a lumped parameter model for the acoustic power output from a vibrating structure previous applications of lumped parameter models to acoustic radiation problems assume that the characteristic dimension of the vibrating structure is small in comparison to the acoustic wavelength in this paper the frequency range of the lumped parameter model is extended by dividing the surface of the structure into elements and characterizing the amplitude of the radiation from each element by its volume velocity the model is derived by truncating all but the lowest order monopole terms of a multipole expansion for the acoustic power output the multipole expansion differs from those derived previously because it is based on elemental quantities rather than global quantities by comparing the full multipole expansion for the power output to the lumped parameter model the error in the lumped parameter model as a function of the acoustic and structural wavelengths k and k and the size of the largest surface element l is determined this approach is general and provides a means of determining bo

reverse inequalities in μ deformed segal bargmann analysis we prove reverse hypercontractivity inequalities as well as reverse log sobolev inequalities in the context of a space of holomorphic functions which is called the deformed segal bargmann space and arises in the works of wigner rosenblum and marron to achieve this we define deformations of energy and entropy our principle results generalize earlier works of carlen and sontz we also show that the semigroup of this theory is lp bounded and we conjecture that it is lp contractive and even more strongly that it is hypercontractive

explicit travelling wave solutions of variants of the k n n and the zk n n equations with compact and noncompact structures in this work two powerful schemes that use the reliable ideas of the sine cosine method and the tanh method are presented variants of the k n n and the zk n n are selected to illustrate the two methods and to derive compact and noncompact solutions for these nonlinear variants with dispersive effects the coefficients of the derivatives of the equation play a major role in change of the physical structures of the solutions

the sine cosine method for obtaining solutions with compact and noncompact structures in this paper we establish compact and noncompact solutions for nonlinear dispersive equations a sine cosine method is used to demonstrate this work the different physical structures of the focusing branch and the defocusing branch are emphasized many models are approached to illustrate the usage of our main results

distinct variants of the kdv equation with compact and noncompact structures in this paper we examine three distinct variants of the generalized kdv equation both the compact and the noncompact structures are treated for these variants we also emphasize the different physical structures of the two classes the focusing branch and the defocusing branch

on a class of nonlinear dispersive dissipative interactions abstract we study a prototype dissipative dispersive equation ut a um x un xxx uk xx a consts which represents a wide variety of interactions at the critical value k m n 2 which separates dispersive and dissipation dominated phenomena these effects are in a detailed balance and the patterns formed do not depend on the amplitude in particular when m n 2 k 1 the equation can be transformed into a form free of convection and dissipation making it accessible to analysis both bounded and unbounded oscillations as well as solitary waves are found a variety of exact solutions are presented with a notable example being a solitary doublet for n 1 and a 2 3 2 the problem may be mapped into a linear equation leading to rational periodic or aperiodic solutions among others

stability of compacton solutions of fifth order nonlinear dispersive equations we consider fifth order nonlinear dispersive k m n p type equations to study the effect of nonlinear dispersion using simple scaling arguments we show how instead of the conventional solitary waves such as solitons the interaction of the nonlinear dispersion with nonlinear convection generates compactons the compact solitary waves free of exponential tails this interaction also generates many other solitary wave structures such as cuspons peakons tipons etc which are otherwise unattainable with linear dispersion various self similar solutions of these higher order nonlinear dispersive equations are also obtained using similarity transformations further it is shown that like the third order nonlinear k m n equations the fifth order nonlinear dispersive equations also have the same four conserved quantities and furthermore even any arbitrary odd order nonlinear dispersive k m n p type equations also have the same three and most likely the four conserved quantities finally the stability of the compacton solutions for the fifth order nonlinear dispersive equations are studied using linear stability analysis from the results of the linear stability analysis it follows that unlike solitons all the allowed compacton solutions are stable since the stability conditions are satisfied for arbitrary values of the nonlinear parameters

compacton solutions in a class of generalized fifth order korteweg de vries equations solitons play a fundamental role in the evolution of general initial data for quasilinear dispersive partial differential equations such as the korteweg de vries kdv nonlinear schrodinger and the kadomtsev petviashvili equations these integrable equations have linear dispersion and the solitons have infinite support we have derived and investigate a new kdv like hamiltonian partial differential equation from a four parameter lagrangian where the nonlinear dispersion gives rise to solitons with compact support compactons the new equation does not seem to be integrable and only mass momentum and energy seem to be conserved yet the solitons display almost the same modal decompositions and structural stability observed in integrable partial differential equations the compactons formed from arbitrary initial data are nonlinearly self stabilizing and maintain their coherence after multiple collisions the robustness of these compactons and the inapplicability of the inverse scattering tools that worked so well for the kdv equation make it clear that there is a fundamental mechanism underlying the processes beyond integrability we have found explicit formulas for multiple classes of compact traveling wave solutions when there are more than one compacton solution for a particular set of parameters the wider compacton is the minimum of a reduced hamiltonian and is the only one that is stable

adiabatic perturbations for compactons under dissipation and numerically induced dissipation compacton propagation under dissipation shows amplitude damping and the generation of tails the numerical simulation of compactons by means of dissipative schemes also show the same behaviors the truncation error terms of a numerical method can be considered as a perturbation of the original partial differential equation and perturbation methods can be applied to its analysis for dissipative schemes or when artificial dissipation is added the adiabatic perturbation method yields evolution equations for the amplitude loss in the numerical solution and the amplitude of the numerically induced tails in this paper such methods are applied to the k 2 2 rosenau hyman equation showing a very good agreement between perturbative and numerical results

reflection positivity and monotonicity we prove general reflection positivity results on riemannian manifolds for both scalar fields and dirac fields and comment on applications to quantum field theory as another application we prove the inequality cd cn between dirichlet and neumann covariance operators on a manifold with a reflection

stability of compacton solutions the stability of the recently discovered compacton solutions is studied by means of both linear stability analysis as well as lyapunov stability criteria from the results obtained it follows that unlike solitons all the allowed compacton solutions are stable as the stability condition is satisfied for arbitrary values of the nonlinearity parameter the results are shown to be true even for the higher order nonlinear dispersion equations for compactons some new conservation laws for the higher order nonlinear dispersion equations are also presented

compact structures for variants of the generalized kdv and the generalized kp equations in this paper we discuss mathematical variants in higher dimensions of the generalized kdv and the generalized kp equations it is shown that the focusing branches of these variants exhibit compactons solitons with finite wavelength whereas the defocusing branches support solitary patterns solutions with infinite slopes or cusps the compact and the noncompact dispersive structures are examined in a general way

compactons and solitary patterns structures for variants of the kdv and the kp equations in this paper we discuss mathematical variants in higher dimensions of the kdv and the kp equations it is shown that the focusing branches of these variants exhibit compactons solitons with finite wavelength whereas the defocusing branches support solitary patterns solutions with infinite slopes or cusps the study presents a fairly complete understanding of the compact and noncompact dispersive structures

a hybrid approach for simulating fluid loading effects on structures using experimental modal analysis and the boundary element method many structural acoustics problems involve a vibrating structure in a heavy fluid however obtaining fluid loaded natural frequencies and damping experimentally can be difficult and expensive this paper presents a hybrid experimental numerical approach to determine the heavy fluid loaded resonance frequencies and damping of a structure from in air measurements the approach combines in air experimentally obtained mode shapes with simulated in water acoustic resistance and reactance matrices computed using boundary element be analysis the procedure relies on accurate estimates of the mass normalized in vacuo mode shapes using singular value decomposition and rational fraction polynomial fitting which are then used as basis modes for the in water be analysis the method is validated on a 4 445 cm 1 75 in thick nickel aluminum bronze rectangular plate by comparing natural frequencies and damping obtained using the hybrid approach to equivalent data obtained from actual in water measurements good agreement is shown for the fluid loaded natural frequencies and one third octave loss factors finally the limitations of the hybrid approach are examined

a repository of equations with cosine sine compactons nonlinear evolution equations with cosine sine compacton solutions are reviewed including the rosenau hyman equation and generalizations of korteweg de vries camassa holm boussinesq benjamin bona mahony klein gordon and other equations each equation is generalized to three dimensions and the conditions for its cosine solitary waves to be either a compacton or a soliton are determined several equations claimed in the literature to be different among them are found to be equivalent

equivariant maps and purely atomic spectrum abstract let g be a connected semisimple lie group with no compact factors and finite center and g an irreducible lattice if x1 1 and x2 2 are g spaces with finite invariant measures and the action of g has purely atomic spectrum and is essentially free or essentially transitive we prove that every measure preserving map x1 x2 is also a g map

the tanh method for compact and noncompact solutions for variants of the kdv burger and the k n n burger equations abstract in this paper we examine variants of the kdv burger equation and the k n n burger equation both compact and noncompact structures are treated for these models the tanh method is employed as a vehicle to achieve this goal three different physical structures are emphasized compactons solitary patterns and blow up solutions

nonlinear dispersive special type of the zakharov kuznetsov equation zk n n with compact and noncompact structures in this paper we study nonlinear dispersive special type of the zakharov kuznetsov equation with positive and negative exponents the approach depends mainly on the sine cosine algorithm compactons solitary patterns solitons and periodic solutions are formally derived

the sine cosine and the tanh methods reliable tools for analytic treatment of nonlinear dispersive equations the sine cosine method and the tanh method are used for analytic treatment of nonlinear dispersive equations nonlinear variants of boussinesq equation are used as vehicles to show the strength of these methods solutions of distinct physical structures solitons compactons solitary patterns solutions and periodic solutions are formally derived the results show that the change in physical structures of the obtained solutions depends mainly on exponents and on the coefficients of the derivatives involved

nonlinear variants of the improved boussinesq equation with compact and noncompact structures variants of the improved boussinesq equation with positive and negative exponents are investigated it is formally shown that these nonlinear variants give rise to compact and non compact physical structures where compactons solitons solitary patterns and periodic solutions are developed the presented sine cosine ansatz is reliable

compact and noncompact solutions for nonlinear dispersive variants of the generalized kdv equation in this paper we examine three distinct nonlinear dispersive variants of the generalized kdv equation we study the compact and the noncompact structures for these variants we also emphasize the fact that purely nonlinear dispersion can cause a deep qualitative change in the genuinely nonlinear phenomenon

an improved state space method for coupled fluid structure interaction analysis this paper presents an improved state space method for incorporating fluid structure interaction into structural acoustic analyses giordano and koopmann j a giordano and g h koopmann state space boundary element finite element coupling for fluid structure interaction analysis j acoust soc am 98 363 372 1995 introduced a state space approach for the coupled analysis of fluid loaded structures giordano s method employed a third order interpolation of the fluid impedance coupled with state space formalism permitting the direct eigenvalue analysis of the coupled system and thereby yielding the fluid loaded modes and natural frequencies this is in contrast to the common technique of sweeping through a range of frequencies so as to identify the natural frequencies and mode shapes the original state space approach yielded system matrices of order 4n where n is the number of degrees of freedom in the underlying model where giordano s method employed an interpolation based on surface velo

modal decomposition of exterior acoustic structure interaction a modal decomposition technique to analyze individual modal contributions to the sound power radiated from an externally excited structure submerged in a heavy fluid is presented the fluid loaded structural modes are calculated by means of a polynomial approximation and symmetric linearization of the underlying nonlinear eigenvalue problem the eigenvalues and eigenfunctions of a fluid loaded sphere with and without internal structures are presented the modal sound power contributions using both fluid loaded structural modes and acoustic radiation modes are presented the results for the resistive and reactive sound power obtained from the superposition of the individual modal sound power contributions are compared to the harmonic solution of the forced problem

compactons solitons and periodic solutions for variants of the kdv and the kp equations studying solitons and solitons with compact support is of important significance in nonlinear phenomena in this paper we study nonlinear variants of the kdv and the kp equations with positive and negative exponents we employ the sine cosine algorithm to back up our analysis exact solutions with compactons solitons solitary patterns and periodic structures are obtained for these variants

stabilizers for ergodic actions of higher rank semisimple groups let g be a connected semisimple lie group with finite center and r rank 2 suppose that each simple factor of g either has r rank 2 or is locally isomorphic to sp l n or f4 20 we prove that any faithful irreducible properly ergodic finite measure preserving action of g is essentially free we extend the result to reducible actions and actions of lattices

a finite difference scheme for the k 2 2 compacton equation the k 2 2 equation introduced by rosenau and hyman is a wave equation that possesses solutions compactons that vanish outside a bounded interval of the spatial axis a finite difference scheme for this equation is suggested that can successfully cope with compacton interactions leading to negative waves we show rigorously that in those interactions a loss of smoothness of the solution necessarily takes place

numerical implementation of the lumped parameter model for the acoustic power output of a vibrating structure in a previous paper a lumped parameter model for the acoustic radiation from a vibrating structure was defined by dividing the surface of the structure into elements expanding the acoustic field from each of the elements in a multipole expansion and truncating all but the lowest order terms in the expansion here the lumped parameter model is implemented numerically by requiring the boundary condition for the normal surface velocity to be satisfied in a lumped parameter sense this alleviates the difficulties typically encountered in enforcing the boundary condition leading to a relatively simple numerical solution with well defined convergence properties the basis functions for the numerical analysis are taken as the acoustic fields of discrete simple dipole and tripole sources located at the geometrical centers of the surface elements the different source types are used to represent the radiation from different kinds of surface elements simple sources for elements in the plane of an infinite baffle dipole sources for very thin structures which deform only in bending and tripole sources for elements associated with parts of a structure enclosing a finite volume the convergence of the numerical solution for the power output as a function of both frequency and element size is demonstrated through several example problems

modal decomposition of exterior acoustic structure interaction problems with model order reduction a numerical technique for modal decomposition of the acoustic responses of structures submerged in a heavy fluid medium using fluid loaded structural modes is presented a krylov subspace model order reduction approach to reduce the computational effort required for a fully coupled finite element boundary element model is described by applying the krylov subspace to only the structural part of the global system of equations for the fully coupled problem only the frequency independent finite element matrices are reduced a fluid loaded cylindrical shell closed at each end by hemispherical end caps is examined the cylinder is excited by a ring of axial or transverse forces acting at one end the individual contributions of the cylinder circumferential modes to the sound power and directivity of the radiated sound pressure are observed the technique presented here provides a tool for greater physical insight into exterior acoustic structure interaction problems using fully coupled numerical models with significantly reduced computational effort

self similar radiation from numerical rosenau hyman compactons the numerical simulation of compactons solitary waves with compact support is characterized by the presence of spurious phenomena as numerically induced radiation which is illustrated here using four numerical methods applied to the rosenau hyman k p p equation both forward and backward radiations are emitted from the compacton presenting a self similar shape which has been illustrated graphically by the proper scaling a grid refinement study shows that the amplitude of the radiations decreases as the grid size does confirming its numerical origin the front velocity and the amplitude of both radiations have been studied as a function of both the compacton and the numerical parameters the amplitude of the radiations decreases exponentially in time being characterized by a nearly constant scaling exponent an ansatz for both the backward and forward radiations corresponding to a self similar function characterized by the scaling exponent is suggested by the present numerical results

stabilizers of ergodic actions of lattices and commensurators we prove that any ergodic measure preserving action of an irreducible lattice in a semisimple group with finite center and each simple factor having rank at least two either has finite orbits or has finite stabilizers the same dichotomy holds for many commensurators of such lattices the above are derived from more general results on groups with the howe moore property and property t we prove similar results for commensurators in such groups and for irreducible lattices and commensurators in products of at least two such groups at least one of which is totally disconnected

state space boundary element finite element coupling for fluid structure interaction analysis state space coupling is a new approach for handling computational fluid structure interaction problems in the low to medium frequency range the method is based on standard boundary element bem and finite element fem discretizations of the acoustic and structural domains respectively the implicit frequency dependence of a traditional acoustic impedance matrix is made explicit through a power series expansion on circular frequency and considering time harmonic motion once expanded the acoustic energy of the fluid is directly coupled to that of the structure via hamilton s principle the coupled system is then recast in a canonical state space form which is also in the form of a standard eigenvalue problem solution of this system produces a series of complex eigenvalues and eigenvectors which represent a modal decomposition of the fluid loaded structure biorthogonality properties of the state space eigensystem allow for an uncoupled modal solution of the forced problem results for a submerged spherical shell and a finite plate in an infinite ridged baffle are given to illustrate the state space approach

general compactons solutions for the focusing branch of the nonlinear dispersive k n n equations in higher dimensional spaces in this paper we will study the focusing branch of the genuinely nonlinear dispersive k n n equation that exhibits compactons solitons with finite wavelengths the equation will be studied in one two and three dimensional spaces general formulas for compactons solutions are developed for all positive integers n n 1 two sets of entirely new formulas one set produces compactons for even integers n whereas the second set produces compactons and anticompactons for odd integers n n 1 are established

variants of the generalized kdv equation with compact and noncompact structures abstract in this paper nonlinear dispersive variants of the generalized kdv equation are investigated the compact and the noncompact physical structures are studied two general formulas for the focusing branch and the defocusing branch that are of substantial interest are formally derived

a retracted boundary integral equation for exterior acoustic problem with unique solution for all wave numbers a regular integral equation based on the surface source distribution method is developed to solve the exterior acoustic radiation and scattering problems this integral equation formed by seeking the equivalent mixed layer potential distributed over an auxiliary surface retracted from the actual boundary is uniquely solvable and has nonsingular kernel function hence it is more amenable to numerical implementation and can circumvent the difficulties of singularity nonuniqueness and slope discontinuity of the conventional integral equation formulations in contrast to the behavior of fredholm integral equations of the second kind the discretization of a regular integral equation will not result in a diagonally dominant coefficient matrix to overcome the undesirable numerical instability the optimal selection of the interior source surface is investigated through error estimate of the numerical integration the versatility and accuracy of the proposed formulation are demonstrated by numerical examples involving spheres prolate spheroids and finite cylinders

the thin shape breakdown tsb of the helmholtz integral equation many numerical implementations of the helmholtz integral equation exist today that can predict routinely the field scattered by a volume holding body one such object is the ellipsoidal core of a typical airborne or submerged vehicle stripped of its thin appendages i e stripped of its finlike control surfaces etc the reason for these omissions has often been an inherent limitation of the cited modeling tools rather than a rational dismissal of the potential effect of these neglected appendages on the complete body s expected scattering cross section the limitation of existing techniques is this the standard form of gauss theorem on which they are based that leads to the helmholtz integral becomes meaningless when the thickness of the shape addressed tapers down to zero even over only part of the structure this paper exposes analytically the fundamental cause of this thin shape breakdown tsb and in the process derives an alternate boundary element formulation for its cure

solitary patterns solutions having infinite slopes or cusps for fifth order kdv like equations in higher dimensions in this paper we consider a modified form of fifth order kdv equation fkdv that exhibits solutions with solitary patterns having cusps or infinite slopes we formally construct a framework for studying this problem in higher dimensions two distinct sets of general formulas that are of substantial interest are developed for this variant fk n n for all positive integers n n 1

compacton solutions for a class of two parameter generalized odd order korteweg de vries equations we study the fifth order fully nonlinear k m n p equations and obtain a class of exact compacton solutions we find that addition of the fifth order dispersion term increases the range of the nonlinear parameters m n and p for which these compacton solutions are allowed we consider the hamiltonian structure and conservation laws of this class of equations we also study the class of two parameter generalized odd order equations and obtain the exact compacton solutions and the range of the nonlinearity and dispersion parameters as well as the relation between them

generalized boussinesq type of equations with compactons solitons and periodic solutions generalized boussinesq type of equations with positive and negative exponents are examined the analysis depends mainly on the sine cosine ansatz it is formally shown that these nonlinear models give rise to compactons solitary patterns solitons and periodic solutions depending on the exponents and the coefficients of the derivatives of u x t the presented scheme reveals quite a number of remarkable features that will be helpful for identical problems

stability and dynamical properties of rosenau hyman compactons using pade approximants we present a systematic approach for calculating higher order derivatives of smooth functions on a uniform grid using pade approximants we illustrate our findings by deriving higher order approximations using traditional second order finite difference formulas as our starting point we employ these schemes to study the stability and dynamical properties of k 2 2 rosenau hyman compactons including the collision of two compactons and resultant shock formation our approach uses a differencing scheme involving only nearest and next to nearest neighbors on a uniform spatial grid the partial differential equation for the compactons involves first second and third partial derivatives in the spatial coordinate and we concentrate on four different fourth order methods which differ in the possibility of increasing the degree of accuracy or not of one of the spatial derivatives to sixth order a method designed to reduce round off errors was found to be the most accurate approximation in stability studies of single solitary waves even though all derivates are accurate only to fourth order simulating compacton scattering requires the addition of fourth derivatives related to artificial viscosity for those problems the different choices lead to different amounts of spurious radiation and we compare the virtues of the different choices

time stepping in petrov galerkin methods based on cubic b splines for compactons abstract four numerical methods with first to fourth order of accuracy have been developed for the time integration of the rosenau hyman k 2 2 equation the error in the solution and the invariants for the propagation of one compacton and the stability in collisions among compactons have been studied using these methods numerically induced radiation has also been characterized by means of wavefront velocity and wavefront amplitude showing that the self similarity of the radiation wavepackets observed in the numerical results is a consequence of the time stepping method among the four methods studied in this paper the best results in terms of accuracy computational cost and stability have been obtained by means of using the second order time integration method

numerical methods based on modified equations for nonlinear evolution equations with compactons abstract compactons are traveling wave solutions with compact support resulting from the balance of both nonlinearity and nonlinear dispersion numerical methods with second fourth sixth and eighth order approximations to the spatial derivatives obtained by means of the method of modified equations applied to the ismail taha finite difference scheme for the rosenau hyman equation are developed the whole set of methods is compared among them in accuracy invariant conservation and in compacton collisions the best method among those studied in terms of the tradeoff between accuracy and computational cost is determined

the tanh coth and the sine cosine methods for kinks solitons and periodic solutions for the pochhammer chree equations abstract in this paper the tanh coth method and the sine cosine method are used for a reliable treatment of the pochhammer chree equations which include a variety of models travelling wave solutions of distinct structures namely bell shaped solitons kink shaped solitons and periodic solutions are formally derived the two methods demonstrate power reliability and efficiency

a class of nonlinear fourth order variant of a generalized camassa holm equation with compact and noncompact solutions abstract in this paper we study a class of nonlinear fourth order analogue of a generalized camassa holm equation it is shown that this class gives compactons conventional solitons solitary patterns and periodic solutions it is also found that the qualitative change in the physical structure of solutions depends mainly on the exponent of the wave function u x t positive or negative and on the coefficient of u n as well

computing fluid coupled resonance frequencies mode shapes and damping loss factors using the singular value decomposition in many acoustic design problems it would be useful to be able to compute fluid coupled resonance frequencies mode shapes and their associated damping levels unfortunately conventional eigenvalue solution procedures are either computationally inefficient unreliable or have limited applicability sophisticated methods for identifying modal parameters using the singular value decomposition have recently emerged in the area of experimental modal analysis where the available data typically consists of velocity to force transfer functions for several drive point locations in this paper we show that these techniques can be applied to numerically generated frequency domain data and are even more effective because full matrices of transfer function data are available this typically allows the modes to be completely separated from each other such that the modal parameters can be identified using analytical formulas several benchmark example problems are solved numerically including a rectangular cantilever plate a baffled circular plate and a baffled circular plate covered by an open ended rigid walled pipe

computations of soliton solutions and periodic solutions for the focusing branch of the nonlinear dispersive k n n equations in higher dimensional spaces in the present paper the focusing branch of the genuinely nonlinear dispersive k n n equation is studied in one two and three dimensional spaces in the case of 0