The Erpenbeck high frequency instability theorem for ZND detonations

The rigorous study of spectral stability for strong detonations was begun by J.J. Erpenbeck in [Er1]. Working with the Zeldovitch-von Neumann-D\"oring (ZND) model, which assumes a finite reaction rate but ignores effects like viscosity corresponding to second order derivatives, he used a normal mode analysis to define a stability function V(\tau,\eps) whose zeros in $\Re \tau>0$ correspond to multidimensional perturbations of a steady detonation profile that grow exponentially in time. Later in a remarkable paper [Er3] he provided strong evidence, by a combination of formal and rigorous arguments, that for certain classes of steady ZND profiles, unstable zeros of $V$ exist for perturbations of sufficiently large transverse wavenumber \eps, even when the von Neumann shock, regarded as a gas dynamical shock, is uniformly stable in the sense defined (nearly twenty years later) by Majda. In spite of a great deal of later numerical work devoted to computing the zeros of V(\tau,\eps), the paper \cite{Er3} remains the only work we know of that presents a detailed and convincing theoretical argument for detecting them. The analysis in [Er3] points the way toward, but does not constitute, a mathematical proof that such unstable zeros exist. In this paper we identify the mathematical issues left unresolved in [Er3] and provide proofs, together with certain simplifications and extensions, of the main conclusions about stability and instability of detonations contained in that paper. The main mathematical problem, and our principal focus here, is to determine the precise asymptotic behavior as \eps\to \infty of solutions to a linear system of ODEs in $x$, depending on \eps and a complex frequency $\tau$ as parameters, with turning points $x_*$ on the half-line $[0,\infty)$

Lubricant degradation, transport and the effect of extended oil drain intervals on piston assembly tribology

There are ever increasing demands on lubricant manufacturers to meet governmental legislation and customer needs by improving fuel economy, engine durability and exhaust system compatibility as shown by the introduction of GF4 and move towards GF5 specification oils. This has created an ever increasing need to understand how oil degrades in an engine and how this degraded oil affects piston assembly tribology. This review conference paper will give an overview of a collaborative project that has been undertaken to further enhance the understanding of how lubricant degrades in an operating engine, its transport through the engine and effect upon piston assembly tribology

An axially-symmetric Newtonian Boson Star

A new solution to the coupled gravitational and scalar field equations for a condensed boson field is found in Newtonian approximation. The solution is axially symmetric, but not spherically symmetric. For N particles the mass of the object is given by $M = Nm - 0.02298 N^3 G_N^2 m^5$, to be compared with $M = Nm - 0.05426 N^3 G_N^2 m^5$ for the spherically symmetric case.Comment: 4 pages, figures available on reques

Extraction and tribological investigation of top piston ring zone oil from a gasoline engine

With tightening emission regulations, increased expected fuel economy, and longer drain intervals impacting on lubricant formulation, greater understanding of how oil degrades in an automotive engine is becoming ever more important. Equally significant is the effect that this degraded lubricant has on the tribological operation of the engine, particularly its overall internal friction and component wear. In a previous paper, four tests to degrade oil in a single cylinder engine were reported [1]. These tests were set up such that the lubricating oil was degraded in the ring pack before returning to the sump, where it was sampled and chemical and rheological analysis undertaken. This paper reports the extension of this work using the same Hydra engine and describes how oil has additionally been extracted from the rear of the top piston ring during engine operation. This extracted oil has then been subjected to similar analysis as the sump oil samples in the previous tests, along with additional analysis to look at the tribological properties of the oil using tribometers. The results clearly show significant differences in the rheological, tribological, and chemical properties of the fresh oil and used sump oil samples when compared with the top ring zone (TRZ) oil samples, particularly the effect of load on the levels of volatiles present in the TRZ samples and their effect on traction and friction coefficient values during tribological testing

Regulation of polar peptidoglycan biosynthesis by Wag31 phosphorylation in mycobacteria

Background. Sensing and responding to environmental changes is a central aspect of cell division regulation. Mycobacterium tuberculosis contains eleven Ser/Thr kinases, two of which, PknA and PknB, are key signaling molecules that regulate cell division/morphology. One substrate of these kinases is Wag31, and we previously showed that partial depletion of Wag31 caused morphological changes indicative of cell wall defects, and that the phosphorylation state of Wag31 affected cell growth in mycobacteria. In the present study, we further characterized the role of the Wag31 phosphorylation in polar peptidoglycan biosynthesis. Results. We demonstrate that the differential growth among cells expressing different wag31 alleles (wild-type, phosphoablative, or phosphomimetic) is caused by, at least in part, dissimilar nascent peptidoglycan biosynthesis. The phosphorylation state of Wag31 is found to be important for protein-protein interactions between the Wag31 molecules, and thus, for its polar localization. Consistent with these results, cells expressing a phosphomimetic wag31 allele have a higher enzymatic activity in the peptidoglycan biosynthetic pathway. Conclusions. The Wag31 Mtbphosphorylation is a novel molecular mechanism by which Wag31 Mtbregulates peptidoglycan synthesis and thus, optimal growth in mycobacteria. © 2010 Jani et al; licensee BioMed Central Ltd

Critical Point Field Mixing in an Asymmetric Lattice Gas Model

The field mixing that manifests broken particle-hole symmetry is studied for a 2-D asymmetric lattice gas model having tunable field mixing properties. Monte Carlo simulations within the grand canonical ensemble are used to obtain the critical density distribution for different degrees of particle-hole asymmetry. Except in the special case when this asymmetry vanishes, the density distributions exhibit an antisymmetric correction to the limiting scale-invariant form. The presence of this correction reflects the mixing of the critical energy density into the ordering operator. Its functional form is found to be in excellent agreement with that predicted by the mixed-field finite-size-scaling theory of Bruce and Wilding. A computational procedure for measuring the significant field mixing parameter is also described, and its accuracy gauged by comparing the results with exact values obtained analytically.Comment: 10 Pages, LaTeX + 8 figures available from author on request, To appear in Z. Phys.

Molecular dynamics simulations of oxide memristors: thermal effects

We have extended our recent molecular-dynamic simulations of memristors to include the effect of thermal inhomogeneities on mobile ionic species appearing during operation of the device. Simulations show a competition between an attractive short-ranged interaction between oxygen vacancies and an enhanced local temperature in creating/destroying the conducting oxygen channels. Such a competition would strongly affect the performance of the memristive devices.Comment: submit/0169777; 6 pages, 4 figure

New spectra in the HEIDI Higgs models

We study the so-called HEIDI models, which are renormalizable extensions of the standard model with a higher dimensional scalar singlet field. As an additional parameter we consider a higher-dimensional mixing mass parameter. This leads to enriched possibilities compared to a previous study. We find effective spectral densities of the Higgs propagator, consisting of one, two or no particle peaks, together with a continuum. We compare with the LEP-2 data and determine for which range of the model parameters the data can be described. Assuming two peaks to be present we find for the new mass scale \nu\approx 56\pm12 \gev, largely independent of the dimension. In the limiting case of $d\rightarrow 6$ and two peaks we find a higher dimensional coupling constant $\alpha_6=0.70 \pm 0.18$, indicative of strong interactions among the higher dimensional fields. The LHC will not be able to study this Higgs field.Comment: 17 pages, 4 figure