Upper Bounds on Coarsening Rates

 We consider two standard models of surface-energy-driven coarsening: a constant-mobility Cahn-Hilliard equation, whose large-time behavior corresponds to Mullins-Sekerka dynamics; and a degenerate-mobility Cahn-Hilliard equation, whose large-time behavior corresponds to motion by surface diffusion. Arguments based on scaling suggest that the typical length scale should behave as in the first case and in the second. We prove a weak, one-sided version of this assertion – showing, roughly speaking, that no solution can coarsen faster than the expected rate. Our result constrains the behavior in a time-averaged sense rather than pointwise in time, and it constrains not the physical length scale but rather the perimeter per unit volume. The argument is simple and robust, combining the basic dissipation relations with an interpolation inequality and an ODE argument. Received: 20 September 2001 / Accepted: 5 February 2002 Published online: 12 August 2002     

Self-injection length in La0.7Ca0.3MnO3-YBa2Cu3O7-δ ferromagnet-superconductor multilayer thin films

We have carried out extensive studies on the self-injection problem in barrierless heterojunctions between La_0.7Ca_0.3MnO₃ (LCMO) and YBa₂Cu₃O_7-δ (YBCO) thin films. The heterojunctions were formed in situ by sequentially growing LCMO and YBCO films on 〈100〉 LaAlO₃ (LAO) substrate using a pulsed laser deposition (PLD) system. YBCO micro-bridges with 64 μm width were patterned both on the LAO (control) and LCMO side of the substrate. Critical current, I _c, was measured at 77 K on both the control side as well as the LCMO side for different YBCO film thickness. It was observed that while the control side showed a J _c of ∼ 2 × 10⁶ A/cm², the LCMO side showed about half the value for the same thickness (1800 ?). The difference in J _c indicates that a certain thickness of YBCO has become ‘effectively’ normal due to self-injection. From the measurement of J _c at two different thicknesses (1800 ? and 1500 ?) of YBCO films both on the LAO as well as the LCMO side, the value of self-injection length (at 77 K) was estimated to be ∼ 900 ?. To the authors’ best knowledge, this is the first time that self-injection length has been quantified. A control experiment carried out with LaNiO₃ deposited by PLD on YBCO did not show any evidence of self-injection.     

Surface energy and microstructure in coherent phase transitions

We study a variational problem involving a nonconvex function of Δu, regularized by a higher order term. The motivation comes from the theory of martensitic phase transformation—specifically, a model for the fine scale structure of twinning near an austenite-twinned-martensite interface. It is widely believed that the fine scale structure can be understood variationally, through the minimization of elastic and surface energy. Our problem represents the essence of this minimization. Similar variational problems have been considered by many authors in the materials science literature. They have always assumed, however, that the twinning should be essentially one-dimensional. This is in general false. Energy minimization can require a complex pattern of twin branching near the austenite interface. There are indications that the states of minimum energy may be asymptotically self-similar. © 1994 John Wiley & Sons., Inc.     

Possibilities of controlling an X-ray beam with a crystal subjected to long-wave ultrasonic vibrations

X-ray diffraction is experimentally studied in the Laue geometry in a germanium crystal carrying a long-wave ultrasonic wave that creates an alternating lattice deformation along the sample surface. Stroboscopic equipment is used to separate different phases and, correspondingly, different profiles of a spatial deformation distribution from the periodic deformation. A uniform deformation is shown to change the angular position of the X-ray beam, and a nonuniform deformation broadens the angular region of reflection and decreases the peak intensity. Ultrasound can be used to compensate for the static deformation at the place where the single-crystal sample and the resonator are glued together. Apart from the fundamental long-wave harmonic, the crystal contains a parasitic deformation with a shorter wavelength. A simple theoretical model is developed, and it rather accurately describes the experimental results.     

Über ein allgemein verwendbares Verfahren der Dampfdichtebestimmung unter beliebigem Drucke

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Das Verhalten des Tribromphenols zu Benzol bei Gegenwart von Aluminiumchlorid

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Variational Bayes With Intractable Likelihood

Variational Bayes (VB) is rapidly becoming a popular tool for Bayesian inference in statistical modeling. However, the existing VB algorithms are restricted to cases where the likelihood is tractable, which precludes their use in many interesting situations such as in state--space models and in approximate Bayesian computation (ABC), where application of VB methods was previously impossible. This article extends the scope of application of VB to cases where the likelihood is intractable, but can be estimated unbiasedly. The proposed VB method therefore makes it possible to carry out Bayesian inference in many statistical applications, including state--space models and ABC. The method is generic in the sense that it can be applied to almost all statistical models without requiring too much model-based derivation, which is a drawback of many existing VB algorithms. We also show how the proposed method can be used to obtain highly accurate VB approximations of marginal posterior distributions. Supplementary material for this article is available online.