rank one property for derivatives of functions with bounded variation when u is a function of bounded variation of the open set r into r du is a measure on which takes values in the space rm n of all m n matrices such that du i j ui xj for every i j with 1 i m 1 j n and we denote by dsu the part of the measure du which is singular with respect to lebesgue measure we recall that the rank of a matrix a rm n is dimension of the space spanned by its columns in r or by its rows in r and in particular the rank of a is one if and only if there exist e r and r with e 6 0 6 0 so that a e i e ai j ei j for all i j cf remark 1 7 when is a measure which takes values in the space rm n and d d denotes the radon nikodym derivative of with respect to the total variation we say that has rank one when the rank of the matrix d d x is one for almost every x in this paper we prove we prove the following statement see theorem 4 5 corollary 4 6 and remark 4 9

on rank one convex functions that are homogeneous of degree one we show that positively 1 homogeneous rank one convex functions are convex at 0 and at matrices of rank one the result is a special case of an abstract convexity result that we establish for positively 1 homogeneous directionally convex functions defined on an open convex cone in a finite dimensional vector space from these results we derive a number of consequences including various generalizations of the ornstein l1 non inequalities most of the results were announced in c r acad sci paris ser i 349 407 409 2011

approximation in higher order sobolev spaces and hodge systems abstract let d 2 be an integer 1 l d 1 and be a differential l form on r d with w 1 d coefficients it was proved by bourgain and brezis 5 theorem 5 that there exists a differential l form on r d with coefficients in l w 1 d such that d d in the same work bourgain and brezis also left as an open problem the extension of this result to the case of differential forms with coefficients in the higher order space w 2 d 2 or more generally in the fractional sobolev spaces w s p with s p d we give a positive answer to this question provided that d l d 1 where is the largest positive integer such that min p d the proof relies on an approximation result interesting in its own right for functions in w s p by functions in w s p l even though w s p does not embed into l in this critical case the proofs rely on some techniques due to bourgain and brezis but the context of higher order and or fractional sobolev spaces creates various difficulties and requires new ideas and methods

an asymptotic membrane like theory for long wave motion in a pre stressed elastic plate an asymptotically consistent two dimensional theory is developed to help elucidate dynamic response in finitely deformed layers the layers are composed of incompressible elastic material with the theory appropriate for long wave motion associated with the fundamental mode and derived in respect of the most general appropriate strain energy function leading order and refined higher order equations for the mid surface deflection are derived in the case of zero normal initial static stress and in plane tension the leading order equation reduces to the classical membrane equation with its refined counterpart also being obtained the theory is applied to a one dimensional edge loading problem for a semi infinite plate in doing so the leading and higher order governing equations are used as inner and outer asymptotic expansions the latter valid within the vicinity of the associated quasi front a solution is derived by using the method of matched asymptotic expansions

on convexity properties of homogeneous functions of degree one keywords rank one convexity quasiconvexity convexity reference caa article 1996 001view record in web of science record created on 2008 11 25 modified on 2017 05 12

second order analysis for thin structures the eective behavior of second order strain energy densities is obtained using relaxation and i convergence techniques the cosserat theory see e g 13 14 and 2 is recovered within a dimension reduction analysis for 3d non linear elastic thin domains with varying profiles homogeneous and inhomogeneous plate models with periodic profiles are treated

a novel boundary element approach to time harmonic dynamics of incremental nonlinear elasticity the role of pre stress on structural vibrations and dynamic shear banding a new boundary element technique is developed to analyze two dimensional time harmonic small amplitude vibrations superimposed upon a homogeneously pre stressed orthotropic and incompressible elastic solid new expressions for the green s functions for incremental applied tractions are obtained in which static and dynamic contributions are uncoupled the dynamic contributions are regular whereas the static terms are strongly singular and are solved in closed form expressions particularly useful for numerical calculations as a consequence of the static dynamic de coupling these expressions turn out to be useful also for quasi static deformation the formulation is tested for different boundary value problems these include a problem with certain boundary conditions investigated by ryzhak in the static case for which an analytic solution is proposed here in the time harmonic regime the effect of pre stress is shown to strongly influence the vibrational response of elastic structures it is shown that natural frequencies strongly decrease when pre stress approaches quasi static bifurcation loads and wave propagation speeds tend to vanish when the boundary of ellipticity is approached near this boundary but still within the elliptic region we observe a focussing of vibrations along plane waves parallel to the shear bands 2007 elsevier b v all rights reserved

interfacial waves and deformations in pre stressed elastic media the propagation of interfacial stoneley waves along the boundary between two half spaces of pre stressed incompressible isotropic elastic material is examined the underlying deformation in each half space corresponds to a pure homogeneous strain with one principal axis of strain normal to the interface and the others having a common orientation the secular equation governing the wave speed for propagation along a principal axis is obtained in respect of general strain energy functions detailed analysis of the secular equation reveals general sufficient conditions for the existence of a wave and in particular cases necessary and sufficient conditions for the existence of a unique interfacial wave it is also shown that when an interfacial wave exists its speed is greater than that of the least of the rayleigh wave speeds for the separate half spaces paralleling a result from the linear theory for the special case of quasi static interfacial deformations corresponding to vanishing wave speed an existence criterion is found moreover it is shown that inequalities that exclude surface deformations in each half space also exclude interfacial deformations dependence of the above results on the underlying homogeneous deformations and on material parameters is illustrated by numerical results for the neo hookean strain energy function

burkholder integrals morrey s problem and quasiconformal mappings inspired by morrey s problem on rank one convex functionals and the burkholder integrals of his martingale theory we find that the burkholder functionals bp p 2 are quasiconcave when tested on deformations of identity f id c with bp df x 0 pointwise or equivalently deformations such that df 6 p p 2jf in particular this holds in explicit neighbourhoods of the identity map among the many immediate consequences this gives the strongest possible l estimates for the gradient of a principal solution to the beltrami equation fz z fz for any p in the critical interval 2 6 p 6 1 1 f examples of local maxima lacking symmetry manifest the intricate nature of the problem

embeddings for a weakly differentiable functions on domains abstract we prove that the inhomogeneous estimate of vector fields on balls in r n b d k 1 u n n 1 d x n 1 n c b a u u d x for all u c b r n holds if and only if the linear constant coefficient differential operator a of order k has finite dimensional null space fdn this generalizes the gagliardo nirenberg sobolev inequality on domains and provides the local version of the analogous homogeneous embedding in full space r n d k 1 u n n 1 d x n 1 n c r n a u d x for all u c c r n r n proved by van schaftingen precisely for elliptic and cancelling ec operators building on fundamental l 1 estimates from the works of bourgain and brezis we prove that fdn strictly implies ec and discuss the contrast between homogeneous and inhomogeneous estimates on both algebraic and analytic level

constrained and unconstrained synthesis of array factor for circular arrays we consider arrays of n isotropic elements equally spaced on a circular ring our purpose is to determine the n element excitations which minimize the mean square distance between the corresponding array factor and a given radiation pattern at first we examine the unconstrained synthesis problem obtaining a closed form solution then we consider the case where each excitation is constrained to belong to a prescribed set of complex numbers to solve this problem we propose an iterative technique which produces a sequence of excitation vectors each point of the sequence is derived from the preceding one by modifying one of its n components within the corresponding constraint set in such a way as to minimize the mean square distance we show that if the constraint sets are closed and convex then the sequence converges to the unique point of global minimum of the mean square distance for any starting point of the sequence if the constraint sets are non convex the sequence admits a convergent subsequence and the limit of the latter is a good approximation of the solution to the problem in some cases of interest some examples illustrate the effectiveness of the method

critical differentiability of maps and canceling operators for a first order homogeneous linear differential operator mathbb a and 1 q infty we show that l n n 1 q differentiability of bv mathbb a text loc maps is equivalent to van schaftingen s elliptic and canceling ec condition for mathbb a for higher order ec operators we give a generalization of dorronsoro s theorem on critical l p taylor expansions for bv k maps here bv mathbb a text loc is the space of u in l 1 text loc such that mathbb a u is a radon measure these results can be formulated as sharp pointwise regularity results for elliptic systems mathbb a u mu where mu is a radon measure thereby covering the limiting case p 1 of a theorem of calder on and zygmund which was open so far

on the gradient set of lipschitz maps we prove that the essential range of the gradient of planar lipschitz maps has a connected rank one convex hull as a corollary in combination with the results in 7 we obtain a complete characterization of incompatible sets of gradients for planar maps in terms of rank one convexity 2008 walter de gruyter berlin new york

liftings young measures and lower semicontinuity this work introduces liftings and their associated young measures as new tools to study the asymptotic behaviour of sequences of pairs uj duj j for u j j subset rm bv omega mathbb r m under weak convergence these tools are then used to prove an integral representation theorem for the relaxation of the functional mathcal f colon u mapsto int omega f x u x nabla u x rm d x quad u in rm w 1 1 omega mathbb r m quad omega subset mathbb r d rm open to the space rm bv omega mathbb r m lower semicontinuity results of this type were first obtained by fonseca and muller arch ration mech anal 123 1 49 1993 and later improved by a number of authors but our theorem is valid under more natural essentially optimal hypotheses than those currently present in the literature requiring principally that f be caratheodory and quasiconvex in the final variable the key idea is that liftings provide the right way of localising mathcal f in the x and u variables simultaneously under weak convergence as a consequence we are able to implement an optimal measure theoretic blow up procedure

bourgain brezis inequalities on symmetric spaces of non compact type abstract let m be a global riemannian symmetric space of non compact type we prove a duality estimate for pairings of divergence free l 1 vector fields with vector fields in a critical sobolev space on m m f d v c f l 1 d v l m d v this estimate provides a remedy for the failure of a critical sobolev embedding on such symmetric spaces

nonlinear cauchy riemann operators in ℝⁿ this paper has arisen from an effort to provide a comprehensive and unifying development of the l p theory of quasiconformal mappings in r n the governing equations for these mappings form nonlinear differential systems of the first order analogous in many respects to the cauchy riemann equations in the complex plane this approach demands that one must work out certain variational integrals involving the jacobian determinant guided by such integrals we introduce two nonlinear differential operators denoted by d and d which act on weakly differentiable deformations f r n of a domain c r n solutions to the so called cauchy riemann equations d f 0 and d f 0 are simply conformal deformations preserving and reversing orientation respectively these operators though genuinely nonlinear possess the important feature of being rank one convex among the many desirable properties we give the fundamental l p estimate d f p a p n d f p in quest of the best constant a p n we are faced with fascinating problems regarding quasiconvexity of some related variational functionals applications to quasiconformal mappings are indicated

on the structure of a free measures and applications we establish a general structure theorem for the singular part of a free radon measures where a is a linear pde operator by applying the theorem to suitably chosen differential operators a we obtain a simple proof of alberti s rank one theorem and for the first time its extensions to functions of bounded deformation bd we also prove a structure theorem for the singular part of a finite family of normal currents the latter result implies that the rademacher theorem on the differentiability of lipschitz functions can hold only for absolutely continuous measures and that every top dimensional ambrosio kirchheim metric current in rd is a federer fleming flat chain

projection matrix method for shaped beam synthesis in phased arrays and reflectors we present the projection matrix method for shaped beam synthesis in a general array of different size elements the method relies on orthogonal projection of the desired far field intensity vector onto the space spanned by the far field intensity vectors of the array elements it is found that for a uniform convergence of the solution the far field sample space must be extended beyond the coverage region otherwise the projection matrix becomes ill conditioned a general guideline for the far field sample space is provided the method with necessary amendments is then employed successfully for a reflector surface synthesis the method is found to be several times faster than the gradient search method commonly used for beam synthesis numerical results for array and shaped reflector syntheses are shown and the advantages discussed

an optimal sobolev embedding for l1 abstract in this paper we establish an optimal lorentz space estimate for the riesz potential acting on curl free vectors there is a constant c c d 0 such that i f l d d 1 r d r d c f l 1 r d r d for all fields f l 1 r d r d such that curl f 0 in the sense of distributions this is the best possible estimate on this scale of spaces and completes the picture in the regime p 1 of the well established results for p 1

tartar s conjecture and localization of the quasiconvex hull in mathbb r 2 times 2 we give a concrete and surprisingly simple characterization of compact sets k subset mathbb r 2 times 2 for which families of approximate solutions to the inclusion problem du k are compact in particular our condition is algebraic and can be tested algorithmically we also prove that the quasiconvex hull of compact sets of 2 2 matrices can be localized this is false for compact sets in higher dimensions in general

oscillations and concentrations in weak solutions of the incompressible fluid equations the authors introduce a new concept of measure valued solution for the 3 d incompressible euler equations in order to incorporate the complex phenomena present in limits of approximate solutions of these equations one application of the concepts developed here is the following important result a sequence of leray hopf weak solutions of the navier stokes equations converges in the high reynolds number limit to a measure valued solution of 3 d euler defined for all positive times the authors present several explicit examples of solution sequences for 3 d incompressible euler with uniformly bounded local kinetic energy which exhibit complex phenomena involving both persistence of oscillations and development of concentrations an extensions of the concept of young measure is developed to incorporate these complex phenomena in the measure valued solutions constructed here

power pattern synthesis of reconfigurable conformal arrays with near field constraints a conformal array power pattern synthesis technique is presented which makes it possible to take into account near field constraints and to reconfigure the radiated pattern by controlling only the phases of the excitation coefficients far field pattern specifications are given by masks while near field constraints are given by prescribing the maximum allowable field intensity at points arbitrarily located in a given near field region the amplitude of the excitations common to all radiated beams and the phases corresponding to each one are obtained as a result of the synthesis algorithm

partial regularity for bv minimizers we establish an varepsilon regularity result for the derivative of a map of bounded variation that minimizes a strongly quasiconvex variational integral of linear growth and as a consequence the partial regularity of such bv minimizers this result extends the regularity theory for minimizers of quasiconvex integrals on sobolev spaces to the context of maps of bounded variation previous partial regularity results for bv minimizers in the linear growth set up were confined to the convex situation

perturbation theory applied to sound propagation in flowing media confined by a cylindrical waveguide first order perturbation theory is employed to examine sound propagation in flowing media confined by a cylindrical waveguide the use of perturbation theory allows examination of mode phase speed changes due to any radially dependent flow w r as long as the flow magnitude is sufficiently small the condition to be fulfilled is satisfied in the flow range 0 0 3 m s for the specific values of cylinder radius ultrasound frequency and sound speed analyzed in the present work in the general case however the condition in eq 1 of the present work must be fulfilled this freedom of choice i e the possibility to handle any radial flow profile is used to analyze two flow profile cases 1 where w r is a linear combination of a laminar flow profile and a flat profile corresponding to turbulent flow and 2 where w r is a linear combination of a laminar flow profile and a more realistic logarithmic dependent turbulent flow profile in both cases it is shown that large errors may result in ultraso

a new approach to counterexamples to l 1 estimates korn s inequality geometric rigidity and regularity for gradients of separately convex functions the derivation of counterexamples to l1 estimates can be reduced to a geometric decomposition procedure along rank one lines in matrix space we illustrate this concept in two concrete applications firstly we recover a celebrated and rather complex counterexample by ornstein proving the failure of korn s inequality and of the corresponding geometrically nonlinear rigidity result in l1 secondly we construct a function f 2 which is separately convex but whose gradient is not in bvloc in the sense that the mixed derivative 2f x1 x2 is not a bounded measure

efficiency constrained particle swarm optimization of a modified bernstein polynomial for conformal array excitation amplitude synthesis as various enabling technologies advance conformal phased arrays are finding more numerous applications because a conformal array is curved new far field pattern behaviors emerge and many of the traditional linear and planar phased array synthesis methods are not valid this paper starts by reviewing the equations for the far field of a curved phased array and provides a generalized definition of aperture efficiency appropriate for conformal arrays a modified bernstein polynomial defined with just five parameters is introduced which provides a flexible method to specify a variety of smooth unimodal amplitude distributions that are shown to give good sidelobe levels and aperture efficiencies by using particle swarm optimization of the modified bernstein polynomial parameters constrained to provide a specified aperture efficiency a family of aperture distributions and corresponding far field patterns is produced that allows aperture efficiency to be traded for sidelobe level

a limiting case for the divergence equation we consider the equation text div mathbb y f with f a zero average function on the torus mathbb t d in their seminal paper bourgain and brezis j am math soc 16 2 393 426 2003 electronic proved the existence of a solution mathbb y in w 1 d cap l infty for a datum f in l d we extend their result to the critical sobolev spaces w s p with s 1 p d and p ge 2 more generally we prove a similar result in the scale of triebel lizorkin spaces we also consider the equation text div mathbb y f in a bounded domain varomega subject to zero dirichlet boundary condition

a perturbation technique for the prediction of the displacement of a line driven plate with discontinuities a novel technique is presented for obtaining approximate analytic expressions for an inhomogeneous line driven plate the equation of motion for the inhomogeneous plate is transformed and the transform of the total displacement is written as a sum of the solution for a homogeneous line driven plate plus a term due to the inhomogeneity the result is an integral equation for the transform of the inhomogeneous contribution this expression may in general be solved numerically however by introducing a small parameter into the problem it may be solved approximately using perturbation techniques this series may not be convergent but its convergence may be improved using pade approximation results are presented for the case of a single mass discontinuity and a distribution of mass discontinuities

a numerical pattern synthesis algorithm for arrays a numerical technique for pattern synthesis in arrays is presented for a given set of elements the technique allows one to find a set of array coefficients that steer the main beam in a given direction and yield sidelobes meeting a specified criterion if such a set of array coefficients exists if the pattern specifications cannot be met with the given elements the algorithm finds the best attainable pattern the advantage of this technique is that it can be used with an arbitrary set of array elements different elements in the array can have different element patterns and the array can have arbitrary nonuniform spacing between elements the synthesis technique is based on adaptive array theory the given array elements are assumed to be used as the elements of an adaptive array the main beam is pointed in the proper direction by choosing the steering vector for that direction and the sidelobes are controlled by introducing a large number of interfering signals at many angles throughout the sidelobe region the algorithm iterates on the interference powers until a suitable pattern is obtained

sidelobe reduction in array pattern synthesis using genetic algorithm a simple and flexible genetic algorithm ga for pattern synthesis of antenna array with arbitrary geometric configuration is presented unlike conventional ga using binary coding and binary crossover this approach directly represents the array excitation weighting vectors as complex number chromosomes and uses decimal linear crossover without a crossover site compared with conventional gas this approach has a few advantages giving a clearer and simpler representation of the problem simplifying chromosome construction and totally avoiding binary encoding and decoding so as to simplify software programming and to reduce cpu time this method also allows us to impose constraints on phases and magnitudes of complex excitation coefficients for preferable implementation in practice using digital phase shifters and digital attenuators successful applications show that the approach can be used as a general tool for pattern synthesis of arbitrary arrays

a low frequency model for dynamic motion in pre stressed incompressible elastic structures an asymptotic one dimensional theory with minimal essential parameters is constructed to help elucidate two dimensional low frequency dynamic motion in a pre stressed incompressible elastic plate in contrast with the classical theory the long wave limit of the fundamental mode of antisymmetric motion is non zero the occurrence of an associated quasi front therefore offers considerable deviation from the classical case moreover the presence of pre stress makes the plate stiffer and thus may preclude bending in the classical sense discontinuities on the associated leading order wavefronts are smoothed by deriving higher order theories both quasi fronts are shown to be either receding or advancing but of differing type the problems of surface and edge loading are considered and in the latter case a specific problem is formulated and solved to illustrate the theory in the case of antisymmetric motion and an appropriate form of pre stress it is shown that the leading order governing equation for the mid surface deflection is essentially that of waves propagating along an infinite string a higher order equation for which is derived

taylor patterns for discrete arrays the equivalent of a taylor pattern for continuous apertures is developed for discrete arrays this array factor can be realized exactly since it belongs to the appropriate class of patterns a method for determining the element excitations is also presented as an example the pattern and excitations are calculated for a 41 element array with bar n 6 and a 25 db design sidelobe level comparison is made with the patterns obtained by applying root matching and sampling of a continuous taylor aperture

on the constrained synthesis of array patterns with applications to circular and arc arrays synthesis of array patterns involving optimization with linear and nonlinear constraints is considered the general solution for the composite weight vector can be decomposed into a part which satisfies the linear constraints and another lying orthogonal to it this decomposition is shown to yield simple solutions to several beam optimization problems including some with nonlinear constraints a geometrical derivation of this result is presented which also provides new insights into the mechanism of null steering via linear constraints application of this approach in conjunction with some search algorithms to the synthesis of optimum array patterns with prescribed narrow or broad nulls is shown to yield interesting and useful solutions the results are illustrated by considering the design of circular and arc arrays

element pattern of an axial dipole in a cylindrical phased array part i theory cylindrical array antennas are attractive for applications requiring uniform 360 deg azimuthal pattern performance for very low sidelobe or precise angle measurement designs an accurate knowledge of the mutually coupled element pattern becomes important a modal solution is presented for an element pattern in a periodic array of axial dipole radiators placed coaxially over a circular cylindrical ground this solution avoids the problems associated with asymptotic appproaches and displays a number of advantages 1 it is exact subject only to truncation errors 2 it is uniformly valid in all spatial regions for both rectangular and with a simple modification for triangular isosceles lattice configurations and 3 it provides absolute gain information the analysis is presented along with numerical results for representative parameter values selected to illustrate the various trade offs comparison with published data employing the asymptotic approach and with planar array results is given

simple method for pattern nulling by phase perturbation a method of sidelobe hulling which involves perturbing the array illumination phase only is presented the general nonlinear problem is linearized by assuming the perturbations to be small and an analytic solution is derived illustrative examples of sinc and chebyshev patterns with imposed nulls are given

characterization of generalized young measures generated by symmetric gradients this work establishes a characterization theorem for generalized young measures generated by symmetric derivatives of functions of bounded deformation bd in the spirit of the classical kinderlehrer pedregal theorem our result places such young measures in duality with symmetric quasiconvex functions with linear growth the local proof strategy combines blow up arguments with the singular structure theorem in bd the analogue of alberti s rank one theorem in bv which was recently proved by the authors as an application of our characterization theorem we show how an atomic part in a bd young measure can be split off in generating sequences

a new low side lobe pattern synthesis technique for conformal arrays the application of the new nonlinear optimization algorithms to array design is demonstrated by the low side lobe pattern synthesis of conformal arrays by adopting the information of array element realized gain patterns the authors formulate synthesis problems as nonlinearly constrained optimization problems and propose a direct method to solve them the technique allows them to find a set of array coefficients that yield a pattern meeting a specified side lobe level and achieving the maximum directivity if such a set of array coefficients exists if the side lobe specifications cannot be met with the given array the technique will result in a set of coefficients that yield a pattern meeting the best attainable side lobe level and having directivity as high as possible simplified synthesis problems for an axial dipole array in an infinite perfectly conducting cylinder are discussed and numerical results are given the synthesis technique works for general array patterns

an effective approach for the optimal focusing of array fields subject to arbitrary upper bounds a new approach to the optimal focusing of array fields subject to arbitrary upper bounds is presented the approach formulates the problem as the minimization of a linear function in a convex set unlike other approaches this one guarantees the achievement of the global optimum by using local optimization techniques and can moreover deal with any convex constraint on the unknowns such as near field constraints optimization is performed by two ad hoc developed solution algorithms which exploit the geometrical characteristics of the problem at hand thus leading to extremely effective and computationally efficient numerical codes an extensive numerical analysis has been performed in all cases of linear planar and circular arc arrays the enhanced performance of the proposed technique with respect to the solution algorithms available in the literature fully confirms the effectiveness of the approach

phase synthesis of conformal array antennas a new phase synthesis method for planar and conformal arrays is presented the method is based on approximate linearized equations for small phase changes in the excitations which can be determined by the least squares method and used iteratively to obtain the final solutions for the excitation phases several different kinds of contoured beams can be used in the same array by using only phase shifters in the elements as demonstrated in the calculated synthesis examples

null lagrangians weak continuity and variational problems of arbitrary order abstract we consider the problem of minimizing integral functionals of the form i u f x k u x dx where r p u r and k u denotes the set of all partial derivatives of u with orders k the method is based on a characterization of null lagrangians l ku depending only on derivatives of order k applications to elasticity and other theories of mechanics are given

quasiconvex functions with subquadratic growth we establish the existence of quasiconvex functions which are not convex and which have subquadratic grow that infinity

rank one convexity does not imply quasiconvexity we consider variational integrals defined for sufficiently regular functions u r m here is a bounded open subset of r n du x denotes the gradient matrix of u at x and f is a continuous function on the space of all real m n matrices m m n one of the important problems in the calculus of variations is to characterise the functions f for which the integral i is lower semicontinuous in this connection the following notions were introduced see 3 9 10

on interfacial waves in pre stressed layered incompressible elastic solids interfacial waves along the plane boundary between two pre stressed incompressible elastic solids are considered one of the solids is a half space while the other has arbitrary uniform thickness the principal axes of the underlying pure homogeneous deformation in the two solids are aligned with one axis normal to the interface for propagation along an in plane principal axis the dispersion equation is derived in respect of a general strain energy function conditions on the pre strain pre stress and material parameters that ensure the existence of a unique interfacial wavespeed at low frequencies are obtained and it is shown that in special circumstances non dispersive waves can exist at the low frequency limit asymptotic results at the high frequency limit are also obtained for the case of equibiaxial pre strain more specific conditions are derived for the existence of interfacial waves at the low and high frequency asymptotes and these provide information on the existence of waves for the whole frequency range a particular feature of the structure considered is that it may act as a mechanical filter in different frequency regimes depending on the pre strain pre stress and material parameters when the wavespeed vanishes the dispersion equation reduces to a bifurcation equation solutions of which define states of stress and deformation which form boundaries of the region of stability of the underlying state of stress and deformation in the two materials for given material properties the bifurcation equation is examined separately and an explicit bifurcation criterion is given for equibiaxial deformations the results are illustrated graphically by considering several numerical examples based on a certain class of strain energy functions which includes the neo hookean strain energy function the results highlight low and high frequency features and demonstrate the influence of pre stress and deformation on the multiplicity of propagating modes

multiobjective optimization of real and coupled antenna array excitations via primal dual interior point filter method from spherical mode expansions a novel method for the multiobjective optimization of arbitrary planar array excitations is presented the optimization problem formulation which inherently takes into account every array element pattern as well as all interelement couplings is based on matrix valued functions which are computed from the generalized scattering matrix characterization of an array and spherical mode expansions of its radiated field it allows the maximization of the directive gain subject to a maximum sidelobe level a maximum crosspolar level and a minimum aperture illumination efficiency the setting of null pointing directions and the dynamic range control to solve the resulting non linear optimization problem we have developed a primal dual interior point method specifically adapted to the presented formulation which makes use of novel filtering techniques numerical examples of arrays of microstrip patches and dielectric resonator antennas covering a wide variety of requirements on these parameters are presented

an efficient and versatile technique for the synthesis of 3d copolar and crosspolar patterns of phase only reconfigurable conformal arrays with drr and near field control an accurate and flexible iterative algorithm of power synthesis for reconfigurable arrays is proposed the algorithm is based on an alternating projection approach and is suitable for arrays of arbitrary geometry thus including conformal and sparse arrays it allows to generate a number of copolar and crosspolar radiation patterns satisfying assigned requirements switching each pattern into any of the others by phase only control of the excitation applied to each array element moreover the algorithm allows to reduce the dynamic range ratio drr of the excitations and the maximum electric field amplitude in a region close to the antenna a modified version of this algorithm including the previous one as a particular case is then proposed which introduces as an additional capability the reduction of the power radiated in the side lobe region in presence of the above constraints and the squared amplitude of the electric field in an assigned region close to the antenna this allows to significantly improve the final results numerical examples including a comparison with existing literature show the effectiveness of the proposed algorithm

characterization of generalized gradient young measures generated by sequences in w1 1 and bv generalized young measures as introduced by diperna and majda commun math phys 108 667 689 1987 provide a quantitative tool for studying the one point statistics of oscillation and concentration in sequences of functions in this work after developing a functional analytic framework for such measures including a compactness theorem and results on the generation of such young measures by l1 bounded sequences or even by sequences of bounded radon measures we turn to investigation of those young measures that are generated by bounded sequences of w1 1 gradients or bv derivatives we provide several techniques to manipulate such measures including shifting averaging and approximation by piecewise homogeneous young measures and then establish the main new result of this work the duality characterization of the set of bv or w1 1 gradient young measures in terms of jensen type inequalities for quasiconvex functions with linear growth at infinity this result is the natural generalization of the kinderlehrer pedregal theorem arch ration mech anal 115 329 365 1991 j geom anal 4 59 90 1994 for classical young measures to the w1 1 and bv case and contains its version for weakly converging sequences in w1 1 as a special case finally we give an application to a new lower semicontinuity theorem in bv

stress distribution determination in isotropic materials via inversion of ultrasonic rayleigh wave dispersion data the possibility of using measurements of the dispersion of rayleigh surface waves propagating on pre stressed initially isotropic materials to determine the surface stress and gradients in such materials is analytically investigated using a first order perturbation formula for the description of the acoustoelastic effect on rayleigh waves it is shown that knowledge of the frequency dependence of the change in phase or phase velocity of the rayleigh wave after propagating a certain distance can in theory be used to determine the stress level at the surface of the medium as well as its derivatives up to a given order basic questions concerning the uniqueness of the inversion are addressed and a formal method of inverting inhomogeneous bi axial stress distributions is presented the effect of the range of frequencies included in the measurements is discussed and illustrated with a numerical example

optimal design of efficient acoustic antenna arrays minimax optimal design of sonar transducer arrays can be formulated as a nonlinear program with many convex quadratic constraints and a nonconvex quadratic efficiency constraint the variables of this problem are a scaling and phase shift applied to the output of each sensor this problem is solved by applying lagrangian relaxation to the convex quadratic constraints extensive computational experience shows that this approach can efficiently find near optimal solutions of problems with up to 391 variables and 579 constraints

the regularity of minima for the dirichlet problem on bd we establish that the dirichlet problem for linear growth functionals on text bd the functions of bounded deformation gives rise to the same unconditional sobolev and partial text c 1 alpha regularity theory as presently available for the full gradient dirichlet problem on text bv functions of bounded deformation play an important role in for example plasticity however by ornstein s non inequality contain text bv as a proper subspace thus techniques to establish regularity by full gradient methods for variational problems on bv do not apply here in particular applying to all generalised minima that is minima of a suitably relaxed problem despite their non uniqueness and reaching the ellipticity ranges known from the text bv case this paper extends previous sobolev regularity results by gmeineder and kristensen in j calc var 58 56 2019 in an optimal way

nonmultipliers of the sobolev spaces wk 1 rn while the class of multipliers of the sobolev space wk 1 rn is strictly larger than the space of bounded measures for n 1 3 we show in this paper that it fails to contain certain natural operators of the singular integral type theorem 1 to prove this we consider the analogous sobolev space wk 1 of the homogeneous type and show that a nonconstant homogeneous function of degree zero cannot be a fourier multiplier of wk 1 rn theorem 2 some of the results of this paper were announced in 4

power synthesis for reconfigurable arrays by phase only control with simultaneous dynamic range ratio and near field reduction an iterative method of power synthesis for reconfigurable arrays of arbitrary geometry is presented which is based on the method of successive projections the algorithm allows to synthesize a number of desired patterns each reconfigurable into any of the others by phase only control the excitation amplitudes are optimized and their dynamic range ratio drr is reduced below a given threshold furthermore the radiated field can be reduced below a prescribed level in a given region close to the antenna as a particular important case the method allows to perform a discrete phase controlled beam scanning

on coercive variational integrals abstract it is well known that sequential weak lower semicontinuity of a variational integral f u f u x d x on the sobolev space w 1 p r n under a p growth condition on the integrand f is equivalent to quasiconvexity in the sense of morrey we show that coercivity on dirichlet classes likewise is equivalent to a quasiconvexity condition we also discuss some examples and extend a sequential weak lower semicontinuity result to the case of signed integrands

pattern synthesis of conformal array antenna in the presence of platform using differential evolution algorithm a synthesis method based on differential evolution algorithm is proposed for conformal antenna arrays in the presence of platform with the desired phase weights determined by the scan angle and array geometry the amplitude weights of elements are optimized by differential evolution algorithm to drive down the side lobes both the effect of platform on radiation pattern of conformal array and the mutual coupling between the elements are taken into account by calculating the antenna array and platform simultaneously using the method of moment application of adaptive integral method reduces the storage and computation time needed by the method of moments

extension of projection method to nonuniformly linear antenna arrays the study of linear arrays has been developed in different regions the computerized techniques that appeared in this century motivated the researchers to find a new techniques that save time in this work the method of succesive projection is used in solving the nonuniform space and phase arrays this technique was used before to solve the nonuniform current arrays the main concept of this method is to find a common point of many different sets this point will have the best solution to satisfy all conditions in this technique the solution of the set of inequalities is the main scope the addition of one or more constraints to the array is only as adding one more set to the group of sets we have this means that the solution of constrained arrays also is available several illustrations are discussed and compared with different other techniques a simple program is available and easy to establish in this work the broadside direction pattern is divided into 180 deg that represent 180 sets at each set the synthesized pattern must satisfy the desired pattern

qp wave at a corrugated interface between two dissimilar pre stressed elastic half spaces abstract a plane qp wave quasi p wave is assumed to be incident at a corrugated interface between two dissimilar pre stressed elastic solid half spaces using rayleigh s method of approximation the reflection and transmission coefficients have been presented for the first order approximation of the corrugation these coefficients are obtained in closed form for a corrugated interface of periodic shape we found that these coefficients depend on the angle of incidence frequency of the incident wave initial stresses and incremental elastic properties of the half spaces the coefficients corresponding to irregularly reflected and transmitted waves are found to be proportional to the amplitude of the corrugated interface and are also influenced significantly by the initial stresses of the half spaces some more results including the results of sidhu and singh reflection of p and sv waves at the free surface of a prestressed elastic half space journal of the acoustical society of america 76 2 1984 594 598 have been deduced as particular cases from the present problem

a new approach to inversion of surface wave dispersion relation for determination of depth distribution of non uniform stresses in elastic materials ultrasonic surface rayleigh waves become dispersive when propagating on non uniformly stressed media in light of this the acoustoelastic effect on their propagation in deformed but initially isotropic materials has been investigated in the past in order to determine the surface stress and gradients of stress with depth an energy perturbation approach considerably reduces the complexity in the treatment of the acoustoelastic effect and inversion of the perturbation relation offers an advantageous route to obtaining the stress gradients this paper presents a new mechanism for effecting this inversion which tries to overcome the effects of the ill posed nature of the problem preliminary simulation results for commonly occurring stress profiles are presented