The thermal noise in multilayer coating

We consider thermal fluctuations in multilayer interferometric coating taking into account light propagation inside the coating. In particular, we calculate the reflected wave phase as a function of small displacements of the boundaries between the layers using transmission line model for interferometric coating and derive formula for spectral density of reflected phase in accordance with Fluctuation-Dissipation Theorem. We apply the developed approach for calculation of the spectral density of coating Brownian noise which makes main contribution into noise budget of second generation gravitational wave detectors.     

Anomaly driven signatures of new invisible physics at the Large Hadron Collider

Many extensions of the Standard Model (SM) predict new neutral vector bosons at energies accessible by the Large Hadron Collider (LHC). We study an extension of the SM with new chiral fermions subject to non-trivial anomaly cancellations. If the new fermions have SM charges, but are too heavy to be created at LHC, and the SM fermions are not charged under the extra gauge field, one would expect that this new sector remains completely invisible at LHC. We show, however, that a non-trivial anomaly cancellation between the new heavy fermions may give rise to observable effects in the gauge boson sector that can be seen at the LHC and distinguished from backgrounds.     

Magnetic and structural anomalies of Na<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>C<Subscript>60</Subscript> (n = 2, 3)

Sodium fullerides Na _n C60 (n = 2, 3) have been synthesized by a liquid phase reaction and investigated with X-ray diffraction (XRD), nuclear magnetic resonance (NMR), electron paramagnetic resonance, and differential thermal analysis. XRD data indicate that the crystal structure of Na₂C₆₀ at 300 K is face centered cubic (FCC). A phase transition from primitive cubic to FCC crystal structure has been observed in this work in Na₂C₆₀ fulleride at 290 K. The transition is accompanied by the step-like change of paramagnetic susceptibility. The crystal structure of Na₃C₆₀ is more complicated than, and different from, what has been reported in the literature. A nearly seven-fold increase of paramagnetic susceptibility with increasing temperature has been observed in the Na₃C₆₀ fulleride at 240–260 K. In the same temperature range, a new line at about 255 ppm appears in the ²³Na NMR spectrum, indicating a significant increase of electron density near the Na nucleus. The observed effect can be explained by a metal-insulator transition caused by a structural transition.     

Topological analysis of real space properties for the solid-state full-potential APW DFT method

For the solid-state density functional program Elk a module was developed that enables to interface the crystal orbitals data into the DGrid package. Within DGrid the real-space electronic properties, like the electron density and its gradient or Laplacian, kinetic energy density, electron localizability indicator, etc., are computed. The properties can be searched for critical points as well as for the interconnection lines between them. Additionally, the basins can be evaluated and the property integrals can be calculated. The results of topological analysis for fcc Al, MgB₂, CaTiO₃, and urea molecular crystal are discussed and compared with the experimental data. The role of certain computation parameters of (L)APW method is also analyzed.     

Solitary surface acoustic waves and bulk solitons in nanosecond and picosecond laser ultrasonics

Recent achievements of nonlinear acoustics concerning the realization of solitons and solitary waves in crystals and their surfaces attained by nanosecond and picosecond laser ultrasonics are discussed and compared. The corresponding pump-probe setups are described, which allow an all-optical contact-free excitation and detection of short strain pulses in the broad frequency range between 10 MHz and about 300 GHz. The formation of solitons in the propagating longitudinal strain pulses is investigated for nonlinear media with intrinsic lattice-based dispersion. The excitation of solitary surface acoustic waves is realized by a geometric film-based dispersion effect. Future developments and potential applications of nonlinear nanosecond and picosecond ultrasonics are discussed.     

A bundle modification strategy for convex minimization

We present a new bundle algorithm for minimizing convex not necessarily smooth functions. The novelty of our approach is based on a bundle modification strategy that we apply whenever the stability center is updated and which is aimed at substituting the points of the bundle by new points characterized by possibly better values of the objective function. Convergence of the algorithm is proved and numerical results are presented.     

Graphs of difference operators for p-ary sequences

For a given prime p and positive integer n, we consider the graph G _n of the difference operator acting on p-ary sequences of length n. We suggest new proofs of some results of V.I. Arnold on the graph G _n and the complexity of sequences and obtain new results for the length of a maximal cycle in the general case of p-ary sequences. We also provide estimates for the number of complicated sequences.      

CATALYTIC PROPERTIES OF NANOFIBROUS CARBON IN SELECTIVE OXIDATION OF HYDROGEN SULPHIDE

Nanofibrous carbonaceous materials （NFC） as a new class of materials having many applications, can catalyze the selective oxidation of H2S to sulfur. The correlation between NFC structure and its activity and selectivity in H2S oxidation was determined. It is demonstrated that selectivity can be improved if NFC with more ordered structure be synthesized and the portion of the original catalyst in carbon be reduced by increasing the carbon accumulated in the catalyst.     

Attainability of the Exponent of Exponential Growth in Free Products of Cyclic Groups

In the paper, the set of exponents of exponential growth (growth exponents) for a finitely generated group with respect to all possible generators of this group is studied. It is proved that the greatest lower bound of this set is attained for the free products of a cyclic group of prime order and a free group of finite rank.