Singular Limit and Homogenization for Flame Propagation in Periodic Excitable Media

This paper is concerned with a class of singular equations modelling the combustion of premixed gases in periodic media. The model involves two parameters: the period of the medium |L| and a singular parameter related to the activation energy. The existence of pulsating travelling fronts for fixed and |L| was proved by Berestycki & Hamel in [BH]. In the present paper, we investigate the behaviour of such solutions when More precisely, we establish that pulsating travelling fronts behave like travelling waves, when the period |L| is small and . We also study the convergence of the solution, as goes to zero (and |L| is fixed), toward a solution of a free boundary problem.     

Conjugates of Rational Equivariant Holomorphic Maps of Symmetric Domains

Let t: D ?D￠\tau: {\cal D} \rightarrow{\cal D}^\prime be an equivariant holomorphic map of symmetric domains associated to a homomorphism r: \Bbb G ?\Bbb G￠{\bf\rho}: {\Bbb G} \rightarrow{\Bbb G}^\prime of semisimple algebraic groups defined over \Bbb Q{\Bbb Q} . If G ì \Bbb G (\Bbb Q)\Gamma\subset {\Bbb G} ({\Bbb Q}) and G￠ ì \Bbb G￠(\Bbb Q)\Gamma^\prime \subset {\Bbb G}^\prime ({\Bbb Q}) are torsion-free arithmetic subgroups with r (G) ì G￠{\bf\rho} (\Gamma) \subset \Gamma^\prime , the map G\D ?G￠\D￠\Gamma\backslash {\cal D} \rightarrow\Gamma^\prime \backslash {\cal D}^\prime of arithmetic varieties and the rationality of D{\cal D} and D￠{\cal D}^\prime as well as the commensurability groups of s ? Aut (\Bbb C)\sigma \in {\rm Aut} ({\Bbb C}) determines a conjugate equivariant holomorphic map t^s: D^s ?D^￠s\tau^\sigma: {\cal D}^\sigma \rightarrow{\cal D}^{\prime\sigma} of f^s: (G\D)^s ?(G￠\D￠)^s\phi^\sigma: (\Gamma\backslash {\cal D})^\sigma \rightarrow(\Gamma^\prime \backslash {\cal D}^\prime)^\sigma of . We prove that is rational if is rational.     

Quantum mechanical single-gold-nanocluster electroluminescent light source at room temperature

Electrically contacted gold-nanocluster arrays formed within electromigration-induced break junctions exhibit bright, field-dependent electroluminescence in the near infrared (650-800 nm). Intensity autocorrelation of spatially isolated individual nanocluster emission driven at high electrical frequency (f(ac)= approximately 200 MHz) reveals antibunched electroluminescence at room temperature. These results demonstrate the single quantum nature of several-atom gold molecules and suggest their use as room-temperature electrically driven single-photon sources.     

A fast Fourier transform on multipoles (FFTM) algorithm for solving Helmholtz equation in acoustics analysis

This article presents a fast algorithm for the efficient solution of the Helmholtz equation. The method is based on the translation theory of the multipole expansions. Here, the speedup comes from the convolution nature of the translation operators, which can be evaluated rapidly using fast Fourier transform algorithms. Also, the computations of the translation operators are accelerated by using the recursive formulas developed recently by Gumerov and Duraiswami [SIAM J. Sci. Comput. 25, 1344-1381(2003)]. It is demonstrated that the algorithm can produce good accuracy with a relatively low order of expansion. Efficiency analyses of the algorithm reveal that it has computational complexities of O(Na), where a ranges from 1.05 to 1.24. However, this method requires substantially more memory to store the translation operators as compared to the fast multipole method. Hence, despite its simplicity in implementation, this memory requirement issue may limit the application of this algorithm to solving very large-scale problems.     

Optically controlled seeding of Raman forward scattering and injection of electrons in a self-modulated laser-wakefield accelerator

Optical seeding of plasma waves and the injection of electrons are key issues in self-modulated laser-wakefield accelerators. By implementing a copropagating laser prepulse with proper timing, we are able to control the growth of Raman forward scattering and the production of accelerated electrons. The dependence of the Raman intensity on prepulse timing indicates that the seeding of Raman forward scattering is dominated by the ionization-induced wakefield, and the dependence of the divergence and number of accelerated electrons further reveals that the stimulated Raman backward scattering of the prepulse plays the essential role of injecting hot electrons into the fast plasma wave driven by the main pulse.     

Time-frequency analysis for pulse driven ultrasonic microscopy for biological tissue characterization

The authors have proposed a new type of ultrasonic microscopy for biological tissue characterization. The system is driven by a nanosecond pulse voltage, the generated acoustic wave being reflected at the front and rear side of the sliced tissue. In this report, a time-frequency analysis was applied to determine the sound speed thorough the tissue. Frequency dependence of sound speed was obtained with a myocardium of a rat sliced into 10 microm. As the reflected waveform had a significant amount of oscillating component, the waveform was once subjected to the deconvolution process. As the result, two reflections were clearly separated in time domain. Then these two reflections were separately analyzed by time-frequency analysis. Each reflection was extracted by using a proper window function. Phase angles of these reflections at the same frequency were compared. A sound speed micrograph at an arbitrary frequency in between 50 and 150 MHz was successfully obtained. A tendency was found that the sound speed slightly increases with frequency.     

Radiance-based monitoring of the extent of tissue coagulation during laser interstitial thermal therapy

Optical monitoring relates the dynamic changes in measured light intensity to the extent of treatment-induced coagulation that occurs during laser interstitial thermal therapy. We utilized a two-region Monte Carlo simulation to elucidate the nature of the changes in interstitial radiance and fluence that result from the formation of a volume of thermal coagulation surrounding a cylindrical emitter. Using simulation results, we demonstrate that radiance sensors are more sensitive than traditional fluence sensors to coagulation-induced scattering changes. Radiance measurements take advantage of directional detection angles that are more receptive to the onset and passing of the coagulation boundary. We performed experiments with albumen phantoms to demonstrate the practicality of the radiance method for monitoring interstitial laser thermal therapy.     

Broadband blazing with artificial dielectrics

The efficiency of conventional diffractive optical elements with échelette-type profiles drops rapidly as the illumination wavelength departs from the blaze wavelength. We use high dispersion of artificial materials to synthesize diffractive optical elements that are blazed over a broad spectral range (approximately 1 octave) or for two different wavelengths.     

All-fiber narrowband polarization controller based on coherent acousto-optic mode coupling in single-mode fiber

An all-fiber, narrowband, tunable polarization controller is proposed and demonstrated. The device is based on coherent acousto-optic mode coupling induced by two orthogonal acoustic waves on a dispersion-compensating fiber. The cooperative coupling between the two polarizations of the core mode and the TE01 cladding mode through the two gratings permits indirect coupling between the two polarizations of the core mode with nearly 100% efficiency, which makes the polarization-controlling function possible. Experimental results verify the operation of the polarization controller with an insertion loss of <1 dB.     

Depth-enhanced integral imaging by use of optical path control

The image depth of integral imaging is enhanced by doubling the number of central depth planes by use of optical path control. To accomplish this, the optical path lengths are changed by controlling whether reflections occur behind the lens array. We propose three schemes that use mirrors, a combination of beam splitters and polarizers, and polarization beam splitters, respectively. In experiments we implement the systems that are completely electronically controllable, are compact, and provide two central depth planes with 50.4-mm separation.