an implicit immersed boundary method for three dimensional fluid membrane interactions we present an implicit immersed boundary method for the incompressible navier stokes equations capable of handling three dimensional membrane fluid flow interactions the goal of our approach is to greatly improve the time step by using the jacobian free newton krylov method jfnk to advance the location of the elastic membrane implicitly the most attractive feature of this jacobian free approach is newton like nonlinear convergence without the cost of forming and storing the true jacobian the generalized minimal residual method gmres which is a widely used krylov subspace iterative method is used to update the search direction required for each newton iteration each gmres iteration only requires the action of the jacobian in the form of matrix vector products and therefore avoids the need of forming and storing the jacobian matrix explicitly once the location of the boundary is obtained the elastic forces acting at the discrete nodes of the membrane are computed using a finite element model we then use the immersed boundary method to calculate the hydrodynamic effects and fluid structure interaction effects such as membrane deformation the present scheme has been validated by several examples including an oscillatory membrane initially placed in a still fluid capsule membranes in shear flows and large deformation of red blood cells subjected to stretching force

travelling solitary waves in the discrete schrodinger equation with saturable nonlinearity existence stability and dynamics the present work examines in detail the existence stability and dynamics of travelling solitary waves in a schrodinger lattice with saturable nonlinearity after analysing the linear spectrum of the problem in the travelling wave frame a pseudo spectral numerical method is used to identify weakly nonlocal solitary waves by finding zeros of an appropriately crafted tail condition we can obtain the genuinely localized pulse like solutions subsequent use of continuation methods allows us to obtain the relevant branches of solutions as a function of the system parameters such as the frequency and intersite coupling strength we examine the stability of the solutions in two ways both by imposing numerical perturbations and observing the solution dynamics as well as by considering the solutions as fixed points of an appropriate map and computing the corresponding floquet matrix and its eigenvalues both methods indicate that our solutions are robustly localized finally the interactions of these solutions are examined in collision type phenomena observing that relevant collisions are near elastic although they may under appropriate conditions lead to the generation of an additional pulse

structural stability of the korteweg de vries solitons under a singular perturbation abstract we investigate the stability of a solitary wave solution of the korteweg de vries equation when a fifth order spatial derivative term is added we show that the solution ceases to be strictly localized but develops an infinite oscillating tail and we compute the amplitude of the latter

discrete nonlinear schrodinger equations with arbitrarily high order nonlinearities a class of discrete nonlinear schrodinger equations with arbitrarily high order nonlinearities is introduced these equations are derived from the same hamiltonian using different poisson brackets and include as particular cases the saturable discrete nonlinear schrodinger equation and the ablowitz ladik equation as a common property these equations possess three kinds of exact analytical stationary solutions for which the peierls nabarro barrier is zero several properties of these solutions including stability discrete breathers and moving solutions are investigated

when gap solitons become embedded solitons a generic unfolding a two parameter unfolding is considered of single pulsed homoclinic orbits to an equilibrium with two real and two zero eigenvalues in fourth order reversible dynamical systems one parameter controls the linearisation with a transition occurring between a saddle centre and a hyperbolic equilibrium in the saddle centre region the homoclinic orbit is of codimension one which is controlled by the second generic parameter whereas when the equilibrium is hyperbolic the homoclinic orbit is structurally stable a geometric approach reveals the homoclinic orbits to the saddle to be generically destroyed either by developing an algebraically decaying tail or through a fold depending on the sign of the perturbation of the second parameter special cases of different actions of z2 symmetry are considered as is the case of the system being hamiltonian application of these results is considered to the transition between embedded solitons corresponding to the codimension one homoclinic orbits and gap solitons the structurally stable ones in nonlinear wave systems the theory is shown to match numerical experiments on two models arising in nonlinear optics and on a form of fifth order korteweg de vries equation

interactions of solitons in nonintegrable systems direct perturbation method and applications abstract problems of approximate description of soliton interaction in nonintegrable systems are discussed it is shown that in an arbitrary lagrangian system in the first nontrivial order of the small parameter asymptotic scheme for a system of solitons with close velocities a lagrangian may be introduced analogous to that for classical particles with a pair interaction potential a classification of possible types of soliton interaction is given and criteria of the existence of bound states are formulated a possibility of generalization of approximated description of soliton interaction in the multidimensional case is noted

homoclinic orbits to a saddle center in a fourth order differential equation abstract we study homoclinic orbits to a saddle center of a fourth order ordinary differential equation which is invariant under the transformation x x involving an eigenvalue parameter q and an odd piece wise cubic type nonlinearity it is found that for a sequence of eigenvalues which tends to infinity homoclinic orbits exist whose complexity increases as the eigenvalue becomes larger these orbits are found to be embedded in branches of homoclinic orbits to periodic orbits as x

scalable parallel methods for monolithic coupling in fluid structure interaction with application to blood flow modeling we introduce and study numerically a scalable parallel finite element solver for the simulation of blood flow in compliant arteries the incompressible navier stokes equations are used to model the fluid and coupled to an incompressible linear elastic model for the blood vessel walls our method features an unstructured dynamic mesh capable of modeling complicated geometries an arbitrary lagrangian eulerian framework that allows for large displacements of the moving fluid domain monolithic coupling between the fluid and structure equations and fully implicit time discretization simulations based on blood vessel geometries derived from patient specific clinical data are performed on large supercomputers using scalable newton krylov algorithms preconditioned with an overlapping restricted additive schwarz method that preconditions the entire fluid structure system together the algorithm is shown to be robust and scalable for a variety of physical parameters scaling to hundreds of processors and millions of unknowns

numerical chaos symplectic integrators and exponentially small splitting distances two discrete versions of duffing s equation are derived as reductions of discretizations of the nonlinear schrodinger nls equation inheriting the properties of the nsl discretizations one is shown to be integrable and using a mel nikov type analysis the other discretization is shown to be nonintegrable arguments are given why it is possible for the nonintegrable scheme to restore the homoclinic orbit at an exponentially fast rate which is faster than the order of the approximation as h 0 this suggests why there can be fundamental differences between symplectic and nonsymplectic discretizations of certain continuous hamiltonian systems

exact static solutions of a generalized discrete φ 4 model including short periodic solutions we carry out a comprehensive analysis of a generalized discrete 4 model of which virtually all 4 models discussed in the literature are particular cases for this model we construct the exact solutions in the form of the basic jacobi elliptic hyperbolic and sine functions and also give a list of short periodic and even aperiodic solutions some of those solutions coincide with the known ones others generalize the existing solutions and the rest of them are new we then discuss the relation between the models supporting exact static solutions and the two point maps in particular we show that some of the short periodic and sine solutions can be found from factorized difference equations and even from a set of two difference equations one of the first and another of the second order particular attention is paid to the discussion of the exceptional discrete ed models defined as models supporting the translationally invariant ti static solutions that can be placed arbitrarily with respect to the lattice we show that some of the derived short periodic solutions are ti ones while the others are not for the ti static solutions we demonstrate the existence of the translational goldstone mode for any location of the solution with respect to the lattice we then analyze numerically the stability and other properties of the ti kink solutions in conclusion we divide the ed models into two classes the ed i models support a two parameter set of ti static solutions while the ed ii models support only a one parameter set of such solutions

soliton internal mode bifurcations pure power law the bifurcation of internal solitary wave modes from the essential spectrum has been one of the most exciting recent developments in the study of soliton dynamics to date it was believed that the bifurcation of such modes due to discretization has a strict power law dependence on the lattice discreteness parameter in this work we prove that this dependence actually possesses relevant exponentially small terms which distinguish between different solutions for the discrete models the theoretical result is established by using a discrete version of the evans function the predictions presented herein compare very favorably with the numerical study of the linear eigenvalue problem and offer explanations of computational effects not possible on the basis of previous theoretical studies

complete integrability of two coupled discrete modified korteweg de vries equations we report that two coupled discrete modified korteweg de vries equations 2 dmkdv governed by nonlinear partial differential difference equations are completely integrable we derive lax matrices for 2 dmkdv and also show that it admits a sequence of generalized non point symmetries and polynomial conserved densities establishing its complete integrability also exact solutions of it expressible in terms of hyperbolic and jacobian elliptic functions have been derived

curvilinear immersed boundary method for simulating fluid structure interaction with complex 3d rigid bodies the sharp interface curvib approach of ge and sotiropoulos l ge f sotiropoulos a numerical method for solving the 3d unsteady incompressible navier stokes equations in curvilinear domains with complex immersed boundaries journal of computational physics 225 2007 1782 1809 is extended to simulate fluid structure interaction fsi problems involving complex 3d rigid bodies undergoing large structural displacements the fsi solver adopts the partitioned fsi solution approach and both loose and strong coupling strategies are implemented the interfaces between immersed bodies and the fluid are discretized with a lagrangian grid and tracked with an explicit front tracking approach an efficient ray tracing algorithm is developed to quickly identify the relationship between the background grid and the moving bodies numerical experiments are carried out for two fsi problems vortex induced vibration of elastically mounted cylinders and flow through a bileaflet mechanical heart valve at physiologic conditions for both cases the computed results are in excellent agreement with benchmark simulations and experimental measurements the numerical experiments suggest that both the properties of the structure mass geometry and the local flow conditions can play an important role in determining the stability of the fsi algorithm under certain conditions the fsi algorithm is unconditionally unstable even when strong coupling fsi is employed for such cases however combining the strong coupling iteration with under relaxation in conjunction with the aitken s acceleration technique is shown to effectively resolve the stability problems a theoretical analysis is presented to explain the findings of the numerical experiments it is shown that the ratio of the added mass to the mass of the structure as well as the sign of the local time rate of change of the force or moment imparted on the structure by the fluid determine the stability and convergence of the fsi algorithm the stabilizing role of under relaxation is also clarified and the upper bound of the under relaxation coefficient required for stability is derived

energy preserving schemes for nonlinear hamiltonian systems of wave equations application to the vibrating piano string the problem of the vibration of a string is well known in its linear form describing the transversal motion of a string nevertheless this description does not explain all the observations well enough nonlinear coupling between longitudinal and transversal modes seams to better model the piano string as does for instance the geometrically exact model gem this report introduces a general class of nonlinear systems nonlinear hamiltonian systems of wave equations in which fits the gem mathematical study of these systems is lead in a first part showing central properties energy preservation existence and unicity of a global smooth solution finite propagation velocity ldots space discretization is made in a classical way variational formulation and time discretization aims at numerical stability using an energy technique a definition of preserving schemes is introduced and we show that explicit schemes or partially implicit schemes which are preserving according to this definition cannot be built unless the model is linear a general energy preserving second order accurate fully implicit scheme is built for any continuous system that fits the nonlinear hamiltonian systems of wave equations class

a new barrier to the existence of moving kinks in frenkel kontorova lattices an explanation is offered for an observed lower bound on the wave speed of travelling kinks in frenkel kontorova lattices kinks exist at discrete wavespeeds within a parameter regime where there is a resonance with linear waves phonons however they fail to exist even in this codimension one sense whenever there is more than one phonon branch in the dispersion relation inside such bands only quasi kinks with nondecaying oscillatory tails are possible the results are presented for a discrete sine gordon lattice with an onsite potential that has a tunable amount of anharmonicity novel numerical methods are used to trace kinks with topological charge q 1 and 2 in three parameters representing the propagation speed lattice discreteness and anharmonicity although none of the analysis is presented as rigorous mathematics numerical results suggest that the bound on allowable wavespeeds is sharp the results also explain why the vanishing at discrete values of anharmonicity of the peierls nabarro barrier between stationary kinks as discovered by savin et al does not lead to bifurcation of kinks with small wave speed 2003 elsevier b v all rights reserved

multi pulse embedded solitons as bound states of quasi solitons abstract embedded solitons ess is a name given to localised solutions of multi component dispersive wave models that occur in resonance with the linear spectrum they exist at isolated codimension one parameter values within the steady state equations which have linearisation with eigenvalues and i at the same time quasi solitons qss or generalised solitary waves with non decaying radiation tails are known to be endemic we consider the general question of when two qss may be glued together to form a two humped bound state bs es in the limit 0 a generalisation of the method of gorshkov and ostrovsky is used within the framework of general normal forms for hamiltonian reversible systems a simple asymptotic formula is derived that governs the existence symmetry and accumulation rate of the bss this generalises earlier ad hoc calculations for specific examples the formula depends on few simple ingredients the eigenvalues of the equilibrium an asymptotic estimate for the tail amplitude of the qss the birkhoff signature and symmetry properties of the hamiltonian only the tail amplitude estimate is difficult to calculate requiring exponential asymptotics but it is shown that this only affects the third order term in the asymptotic formula the calculation is worked out in detail for the steady states of several example pde systems taken from nonlinear optics and fluid mechanics and excellent agreement with numerical results is found

exact static solutions for discrete ϕ 4 models free of the peierls nabarro barrier discretized first integral approach we propose a generalization of the discrete klein gordon models free of the peierls nabarro barrier derived in spreight nonlinearity 12 1373 1999 and barashenkov et al phys rev e 72 035602 r 2005 such that they support not only kinks but a one parameter set of exact static solutions these solutions can be obtained iteratively from a two point nonlinear map whose role is played by the discretized first integral of the static klein gordon field as suggested by dmitriev et al j phys a 38 7617 2005 we then discuss some discrete ensuremath phi 4 models free of the peierls nabarro barrier and identify for them the full space of available static solutions including those derived recently by cooper et al phys rev e 72 036605 2005 but not limited to them these findings are also relevant to standing wave solutions of discrete nonlinear schr odinger models we also study stability of the obtained solutions as an interesting aside we derive the list of solutions to the continuum ensuremath phi 4 equation that fill the entire two dimensional space of parameters obtained as the continuum limit of the corresponding space of the discrete models

multistable solitons in higher dimensional cubic quintic nonlinear schrodinger lattices abstract we study the existence stability and mobility of fundamental discrete solitons in two and three dimensional nonlinear schrodinger lattices with a combination of cubic self focusing and quintic self defocusing onsite nonlinearities several species of stationary solutions are constructed and bifurcations linking their families are investigated using parameter continuation starting from the anti continuum limit and also with the help of a variational approximation in particular a species of hybrid solitons intermediate between the site and bond centered types of the localized states with no counterpart in the 1d model is analyzed in 2d and 3d lattices we also discuss the mobility of multi dimensional discrete solitons that can be set in motion by lending them kinetic energy exceeding the appropriately defined peierls nabarro barrier however they eventually come to a halt due to radiation loss

hamiltonian conserving discrete canonical equations based on variational difference quotients abstract new discrete mechanics based on the assumption of the discrete time is proposed the discrete mechanics does not contain any continuous differentiation but contains only difference quotients resulting discrete hamiltonian s canonical equations are single time step difference equations and exactly conserve the hamiltonian the canonical equations give the numerical results more accurately than the heun scheme and the 4th order runge kutta scheme

exact static solutions to a translationally invariant discrete phi4 model for a discrete translationally invariant 4 model introduced by barashenkov et al 2005 phys rev e 72 35602r we provide the momentum conservation law and demonstrate how the first integral of the static version of the discrete model can be constructed from a jacobi elliptic function jef solution the first integral can be written in the form of a nonlinear map from which the static solution supported by the model can be constructed a set of jef solutions including the staggered ones is derived we also report on the stability analysis for the static bounded solutions and exemplify the dynamical behaviour of the unstable solutions this work provides a road map through this illustrative example on how to fully analyse translationally invariant models in terms of their static problem its first integral their full set of static solutions and associated conservation laws

a numerical method for solving the 3d unsteady incompressible navier stokes equations in curvilinear domains with complex immersed boundaries a novel numerical method is developed that integrates boundary conforming grids with a sharp interface immersed boundary methodology the method is intended for simulating internal flows containing complex moving immersed boundaries such as those encountered in several cardiovascular applications the background domain e g the empty aorta is discretized efficiently with a curvilinear boundary fitted mesh while the complex moving immersed boundary say a prosthetic heart valve is treated with the sharp interface hybrid cartesian immersed boundary approach of gilmanov and sotiropoulos a gilmanov f sotiropoulos a hybrid cartesian immersed boundary method for simulating flows with 3d geometrically complex moving bodies journal of computational physics 207 2005 457 492 to facilitate the implementation of this novel modeling paradigm in complex flow simulations an accurate and efficient numerical method is developed for solving the unsteady incompressible navier stokes equations in generalized curvilinear coordinates the method employs a novel fully curvilinear staggered grid discretization approach which does not require either the explicit evaluation of the christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations the equations are integrated in time using an efficient second order accurate fractional step methodology coupled with a jacobian free newton krylov solver for the momentum equations and a gmres solver enhanced with multigrid as preconditioner for the poisson equation several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady pulsatile flow through a curved pipe bend to demonstrate the ability of the method to simulate flows with complex moving immersed boundaries we apply it to calculate pulsatile physiological flow through a mechanical bileaflet heart valve mounted in a model straight aorta with an anatomical like triple sinus

a moving least squares immersed boundary method for simulating the fluid structure interaction of elastic bodies with arbitrary thickness a versatile numerical method is presented to predict the fluid structure interaction of bodies with arbitrary thickness immersed in an incompressible fluid with the aim of simulating different biological engineering applications a direct forcing immersed boundary method is adopted based on a moving least squares approach to reconstruct the solution in the vicinity of the immersed surface a simple spring network model is considered for describing the dynamics of deformable structures so as to easily model and simulate different biological systems that not always may be described by simple continuum models without affecting the computational time and simplicity of the overall method the fluid and structures are coupled in a strong way in order to avoid instabilities related to large accelerations of the bodies the effectiveness of the method is validated by means of several test cases involving rigid bodies either falling in a quiescent fluid fluttering or tumbling or transported by a shear flow infinitely thin elastic structures with mass such as a two dimensional flexible filament and concerning three dimensional cases a flapping flag and an inverted flag in a free stream finally a three dimensional model of a bio prosthetic aortic valve opening and closing under a pulsatile flowrate a very good agreement is obtained in all the cases comparing with available experimental data and numerical results obtained by different methods in particular the method is shown to be second order accurate by means of a mesh refinement study moreover it is able to provide results comparable with those of sharp direct forcing approaches and can manage high pressure differences across the surface still obtaining very smooth hydrodynamic forces

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

a general reconstruction algorithm for simulating flows with complex 3d immersed boundaries on cartesian grids in the present note a general reconstruction algorithm for simulating incompressible flows with complex immersed boundaries on cartesian grids is presented in the proposed method an arbitrary three dimensional solid surface immersed in the fluid is discretized using an unstructured triangular mesh and all the cartesian grid nodes near the interface are identified then the solution at these nodes is reconstructed via linear interpolation along the local normal to the body in a way that the desired boundary conditions for both pressure and velocity fields are enforced the overall accuracy of the resulting solver is second order as it is demonstrated in two test cases involving laminar flow past a sphere

exact moving and stationary solutions of a generalized discrete nonlinear schrodinger equation we obtain exact moving and stationary spatially periodic and localized solutions of a generalized discrete nonlinear schrodinger equation more specifically we find two different moving periodic wave solutions and a localized moving pulse solution we also address the problem of finding exact stationary solutions and for a particular case of the model when stationary solutions can be expressed through the jacobi elliptic functions we present a two point map from which all possible stationary solutions can be found numerically we demonstrate the generic stability of the stationary pulse solutions and also the robustness of moving pulses in long term dynamics

a variational approach to the stability of an embedded nls soliton at the edge of the continuum a lagrangian based method is used to construct embedded soliton solutions of a nonlinear schrodinger equation with higher order dispersive terms it is shown that the embedded soliton consists of two widely separated peaks with linear dispersive radiation of exponentially small amplitude between the peaks this radiation acting to hold the pulses together the lagrangian based technique determines the details of this embedded soliton including the amplitude of the pulses the separation of the pulses and the amplitude of the radiation in addition it is found that the embedded soliton exists for only discrete eigenvalues related to the separation of the pulses moreover since the embedded soliton solutions are steady they are at the lower edge of the continuous spectrum finally by allowing the parameters of the embedded soliton to be time dependent it is found that the embedded soliton develops an oscillatory type of one sided stability this one sided stability is different from the usual monotone one sided stability found for solitons embedded inside the continuous spectrum

dynamical transitions between equilibria in a dissipative klein gordon lattice abstract we consider the energy landscape of a dissipative klein gordon lattice with a 4 on site potential our analysis is based on suitable energy arguments combined with a discrete version of the ojasiewicz inequality in order to justify the convergence to a single nontrivial equilibrium for all initial configurations of the lattice then global bifurcation theory is explored to illustrate that in the discrete regime all linear states lead to nonlinear generalizations of equilibrium states direct numerical simulations reveal the rich structure of the equilibrium set consisting of non trivial topological kink shaped interpolations between the adjacent minima of the on site potential and the wealth of dynamical convergence possibilities these dynamical evolution results also provide insight on the potential stability of the equilibrium branches and glimpses of the emerging global bifurcation structure elucidating the role of the interplay between discreteness nonlinearity and dissipation

moving discrete breathers abstract we give definitions for different types of moving spatially localized objects in discrete nonlinear lattices we derive general analytical relations connecting frequency velocity and localization length of moving discrete breathers and kinks in nonlinear one dimensional lattices then we propose a new numerical algorithm to find these solutions

a convergence study of a new partitioned fluid structure interaction algorithm based on fictitious mass and damping we develop analyze and validate a new method for simulating fluid structure interactions fsis which is based on fictitious mass and fictitious damping in the structure equation we employ a partitioned method for the fluid and structure motions in conjunction with sub iteration and aitken relaxation in particular the use of such fictitious parameters requires sub iterations in order to reduce the induced error in addition to the local temporal truncation error to this end proper levels of tolerance for terminating the sub iteration procedure have been obtained in order to recover the formal order of temporal accuracy for the coupled fsi problem these fictitious terms have a significant effect leading to better convergence rate and hence substantially smaller number of sub iterations through analysis we identify the proper range of these parameters which we then verify by corresponding numerical tests we implement the method in the context of spectral element discretization which is more sensitive than low order methods to numerical instabilities arising in the explicit fsi coupling however the method we present here is simple and general and hence applicable to fsi based on any other discretization we demonstrate the effectiveness of the method in applications involving 2d vortex induced vibrations viv and in 3d flexible arteries with structural density close to blood density we also present 3d results for a patient specific aneurysmal flow under pulsatile flow conditions examining in particular the sensitivity of the results on different values of the fictitious parameters

exact stationary solutions for the translationally invariant discrete nonlinear schrodinger equations from a wide class of translationally invariant discrete nonlinear schrodinger dnls equations we extract a two parameter subclass corresponding to kerr nonlinearity for which any stationary solution can be derived recurrently from a quadratic equation this subclass which incorporates the integrable ablowitz ladik lattice as a special case admits exact stationary solutions that are derived in terms of the jacobi elliptic functions exact moving solutions for the discrete equations are also obtained in the continuum limit the constructed stationary solutions reduce to the exact moving solutions to the continuum nls equation with kerr nonlinearity numerical results are also presented for the special case of localized solutions including sech pulse or bright soliton tanh kink or dark soliton and 1 tanh called here inverted kink profiles for these solutions we discuss their linearization spectra and their mobility particularly we demonstrate that discrete dark solitons are dynamically stable for a wide range of lattice spacings contrary to what is the case for their standard dnls counterparts furthermore the bright and dark solitons in the non integrable translationally invariant lattices can propagate at slow speed without any noticeable radiation

breaking of solitary and periodic nonlinear waves abstract a nontrivial behaviour of a nonlinear wave under influence of small disturbing factors like dissipation smooth inhomogeneity of medium parameters etc is considered by the example of sine gordon equation the stage of slow adiabatic variation of the parameters of quasi stationary wave is shown to change at some finite distance due to strong instability the wave form becomes essentially non stationary breaking of stationary wave structure the breaking condition is defined by the extremum of the wave adiabatic invariant the behaviour of a wave at the nonadiabatic stage is described using a galerkin procedure

high speed kinks in a generalized discrete phi 4 model we consider a generalized discrete ensuremath phi 4 model and demonstrate that it can support exact moving kink solutions in the form of tanh with an arbitrarily large velocity the constructed exact moving solutions are dependent on the specific value of the propagation velocity we demonstrate that in this class of models given a specific velocity the problem of finding the exact moving solution is integrable namely this problem originally expressed as a three point map can be reduced to a two point map from which the exact moving solutions can be derived iteratively it was also found that these high speed kinks can be stable and robust against perturbations introduced in the initial conditions

exceptional discretizations of the sine gordon equation the method of one dimensional maps was recently introduced as a means of generating exceptional discretizations of the phi 4 theory i e discrete phi 4 models which support kinks centered at a continuous range of positions relative to the lattice in this paper we employ this method to obtain exceptional discretizations of the sine gordon equation i e exceptional frenkel kontorova chains we also use one dimensional maps to construct a discrete sine gordon equation supporting kinks which move with arbitrary velocities without emitting radiation

standard nearest neighbour discretizations of klein gordon models cannot preserve both energy and linear momentum we consider nonlinear klein gordon wave equations and illustrate that standard discretizations thereof involving nearest neighbours may preserve either standardly defined linear momentum or standardly defined total energy but not both this has a variety of intriguing implications for the non potential discretizations that preserve only the linear momentum such as the self accelerating or self decelerating motion of coherent structures such as discrete kinks in these nonlinear lattices

homoclinic bifurcations in reversible hamiltonian systems abstract we study the existence of homoclic solutions for reversible hamiltonian systems taking the family of differential equations u iv au u f u b 0 as a model where f is an analytic function and a b real parameters these equations are important in several physical situations such as solitons and in the existence of finite energy stationary states of partial differential equations but no assumptions of any kind of discrete symmetry is made and the analysis here developed can be extended to others hamiltonian systems and successfully employed in situations where standard methods fail we reduce the problem of computing these orbits to that of finding the intersection of the unstable manifold with a suitable set and then apply it to concrete situations we also plot the homoclinic values configuration in parameters space giving a picture of the structural distribution and a geometrical view of homoclinic bifurcations

a numerical approach for simulating fluid structure interaction of flexible thin shells undergoing arbitrarily large deformations in complex domains we present a new numerical methodology for simulating fluid structure interaction fsi problems involving thin flexible bodies in an incompressible fluid the fsi algorithm uses the dirichlet neumann partitioning technique the curvilinear immersed boundary method curvib is coupled with a rotation free finite element fe model for thin shells enabling the efficient simulation of fsi problems with arbitrarily large deformation turbulent flow problems are handled using large eddy simulation with the dynamic smagorinsky model in conjunction with a wall model to reconstruct boundary conditions near immersed boundaries the curvib and fe solvers are coupled together on the flexible solid fluid interfaces where the structural nodal positions displacements velocities and loads are calculated and exchanged between the two solvers loose and strong coupling fsi schemes are employed enhanced by the aitken acceleration technique to ensure robust coupling and fast convergence especially for low mass ratio problems the coupled curvib fe fsi method is validated by applying it to simulate two fsi problems involving thin flexible structures 1 vortex induced vibrations of a cantilever mounted in the wake of a square cylinder at different mass ratios and at low reynolds number and 2 the more challenging high reynolds number problem involving the oscillation of an inverted elastic flag for both cases the computed results are in excellent agreement with previous numerical simulations and or experiential measurements grid convergence tests studies are carried out for both the cantilever and inverted flag problems which show that the curvib fe fsi method provides their convergence finally the capability of the new methodology in simulations of complex cardiovascular flows is demonstrated by applying it to simulate the fsi of a tri leaflet prosthetic heart valve in an anatomic aorta and under physiologic pulsatile conditions

normal form for travelling kinks in discrete klein gordon lattices abstract we study travelling kinks in the spatial discretizations of the nonlinear klein gordon equation which include the discrete 4 lattice and the discrete sine gordon lattice the differential advance delay equation for travelling kinks is reduced to the normal form a scalar fourth order differential equation near the quadruple zero eigenvalue we show numerically the non existence of monotonic kinks heteroclinic orbits between adjacent equilibrium points in the fourth order equation making generic assumptions on the reduced fourth order equation we prove the persistence of bounded solutions heteroclinic connections between periodic solutions near adjacent equilibrium points in the full differential advance delay equation with the technique of centre manifold reduction existence of multiple kinks in the discrete sine gordon equation is discussed in connection to recent numerical results of aigner et al a a aigner a r champneys v m rothos a new barrier to the existence of moving kinks in frenkel kontorova lattices physica d 186 2003 148 170 and results of our normal form analysis

one parameter localized traveling waves in nonlinear schrodinger lattices we address the existence of traveling single humped localized solutions in the spatially discrete nonlinear schr nls equation a mathematical technique is developed for analysis of persistence of these solutions from a certain limit in which the dispersion relation of linear waves contains a triple zero the technique is based on using the implicit function theorem for solution of an appropriate differential advance delay equation in exponentially weighted spaces the resulting melnikov calculation relies on a number of assumptions on the spectrum of the linearization around the pulse which are checked numerically we apply the technique to the so called salerno model and the translationally invariant discrete nls equation with a cubic nonlinearity we show that the traveling solutions terminate in the salerno model whereas they generally persist in the translationally invariant nls lattice as a one parameter family of solutions these results are found to be in a close correspondence with numerical approximations of traveling solutions with zero radiation tails analysis of persistence also predicts the spectral stability of the one parameter family of traveling solutions under time evolution of the discrete nls equation c 2007 elsevier b v all rights reserved

on a class of discretizations of hamiltonian nonlinear partial differential equations abstract we present a new class of discretizations of partial differential equations pdes that preserve a momentum like integral of the motion this results in an effective translational invariance for the dynamical problem and the absence of a peierls nabarro barrier that is usually present in discretizations of hamiltonian pdes a general method to construct such discretizations for any nonlinearity is given and the properties of the resulting differential difference equations are analyzed in a number of different cases for nonlinear klein gordon as well for nonlinear schrodinger type systems while for the former nonintegrability of the dynamical problem is evident in the latter case numerical evidence suggests that the behavior is close to the one of integrable systems we also show how static solutions of the equations can be constructed for these discretizations and discuss the similarities and differences of the method with previously reported ones

on the numerical solution of the sine gordon equation in this the first of two papers on the numerical solution of the sine gordon equation we investigate the numerical behavior of a double discrete completely integrable discretization of the sine gordon equation for certain initial values in the vicinity of homoclinic manifolds this discretization admits an instability in the form of grid scale oscillations we clarify the nature of the instability through an analytical investigation supported by numerical experiments in particular a perturbation analysis of the associated linear spectral problem shows that the initial values used for the numerical experiments lie exponentially close to a homoclinic manifold this paves the way for the second paper where we use the non linear spectrum as a basis for comparing different numerical schemes

conformal conservation laws and geometric integration for damped hamiltonian pdes conformal conservation laws are defined and derived for a class of multi symplectic equations with added dissipation in particular the conservation laws of energy and momentum are considered along with those that arise from linear symmetries numerical methods that preserve these conformal conservation laws are presented in detail providing a framework for proving a numerical method exactly preserves the dissipative properties considered the conformal methods are compared analytically and numerically to standard conservative methods which includes a thorough inspection of numerical solution behavior for linear equations damped klein gordon and sine gordon equations and a damped nonlinear schrodinger equation are used as examples to demonstrate the results

bifurcations of travelling wave solutions in the discrete nls equations abstract we study discrete nonlinear schrodinger nls equations which include the cubic nls lattice with on site interactions and the integrable ablowitz ladik lattice standing wave solutions are known to exist in the discrete nls equations outside of the finite spectral band we study travelling wave solutions which have nonlinear resonances with unbounded linear spectrum by using center manifold and normal form reductions we show that a continuous nls equation with the third order derivative term is a canonical normal form for the discrete nls equation near the zero dispersion limit bifurcations of travelling wave solutions near the zero dispersion limit are analyzed in the framework of the third order derivative nls equation we show that there exists a continuous two parameter family of single humped travelling wave solutions in the third order derivative nls equation when it is derived from the integrable ablowitz ladik lattice on the contrary there are no single humped solutions in the third order derivative nls equation when it is derived from the cubic nls equation with on site interactions nevertheless we show that there exists an infinite discrete set of one parameter families of double humped travelling wave solutions in the latter case our results are valid in the neighborhood of the zero dispersion point on the two parameter plane of travelling wave solutions

a normal form for nonlinear resonance of embedded solitons a normal form for nonlinear resonance of embedded solitons is derived for a coupled two wave system that generalizes the second harmonic generating model this wave system is non hamiltonian in general an embedded soliton is a localized mode of the nonlinear system that coexists with the linear wave spectrum it occurs as a result of a codimension one bifurcation of non local wave solutions nonlinearity couples the embedded soliton and the linear wave spectrum and induces a one sided radiation driven decay of embedded solitons the normal form shows that the embedded soliton is semi stable i e it survives under perturbations of one sign but is destroyed by perturbations of the opposite sign when a perturbed embedded soliton sheds continuous wave radiation the radiation amplitude is generally not minimal even if the wave system is hamiltonian the results of the analytical theory are confirmed by numerical computations

conditions on the existence of localized excitations in nonlinear discrete systems we use recent results that localized excitations in nonlinear hamiltonian lattices can be viewed and described as multiple frequency excitations their dynamics in phase space takes place on tori of corresponding dimension for a one dimensional hamiltonian lattice with nearest neighbour interaction we transform the problem of solving the coupled differential equations of motion into a certain mapping m l 1 f m l m l 1 where m l for every l lattice site is a function defined on an infinite discrete space of the same dimension as the torus we consider this mapping in the tails of the localized excitation i e for l rightarrow pm infty for a generic hamiltonian lattice the thus linearized mapping is analyzed we find conditions of existence of periodic one frequency localized excitations as well as of multiple frequency excitations the symmetries of the solutions are obtained as a result we find that the existence of localized excitations can be a generic property of nonlinear hamiltonian lattices in contrast to nonlinear hamiltonian fields

energetic pulses in exciton phonon molecular chains and conservative numerical methods for quasilinear hamiltonian systems the phenomenon of coherent energetic pulse propagation in exciton phonon molecular chains such as helix protein is studied using an ode system model of davydov scott type both with numerical studies using a new unconditionally stable fourth order accurate energy momentum conserving time discretization and with analytical explanation of the main numerical observations physically natural impulsive initial data associated with the energy released by atp hydrolysis are used and the best current estimates of physical parameter values in contrast to previous studies

existence of perturbed solitary wave solutions to a model equation for water waves abstract we prove the existence of travelling wave solutions to a fifth order partial differential equation which is a formal asymptotic approximation for water waves with surface tension these travelling waves are arbitrarily small perturbations of solitary waves but are not solitary waves themselves because they approach small amplitude oscillations for large values of the independent variable this result suggests that for bond numbers less than one third there are branches of travelling wave solutions to the water wave equations which are perturbations of supercritical elevation solitary waves and which bifurcate from froude number one and bond number one third

a note on the interaction between solitary waves in a singularly perturbed korteweg de vries equation for the fifth order korteweg de vries equation with a small parameter multiplying the highest derivative term it is known that solitary waves are non local and are accompanied by co propagating oscillatory waves of small amplitude and short wavelength here the authors report on some preliminary results for mutual interactions of these waves first they impose a quantization condition upon a chain of solitary waves to obtain a periodic solution then they compute the interaction force between two neighbouring waves and hence estimate the conditions for a bound state to occur

a hybrid cartesian immersed boundary method for simulating flows with 3d geometrically complex moving bodies a numerical method is developed for solving the 3d unsteady incompressible navier stokes equations in cartesian domains containing immersed boundaries of arbitrary geometrical complexity moving with prescribed kinematics the governing equations are discretized on a hybrid staggered non staggered grid layout using second order accurate finite difference formulas the discrete equations are integrated in time via a second order accurate dual time stepping artificial compressibility iteration scheme unstructured triangular meshes are employed to discretize complex immersed boundaries the nodes of the surface mesh constitute a set of lagrangian control points used to track the motion of the flexible body at every instant in time the influence of the body on the flow is accounted for by applying boundary conditions at cartesian grid nodes located in the exterior but in the immediate vicinity of the body by reconstructing the solution along the local normal to the body surface grid convergence tests are carried out for the flow induced by an oscillating sphere in a cubic cavity which show that the method is second order accurate the method is validated by applying it to calculate flow in a cartesian domain containing a rigid sphere rotating at constant angular velocity as well as flow induced by a flapping wing the ability of the method to simulate flows in domains with arbitrarily complex moving bodies is demonstrated by applying to simulate flow past an undulating fish like body and flow past an anatomically realistic planktonic copepod performing an escape like maneuver euver

isogeometric fluid structure interaction analysis with emphasis on non matching discretizations and with application to wind turbines abstract in this paper we develop a framework for fluid structure interaction fsi modeling and simulation with emphasis on isogeometric analysis iga and non matching fluid structure interface discretizations we take the augmented lagrangian approach to fsi as a point of departure here the lagrange multiplier field is defined on the fluid structure interface and is responsible for coupling of the two subsystems thus the fsi formulation does not rely on the continuity of the underlying function spaces across the fluid structure interface in order to produce the correct coupling conditions between the fluid and structural subdomains however in deriving the final fsi formulation the interface lagrange multiplier is formally eliminated and the formulation is written purely in terms of primal variables avoiding the use of lagrange multipliers adds efficiency to the proposed formulation as an added benefit the ability to employ non matching grids for multi physics simulations leads to significantly relaxed requirements that are placed on the geometry modeling and meshing tools for iga we show an application of the proposed fsi formulation to the simulation of the nrel 5 mw offshore wind turbine rotor where the aerodynamics domain is modeled using volumetric quadratic nurbs while the rotor structure is modeled using a cubic t spline based discretization of a rotation free kirchhoff love shell we conclude the article by showing fsi coupling of a t spline shell with a low order finite element method fem discretization of the aerodynamics equations this combined use of iga and fem is felt to be a good balance between speed robustness and accuracy of fsi simulations for this class of problems

standard and embedded solitons in nematic optical fibers a model for a non kerr cylindrical nematic fiber is presented we use the multiple scales method to show the possibility of constructing different kinds of wave packets of transverse magnetic modes propagating through the fiber this procedure allows us to generate different hierarchies of nonlinear partial differential equations which describe the propagation of optical pulses along the fiber we go beyond the usual weakly nonlinear limit of a kerr medium and derive a complex modified korteweg de vries equation cm kdv which governs the dynamics for the amplitude of the wave packet in this derivation the dispersion self focussing and diffraction in the nematic fiber are taken into account it is shown that this cm kdv equation has two parameter families of bright and dark complex solitons we show analytically that under certain conditions the bright solitons are actually double embedded solitons we explain why these solitons do not radiate at all even though their wave numbers are contained in the linear spectrum of the system we study numerically and analytically the stability of these solitons our results show that these embedded solitons are stable solutions which is an interesting property since in most systems the embedded solitons are weakly unstable solutions finally we close the paper by making comments on the advantages as well as the limitations of our approach and on further generalizations of the model and method presented

model checks for regression an innovation process approach in the context of regression analysis it is known that the residual cusum process may serve as a basis for the construction of various omnibus smooth and directional goodness of fit tests since a deeper analysis requires the decomposition of the cusums into their principal components and this is difficult to obtain we propose to replace this process by its innovation martingale it turns out that the resulting tests are asymptotically distribution free under composite null models and may be readily performed a simulation study is included which indicates that the distributional approximations already work for small to moderate sample sizes

a simple global characterization for normal forms of singular vector fields we derive a new global characterization of the normal forms of amplitude equations describing the dynamics of competing order parameters in degenerate bifurcation problems using an appropriate scalar product in the space of homogeneous vector polynomials we show that the resonant terms commute with the group generated by the adjoint of the original critical linear operator this leads to a very efficient constructive method to compute both the nonlinear coefficients and the unfolding of the normal form explicit examples and results obtained when there are additional symmetries are also presented

a monolithic approach to fluid structure interaction using space time finite elements abstract the paper presents a simultaneous solution procedure for fluid structure interaction problems the structural motion is described by geometrically nonlinear elastodynamics the fluid is modeled by the incompressible navier stokes equations the space time finite element method is applied to both continua leading to an almost uniform discretization in which velocity variables are used for fluid and structure in order to enforce momentum conservation and geometric continuity at the interface a weighted residual formulation of coupling conditions is introduced the discretized model equations for fluid structure and coupling conditions are formulated in a single equation system the nonlinear system and the fluid mesh movement are solved in a single iteration loop two dimensional examples of membrane flutter and vortex excited plate vibrations demonstrate the efficiency of the methodology

a projection semi implicit scheme for the coupling of an elastic structure with an incompressible fluid we address the numerical simulation of fluid structure systems involving an incompressible viscous fluid this issue is particularly difficult to face when the fluid added mass acting on the structure is strong as it happens in hemodynamics for example indeed several works have shown that in such situations implicit coupling seems to be necessary in order to avoid numerical instabilities although significant improvements have been achieved during the last years solving implicit coupling often exhibits a prohibitive computational cost in this work we introduce a semi implicit coupling scheme which remains stable for a reasonable range of the discretization parameters the first idea consists in treating implicitly the added mass effect whereas the other contributions geometrical non linearities viscous and convective effects are treated explicitly the second idea relies on the fact that this kind of explicit implicit splitting can be naturally performed using a chorin temam projection scheme in the fluid we prove conditional stability of the scheme for a fully discrete formulation several numerical experiments point out the efficiency of the present scheme compared to several implicit approaches

weakly nonlocal solitary waves in a singularly perturbed korteweg de vries equation a fifth order korteweg de vries equation is considered where the fifth order derivative term is multiplied by a small parameter it is known that solitary wave solutions of this model equation are nonlocal in that the central core of the wave is accompanied by copropagating trailing oscillations here using the techniques of exponential asymptotics these solutions are reexamined and it is established that they form a one parameter family characterized by the phase shift of the trailing oscillations explicit asymptotic formula relating the oscillation amplitude to the phase shift are obtained

traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators abstract motivated by earlier studies of artificial perceptions of light called phosphenes we analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon we examine the discrete model problem in its co traveling frame and systematically obtain the corresponding traveling waves in one spatial dimension direct numerical simulations as well as linear stability analysis are employed to reveal the parameter regions where the traveling waves are stable and these waves are in turn connected to the standing waves analyzed in earlier work we also consider a two dimensional extension of the model and demonstrate the robust evolution and stability of planar fronts our simulations also suggest the radial fronts tend to either annihilate or expand and flatten out depending on the phase value inside and the parameter regime finally we observe that solutions that initially feature two symmetric fronts with bulged centers evolve in qualitative agreement with experimental observations of phosphenes

computational aspects of some autonomous differential equations this paper deals principally with the differential equation d 4 y d x 4 d 2 y d x 2 y y 2 0 x y 0 d x 0 d y d x x x y x 0 where 0 is a prescribed constant the equation has served as a model for water waves with surface tension interest centres on the behaviour of d 3 y d x 3 at the point x 0 and we prove that this quantity is strictly positive and investigate its numerical behaviour as a function of a summary of principal formulae appears in 4 at the end of the paper and table 1 gives numerical results the introductory section of the paper speculates on whether our method might have wider application to similar autonomous differential equations which involve a small positive multiple of the highest derivative

non body fitted fluid structure interaction divergence conforming b splines fully implicit dynamics and variational formulation abstract immersed boundary ib methods deal with incompressible visco elastic solids interacting with incompressible viscous fluids a long standing issue of ib methods is the challenge of accurately imposing the incompressibility constraint at the discrete level we present the divergence conforming immersed boundary dcib method to tackle this issue the dcib method leads to completely negligible incompressibility errors at the eulerian level and various orders of magnitude of increased accuracy at the lagrangian level compared to other ib methods furthermore second order convergence of the incompressibility error at the lagrangian level is obtained as the discretization is refined in the dcib method the eulerian velocity pressure pair is discretized using divergence conforming b splines leading to inf sup stable and pointwise divergence free eulerian solutions the lagrangian displacement is discretized using non uniform rational b splines which enables to robustly handle large mesh distortions the data transfer needed between the eulerian and lagrangian descriptions is performed at the quadrature level using the same spline basis functions that define the computational meshes this conduces to a fully variational formulation sharp treatment of the fluid solid interface and a 0 5 increase in the convergence rate of the eulerian velocity and the lagrangian displacement measured in l 2 norm in comparison with using discretized dirac delta functions for the data transfer by combining the generalized method and a block iterative solution strategy the dcib method results in a fully implicit discretization which enables to take larger time steps various two and three dimensional problems are solved to show all the aforementioned properties of the dcib method along with mesh independence studies verification of the numerical method by comparison with the literature and measurement of convergence rates

a computational framework for fluid structure interaction finite element formulation and applications abstract this work is concerned with the modelling of the interaction of fluid flow with flexibly supported rigid bodies the fluid flow considered is governed by the incompressible navier stokes equations and modelled by employing stabilised low order velocity pressure finite elements the motion of the fluid domain is accounted for by an arbitrary lagrangian eulerian ale strategy the rigid body motion excited by the fluid flow is restricted by the elastic and damping properties of the supports for the temporal discretisation the discrete implicit generalised method is employed the resulting strongly coupled set of nonlinear equations is solved by means of a novel partitioned solution procedure which is based on the newton raphson methodology and incorporates full linearisation of the overall incremental problem the strong coupling is resolved and optimal convergence of the residuals is achieved several numerical examples are presented to demonstrate the robustness and efficiency of the methodology the examples clearly capture the phenomena of vortex induced oscillations and galloping

kink dynamics in the highly discrete sine gordon system abstract we study kink dynamics in a very discrete sine gordon system where the kink width is of the order of the lattice spacing numerical simulations exhibit new properties of kinks in this case they lose the memory of their initial velocity and propagate preferentially at well defined velocities which correspond to quasi steady states while a kink moving at other velocities suffers relatively high rates of radiation of small amplitude oscillations when a small external driving force is applied to the system the same velocities appear as plateus in the strongly nonlinear mobility of the kink the energy radiated by the kink is calculated for a simple model that preserves the discrete character of the system and the preferential velocities for the kink are obtained to good accuracy similar results may be expected to be valid for other discrete systems manifesting topological solitons the numerical simulations reveal also new stable multiple kink excitations which can propagate almost freely in extremely discrete systems where ordinary simple kinks are pinned to the lattice by discreteness the stability of the multiple kinks is discussed

completely conservative covariant numerical methodology for a distance dependent potential o newtonian dynamics is characterized by conservation of energy linear momentum and angular momentum in addition the basic dynamical equations are covariant that is invariant under fundamental coordinate transformations in this paper it is shown that related n body problems can be solved numerically in such a fashion that independently of the time step the identical conservation laws continue to be valid for the approximating difference equations in addition the numerical method is covariant

ranking and empirical minimization of u statistics the problem of ranking ordering instances instead of simply classifying them has recently gained much attention in machine learning in this paper we formulate the ranking problem in a rigorous statistical framework the goal is to learn a ranking rule for deciding among two instances which one is better with minimum ranking risk since the natural estimates of the risk are of the form of a u statistic results of the theory of u processes are required for investigating the consistency of empirical risk minimizers we establish in particular a tail inequality for degenerate u processes and apply it for showing that fast rates of convergence may be achieved under specific noise assumptions just like in classification convex risk minimization methods are also studied

an efficient parallel immersed boundary algorithm using a pseudo compressible fluid solver we propose an efficient algorithm for the immersed boundary method on distributed memory architectures that has the computational complexity of a completely explicit method and also has excellent parallel scaling the algorithm utilizes the pseudo compressibility method recently proposed by guermond and minev that uses a directional splitting strategy to discretize the incompressible navier stokes equations thereby reducing the linear systems to a series of one dimensional tridiagonal systems we perform numerical simulations of several fluid structure interaction problems in two and three dimensions and study the accuracy and convergence rates of the proposed algorithm we also compare the proposed algorithm with other second order projection based fluid solvers lastly the execution time and scaling properties of the proposed algorithm are investigated and compared to alternate approaches

exact static solutions of a two dimensional discrete ϕ4 model for a two dimensional scalar discrete 4 model we obtain several exact static solutions in the form of the jacobi elliptic functions jef with arbitrary shift along the lattice the quispel roberts thompson type quadratic maps are identified for the considered two dimensional model by using a jef solution we also show that many of the static solutions can be constructed iteratively from these quadratic maps by starting from an admissible initial value the kink solution having the form of tanh is numerically demonstrated to be generically stable

origin of multikinks in dispersive nonlinear systems we develop em the first analytical theory of multikinks for strongly em dispersive nonlinear systems considering the examples of the weakly discrete sine gordon model and the generalized frenkel kontorova model with a piecewise parabolic potential we reveal that there are no 2 pi kinks for this model but there exist em discrete sets of 2 pi n kinks for all n 1 we also show their bifurcation structure in driven damped systems

discrete klein gordon models with static kinks free of the peierls nabarro potential for the nonlinear klein gordon type models we describe a general method of discretization in which the static kink can be placed anywhere with respect to the lattice these discrete models are therefore free of the peierls nabarro potential previously reported models of this type are shown to belong to a wider class of models derived by means of the proposed method a relevant physical consequence of our findings is the existence of a wide class of discrete klein gordon models where slow kinks practically do not experience the action of the peierls nabarro potential such kinks are not trapped by the lattice and they can be accelerated by even weak external fields