Utilization of inverse approach in the design of materials over nano‐ to macro‐scale

In the light of recent developments in computer technology, a promising and efficient way to design a material with a desired property would be to solve the inverse problem: use a physical property to predict structure. Here, we discuss the basic idea and mathematical foundation of the inverse approach, and proposed strategies for its utilization in the design of materials over nano‐ to macro‐scales. At the nano‐scale, analyzed strategies include scanning of a high‐dimensional space of chemical compounds for those compounds that have a targeted property, and identification of correlations in large databases of materials. However, unlike utilization of inverse approach at nano‐scale where full structural information ‐ atoms and their positions‐ is linked to targeted properties, at the meso‐ and macro‐scale, only partial structural information, manifested via structural motifs or representative volume elements, is available. We discuss the role of partial structural information in the inverse approach to the design of materials at those scales. Risks and limitations of the inverse approach are analyzed and dependence of the approach on factors such as structure parametrization, approximations in theoretical models, and feedback from structural characterization, is addressed.

     

Impact of the Casimir-Polder potential and Johnson noise on Bose-Einstein condensate stability near surfaces

We investigate the stability of magnetically trapped atomic Bose-Einstein condensates and thermal clouds near the transition temperature at small distances 0.5 microm< or =d< or =10 microm from a microfabricated silicon chip. For a 2 microm thick copper film, the trap lifetime is limited by Johnson noise induced currents and falls below 1 s at a distance of 4 microm. A dielectric surface does not adversely affect the sample until the attractive Casimir-Polder potential significantly reduces the trap depth.     

Observation of collective-emission-induced cooling of atoms in an optical cavity

We report the observation of collective-emission-induced, velocity-dependent light forces. One-third of a falling sample containing 3 x 10(6) cesium atoms illuminated by a horizontal standing wave is stopped by cooperatively emitting light into a vertically oriented, confocal resonator. We observe decelerations up to 1500 m/s(2) and cooling to temperatures as low as 7 microK, well below the free-space Doppler limit. The measured forces substantially exceed those predicted for a single two-level atom.     

Superspin-glass like behavior of nanoparticle La<Subscript>0.7</Subscript>Ca<Subscript>0.3</Subscript>MnO<Subscript>3</Subscript> obtained by mechanochemical milling

Single-phase perovskite compound La_0.7Ca_0.3MnO₃ was synthesised by a high-energy ball milling in a single step processing. Structure and morphology characterizations revealed nanoparticle nature of this mixed valent manganite with the average particle diameter of 9 nm. Comprehensive set of magnetic measurements showed that the system can be described as an ensemble of interacting magnetic nanoparticles where each particle possesses high magnetic moment, i.e., superspin. Furthermore, magnetic behavior showed contributions from both superspin-glass (SSG) and superparamagnetic (SP) states, and the prevailing properties depended on the experimental conditions. It was established that SSG state dominated in low magnetic fields up to 500 Oe while in higher applied fields suppression of collective behavior occurred and individual characteristics of nanoparticles prevailed. It was also concluded that the applied method of synthesis produced system with high magnetic anisotropy as well as with the large nanoparticle shell whose thickness amounts 30% of a particle diameter.     

A semiclassical model of the interior of Uranus

Abstract

Using the mass and radius of Uranus, as determined by Voyager, and a particular semiclassical theory of dense matter, a model of its interior has been developed. Details of the model, the underlying theory and possible sources of discrepancies with recent work on this topic are briefly presented.     

On Extended Polar Decomposition

In this study, we considered the extended polar decomposition using a more general approach than the one provided by Boulanger and Hayes [Int. J. Non-Linear Mech. 36 (2001) 399–420]. We showed that the procedure of the decomposition could be simplified by considering its rotation tensor. Our method is illustrated by examples.     

A three-stage, VSVO, Hermite-Birkhoff-Taylor, ODE solver

The new variable-step, variable-order, ODE solver, HBT(p) of order p, presented in this paper, combines a three-stage Runge-Kutta method of order 3 with a Taylor series method of order p-2 to solve initial value problems , where y:R→R^d and f:R×R^d→R^d. The order conditions satisfied by HBT(p) are formulated and they lead to Vandermonde-type linear algebraic systems whose solutions are the coefficients in the formulae for HBT(p). A detailed formulation of variable-step HBT(p) in both fixed-order and variable-order modes is presented. The new method and the Taylor series method have similar regions of absolute stability. To obtain high-accuracy results at high order, this method has been implemented in multiple precision.     

Inherent limits on optimization and discovery in physical systems

Topological mapping of a large physical system on a graph, and its decomposition using universal measures are proposed. We find inherent limits to the potential for optimization of a given system and its approximate representations by motifs, and the ability to reconstruct the full system given approximate representations. The approximate representation of the system most suited for optimization may be different from that which most accurately describes the full system.