Stochastic jets and nonhomogeneous transport in Lagrangian turbulence

Computer simulations are presented for a new object of chaos, stochastic jets, for a steady flow with five-fold symmetry with the Beltrami property. Lagrangian chaos of streamlines can reveal itself in the existence of huge flights which is connected with the asymptotic laws of anomalous transport of passive particles.     

On the structure of field at the phase transition to the superradiance state

It is shown that at the phase transition to the superradiance state a nonlinear periodic wave structure of the field may be excited. Amplitude, width and number harmonics in the wave packet are determined by the boundary conditions and temperature.     

Weak mixing and anomalous kinetics along filamented surfaces

We consider chaotic properties of a particle in a square billiard with a horizontal bar in the middle. Such a system can model field-line windings of the merged surfaces. The system has weak-mixing properties with zero Lyapunov exponent and entropy, and it can be also interesting as an example of a system with intermediate chaotic properties, between the integrability and strong mixing. We show that the transport is anomalous and that its properties can be linked to the ergodic properties of continued fractions. The distribution of Poincare recurrences, distribution of the displacements, and the moments of the truncated distribution of the displacements are obtained. Connections between different exponents are found. It is shown that the distribution function of displacements and its truncated moments as a function of time exhibit log-periodic oscillations (modulations) with a universal period T(log)=pi(2)/12 ln 2. We note that similar results are valid for a family of billiard, particularly for billiards with square-in-square geometry. (c) 2001 American Institute of Physics.     

Sensitivity of ray travel times

Ray in a waveguide can be considered as a trajectory of the corresponding Hamiltonian system, which appears to be chaotic in a nonuniform environment. From the experimental and practical viewpoints, the ray travel time is an important characteristic that, in some way, involves an information about the waveguide condition. It is shown that the ray travel time as a function of the initial momentum and propagation range in the unperturbed waveguide displays a scaling law. Some properties of the ray travel time predicted by this law still persist in periodically nonuniform waveguides with chaotic ray trajectories. As examples we consider few models with special attention to the underwater acoustic waveguide. It is demonstrated for a deep ocean propagation model that even under conditions of ray chaos the ray travel time is determined, to a considerable extent, by the coordinates of the ray endpoints and the number of turning points, i.e., by a topology of the ray path. We show how the closeness of travel times for rays with equal numbers of turning points reveals itself in ray travel time dependencies on the starting momentum and on the depth of the observation point. It has been shown that the same effect is associated with the appearance of the gap between travel times of chaotic and regular rays. The manifestation of the stickiness (the presence of such parts in a chaotic trajectory where the latter exhibits an almost regular behavior) in ray travel times is discussed. (c) 2002 American Institute of Physics.     

Strain-induced quantum ring hole states in a gated vertical quantum dot

We have experimentally investigated the hole states in a gated vertical strained Si/SiGe quantum dot. We demonstrate the inhomogeneous-strain relaxation on the lateral surface creates a ringlike potential near the perimeter of the dot, which can confine hole states exhibiting quantum ring characteristics. The magnetotunneling spectroscopy exhibits the predicted periodicity of energy states in phi/phi(0), but the magnitude of the energy shifts is larger than predicted by simple ring theory. Our results suggest a new way to fabricate and study quantum ring structures.     

Motion of a liquid droplet in a capillary under the action of static force and an acoustic field

We consider the motion of a liquid droplet inside a capillary of a porous medium under the action of a static force and an acoustic field. We derive the equation of motion of the droplet in the capillary and analyze numerically its solution. We show that the vibration attenuates the influence of the capillary force. Due to the effect of the acoustic field, the droplet motion in a capillary of constant cross-section starts at a lower value of the static force, and the reciprocal velocity of the droplet increases. Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 2, pp. 155–161, February 2000.     

TWO-DIMENSIONAL NUMERICAL SIMULATION OF LOW FREQUENCY OSCILLATIONS OF SPACE CHARGE AND POTENTIAL IN THE GYROTRON ADIABATIC TRAP

The development of oscillations of the space charge and potential in the adiabatic trap of a gyrotron between the cathode and the cavity is studied numerically. The PIC method is applied, with the real two-dimensional distributions of the electric and magnetic fields taken into account. Secondary emission is included into the numerical model, as well as such factors as the electron beam space charge, thermal velocities of electrons, and emitter roughness. The value of the trapped space charge as a function of time is calculated. Time dependences of the potential in various cross-sections of the formation system are traced. The amplitudes of its variable component have been found and then the corresponding frequency spectra have been calculated. The process of cathode bombardment is investigated. The energy distribution and time dependence of the current in the electron beam coming to the operating space are found. Some ways to reduce the oscillations of the potential and the space charge are discussed.     

Four (algorithms) in one (bag): an integrative framework of knowledge for teaching the standard algorithms of the basic arithmetic operations

In this article we present an integrative framework of knowledge for teaching the standard algorithms of the four basic arithmetic operations. The framework is based on a mathematical analysis of the algorithms, a connectionist perspective on teaching mathematics and an analogy with previous frameworks of knowledge for teaching arithmetic operations with rational numbers. In order to evaluate the potential applicability of the framework to task design, it was used for the design of mathematical learning tasks for teachers. The article includes examples of the tasks, their theoretical analysis, and empirical evidence of the sensitivity of the tasks to variations in teachers’ knowledge of the subject. This evidence is based on a study of 46 primary school teachers. The article concludes with remarks on the applicability of the framework to research and practice, highlighting its potential to encourage teaching the four algorithms with an emphasis on conceptual understanding.