vibro acoustic response of orthogonally stiffened panels the effects of finite dimensions abstract this paper investigates the effects of finite dimensions on the vibro acoustic response of orthogonally stiffened panels three types of excitations are considered acoustical excitation point force excitation and random excitation by a turbulent boundary layer in each case a spatially windowed periodic model is compared with a rayleigh ritz model where the modes of the un stiffened panel are used as the basis functions the latter model accounts for the reflected wave field generated at the boundaries by assuming that the panel is simply supported on the contrary the windowed periodic model only accounts for finiteness on sound radiation the assumption of an infinite periodic structure is used to calculate the panel response numerical studies show that when the bending wavelength becomes comparable or smaller than the stiffener spacing the periodic model is able to reproduce the results obtained with the rayleigh ritz model to complement the study the developed models are compared with numerical simulations finite element method and with experimental results

on the positivity of the effective action in a theory of random surfaces it is shown that the functional s eta frac 1 24 pi int left frac 1 2 left nabla eta right 2 2 eta right d mu 0 defined onc functions on the two dimensional sphere satisfies the inequalitys 0 if is subject to the constraint int e eta 1 d mu 0 0 the minimums 0 is attained at the solutions of the euler lagrange equations the proof is based on a sharper version of moser trudinger s inequality due to aubin which holds under the additional constraint int e eta xd mu 0 0 this condition can always be satisfied by exploiting the invariance ofs under the conformal transformations ofs2 the result is relevant for a recently proposed formulation of a theory of random surfaces

statistical mechanics of classical particles with logarithmic interactions the inhomogeneous mean field thermodynamic limit is constructed and evaluated for both the canonical thermodynamic functions and the states of systems of classical point particles with logarithmic interactions in two space dimensions the results apply to various physical models of translation invariant plasmas gravitating systems as well as to planar fluid vortex motion for attractive interactions a critical behavior occurs which can be classified as an extreme case of a second order phase transition to include in particular attractive interactions a new inequality for configurational integrals is derived from the arithmetic geometric mean inequality the method developed in this paper is easily seen to apply as well to systems with fairly general interactions in all space dimensions in addition it also provides us with a new proof of the trudinger moser inequality known from differential geometry in its sharp form

parametric uncertainty quantification of sound insulation values a probabilistic framework is developed for quantifying the combined effect of uncertain parameters in sound insulation measurements such as test sample dimensions room properties and loudspeaker positions on the sound insulation values the joint probability distribution of the uncertain parameters is constructed from the available information by means of a maximum entropy approach the resulting sound insulation predictions are fully compatible with the available information but otherwise maximally conservative so that the robustness of the predictions is guaranteed fundamental insight in the inherent uncertainty of the measurement procedure for airborne sound insulation is obtained by combining the method with detailed numerical simulations of the measurement procedure for single and double walls the resulting uncertainty levels are very large especially in the lowest frequency bands and agree with experimental results furthermore the probability distribution of the band averaged sound reduction index of modally sparse walls can be of bimodal form

fuzzy interval finite element statistical energy analysis for mid frequency analysis of built up systems with mixed fuzzy and interval parameters abstract this paper introduces mixed fuzzy and interval parametric uncertainties into the fe components of the hybrid finite element statistical energy analysis fe sea model for mid frequency analysis of built up systems thus an uncertain ensemble combining non parametric with mixed fuzzy and interval parametric uncertainties comes into being a fuzzy interval finite element statistical energy analysis fife sea framework is proposed to obtain the uncertain responses of built up systems which are described as intervals with fuzzy bounds termed as fuzzy bounded intervals fbis in this paper based on the level cut technique a first order fuzzy interval perturbation fe sea ffipfe sea and a second order fuzzy interval perturbation fe sea method sfipfe sea are developed to handle the mixed parametric uncertainties efficiently ffipfe sea approximates the response functions by the first order taylor series while sfipfe sea improves the accuracy by considering the second order items of taylor series in which all the mixed second order items are neglected to further improve the accuracy a chebyshev fuzzy interval method cfim is proposed in which the chebyshev polynomials is used to approximate the response functions the fbis are eventually reconstructed by assembling the extrema solutions at all cut levels numerical results on two built up systems verify the effectiveness of the proposed methods

transient response of structures with uncertain properties to nonlinear shock loading abstract a method is presented to predict the transient response of a structure at the driving point following an impact or a shock loading the displacement and the contact force are calculated solving the discrete convolution between the impulse response and the contact force itself expressed in terms of a nonlinear hertzian contact stiffness application of random point process theory allows the calculation of the impulse response function from knowledge of the modal density and the geometric characteristics of the structure only the theory is applied to a wide range of structures and results are experimentally verified for the case of a rigid object hitting a beam a plate a thin and a thick cylinder and for the impact between two cylinders the modal density of the flexural modes for a thick slender cylinder is derived analytically good agreement is found between experimental simulated and published results showing the reliability of the method for a wide range of situations including impacts and pyroshock applications

existence of solution for a nonvariational elliptic system with exponential growth in dimension two abstract we prove existence of solution for an elliptic system on a bounded domain in dimension two we use the galerkin scheme in the product of hilbert spaces the nonlinearities may have subcritical or critical exponential growth

a graph theory approach to identify resonant and non resonant transmission paths in statistical modal energy distribution analysis statistical modal energy distribution analysis smeda extends classical statistical energy analysis sea to the mid frequency range by establishing power balance equations between modes in different subsystems this circumvents the sea requirement of modal energy equipartition and enables applying smeda to the cases of low modal overlap locally excited subsystems and to deal with complex heterogeneous subsystems as well yet widening the range of application of sea is done at a price with large models because the number of modes per subsystem can become considerable when the frequency increases therefore it would be worthwhile to have at one s disposal tools for a quick identification and ranking of the resonant and non resonant paths involved in modal energy transmission between subsystems it will be shown that previously developed graph theory algorithms for transmission path analysis tpa in sea can be adapted to smeda and prove useful for that purpose the case of airborne transmission between two cavities separated apart by homogeneous and ribbed plates will be first addressed to illustrate the potential of the graph approach a more complex case representing transmission between non contiguous cavities in a shipbuilding structure will be also presented

response probability distribution of built up vibro acoustic systems the vibro acoustic response of built up structures consisting of stiff components with low modal density and flexible components with high modal density is sensitive to small imperfections in the flexible components in this paper the uncertainty of the response is considered by modeling the low modal density master system as deterministic and the high modal density subsystems in a nonparametric stochastic way i e carrying a diffuse wave field and by subsequently computing the response probability density function the master system s mean squared response amplitude follows a singular noncentral complex wishart distribution conditional on the subsystem energies for a single degree of freedom this is equivalent to a chi square or an exponential distribution depending on the loading conditions the subsystem energies follow approximately a chi square distribution when their relative variance is smaller than unity the results are validated by application to plate structures and good agreement with monte carlo simulations is found

the wave transmission coefficients and coupling loss factors of point connected structures this analysis is concerned with the calculation of the elastic wave transmission coefficients and coupling loss factors between an arbitrary number of structural components that are coupled at a point a general approach to the problem is presented and it is demonstrated that the resulting coupling loss factors satisfy reciprocity a key aspect of the method is the consideration of cylindrical waves in two dimensional components and this builds upon recent results regarding the energetics of diffuse wavefields when expressed in cylindrical coordinates specific details of the method are given for beam and thin plate components and a number of examples are presented

vortex condensations of a non relativistic maxwell chern simons theory abstract we study an elliptic system subject to periodic boundary conditions arising from the study of vortex condensates for a selfdual non relativistic model introduced by dunne et al phys rev d 43 1332 1345 1990 in the framework of chern simons gauge theory we prove the existence of a vortex condensate for all values of the relevant physical parameters involved in the model this completes a recent work of spruck and yang 16 who could deal only with a restricted set of those parameters uniqueness is also discussed

hybrid deterministic statistical analysis of vibro acoustic systems with domain couplings on statistical components abstract recently a hybrid analysis method has been developed in which the various components of a complex vibro acoustic system can be modeled either deterministically or statistically the coupling between these two types of component is effected by using a diffuse field reciprocity relation which relates the cross spectrum of the forces at the boundary of a statistical component to the vibrational energy level of the component in practical applications components may be coupled over a domain rather than just at the component boundaries for example the coupling between a plate and an acoustic volume involves the surface of the plate it is shown in the present work that the reciprocity relation and the hybrid method can be extended to this situation so that for example it is possible to couple a statistical model of a plate to a finite element model of an acoustical cavity or to a statistical acoustical cavity the coupling of statistical acoustical and structural components is not new but rather is done routinely within statistical energy analysis sea this part of the present work demonstrates that the relevant coupling loss factors can be found by using the hybrid method the analysis is illustrated by various numerical examples

sharp sobolev inequalities on the sphere and the moser trudinger inequality where de denotes normalized surface measure v is the conformal gradient and q 2n n 2 a modern folklore theorem is that by taking the infinitedimensional limit of this inequality one obtains the gross logarithmic sobolev inequality for gaussian measure which determines nelson s hypercontractive estimates for the hermite semigroup see 8 one observes using conformal invariance that the above inequality is equivalent to the sharp sobolev inequality on rn for which boundedness and extremal functions can be easily calculated using dilation invariance and geometric symmetrization the roots here go back to hardy and littlewood the advantage of casting the problem on the sphere is that the role of the constants is evident and one is led immediately to the conjecture that this inequality should hold whenever possible for example 2 q 0o if n 2 this is in fact true and will be demonstrated in section 2 a clear question at this point is what is the situation in dimension 2 two important arguments 25 26 27 dealt with this issue both motivated by geometric variational problems because q goes to infinity for dimension 2 the appropriate function space is the exponential class responding in part

on the solutions of liouville systems for some prescribed m 0 together with the dirichlet boundary condition u 0 on 0 the liouville equation finds applications in various fields of physics and mathematics to name a few it represents the newtonian potential of a cluster of self gravitating mass distribution where a 0 1 6 36 37 the electric potential induced by charge carriers in the theory of electrolytes where a 0 31 and maximal entropy solutions of the incompressible euler equation 23 9 in the field of differential geometry it stands for the problem of finding a metric corresponding to a prescribed gaussian curvature 3 10 the system analog of l takes the form

on the applicability of the lognormal distribution in random dynamical systems this paper is concerned with the probability density function of the energy of a random dynamical system subjected to harmonic excitation it is shown that if the natural frequencies and mode shapes of the system conform to the gaussian orthogonal ensemble then under common types of loading the distribution of the energy of the response is approximately lognormal providing the modal overlap factor is high typically greater than two in contrast it is shown that the response of a system with poisson natural frequencies is not approximately lognormal numerical simulations are conducted on a plate system to validate the theoretical findings and good agreement is obtained simulations are also conducted on a system made from two plates connected with rotational springs to demonstrate that the theoretical findings can be extended to a built up system the work provides a theoretical justification of the commonly used empirical practice of assuming that the energy response of a random system is lognormal

complex power reciprocity and radiation modes for submerged bodies this study of the surface interaction between a submerged body and the surrounding fluid begins by developing reciprocity relations between alternative pressure and normal velocity distributions on the wetted surface a corollary of these principles is proof of the symmetry of the matrix representing the acoustic contribution to the structural impedance even in situations where the acoustic relation between surface pressure and normal velocity is not symmetric the reciprocity properties lead to two eigenvalue problems whose solution yields velocity and pressure radiation modes each of which decouples the complex surface acoustic power the matrices required to obtain the eigensolutions are shown to arise in the ordinary course of modeling fluid structure interaction further analysis reveals that the velocity and pressure modes occur in a one to one correspondence with a relative phase angle that decreases monotonically as the radiated power increases relative to the reactive power using the radiati

qualitative properties of solutions to some nonlinear elliptic equations in r 2 o introduction elliptic equations in this paper we investigate properties of the solutions to the au r x e u x x r 2 for functions r x which are positive near infinity equations of this kind arise from a variety of situations such as from prescribing gaussian curvature in geometry i 2 and from combustion theory in physics 3 recently a series ofworks have been sought to understand the existence and the qualitative properties of the solutions of ni i 5 and ni cheng 4 1 considered the case where r x is nonpositive mcowen 6 1 and aviles 7 investigated the situation where r x 0 in some order as ixl in our previous paper 1 we consider a special case where r is a constant we proved that the solutions are radially symmetric and hence classified all the solutions in this paper we consider more general functions r x first we obtain the asymptotic behavior of the solution near infinity consequently we prove that all the solutions satisfy an identity which is somewhat of a generalization of the well known kazdan warner condition finally using the asymptotic behavior together with the further development of the method employed in our previous paper i 1 we show that all the solutions are radially symmetric provided r is radially symmetric and nonincreasing this part can be viewed as the completion of 1 throughout this paper we assume that the function r x is positive near infinity in 1 we study the asymptotic behavior of the solution u x of let fl 1 2n r2 r x e dx under some appropriate conditions we show that the solutions approach

graph theory applied to noise and vibration control in statistical energy analysis models a fundamental aspect of noise and vibration control in statistical energy analysis sea models consists in first identifying and then reducing the energy flow paths between subsystems in this work it is proposed to make use of some results from graph theory to address both issues on the one hand linear and path algebras applied to adjacency matrices of sea graphs are used to determine the existence of any order paths between subsystems counting and labeling them finding extremal paths or determining the power flow contributions from groups of paths on the other hand a strategy is presented that makes use of graph cut algorithms to reduce the energy flow from a source subsystem to a receiver one modifying as few internal and coupling loss factors as possible

conformal deformation of metrics on s 2 soit d un domaine lisse de s 2 et k une fonction lisse definie sur d alors pour que le probleme aux limites de neumann u k exp 2u 1 sur d u n 0 sur d ait une solution u on a a quand aire d max x d k x 0

diffuse wavefields in cylindrical coordinates a diffuse wavefield is normally defined in terms of plane waves to quote one textbook definition plane waves are incident from all directions with equal probability and random phase in some vibro acoustic problems the response of a two dimensional component such as a plate is more conveniently expressed in terms of cylindrical waves and it is not immediately obvious what properties should be assigned to the cylindrical waves to constitute a diffuse field it is shown here that a diffuse wavefield can be modeled as a summation of statistically independent cylindrical waves apart from the fact that each outgoing wave of a particular order is fully correlated to an incoming wave of the same order a simple relationship is derived between the energy flow p in each wave component and the energy density e of the wavefield p ec g k where c g is the group velocity and k is the wavenumber this result is shown to hold true for both bending waves and in plane waves longitudinal and shear in a plate the work has application to the calculation of coupling loss factors in statistical energy analysis

a special class of stationary flows for two dimensional euler equations a statistical mechanics description we consider the canonical gibbs measure associated to an vortex system in a bounded domain at inverse temperature widetilde beta and prove that in the limitn widetilde beta n n 1 where 8 here denotes the vorticity intensity of each vortex the one particle distribution function n nx x converges to a superposition of solutions of the following mean field equation left begin array 20 c varrho beta x frac e beta psi mathop smallint limits lambda e beta psi delta psi varrho beta in lambda psi partial lambda 0 end array right

an efficient probabilistic approach to vibro acoustic analysis based on the gaussian orthogonal ensemble vibro acoustic analysis of complex systems at higher frequencies faces two challenges how to compute the response without using an excessive number of degrees of freedom dofs and how to quantify the uncertainty of the response due to small spatial variations in geometry material properties and boundary conditions which have a wave scattering effect in this study a general method of analysis is presented that provides an answer to both questions while overcoming most limitations of statistical energy analysis the fundamental idea is to numerically compute an artificial ensemble of realizations for the components of the built up system that are highly sensitive to small random wave scatterers this can be efficiently performed because their eigenvalue spacings and mode shapes conform to gaussian orthogonal ensemble spacings and gaussian random fields respectively the dofs of the overall system are therefore limited to those of the deterministic components and the interface dofs of the random components the method is extensively validated by application to plate structures good agreement between the predicted response probability distributions and the results of detailed parametric probabilistic models is obtained also for cases of low modal overlap single point loading and strong subsystem coupling

efficient modeling of flat and homogeneous acoustic treatments for vibroacoustic finite element analysis direct field formulations abstract this paper is concerned with the development of a simplified model for noise control treatments to speed up finite element analysis in vibroacoustic applications the methodology relies on the assumption that the acoustic treatment is flat and homogeneous moreover its finite lateral extent is neglected this hypothesis is justified by short wavelength and large dissipation which suggest that the reflected field emanating from the acoustic treatment lateral boundaries does not substantially affect its dynamic response under these circumstances the response of the noise control treatment can be formally obtained by means of convolution integrals involving simple analytical kernels i e green functions such fundamental solutions can be computed efficiently by the transfer matrix method however some arbitrariness arises in the formulation of the mathematical model resulting in different baffling conditions at the two ends of the treatment to be considered thus the paper investigates the possibility of different formulations i e baffling conditions within the same hybrid finite element transfer matrix framework seeking for the best strategy in terms of tradeoff between efficiency and accuracy numerical examples are provided to show strengths and limitations of the proposed methodology

a hybrid finite element statistical energy analysis method for impulsive and transient loading abstract the hybrid approach coupling statistical energy analysis sea and the finite element method has become a prominent technique for analysing structures under steady state loads in the mid frequency range where some components behave in a deterministic manner with low modal density and others in a statistical manner with high modal density and statistical overlap in this paper the method is extended from its current steady state capability to provide calculation of structural responses under impulsive and time varying loads similar to the steady state method a system is split into deterministic components that are modelled using the finite element approach and statistical components that are modelled as sea subsystems an evolutionary spectrum approach based on the priestley description of random processes is applied to model the response of both the sea and deterministic components which are coupled by considering a power balance between the sea subsystems the diffuse field reciprocity relationship that relates the reverberant forces generated by a subsystem to the energy within it is explored under transient conditions where it is found that it can be important to account for the build up of a reverberant field following an impulse results from the method are compared against finite element simulations for a system of plates coupled by a beam and it is found to generate predictions with the accuracy expected of an sea based method although deterministic oscillations of the deterministic system at early times are not accounted for

hybrid finite element statistical energy method for mid frequency analysis of structure acoustic systems with interval parameters abstract the hybrid finite element statistical energy analysis fe sea model for mid frequency analysis consists of two parts the fe components and the sea components which are called as the master system and the subsystem respectively the hybrid finite element statistical energy analysis approach is established on the assumption that the fe components have fully deterministic properties while the sea subsystems have a high degree of randomness this method has been recently extended to allow the properties of the fe components of built up structures to be uncertain like interval or probabilistic and the hybrid model with parametric and non parametric uncertainties is obtained by dealing with the non parametric uncertainty analytically and the parametric uncertainty with monte carlo simulations the distribution of the responses of the hybrid model can be obtained in this paper the interval parametric uncertainty is introduced into the hybrid fe sea framework for structure acoustic systems and the interval dynamic equilibrium equations are established thus a hybrid model with non parametric and interval parametric uncertainties for structure acoustic systems is obtained to improve the computational efficiency the second order interval perturbation finite element method is introduced into the hybrid fe sea framework and the second order interval perturbation finite element statistical energy analysis sipfem sea method is proposed for the structure acoustic system with interval parameters modeled by fe sea the parameters of fe components are considered as interval parameters instead of deterministic ones thus the expectations of the second order quantities such as the vibrational energy and the response cross spectrum in the fe sea framework become interval variables too in the sipfem sea the expectations of the second order response quantities of a structure acoustic system are expanded with the second order taylor series at the nominal values of interval parameters and for the sake of simplicity and efficiency the non diagonal elements of the hessian matrices are neglected then by searching the target positions of interval parameters that maximize or minimize the objective functions the bounds of the vibrational energy and the response cross spectrum can be obtained because of the neglect of the higher order terms of taylor series sipfem sea is limited to the interval analysis with narrow parameter intervals for larger parameter intervals the sub interval perturbation method based on the sipfem sea is introduced the proposed methods are illustrated by applications to two example structure acoustic systems in which the acoustic cavities are modeled by using the interval fe method and the structures are modeled by using the sea reference comparisons are made with the monte carlo simulations of the hybrid fe sea model the numerical results verify the accuracy and efficiency of the proposed methods

uncertainty propagation in sea for structural acoustic coupled systems with non deterministic parameters abstract considering limited available information on uncertainties in structural acoustic coupled systems two methods namely the vertex method and the legendre orthogonal polynomial based method for predicting their dynamic behavior are developed based on the statistical energy analysis sea approach for the vertex method an efficient program for determining coordinates of all vertices of the rectangular spanned by entries of the involved interval input vector is coded which is well suited for an interval input vector in arbitrary dimension instead of calculating the extremum of the response of interest a method for determining its minimal and maximal point vectors dimension by dimension with respect to uncertain parameters is proposed based on the legendre orthogonal polynomial approximation following the theoretical analysis of the accuracy and efficiency of the proposed methods their validation is performed by one numerical example and two applications

a note on the eigenvalue density of random matrices the distribution of eigenvalues of n n random matrices in the limit n is the solution to a variational principle that determines the ground state energy of a confined fluid of classical unit charges this fact is a consequence of a more general theorem proven here in the statistical mechanics of unstable interactions our result establishes the eigenvalue density of some ensembles of random matrices which were not covered by previous theorems

group representations arising from lorentz conformal geometry abstract it is shown that there exist conformally covariant differential operators d 2 l k of all even orders 2 l on differential forms of all orders k in the double cover n of the n dimensional compactified minkowski space n these act as intertwining differential operators for natural representations of o 2 n the conformal group of n for even n the resulting decompositions of differential form representations of o 2 n the orthochronous conformal group produce infinite families of unitary representations the most interesting of which are carried by positive mass squared positive frequency quotients for 2l n 2k physically these generalize unitary representations of the conformal group associated with the modified wave operator d 2 0 n 2 2 2 and the maxwell operator on vector potentials d 2 n 2 2 d all the representation spaces produced unitary and nonunitary may be viewed as infinite systems of harmonic oscillators as a by product of the spectral resolution of the d 2 l k one gets some striking wave propagative properties for all of the equations d 2 l k 0 including huygens principle in the curved spacetime n the operators d 2 l k have not been seen before except in the special cases k 0 or n and k n 2 2 l 1 the maxwell operator thus much new information is obtained even in the physical case n 4

blow up analysis for a cosmic strings equation abstract in this paper we develop a blow up analysis for solutions of an elliptic pde of liouville type over the plane such solutions describe the behavior of cosmic strings parallel in a given direction for a w boson model coupled with einstein s equation we show how the blow up behavior of the solutions is characterized according to the physical parameters involved by new and surprising phenomena for example in some cases after a suitable scaling the blow up profile of the solution is described in terms of an equations that bares a geometrical meaning in the context of the uniformization of the riemann sphere with conical singularities

statistical mechanics approach to some problems in conformal geometry a weak law of large numbers is established for a sequence of systems of n classical point particles with logarithmic pair potential in rn or sn n n which are distributed according to the configurational microcanonical measure e h or rather some regularization thereof where h is the configurational hamiltonian and e the configurational energy when n with non extensive energy scaling e n2e the particle positions become i i d according to a self consistent boltzmann distribution respectively a superposition of such distributions the self consistency condition in n dimensions is some nonlinear elliptic pde of order n pseudo pde if n is odd with an exponential nonlinearity when n 2 this pde is known in statistical mechanics as poisson boltzmann equation with applications to point vortices 2d coulomb and magnetized plasmas and gravitational systems it is then also known in conformal differential geometry where it is the central equation in nirenberg s problem of prescribed gaussian curvature for constant gauss curvature it becomes liouville s equation which also appears in two dimensional so called quantum liouville gravity the pde for n 4 is paneitz equation and while it is not known in statistical mechanics it originated from a study of the conformal invariance of maxwell s electromagnetism and has made its appearance in some recent model of four dimensional quantum gravity in differential geometry the paneitz equation and its higher order n generalizations have applications in the conformal geometry of n manifolds but no physical applications yet for general n interestingly though all the paneitz equations have an interpretation in terms of statistical mechanics

fractional adams moser trudinger type inequalities abstract extending several works we prove a general adams moser trudinger type inequality for the embedding of bessel potential spaces h n p p into orlicz spaces for an arbitrary domain with finite measure in particular we prove sup u h n p p n 2 p u l p 1 e n p u p p 1 d x c n p for a positive constant n p whose sharpness we also prove we further extend this result to the case of lorentz spaces i e n 2 p u l p q the proofs are simple as they use green functions for fractional laplace operators and suitable cut off procedures to reduce the fractional results to the sharp estimate on the riesz potential proven by adams and its generalization proven by xiao and zhai we also discuss an application to the problem of prescribing the q curvature and some open problems

complex singular wishart matrices and applications in this paper complex singular wishart matrices and their applications to information theory are investigated in particular a volume element on the space of positive semidefinite m x m hermitian matrices of rank n m is introduced and some transformation properties are established the jacobian for the change of variables in the singular value decomposition of general m x n complex matrices is derived then the density functions are formulated for all rank n complex singular wishart distributions from this the joint eigenvalue density of low rank complex wishart matrices are derived the derived densities are used to evaluate the most important information theoretic measure the so called ergodic channel capacity of multiple input multiple output mimo spatially correlated rayleigh distributed wireless communication channels

on the structure of the conformal gaussian curvature equation on r2 ii in this paper we continue our investigation initiated in ecn on the structure of the set of all possible solutions of the equation 1 1 au ke2 o in r 2 where a is the laplace operator and k is a given nonpositive locally hslder continuous function in r 2 equation 1 1 arises in the problem of finding a riemannian metric which realizes the given function k as its gaussian curvature and is conformal to the standard euclidean metric in r 2 we refer the reader to cn for a brief description of the background and the history of this problem the study of the equation 1 1 dates back to at least 1930 s but it seems that a complete classification of all solutions of 1 1 was obtained only very recently in cn for the case k x ix t near oo where l 2 is a constant here we continue to use the notation g near to denote that there exist two positive constants cl c2 such that c l f g c2f near oo as we did in cn more precisely the following result was established in cn theorem suppose that k 2 then the following conclusions hold i for each 0 1 1 possesses a unique solution u such that

analytic aspects of the toda system i a moser trudinger inequality in this paper we analyze solutions of the open toda system and establish an optimal moser trudinger type inequality for this system let be a closed surface with area 1 and k aij n n the cartan matrix for su n 1 i e we show that has a lower bound in h1 n if and only if this inequality is optimal as a direct consequence if mj for 4 for j 1 2 n m has a minimizer u that satisfies 2001 john wiley sons inc

stochastic hybrid perturbation technique based smoothed finite element statistical energy method for mid frequency analysis of structure acoustic systems with parametric and nonparametric uncertainties abstract at present the most widely used mid frequency method i e the hybrid finite element statistical energy analysis method fe sea still holds potential flaws e g low accuracy and ignoring uncertain factors in order to eliminate these problems a generalized smoothing finite element statistical energy analysis method sfe sea is first proposed in this work which is constructed based on the edge based gradient smoothing technique thus reducing the dispersion error in the deterministic calculations second on the basis of the proposed sfe sea the parametric uncertainty models will be introduced combining the second order random interval perturbation method and the random interval moment method etc thus a mid frequency analysis method shpsfem sea considering both parametric uncertainties both the random and interval variables and nonparametric uncertainties is proposed to effectively analyze the probability and interval characteristics of the random structural acoustic coupled systems moreover for the interval parameters with wide variation range the subinterval perturbation method s shpsfem sea is introduced by dividing the large interval parameters into small interval parameters the proposed methods are compared with the monte carlo simulations of the hybrid fe sea model the high accuracy and efficiency of the proposed methods are verified by two numerical examples

the conformal plate buckling equation the linear equation 2 u 1 for the infinitesimal buckling under uniform unit load of a thin elastic plate over r 2 has the particularly interesting nonlinear generalization g 2 u 1 where ag e 2u is the laplace beltrami operator for the metric g e 2u g 0 with g 0 the standard euclidean metric on r 2 this conformal elliptic pde of fourth order is equivalent to the nonlinear system of elliptic pdes of second order u x k g x exp 2u x 0 and k g x exp 2u x 0 with x r 2 describing a conformally flat surface with a gauss curvature function k g that is generated self consistently through the metric s conformal factor we study this conformal plate buckling equation under the hypotheses of finite integral curvature f kg exp 2u dx k finite area exp 2u dx a and the mild compactness condition k l 1 b 1 y uniformly with respect to y r 2 we show that asymptotically for x all solutions behave like u x 2 ln x c o 1 and k x 2 ln x c o 1 with 2 4 and 2 4 we also show that for each k 2 4 there exists a k and a radially symmetric solution pair u k satisfying k u k and max k k which is unique modulo translation of the origin and scaling of x coupled with a translation of u

response variance prediction for uncertain vibro acoustic systems using a hybrid deterministic statistical method imperfections during the manufacturing process can cause significant variations in the noise and vibration levels exhibited by nominally identical structures any response calculations employed during the design process should ideally take account of these uncertainties and predict the expected range in performance recently a hybrid method has been developed to predict the ensemble average response of a built up system by combining a deterministic model of parts of the system with a statistical model of other components shorter p j and langley r s 2005 j sound vib 288 669 700 in this paper the method is extended to predict the ensemble variance of the response expressions are derived for the variance of the vibrational energies in the statistical components and for the variance of the cross spectrum of the response of the deterministic components which augment the mean values of these quantities predicted by the original theory the method employs a nonparametric model of uncertainty in the sense that the statistical components are taken to carry diffuse wave fields and this obviates the requirement for a detailed description of the system uncertainties the method is validated by application to a range of coupled plate structures and good agreement with detailed monte carlo simulations is found

on the diffuse field reciprocity relationship and vibrational energy variance in a random subsystem at high frequencies a recent paper has shown that under certain conditions the cross spectral matrix of the forces exerted by a vibrational or acoustic wave field on its surrounding boundaries can be expressed in terms of i the energy of the wave field and ii the direct field dynamic stiffness matrix of the boundary this diffuse field reciprocity relation was derived using wave mechanics and it is not immediately clear how the required wave field properties translate to conditions on the vibrational modes of the system or the applied forcing this issue is addressed here by deriving an extended version of the reciprocity relation using modal methods and the conditions required for the extended version to reduce to the existing relation are delineated it is shown that the existing diffuse field reciprocity relation leads to an anomalous result when used to predict the energy variance of a subsystem and that this anomaly is resolved by using the present extended version of the relation a supplementary result arising from the analysis is that for systems with a sufficient degree of randomness the ensemble average of the dynamic stiffness matrix of a random subsystem is equal to the inverse of the ensemble average of the receptance matrix

on the reciprocity relationship between direct field radiation and diffuse reverberant loading this analysis is concerned with the derivation of a diffuse field reciprocity relationship between the diffuse field excitation of a connection to a structural or acoustic subsystem and the radiation impedance of the connection such a relationship has been derived previously for connections described by a single degree of freedom in the present work it is shown that the diffuse field reciprocity relationship also arises when describing the ensemble average response of connections to structural or acoustic subsystems with uncertain boundaries furthermore it is shown that the existing diffuse field reciprocity relationship can be extended to encompass connections that possess an arbitrary number of degrees of freedom the present work has application to i the calculation of the diffuse field response of structural acoustic systems modeled by finite elements boundary elements and infinite elements ii the general calculation of the coupling loss factors employed in statistical energy analysis sea and iii the derivation of an alternative analysis method for describing the dynamic interactions of coupled subsystems with uncertain boundaries a generalized boundary approach to sea

the first l2 betti number of certain homogeneous spaces including classifying spaces for variations of hodge structures in this paper we prove the vanishing of the first l betti number for certain complex homogeneous spaces d g v where g is a semi simple lie group and v is a compact subgroup l cohomology is the appropriate extension of hodge theory for harmonic forms to the case of a noncompact complete manifold x inasmuch as here every l cohomology class can be represented by an l harmonic form see 1 in particular non existence of non trivial l harmonic p forms means that the p th l betti number vanishes besides offering the possibility to extend hodge theory to the noncompact case it can be used to obtain topological information about compact quotients of x by the lindex theorem of atiyah 1 based on this theorem dodziuk singer 4 12 suggested to use l cohomology to approach the hopf conjecture concerning the euler characteristic of riemannian manifolds of non positive curvature which has been verified in several special but important cases 2 3

boundary effects on the vibration statistics of a random plate abstract this paper considers the estimation of statistics of displacement of a vibrating rectangular plate with random wave scatterers the influence of uncertainty is investigated using point impedance theory coherent boundary effects are seen which decrease when the number of scatterers increases the boundary effect is investigated using images and the first side and corner reflections are found to be a minimum requirement to estimate the spatial correlation statistics for point driven response are investigated under the assumption that the statistics of the natural frequencies follow those of the gaussian orthogonal ensemble goe the estimates are compared with monte carlo simulation results and they show good agreement

the minimum multimodal radiation efficiency of baffled finite beams a technique for deriving the optimal surface velocity distribution on the surface of a finite baffled beam has been developed the optimal velocity distribution minimizes the radiation efficiency of the beam for a specified maximum permissible mode and frequency a modal expansion of the surface velocity in terms of unknown modal amplitude coefficients the rayleigh integral and a far field intensity integration are employed to obtain a quadratic expression for the radiation efficiency of the beam application of a suitable constraint to avoid trivial solutions leads to an eigenvalue problem identical in form to the rayleigh quotient employed in dynamic mechanical systems the eigenvector of modal amplitude coefficients corresponding to the lowest eigenvalue yields the minimum radiation efficiency while the eigenvalue itself is the actual value of the minimum radiation efficiency near and below coincidence the optimal eigenvector of modal amplitude coefficients yields a radiation efficiency significantly less than the radiation efficiency of any single modal component acting alone simply supported and clamped clamped boundary conditions are considered and numerical examples are presented for each

acoustic radiation from finite structures recently the application of singular value decomposition has been discussed in identifying source modes of a radiating structure by providing a representation to the neumann green s function for the far field of the structure the source modes identified as such will form eigenstates of radiated power the determination of such states is of significant interest in acoustics having applications in radiation filtering and beaming a different algorithm is introduced for the computation of the modes which does not require the application of singular value decomposition since eigenstates of radiated power are also eigenstates of the surface acoustic resistance these modes may be computed by simply diagonalizing this operator which is real and symmetric the eigenvalues computed will be proportional to the radiated power from each mode

on the conformal gaussian curvature equation inr2 abstract in this paper we consider the equation u k x e 2u 0 in r 2 0 1 wherek x k x inr2andk x does not decay at x large from the geometric viewpoint it is quite interesting to ask what the best possible range is of total curvature of all solutions of 0 1 in this paper we study this problem for radial solutions we also construct some particularkto demonstrate the rich phenomenon in particular we show by examples that whenk x is negative for x large eq 0 1 possess a branch of solutions which satisfies some monotonicity property

a quantitative criterion validating coupling power proportionality in statistical energy analysis the response of two general spring coupled elements is investigated to develop a unifying approach to the weak coupling criterion in statistical energy analysis sea first the coupled determinis