Possible one-dimensional 3He quantum fluid formed in nanopores

Heat capacity measurements have been made down to 5 mK for 3He fluid films adsorbed in one-dimensional (1D) nanometer-scale pores, 28 A in diameter, preplated with 4He of 1.47 atomic layers. At low 3He density, the heat capacity shows a density-dependent, Schottky-like peak near 150 mK asymptoting to the value corresponding to a 2D Boltzmann gas at high temperatures. The peak behavior is attributed to the crossover from a 2D gas to a 1D state at low temperatures. The degenerate state of the 1D 3He fluid is indicated by a predominantly linear temperature dependence below about 30 mK.     

Kato's inequality when Δu is a measure

We extend the classical version of Kato's inequality in order to allow functions u∈L¹_loc such that Δu is a Radon measure. This inequality has been recently applied by Brezis, Marcus, and Ponce to study the existence of solutions of the nonlinear equation ?Δu+g(u)=μ, where μ is a measure and $\text{g}\text{:}\text{R}\text{→}\text{R}$ is a nondecreasing continuous function. To cite this article: H. Brezis, A.C. Ponce, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Brane-World Models Emerging from Collisions of Plane Waves in 5D

We consider brane-world models embedded in a five-dimensional bulk spacetime with a large extra dimension and a cosmological constant. The cosmology in 5D possesses wave-like character in the sense that the metric coefficients in the bulk are assumed to have the form of plane waves propagating in the fifth dimension. We model the brane as the plane of collision of waves propagating in opposite directions along the extra dimension. This plane is a jump discontinuity which presents the usual Z ₂ symmetry of brane models. The model reproduces the generalized Friedmann equation for the evolution on the brane, regardless of the specific details in 5D. Model solutions with spacelike extra coordinate show the usual big-bang behavior, while those with timelike extra dimension present a big bounce. This bounce is an genuine effect of a timelike extra dimension. We argue that, based on our current knowledge, models having a large timelike extra dimension cannot be dismissed as mathematical curiosities in non-physical solutions. The size of the extra dimension is small today, but it is increasing if the universe is expanding with acceleration. Also, the expansion rate of the fifth dimension can be expressed in a simple way through the four-dimensional deceleration and Hubble parameters as – q H. These predictions could have important observational implications, notably for the time variation of rest mass, electric charge and the gravitational constant. They hold for the three (k = 0, + 1, – 1) models with arbitrary cosmological constant, and are independent of the signature of the extra dimension.     

Grating-enhanced through-wafer optical microprobe for microelectromechanical system high-resolution optical position feedback

We present modeling and experimental results from the use of a 1310-nm-wavelength through-wafer optical microprobe in conjunction with a microstructure grating to monitor the motion of a lateral comb resonator stage. The optical signal that results from shuttle interaction with the microprobe beam exhibits a peak-to-valley dynamic range that corresponds to 2-microm microstructure displacement, facilitating submicrometer positional resolution on digitization. This signal was used to achieve microstructure positional feedback and effective microsystem model parameter extraction, which are essential for structure control and model-based fault detection.     

Solution crystallisation via a submerged liquid-liquid phase boundary: oiling out

In many situations the process of crystallisation from solution is known to occur via metastable crystalline states (polymorphs or solvates). Here we present what we believe to be a novel example of small molecule crystallisation in which the initial separation of a solute rich liquid phase precedes the crystallisation event. We believe this occurs because a submerged liquid-liquid phase boundary is accessible within the metastable zone of the crystal nucleation process.     

On the denseness of the invertible group in Banach algebras

We examine the condition that a complex Banach algebra has dense invertible group. We show that, for commutative algebras, this property is preserved by integral extensions. We also investigate the connections with an old problem in the theory of uniform algebras.

     

Study of the action of flavonoids on xanthine-oxidase by molecular topology

A study was performed on xanthine-oxidase inhibition by 22 flavonoids, including flavones, flavonols, flavanones, and chalcones, using UV spectroscopy for experimental data and molecular topology to establish the structure-activity relationship (SAR) model. The flavonoids were classified into four groups according to their activity on xanthine-oxidase (inactive, low, significant, or high), and linear discriminant analysis was used to classify each compound within a group. The results led to a very good model, which was able to classify correctly as xanthine oxidase inhibitors, along with a test set of molecules including a variety of different compounds such as allopurinol, caffeic acid, esculetin, and alloxantin.