Self-avoiding walks on strongly diluted lattices: Chain-growth simulations vs. exact enumeration

We discuss and compare two different methods that can be used to investigate self-avoiding walks on lattices with random site dilution. One is the so-called pruned-enriched Rosenbluth method (PERM), a chain-growth Monte Carlo algorithm, the other is a recently developed exact enumeration technique. While the latter is highly efficient for systems close to the critical concentration, it cannot be used for less dilute systems. PERM is more versatile but appears to have difficulties coping with strong confinement.     

Critical amplitude ratios of the Baxter–Wu model

A Monte Carlo simulation study of the critical and off-critical behavior of the Baxter–Wu model, which belongs to the universality class of the 4-state Potts model, was performed. We estimate the critical temperature window using known analytical results for the specific heat and magnetization. This helps us to extract reliable values of universal combinations of critical amplitudes with reasonable accuracy. Comparisons with approximate analytical predictions and other numerical results are discussed.     

Shape anisotropy of polymers in disordered environment

We study the influence of structural obstacles in a disordered environment on the size and shape characteristics of long flexible polymer macromolecules. We use the model of self-avoiding random walks on diluted regular lattices at the percolation threshold in space dimensions d=2 and d=3. Applying the pruned-enriched Rosenbluth method, we numerically estimate rotationally invariant universal quantities such as the averaged asphericity and prolateness of polymer chain configurations. Our results quantitatively reveal the extent of anisotropy of macromolecules due to the presence of structural defects.     

Comparison of noncontact and fiber-based fluorescence-mediated tomography

We present a comparative experimental phantom study of fiber-based and noncontact fluorescence tomography with respect to quantitation and localization of reconstructed fluorescent inclusions in turbid media such as tissue. Noncontact acquisition is usually considered potentially superior to fiber-based techniques because of the availability of a large number of detector readouts through a CCD. Our results indicate, however, that noncontact acquisition itself might improve the quality of reconstructions significantly, even without increasing the number of detectors and thus keeping the inverse problem moderately complex.     

Infima of superharmonic functions

Let Ω be a Greenian domain in ℝ ^d , d≥2, or—more generally—let Ω be a connected -Brelot space satisfying axiom D, and let u be a numerical function on Ω, , which is locally bounded from below. A short proof yields the following result: The function u is the infimum of its superharmonic majorants if and only if each set {x:u(x)>t}, t∈ℝ, differs from an analytic set only by a polar set and , whenever V is a relatively compact open set in Ω and x∈V.     

Simplified method for the determination of Ru, Pd, Re, Os, Ir and Pt in chromitites and other geological materials by isotope dilution ICP-MS and acid digestion

A method for the determination of low Ru, Pd, Re, Os, Ir and Pt abundances in geological reference materials by isotope dilution inductively coupled plasma mass spectrometry (ICP-MS) after acid digestion in a high pressure asher (HPA-S) is presented. The digestion technique is similar to that using Carius tubes but easier to handle and reaches higher temperatures. Osmium can be determined as OsO4 with ICP-MS directly after digestion through a sparging technique. The remaining elements are preconcentrated by means of anion column chromatography. The resin is digested directly without elution leading to high yields but this causes problems if Zr is present at higher levels in the silicate rich materials. The analytical results for international platinum group element (PGE) reference materials, chromitite CHR-Bkg, basalt TDB-1 and gabbro WGB-1, are presented and compared with literature data, demonstrating the validity of the described method. Although higher in concentration, PGEs determined for reference material WGB-1 were worse than for TDB-1 indicating a more inhomogeneous distribution of the platinum group mineral phases. The low PGE abundance chromitite standard, CHR-Bkg, is likely to be homogeneous for Ru, Re, Os and Ir and is recommended as a reference material for the study of chromitites. Detection limits (3s x total procedure blank) range from 0.012 ng (Re and Os) to 0.77 ng (Pt), which could be further improved by applying higher quality acids.