equilibrium problem for elastic body with delaminated t shape inclusion abstract we analyze an equilibrium problem for 2d elastic body with a t shape thin inclusion in presence of damage a part of the inclusion is elastic and the other part is a rigid one a delamination of the inclusion from the elastic body is assumed thus forming a crack between the elastic body and the inclusion nonlinear boundary conditions at the crack faces are considered to prevent a mutual penetration between the faces the damage is characterized by a positive parameter the paper provides an asymptotic analysis of the solutions as the damage parameter tends to infinity and to zero a passage to infinity of a rigidity parameter of the elastic part of the inclusion is also analyzed junction conditions are determined at the connection point between the elastic and rigid parts of the inclusion an existence theorem is proved for an inverse problem of finding displacement fields and the damage and rigidity parameters provided that a displacement of the tip point of the inclusion is known

an electromagnetic inverse problem in chiral media we consider the inverse boundary value problem for maxwell s equations that takes into account the chirality of a body in r3 more precisely we show that knowledge of a boundary map for the electromagnetic fields determines the electromagnetic parameters namely the conductivity electric permittivity magnetic permeability and chirality in the interior we rewrite maxwell s equations as a first order perturbation of the laplacian and construct exponentially growing solutions and obtain the result in the spirit of complex geometrical optics

capabilities and limitations of multirate control schemes abstract a fundamental obstacle in control system design is the presence of plant zeros recently it has been suggested that in digital control systems such problems may be overcome by using multirate sampling in this paper we describe the capabilities of such multirate control schemes with regard to pole and zero assignment we also point out a limitation of the approach due to degradation in the intersample behavior in mita and chida 1988 proc 27th conf on dec and control pp 1883 1888 it is shown that with a two delay input control scheme it is possible to assign all the poles and zeros of the closed loop system using state feedback in this paper we generalize this result to the case of n delay input control using dynamic compensators in an n delay input control scheme the input to the continuous system is changed n times more often than the output is sampled using such a scheme we show how to design output feedback controllers for siso systems that ensure arbitrary placement of all the poles and zeros of the closed loop system corresponding results for the mimo regulator and the siso servomechanism are given we also show that a hidden cost associated with the use of n delay input control is a degradation in the intersample behavior we demonstrate this via simulation and present an analysis which explains why this degradation arises

decoupling elastic waves and its applications abstract in this paper we consider time harmonic elastic wave scattering governed by the lame system it is known that the elastic wave field can be decomposed into the shear and compressional parts namely the pressure and shear waves that are generally coexisting but propagating at different speeds we consider the third or fourth kind impenetrable scatterer and derive two geometric conditions respectively related to the mean and gaussian curvatures of the boundary surface of the scatterer that can ensure the decoupling of the shear and pressure waves the decoupling results are new to the literature and are of significant interest for their own sake as an interesting application we apply the decoupling results to the uniqueness and stability analysis for inverse elastic scattering problems in determining polyhedral scatterers by a minimal number of far field measurements

reconstructing discontinuities using complex geometrical optics solutions in this paper we provide a framework for constructing general complex geometrical optics solutions for several systems of two variables that can be reduced to a system with the laplacian as the leading order term we apply these special solutions to the problem of reconstructing inclusions inside a domain filled with known conductivity from local boundary measurements computational results demonstrate the versatility of these solutions to determine electrical inclusions

layer stripping for a transversely isotropic elastic medium in this paper we develop a layer stripping algorithm for transversely isotropic elastic materials in three dimensional space we first prove that by making displacement and traction measurements at the boundary of these elastic materials one can determine the elastic tensor and all its derivatives at the boundary the elastic measurements made at the boundary are encoded in the dirichlet to neumann dn map then we use the riccati equation developed in g nakamura and g uhlmann a layer stripping algorithm in elastic impedance tomography in inverse problems in wave propagation ima vol math appl 90 springer verlag new york 1997 pp 375 384 for the dn map in any anisotropic elastic medium to approximate the elastic tensor in the interior

global uniqueness in the inverse scattering problem for the schrodinger operator with external yang mills potentials we consider the schrodinger equation in r n n 3 with external yang mills potentials having compact supports we prove the uniqueness modulo a gauge transformation of the solution of the inverse boundary value problem in a bounded convex domain a similar uniqueness result holds for the inverse scattering problem at a fixed energy

inverse scattering for the magnetic schrodinger operator abstract we show that fixed energy scattering measurements for the magnetic schrodinger operator uniquely determine the magnetic field and electric potential in dimensions n 3 the magnetic potential its first derivatives and the electric potential are assumed to be exponentially decaying this improves an earlier result of eskin and ralston 1995 5 which considered potentials with many derivatives the proof is close to arguments in inverse boundary problems and is based on constructing complex geometrical optics solutions to the schrodinger equation via a pseudodifferential conjugation argument

shaping of the output response in a class of linear multivariable systems a state feedback controller is designed to regulate as desired the output response of minimum phase linear multivariable square plants with cb having full rank b input matrix and c output matrix properties of the controller are given and an example is worked out for illustration

completeness of products of solutions and some inverse problems for pde abstract in this paper we give conditions which guarantee that products of solutions of partial differential equations pu au 0 are complete in l 2 here p is a linear partial differential operator with constant coefficients and a is a function in l we check these conditions for elliptic parabolic and hyperbolic equations of second order and give applications to inverse problems for related equations where a is to be found

boundary integral formulae for the reconstruction of imperfections of small diameter in an elastic medium we consider an isotropic lame system for an elastic medium consisting of finitely many imperfections of small diameter embedded in a homogeneous reference medium the lame coefficients of the imperfections are different from those of the background medium first we establish an asymptotic formula for the displacement vector in terms of the reference lame coefficients the location of the imperfections and their geometry second we use this asymptotic expansion to establish continuous dependence estimates for certain characteristics of the imperfections in terms of the boundary data and to derive integral boundary formulae that yield to a very effective identification procedure

lagrange multipliers in stochastic programming a fritz john multiplier rule is given for discrete time finite horizon stochastic programs particular emphasis is placed on constraint qualifications that allow for the application of this rule in normal lagrange form

determination of viscosity in the stationary navier stokes equations abstract in this paper we consider the stationary navier stokes equations in a bounded domain with a variable viscosity we prove that one can uniquely determine the viscosity function from the knowledge of boundary data

artificial conditions for the linear elasticity equations in this paper we consider the equations of linear elasticity in an exterior domain we exhibit artificial boundary conditions on a circle which lead to a non coercive second order boundary value problem in the particular case of an axisymmetric geometry explicit computations can be performed in fourier series proving the well posedness except for a countable set of parameters a perturbation argument allows to consider near circular domains we complete the analysis by some numerical simulations

global uniqueness for an inverse boundary value problem arising in elasticity we prove that we can determine the lame parameters of an elastic isotropic inhomogeneous medium in dimensionsn 3 by making measurements of the displacements and corresponding stresses at the boundary of the medium

an inverse problem in elastodynamics uniqueness of the wave speeds in the interior abstract we consider the unique determination of internal properties of a nonhomogeneous isotropic elastic object from measurements made at the surface the 3 dimensional object is modelled by solutions of the linear hyperbolic system of equations for elastodynamics whose leading coefficients correspond to the internal properties of the object its density and elasticity we model surface measurements by the dirichlet to neumann map on a finite time interval in a previous paper the author has shown that the density and elastic properties of the surface of the object are uniquely determined by the dirichlet to neumann map here we apply that result to conclude that certain properties of the interior of the object the wave speeds are also determined we then observe that the elastodynamic polarization is determined outside the object by the dirichlet to neumann map we conclude in the case that the wave speeds are constant that the polarization data do not determine the density in the interior this problem and techniques used in its study are closely related to those in for example seismology and medical imaging the techniques used here though from geometric optics integral geometry and microlocal analysis lead to the solution of this fully three dimensional problem

a special green s function for the biharmonic operator and its application to an inverse boundary value problem abstract a construction of the special green s function for the biharmonic operator is given this result is used to recover the operator a2 v x from its diricldet to neumann map 1 introduction let n 2 and put az e ix a z z ei z for z e c r with z z o since the inverse of the symbol of az is locally absolutely integrable and decays algebraically at infinity its inverse fourier transform defines a tempered distribution which is a fundamental solution of az and called a green faddeev function at z z for the laplace operator this terminology is seen in 1 this function plays an important role in studying several inverse problems for example inverse scattering problems see 1 2 inverse boundary value problems see 3 in short those problems are to determine the coefficients of an elliptic partial differential operator l in r n or a bounded domain f by the scattering datum at izl oo or the cauchy datum on a of the solutions of

design of a stable state feedback controller based on the multirate sampling of the plant output a new type of controller is proposed which detects the ith plant output n sub i times during a period of t sub 0 and changes the plant inputs once during t sub 0 it is shown that an arbitrary state feedback can be realized by such controllers if the plant is observable this implies for instance that arbitrary symmetric pole assignment is possible if the plant is controllable it is also shown that if the plant has no zeros at the origin the state transition matrix of the controller itself can be set arbitrarily without changing the state feedback to be realized that is to say inversely expressed any state feedback can be equivalently realized by a controller with any prescribed degree of stability

recovering complex elastic scatterers by a single far field pattern abstract we consider the inverse scattering problem of reconstructing multiple impenetrable bodies embedded in an unbounded homogeneous and isotropic elastic medium the inverse problem is nonlinear and ill posed our study is conducted in an extremely general and practical setting the number of scatterers is unknown in advance and each scatterer could be either a rigid body or a cavity which is not required to be known in advance and moreover there might be components of multiscale sizes presented simultaneously we develop several locating schemes by making use of only a single far field pattern which is widely known to be challenging in the literature the inverse scattering schemes are of a totally direct nature without any inversion involved for the recovery of multiple small scatterers the nonlinear inverse problem is linearized and to that end we derive sharp asymptotic expansion of the elastic far field pattern in terms of the relative size of the cavities the asymptotic expansion is based on the boundary layer potential technique and the result obtained is of significant mathematical interest for its own sake the recovery of regular size extended scatterers is based on projecting the measured far field pattern into an admissible solution space with a local tuning technique we can further recover multiple multiscale elastic scatterers

on the determination of radially dependent lame coefficients in this paper we prove that one can determine radially dependent lame coefficients lambda and mu of an isotropic elastic ball by choosing only two correspondences in the dirichlet to neumann map i e twice making measurements of displacement and stress on the surface of the ball this is a one dimensional multiunknown undetermined coefficient problem for a system of partial differential equations we use a matrix form of the transmutation mapping for solving this problem the procedure for proving the uniqueness based on transmutation can be viewed as a computational algorithm also the method we develop has the potential of solving other one dimensional multiunknown inverse problems