Optimal focusing by spatio-temporal inverse filter. I. Basic principles

A focusing technique based on the inversion of the propagation operator relating an array of transducers to a set of control points inside a medium was proposed in previous work [Tanter et al., J. Acoust. Soc. Am. 108, 223-234 (2000)] and is extended here to the time domain. As the inversion of the propagation operator is achieved both in space and time, this technique allows calculation of the set of temporal signals to be emitted by each element of the array in order to optimally focus on a chosen control point. This broadband inversion process takes advantage of the singular-value decomposition of the propagation operator in the Fourier domain. The physical meaning of this decomposition is explained in a homogeneous medium. In particular, a definition of the number of degrees of freedom necessary to define the acoustic field generated by an array of limited aperture in a focal plane of limited extent is given. This number corresponds to the number of independent signals that can be created in the focal area both in space and time. In this paper, this broadband inverse-focusing technique is compared in homogeneous media with the classical focusing achieved by simple geometrical considerations but also with time-reversal focusing. It is shown that, even in a simple medium, slight differences appear between these three focusing strategies. In the companion paper [Aubry et al., J. Acoust. Soc. Am. 110, 48-58 (2001)] the three focusing techniques are compared in heterogeneous, absorbing, or complex media where classical focusing is strongly degraded. The strong improvement achieved by the spatio-temporal inverse-filter technique emphasizes the great potential of multiple-channel systems having the ability to apply completely different signal waveforms on each transducer of the array. The application of this focusing technique could be of great interest in various ultrasonic fields such as medical imaging, nondestructive testing, and underwater acoustics.     

Obtaining the dividends-penalty identities by interpretation

The dividends-penalty identity is a relation between three functions: the discounted penalty function without dividends, the discounted penalty function if a barrier dividend strategy is applied, and the expected discounted dividends until ruin. The classical model of risk theory is modified in that the deterministic premiums are replaced by a compound Poisson process with exponential jumps. In this model, the dividends-penalty identity is new and can be derived by interpretation. Then the dividends-penalty identity in the classical model is obtained as a limit.     

Can projectiles traversing solids bind electrons at all velocities?

PAC measurements on the 4.43 MeV ¹²C(2⁺) state on recoil in magnetized iron at velocities υ_ion = 0.058c, 0.071c yield integral nuclear precession angles of Φ = ?0.18 (30), +0.17 (39) mrad respectively. Evidently, the high electron-spin-polarization transfer to the innermost carbon orbits implied by a previous measurement (υ_ion = 0.03c, Φ = +0.85 (14) mrad) is suppressed at higher ion velocities.     

Calculated correlations between material parameters and electro-optical performance of twisted nematic displays

Computer calculations of the optical transmission of TN-LCDs as a function of the applied voltage are presented. In particular, the wavelength and angular dependence of half transmission voltages and sharpness of transmission curves are examined. Furthermore the lowest relaxation rates of the linearized dynamical equations, neglecting backflow effects are calculated. The dielectrical anisotropy and the elastic parameters are varied systematically in the calculations over ranges that actually occur in nematics. Although the results are too complex to be condensed in simple general statements they are helpfull in designing optimal nematic mixtures for a given display application.     

Ring inversion process for a series of 3,5‐dialkyl‐1‐oxa‐3,5‐diazacyclohexanes: 1H DNMR study and semiempirical calculations

The ring inversion process for a series of 3,5‐dialkyl‐1‐oxa‐3,5‐diazacyclohexanes was studied using proton dynamic nuclear magnetic resonance (¹H DNMR) spectroscopy in conjunction with semiempirical calculations. At low temperature, the ring methylene protons decoalesced into two AB spin systems in a 2:1 ratio. Lineshape simulations of the DNMR spectra provided first‐order rate constants for magnetic exchange. The energy barrier for each inversion reaction was calculated from the respective rate constants. In general, as the size of the N‐alkyl group increased, the barrier to ring inversion decreased. A similar trend was seen in semiempirical calculations that modeled the ring inversion process. Copyright © 2010 John Wiley & Sons, Ltd.     

X-Ray Bremsstrahlung Measurements of an Intense Relativistic Electron Beam Propagating in a Plasma

Information on the peak electron energy, angular spread, and current density of a relativistic electron beam propagating in a plasma column is obtained from measurements of two-absorber transmission ratios, anistropy, and intensity, respectively, of x-ray bremsstrahlung from thin target foils in the plasma. Measurements indicate a 10% loss in peak electron energy and a factor of two loss in peak beam intensity over the distance of the plasma column, and show a large angular spread in the beam.     

Chains of reinsurance

A one-dimensional, hierarchical system of reinsurance is considered. A member of the chain is in direct contact with only two other members: the one from which coverage is bought and the one to which coverage is sold. Exceptions are the first link (which does not sell any reinsurance coverage) and the last link (which does not buy any). The problem is to find the values of the quotas and the loadings that are optimal in some sense. Assuming exponential utility functions and a normal distribution for the claims, an explicit solution is found for two versions of the model.     

Dissociation dynamics of Ar3 in the time-dependent self-consistent field (TDSCF) approximation

The TDSCF approximation is applied to dissociation of Ar₃, which exhibits strong-coupling behavior (efficient internal energy transfer). The TDSCF results are in excellent agreement with those of exact classical dynamics. Combined with earlier findings for weak-coupling cases, this suggests validity of TDSCF for dissociation at all coupling strengths.     

On the numerical evaluation of the distribution of aggregate claims and its stop-loss premiums

The paper develops a method for the numerical evaluation of the distribution of aggregate claims and its stop-loss premiums.