Scattering of Laser Light from Mixed Micelles

Dynamic and static scattering of light was employed to investigate mixed micelles of two homologous anionic surfactants-sodium octyl sulfate and sodium hexadecyl sulfate, above the phase boundary temperature and critical micelle concentrations (cmc). The results indicate that the mixed micelles change from prolate to sphcrical as the molar ratio SOS/SHS increases from 1 to 8. Below 1 or above 8, the formation of micelles is due to one surfactant dissolving the other.     

Diode-pumped 671 nm laser frequency doubled by CPM LBO

A design of diode-pumped high-efficiency Nd:YVO₄/LBO red laser is reported. Using critical phase-matching (CPM) LBO, 671 nm red laser was obtained from 1342 nm light by intracavity frequency doubling. With an incident pump laser of 800 mW, using type-I and type-II CPM LBO, 97 and 52 mWTEM₀₀ mode red laser outputs were obtained, with optical-to-optical conversion efficiencies of up to 12.1% and 6.5%, respectively.     

Critical Point Theorems and Applications to Differential Equations

This paper contains a generalization of the well-known Palais-Smale and Cerami compactness conditions. The compactness condition introduced is used to prove some general existence theorems for critical points. Some applications are given to differential equations.     

Effect of core-shell micelle formation on the redox properties of phenothiazine-labeled poly(ethyl glycidy ether)-block-poly(ethylene oxide)

Redox properties of phenothiazine-labeled poly(ethyl glycidy ether)-block-poly(ethylene oxide) (PT-EGE_n-b-EO_m) are reversibly changed by core-shell micelle formation. In the temperature range higher than the critical micellization temperature (cmt), the anodic potential of PT group positively shifts and concomitantly its anodic current decrease, or levels off compared to those of the reference polymer PT-EO_m without the thermo-responsive EGE_n segment. The former alteration is caused by incorporation of hydrophobic PT groups into a core of the micelle and the latter by the decrease in the diffusion coefficient of PT groups due to formation of the core-shell micelles. The cmt value and the temperature-dependent alteration in the redox properties strongly depend on the polymer structure, especially the length of thermo-responsive EGE_n segment. The electrochemically determined hydrodynamic radii of the polymer aggregates seem to be overestimated, compared to the values reported for the aggregates of other thermo-responsive polymers with similar molecular weights, implying the presence of electrochemically inactive PT groups in the copolymers having longer thermo-responsive segments.     

Sizes of Critical Graphs with Small Maximum Degrees

In this paper, we give new lower bounds for the size of Δ-critical graphs with Δ=8,9 which improve the partial results of Luo [6] and Y. Zhao [12].     

Network externalities in a dynamic monopoly

We reconsider the role of network externalities in a dynamic spatial monopoly where the firm must invest in order to accumulate capacity, while consumers may have either linear or quadratic preferences. We (1) characterise saddle point equilibria, (2) prove that the extent of market coverage is increasing in the network effect and (3) unlike the existing static literature on the same problem, the monopolist may not make introductory price offers. Then, we briefly deal with the socially optimal solution, showing that, in general, a planner would serve more consumers than a profit-seeking monopolist.      

Computations of critical groups and applications to asymptotically linear wave equation and beam equation

In this paper, by using the Morse index theory for strongly indefinite functionals developed in [Nonlinear Anal. TMA, in press], we compute precisely the critical groups at the origin and at infinity, respectively. The abstract theorems are used to study the existence (multiplicity) of nontrivial periodical solutions for asymptotically wave equation and beam equation with resonance both at infinity and at zero.     

Nonlinear Schrödinger equations with symmetric multi-polar potentials

This paper deals with a class of nonlinear elliptic equations involving a critical power-nonlinearity as well as a potential featuring multiple inverse square singularities. When the poles form a symmetric structure, it is natural we wonder how the symmetry affects such mutual interaction. The present paper means to study this aspect from the point of view of the existence of solutions inheriting the same symmetry properties as the set of singularities. Mathematics Subject Classification (2000) 35J60, 35J20, 35B33     

Crossover Critical Behavior in the Three-Dimensional Ising Model

The character of critical behavior in physical systems depends on the range of interactions. In the limit of infinite range of the interactions, systems will exhibit mean-field critical behavior, i.e., critical behavior not affected by fluctuations of the order parameter. If the interaction range is finite, the critical behavior asymptotically close to the critical point is determined by fluctuations and the actual critical behavior depends on the particular universality class. A variety of systems, including fluids and anisotropic ferromagnets, belongs to the three-dimensional Ising universality class. Recent numerical studies of Ising models with different interaction ranges have revealed a spectacular crossover between the asymptotic fluctuation-induced critical behavior and mean-field-type critical behavior. In this work, we compare these numerical results with a crossover Landau model based on renormalization-group matching. For this purpose we consider an application of the crossover Landau model to the three-dimensional Ising model without fitting to any adjustable parameters. The crossover behavior of the critical susceptibility and of the order parameter is analyzed over a broad range (ten orders) of the scaled distance to the critical temperature. The dependence of the coupling constant on the interaction range, governing the crossover critical behavior, is discussed.     

A note on the critical points of equilibrium paths in imperfect structures

In a recent work (Int. J. Solids Struct. 37 (2000) 1561) by one of the authors, an extended system for calculating critical points of equilibrium paths in imperfect structures was presented. However, the extremum nature of these points was not analyzed explicitly in that paper. In this note, we will fill in the gap and establish a sufficient condition for determining the buckling strength of imperfect structures.