Critical behavior of light in mode-locked lasers

Light is shown to exhibit critical and tricritical behavior in passively mode-locked lasers with externally injected pulses. It is a first and unique example of critical phenomena in a one-dimensional many-body light-mode system. The phase diagrams consist of regimes with continuous wave, driven parapulses, spontaneous pulses via mode condensation, and heterogeneous pulses, separated by phase transition lines that terminate with critical or tricritical points. Enhanced non-Gaussian fluctuations and collective dynamics are present at the critical and tricritical points, showing a mode system analog of the critical opalescence phenomenon. The critical exponents are calculated and shown to comply with the mean field theory, which is rigorous in the light system.     

Collisional quenching of resonance states of rare gases

We report an experimental study of Xe(³P₁) → Xe(³P₂) electronic quenching by Ar in Xe/Ar mixtures optically excited by the 1470 Å line of Xe. The quenching process was monitored by the observation of the Xe^*₂ second emission continuum at low Xe pressures.     

Latex Fractionation by Sedimentation and Colloidal Crystallization: The Case of Poly(styrene-co-acrylamide)

Poly(styrene-co-acrylamide) (PS-AAM) latex was prepared, fractionated by sedimentation under gravity, and characterized by PCS, infrared spectra, secondary and backscattered electron imaging in the scanning electron microscope, and electron spectroscopy imaging in an analytical transmission electron microscope. Three latex fractions were obtained. The lower fraction was opalescent and its particles were the more uniform, concerning size, chemical composition, and topochemical features. This lower fraction was still further fractionated by zonal centrifugation in a density gradient, yielding two fractions with similar macrocrystal-forming abilities but different sizes and chemical compositions. These results confirm those previously obtained for the PS-HEMA latex. Copyright 2000 Academic Press.     

Binomial moment equations for stochastic reaction systems

A highly efficient formulation of moment equations for stochastic reaction networks is introduced. It is based on a set of binomial moments that capture the combinatorics of the reaction processes. The resulting set of equations can be easily truncated to include moments up to any desired order. The number of equations is dramatically reduced compared to the master equation. This formulation enables the simulation of complex reaction networks, involving a large number of reactive species much beyond the feasibility limit of any existing method. It provides an equation-based paradigm to the analysis of stochastic networks, complementing the commonly used Monte Carlo simulations.     

Heterocyclic fused tropylium ions VII. On the synthesis of 9H-dithieno[2,1 -b:4,5-c′]tropylium fluoborate and 4H-dithieno[1,2-b:4,5-c′]tropylium fluoborate

9H-Dithieno[2,1 -b:4,5-c′]tropylium ion (III) and 4ii-dithieno[1,2-b:4,5-c′]tropylium ion (IV) have been synthesized by ring-closure of 1-(4-carboxy-3-thienyl)-2-(3′-thienyl)ethane (IX) and 1-(4-carboxy-3-thienyl)-2-(2′-thienyl)ethane (XVI), respectively, followed by bromination-debrom-ination to 9H-cyclohepta[2,1-b:4,5-c′] dithiophen-9-one (XI) and 4H-cyclohepta[1,2-b:4,5-c′]-dithiophen-4-one (XVIII), and finally by reduction and hydride transfer. The tropylium ions III and IV were less stable than the [b,b′]-fused isomers previously studied.     

Study of dynamic end effects in an elastic strip with sliding boundary conditions

The dynamic response of an elastic, semi-infinite strip with sliding surfaces, subjected to various forms of end excitations, was solved analytically employing the property of bi-orthogonality of wave modes. An explicit relation between the amplitudes of evanescent waves and the form of the excitation was obtained. Quantitative measure for dynamic end effects was suggested, termed Saint-Venant ratio (SVR). It was shown that two qualities of that ratio are useful for monitoring the health of structural joints (SHM): being that ratio not affected by the intensity of the end excitation and its high sensitivity to small variations in the form of the excitation. The axial behavior of the strip subjected to several forms of end excitations was further used to demonstrate the validity of a previously suggested dynamic version of Saint-Venant’s principle.     

Representations of Hardy Algebras: Absolute Continuity,Intertwiners, and Superharmonic Operators

Suppose T₊(E){\mathcal{T}_{+}(E)} is the tensor algebra of a W*-correspondence E and H ^∞(E) is the associated Hardy algebra. We investigate the problem of extending completely contractive representations of T₊(E){\mathcal{T}_{+}(E)} on a Hilbert space to ultra-weakly continuous completely contractive representations of H ^∞(E) on the same Hilbert space. Our work extends the classical Sz.-Nagy–Foiaş functional calculus and more recent work by Davidson, Li and Pitts on the representation theory of Popescu’s noncommutative disc algebra.     

Addition of trichloromethyl radicals to tetrachloroethylene

The gamma-radiation-induced free-radical chain reactions in liquid CCl₄? C₂Cl₄? c? C₆H₁₂ mixtures were studied in the temperature range of 363–448°K. The main products in this system are chloroform, hexachloropropene and chlorocyclohexane. These products are formed via reactions (1)–(5): with G values (molec/100 eV) of the order of magnitude of 10² and 10³ at the lowest and highest temperatures, respectively. Values of k₂/k₁ were determined from the product distribution. In turn, these values gave the following Arrhenius expression for k₂/k₁ (θ = 2.303RT, in kcal/mol): From this result and the previously determined Arrhenius parameters of reaction (1), k₂ is found to be given by .     

Radiation-induced dechlorination of carbon tetrachloride in cyclohexane and n-hexane mixtures. III. The kinetics of liquid-phase reactions of trichloromethyl radicals

The kinetics of gamma-radiation-induced free-radical chain reactions in solutions of carbon tetrachloride in mixtures of varying composition of cyclohexane and n-hexane was investigated in the temperature range of 296°–413°K. Trichloromethyl radicals were produced by the reaction of radiolytically generated alkyl radicals with the solute. The kinetics of the following reactions were studied: The following rate expression was obtained: The error limits are the standard deviation from the least mean-square Arrhenius plots. The present results, combined with previously measured activation parameters for hydrogen-atom abstraction from c-C₆H₁₂ and n-C₆H₁₄ by CCl₃ radicals relative to CCl₃ combination, afford experimental evidence that the decay of trichloromethyl species in alkane solutions is a diffusion-limited process. The thesis that activation energies of reactions (4) and (5) in the liquid phase are equal to their respective values in the gas phase is confirmed.