Bimodal Nanoparticle Size Distributions Produced by Laser Ablation of Microparticles in Aerosols

Silver nanoparticles were produced by laser ablation of a continuously flowing aerosol of microparticles in nitrogen at varying laser fluences. Transmission electron micrographs were analyzed to determine the effect of laser fluence on the nanoparticle size distribution. These distributions exhibited bimodality with a large number of particles in a mode at small sizes (3–6-nm) and a second, less populated mode at larger sizes (11–16-nm). Both modes shifted to larger sizes with increasing laser fluence, with the small size mode shifting by 35% and the larger size mode by 25% over a fluence range of 0.3–4.2-J/cm². Size histograms for each mode were found to be well represented by log-normal distributions. The distribution of mass displayed a striking shift from the large to the small size mode with increasing laser fluence. These results are discussed in terms of a model of nanoparticle formation from two distinct laser–solid interactions. Initially, laser vaporization of material from the surface leads to condensation of nanoparticles in the ambient gas. Material evaporation occurs until the plasma breakdown threshold of the microparticles is reached, generating a shock wave that propagates through the remaining material. Rapid condensation of the vapor in the low-pressure region occurs behind the traveling shock wave. Measurement of particle size distributions versus gas pressure in the ablation region, as well as, versus microparticle feedstock size confirmed the assignment of the larger size mode to surface-vaporization and the smaller size mode to shock-formed nanoparticles.     

Mappings of finite distortion: the degree of regularity

This paper investigates the self-improving integrability properties of the so-called mappings of finite distortion. Let K(x)1 be a measurable function defined on a domain ΩRⁿ, n2, and such that exp(βK(x))L_loc¹(Ω), β>0. We show that there exist two universal constants c₁(n),c₂(n) with the following property: Let f be a mapping in W_loc^1,1(Ω,Rⁿ) with |Df(x)|ⁿK(x)J(x,f) for a.e. xΩ and such that the Jacobian determinant J(x,f) is locally in L¹ log^−c₁(n)βL. Then automatically J(x,f) is locally in L¹ log^c₂(n)βL(Ω). This result constitutes the appropriate analog for the self-improving regularity of quasiregular mappings and clarifies many other interesting properties of mappings of finite distortion. Namely, we obtain novel results on the size of removable singularities for bounded mappings of finite distortion, and on the area distortion under this class of mappings.     

Testing Extreme Value Conditions

A test statistic is developed that checks the validity of the extreme value conditions without specifiying the shape parameter of the limiting extreme value distribution.     

The Rank of a Direct Power of a Small-Cancellation Group

We construct an example of a finitely generated group G such that rank((G )ⁿ)=2 for all n1. For each n, we construct a finitely presented group G _n such that rank((G _n )ⁿ)=2. We conjecture that if G is a word-hyperbolic group then rank(G ⁿ ) as $ n. For each m we give an example of a residually finite group K _m such that K _m has exactly two relators, but K _m has no proper subgroups of index $ m. We construct a finitely generated group D such that there is an epimorphism DD×D.     

Statistical shape priors for level set segmentation

Starting in the early 1990's level set methods have become a popular mathematical framework for variational image segmentation. In many applications of segmentation, however, cost functionals which merely take into account the intensity information of the input image will not give rise to the desired segmentation results. To cope with missing or misleading image information, researchers have proposed to impose statistical shape priors into the segmentation process. Such shape priors favor the evolving embedding function to remain similar to embedding functions associated with a collection of training shapes. As a consequence, one can obtain shape-consistent segmentation despite large amounts of noise, background clutter and partial occlusion of the object of interest. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Carleson Measures for the Bloch Space

In this paper we study the positive Borel measures μ on the unit disc in for which the Bloch space is continuously included in , 0 < p < ∞. We call such measures p-Bloch-Carleson measures. We give two conditions on a measure μ in terms of certain logarithmic integrals one of which is a necessary condition and the other a sufficient condition for μ being a p-Bloch-Carleson measure. We also give a complete characterization of the p-Bloch-Carleson measures within certain special classes of measures. It is also shown that, for p > 1, the p-Bloch-Carleson measures are exactly those for which the Toeplitz operator , defined by , maps continuously into the Bergman space A ¹, . Furthermore, we prove that if p > 1, α >-1 and ω is a weight which satisfies the Bekollé-Bonami -condition, then the measure defined by is a p-Bloch-Carleson-measure. We also consider the Banach space of those functions f which are analytic in and satisfy , as . The Bloch space is contained in . We describe the p-Carleson measures for and study weighted composition operators and a class of integration operators acting in this space. We determine which of these operators map continuously to the weighted Bergman space and show that they are automatically compact. This research is partially supported by several grants from “the Ministerio de Educación y Ciencia, Spain” (MTM2005-07347, MTM2007-60854, MTM2006-26627-E, MTM2007-30904-E and Ingenio Mathematica (i-MATH) No. CSD2006-00032); from “La Junta de Andalucía” (FQM210 and P06-FQM01504); from “the Academy of Finland” (210245) and from the European Networking Programme “HCAA” of the European Science Foundation.     

Eigenvalues Estimate for the Neumann Problem of a Bounded Domain

In this note, we investigate upper bounds of the Neumann eigenvalue problem for the Laplacian of a domain Ω in a given complete (not compact a priori) Riemannian manifold (M,g). For this, we use test functions for the Rayleigh quotient subordinated to a family of open sets constructed in a general metric way, interesting for itself. As applications, we prove that if the Ricci curvature of (M,g) is bounded below Ric  ^g ≥−(n−1)a ², a≥0, then there exist constants A _n >0,B _n >0 only depending on the dimension, such that

Atomic decompositions for tensor products and polynomial spaces

We study the existence of atomic decompositions for tensor products of Banach spaces and spaces of homogeneous polynomials. If a Banach space X admits an atomic decomposition of a certain kind, we show that the symmetrized tensor product of the elements of the atomic decomposition provides an atomic decomposition for the symmetric tensor product , for any symmetric tensor norm μ. In addition, the reciprocal statement is investigated and analogous consequences for the full tensor product are obtained. Finally we apply the previous results to establish the existence of monomial atomic decompositions for certain ideals of polynomials on X.     

Micromixing models for turbulent flows

In transported probability density function and filtered density function methods, micromixing models are required to close the molecular mixing term. The accuracy and computational efficiency of improved versions of the parameterized scalar profile (PSP) model are assessed and compared with commonly used mixing models such as Curl, modified Curl, interaction by exchange with the mean and Euclidean minimum spanning tree. Different generalizations of the PSP mixing model for spatially inhomogeneous flow configurations are presented. The selected test cases focus on molecular mixing and avoid interference with other models. Simulation results for a three-stream problem, involving two inert scalars, and a multi-scalar test case with mean-scalar-gradients are presented.