Raman and resonance-Raman spectra of CsI/I−3

Raman and resonance-Raman spectra of the I^?₃ ion isolated within CsI crystals have been studied using 647 nm and 488 nm exciting radiation. Sample temperatures between 300 and 20 K have been used. Eleven overtones of the symmetric stretching mode (nν₁) have been observed in the resonance-Raman spectrum excited by the 488 nm Ar⁺ laser line. Bands centred at 153, 170, 264 and 304 cm^?1 have been assigned as ν₃, 2ν₂, ν₁+ν₃ and 2ν₃(Σ⁺) respectively. The remaining structure between the nν₁ lines has been assigned as due to combinations of these lines with the lattice vibrations of the CsI crystal.     

Spectral Properties of the Cauchy Operator and Its Product with Bergman's Projection on a Bounded Domain

In this paper exact asymptotic formulae are found for singularvalues of the Cauchy operator and the logarithmic potentialtype operator (on a bounded domain), as well as their productswith Bergman's projection. It is shown that these spectral characteristicsdetect geometric properties of a domain (area and the lengthof the boundary). The hypothesis "can we hear the shape of adrum", from a paper by J.M. Anderson, D. Khavinson, and V. Lomonosov[‘Spectral properties of some integral operators arisingin potential theory’, Quart. J. Math. Oxford (2) 43 (1992)387-407], is correct in the above sense. 1991 Mathematics SubjectClassification: 47B10.     

Far downstream analysis for the Blasius boundary-layer stability problem

In this paper, we examine the large Reynolds number (Re) asymptoticstructure of the wave number in the Orr–Sommerfeld regionfor the Blasius boundary layer on a semi-infinite flat plategiven by Goldstein (1983, J. Fluid Mech., 127, 59–81).We show that the inclusion of the term which contains the leading-ordernon-parallel effects, at O(Re^{– 1/2}), leads to a non-uniformexpansion. By considering the far downstream form of each termin the asymptotic expansion, we derive a length scale at whichthe non-uniformity appears, and compare this position with theposition seen in plots of the wave number.     

Weak Nonlinear Long Waves in Channel Flow with Internal Dissipation

This article concerns the evolution of long waves ( O (ε^−1/2) wavelength) of small [ O (ε)] amplitude in channel flow with internal dissipation. We use multiple scale expansions to derive a generalized Kuramoto–Sivashinsky (GKS) equation that governs the dominant asymptotic solution in the limit of small disturbances and marginal linear instability. We compare this solution with numerical integrations of the full quasilinear system, and show that the error is consistent with an asymptotic solution to ε^3/2 over a time interval of order ε^−3/2.     

Design,Manufacture, and Quasi-Static Testing of Metallic Negative Stiffness Structures within a Polymer Matrix

A composite material system comprised of a monostable negative stiffness (NS) structure within a polymer matrix was designed, fabricated, and experimentally evaluated. The monostable negative stiffness (NS) structure was designed using a combination of analytical and numerical models and manufactured in stainless steel. The NS structure was arranged in parallel with different polymer matrices to experimentally evaluate the effects of the matrix properties on the overall stiffness and energy dissipation of the composite NS-matrix system when loaded in uniaxial compression. A strong influence of the matrix properties on the stiffness and energy absorption capacity of the composite system was observed. Unlike conventional composites for which there is a natural tradeoff between stiffness and energy absorption capacity, the composite NS-matrix system enhanced stiffness while simultaneously improving energy absorption relative to a neat matrix, but only when the stiffness of the matrix was carefully matched to the stiffness of the NS structure.     

A universal separatrix map for weak interactions of solitary waves in generalized nonlinear Schrödinger equations

It is known that weak interactions of two solitary waves in generalized nonlinear Schrödinger (NLS) equations exhibit fractal dependence on initial conditions, and the dynamics of these interactions is governed by a universal two-degree-of-freedom ODE system [Y. Zhu J. Yang, Universal fractal structures in the weak interaction of solitary waves in generalized nonlinear Schrödinger equations, Phys. Rev. E 75 (2007) 036605]. In this paper, this ODE system is analyzed comprehensively. Using asymptotic methods along separatrix orbits, a simple second-order map is derived. This map does not have any free parameters after variable rescalings, and thus is universal for all weak interactions of solitary waves in generalized NLS equations. Comparison between this map’s predictions and direct simulations of the ODE system shows that the map can capture the fractal-scattering phenomenon of the ODE system very well both qualitatively and quantitatively.     

Critical Layers m Parallel Flows

Finite amplitude neutrally stable two-dimensional disturbances in parallel flows are determined for large Reynolds numbers when both nonlinearity and viscosity are important in the critical layer. The phase shift across the critical layer depends on the local vertical Reynolds number in the critical layer, and it varies monotonically between the value zero of the nonlinear theory and — π of the viscous theory. An O(?^½) distortion of both the mean and fundamental harmonic is shown to be necessary. The eigenvalue problem is solved for long waves yielding neutral modes which link the two previous theories. In particular certain difficulties of the nonlinear theory are resolved.     

Photoinduced cutaneous inflammatory response by psoralens.

Our studies describe the inflammatory response in rabbit skin induced by topical application of 8-methoxypsoralen (8-MOP) and UVA-visible irradiation (320-700 nm). Increase in vascular permeability (iVP) and accumulation of polymorphonuclear leucocytes (aPMN) at the test sites were quantitated using 125I-albumin and 51Cr-labelled PMNs respectively. Erythema was graded visually. 8-MOP cream was applied topically and irradiated. The erythemal response, aPMN and iVP at the test sites were quantitated at 6, 24, 48 and 72 h post-irradiation. The iVP and aPMN were maximal at 24 h; the erythemal response was the same at 24-48 h. The responses were dependent on 8-MOP concentration and irradiation dose. Topical application of 200 micrograms 8-MOP cream followed by irradiation for 2 h (9.4 J cm-2) produced 3-7 times iVP, 2-4 times aPMN and intense erythema at the test sites after 24 h. Neither aPMN nor iVP was detected before 6 h and erythemal response was not observable up to 16 h after irradiation. The aPMN and iVP gradually subsided in 72 h, although the erythemal response was still present. The repeated exposure of 8-MOP-treated sites for three consecutive days 24 h apart did not produce appreciable iVP or aPMN at 72 h or 24 h after the last exposure; however, erythema persisted. The 8-MOP-treated sites previously exposed for three consecutive days on reapplication of 8-MOP cream plus irradiation showed significantly less response compared with non-pretreated sites. Our results suggest that the erythemal response is not directly related to either iVP or aPMN.     

Wrap-around partitioning for block bidiagonal linear systems

A stable vector algorithm for the solution of block diagonallinear systems is obtained by a permutation of the unknownscalled wrap-around partitioning combined with standard QR factorization.Wrap-around partitioning uses blocking and selects the unknownsin the blocks in turns. After a suitable orthogonal eliminationstep one ends up with a reduced system which is again blockbidiagonal and so wrap-around partitioning can be applied again.Using a simple model for vectorization overhead it is shownthat small block sizes give best performance. The minimal blocksize 2, which corresponds to cyclic reduction, is suboptimaldue to memory bank conflicts.     

Connection across a Separatrix with Dissipation

Dissipative perturbations of strongly nonlinear oscillators that correspond to slowly varying double-well potentials are considered. The method of averaging, which describes the solution as nearly periodic, fails as the trajectory approaches the unperturbed separatrix, a homoclinic orbit of the saddle point, significantly before it is captured in either well. Nevertheless, perturbed initial conditions corresponding to the boundary of the basin of attraction for each well, which are the perturbed stable manifolds of the saddle point, are accurately determined using only the method of averaging modified by Melnikov energy ideas near the separatrix. To determine the amplitude and phase of the captured oscillations after crossing the separatrix, a transition region is constructed consisting of a large sequence of nearly solitary pulses along the separatrix. The amplitude and phases of the slowly varying nonlinear oscillations away from the separatrix, both before and after capture, are matched to this transition region. In this way, analytic connection formulas across the separatrix are obtained and are shown to depend on the perturbed initial conditions.