Nonlinear Stability of Time-Periodic Viscous Shocks

In order to understand the nonlinear stability of many types of time-periodic travelling waves on unbounded domains, one must overcome two main difficulties: the presence of embedded neutral eigenvalues and the time-dependence of the associated linear operator. This problem is studied in the context of time-periodic Lax shocks in systems of viscous conservation laws. Using spatial dynamics and a decomposition into separate Floquet eigenmodes, it is shown that the linear evolution for the time-dependent operator can be represented using a contour integral similar to that of the standard time-independent case. By decomposing the resulting Green’s distribution, the leading order behavior associated with the embedded eigenvalues is extracted. Sharp pointwise bounds are then obtained, which are used to prove that time-periodic Lax shocks are linearly and nonlinearly stable under the necessary conditions of spectral stability and minimal multiplicity of the translational eigenvalues. The latter conditions hold, for example, for small-oscillation time-periodic waves that emerge through a supercritical Hopf bifurcation from a family of time-independent Lax shocks of possibly large amplitude.     

Boundary Layer Stability¶in Real Vanishing Viscosity Limit

In the previous paper [20], an Evans function machinery for the study of boundary layer stability was developed. There, the analysis was restricted to strongly parabolic perturbations, that is to an approximation of the form u _t +(F(u)) _x =ν(B(u)u _x ) _x $ (ν≪1) with an “elliptic” matrix B. However, real models, like the Navier–Stokes approximation of the Euler equations for a gas flow, involve incompletely parabolic perturbations: B is not invertible in general. We first adapt the Evans function to this realistic framework, assuming that the boundary is not characteristic, neither for the hyperbolic first order system u _t +(F(u)) _x = 0, nor for the perturbed system. We then apply it to the various kinds of boundary layers for a gas flow. We exhibit some examples of unstable boundary layers for a perfect gas, when the viscosity dominates heat conductivity. Received: 27 November 2000/ Accepted: 16 March 2001     

Forbidden minors to graphs with small feedback sets

Finite obstruction set characterizations for lower ideals in the minor order are guaranteed to exist by the graph minor theorem. In this paper we characterize several families of graphs with small feedback sets, namely k₁-F V S , k₂-F E S and (k₁,k₂)-F V /E S , for small integer parameters k₁ and k₂. Our constructive methods can compute obstruction sets for any minor-closed family of graphs, provided the pathwidth (or treewidth) of the largest obstruction is known.     

Continuous cellulose fiber-reinforced cellulose ester composites III. Commercial matrix and fiber options

Thermoplastic composites were prepared using two continuous regenerated cellulose fiber types, rayon and lyocell, and with several different commercially-available thermoplastic cellulose esters as matrix. Matrix options included cellulose acetate propionate (CAP), and several cellulose acetate butyrates (CAB) with different butyryl content, having different molecular weights and different methods of plasticization (adipates and very low molecular weight cellulose ester fractions). Choice of cellulose ester type was generally found to have little or no effect on mechanical properties. A significant effect, however, was revealed for fiber type. The lyocell-based composites thereby were reflective of the greater stiffness of a fiber produced from anisotropic solution state. Their modulus consistently exceeded 20GPa whereas the rayon fiber-based composites had moduli between 6 and 8GPa. The latter, however, possessed failure strains that were 3 to 4 times greater than their stiffer counterparts.     

N‐Acetyl‐l‐phenyl­alanine

The structure of the title compound, C₁₁H₁₃NO₃, is characterized by a two‐dimensional infinite network of intermolecular N—H?O and O—H?O hydrogen bonds.     

Microstructure in a Cubic to Orthorhombic Transition

Microstructures for a cubic to orthorhombic transition are constructed using a geometrically nonlinear, thermoelastic theory of martensitic transformations. Such microstructures are of interest because they provide low energy paths along which a specimen can transform. The particular microstructures considered are the twinned martensite, austenite–martensite, wedge, triangle, and diamond. More specifically, all possible twins are found along with the corresponding twinning elements and magnitude of the twin shear. Further, two kinds of austenite–martensite microstructures are studied: those with a single variant of martensite and those with twinned martensite. The regions in the space of transformation stretches in which each of these microstructures exist are determined, and the shape strains and habit plane normals are found as well. In addition, special microstructures, the wedge, triangle, and diamond, are constructed with both the austenite-single variant and austenite-twinned martensite microstructures. These special microstructures are of interest because they provide a mechanism through which the transformation may proceed more easily, and they are possible only in alloys with particular transformation stretches. Numerically computed level curves in the space of the stretches are presented on which the special microstructures are possible. These results may be useful in providing guidelines for alloy design.     

Nuclear magnetic resonance studies of acetic acid inhibition of rec Zymomonas mobilis ZM4(pZB5)

The fermentation characteristics and effects of lignocelulosic toxic compounds on recombinant Zymomonas mobilis ZM4(pZB5), which is capable of converting both glucose and xylose to ethanol, and its parental strain, ZM4, were characterized using ¹³C and ³¹P nuclear magnetic resonance (NMR) in vivo. From the ³¹P NMR data, the levels of nucleoside triphosphates (NTP) of ZM(pZB5) using xylose were lower than those of glucose. This can be related to the intrinsically slower assimilation and/or metabolism of xylose compared to glucose and is evidence of a less energized state of ZM4(pZB5) cells during xylose fermentation. Acetic acid was shown to be strongly inhibitory to ZM4(pZB5) on xylose medium, with xylose utilization being completely inhibited at pH 5.0 or lower in the presence of 10.9 g/L of sodium acetate. From the ³¹P NMR results, the addition of sodium acetate caused decreased NTP and sugar phosphates, together with acidification of the cytoplasm. Intracellular deenergization and acidification appear to be the major mechanisms by which acetic acid exerts its toxic effects on this recombinant strain.     

Synthesis of Conjugated Polymer Nanoparticles in Non‐Aqueous Emulsions

Summary: A novel non‐aqueous emulsion system, consisting of cyclohexane as the continuous and acetonitrile as the dispersed phase, is described. Stabilization of the system can be achieved by using polyisoprene‐block‐poly(methyl methacrylate) copolymers as emulsifiers. The suitability of this system for performing water‐sensitive, catalytic, and oxidative polymerizations and polycondensations is demonstrated by the synthesis of poly(3,4‐ethylenedioxythiophene), poly(thiophene‐3‐yl‐acetic acid), and polyacetylene. In all cases spherical nanoparticles with diameters as small as 23 nm can be obtained.

     

Sorption and Swelling of Poly(D,L-lactic acid) and Poly(lactic-co-glycolic acid) in Supercritical CO2

Summary: The equilibrium sorption and swelling behavior in supercritical CO₂ of poly(D,L-lactic acid) and poly(lactic-co-glycolic acid) has been studied at a temperature of 35 °C and at pressures up to 200 bar. Sorption was measured through a gravimetric technique and swelling by visualization. From these data, the behavior of the different polymers can be compared. In terms of partial molar volume of CO₂ in the polymer matrix, all the polymers exhibit a behavior typical of rubbery systems. The experimental results have been modeled using the Sanchez-Lacombe equation of state, which is able to represent the actual behavior of the polymer-CO₂ systems with reasonable accuracy.