the hille yosida space of an arbitrary operator abstract let a be an arbitrary banach space operator with resolvent defined for all 0 we define a linear manifold z in the given space and a norm on z majorizing the given norm such that z is a banach space and the restriction of a to z generates a strongly continuous semigroup of contractions in z this so called hille yosida space z is maximal unique in a suitable sense

numerical simulation of three dimensional nonlinear water waves we present an accurate and efficient numerical model for the simulation of fully nonlinear non breaking three dimensional surface water waves on infinite or finite depth as an extension of the work of craig and sulem 19 the numerical method is based on the reduction of the problem to a lower dimensional hamiltonian system involving surface quantities alone this is accomplished by introducing the dirichlet neumann operator which is described in terms of its taylor series expansion in homogeneous powers of the surface elevation each term in this taylor series can be computed efficiently using the fast fourier transform an important contribution of this paper is the development and implementation of a symplectic implicit scheme for the time integration of the hamiltonian equations of motion as well as detailed numerical tests on the convergence of the dirichlet neumann operator the performance of the model is illustrated by simulating the long time evolution of two dimensional steadily progressing waves as well as the development of three dimensional short crested nonlinear waves both in deep and shallow water

evolution equation for short surface waves on water of finite depth abstract we address the question of determining the evolution equation for surface waves propagating in water whose depth is much larger than the typical wavelength of the surface disturbance we avoid making the usual approximation of supposing the evolution to be given in the form of a modulated wave packet we treat the problem by means of a conformal transformation allowing to explicitly find the dirichlet to neumann operator for the problem together with asymptotic expansions in parameters measuring the nonlinearity and depth this allows us to obtain an equation in physical variables valid in the weakly nonlinear deep water regime the equation is an integro differential equation which reduces to known cases for infinite depth we discuss solutions in a perturbative setting and show that the evolution equation describes stokes like waves

a disorder solution for a cubic ising model the exact expression of the partition function of a three dimensional cubic ising model with nearest neighbour interactions is given when a certain relation between the coupling constants of the model is satisfied this disorder solution is then compared with a partially resummed high temperature expansion of the partition function of the model the constraints on this expansion which result from the existence of the disorder solution and from the inversion relation are discussed

a high order spectral method for nonlinear water waves over moving bottom topography we present a numerical method for simulations of nonlinear surface water waves over variable bathymetry it is applicable to either two or three dimensional flows as well as to either static or moving bottom topography the method is based on the reduction of the problem to a lower dimensional hamiltonian system involving boundary quantities alone a key component of this formulation is the dirichlet neumann operator which in light of its joint analyticity properties with respect to surface and bottom deformations is computed using its taylor series representation we present new stabilized forms for the taylor terms each of which is efficiently computed by a pseudospectral method using the fast fourier transform physically relevant applications are displayed to illustrate the performance of the method comparisons with analytical solutions and laboratory experiments are provided

instability of solitary waves for a generalized benney luke equation abstract we study linear instability of solitary wave solutions of a one dimensional generalized benney luke equation which is a formally valid approximation for describing two way water wave propagation in the presence of surface tension further we implement a finite difference numerical scheme which combines an explicit predictor and an implicit corrector step to compute solutions of the model equation which is used to validate the theory presented

wronskian and grammian determinant structure solutions for a variable coefficient forced kadomtsev petviashvili equation in fluid dynamics abstract taking the inhomogeneities of media and nonuniform boundaries into account the variable coefficient equations can describe more realistic physical phenomena than their constant coefficient counterparts in this paper a variable coefficient forced kadomtsev petviashvili equation with inhomogeneous nonlinearity dispersion perturbed term and external force is investigated using a modified dependent variable transformation this equation is first bilinearized then the n soliton solutions in two different kinds of determinant structure that is the wronskian and grammian determinant soliton solutions for the variable coefficient forced kadomtsev petviashvili equation are presented and verified under certain coefficient constraints the sample soliton solutions are given by choosing suitable determinant elements and several kinds of soliton evolution situations are discussed and illustrated

theorems of hardy and paley for vector valued analytic functions and related classes of banach spaces we investigate the classes of banach spaces where analogues of the classical hardy inequality and the paley gap theorem hold for vector valued functions we show that the vector valued paley theorem is valid for a large class of banach spaces necessarily of cotype 2 which includes all banach lattices of cotype 2 all banach spaces whose dual is of type 2 and also the preduals of c algebras for the trace class s1 and the dual of the algebra of all bounded operators on a hilbert space a stronger result holds namely the vector valued analogue of the fefferman theorem on multipliers from h into in particular for the latter spaces the vector valued hardy inequality holds this inequality is also true for every banach space of type 1 bourgain 0 introduction if f z oajeiit is an analytic trigonometric polynomial then j o j elajl j 1 1 c1 r if t i dt

a terrain following boussinesq system a long wave model is derived asymptotically from the nonlinear potential theory equations the flow regime of interest is incompressible irrotational and inviscid asymptotic analysis leads to a weakly nonlinear weakly dispersive variable coefficient boussinesq system valid for a wide class of topographies the mild slope hypothesis is not required and rapidly varying topographies are also considered in analogy with atmospheric models we use a terrain following coordinate system the novelty is that this coordinate system naturally suggests the weighted averaging of terrain following velocity components as opposed to the depth average of horizontal velocity components found in standard shallow water formulations furthermore a schwarz christoffel toolbox is used to provide additional insight on these new results regarding applications the proposed model can be used for studying solitary waves interacting with fine scale inhomogeneities a theme of great interest the terrain following model als

order and disorder lines in systems with competing interactions iii exact results from stochastic crystal growth the methods presented in the first two articles of this series are simplified and generalized by growing stationary stochastic crystals from a given ansatz layer on the disorder trajectory the free energy correlation functions and multicritical points are calculated explicitly for a large class of models with competing interactions including the staggered eight vertex model the general sixteen vertex model theq state potts model on a triangular lattice a generalz q model and restricted spin glass models in two dimensions

disorder points of the irf and checkerboard potts models conditions are given for a general interactions round a face irf model in statistical mechanics to have a disorder point and expressions obtained for the free energy and intra low correlations these are applied to the checkerboard potts model thereby verifying a recent conjecture by jaeckel and maillard 1984

exact solution of a triangular ising model in a nonzero magnetic field a closed form expression is obtained for the free energy per site of the ising model on the triangular lattice in a nonzero magnetic field and with two and three site interactions the solution is valid along a trajectory in the parameter space and is derived using a method of exact decimation a criterion determining the validity of the decimation method is also established

nonlinear waves and solitons in physical systems abstract advances in nonlinear science have been plentiful in recent years in particular interest in nonlinear wave propagation continues to grow stimulated by new applications such as fiber optic communication systems as well as the many classical unresolved issues of fluid dynamics what is arguably the turning point for the modern perspective of nonlinear systems took place at los alamos over 40 years ago with the pioneering numerical simulations of fermi pasta and ulam a decade later this research initiated the next major advance of zabusky and kruskal that motivated the revolution in completely integrable systems with this in mind the conference on nonlinear waves in solitions in physical systems nwsps was organized by the center for nonlinear studies cnls at los alamos national laboratory in may of 1997 to assess the current state of the art in this very active field papers from the conference attendees as well as from researchers unable to attend the conference were collected in this special volume of physica d in this paper the contributions to the conference and to this special issue are reviewed with an emphasis on the many unifying principles that all these works share

b convexity the analytic radon nikodym property and individual stability ofc0 semigroups abstract lett t t t 0be ac0 semigroup on a banach spacex with generatoraand growth bound assume thatx0 xis such that the local resolvent r a x0admits a bounded holomorphic extension to the right half plane re 0 we prove the following results i ifhas fourier type 1 2 then lim 0 for all 1 and ii ifhas the analytic rnp then lim 0 for all 1 and iii ifis arbitrary then weak lim 0 for all 1 and as an application we prove a tauberian theorem for the laplace transform of functions with values in ab convex banach space

algebraic invariants in soluble models exhibits on the known solutions of the triangle relation for the exactly solved models some simplifying methods of recovering their parametrisation in terms of algebraic varieties the relation to the automorphy group generated by the inverse and spatial symmetries of the model is also analysed

long wave interaction over varying topography abstract the propagation of long waves on the surface of a three dimensional fluid domain bounded below by slowly varying topography is considered there are two important limits if the initial data can be written in terms of a discrete set of one dimensional wavefronts the resulting wave field is described by a set of variable coefficient korteweg de vries kdv equations for each wave along its characteristic curve waves along different characteristics interact with each other yielding phase shifts that depend on the wave amplitudes the angle between the rays and the local depth if the initial data is modulated slowly in the direction parallel to the wavefronts the wave field is described by variable coefficient kadomtsev petviashvili kp equations along rays for topography varying only in one direction we calculate explicit results for the interaction between two sets of periodic or solitary waves and show the equivalence of a single nearly normally incident kdv wave and a normally incident kp wave

disorder solutions and the star triangle relation it is shown that the disorder solutions exhibited by two dimensional statistical lattice systems verify the star triangle relation these solutions of the star triangle relation are of a different type than those corresponding to completely integrable models

optimal boussinesq model for shallow water waves interacting with a microstructure in this paper we consider the propagation of water waves in a long wave asymptotic regime when the bottom topography is periodic on a short length scale we perform a multiscale asymptotic analysis of the full potential theory model and of a family of reduced boussinesq systems parametrized by a free parameter that is the depth at which the velocity is evaluated we obtain explicit expressions for the coefficients of the resulting effective korteweg de vries kdv equations we show that it is possible to choose the free parameter of the reduced model so as to match the kdv limits of the full and reduced models hence the reduced model is optimal regarding the embedded linear weakly dispersive and weakly nonlinear characteristics of the underlying physical problem which has a microstructure we also discuss the impact of the rough bottom on the effective wave propagation in particular nonlinearity is enhanced and we can distinguish two regimes depending on the period of the bottom where the dispersion is either enhanced or reduced compared to the flat bottom case

uniformly non ln 1 locally uniformly non ln 1 and non ln 1 properties in orlicz bochner function spaces endowed with the orlicz norm abstract some criteria are given in this paper for uniformly non l n 1 locally uniformly non l n 1 and non l n 1 properties of orlicz bochner function spaces endowed with the orlicz norm as the consequence we can immediately get the characterization of b convexity uniform nonsquareness local uniform nonsquareness and nonsquareness in orlicz bochner function spaces although some of them were obtained in recent years

order and disorder lines in systems with competing interactions ii the irf model systems with competing interactions can be often exactly solved on a restricted subspace of the parameter space called an order or disorder trajectory a simple method introduced within the transfer matrix formalism allows for the calculation of the free energy and spin spin correlation functions along the order and disorder lines of the ising model with all possible interactions around a face of the square lattice irf model the general eight vertex model is thoroughly examined and shows full analogy with the quantum spin chain results of the previous paper

transformations and multi solitonic solutions for a generalized variable coefficient kadomtsev petviashvili equation kadomtsev petviashvili equations with variable coefficients can be used to characterize many nonlinear phenomena in fluid dynamics and plasma physics more realistically than the equations with constant coefficients hereby a generalized variable coefficient kadomtsev petviashvili equation with nonlinearity dispersion and perturbed terms is investigated transformations of which the consistency conditions are exactly the painleve integrability conditions to the korteweg de vries equation cylindrical korteweg de vries equation kadomtsev petviashvili equation and cylindrical kadomtsev petviashvili equation are presented by formal dependent variable transformation assumptions using the hirota bilinear method from the variable coefficient bilinear equation the multi solitonic solution auto backlund transformation and lax pair for the variable coefficient kadomtsev petviashvili equation are obtained moreover the influence of inhomogeneity coefficients on solitonic structures and interaction properties is discussed for physical interest and possible applications

necessary versus sufficient conditions for exact solubility of statistical models on lattices it is shown that under rather mild conditions the triangle relation represents a necessary condition for the existence of commuting transfer matrices of arbitrary size the cases of spin models and vertex models are treated separately

quantitative characterization of 2d traveling wave patterns abstract two dimensional traveling wave convection patterns in ethanol water mixtures with negative separation ratio are discussed a review is given for several numerical techniques that have been developed to characterize traveling wave patterns the basic properties of the patterns are determined using the spatiotemporal fourier transform temporal demodulation of each pixel is used to calculate the complex order parameter of the pattern the kinematics of the large domains of waves are derived from the complex order parameter using the assumption that the pattern consists of a single deformed wave component the interactions of waves at the domain boundaries is measured by performing a rigorous spatiotemporal demodulation of the pattern finally the topological structure of the complex order parameter is investigated and spatiotemporal disorder in the pattern is described in terms of the statistics and dynamics of phase defects

tauberian theorems and stability of solutions of the cauchy problem let f r x be a bounded strongly measurable function with values in a banach space x and let ie be the singular set of the laplace transform f in ir suppose that e is countable and 0 e i uf s u du 0 uniformly for s 0 as 0 for each in e it is shown that t 0 e i uf u du f i 0 as t for each in r e in particular f t 0 if f is uniformly continuous this result is similar to a tauberian theorem of arendt and batty it is obtained by applying a result of the authors concerning local stability of bounded semigroups to the translation semigroup on buc r x and it implies several results concerning stability of solutions of cauchy problems

optimal polynomial decay of functions and operator semigroups we characterize the polynomial decay of orbits of hilbert space c 0 semigroups in resolvent terms we also show that results of the same type for general banach space semigroups and functions obtained recently in batty and duyckaerts j evol eq 8 765 780 2008 are sharp this settles a conjecture posed in batty and duyckaerts 2008

a disorder solution of the general 8 vertex model a disorder solution for the general 8 vertex model is found by applying a procedure recently developed by baxter 1984 the solution is valid when an adequate relation between the vertex weights of the model is satisfied