Phase-matched four-wave mixing of isolated waveguide modes of high-intensity femtosecond pulses in a hollow photonic-crystal fiber

Hollow-core photonic-crystal fibers with a special dispersion profile are shown to allow phase-matched nonlinear optical interactions of isolated air-guided modes of high-intensity femtosecond laser pulses confined in the hollow fiber core. We present theoretical and experimental studies of the four-wave mixing of fundamental and second-harmonic pulses of a Cr:forsterite laser with an initial pulse duration of about 50 fs and an intensity on the order of 10¹⁴ W/cm² in waveguide modes of a hollow photonic-crystal fiber with a core diameter of about 13μm.     

Annihilation of positrons in hydrogen-saturated titanium

The effect of atomic hydrogen on the electronic structure of α-titanium samples is studied using the electron-positron annihilation methods. It is shown that different states of hydrogen atoms are manifested in different ways in the positron lifetime distribution spectrum. The results of theoretical calculations of the first component of the positron lifetime are in accord with the obtained experimental data.     

Global Attractor for a Nonautonomous Inclusion with Discontinuous Right-Hand Side

We consider a nonautonomous inclusion the upper and lower selectors of whose right-hand side are determined by functions with discontinuities of the first kind. We prove that this problem generates a family of multivalued semiprocesses for which there exists a global attractor compact in the phase space.     

Ionization of two-electron atom in ultrashort laser pulse

The method of numerical integration of the classical equations of motion was used to study interaction of a model two-electron atom with ultrashort laser pulses. Mechanisms and specific features of the ionization process were analyzed in a broad range of laser-field parameters.     

Fluid-fluid phase separation in colloid-polymer mixtures studied with small angle light scattering and light microscopy

Mixtures of colloidal silica spheres and polydimethylsiloxane in cyclohexane with a colloid-polymer size ratio of about one were found to phase separate into two fluid phases, one which is colloid-rich and one which is colloid-poor. In this work the phase separation kinetics of this fluid-fluid phase separation is studied for different compositions of the colloid-polymer mixtures, and at several degrees of supersaturation, with small angle light scattering and with light microscopy. The small angle light scattering curve exhibits a peak that grows in intensity and that shifts to smaller wave vector with time. The characteristic length scale that is obtained from the scattering peak is of the order of a few μm, in agreement with observations by light microscopy. The domain size increases with time as , which might be an indication of coarsening by diffusion and coalescence, like in the case of binary liquid mixtures and polymer blends. For sufficiently low degrees of supersaturation the angular scattering intensity curves satisfy dynamical scaling behavior.     

An exponential lower bound to the size of bounded depth frege proofs of the pigeonhole principle

We prove lower bounds of the form exp(n^{ε d}), ε_d > 0, on the length of proofs of an explicit sequence of tautologies, based on the Pigeonhole Principle, in proof systems using formulas of depth d, for any constant d. This is the largest lower bound for the strongest proof system, for which any superpolynomial lower bounds are known.