Neumann resonances in linear elasticity for an arbitrary body

We study resonances (scattering poles) associated to the elasticity operator in the exterior of an arbitrary obstacle inR ³ with Neumann boundary conditions. We prove that there exists a sequence of resonances tending rapidly to the real axis.Partly supported by BSF under grant MM 401.     

Incompressible Flow Around a Small Obstacle and the Vanishing Viscosity Limit

In this article we consider viscous flow in the exterior of an obstacle satisfying the standard no-slip boundary condition at the surface of the obstacle. We seek conditions under which solutions of the Navier-Stokes system in the exterior domain converge to solutions of the Euler system in the full space when both viscosity and the size of the obstacle vanish. We prove that this convergence is true assuming two hypotheses: first, that the initial exterior domain velocity converges strongly in L ² to the full-space initial velocity and second, that the diameter of the obstacle is smaller than a suitable constant times viscosity, or, in other words, that the obstacle is sufficiently small. The convergence holds as long as the solution to the limit problem is known to exist and stays sufficiently smooth. This work complements the study of incompressible flow around small obstacles, which has been carried out in [4–6].     

Classification of Subsystems for Local Nets¶with Trivial Superselection Structure

Let ℱ be a local net of von Neumann algebras in four spacetime dimensions satisfying certain natural structural assumptions. We prove that if ℱ has trivial superselection structure then every covariant, Haag-dual subsystem ℬ is of the form ℱ₁ ^G ⊗I for a suitable decomposition ℱ=ℱ₁⊗ℱ₂ and a compact group action. Then we discuss some application of our result, including free field models and certain theories with at most countably many sectors. Received: 26 January 2000 / Accepted: 28 September 2000     

On the Discrete Spectrum of a Spatial Quantum Waveguide with a Disc Window

In this study we investigate the bound states of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width d. We impose the Neumann boundary condition on a disc window of radius a and Dirichlet boundary conditions on the remained part of the boundary of the strip. We prove that such system exhibits discrete eigenvalues below the essential spectrum for any a > 0. We give also a numeric estimation of the number of discrete eigenvalue as a function of \fracad\frac{a}{d}. When a tends to the infinity, the asymptotic of the eigenvalue is given.     

Gibbsian Dynamics and Ergodicity¶for the Stochastically Forced Navier–Stokes Equation

We study stationary measures for the two-dimensional Navier–Stokes equation with periodic boundary condition and random forcing. We prove uniqueness of the stationary measure under the condition that all “determining modes” are forced. The main idea behind the proof is to study the Gibbsian dynamics of the low modes obtained by representing the high modes as functionals of the time-history of the low modes. Received: 21 November 2000 / Accepted: 9 December 2000     

Photoproduction of η and η' mesons off nucleons close to threshold

The importance of Born terms and resonance exchange for η and η' photoproduction off both the proton and neutron within U(3) baryon chiral perturbation theory is investigated. Low-lying resonances such as the vector mesons and J ^P = 1/2⁺, 1/2^- baryon resonances are included explicitly and their contributions together with the Born terms are calculated. The coupling constants of the resonances are determined from strong and radiative decays. We obtain reasonable agreement with experimental data near threshold. Received: 17 March 2000 / Accepted: 8 September 2000     

Are There Incongruent Ground States in 2D Edwards–Anderson Spin Glasses?

We present a detailed proof of a previously announced result [1] supporting the absence of multiple (incongruent) ground state pairs for 2D Edwards–Anderson spin glasses (with zero external field and, e.g., Gaussian couplings): if two ground state pairs (chosen from metastates with, e.g., periodic boundary conditions) on ℤ² are distinct, then the dual bonds where they differ form a single doubly-infinite, positive-density domain wall. It is an open problem to prove that such a situation cannot occur (or else to show – much less likely in our opinion – that it indeed does happen) in these models. Our proof involves an analysis of how (infinite-volume) ground states change as (finitely many) couplings vary, which leads us to a notion of zero-temperature excitation metastates, that may be of independent interest. Received: 3 December 2000/ Accepted: 30 April 2001     

String Non(anti)commutativity for Neveu-Schwarz Boundary Conditions

The appearance of non(anti)commutativity in superstring theory, satisfying the Neveu-Schwarz boundary conditions is discussed in this paper. Both an open free superstring and also one moving in a background antisymmetric tensor field are analyzed to illustrate the point that string non(anti)commutativity is a consequence of the nontrivial boundary conditions. The method used here is quite different from several other approaches where boundary conditions were treated as constraints. An interesting observation of this study is that, one requires that the bosonic sector satisfies Dirichlet boundary conditions at one end and Neumann at the other in the case of the bosonic variables X ^μ being antiperiodic. The non(anti)commutative structures derived in this paper also leads to the closure of the super constraint algebra which is essential for the internal consistency of our analysis.     

Identification of baryon resonances in central heavy-ion collisions at energies between 1 and 2 AGeV

The mass distributions of baryon resonances populated in near-central collisions of Au on Au and Ni on Ni are deduced by defolding the p_t spectra of charged pions by a method which does not depend on a specific resonance shape. In addition the mass distributions of resonances are obtained from the invariant masses of (p, π^±) pairs. With both methods the deduced mass distributions are shifted by an average value of −60 MeV/c² relative to the mass distribution of the free Δ(1232) resonance, the distributions descent almost exponentially towards mass values of 2000 MeV/c². The observed differences between (p, π⁻) and (p, π⁺) pairs indicate a contribution of isospin I = 1/2 resonances. The attempt to consistently describe the deduced mass distributions and the reconstructed kinetic energy spectra of the resonances leads to new insights about the freeze out conditions, i.e. to rather low temperatures and large expansion velocities. Received: 26 June 1998 / Revised version: 2 September 1998     

Waveguides with Combined Dirichlet and Robin Boundary Conditions

We consider the Laplacian in a curved two-dimensional strip of constant width squeezed between two curves, subject to Dirichlet boundary conditions on one of the curves and variable Robin boundary conditions on the other. We prove that, for certain types of Robin boundary conditions, the spectral threshold of the Laplacian is estimated from below by the lowest eigenvalue of the Laplacian in a Dirichlet-Robin annulus determined by the geometry of the strip. Moreover, we show that an appropriate combination of the geometric setting and boundary conditions leads to a Hardy-type inequality in infinite strips. As an application, we derive certain stability of the spectrum for the Laplacian in Dirichlet–Neumann strips along a class of curves of sign-changing curvature, improving in this way an initial result of Dittrich and Kříž (J. Phys. A, 35:L269–275, 2002).      

Nanoscopic measurements of the electrostriction responses in P(VDF/TrFE) ultra-thin-film copolymer using atomic force microscopy

Atomic force microscopy (AFM) has been used as a new method to perform nanoscale measurements of the electrostriction coefficients in the lamellae structure of the ferroelectric P(VDF/TrFE) 73/27 copolymers. The result found shows that the electrostriction coefficient inside (in the middle of) the lamella crystals is 6×10^-19 (m²V^-2), which is three times larger than that at the boundary, 2×10^-19 (m²V^-2). To explain the dependence of the electrostriction coefficients with those two regions, some suggestions are proposed. By heat treatment at 140 °C during 2 h, the sample changed its morphology as well as its crystallinity; the amorphous phase is much reduced and the degree of the crystallinity inside the lamellae is higher than that in the border. Also, it is suggested that in the lamellae’s boundary the macromolecular chains come to an end, or one monolayer folds over the other layer. In this case, the electrostriction was suppressed due to the loss of surface energy in the lamellae’s boundary. The achievements will supply a guideline to develop new and better devices for electromechanical and actuator applications. Received: 23 June 2000 / Accepted: 23 August 2000 / Published online: 5 October 2000     

On the Uniqueness of Diffeomorphism Symmetry in Conformal Field Theory

A Möbius covariant net of von Neumann algebras on S¹ is diffeomorphism covariant if its Möbius symmetry extends to diffeomorphism symmetry. We prove that in case the net is either a Virasoro net or any at least 4-regular net such an extension is unique: the local algebras together with the Möbius symmetry (equivalently: the local algebras together with the vacuum vector) completely determine it. We draw the two following conclusions for such theories. (1) The value of the central charge c is an invariant and hence the Virasoro nets for different values of c are not isomorphic as Möbius covariant nets. (2) A vacuum preserving internal symmetry always commutes with the diffeomorphism symmetries. We further use our result to give a large class of new examples of nets (even strongly additive ones), which are not diffeomorphism covariant; i.e. which do not admit an extension of the symmetry to Diff⁺(S¹).Supported in part by the Italian MIUR and GNAMPA-INDAM.     

Mapping of the <Superscript>12</Superscript>C* states via the <Superscript>10</Superscript>B(<Superscript>3</Superscript>He,pααα) reaction

We have studied ¹²C in full kinematics via the ¹⁰B(³He,pααα) reaction at an energy of 2.45 MeV. In our data we have identified states in ¹²C from the ground state up to about 18 MeV, with spins ranging from 0 to 4. Due to the very good resolution, we are able to determine properties of these ¹²C resonances, such as their energy, width, and spin. In this contribution preliminary results from the ongoing analysis are presented. Main focus on the precise determination of the breakup spectra for all resonances.     

Global Uniqueness in the Inverse Scattering Problem¶for the Schrödinger Operator¶with External Yang–Mills Potentials

We consider the Schr?dinger 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. Received: 11 August 2000 / Accepted: 24 May 2001     

On Uniqueness in the General Inverse Transmisson Problem

In this paper we demonstrate uniqueness of a transparent obstacle, of coefficients of rather general boundary transmission condition, and of a potential coefficient inside obstacle from partial Dirichlet-to Neumann map or from complete scattering data at fixed frequency. The proposed transmission problem includes in particular the isotropic elliptic equation with discontinuous conductivity coefficient. Uniqueness results are shown to be optimal. Hence the considered form can be viewed as a canonical form of isotropic elliptic transmission problems. Proofs use singular solutions of elliptic equations and complex geometrical optics. Determining an obstacle and boundary conditions (i.e. reflecting and transmitting properties of its boundary and interior) is of interest for acoustical and electromagnetic inverse scattering, for modeling fluid/structure interaction, and for defects detection.     

Distribution of Lattice Points Visible from the Origin

Let Ω be a region in the plane which contains the origin, is star-shaped with respect to the origin and has a piecewise C ¹ boundary. For each integer Q≥ 1, we consider the integer lattice points from which are visible from the origin and prove that the 1 ^st consecutive spacing distribution of the angles formed with the origin exists. This is a probability measure supported on an interval [m _Ω,∞), with m _Ω >0. Its repartition function is explicitly expressed as the convolution between the square of the distance from origin function and a certain kernel. Received: 2 November 1999 / Accepted: 2 March 2000     

Spectrum of the H− Ion in the s-Wave Model

 The H⁻ ion in the s-wave model has one bound state and a Rydberg series of resonances, one associated with each inelastic threshold of the electron hydrogen system. We calculate the energy of the bound state and the energies of the resonances as well as their total widths up to N = 9 and partial widths up to N = 7. Received July 5, 1999; revised February 18, 2000; accepted for publication February 22, 2000     

Surface States and Spectra

Let ℤ₊ ^{d +1}= ℤ⁺×ℤ₊, let H ₀ be the discrete Laplacian on the Hilbert space l ²(ℤ₊ ^{d +1}) with a Dirichlet boundary condition, and let V be a potential supported on the boundary ∂ℤ₊ ^{d +1}. We introduce the notions of surface states and surface spectrum of the operator H=H ₀+V and explore their properties. Our main result is that if the potential V is random and if the disorder is either large or small enough, then in dimension two H has no surface spectrum on σ(H ₀) with probability one. To prove this result we combine Aizenman–Molchanov theory with techniques of scattering theory. Received: 18 September 2000 / Accepted: 21 November 2000     

Stochastic Dissipative PDE's and Gibbs Measures

We study a class of dissipative nonlinear PDE's forced by a random force η^{omega( t} , ^x ), with the space variable x varying in a bounded domain. The class contains the 2D Navier–Stokes equations (under periodic or Dirichlet boundary conditions), and the forces we consider are those common in statistical hydrodynamics: they are random fields smooth in t and stationary, short-correlated in time t. In this paper, we confine ourselves to “kick forces” of the form

A Maximum Principle for the Muskat Problem for Fluids with Different Densities

We study the fluid interface problem given by two incompressible fluids with different densities evolving by Darcy’s law. This scenario is known as the Muskat problem for fluids with the same viscosities, being in two dimensions mathematically analogous to the two-phase Hele-Shaw cell. We prove in the stable case (the denser fluid is below) a maximum principle for the L ^∞ norm of the free boundary.