease in kinetic energy caused by surface tension forcing an o h 4 e 4 compact scheme is introduced that takes advantage of the asymptotic comparatively smooth behavior of the chemical potential for o e accurate phase field models the optimum path to convergence for this scheme appears to be email protected 4 5 the asymptotic rate of convergence corresponding to this is o h 4 5 but results at practical resolutions show that the practical convergence of the method is generally considerably faster than linear extensive analysis and computations show that this scheme is very effective and accurate it allows the accurate calculation of two phase flows with interfaces only two cells wide computational results are given for linear capillary waves and for rayleigh taylor instabilities the first set of computations is compared to exact solutions of the diffuse interface equations and of the original sharp interface equations the rayleigh taylor computations test the ability of the method to compute highly deforming flows these flows include near singular phenomena such as interface coalescences and breakups contact line movement and the formation and breakup of thin wall films grid refinement studies are made and rapid convergence is found for macroscopic flow features such as instability growth rate and propagation speed wavelength and the general physical characteristics of the instability and mass transfer rates

supercritical series expansion for the contact process in heterogeneous and disordered environments the supercritical series expansion of the survival probability for the one dimensional contact process in heterogeneous and disordered lattices is used for the evaluation of the loci of critical points and critical exponents beta the heterogeneity and disorder are modeled by considering binary regular and irregular lattices of nodes characterized by different recovery rates and identical transmission rates two analytical approaches based on nested pade approximants and partial differential approximants were used in the case of expansions with respect to two variables two recovery rates for the evaluation of the critical values and critical exponents the critical exponents in heterogeneous systems are very close to those for the homogeneous contact process thus confirming that the contact process in periodic heterogeneous environment belongs to the directed percolation universality class the disordered systems in contrast seem to have continuously varying critical exponents

a family of completely integrable multi hamiltonian systems explicitly related to some celebrated equations by introducing a spectral problem with an arbitrary parameter we derive a kaup newell type hierarchy of nonlinear evolution equations which is explicitly related to many important equations such as the kundu equation the kaup newell kn equation the chen lee liu cll equation the gerdjikov ivanov gi equation the burgers equation the modified korteweg devries mkdv equation and the sharma tasso olver equation it is shown that the hierarchy is integrable in liouville s sense and possesses multi hamiltonian structure under the bargann constraint between the potentials and the eigenfunctions the spectral problem is nonlinearized as a finite dimensional completely integrable hamiltonian system the involutive representation of the solutions for the kaup newell type hierarchy is also presented in addition an n fold darboux transformation of the kundu equation is constructed with the help of its lax pairs and a reduction technique according to the darboux transformation the solutions of the ku

neugebauer kramer solutions of the ernst equation in hirota s direct method we prove analytically the sasa satsuma conjecture which states that their solution of bilinear form of the ernst equation gives the neugebauere kramer solution in particular cases this proof relates hirota s direct method with the backlund transformation method and opens the way towards the comprehensive interpretation of the ernst equation