Electronic optics in graphene in the semiclassical approximation

We study above-barrier scattering of Dirac electrons by a smooth electrostatic potential combined with a coordinate-dependent mass in graphene. We assume that the potential and mass are sufficiently smooth, so that we can define a small dimensionless semiclassical parameter $h \ll 1$. This electronic optics setup naturally leads to focusing and the formation of caustics, which are singularities in the density of trajectories. We construct a semiclassical approximation for the wavefunction in all points, placing particular emphasis on the region near the caustic, where the maximum of the intensity lies. Because of the matrix character of the Dirac equation, this wavefunction contains a nontrivial semiclassical phase, which is absent for a scalar wave equation and which influences the focusing. We carefully discuss the three steps in our semiclassical approach: the adiabatic reduction of the matrix equation to an effective scalar equation, the construction of the wavefunction using the Maslov canonical operator and the application of the uniform approximation to the integral expression for the wavefunction in the vicinity of a caustic. We consider several numerical examples and show that our semiclassical results are in very good agreement with the results of tight-binding calculations. In particular, we show that the semiclassical phase can have a pronounced effect on the position of the focus and its intensity.Comment: 103 pages, 11 figure

Classical and quantum dynamics of a particle in a narrow angle

We consider the 2D Schr¨odinger equation with variable potential in the narrow domain diffeomorphic to the wedge with the Dirichlet boundary condition. The corresponding classical problem is the billiard in this domain. In general, the corresponding dynamical system is not integrable. The small angle is a small parameter which allows one to make the averaging and reduce the classical dynamical system to an integrable one modulo exponential small correction. We use the quantum adiabatic approximation (operator separation of variables) to construct the asymptotic eigenfunctions (quasimodes) of the Schrodinger operator. We discuss the relation between classical averaging and constructed quasimodes. The behavior of quasimodes in the neighborhood of the cusp is studied. We also discuss the relation between Bessel and Airy functions that follows from different representations of asymptotics near the cusp

Analysis of 3 years of data from the gravitational wave detectors EXPLORER and NAUTILUS

We performed a search for short gravitational wave bursts using about 3 years of data of the resonant bar detectors Nautilus and Explorer. Two types of analysis were performed: a search for coincidences with a low background of accidentals (0.1 over the entire period), and the calculation of upper limits on the rate of gravitational wave bursts. Here we give a detailed account of the methodology and we report the results: a null search for coincident events and an upper limit that improves over all previous limits from resonant antennas, and is competitive, in the range h_rss ~1E-19, with limits from interferometric detectors. Some new methodological features are introduced that have proven successful in the upper limits evaluation.Comment: 12 pages, 12 figure

Study of the coincidences between the gravitational wave detectors EXPLORER and NAUTILUS in 2001

We report the result from a search for bursts of gravitational waves using data collected by the cryogenic resonant detectors EXPLORER and NAUTILUS during the year 2001, for a total measuring time of 90 days. With these data we repeated the coincidence search performed on the 1998 data (which showed a small coincidence excess) applying data analysis algorithms based on known physical characteristics of the detectors. With the 2001 data a new interesting coincidence excess is found when the detectors are favorably oriented with respect to the Galactic Disk

All-sky upper limit for gravitational radiation from spinning neutron stars

We present results of the all-sky search for gravitational-wave signals from spinning neutron stars in the data of the EXPLORER resonant bar detector. Our data analysis technique was based on the maximum likelihood detection method. We briefly describe the theoretical methods that we used in our search. The main result of our analysis is an upper limit of ${\bf 2\times10^{-23}}$ for the dimensionless amplitude of the continuous gravitational-wave signals coming from any direction in the sky and in the narrow frequency band from 921.00 Hz to 921.76 Hz.Comment: 12 pages, 4 figures, submitted to Proceedings of 7th Gravitational Wave Data Analysis Workshop, December 17-19, 2002, Kyoto, Japa

Increasing the bandwidth of resonant gravitational antennas: The case of Explorer

Resonant gravitational wave detectors with an observation bandwidth of tens of hertz are a reality: the antenna Explorer, operated at CERN by the ROG collaboration, has been upgraded with a new read-out. In this new configuration, it exhibits an unprecedented useful bandwidth: in over 55 Hz about its frequency of operation of 919 Hz the spectral sensitivity is better than 10^{-20} /sqrt(Hz) . We describe the detector and its sensitivity and discuss the foreseable upgrades to even larger bandwidths.Comment: 4 pages- 4 figures Acceted for publication on Physical Review Letter

Реализация фармацевтической разработки с применением многофакторного анализа многокритериальной оптимизации на примере этапа очистки гидросукцината олигогексаметиленгуанидина

Objectives. The study set out to use mathematical modeling, in particular the method of multifactorial analysis of multicriteria optimization (MAMO), in the development of a pharmaceutical product.Methods. After carrying out experimental tests based on the proposed algorithmic sequence, the obtained data were interpreted using MAMO.Results. The possibility of using MAMO to solve the applied problem of purifying oligohexamethyleneguanidine hydrosuccinate (OHMG-HS), considered as a pharmaceutical precursor for the creation of medicines, was demonstrated.Conclusions. The expediency of using the proposed algorithm as a tool for pharmaceutical development is substantiated by identifying dependencies of the influence of purification conditions on the final content of admixtures in the target product.Цели. Данное исследование посвящено использованию математического моделирования, в частности метода многофакторного анализа многокритериальной оптимизации (МАМО), в фармацевтической разработке.Методы. В ходе исследования была предложена алгоритмическая последовательность эксперимента и проведены необходимые испытания. Полученные данные были интерпретированы при помощи МАМО.Результаты. Изучена возможность применения МАМО для решения прикладной проблемы очистки гидросукцината олигогексаметиленгуанидина (ОГМГ-ГС), рассматриваемого в качестве фармацевтической субстанции для создания лекарственных средств.Выводы. Были выявлены зависимости влияния условий очистки на конечное содержание примесей в целевом продукте и доказана целесообразность использования предложенного алгоритма в качестве инструмента фармацевтической разработки