Markov evolutions and hierarchical equations in the continuum I. One-component systems

General birth-and-death as well as hopping stochastic dynamics of infinite particle systems in the continuum are considered. We derive corresponding evolution equations for correlation functions and generating functionals. General considerations are illustrated in a number of concrete examples of Markov evolutions appearing in applications.Comment: 47 page

Markov Process of Muscle Motors

We study a Markov random process describing a muscle molecular motor behavior. Every motor is either bound up with a thin filament or unbound. In the bound state the motor creates a force proportional to its displacement from the neutral position. In both states the motor spend an exponential time depending on the state. The thin filament moves at its velocity proportional to average of all displacements of all motors. We assume that the time which a motor stays at the bound state does not depend on its displacement. Then one can find an exact solution of a non-linear equation appearing in the limit of infinite number of the motors.Comment: 10 page

Tagged particle process in continuum with singular interactions

By using Dirichlet form techniques we construct the dynamics of a tagged particle in an infinite particle environment of interacting particles for a large class of interaction potentials. In particular, we can treat interaction potentials having a singularity at the origin, non-trivial negative part and infinite range, as e.g., the Lennard-Jones potential.Comment: 27 pages, proof for conservativity added, tightened presentatio

Multifrequency Study of Giant Radio Pulses from the Crab Pulsar with the K5 VLBI Recording Terminal

Simultaneous multifrequency observations of the Crab pulsar giant pulses (GPs) were performed with the 64-m Kalyazin radio telescope at four frequencies 0.6, 1.4, 2.2 and 8.3 GHz using the K5 VLBI recording terminal. The K5 terminal provided continuous recording in 16 4-MHz wide frequency channels distributed over 4 frequency bands. Several thousands of GPs were detected during about 6 hours of observations in two successive days in July 2005. Radio spectra of single GPs were analysed at separate frequencies and over whole frequency range. These spectra manifest notable modulation over frequency ranges, $\Delta\nu$, both on large ($\Delta\nu/\nu\approx 0.5$) and small ($\Delta\nu/\nu\approx 0.01$) frequency scales. Cross-correlation analysis of GPs at 2.2 GHz showed that their pulse shapes can be interpreted as an ensemble of unresolved bursts grouped together at time scales of $\approx 1$ mcs being well-correlated over a 60-MHz band. The corresponding GP cross-correlation functions do not obey the predictions of the amplitude-modulated noise model of Rickett (1975), thus indicating that unresolved components represent a small number of elementary emitters.Comment: 22 pages, 11 figures, 3 tables, submitted to PAS

Giant Pulses from PSR B1937+21 with widths <= 15 nanoseconds and T_b >= 5 x 10^39 K, the Highest Brightness Temperature Observed in the Universe

Giant radio pulses of the millisecond pulsar B1937+21 were recorded with the S2 VLBI system at 1.65 GHz with NASA/JPL's 70-m radio telescope at Tidbinbilla, Australia. These pulses have been observed as strong as 65000 Jy with widths <= 15 ns, corresponding to a brightness temperature T_b >= 5 x 10^39 K, the highest observed in the universe. The vast majority of these pulses occur in a 5.8 mcs and 8.2 mcs window at the very trailing edges of the regular main pulse and interpulse profiles, respectively. Giant pulses occur in general with a single spike. Only in one case out of 309 was the structure clearly more complex. The cumulative distribution is fit by a power law with index -1.40 +/- 0.01 with a low-energy but no high-energy cutoff. We estimate that giant pulses occur frequently but are only rarely detected. When corrected for the directivity factor, 25 giant pulses are estimated to be generated in one neutron star revolution alone. The intensities of the giant pulses of the main pulses and interpulses are not correlated with each other nor with the intensities or energies of the main pulses and interpulses themselves. Their radiation energy density can exceed 300 times the plasma energy density at the surface of the neutron star and can even exceed the magnetic field energy density at that surface. We therefore do not think that the generation of giant pulses is linked to the plasma mechanisms in the magnetosphere. Instead we suggest that it is directly related to discharges in the polar cap region of the pulsar.Comment: 14 pages, 13 figures, to be published in ApJ, November 2004, v. 616, also was presented in Russian National Astronomical Conference VAK-2004, "Horizons of the Universe" held in Moscow State University, Sternberg Astronomical Institute, June 3-10, 2004, page 19

Measurement of the transverse target and beam-target asymmetries in η\eta meson photoproduction at MAMI

We present new data for the transverse target asymmetry T and the very first data for the beam-target asymmetry F in the $\vec \gamma \vec p\to\eta p$ reaction up to a center-of-mass energy of W=1.9 GeV. The data were obtained with the Crystal-Ball/TAPS detector setup at the Glasgow tagged photon facility of the Mainz Microtron MAMI. All existing model predictions fail to reproduce the new data indicating a significant impact on our understanding of the underlying dynamics of $\eta$ meson photoproduction. The peculiar nodal structure observed in existing T data close to threshold is not confirmed.Comment: 5 pages, 3 figures, accepted for publication in PR