Heat-conduction theory for composite materials

The problem of the macroscopic conduction of heat in a composite medium is considered. The medium consists of inclusions of arbitrary geometry embedded in a matrix. Starting with an analysis of the micro-conduction in a suitably defined representative volume, a fourth order equation governing the macro-conduction is deduced together with appropriate boundary conditions. The theory closely resembles the mechanical theory of non-simple materials of grade 2 developed by Toupin [2]. In particular, the well known characteristic material length encountered in stress-gradient theories is evaluated in terms of constituent material properties. It is further shown, as a basis of the theory, that anatural ratio exists between the dimensions of a local representative volume and those of a unit-cell given by the ratio of the classical Voigt and Reuss bounds on the effective diffusivities. In consequence, application of the theory hinges on the evaluation of certain material constants from given information on the inclusion arrangement in a representative volume of specific dimensions. Differences in the behaviour of media with different inclusion distributions depend entirely on the magnitude of such constants.

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Zusammenfassung Aus der Variationsgleichung für die Mikroleitung wird eine Beziehung für Makroleitung mit mikrostrukturellen Einflüssen hergeleitet. Bei diesem Herleitungsprozess entsteht ein natürliches Verhältnis zwischen den Dimensionen eines representativen Volumens und jenen der Einheitszelle. Das Verhältnis drückt sich durch die effektiven Voigt und Reuss Diffusionskoeffizienten aus. Daraus ergeben sich eine natürliche Materiallänge und eine Zeitskala, welche sich explizit in Funktion der Materialgrössen darstellen lassen. Man kann schliesslich bemerken, dass wegen der mathematischen Aehnlichkeiten die vorliegende Theorie auf alle physikalischen Prozesse mit der Diffusionsgleichung anwendbar ist.

     

Hermite-Fejér type interpolation processes

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The Complete Differential Game of Active Target Defense

In the Target–Attacker–Defender differential game, an Attacker missile strives to capture a Target aircraft. The Target tries to escape the Attacker and is aided by a Defender missile which aims at intercepting the Attacker, before the latter manages to close in on the Target. The conflict between these intelligent adversaries is naturally modeled as a zero-sum differential game. The Game of Degree when the Attacker is able to win the Target–Attacker–Defender differential game has not been fully solved, and it is addressed in this paper. Previous attempts at designing the players’ strategies have not been proven to be optimal in the differential game sense. In this paper, the optimal strategies of the Game of Degree in the Attacker’s winning region of the state space are synthesized. Also, the value function is obtained, and it is shown that it is continuously differentiable, and it is the solution of the Hamilton–Jacobi–Isaacs equation. The obtained state feedback strategies are compared to recent results addressing this differential game. It is shown that the correct solution of the Target–Attacker–Defender differential game that provides a semipermeable Barrier surface is synthesized and verified in this paper.

     

Dynamics of cooperativity in chemical sensing among cell-surface receptors

Cooperative interactions among sensory receptors provide a general mechanism to increase the sensitivity of signal transduction. In particular, bacterial chemotaxis receptors interact cooperatively to produce an ultrasensitive response to chemoeffector concentrations. However, cooperativity between receptors in large macromolecular complexes is necessarily based on local interactions and consequently is fundamentally connected to slowing of receptor-conformational dynamics, which increases intrinsic noise. Therefore, it is not clear whether or under what conditions cooperativity actually increases the precision of the concentration measurement. We explicitly calculate the signal-to-noise ratio (SNR) for sensing a concentration change using a simple, Ising-type model of receptor-receptor interactions, generalized via scaling arguments, and find that the optimal SNR is always achieved by independent receptors.     

Indistinguishable photon pairs from independent true chaotic sources

Indistinguishability of events in quantum mechanics is manifested by interference between their probability amplitudes. We report a unique kind of interference occurring between indistinguishable events of photon-pair emission, where each photon of the pair is emitted from a distinct true chaotic light source and has a different energy. The indistinguishability results in an interference which is observed as an ultrafast modulation of the second-order coherence function, measured on a femtosecond time scale by two-photon absorption in a semiconductor photomultiplier tube.     

Homochiral oligopeptides generated by induced "mirror symmetry breaking" lattice-controlled polymerizations in racemic crystals of phenylalanine N-carboxyanhydride

The formation of diastereoisomeric libraries of oligopeptides through the heterogeneous polymerization of racemic crystals of phenylalanine N-carboxyanhydride (PheNCA) is reported. The diastereoisomeric compositions of the oligopeptides formed on polymerization of (R,S) crystals incorporating the deuterium-tagged S enantiomer were determined by MALDI-TOF mass spectrometry. The racemic mixtures of the oligopeptides longer than pentamers are represented primarily by diastereoisomers of homochiral sequence and with peptides containing only one heterochiral repeating unit. A mechanism comprising the following three sequential steps to account for this unusual observation is proposed: 1) formation of dimers and trimers at a partially damaged liquid/solid interface, 2) chain propagation that takes place within the bulk of the crystal through a lattice-controlled "zipper-like" mechanism between homochiral molecules arranged in a head-to-tail motif to yield crystalline antiparallel beta-sheets of alternating oligopeptide chains of homochiral sequence of opposite handedness, and 3) enantiomeric cross-inhibition that results in chain termination. Induced desymmetrization of the racemic mixtures of the formed peptides was achieved by the polymerization of the mixed quasi-racemic crystals of (R)-PheNCA, ((S)-PheNCA), and (S)-ThieNCA (3-(2-thienyl)-alanine N-carboxyanhydride) of various compositions. These experiments resulted in the formation of nonracemic libraries of oligopeptides composed of homochiral chains of (R)-Phe and copolymers of randomly distributed (S)-Phe and (S)-Thie sequences. From these findings, we propose a stochastic model for the generation of libraries of nonracemic mixtures of oligopeptides from the polymerization of host (R,S)-PheNCA with racemic mixtures of other guest NCA amino acids dissolved in limited quantities in the crystal.     

Homochiral oligopeptides by chiral amplification within two-dimensional crystalline self-assemblies at the air-water interface; relevance to biomolecular handedness

A possible role that might have been played by ordered clusters at interfaces for the generation of homochiral oligopeptides under prebiotic conditions has been probed by a catalyzed polymerization of amphiphilic activated alpha-amino acids, in racemic and chiral non-racemic forms, which had self-assembled into two-dimensional (2D) ordered crystallites at the air-aqueous solution interface. As model systems we studied N(epsilon)-stearoyl-lysine thioethyl ester (C(18)-TE-Lys), gamma-stearyl-glutamic thioethyl ester (C(18)-TE-Glu), N(alpha)-carboxyanhydride of gamma-stearyl-glutamic acid (C(18)-Glu NCA) and gamma-stearyl-glutamic thioacid (C(18)-thio-Glu). According to in-situ grazing incidence X-ray diffraction measurements on the water surface, (R,S)-C(18)-TE-Lys, (R,S)-C(18)-TE-Glu, and (R,S)-C(18)-Glu-NCA amphiphiles self-assembled into ordered racemic 2D crystallites. Oligopeptides 2-12 units long were obtained at the air-aqueous solution interface after injection of appropriate catalysts into the water subphase. The experimental relative abundance of oligopeptides with homochiral sequence generated from (R,S)-C(18)-TE-Lys and (R,S)-C(18)-TE-Glu, as determined by mass spectrometry on enantioselectively deuterium-labeled samples, was found to be significantly larger than that obtained from (R,S) C(18)-thio-Glu which polymerizes randomly. An efficient chiral amplification was obtained in the polymerization of non-racemic mixtures of C(18)-Glu-NCA since the monomer molecules in the racemic 2D crystallites are oriented such that the reaction occurs between heterochiral molecules related by glide symmetry to yield heterochiral oligopeptides whereas the enantiomer in excess, in the enantiomorphous crystallites, yield oligopeptides of a single handedness.     

Enrichment of high-throughput screening data with increasing levels of noise using support vector machines, recursive partitioning, and laplacian-modified naive bayesian classifiers

High-throughput screening (HTS) plays a pivotal role in lead discovery for the pharmaceutical industry. In tandem, cheminformatics approaches are employed to increase the probability of the identification of novel biologically active compounds by mining the HTS data. HTS data is notoriously noisy, and therefore, the selection of the optimal data mining method is important for the success of such an analysis. Here, we describe a retrospective analysis of four HTS data sets using three mining approaches: Laplacian-modified naive Bayes, recursive partitioning, and support vector machine (SVM) classifiers with increasing stochastic noise in the form of false positives and false negatives. All three of the data mining methods at hand tolerated increasing levels of false positives even when the ratio of misclassified compounds to true active compounds was 5:1 in the training set. False negatives in the ratio of 1:1 were tolerated as well. SVM outperformed the other two methods in capturing active compounds and scaffolds in the top 1%. A Murcko scaffold analysis could explain the differences in enrichments among the four data sets. This study demonstrates that data mining methods can add a true value to the screen even when the data is contaminated with a high level of stochastic noise.     

Low-concentration series in general dimension

We discuss recent work on the development and analysis of low-concentration series. For many models, the recent breakthrough in the extremely efficient no- free-end method of series generation facilitates the derivation of 15th-order series for multiple moments in general dimension. The 15th-order series have been obtained for lattice animals, percolation, and the Edwards-Anderson Ising spin glass. In the latter cases multiple moments have been found. From complete graph tables through to 13th order, general dimension 13th-order series have been derived for the resistive susceptibility, the moments of the logarithms of the distribution of currents in resistor networks, and the average transmission coefficient in the quantum percolation problem, 11th-order series have been found for several other systems, including the crossover from animals to percolation, the full resistance distribution, nonlinear resistive susceptibility and current distribution in dilute resistor networks, diffusion on percolation clusters, the dilute Ising model, dilute antiferromagnet in a field, and random field Ising model and self-avoiding walks on percolation clusters. Series for the dilute spin-1/2 quantum Heisenberg ferromagnet are in the process of development. Analysis of these series gives estimates for critical thresholds, amplitude ratios, and critical exponents for all dimensions. Where comparisons are possible, our series results are in good agreement with both-expansion results near the upper critical dimension and with exact results (when available) in low dimensions, and are competitive with other numerical approaches in intermediate realistic dimensions.     

Standing-wave nonlinear optics in an integrated semiconductor microcavity

We present a concept of standing-wave optical frequency conversion in dispersive microcavities theoretically and experimentally, allowing efficient ultracompact nonlinear photonics. We developed a time-dependent model, incorporating the dispersion into the structure of the spatial cavity modes, where the conversion efficiency is enhanced by the optimization of a nonlinear cavity mode overlap. We designed and fabricated integrated double-resonance semiconductor microcavities for standing-wave second-harmonic generation. The measured efficiency exhibits a significant maximum near the cavity resonance owing to the intracavity power enhancement and the dispersion-induced wavelength detuning effect on the mode overlap, in good agreement with our theoretical predictions.