Saturation Effects and the Colored Pump Noise in a Dye Laser

We investigate the statistical properties of two single-mode dye-laser models-the colored-loss-noise model and the colored-gain-noise model. Analytic expressions of the probability,the mean and the variance of the steady-state laser intensity are obtained through the unified expansion theory [Phys. Rev. A43 (1991) 700]. By comparison we find that when the cavity decay rate for the electric field is large and the pump parameter a₀ is small, the differences of the results of the two laser models are small. Otherwise, the differences are large. And the correlation time of the noise has very obvious influence on the results of the two models.     

Multiple and maximal periodicity in linear elastostatics

Properties of elastic states in which the strain is periodic in an arbitrary number of directions are investigated. It is shown that, even though the corresponding displacements might not, in a non-trivial sense, be periodic, they do satisfy a semi-periodicity condition. Other general results, including a version of Betti's reciprocal theorem and a theorem of work and energy are derived and discussed. Problems involving periodicity in a maximal number of directions are examined in greater detail. Additional restrictions on the displacement corresponding to maximally periodic strains are derived and the uniqueness and periodicity of solutions to maximally periodic and slightly maximally periodic boundary value problems are discussed.     

Cobalt Boryl Complexes: Enabling and Exploiting Migratory Insertion in Base‐Metal‐Mediated Borylation

Cobalt boryl complexes, which have only been sporadically reported, can be accessed systematically with remarkable (but controllable) variation in the nature of the M? B bond. Complexes incorporating a very strong trans σ‐donor display unparalleled inertness, reflected in retention of the M? B bond even in the presence of extremely strong acid. By contrast, the use of the strong π‐acceptor CO in the trans position, results in significant Co? B elongation and to labilization of the boryl ligand via unprecedented CO migratory insertion. Such chemistry provides a pathway for the generation of coordinative unsaturation, thereby enabling ligand substitution and/or substrate assimilation. Alkene functionalization by boryl transfer, a well‐known reaction for noble metals such as Rh or Pt, can thus be effected by an 18‐electron base‐metal complex.     

Raman spectroscopy of benzenesulfonic and 4-toluenesulfonic acids dissolved in dimethylsulfoxide

Solutions of benzenesulfonic acid (BSA) and 4-toluenesulfonic acid monohydrate (PTSA) in dimethylsulfoxide (DMSO) were studied by FT-Raman spectroscopy in the concentration range 1.0-3.5 mol dm(-3) (BSA) and 1.0-4.8 mol dm(-3) (PTSA). Spectra in the region of the Raman acid complex band (C-S + C-C + SO3) stretches, at 1124 cm(-1) were analysed by band-fitting procedures in order to ascertain the degree of acid dissociation. In BSA solutions, this parameter changes from 0.78 at 1.02 M to 0.47 at 3.5M, despite the strong character of the acid. Interaction of DMSO with undissociated BSA produces a new band in the solvent nu(C-S) Raman spectral region near 671 cm(-1), displaced >15.0 cm(-1), and assigned to DMSO molecules H-bonded to BSA. In PTSA solutions, hydrogen bonds are formed with the oxonium ion (H3O+) dissociated from the acid. In this case, the displacement observed is only >10.0 cm(-1), indicating a weaker interaction. From the concentration of H-bonded DMSO, the solute/solvent coordination number and its inverse, the mean number of H-bonds participating in bonding with each solvent molecule can be calculated. This coordination number changes in BSA solutions in bimodal way, passing through a maximum and reaching a limit of 2 in the most concentrated solution. This number agrees with that found in the solid solvate BSA.2DMSO. In PTSA solutions, the general trend is similar, but low coordination numbers are obtained, in agreement with the low acidity of the oxonium ion. The bimodal behaviour observed in both acids is explained by the self-associated structure of the solvent.     

Aero-/hydro-elastic stability of flexible panels: Prediction and control using localised spring support

We study the effect of adding localised stiffness, via a spring support, on the stability of flexible panels subjected to axial uniform incompressible flow. Applications are considered that range from the hydro-elasticity of hull panels of high-speed ships to the aero-elasticity of glass panels in the curtain walls of high-rise buildings in very strong winds. A two-dimensional linear analysis is conducted using a hybrid of theoretical and computational methods that calculates the system eigen-states but can also be used to capture the transient behaviour that precedes these. We show that localised stiffening is a very effective means to increase the divergence-onset flow speed in both hydro- and aero-elastic applications. It is most effective when located at the mid-chord of the panel and there exists an optimum value of added stiffness beyond which further increases to the divergence-onset flow speed do not occur. For aero-elastic applications, localised stiffening can be used to replace the more destructive flutter instability that follows divergence at higher flow speeds by an extended range of divergence. The difference in eigen-solution morphology between aero- and hydro-elastic applications is highlighted, showing that for the former coalescence of two non-oscillatory divergence modes is the mechanism for flutter onset. This variation in solution morphology is mapped out in terms of a non-dimensional mass ratio. Finally, we present a short discussion of the applicability of the stabilisation strategy in a full three-dimensional system.     

Monte Carlo simulation algorithm for B‐DNA

Understanding the structure–function relationship of biomolecules containing DNA has motivated experiments aimed at determining molecular structure using methods such as small‐angle X‐ray and neutron scattering (SAXS and SANS). SAXS and SANS are useful for determining macromolecular shape in solution, a process which benefits by using atomistic models that reproduce the scattering data. The variety of algorithms available for creating and modifying model DNA structures lack the ability to rapidly modify all‐atom models to generate structure ensembles. This article describes a Monte Carlo algorithm for simulating DNA, not with the goal of predicting an equilibrium structure, but rather to generate an ensemble of plausible structures which can be filtered using experimental results to identify a sub‐ensemble of conformations that reproduce the solution scattering of DNA macromolecules. The algorithm generates an ensemble of atomic structures through an iterative cycle in which B‐DNA is represented using a wormlike bead–rod model, new configurations are generated by sampling bend and twist moves, then atomic detail is recovered by back mapping from the final coarse‐grained configuration. Using this algorithm on commodity computing hardware, one can rapidly generate an ensemble of atomic level models, each model representing a physically realistic configuration that could be further studied using molecular dynamics. © 2016 Wiley Periodicals, Inc.     

Rhodium‐Catalyzed Transnitrilation of Aryl Boronic Acids with Dimethylmalononitrile

An efficient transnitrilation of aryl boronic acids with dimethylmalononitrile (DMMN) is described. This rhodium‐catalyzed electrophilic cyanation presents a novel approach to prepare aryl nitriles by using a carbon‐bound cyanating reagent which undergoes cross‐coupling with the aryl boronic acid. The reaction expands the degree of functional‐group compatibility exhibited by the transnitrilation of aryl Grignard and aryllithium reagents. A variety of aryl boronic acid derivatives and dialkylmalononitriles were amenable to the transnitrilation.