analytical and numerical approaches to nonlinear galloping of internally resonant suspended cables a study is carried out on nonlinear multimodal galloping of suspended cables a consistent model of a curved cable beam geometrically nonlinear and able to torque recently formulated by the authors is used the model accounts for quasi steady aerodynamic forces including the effect of static swing of the cable and dynamic twist of the cross section complementary solution methods are employed namely finite difference and galerkin spatial discretization followed by numerical time integration or galerkin spatial discretization in conjunction with multiple scale perturbation analysis the different techniques are applied to a cable close to the first cross over point at which a number of internal resonances exist branches of periodic solutions and their stability are evaluated as functions of wind velocity the existence of branches of quasi periodic solutions originating from narrow unstable intervals and propagating elsewhere is also proved qualitative and quantitative results furnished by the different investigation tools are compared among them and the importance of the various components of motion accounted or neglected in the reduced models is discussed

global strong solution for the korteweg system in dimension n 2 this work is devoted to prove the existence of global strong solution in dimension n 2 for a general isothermal model of capillary fluids derived by j e dunn and j serrin 1985 see 16 which can be used as a phase transition model in a first part we prove the existence of strong solution in finite time for large initial data with a precise bound by below on the life span t of existence of the solution this one depends on the norm of the initial data 0 v 0 the second part consists in proving the existence of global strong solution with particular choice on the capillary coefficient 2 and on the viscosity tensor which corresponds to the shallow water case 2 div du to do this we derivate different energy estimate on the density and the effective velocity v which ensures that the strong solution can be extended beyond t the main difficulty consists in controlling the vacuum or in other words to estimate the l norm of 1 the proof relies mostly on a method introduced by de giorgi 14 see also ladyzhenskaya et al in 30 for the parabolic case to obtain regularity results for elliptic equations with discontinuous diffusion coefficients and a suitable bootstrap argument

a comparison of approximate boundary conditions and infinite element methods for exterior helmholtz problems we compare the accuracy of a variety of approximate boundary conditions abcs and two versions of an infinite element method iem for approximating solutions of exterior helmholtz problems the infinite elements are of variable order in the radial direction and differ only in whether the test functions in the weak formulation are conjugated or not we find that the accuracy of the abcs decreases with increasing frequency and that at higher frequencies their accuracy is several orders of magnitude lower than that obtained with the iems we show that the convergence rate of the conjugated element is slower than the rate for the unconjugated element and that the latter element fails to converge in the far field

a hybrid boundary element wave based method for an efficient solution of bounded acoustic problems with inclusions abstract this paper presents a novel hybrid approach for the efficient solution of bounded acoustic problems with arbitrarily shaped inclusions the hybrid method couples the wave based method wbm and the boundary element method bem in order to benefit from the prominent advantages of both the wbm is based on an indirect trefftz approach as such it uses exact solutions of the governing equations to approximate the field variables it has a high computational advantage as compared to conventional element based methods when applied on moderately complex geometries the bem on the other hand can tackle complex geometries with ease however it can be computationally expensive the hybrid boundary element wave based method be wbm combines the best properties of the two it makes use of the efficient wbm for the moderately complex bounded domains and utilizes the flexibility of the bem for the complex objects that reside in the bounded domains the accuracy and the efficiency of the method is demonstrated with three numerical examples where the hybrid be wbm is shown to be more efficient than a quadratic finite element method fem while the hybrid method provides efficient solution for the bounded problems with inclusions it also brings certain conceptual advantages over the fem the fact that it is a boundary type method with an easy refinement concept reduces the modeling effort on the preprocessing step moreover for certain optimization scenarios such as optimization of the position of inclusions the fem becomes disadvantageous because of its domain discretization requirements for each iteration on the other hand the hybrid method allows reusing of the fixed geometries and only needs recalculation of the coupling matrices without a further need of preprocessing as such the hybrid method combines efficiency with versatility

a differential quadrature hierarchical finite element method using fekete points for triangles and tetrahedrons and its applications to structural vibration abstract a differential quadrature hierarchical finite element method dqhfem using fekete points was formulated for triangles and tetrahedrons and applied to structural vibration analyses first orthogonal polynomials on triangles and tetrahedrons that can be used as bases of the hierarchical finite element method hfem were derived and simple formulas of transforming one dimensional non uniform nodes to simplexes were presented then the non uniform nodes were used as initial guesses to solve the fekete points on simplexes through newton raphson s method together with the orthogonal polynomials new differential quadrature dq rules on simplexes were formulated using the hfem bases and the fekete points the numbers of nodes or bases on different edges and faces and inside the body of the new dq elements do not relate with each other like the hfem that can freely assign different numbers of bases on different edges and faces and inside the body so the new dq method was named as a differential quadrature hierarchical dqh method that uses either interpolation functions or orthogonal polynomials as bases inside the element its weak form was named as the dqhfem besides the dqh method and its weak form a simple method of generating high quality linear and high order triangular and tetrahedral meshes from a single nurbs patch was presented numerical tests of the dqhfem through structural vibration analyses showed that high accuracy results can be obtained using only a few nodes even on curvilinear domains using the dqh bases on both physical and geometric fields it was concluded that wide applications of the dqh method and the dqhfem to science and engineering are possible and commercial codes based on them are deserved to be developed

an integral formulation for wave propagation on weakly non uniform potential flows abstract an integral formulation for acoustic radiation in moving flows is presented it is based on a potential formulation for acoustic radiation on weakly non uniform subsonic mean flows this work is motivated by the absence of suitable kernels for wave propagation on non uniform flow the integral solution is formulated using a green s function obtained by combining the taylor and lorentz transformations although most conventional approaches based on either transform solve the helmholtz problem in a transformed domain the current green s function and associated integral equation are derived in the physical space a dimensional error analysis is developed to identify the limitations of the current formulation numerical applications are performed to assess the accuracy of the integral solution it is tested as a means of extrapolating a numerical solution available on the outer boundary of a domain to the far field and as a means of solving scattering problems by rigid surfaces in non uniform flows the results show that the error associated with the physical model deteriorates with increasing frequency and mean flow mach number however the error is generated only in the domain where mean flow non uniformities are significant and is constant in regions where the flow is uniform

a fully locking free isogeometric approach for plane linear elasticity problems a stream function formulation in this paper we study plane incompressible elastic problems by means of a stream function formulation such that a divergence free displacement field can be computed from a scalar potential the numerical scheme is constructed within the framework of nurbs based isogeometric analysis and we take advantage of the high continuity guaranteed by nurbs basis functions in order to obtain the displacement field from the potential differentiation as a consequence the obtained numerical scheme is automatically locking free in the presence of the incompressibility constraint a discontinuous galerkin approach is proposed to deal with multiple mapped possibly multiply connected domains extensive numerical results are provided to show the method capabilities 2007 elsevier b v all rights reserved

interior two dimensional acoustic modelling and modal analysis using isogeometric approach abstract in this paper the interior two dimensional acoustic modelling and modal analysis are presented in the framework of isogeometric analysis iga the acoustic domain governed by the helmholtz equation is parameterized and analysed by non uniform rational lagrange nurl basis which can construct exact geometry model inherently like non uniform rational b spines nurbs and can provide a more straightforward way than nurbs to impose dirichlet boundary conditions the verification and versatility of iga using nurl are assessed in the investigation of a unit square domain and a unit circular domain by comparison with analytical solutions furthermore a quadrilateral domain with concave or convex conics is studied and some innovative results are presented which can be the benchmark data for other algorithm researches the effects of geometric weight and aspect ratio on acoustic eigenvalue and eigenmode of the quadrilateral domain are investigated in detail

a variational formulation for vibro acoustic analysis of a panel backed by an irregularly bounded cavity abstract a weak form variational based method is developed to study the vibro acoustic responses of coupled structural acoustic system consisting of an irregular acoustic cavity with general wall impedance and a flexible panel subjected to arbitrary edge supporting conditions the structural and acoustical models of the coupled system are formulated on the basis of a modified variational method combined with multi segment partitioning strategy meanwhile the continuity constraints on the sub segment interfaces are further incorporated into the system stiffness matrix by means of least squares weighted residual method orthogonal polynomials such as chebyshev polynomials of the first kind are employed as the wholly admissible unknown displacement and sound pressure field variables functions for separate components without meshing and hence mapping the irregular physical domain into a square spectral domain is necessary the effects of weighted parameter together with the number of truncated polynomial terms and divided partitions on the accuracy of present theoretical solutions are investigated it is observed that applying this methodology accurate and efficient predictions can be obtained for various types of coupled panel cavity problems and in weak or strong coupling cases for a panel surrounded by a light or heavy fluid the inherent principle of velocity continuity on the panel cavity contacting interface can all be handled satisfactorily key parametric studies concerning the influences of the geometrical properties as well as impedance boundary are performed finally by performing the vibro acoustic analyses of 3d car like coupled miniature we demonstrate that the present method seems to be an excellent way to obtain accurate mid frequency solution with an acceptable cpu time

bayesian based estimation of acoustic surface impedance finite difference frequency domain approach acoustic performance for an interior requires an accurate description of the boundary materials surface acoustic impedance analytical methods may be applied to a small class of test geometries but inverse numerical methods provide greater flexibility the parameter estimation problem requires minimizing prediction vice observed acoustic field pressure the bayesian network sampling approach presented here mitigates other methods susceptibility to noise inherent to the experiment model and numerics a geometry agnostic method is developed here and its parameter estimation performance is demonstrated for an air backed micro perforated panel in an impedance tube good agreement is found with predictions from the iso standard two microphone impedance tube method and a theoretical model for the material data by products exclusive to a bayesian approach are analyzed to assess sensitivity of the method to nuisance parameters

toward a moyal quantization program of the membrane a moyal deformation quantization approach to a spherical membrane moving in flat target backgrounds in the light cone gauge is presented the physical picture behind this construction relies on viewing the two spatial membrane coordinates 1 2 as the two phase space variables q p and the temporal membrane coordinate as time solutions to the moyal deformed equations of motion are explicitly constructed in terms of elliptic functions a knowledge of the moyal deformed light cone membrane s hamiltonian density h q p allows us to construct a time dependent wigner function q p as solutions of the moyal liouville equation and from which one can obtain the expectation values of the operator that define the quantum average values of the energy density configurations of the membrane at any instant it is shown how a time dependent quartic oscillator with q4 p4 q2p2 terms plays a fundamental role in the quantum treatment of membranes and displays an important p q duality symmetry

extended isogeometric boundary element method xibem for three dimensional medium wave acoustic scattering problems a boundary element method bem based on non uniform rational b splines nurbs is used to find solutions to three dimensional wave scattering problems governed by the helmholtz equation the method is extended in a partition of unity sense multiplying the nurbs functions by families of plane waves this method is called the extended isogeometric boundary element method xibem in this paper the collocation xibem formulation is described and numerical results are given the numerical results are compared against closed form or converged solutions comparisons are made against the conventional boundary element method and the non enriched isogeometric bem igabem when compared to non enriched boundary element simulations using xibem significantly reduces the number of degrees of freedom required to obtain a solution of a given error thus with a fixed computational resource problems of a shorter wavelength can be solved

duality and unified analysis of discrete approximations in structural dynamics and wave propagation comparison of p method finite elements with k method nurbs we study the discretization behavior of classical finite element and nurbs approximations on problems of structural vibrations and wave propagation we find that on the basis of equal numbers of degrees of freedom and bandwidth nurbs have superior approximation properties in fact we observe that the high mode behavior of classical finite elements is divergent with the order of approximation a surprisingly negative result on the other hand nurbs offer almost spectral approximation properties and all modes converge with increasing order of approximation

a unified approach for nonlinear vibration analysis of curved structures using non uniform rational b spline representation abstract a novel procedure for the nonlinear vibration analysis of curved beam is presented the non uniform rational b spline nurbs is combined with the euler bernoulli beam theory to define the curvature of the structure the governing equation of motion and the general frequency formula using the nurbs variables is applicable for any type of curvatures is developed the galerkin procedure is implemented to obtain the nonlinear ordinary differential equation of curved system and the multiple time scales method is utilized to find the corresponding frequency responses as a case study the nonlinear vibration of carbon nanotubes with different shapes of curvature is investigated the effect of oscillation amplitude and the waviness on the natural frequency of the curved nanotube is evaluated and the primary resonance case of system with respect to the variations of different parameters is discussed for the sake of comparison of the results obtained with those from the molecular dynamic simulation the natural frequencies evaluated from the proposed approach are compared with those reported in literature for few types of carbon nanotube simulation

on the existence regularity and decay of solitary waves to a generalized benjamin ono equation in r2 where 0 and 1 2 is the operator de2ned by f 1 2u u f or represent the fourier transform eq 1 describes the dynamics of three dimensional slightly nonlinear disturbances in boundary layer shear ows without the assumption of a di erence in their scales along and across the ow see 1 6 the solitary waves of 1 are solutions of the form a x y t v x ct y where c is the speed of the solitary wave it seems that solitary waves play an important role in the evolution of 1 such a solution must satisfy the equation

plane wave enriched partition of unity isogeometric analysis puiga for 2d helmholtz problems abstract in general numerical concerns in simulation of time harmonic acoustic waves are mainly due to the dispersion errors and the demands in modeling the problems with higher number of degrees of freedom per wavelength to obtain acceptable results as a remedy plane wave enriched partition of unity finite element method pufem was earlier proposed by melenk and babuska 1996 even though pufem gives accurate results with lesser degrees of freedom and shows exponential convergence it suffers from the approximate representation of geometry and leads to the boundary representation induced errors in this regard plane wave enriched pufem under isogeometric framework named partition of unity isogeometric analysis puiga is proposed for accurate geometry representation and smooth solution approximation which can lead to a better solution several benchmark problems are considered in the present study to illustrate the computational effectiveness of puiga

infinite dimensional algebras and a trigonometric basis for the classical lie algebras this paper explores features of the infinite dimensional algebras that have been previously introduced in particular it is shown that the classical simple lie algebras an bn cn dn may be expressed in an egalitarian basis with trigonometric structure constants the transformation to the standard cartan weyl basis and the particularly transparent n limit that this formulation allows is provided

cubic spline interpolation based time domain equivalent source method for modeling transient acoustic radiation abstract transient acoustic radiation from an arbitrarily shaped source is modeled using a cubic spline interpolation based time domain equivalent source method in the method the cubic spline interpolation function is introduced to approximate the equivalent source strengths in the time domain for establishing the relationships between the acoustic quantities in the field the normal acceleration on the source surface and the equivalent sources and the least squares solution of the equivalent source strengths at each time step is determined by an iterative solving process with the singular value decomposition technique the proposed method has the abilities of calculating the acoustic quantities directly in the time domain and applying to arbitrarily shaped sources numerical examples of calculating the transient acoustic fields from a baffled planar piston and an impulsively accelerating sphere demonstrate that the proposed method can model the transient acoustic radiation very well the experimental results also further verify the validity of the proposed method

numerical difficulties with boundary element solutions of interior acoustic problems although boundary element methods have been applied to interior problems for many years the numerical difficulties that can occur have not been thoroughly explored various authors have reported low frequency breakdowns and artificial damping due to discretization errors in this paper it is shown through a simple example problem that the numerical difficulties depend on the solution formulation when the boundary conditions are imposed directly the solution suffers from artificial damping which may potentially lead to erroneous predictions when boundary element methods are used to evaluate the performance of damping materials this difficulty can be alleviated by first computing an impedance or admittance matrix and then using its reactive component to derive the solution for the acoustic field numerical computations are used to demonstrate that this technique eliminates artificial damping but does not correct errors in the reactive components of the impedance or admittance matrices which then causes nonexistence and nonuniqueness difficulties at the interior resonance frequencies for hard wall and pressure release boundary conditions respectively it is shown that the admittance formulation is better suited to boundary element computations for interior problems because the resonance frequencies for pressure release boundary conditions do not begin until the smallest dimension of the boundary surface is at least one half the acoustic wavelength aside from producing much more accurate predictions the admittance matrix is also much easier to interpolate at low frequencies due to the absence of interior resonances for the example problem considered only the formulation using the reactive component of the admittance matrix produces accurate solutions as long as the surface element discretization satisfies the standard six element per wavelength rule

solitons and scattering for the cubic quintic nonlinear schrodinger equation on mathbb r 3 r 3 we consider the cubic quintic nonlinear schrodinger equation i partial t u delta u u 2u u 4u in the first part of the paper we analyze the one parameter family of ground state solitons associated to this equation with particular attention to the shape of the associated mass energy curve additionally we are able to characterize the kernel of the linearized operator about such solitons and to demonstrate that they occur as optimizers for a one parameter family of inequalities of gagliardo nirenberg type building on this work in the latter part of the paper we prove that scattering holds for solutions belonging to the region mathcal r of the mass energy plane where the virial is positive we show that this region is partially bounded by solitons also by rescalings of solitons which are not soliton solutions in their own right the discovery of rescaled solitons in this context is new and highlights an unexpected limitation of any virial based methodology

a performance study of nurbs based isogeometric analysis for interior two dimensional time harmonic acoustics abstract this work evaluates the performance of a nurbs based isogeometric finite element formulation for solving stationary acoustic problems in two dimensions an initial assessment is made by studying eigenvalue problems for a square and a circular domain the spectral approximation properties of nurbs functions of varying order are compared to those of conventional polynomials and are found to be superior yielding more accurate representations of eigenvalues as well as eigenmodes the higher smoothness of nurbs shape functions yields better approximations over an extended frequency range when compared to conventional polynomials two numerical case studies including a geometrically complex domain are used to benchmark the method versus the traditional finite element method a convergence analysis confirms the higher efficiency of the isogeometric method on a per degree of freedom basis simulations over a wider frequency range also illustrate that the method suffers less from the dispersion effects that deteriorate the acoustic response towards higher frequencies the tensor product structure of nurbs however also imposes practical considerations when modelling a complex geometry consisting of multiple patches

asymptotics for the ginzburg landau equation in arbitrary dimensions let be a bounded simply connected regular domain of rn n 2 for 0 e 1 let ue c be a smooth solution of the ginzburg landau equation in with dirichlet boundary condition ge i e formula we are interested in the asymptotic behavior of ue as e goes to zero under the assumption that ee ue m0 log e and some conditions on ge which allow singularities of dimension n 3 on

the effect of temperature on the large amplitude vibrations of curved beams the thermoelastic geometrically nonlinear vibrations of isotropic straight and curved beams are studied using p version hierarchical finite elements first order shear deformation theory is followed and both the longitudinal displacements and inertia are taken into account the nonlinear equations of motion are solved in the time domain by newmark s method the influence of parameters like the temperature variation the thickness and the ratio of curvature on the beams nonlinear dynamics is studied periodic and non periodic motions are found

boundary element acoustics fundamentals and computer codes fundamentals of linear acoustics the helmholtz integral equation two dimensional problems three dimensional problems the normal derivative integral equation indirect variational boundary element method in acoustics acoustic eigenvalue analysis by boundary element methods time domain three dimensional analysis extended kirchhoff integral formulations

rotating 2n vortex solutions to the gross pitaevskii equation on s2 we establish the existence of rotating solutions to the gross pitaevskii equation iut u 1 2 1 u 2 uposed on s2 that is for u s2 r c these solutions possess vortices that for all time follow the vortex paths of known relative equilibria to the point vortex problem on the two sphere in the asymptotic regime 1 the approach is variational based on minimization of the ginzburg landau energy subject to a momentum constraint we also establish orbital stability within a class of symmetric initial data

an improved nurbs based isogeometric analysis with enhanced treatment of essential boundary conditions the nurbs based isogeometric analysis offers a seamless integration between the cad and subsequent finite element analysis and has been shown to be very effective for wide classes of problems due to its accurate geometric description however similar to the moving least square or reproducing kernel meshfree shape functions the nurbs basis functions generally are not interpolatory functions in this work it is shown that the direct imposition of the inhomogeneous essential boundary conditions to the nurbs control points may lead to significant errors with deteriorated rates of convergence consequently an improved formulation for nurbs based isogeometric analysis is proposed this is fulfilled by employing a transformation method that relates the control variables to the collocated nodal values at the essential boundary by using open knot vectors the resulting nurbs basis functions associated with the interior control points vanish at the boundary thus unlike the meshfree approximation the nurbs control points can be clearly partitioned into boundary and interior groups therefore the transformation method can be only applied to the boundary control points via invoking collocation of physical values at a set of boundary points the nurbs approximation enhanced with transformed physical boundary variables is kinematically admissible and the essential boundary conditions can be enforced straightforwardly like the finite element method several potential and elasticity problems evince that much higher solution accuracy with optimal convergence rates can be achieved by the present improved formulation compared with the method with direct imposition of essential boundary conditions to control variables

isogeometric indirect boundary element method for solving the 3d acoustic problems abstract this paper provides an isogeometric indirect boundary element method igibem based on nurbs non uniform rational b splines and pht splines polynomial splines over hierarchical t meshes for analyzing the three dimensional 3d acoustic problems in the classical procedure the geometries are discretized by lagrange polynomials elements which leads to both substantial geometrical error and time consuming meshing steps however these deficiencies can be eliminated by the isogeometric analysis iga directly incorporating the geometry description generated from the cad computer aided design software into cae computer aided engineering analysis unlike the dbem direct boundary element method the ibem indirect boundary element method allows different types of boundary conditions on the two sides of a surface moreover the hypersingular integrals in ibem can be transformed to a weakly singular form in addition the pht based ibem is used to investigate the influence of local refinement on the accuracy of solutions finally the non uniqueness problem is solved which is a fatal defect in the acoustic bem for the exterior problem four different methods to handle the non uniqueness problem are discussed and compared the results obtained by the proposed method were compared with analytical solutions and the results computed by lagrange based ibem several benchmark examples demonstrate 1 the present method i e igibem has super accuracy over conventional ibem for the acoustic problems 2 local refinement has a significant influence on the convergence rate of the solutions and the numerical accuracy is relevant to the distance to the boundary where the local refinement acted 3 as for the non uniqueness problem the imposition of specific interior boundary conditions not only obtains the best calculation result over the entire range of frequencies but also has a simple integral formulation

vibro acoustic design sensitivity analysis using the wave based method abstract conventional element based methods such as the finite element method fem and boundary element method bem require mesh refinements at higher frequencies in order to converge therefore their applications are limited to low frequencies compared to element based methods the wave based method wbm adopts exact solutions of the governing differential equation instead of simple polynomials to describe the dynamic response variables within the subdomains as such the wbm does not require a finer division of subdomains as the frequency increases in order to exhibit high computational efficiency in this paper the design sensitivity formulation of a semi coupled structural acoustic problem is implemented using the wbm here the results of structural harmonic analyses are imported as the boundary conditions for the acoustic domain which consists of multiple wave based subdomains the cross sectional area of each beam element is considered as a sizing design variable then the adjoint variable method avm is used to efficiently compute the sensitivity the adjoint variable is obtained from structural reanalysis using an adjoint load composed of the system matrix and an evaluation of the wave functions of each boundary the proposed sensitivity formulation is subsequently applied to a two dimensional 2d vehicle model finally the sensitivity results are compared to the finite difference sensitivity results which show good agreement

quantization and motion law for ginzburg landau vortices we study the vortex trajectories for the two dimensional complex parabolic ginzburg landau equation without a well preparedness assumption we prove that the trajectory set is rectifiable and satisfies a weak motion law in the case of degree 1 vortices the motion law is satisfied in the classical sense moreover dissipation occurs only at a finite number of times away from these times possible collisions and splittings of vortices are constrained by algebraic equations involving their topological degrees

a comparison of two trefftz type methods the ultraweak variational formulation and the least squares method for solving shortwave 2 d helmholtz problems trefftz methods for the numerical solution of partial differential equations pdes on a given domain involve trial functions which are defined in subdomains are generally discontinuous and are solutions of the governing pde or its adjoint within each subdomain the boundary conditions and matching conditions between subdomains must be enforced separately an interesting novel result presented in this paper is that the least squares method lsm and the ultraweak variational formulation two methods already established for solving the helmholtz equation can be derived in the framework of the trefftz type methods in the first case the boundary conditions and interelement continuity are enforced by means of a least squares procedure in the second a galerkin type weighted residual method is used another goal of the work is to assess the relative efficiency of each method for solving shortwave problems in acoustics and to study the stability of each method the numerical performance of each scheme is assessed with reference to two 2 d test problems acoustic propagation in an uniform soft walled duct and propagation in an l shaped domain the latter involving singular behaviour at a sharp corner

non uniform rational lagrange functions and its applications to isogeometric analysis of in plane and flexural vibration of thin plates abstract new basis functions were developed for isogeometric analysis iga to overcome the difficulties of iga using nurbs non uniform rational b splines on coping with dirichlet boundary conditions the new basis functions were constructed through nesting rational local lagrange interpolations like the t spline and were evaluated in similar procedure as the finite difference method explicit expressions for the new basis functions were presented due to their equivalence to the nurbs the new basis functions were named as non uniform rational lagrange nurl basis iga using nurl includes the finite element method as a special case but the geometry in iga using nurl is exact iga using nurl can carry out p refinement that has the nesting feature of the k refinement of nurbs dirichlet boundary conditions can be directly imposed in iga using nurl because the nurl are interpolation basis functions a method of directly transforming the tensor product basis of triangular patches to area coordinates was presented and the singularity problem at the edge degenerated to a single point was solved the methods developed in this work were applied to in plane and flexural vibration of thin plates comparisons with available results in literatures showed the fast convergence and high accuracy of iga using nurl and the transformation method for triangular patches introduction of a matlab toolbox of the nurl was appended

travelling waves for the gross pitaevskii equation ii the purpose of this paper is to provide a rigorous mathematical proof of the existence of travelling wave solutions to the gross pitaevskii equation in dimensions two and three our arguments based on minimization under constraints yield a full branch of solutions and extend earlier results see 3 4 8 where only a part of the branch was built in dimension three we also show that there are no travelling wave solutions of small energy

isogeometric analysis for geometric modelling and acoustic attenuation performances of reactive mufflers abstract in the present study the acoustic attenuation performances of mufflers are predicted by employing three dimensional isogeometric analysis iga and multi patch technique for the first time circular elliptical and conical reactive expansion chamber mufflers are exactly parameterized by non uniform rational b splines nurbs and the helmholtz equation governing the interior acoustic field is also solved by nurbs compared with traditional finite element method fem which is rooted in lagrange and hermite functions iga can effectively avoid the time consuming meshing and totally preserve exact geometrical information during the modelling analysis process the computational effectiveness of multi patch iga for calculating transmission loss is verified by comparing with experimental approach boundary element method and other numerical methods from available research articles the effects of geometry such as shapes of the expansion cavity and lengths of the extended inlet outlet are discussed in detail

existence of global strong solution for korteweg system with large infinite energy initial data this work is devoted to the study of the initial boundary value problem for a general isothermal model of capillary fluids derived by j e dunn and j serrin 1985 see cite fds which can be used as a phase transition model we will prove the existence of local and global under a condition of smallness on the initial data strong solutions with discontinuous initial density where ln rho 0 belongs to the besov space b n 2 infty r n in passing our result allow to consider initial data with discontinuous interfaces up our knowledge in the literature the results of existence of strong solutions require generally continuous initial density it implies also that we can work with initial data space of infinite energy our result relies on the fact that the density can be written as the sum of the solution rho l associated to linear system and a remainder density bar rho which is more regular than rho l by taking into account the regularizing effects induced on the bilinear convection term the main difficulty concerns the proof of new estimate of maximum principle type for the linear system associated to the korteweg system the proof is based on a characterization of the besov space in terms of the semi group associated to this linear system let also mention that we prove the existence of global strong solution with a smallness hypothesis which is subcritical in terms of the scaling of the equations it allows us to exhibit a family of large energy initial data for the scaling of the equations providing global strong solution in particular for the first time up our knowledge we show the existence of global strong solution for some large energy initial data when n 2 we finish this paper by introducing the notion of quasi solutions for the korteweg s system a tool which has been developed in the framework of the compressible navier stokes equations cite arxiv arxiv1 hal cras1 cras2 which enables us to improve the previous result and by obtaining the existence of global strong solution with large initial velocity in b n 1 2 infty in particular when n 2 it implies the existence of global strong solution with large energy data as a corollary we get global existence and uniqueness for highly compressiblekorteweg system when n geq2 it means that for any large initial data under an irrotational condition on the initial velocity we have the existence of global strong solution provided that the pressure is sufficiently highly compressible

stability of traveling waves of nonlinear schrodinger equation with nonzero condition at infinity we study the stability of traveling waves of the nonlinear schrodinger equation with nonzero condition at infinity obtained via a constrained variational approach two important physical models for this are the gross pitaevskii gp equation and the cubic quintic equation first under a non degeneracy condition we prove a sharp instability criterion for 3d traveling waves of gp which had been conjectured in the physical literature this result is also extended for general nonlinearity and higher dimensions including 4d gp and 3d cubic quintic equations second for cubic quintic type nonlinearity we construct slow traveling waves and prove their nonlinear instability in any dimension for dimension two the non degeneracy condition is also proved for these slow traveling waves for general traveling waves without vortices that is nonvanishing and with general nonlinearity in any dimension we find a sharp condition for linear instability third we prove that any 2d traveling wave of gp is transversally unstable and we find the sharp interval of unstable transversal wave numbers near unstable traveling waves of all of the above cases we construct unstable and stable invariant manifolds

three dimensional acoustic scattering by multiple spheres using collocation multipole method abstract this paper presents a semi analytical approach to solve the three dimensional acoustic scattering problems with multiple spheres subjected to a plane sound wave to satisfy the three dimensional helmholtz equation in a spherical coordinate system the multipole expansion for the scattered acoustic field is formulated in terms of the associated legendre functions and the spherical hankel functions that also satisfy the radiation condition at infinity the multipole method the directional derivative and the collocation technique are combined to propose a collocation multipole method in which the acoustic field and its normal derivative with respect to the non local spherical coordinate system can be calculated without any truncated error frequently occurred when using the addition theorem the boundary conditions are satisfied by collocating points on the surface of each sphere by truncating the higher order terms of the multipole expansion a finite linear algebraic system is acquired the scattered field can then be determined according to the given incident sound wave the convergence analysis considering the specified error the separation of spheres and the wave number of an incident wave is first carried out to provide guide lines for the proposed method then the proposed results for acoustic scattering by one two and three spheres are validated by using the available analytical method and numerical methods such as boundary element method finally the effects of the separation between scatterers the incident wave number and the incident angle on the acoustic scattering are investigated extensively

optimal placement of constrained layer damping for reduction of interior noise in this paper an efficient constrained layer damping layout optimization method in structural acoustic systems is proposed to simulate vibro acoustic systems a hybrid model that uses finite elements for structures and boundary elements for the cavity is developed with a finite element formulation the intrinsic nonlinearities of viscoelastic damping materials with respect to frequency and temperature are included using a fractional derivative model the resulting complex eigenvalue problem is solved using an iterative scheme the optimal layout of the constrained viscoelastic layer damping on the structure is identified using a gradient based numerical search algorithm the sensitivity formulas are derived analytically for acoustic and structural responses the optimal damping layer layouts that minimize the added mass with minimum sound pressure level requirements are obtained for different temperatures

isogeometric methods for computational electromagnetics b spline and t spline discretizations in this paper we introduce methods for electromagnetic wave propagation based on splines and on t splines we define spline spaces which form a de rham complex and following the isogeometric paradigm we map them on domains which are piecewise spline or nurbs geometries we analyze their geometric and topological structure as related to the connectivity of the underlying mesh and we present degrees of freedom together with their physical interpretation the theory is then extended to the case of meshes with t junctions leveraging on the recent theory of t splines the use of t splines enhance our spline methods with local refinement capability and numerical tests show the efficiency and the accuracy of the techniques we propose

extended isogeometric boundary element method xibem for two dimensional helmholtz problems isogeometric analysis is a topic of considerable interest in the field of numerical analysis the boundary element method bem requires only the bounding surface of geometries to be described this makes non uniform rational b splines nurbs which commonly describe the bounding curve or surface of geometries in cad software appear to be a natural tool for the approach this isogeometric analysis bem igabem provides accuracy benefits over conventional bem schemes due to the analytical geometry provided by nurbs when applied to wave problems it has been shown that enriching bem approximations with a partition of unity basis in what has become known as the pu bem allows highly accurate solutions to be obtained with a much reduced number of degrees of freedom this paper combines these approaches and presents an extended isogeometric bem xibem which uses partition of unity enriched nurbs functions this new approach provides benefits which surpass those of both the igabem and the pu bem two numerical examples are given a single scattering cylinder and a multiple scatterer made up of two capsules and a cylinder

travelling waves for the gross pitaevskii equation in dimension larger than two abstract we present a different approach than the one given in bethuel et al j eur math soc 6 1 2004 17 of the existence of travelling vortex rings solutions to the gross pitaevskii equation in dimension n 3 we follow an idea which was used before in bethuel and saut ann ihp phys theor 70 2 1999 147 in dimension 2 invoking the mountain pass lemma it has the advantage of providing a full interval of propagation speeds 0 c 0

traveling wave solutions of the schrodinger map equation we first construct traveling wave solutions for the schrodinger map in r 2 m t m m m 3 e 3 in 2 of the form m x 1 x 2 t where m has exactly two vortices at approximately 1 2 0 r 2 of degree 1 we use a perturbative approach that gives a complete characterization of the asymptotic behavior of the solutions with a few modifications a similar construction yields traveling wave solutions of schrodinger map equations in higher dimensions 2010 wiley periodicals inc

nondegeneracy morse index and orbital stability of the kp i lump solution using backlund transformation we analyze the spectral property of the kp i lump solution it is proved that the lump is nondegenerate and its morse index equals one as a consequence we show that it is orbitally stable

traveling waves for nonlinear schrodinger equations with nonzero conditions at infinity for a large class of nonlinear schrodinger equations with nonzero conditions at infinity and for any speed c less than the sound velocity we prove the existence of nontrivial finite energy traveling waves moving with speed c in any space dimension n 3 our results are valid as well for the gross pitaevskii equation and for nls with cubic quintic nonlinearity

moyal nahm equations various aspects of the nahm equations in three and seven dimensions are investigated the residues of the variables at simple poles in the seven dimensional case form an algebra a large class of matrix representations of this algebra is constructed the large n limit of these equations is taken by replacing the commutators by moyal brackets and a set of nontrivial solutions in a generalized form of wigner distribution functions is obtained

nonlinear vibration of a curved beam under uniform base harmonic excitation with quadratic and cubic nonlinearities abstract this paper presents nonlinear vibration analysis of a curved beam subject to uniform base harmonic excitation with both quadratic and cubic nonlinearities the galerkin method is employed to discretize the governing equations a high dimensional model that can take nonlinear model coupling into account is derived and the incremental harmonic balance ihb method is employed to obtain the steady state response of the curved beam the cases investigated include softening stiffness hardening stiffness and modal energy transfer the stability of the periodic solutions for given parameters is determined by the multi variable floquet theory using hsu s method particular attention is paid to the anti symmetric response with and without excitation as the excitation frequency is close to the first and third natural frequencies of the system the results obtained with the ihb method compare very well with those obtained via numerical integration

a 2 5d boundary element formulation for modeling damped waves in arbitrary cross section waveguides and cavities a regularized 2 5d boundary element method bem is proposed to predict the dispersion properties of damped stress guided waves in waveguides and cavities of arbitrary cross section the wave attenuation induced by material damping is introduced using linear viscoelastic constitutive relations and described in a spatial manner by the imaginary component of the axial wavenumber the discretized dispersive wave equation results in a nonlinear eigenvalue problem which is solved obtaining complex axial wavenumbers for a fixed frequency using a contour integral algorithm due to the singular characteristics and the multivalued feature of the wave equation the requirement of holomorphicity inside the contour region over the complex wavenumber plane is fulfilled by the introduction of the sommerfeld branch cuts and by the choice of the permissible riemann sheets a post processing analysis is developed for the extraction of the energy velocity of propagative guided waves the reliability of the method is demonstrated by comparing the results obtained for a rail and a bar with square cross section with those obtained from a 2 5d finite element formulation also known in literature as semi analytical finite element safe method next to show the potential of the proposed numerical framework dispersion properties are predicted for surface waves propagating along cylindrical cavities of arbitrary cross section it is demonstrated that the attenuation of surface waves approaches asymptotically the attenuation of rayleigh waves

acoustic isogeometric boundary element analysis an isogeometric boundary element method based on t splines is used to simulate acoustic phenomena we restrict our developments to low frequency problems to establish the fundamental properties of the proposed approach using t splines the computer aided design cad and boundary element analysis are integrated without recourse to geometry clean up or mesh generation a regularized burton miller formulation is used resulting in integrals which are at most weakly singular we employ a collocation based approach to generate the linear system of equations the method is verified against closed form solutions and direct comparisons are made with conventional lagrangian discretizations it is demonstrated that the superior accuracy of the isogeometric approach emanates from the exact geometric description encapsulated in the t spline the method is then applied to a real world application to illustrate the potential for integrated engineering design and analysis

an isogeometric indirect boundary element method for solving acoustic problems in open boundary domains abstract this work introduces an indirect boundary element method bem within a nurbs based isogeometric framework for solving three dimensional acoustic problems in the frequency domain developments of isogeometric boundary elements so far have focused on the direct bem yet a multitude of common problems in acoustics involves open boundary surfaces which require a more involved indirect boundary element formulation the current work presents an indirect variational bem which makes use of nurbs shape functions additionally a novel technique for coupling strongly non conforming patches is introduced to allow the analysis of more complex geometries the proposed isogeometric indirect boundary element method is verified against analytical solutions and benchmarked against the conventional polynomial based indirect bem also two open boundary problems are studied including analyses over wider frequency ranges and one industrial type complex geometry containing multiple non conforming patches the proposed method is found to be not only significantly more efficient than its polynomial based counterpart but also very robust against strong non conformities in the nurbs descriptions

a new fast multipole boundary element method for two dimensional acoustic problems abstract a new fast multipole boundary element method bem is presented in this paper for solving large scale two dimensional 2d acoustic problems based on the improved burton miller formulation this algorithm has several important improvements the fast multipole bem employs the improved burton miller formulation and successfully overcomes the non uniqueness difficulty associated with the conventional bem for exterior acoustic problems the improved burton miller formulation contains only weakly singular integrals and avoids the numerical difficulties associated to the evaluation of the hypersingular integral it leads to the numerical implementations more efficient and straightforward furthermore the fast multipole method fmm and the approximate inverse preconditioned generalized minimum residual method gmres iterative solver are adopted to greatly improve the overall computational efficiency the numerical examples with neumann boundary conditions are presented that clearly demonstrate the accuracy and efficiency of the developed fast multipole bem for solving large scale 2d acoustic problems in a wide range of frequencies

symmetrization procedure for structure fluid cavity system involving pseudostatic correction this paper deals with a pressure displacement formulation based on the finite element method of an elastoacoustic coupling problem since directly solving the resulting system iscpu intensive for large models the solution is usually based on only a few uncoupled structural modes in vacuum and rigid cavity modes however this classical pressuredisplacement formulation leads to nonsymmetric eigenvalue problems furthermore if this method is accurate for weak coupling models significant errors occur when the truncated modes are coupled to the ones used in the analysis the present paper suggests a method combining the pseudostatic correction of the truncated modes in modal analysis with a symmetrization technique of the eigenvalue problems it allows the calculation of the real coupled modes and frequencies as well as the computation of an accurate elastoacoustic response even for the strong coupling of a structure with a heavy fluid liquid it is less cpu expensive than the classical method because it leads to a diagonalized system

rarefaction pulses for the nonlinear schrodinger equation in the transonic limit we investigate the properties of finite energy travelling waves to the nonlinear schrodinger equation with nonzero conditions at infinity for a wide class of nonlinearities in space dimension two and three we prove that travelling waves converge in the transonic limit up to rescaling to ground states of the kadomtsev petviashvili equation our results generalize an earlier result of f bethuel p gravejat and j c saut for the two dimensional gross pitaevskii equation and provide a rigorous proof to a conjecture by c jones and p h roberts about the existence of an upper branch of travelling waves in dimension three