Dynamics of Maxwell’s pendulum

The stability of motion of Maxwell’s pendulum is investigated in a uniform gravity field. By means of several canonic transforms of the equations of pendulum motion and the method of the surfaces of Poincaré sections, the problem is reduced to investigation of the immobile-point stability retaining the area of mapping of the plane into itself. In the space of dimensionless parameters, the stability and instability regions are singled out.     

Non-Equilibrium Dynamics of Dyson’s Model with an Infinite Number of Particles

Dyson’s model is a one-dimensional system of Brownian motions with long-range repulsive forces acting between any pair of particles with strength proportional to the inverse of distances with proportionality constant β/2. We give sufficient conditions for initial configurations so that Dyson’s model with β = 2 and an infinite number of particles is well defined in the sense that any multitime correlation function is given by a determinant with a continuous kernel. The class of infinite-dimensional configurations satisfying our conditions is large enough to study non-equilibrium dynamics. For example, we obtain the relaxation process starting from a configuration, in which every point of \mathbbZ{\mathbb{Z}} is occupied by one particle, to the stationary state, which is the determinantal point process with the sine kernel.     

Dynamics of Gliding Arc Climbing in a Unipolar Jacob’s Ladder

Technical Physics - We have designed a device with a gliding unipolar arc of the Jacob’s ladder type. The dynamics of arc rising has been investigated. It is found that the arc climbs at a...     

Dynamics of the Earth’s radiation belts

In this article, we provide a short review of the current state of the field of the radiation belts of the Earth. The main attention is given to the variations of energetic particle fluxes during geomagnetic storms. Electron and proton acceleration mechanisms in the terrestrial magnetosphere are discussed. The possibility of predicting various space weather parameters using the data on relativistic electrons of the outer radiation belt is discussed.     

Propagation of elastic waves in a plate with rough surfaces

Abstract The characteristics of Lamb wave propagating in a solid plate with rough surfaces are studied on the basis of small perturbation approximation. The Rayleigh-Lamb frequency equation expressed with SA matrix is presented. The Rayleigh-Lamb frequency equation fora rough surface plate is different from that for a smooth surface plate, resulting in a small perturbation Δk on Lamb wave vector k. The imaginary part of Δk gives the attenuation caused by wave scattering. An experiment is designed to test our theoretical predications.By using wedge-shape pipes, different Lamb Wave modes are excited. The signals at different positions are received and analyzed to get the dispersion curves and attenuations of different modes. The experimental results are compared with the theoretical predications.     

“Wandering” eigenfrequencies of a two-dimensional elastic body with a blunted cusp

At the pointed cusp of a two-dimensional plate, a tip of small length h is broken off. By means of asymptotic analysis, a new effect of “wandering” of eigenfrequencies of longitudinal vibrations of the plate with the blunted cusp is found: as h → +0, the frequencies prove to be almost periodic functions in the logarithmic scale ln h; i.e., when the fragment length decreases, they chaotically move at a high speed O(h^?1) along the real semi-axis (κ_?, +∞), while κ_? > 0 is the cutoff point of the continuous spectrum of the problem with an ideal cusp.     

Dynamics of Chapman-Jouguet pulsating detonations with Chain-Branching kinetics: Fickett’s analogue and Euler equations

The present study examines the spatiotemporal nonlinear dynamics of detonations over a wide range of reaction time scales away from the neutral stability region. This is addressed by one-dimensional numerical simulations with chain-branching kinetics. Fickett’s detonation analogue and Euler’s equations were used as evolution equations. A shock-fitting solver is used to reduce CPU time. Up to four thousand five hundred simulations have been carried out. Detailed bifurcation diagrams have been generated to explore the detonation dynamics. For long/intermediate reaction time scales, away from the neutral boundary, the traditional period-doubling cascade to chaos is seen. For square wave detonations, away from the neutral stability, almost periodic oscillations are recorded. This result might have implications for the existence of a characteristic length scale, the cell size, on typical cellular detonations which have a short reaction length.     

Enhancement of Smith—Purcell radiation with surface-plasmon excitation

With the aid of a three-dimensional particle-in-cell code simulation,the enhancement of Smith-Purcell radiation with a surface-plasmon mode excited by a single electron bunch and by a premodulated electron beam is considered in the paper.In the simulation,the model is a grating covered by Ag film.The results demonstrate that when the surface-plasmon mode is excited by a single electron bunch,the maximum radiation occurs at an observation angle depending on the surface-plasmon frequency,and the radiation power can be enhanced more than ten times.And for pre-bunched electron beam excitation,when one of the harmonics of the bunching frequency is resonant with that of the surface-plasmon mode,the radiation power is twenty times more than that from a perfectly conducting grating excited by the same premodulated electron beam.     

Generalization of Biot’s equations with allowance for shear relaxation of a fluid

On the basis of the generalized variational principle for dissipative continuum mechanics, a system of generalized Biot’s equations is derived to describe the wave propagation in a two-phase porous permeable medium in the presence of shear relaxation in the pore-filling fluid. It was shown that the inclusion of shear viscoelasticity of the fluid leads to the appearance of two transverse modes in addition to two longitudinal modes described by the Biot theory. One of the transverse modes is an acoustic mode, whereas the other is a diffusion mode characterized by the linear frequency dependence of phase velocity and attenuation coefficient in the low-frequency region.     

Laser detection of elastic waves diffraction by the crack’s edge

Diffraction effects and features of acoustic wave propagation in elastic media with the surface-breaking microcrack were investigated in detail for the pulse probing signals. The crack’s plane was oriented along the direction of longitudinal ultrasonic wave incidence in such a way that the detection of the crack with such an unfavorable spatial location was difficult by means of traditional acoustic techniques. Using laser Doppler interferometer a set of instantaneous pictures of acoustic field on the specimen’s surface, corresponding to the different moments of time was obtained. This allowed us to investigate and visualize the diffraction effects of acoustic field in dynamics. Using numerical modeling of diffraction processes of acoustic waves on the crack’s edge and top for pulse signals the origin of V-like structures on the snapshots of acoustic fields was explained and analyzed.     

On Gammelgaard’s Formula for a Star Product with Separation of Variables

We show that Gammelgaard’s formula expressing a star product with separation of variables on a pseudo-Kähler manifold in terms of directed graphs without cycles is equivalent to an inversion formula for an operator on a formal Fock space. We prove this inversion formula directly and thus offer an alternative approach to Gammelgaard’s formula which gives more insight into the question why the directed graphs in his formula have no cycles.     

Structural state of erythrocyte membranes in a human with Alzheimer’s disease

The structural state of erythrocyte membranes collected from patients with Alzheimer’s disease (AD) was studied. The structural state was characterized by the degree of hemolysis and the content of malonic dialdehyde (MDA), as measures of the peroxide oxidation of lipids (POL), and by the microviscosity of the lipid bilayer. The microviscosity of the membranes was measured by the EPR spin probe method, with 2,2,6,6-tetramethyl-4-capryloyl-oxypiperidine-1-oxyl (lipid probe) and 5,6-benzo-2,2,6,6-tetramethyl-1,2,3,4-tetrahydro-gamma-carboline-3-oxyl (protein probe). It was established that all patients with AD feature an increased fluidity of both the lipid and near-protein areas of erythrocyte membranes. Based on the POL intensity, three groups of patients were identified. The first group was characterized by an increased POL intensity. This group featured a high degree of hemolysis and a high MDA content both before and after incubation, with increases in both these parameters being observed upon incubation. The second and third groups were characterized by a low POL intensity. The second group exhibited a low degree of hemolysis and no increment upon incubation, with the MDA/PH ratio being much higher than unity. The third group was characterized by an increased degree of mechanical hemolysis and by decreases in the degree of homolysis and the MDA content upon incubation.     

Dynamics of charged particle fluxes in Earth’s troposphere since 1990

Temporal variations of charged particle fluxes in the Earth’s atmosphere at altitudes below ～16 km do not always correlate with variations above ～16 km and the dynamics of primary cosmic rays. Variations of particle fluxes in the troposphere grew in the 1990s, rather synchronously in the Murmansk and Moscow regions but not in Antarctica. During the last decade, the annual wave in the opposite phase with temperature has often been observed in the northern hemisphere at all altitudes below ～16 km. The phase of this variation coincides with the phase of the expected temperature effect of cosmic ray muons but its amplitude is several times larger than expected.     

Dynamics of Mandel’shtam-Brillouin induced scattering during self-focusing of a laser beam

It is shown that the size of the focal spot has a substantial influence on the dynamics of Mandel’shtam-Brillouin induced scattering (MBIS) for the laser beam power near critical for striction self-focusing. For small focal spots MBIS suppresses self-focusing. An increase in the size of the focal spot leads to growth of the MBIS pulsations and the steady-state setup time. For large enough focal spots MBIS arises in the form of regular intense spikes. Physical processes shaping the dynamics of MBIS are discussed. Zh. éksp. Teor. Fiz. 115, 1950–1960 (June 1999)     

Dynamics of shock induced ignition in Fickett’s model: Influence of χ

Using Fickett’s model for reactive compressible flows, i.e., the reactive form of Burgers’ equation, we address the problem of shock induced ignition by a piston in a reactive medium characterized by a 2 step induction-reaction kinetics. Owing to the model’s simplicity, the ignition and acceleration mechanism is explained using the two families of characteristics admitted by the model. The energy release along the particle paths provides the amplification of forward-traveling pressure waves. These waves pre-compress the medium in the induction layer ahead of the reaction zone, therefore changing the induction delays of successive particles. The variation of the induction delay provides the modulation of the amplification of the forward traveling pressure waves by controlling the residence time of the pressure waves in the reaction zone. A closed form analytical solution is obtained by the method of characteristics and high activation energy asymptotics. The acceleration of the reaction zone was found to be proportional to the product of the activation energy, the ratio of the induction to reaction time and the heat release. This finding provides a theoretical justification for the previous use of this non-dimensional number to characterize the ignition regimes observed experimentally in detonations and shock induced ignition phenomena. Numerical simulations are presented and analyzed. Both subsonic and supersonic internal flame propagation are observed, consistent with experiment and previous reactive Euler models.     

Fuzzy Space-Time Geometry and Particle’s Dynamics

The quantum space-time with Dodson-Zeeman topological structure is studied. In its framework, the states of massive particle m correspond to the elements of fuzzy ordered set (Foset), i.e. the fuzzy points. Due to their partial ordering, m space coordinate x acquires principal uncertainty σ _x . Schroedinger formalism of Quantum Mechanics is derived from consideration of m evolution in fuzzy phase space with minimal number of additional axioms. The possible particle’s interactions on fuzzy manifold are studied and shown to be gauge invariant.     

Dynamics of Skew-Information and Bell’s Inequality Correlations for Two Coupled Dipole Qubits with 2-Photon Transition

International Journal of Theoretical Physics - We consider a dissipative system of two qubits interacting with a cavity field through the degenerate 2-photon transitions. The cavity is initially...     

The Green’s function in a channel with a sound-absorbing cover in the case of a uniform flow

We study the modal structure of an acoustic field of a point source as function of channel wall admittance in the case of a two-dimensional channel. The characteristic equation for determining the eigen-values corresponding to the boundary problem is studied in the form of this equation??s dependence on the admittance, which varies in the entire complex plane. All modes, without exception, existing in the channel and forming the source field are classified based on the obtained topography of the characteristic equation. The expressions that describe the amplitudes and spatial distribution of the hydrodynamic modes, attenuation rate (for stable modes), or increment (for unstable modes) were obtained as functions of the wall admittance and flow velocity. It is shown that in addition to the hydrodynamic unstable modes existing downstream from the source, hydrodynamic unstable modes exist upstream from the source at any admittance. They appear only when the admittance has an elastic character. It is shown that hydrodynamic modes are induced only in the case when the source is located close to the wall or on the wall. The amplitude of these modes decreases exponentially with distance from the wall.