A recipe for making materials with negative refraction in acoustics

A recipe is given for making materials with negative refraction in acoustics, i.e., materials in which the group velocity is directed opposite to the phase velocity. The recipe consists of injecting many small particles into a bounded domain, filled with a material whose refraction coefficient is known. The number of small particles to be injected per unit volume around any point x is calculated as well as the boundary impedances of the embedded particles.     

Corrigendum to “Discrepancy principle for the dynamical systems method” [Communications in Nonlinear Science and Numerical Simulation 10 (2005) 95–101]

Consider an operator equation B(u) − f = 0 in a real Hilbert space. Let us call this equation ill-posed if the operator B′(u) is not boundedly invertible, and well-posed otherwise. The dynamical systems method (DSM) for solving this equation consists of a construction of a Cauchy problem, which has the following properties: (1) it has a global solution for an arbitrary initial data, (2) this solution tends to a limit as time tends to infinity, (3) the limit is the minimal-norm solution to the equation B(u) = f. A global convergence theorem is proved for DSM for equation B(u) − f = 0 with monotone operators B.     

Comparative investigation of the structure of complexes of DNA with the polypeptide fragment 152–184 of histone H1 and the polypeptide (Lys-Ala-Ala)n

The interactions with DNA of a synthetic peptide fragment of histone H1 33 amino acid residues long the sequence of which corresponds to fragment 152–184 and of a synthetic polypeptide (Lys-Ala-Ala)_n modeling the properties of the C-terminal fragments of histone H1 have been studied by the CD method. The use of the CD method for recording the spectra of the polypeptides under investigation in the free state and of the artificial complexes of DNA formed with them has permitted the characterization of different structural possibilities of the polypeptides in solution and of their complexes with DNA, and the conformational changes of the components of the complex under various ionic conditions.     

Calculating singular integrals as an ill-posed problem

Summary Applying numerical quadrature to singular integrals in a straightforward way leads to uncontrolled instability with respect to data errors. In this paper we describe how to control this instability.Dedicated to Professor G. Hämmerlin on the occasion of his 60th birthday.     

All solid state ion-conducting cesium source for atomic clocks

Cesium containing glass with solid metal electrodes was used as a Cs atom source in a high vacuum system. A silver anode provides an injection source of highly mobile ions which sweep Cs to the cathode surface, from which they evaporate into the vacuum. Cathode metallization with finger patterns was used leaving bare glass for Cs evaporation. Laser absorption measurements show Cs vapor generation synchronous with an applied DC voltage.     

On a new notion of the solution to an ill-posed problem

A new understanding of the notion of the stable solution to ill-posed problems is proposed. The new notion is more realistic than the old one and better fits the practical computational needs. A method for constructing stable solutions in the new sense is proposed and justified. The basic point is: in the traditional definition of the stable solution to an ill-posed problem Au=f, where A is a linear or nonlinear operator in a Hilbert space H, it is assumed that the noisy data {f_δ,δ} are given, ‖f−f_δ‖≤δ, and a stable solution u_δ:=R_δf_δ is defined by the relation lim_δ→0‖R_δf_δ−y‖=0, where y solves the equation Au=f, i.e., Ay=f. In this definition y and f are unknown. Any f∈B(f_δ,δ) can be the exact data, where B(f_δ,δ):={f:‖f−f_δ‖≤δ}.The new notion of the stable solution excludes the unknown y and f from the definition of the solution. The solution is defined only in terms of the noisy data, noise level, and an a priori information about a compactum to which the solution belongs.     

Comparison of a vectorial and new semivectorial finite-difference approach for optical waveguides

In this article, a new semivectorial finite-difference method is presented. By comparing the results obtained by the new approach with a vectorial method, it is shown that the accuracy is still very high with costs reduced by a factor of two. This revised version was published online in November 2006 with corrections to the Cover Date.     

Recovery of small electromagnetic inhomogeneities from partial boundary measurementsIdentification de petites inhomogénéités diélectriques à partir de mesures partielles

We consider for the inverse problem of identifying locations and certain properties of the shapes of small dielectric inhomogeneities in a homogeneous background medium from boundary measurements on part of the boundary or dynamic boundary measurements for a finite time interval. Using as weights particular background solutions we develop asymptotic methods based on appropriate averaging of the data. To cite this article: H. Ammari, A.G. Ramm, C. R. Mecanique 330 (2002) 199–205.