A numerical study of a spectral problem in solid-fluid type structures

This article presents a numerical study of a spectral problem that models the vibrations of a solid–fluid structure. It is a quadratic eigenvalue problem involving incompressible Stokes equations. In its numerical approximation we use Lagrange finite elements. To approximate the velocity, degree 2 polynomials on triangles are used, and for the pressure, degree 1 polynomials. The numerical results obtained confirm the theory, as they show in particular that the known theoretical bound for the maximum number of nonreal eigenvalues admitted by such a system is optimal. The results also take account of the dependence of vibration frequencies with respect to determined physical parameters, which have a bearing on the model. © 1995 John Wiley & Sons, Inc.     

Sorption of Iron(II) on Ferromanganese Nodules

The dynamic capacity, specific surface area, grindability, and wearability of filter materials based on pyrolusite were determined. The dynamic capacity of ferromanganese nodules was compared with the capacity of imported filter materials.__________Translated from Zhurnal Prikladnoi Khimii, Vol. 78, No. 4, 2005, pp. 599-605.Original Russian Text Copyright © 2005 by Chirkst, Cheremisina, Ivanov, Chistyakov.     

Polarization-sensitive non-3ω third-harmonic generation by femtosecond Cr: Forsterite laser pulses in birefringent microchannel waveguides of photonic-crystal fibers

Femtosecond Cr: forsterite laser pulses coupled into small-diameter birefringent channel waveguides off the central core of a photonic-crystal fiber are shown to generate multiple narrowband spectral peaks within the 380–460 nm wavelength region through multimode-phase-matched third-harmonic generation. Some of these peaks are shifted by tens of terahertz from the tripled frequency of the pump field, dictated by standard energy conservation for third-harmonic generation in monochromatic fields. The spectral contents of the third-harmonic signal generated in such a regime are controlled by changing polarization and the intensity of the input pump field.     

The Gamow vectors and the Schwinger effect

We introduce a ‘proper time’ formalism to study the instability of the vacuum in a uniform external electric field due to particle production. This formalism allows us to reduce a quantum field-theoretic problem to a quantum mechanical one in a higher dimension. The instability results from the inverted oscillator structure which appears in the Hamiltonian. We show that the ‘proper time’ unitary evolution splits into two semigroups. The semigroup associated with decaying Gamov vectors is related to the Feynman boundary conditions for the Green functions and the semigroup associated with growing Gamov vectors is related to the Dyson boundary conditions.     

Spectroelectrochemical identity of Prussian blue films in various electrolytes: comparison of time-derivative voltabsorptometric responses with conventional cyclic voltammetry

Using Prussian blue (PB) electrodeposited on gold-covered foil as a model system, we have demonstrated the usefulness of the time-derivative measurements of absorbance versus potential (linear potential-scan voltabsorptometry) for spectroelectrochemical characterization of thin electrochromic films. The time-derivative signals were monitored for PB at 680 and 420 nm in potassium, sodium and lithium electrolytes. Information obtained from cyclic voltabsorptometry is equivalent or complementary to that from conventional cyclic voltammetry. In the case of PB films investigated in lithium electrolyte, the voltabsorptometric time-derivative peaks are better defined than the respective voltammetric peaks. The combination of voltabsorptometry with voltammetry enables molar absorptivity and/or film loading to be determined. Also, concentration changes of differently colored mixed-valence redox centers can be monitored as a function of applied potential. Received: 16 January 1997 / Accepted: 11 March 1997     

Controlled supercontinuum generation for optimal pulse compression: a time-warp analysis of nonlinear propagation of ultra-broad-band pulses

We describe the virtues of the pump–probe approach for controlled supercontinuum generation in nonlinear media, using the example of pulse compression by cross-phase modulation in dielectrics. Optimization of a strong (pump) pulse and a weak (probe) pulse at the input into the medium opens the route to effective control of the supercontinuum phases at the output. We present an approximate semi-analytical approach which describes nonlinear transformation of the input pulse into the output pulse. It shows how the input and the output chirps are connected via a time-warp transformation which is almost independent of the shape of the probe pulse. We then show how this transformation can be used to optimize the supercontinuum generation to produce nearly single-cycle pulses tunable from mid-infrared to ultraviolet. PACS 42.65.Re; 42.65.Ky     

Elastic scattering of an electron by the negative lithium ion

In the framework of the many-body theory, the differential and total cross sections of elastic scattering of slow electrons by the negative lithium ion Li⁻ are obtained. Calculations are performed both in the Hartree-Fock single-particle approximation and with regard to many-electron correlations, which take into account the dynamic polarization of the core. Features observed in the behavior of the phases and cross sections for p and d partial waves are associated with resonance scattering of electron waves. Considering the dynamic polarization of the core by an incident electron heightens the diffraction character of the scattering. The real process is compared with particle scattering in models with a repulsive potential.     

Embedding Free Burnside Groups in Finitely Presented Groups

We construct an embedding of a free Burnside group B(m,n) of odd exponent n > 2⁴⁸ and rank m >1 in a finitely presented group with some special properties. The main application of this embedding is an easy construction of finitely presented nonamenable groups without noncyclic free subgroups (which provides a new finitely presented counterexample to the von Neumann problem on amenable groups). As another application, we construct weakly finitely presented groups of odd exponent n ≫ 1 which are not locally finite.