Band-gaps in electrostatically controlled dielectric laminates subjected to incremental shear motions

The thickness vibrations of a finitely deformed infinite periodic laminate made out of two layers of dielectric elastomers is studied. The laminate is pre-stretched by inducing a bias electric field perpendicular to the layers. Incremental time-harmonic fields superimposed on the initial finite deformation are considered next. Utilizing the Bloch-Floquet theorem along with the transfer matrix method we determine the dispersion relation which relates the incremental fields frequency and the phase velocity.Ranges of frequencies at which waves cannot propagate are identified whenever the Bloch-parameter is complex. These band-gaps depend on the phases properties, their volume fraction, and most importantly on the electric bias field. Our analysis reveals how these band-gaps can be shifted and their width can be modified by changing the bias electric field. This implies that by controlling the electrostatic bias field desired frequencies can be filtered out. Representative examples of laminates with different combinations of commercially available dielectric elastomers are examined.     

Two graph isomorphism polytopes

The convex hull ψ_n,n of certain (n!)² tensors was considered recently in connection with graph isomorphism. We consider the convex hull ψ_n of the n! diagonals among these tensors. We show: 1. The polytope ψ_n is a face of ψ_n,n. 2. Deciding if a graph G has a subgraph isomorphic to H reduces to optimization over ψ_n. 3. Optimization over ψ_n reduces to optimization over ψ_n,n. In particular, this implies that the subgraph isomorphism problem reduces to optimization over ψ_n,n.     

Analysis and design of selection committees: a game theoretic secretary problem

Firms often delegate important decisions to committees which are set up specifically for that purpose; for example selection committees. We analyze the equilibrium behavior of a game in which committee members (the players) interview candidates sequentially, either hiring or going on to the next one. The players have differing evaluations of candidates (e.g. one cares about typing skills; the other about IT skills), which become their utilities if the candidate is hired. We then consider the optimal design (rules of the game) of such a committee, from the point of view of the firm. That is, which rules hire candidates which maximize the firm’s utility. Our committee game has a first round in which the members sequentially, by order of player number, say ‘yea’ or ‘nea’ to the candidate. If there are sufficient ‘yeas’ then she is tentatively hired; otherwise she is rejected. In the former case, members who said nea can veto the candidate in the second round. Thus the candidate is either hired, rejected, or vetoed. In the last case, the member casting a veto has one less to use on later candidates. We analyze equilibria where a player may say ‘yea’ to a candidate he would prefer not to hire, in order to force the other player to use up a valuable veto. We show that for the uniform candidate distribution there is a unique equilibrium and better candidates for the firm are hired when there are more vetoes. However we exhibit a candidate distribution where increasing the numbers of vetoes results in hiring worse candidates.     

Narrow spectral response of a Brillouin generator

We analyze both theoretically and experimentally the temporal response of a stimulated Brillouin scattering generator to an harmonically modulated pump beam in a 2.1 km optical fiber. It is shown that at certain frequencies (where m is an integer number and are frequencies which depends mainly on the fiber’s length L but also on the beam’s intensity via G) the first harmonic of the generated Stokes beam is relatively suppressed but never vanishes. These frequencies are considerably smaller than the Brillouin’s spectral width (∼20 MHz). Excellent agreement with the analytical model is presented.     

Effect of an energy reservoir on the atmospheric propagation of laser-plasma filaments

The ability to select and stabilize a single filament during propagation of an ultrashort, high-intensity laser pulse in air makes it possible to examine the longitudinal structure of the plasma channel left in its wake. We present the first detailed measurements and numerical 3-D simulations of the longitudinal plasma density variation in a laser-plasma filament after it passes through an iris that blocks the surrounding energy reservoir. Since no compensation is available from the surrounding background energy, filament propagation is terminated after a few centimeters. For this experiment, simulations indicate that filament propagation is terminated by plasma defocusing and ionization loss, which reduces the pulse power below the effective self-focusing power. With no blockage, a plasma filament length of over a few meters was observed.     

Searching for a set of correlated patterns

New algorithms for searching simultaneously for a set of patterns in a text are suggested, for the special case where these patterns are correlated and have a common substring. This is then extended to the case where it could be more profitable to look for more than a single overlap, and a problem related to the generalization of this idea is shown to be NP-complete. Experimental results suggest that for this particular application, the suggested algorithm yields significant improvements over previous methods.     

On an inverse problem for nonnegative and eventually nonnegative matrices

Let σ= (λ₁,···λ_n)⊂C. We discuss conditions for which σ is the spectrum of a nonnegative or eventually nonnegative matrix. This brings us to study rational functions with nonnegative Maclaurin coefficients. A conjecture for special sets σ is stated and some evidence in support of this conjecture is given. Dedicated to my teacher Professor Menachem Schiffer on the occasion of his sixty-fifth birthday.     

A generalization of the Motzkin-Taussky theorem

In this paper we generalize the Motzkin-Taussky theorem to matrices with polynomial entries.     

ACOUSTIC DETECTION OF TRIPLET STATES FORMED BY RADICAL PAIR RECOMBINATION IN QUINONE-DEPLETED PHOTOSYNTHETIC REACTION CENTERS, BY MAGNETIC FIELD MODULATION (MAGNETOPHOTOACOUSTIC EFFECT)-A FEASIBILITY STUDY

Abstract –An acoustic method is outlined to detect triplet states formed by radical pair recombination in photosyn-thetic reaction centers. It is based on magnetic field effect on the probability of triplet state formation by recombination. Using a periodically modulated magnetic field in the presence of constant exciting light, a periodic modulation of the triplet state concentration is set in the sample, which is detected through the corresponding modulated heat emission, transduced to acoustic vibration of the gas phase around the sample. This effect is similar to the photoacoustic effect, except that here the light is not modulated. The feasibility of detecting such an effect was proven experimentally, by obtaining a signal from quinone-depleted reaction centers of Rhodobacter sphaeroides. The signal had twice the frequency of the magnetic field modulation; it was proportional to the light intensity and significantly stronger at the lower temperatures (in the investigated range 113–278 K). No signal was obtained from quinone-containing reaction centers, which do not produce triplets. A theoretical outline of the effect and the experimental set-up are described. The "magnitude of the effect was calibrated against ordinary photoacoustic measurements, allowing numerical evaluation of certain parameters of the triplet state ( e.g. triplet energy or yield) with the aid of auxiliary information from the literature.