Winding Clusters in Percolation on the Torus and the Möbius Strip

Using a simulation technique introduced recently, we study winding clusters in percolation on the torus and the Möbius strip for different aspect ratios. The asynchronous parallelization of the simulation makes very large system and sample sizes possible. Our high accuracy results are fully consistent with predictions from conformal field theory. The numerical results for the Möbius strip and the number distribution of winding clusters on the torus await theoretical explanation. To our knowledge, this study is the first of its kind.     

Sparse generalized Fourier transforms

Block-diagonalization of sparse equivariant discretization matrices is studied. Such matrices typically arise when partial differential equations that evolve in symmetric geometries are discretized via the finite element method or via finite differences. By considering sparse equivariant matrices as equivariant graphs, we identify a condition for when block-diagonalization via a sparse variant of a generalized Fourier transform (GFT) becomes particularly simple and fast. Characterizations for finite element triangulations of a symmetric domain are given, and formulas for assembling the block-diagonalized matrix directly are presented. It is emphasized that the GFT preserves symmetric (Hermitian) properties of an equivariant matrix. By simulating the heat equation at the surface of a sphere discretized by an icosahedral grid, it is demonstrated that the block-diagonalization is beneficial. The gain is significant for a direct method, and modest for an iterative method. A comparison with a block-diagonalization approach based upon the continuous formulation is made. It is found that the sparse GFT method is an appropriate way to discretize the resulting continuous subsystems, since the spectrum and the symmetry are preserved. AMS subject classification (2000)  43A30, 65T99, 20B25     

Quantum correlations in dual quantum measurements

 We analyze the quantum measurement properties of dual non-degenerate parametric amplifers in the twin-beam configuration, in the cascaded back-action-evasion configuration, and in Kerr-type photon-number quantum non-demolition measurements. It is found that Einstein-Podolsky-Rosen correlations can be obtained between the quadrature components of an idler mode and the sum of the readout of two signal modes. Furthermore, we discuss dual-mode quantum non-demolition measurements on the combination of two light modes, and the generation of number-state entanglement. Received: 12 April 1996/Revised version: 2 July 1996     

Narrow linewidth 2 μm optical parametric oscillation in periodically poled LiNbO<Subscript>3</Subscript> with volume Bragg grating outcoupler

An optical parametric oscillator using a periodically poled LiNbO₃ crystal and a volume Bragg grating output coupler is presented. Signal and idler wavelengths of 2008 and 2264 nm were generated from the 1064 nm Nd:YVO₄ pump laser. The Bragg grating was reflecting in a narrow band around 2008 nm, creating a purely singly resonant cavity. Signal and idler linewidths of approximately 0.44 and 0.72 nm, respectively, were measured. This is a reduction of 80 and 60 times compared to when using a mirror as output coupler. A total output energy of 156 μJ was measured with 47% slope efficiency. PACS 42.65.Yj; 42.72.Ai; 42.40.Eq     

On certainp-harmonic functions in the plane

A representation theorem is given for certainp-harmonic functions (1<p<) in the plane, near a corner of the domain of definition. The proof uses stream functions and the hodograph transformation. The stream function of ap-harmonic function isp-harmonic, where 1/p+1/p=1. Solutions of the formr ^k f(ø) (polar coord.) are crucial for the representation.     

The investigation of critical parameters in the glycolytic response of single living cells by rapid microspectrofluorometric analysis

Summary NAD(P)H fluorescence emission spectra are recorded from single living cells, by a recently developed multichannel microspectrofluorometric technique, in correlation with the intracellular microelectrophoretic addition of substrate (i. e., glucose-6-P). These spectra may be used as a reference basis in establishing the critical parameters to be followed when the same studies are extended to a variety of cells, submitted to various drug effects or physical treatments. The sum-spectra corresponding to channel by channel (wavelength by wavelength) summation of spectra obtained from various cells within a series, before and after addition of substrate, and their difference spectrum may be normalized and evaluated comparatively. The NAD(P)H emission maximum prior to addition of substrate seems to present a mixture of dehydrogenase-bound and free coenzyme. There is a suggestion that immediately after substrate, i. e., at 5 sec, an increase in free NADH is first observed. While the overall changes in fluorescence intensity associated with substrate are quite large (50–150% increase), the counts (i. e., an expression of photons) associated with shifts in the emission maximum (free vs. bound NAD(P)H changes) are at times barely above noise. Rapid microspectrofluorometry provides in principle the most direct approach for the identification of coenzyme bound to various dehydrogenases in single living cells, but further improvements in spectral resolution and signal-to-noise ratio are required, for a better definition of the spectral shifts which may be observed.

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Zusammenfassung Mit Hilfe einer kürzlich entwickelten Mehrkanal-Mikrospektrofluorometer-Methode wurden von einzelnen lebenden Zellen nach intrazellulär mikroelektrophoretischer Substratzugabe (z. B. Glucose-6-P) NAD(P)H Fluoreszenz-Emissionsspektren aufgenommen. Diese Spektren können als Vergleichsbasis bei der Festsetzung der entscheidenden Parameter verwendet werden, wenn die gleichen Untersuchungen auf eine Reihe von Zellen ausgedehnt werden sollen, die verschiedenen Medikamenteffekten oder physikalischer Behandlung ausgesetzt werden. Die Summenspektren, die der kanalmäßigen (wellenlängenmäßigen) Summierung der Spektren von verschiedenen Zellen innerhalb einer Serie, vor und nach Substratzugabe entsprechen, sowie ihre Differenzspektren können normalisiert und vergleichsweise ausgewertet werden. Das NAD(P)H-Emissionsmaximum vor der Substratzugabe scheint ein Gemisch von freiem und dehydrogenasegebundenem Coenzym darzustellen. Unmittelbar nach Substratzugabe (d. h. nach 5 sec) ist ein Anstieg an freiem NADH das erste Mal zu beobachten. Während die mit dem Substrat einhergehenden Gesamtveränderungen der Fluoreszenzintensität recht groß sind (50–150% Anstieg), sind die Impulse (als Effekt der Photonen), die mit einer Verschiebung im Emissionsmaximum verbunden sind (Veränderungen von freiem und gebundenem NAD(P)H) zu manchen Zeiten kaum höher als das Rauschen. Die rasche Mikrospektrofluorometrie stellt im Prinzip die direkteste Methode zur Identifizierung von Coenzymen dar, die an verschiedenen Dehydrogenasen in einzelnen lebenden Zellen gebunden sind. Weitere Verbesserungen der Spektralauflösung und der Empfindlichkeit (signal-to-noise ratio) sind notwendig, um die Spektralverschiebungen, die beobachtet werden, besser auswerten zu können.

     

Electrochemical characteristics of Ce0.8Gd0.2O1.9|La0.6Sr0.4CoO3-δ + Ce0.8Gd0.2O1.9 half-cell

The analysis of the medium temperature half-cell Ce_0.8Gd_0.2O_1.9|70 wt% La_0.6Sr_0.4CoO_3- (LSCO) + 30 wt % Ce_0.8Gd_0.2O_1.9 (CGO) has been made by electrochemical impedance, cyclic voltammetry and chronoamperometry. The shape of complex impedance plots depends on temperature and cathodic polarisation of the electrode. Nyquist (Z, Z-) plots were fitted by equivalent circuit taking into account the electrolyte properties (at very high frequencies), charge transfer process at grain boundaries (at high frequencies), and medium and low frequency O₂ reduction process at the cathode surface and inside the porous cathode material. Two different time constants have been obtained for the cathode process, i.e. for electroreduction of oxygen. It was found that the addition of CGO into the cathode material (LSCO) only somewhat decreases the surface catalytic activity but the noticeably higher low-frequency resistance (i.e. mainly diffusion-like mass transfer resistance R_D) values at lower temperatures have been calculated. It was found that the mainly bulk diffusion-limited process at T773 K deviates toward the kinetically mixed process (diffusion + charge transfer) with increasing temperature.     

The N1s ESCA Spectrum of Protonated 1,8-Bis-(Dimethylamino) Naphthalene (“proton sponge”)

The ESCA spectrum of protonated 1,8-bis-(dimethylamino) naphthalene (“proton sponge”) (I) has been recorded in the region of N1s binding energies. The results indicate that IH⁺ possesses an unsymmetrical N? H…?N hydrogen bridge.     

Local polarizabilities in molecules,based on ab initio Hartree-Fock calculations

A method to separate the total molecular polarizability, calculated in the uncoupled Hartree-Fock approximations, into local contributions is proposed. The method is tested for H₂, H₂O, H₂CO and C₆H₆ and the results are discussed. It is found that the ratio of the polarizability contributions for two atoms in a molecule almost only depends on the type of atoms and is almost independant of molecule.