Surface grating formation and erasing on a-Se films

Surface relief formation at holographic recording on amorphous selenium films was demonstrated and investigated. The presence of this optical phase modulation component is essential for ensuring significant, stable and erasable optical recording in a-Se films at 290–320 K temperatures, where conventional photodarkening was known as insignificant and unstable. Photocrystallization can only be observed in super-exposed a-Se films at the given experimental conditions of hologram recording. Erasing behavior of surface relief gratings under heat treatment was also investigated in order to reveal further details of the mechanism. Photoinduced structural transformations within the amorphous phase, connected to local ordering under the condition of light-induced fluidity, are proposed as an explanation for the relief formation and erasing. The observed reversible optical recording process may be useful for the various optoelectronic applications of photoconductive a-Se layers. Received: 12 June 2000 / Accepted: 6 June 2001 / Published online: 30 August 2001     

Some remarks on metaplectic cusp forms and the correspondences of Shimura and Waldspurger

The simple relation between representations of the covering groups of SL₂ and GL₂ makes it possible to fuse and extend the recent metaplectic results of Shimura, Waldspurger, Flicker, and ourselves. By giving a new (purely local andL-function theoretic) treatment of the Waldspurger-Shintani correspondence, we also simplify some of Waldspurger’s original results.     

Van der Waerden continuity theorem for semisimple lie groups

As was proved by van der Waerden in 1933, every finite-dimensional locally bounded representation of a semisimple compact Lie group is continuous. This is the famous “van der Waerden continuity theorem,” and it motivated a vast literature. In particular, relationships between the assertion of the theorem (and of the inverse, in a sense, to this theorem) and some properties of the Bohr compactifications of topological groups were established, which led to the introduction and the study of certain classes of the so-called van der Waerden groups and algebras. Until now, after more than 70 years have passed, the van der Waerden theorem appears in monographs and surveys in diverse forms; new proofs were found and then simplified in important special cases. In this paper, we prove that the statement of the van der Waerden theorem remains valid for all (not necessarily compact) real semisimple Lie groups, i.e., any given finite-dimensional representation of a real semisimple Lie group is continuous if and only if this representation is locally bounded. More subtle results are also obtained. The main theorem contains several conditions equivalent to the continuity condition for a finite-dimensional representation. In particular, it is proved that every finite-dimensional representation of a real semisimple Lie group is continuous if and only if the restriction of this representation to the “compact” part, to the Abelian part, or to the nilpotent part of the Iwasawa decomposition is locally bounded, and the original van der Waerden theorem is also somewhat refined. For instance, the following assertion holds: every finite-dimensional representation of a compact semisimple Lie group is continuous if and only if the restriction of this representation to some maximal torus is locally bounded. Dedicated to the memory of George Mackey (1916–2006) Partially supported by the Russian Foundation for Basic Research under grant no. 02-01-00574, by the Program of Supporting the Leading Scientific Schools under grant no. NSh 619.203.1, and by the INTAS grant.     

Logarithmic L 2-Small Ball Asymptotics with Respect to a Self-Similar Measure for Some Gaussian Processes

We find logarithmic small ball asymptotics for the L₂-norm with respect to self-similar measures for a certain class of Gaussian processes including Brownian motion, Ornstein-Uhlenbeck process, and their integrated counterparts. Bibliography: 46 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 311, 2004, pp. 190–213.     

Scattering of surface plasmon polaritons by a nanoparticle with the inclusion of the magnetic dipole contribution

Using the method of the tensor Green’s function of the wave equation, the differential and total cross sections for the scattering of surface optical electromagnetic waves (surface plasmon polaritons) by a spherical nanoparticle into surface plasmon polaritons and light have been obtained with the inclusion of the magnetic dipole contribution. Using the example of noble metal systems, it has been shown that the magnetic dipole contribution may significantly affect the angular dependence of the differential cross sections and increase their anisotropy as the plasmon wavelength increases.     

Onset of crater formation during short pulse laser ablation

We report morphologic changes of metallic surfaces at the onset of ablation, starting from gentle ablation to the emergence of ablation craters. The evolution of both observed melting zones and of ablation craters therein are investigated in dependence of the ablation laser fluence for nanosecond ultraviolet laser pulses. Further, consequences of crater formation for cluster synthesis within the released atomic vapor are pointed out. PACS 52.38.Mf; 79.20.Ds; 65.40.De     

Analysis of packing factors of crystalline polymers in terms of the glass transition to melting temperature radio

An expression for the ratio of the glass transition temperature to the melting temperature, T _g/T _m, was derived with allowance for fluctuations of the packing factor in the amorphous state. This relationship made it possible to describe the actual range of variation in T _g/T _m depending on a change in the packing factor in the crystalline state k _{o, cr}. The proposed approach forms the basis for the method of determination of increments in the packing ratio k _{o, cr} and formulation of the principles of selection of experimental data for calculations. The glass transition temperatures in polyethylene depending on the type of unit cell were calculated.     

Definition and properties of characteristic frequencies of a linear equation

The definition of the characteristic frequencies of zeroes and changes of sign for solutions is given. It is equal to the upper medium (with respect to the time half-axis) of their number on the half-interval of length π. We also define the main frequencies for a linear homogeneous equation of order n. These main frequencies for an equation with constant coefficients coincide with the absolute values of the imaginary parts of the roots of the corresponding characteristic polynomial. It is proved that for the second-order equation the main frequencies are the same for all solutions and that they are stable with respect to uniformly small and infinitely small perturbations of the coefficients. For the third-order equation they can be different, and for any of the main frequencies an example of nonstability is given. __________ Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 25, pp. 249–294, 2005.