Nucleation of colloids and macromolecules: does the nucleation pathway matter?

A recent description of diffusion-limited nucleation based on fluctuating hydrodynamics that extends classical nucleation theory predicts a very non-classical two-step scenario whereby nucleation is most likely to occur in spatially-extended, low-amplitude density fluctuations. In this paper, it is shown how the formalism can be used to determine the maximum probability of observing \emph{any} proposed nucleation pathway, thus allowing one to address the question as to their relative likelihood, including of the newly proposed pathway compared to classical scenarios. Calculations are presented for the nucleation of high-concentration bubbles in a low-concentration solution of globular proteins and it is found that the relative probabilities (new theory compared to classical result) for reaching a critical nucleus containing $N_c$ molecules scales as $e^{-N_c/3}$ thus indicating that for all but the smallest nuclei, the classical scenario is extremely unlikely.Comment: 7 pages, 5 figure

Single-shot optical conductivity measurement of dense aluminum plasmas

The optical conductivity of a dense femtosecond laser-heated aluminum plasma heated to 0.1-1.5 eV was measured using frequency-domain interferometry with chirped pulses, permitting simultaneous observation of optical probe reflectivity and probe pulse phase shift. Coupled with published models of bound-electron contributions to the conductivity, these two independent experimental data yielded a direct measurement of both real and imaginary components of the plasma conductivity.DOE National Nuclear Security Administration DE-FC52-03NA00156Physic

Splines and Wavelets on Geophysically Relevant Manifolds

Analysis on the unit sphere $\mathbb{S}^{2}$ found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics. In the last two decades, the importance of these and other applications triggered the development of various tools such as splines and wavelet bases suitable for the unit spheres $\mathbb{S}^{2}$, $\>\>\mathbb{S}^{3}$ and the rotation group $SO(3)$. Present paper is a summary of some of results of the author and his collaborators on generalized (average) variational splines and localized frames (wavelets) on compact Riemannian manifolds. The results are illustrated by applications to Radon-type transforms on $\mathbb{S}^{d}$ and $SO(3)$.Comment: The final publication is available at http://www.springerlink.co

Unitary Dual of GL_n at archimedean places and global Jacquet-Langlands correspondence

In [7], results about the global Jacquet-Langlands correspondence, (weak and strong) multiplicity-one theorems and the classification of automorphic representations for inner forms of the general linear group over a number field are established, under the condition that the local inner forms are split at archimedean places. In this paper, we extend the main local results of [7] to archimedean places so that this assumption can be removed. Along the way, we collect several results about the unitary dual of general linear groups over \bbR, \bbC or \bbH of independent interest

Spherically symmetric space-time with the regular de Sitter center

The requirements are formulated which lead to the existence of the class of globally regular solutions to the minimally coupled GR equations which are asymptotically de Sitter at the center. The brief review of the resulting geometry is presented. The source term, invariant under radial boots, is classified as spherically symmetric vacuum with variable density and pressure, associated with an r-dependent cosmological term, whose asymptotic in the origin, dictated by the weak energy condition, is the Einstein cosmological term. For this class of metrics the ADM mass is related to both de Sitter vacuum trapped in the origin and to breaking of space-time symmetry. In the case of the flat asymptotic, space-time symmetry changes smoothly from the de Sitter group at the center to the Lorentz group at infinity. Dependently on mass, de Sitter-Schwarzschild geometry describes a vacuum nonsingular black hole, or G-lump - a vacuum selfgravitating particlelike structure without horizons. In the case of de Sitter asymptotic at infinity, geometry is asymptotically de Sitter at both origin and infinity and describes, dependently on parameters and choice of coordinates, a vacuum nonsingular cosmological black hole, selfgravitating particlelike structure at the de Sitter background and regular cosmological models with smoothly evolving vacuum energy density.Comment: Latex, 10 figures, extended version of the plenary talk at V Friedmann Intern. Conf. on Gravitation and Cosmology, Brazil 2002, to appear in Int.J.Mod.Phys.

The Shapovalov determinant for the Poisson superalgebras

Among simple Z-graded Lie superalgebras of polynomial growth, there are several which have no Cartan matrix but, nevertheless, have a quadratic even Casimir element C_{2}: these are the Lie superalgebra k^L(1|6) of vector fields on the (1|6)-dimensional supercircle preserving the contact form, and the series: the finite dimensional Lie superalgebra sh(0|2k) of special Hamiltonian fields in 2k odd indeterminates, and the Kac--Moody version of sh(0|2k). Using C_{2} we compute N. Shapovalov determinant for k^L(1|6) and sh(0|2k), and for the Poisson superalgebras po(0|2k) associated with sh(0|2k). A. Shapovalov described irreducible finite dimensional representations of po(0|n) and sh(0|n); we generalize his result for Verma modules: give criteria for irreducibility of the Verma modules over po(0|2k) and sh(0|2k)

Asymptotic Learning Curve and Renormalizable Condition in Statistical Learning Theory

Bayes statistics and statistical physics have the common mathematical structure, where the log likelihood function corresponds to the random Hamiltonian. Recently, it was discovered that the asymptotic learning curves in Bayes estimation are subject to a universal law, even if the log likelihood function can not be approximated by any quadratic form. However, it is left unknown what mathematical property ensures such a universal law. In this paper, we define a renormalizable condition of the statistical estimation problem, and show that, under such a condition, the asymptotic learning curves are ensured to be subject to the universal law, even if the true distribution is unrealizable and singular for a statistical model. Also we study a nonrenormalizable case, in which the learning curves have the different asymptotic behaviors from the universal law

Laser-Induced Spall Of Aluminum And Aluminum Alloys At High Strain Rates

We conducted laser-induced spall experiments aimed at studying how a material's microstructure affects the tensile fracture characteristics at high strain rates (> 10(6) s(-1)). We used the Z-Beamlet Laser at Sandia National Laboratory to drive shocks and to measure the spall strength of aluminum targets with various microstructures. The targets were recrystallized, high-purity aluminum (Al-HP RX), recrystallized aluminum + 3 wt.% magnesium (Al-3Mg RX), and cold-worked aluminum + 3 wt.% magnesium (Al-3Mg CW). The Al-3Mg RX and Al-3Mg CW are used to explore the roles that solid-solution alloying and cold-work strengthening play in the spall process. Using a line-VISAR (Velocity Interferometer System for Any Reflector) and analysis of recovered samples, we were able to measure spall strength and determine failure morphology in these targets. We find that the spall strength is highest for Al-HP RX. Analysis reveals that material grain size plays a vital role in the fracture morphology and spall strength results.Mechanical Engineerin