Spinodal phase separation of unstable solid-state binary n-alkane mixtures

Two mixtures of unequal chain length n-alkanes in which one component is deuterated have been investigated by infrared spectroscopy as they demixed. The measurements followed the band shapes of the scissors vibrations as a function of time. The band envelopes are analyzed as composites of a number of reference mixtures of known concentration. The unequal-chain mixtures separate into phases that slowly change their composition toward pure alkane phases. The method of analysis, which reveals local concentrations, should be generally applicable to polymethylene systems.     

Trochoidal Solutions to the Incompressible Two-Dimensional Euler Equations

Within the Lagrangian framework we present an approach yielding some explicit solutions to the incompressible two-dimensional Euler equations, generalizing the celebrated Gerstner flow. The solutions so obtained, for which explicit formulas of each particle trajectory are provided, represent either flows in domains with a rigid boundary or free-surface flows for a fluid of infinite depth. For some of these solutions the trajectories are epitrochoids or hypotrochoids. Possibilities for obtaining further flows of this type are indicated.     

Magnetic face-to-face interaction and electrocommunication in chromium sandwich compounds

The reaction of [{(C5Me5)CrCl2}2] with [2.2](1,4)cyclophane gave [(C5Me5)Cr{[2.2](1,4)cyclophane}] (1) and [(C5Me5)Cr{[2.2](1,4)cyclophane}Cr(C5Me5)] (2), depending on the reaction conditions. X-ray structure analysis showed 2 to be a ministack which in turn is stacked in the lattice. The chromium atoms are 6.035 A apart, and the distortion of the benzene rings to boat-shaped moieties is less pronounced than in parent [2.2](1,4)cyclophane. The NMR and EPR spectra were consistent with a S=1/2 ground state for 1 and with two interacting S=1/2 centers in 2. Spin density was found in the ligand pi systems, where its sign was negative when the pi system was adjacent to chromium, while on the nonbonded benzene moiety of 1 it was positive. Cyclic voltammograms showed reductions to 1- and 2(2-), as well as oxidations to 1+, 2+, and 2(2+) which were quasireversible, whereas oxidations to 1(2+) and 2(3+) were irreversible. Interaction between the metal ions was revealed by a 260 mV separation of the redox waves belonging to 2+, and 2(2+). Both cations were isolated as [B(C6H5)4]- salts, which in solution decomposed to [2.2](1,4)cyclophane and [(C5Me5)Cr{(eta6-C6H5)B(C6H5)3}] (3). The 1H and 13C NMR spectra of 3 were in accordance with an S=1 ground state. Solid-state magnetic measurements of the dimetallic compounds showed antiferromagnetic interaction with J=-122 cm-1 for 2, J=-31 cm-1 for 2+ (ground state S=1/2), and J=-23.5 cm-1 for 2(2+) (with H=-JS1S2). The decrease of J in the series 2, 2+, and 2(2+) was traced to the number of unpaired electrons and, for the mixed-valent cation 2+, to additional double exchange.     

Simultaneous determination of lidocaine and its metabolites in plasma and myocardium

No validated method exists for measuring lidocaine and its metabolites in myocardial tissue. We modified a previously described high-performance liquid chromatographic assay and applied it to plasma and to homogenized myocardial samples obtained from dogs that had received lidocaine by a double-infusion technique. Recovery of lidocaine, monoethylglycylxylidide and glycylxylidide after homogenization and extraction is reported. Assay variability, sensitivity and linearity over a wide range of sample sizes are also described. The results obtained with high-performance liquid chromatographic analysis are compared to quantitation of 14C-labeled lidocaine plus metabolites measured by an oxidation-scintillation technique. Myocardium to plasma partition coefficients for lidocaine, monoethylglycylxylidide and glycylxylidide were 2.16, 4.27, and 2.91, respectively.     

Rotating frames in special relativity. II. Generalized theory

The transformation theory for rotating frames presented in a previous paper (Strauss, 1974) is generalized by replacing the usual conditionr=R for Rr=Rg( _R ) so thatr is now defined for all values ofR,0R. This generalization does not affect the kinematic transformation {,T}{^(r),{^(r)}}, and the result group structure required by the theoretical constraints previously established, provided the old parameter r (=R) is now identified throughout with eitherr orR; for physical reasons it must be identified withR. The functiong, which cannot be fixed by theoretical constraints, determines the degree of geometrical anisotropy in the rotating planez=const. More specifically, sinceg enters the expression for the ratioC/D (circumference/diameter) its choice corresponds to the choice of a congruence definition for lengths in radial and tangential directions. While on this (purely geometrical) levelg remains undetermined, it can be uniquely determined experimentally on the kinematic level, e.g., by observing in the motion of a free particle. Thus the supremacy of kinematics over geometry is explicated by a further instance. At the same time, special relativity theory (SRT) is shown to belong to the class of theories with theoretically unsolvable problems.     

Linear stability and instability of relativistic Vlasov‐Maxwell systems

We consider the linear stability problem for a symmetric equilibrium of the relativistic Vlasov‐Maxwell (RVM) system. For an equilibrium whose distribution function depends monotonically on the particle energy, we obtain a sharp linear stability criterion. The growing mode is proved to be purely growing, and we get a sharp estimate of the maximal growth rate. In this paper we specifically treat the periodic 1½D case and the 3D whole‐space case with cylindrical symmetry. We explicitly illustrate, using the linear stability criterion in the 1½D case, several stable and unstable examples. © 2006 Wiley Periodicals, Inc.     

Nonlinear stability and instability of relativistic Vlasov‐Maxwell systems

We prove the nonlinear stability or instability of certain periodic equilibria of the 1½D relativistic Vlasov‐Maxwell system. In particular, for a purely magnetic equilibrium with vanishing electric field, we prove its nonlinear stability under a sharp criterion by extending the usual Casimir‐energy method in several new ways. For a general electromagnetic equilibrium we prove that nonlinear instability follows from linear instability. The nonlinear instability is macroscopic, involving only the L¹‐norms of the electromagnetic fields. © 2006 Wiley Periodicals, Inc.     

Stability properties of steady water waves with vorticity

We present two stability analyses for exact periodic traveling water waves with vorticity. The first approach leads in particular to linear stability properties of water waves for which the vorticity decreases with depth. The second approach leads to a formal stability property for long water waves that have small vorticity and amplitude although we do not use a small‐amplitude or long‐wave approximation. © 2006 Wiley Periodicals, Inc.