Large Initial Velocity Research Articles

Erratum to: Global Wellposed Problem for the 3-D Incompressible Anisotropic Navier-Stokes Equations in an Anisotropic Space

In this paper, we consider a global wellposed problem for the 3-D incompressible anisotropic Navier-Stokes equations (ANS). We prove the global wellposedness for ANS provided the initial horizontal data are sufficient small in the scaling invariant Besov-Sobolev type space \({B^{0,\frac{1}{2}}}\) . In particular, the result implies the global wellposedness of ANS with large initial vertical velocity.

Approximate methods based on order reduction for the periodic solutions of nonlinear third-order ordinary differential equations

Four approximate methods based on order reduction, the introduction of a book-keeping parameter and power series expansions for the solution and the frequency of oscillation are used to analyze three autonomous, nonlinear, third-order ordinary differential equations which have analytical periodic solutions. The first method introduces the velocity in both sides of the equation if this (linear) term is not present. The second one is based on the first one but employs a new independent variable, whereas, in the third and fourth techniques, a term equal to the velocity times the square of the unknown frequency of oscillation is introduced in both sides of the equation. The third method uses the original independent variable, whereas the fourth one employs a new independent variable which depends linearly on the unknown frequency of oscillation. It is shown that the second method provides accurate solutions only for initial velocities close to unity, whereas the third one is found to yield very accurate results for the first and second equations considered here and only for large initial velocities for the third one. The fourth technique provides as accurate results as or more accurate results than parameter-perturbation techniques which deal with the third-order equations directly and are based on the expansion of certain constants that appear in the differential equations in terms of a book-keeping parameter.

Tribo-Charge of Diamond-Like Carbon (DLC) Contact at Slider Disk Interface and Tribo Current Flow Through Disk DLC

This paper reports an experimental investigation on tribo-charging of diamond-like carbon (DLC) at the slider-disk interface and tribo-current flow through disk DLC. Measurements of the tribo-current are in three regimes-slider flying and touch down during disk deceleration, slider dragging on disk surface, and slider takeoff and flying during disk acceleration. Comparisons are made for tribo-charge currents at different disk initial linear velocities. It is observed that the tribo-current appears earlier with larger amplitude for a disk with larger initial velocities. During disk constant velocity phase, tribo-current ripple was observed while the slider is dragging on the disk surface due to intermittent slider/disk interactions. Despite having the same constant velocity, the equilibrium level of the ripple is different and depends on the disk initial velocity. Additional tribo-voltage and acoustic emission measurements were performed and compared with the tribo-current measurement to provide more insight to the tribo-charging process.

Binary collisions of charged particles in a magnetic field

Binary collisions between charged particles in an external magnetic field are considered within a classical second-order perturbation theory, i.e., up to contributions which are quadratic in the binary interaction, starting from the unperturbed helical motion of the particles. The calculations are done with the help of an improved binary collisions treatment which is valid for any strength of the magnetic field, where the second-order energy and velocity transfers are represented in Fourier space for arbitrary interaction potentials. The energy transfer is explicitly calculated for a regularized and screened potential which is both of finite range and nonsingular at the origin, and which involves as limiting cases the Debye (i.e., screened) and Coulomb potential. Two distinct cases are considered in detail: (i) the collision of two identical (e.g., electron-electron) particles, and (ii) the collision between a magnetized electron and a uniformly moving heavy ion. The energy transfer involves all harmonics of the electron cyclotron motion. The validity of the perturbation treatment is evaluated by comparing with classical trajectory Monte Carlo calculations which also allows to investigate the strong collisions with large energy and velocity transfer at low velocities. For large initial velocities on the other hand, only small velocity transfers occur. There the nonperturbative numerical classical trajectory Monte Carlo results agree excellently with the predictions of the perturbative treatment.

Stochastic Acceleration in an Inhomogeneous Time Random Force Field

This paper studies the asymptotic behavior of a particle with large initial velocity and subject to a force field which is randomly time dependent and inhomogeneous in space. We analyze the diffusive limit � → 0 of the position‐velocity pair under the appropriate space‐time rescaling: (� 3 Y(s/� 2 ), � ˙ Y(s/� 2 )). Two alternative approaches are proposed. The first one is based on hydrodynamic limits and homogenization techniques for the underlying kinetic equation; the second one is based on homogenization of the random distribution of trajectories. Time randomness is embodied into an underlying Markov process. Space inhomogeneity is modeled by a periodic structure in the first approach, and by a random field in the second one. In the first case, the analysis relies on the dissipation properties of the Markov process, whereas in the second case, the mixing properties of the random field are used. We point out more analogies and differences of the two obtained results.

Analytical and approximate solutions to autonomous, nonlinear, third-order ordinary differential equations

Abstract Analytical solutions to autonomous, nonlinear, third-order nonlinear ordinary differential equations invariant under time and space reversals are first provided and illustrated graphically as functions of the coefficients that multiply the term linearly proportional to the velocity and nonlinear terms. These solutions are obtained by means of transformations and include periodic as well as non-periodic behavior. Then, five approximation methods are employed to determine approximate solutions to a nonlinear jerk equation which has an analytical periodic solution. Three of these approximate methods introduce a linear term proportional to the velocity and a book-keeping parameter and employ a Linstedt–Poincare technique; one of these techniques provides accurate frequencies of oscillation for all the values of the initial velocity, another one only for large initial velocities, and the last one only for initial velocities close to unity. The fourth and fifth techniques are based on the Galerkin procedure and the well-known two-level Picard’s iterative procedure applied in a global manner, respectively, and provide iterative/sequential approximations to both the solution and the frequency of oscillation.

High-speed collapse of a hollow sphere of type I matter

In this paper, we study the dynamics of a hollow spherical matter collapsing with a very large initial velocity. The spacetime is initially very similar to the Vaidya solution, and the deviations from this background are treated perturbatively. The equations of state for radial pressure pR = kρ and tangential one pT = wρ with constants k and w are assumed. We find for the case of equations of state k < 1 and 0 < w ⩽ 1 that the initial velocity, which is nearly the speed of light, is strongly decelerated. This result implies that the pressure is essential to the property of singularity formation in gravitational collapse even for initially nearly light-speed collapse. By contrast, in cases with the negative tangential pressure, the present result implies that the central naked singularity similar to that of the Vaidya spacetime can be formed, even though the radial pressure is positive, and the weak, strong and dominant energy conditions hold. Especially, in the case of w < −(1 − k)/4, the high-speed collapse will produce the spacetime structure very similar to that of the Vaidya spacetime.

Global Wellposed Problem for the 3-D Incompressible Anisotropic Navier-Stokes Equations in an Anisotropic Space

In this paper, we consider a global wellposed problem for the 3-D incompressible anisotropic Navier-Stokes equations (ANS). We prove the global wellposedness for ANS provided the initial horizontal data are sufficient small in the scaling invariant Besov-Sobolev type space \({B^{0,\frac{1}{2}}}\) . In particular, the result implies the global wellposedness of ANS with large initial vertical velocity.

Spectroscopy of low-energy atoms released from a solid noble-gas matrix: Proposal for a trap-loading technique

We have studied the velocity distribution of chromium atoms released from a solid neon matrix at cryogenic temperatures via Doppler spectroscopy. The Ne matrix is grown by directing a small flux of gas onto a cold substrate, while Cr atoms are simultaneously implanted by laser ablation, with the resultant plume directed toward the growing matrix. The atoms are then released by a heat pulse. We have observed neutral Cr atoms at temperatures around $13\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ with densities close to ${10}^{12}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. The released atoms have a large initial drift velocity, explained by simple kinetic theory arguments, due to the light species' drag force. The scheme could be adapted to produce cryogenic beams of atoms, molecules, and possibly ions, for collisional studies and spectroscopy. However, our main motivation was the construction of a hydrogen trap, and here we discuss the prospects and problems of using this technique for this purpose.

Multipactor in a coaxial transmission line. II. Particle-in-cell simulations

The effects of nonuniform radiofrequency fields are analyzed for a cylindrical coaxial transmission line using a particle-in-cell code. The behavior predicted by the analytical analysis is confirmed by this study. In addition, by including an initial velocity spread and different maximum secondary electron yields, a more elaborate analysis is performed. It is found that in the case of high secondary emission, an increase in the spread of initial velocities results in an overlapping of the multipactor zones for both double and single sided multipactor. In the other case, when the secondary emission is low, a large enough initial velocity spread can lead to total suppression of the electron avalanche for the higher order modes. Comparison with available experimental data shows good agreement.

Toy models: The jumping pendulum

We consider a simple pendulum consisting of a mass attached to an inextensible string of negligible mass. For small or large initial velocities, the motion of the pendulum is along a circle. When given sufficient but not too large an initial velocity, the mass will reach a certain height and leave the circle. After such a jump, it will follow a parabolic path until the string is again fully extended and the motion is again constrained by the string. We assume that the radial component (along the string) of the velocity of the mass instantaneously vanishes when the string becomes taut and that the mass loses some of its energy in the shock and resumes its circular motion. What is the dynamics of such a pendulum? Can it jump more than once? How many times can it jump?

FROM DISCRETE DETERMINISTIC DYNAMICS TO BROWNIAN MOTIONS

Two types of point particles, large and small, with state space ℝd are considered, where d ≥ 2 and "large" and "small" refer to different masses. The small particles move deterministically with very large initial velocities. They transfer their momenta to the large particles through a smooth mean field interaction which completely determines the motion of the large particles. The joint dynamics is described in a spacetime lattice by an Euler scheme for coupled oscillators with a friction term for the large particles. This lattice defines the mesoscale for the system. A scaling limit leads to a replacement of the mesoscale by the macroscale as follows: The very large initial velocities are assumed to be independent and they let a small particle interact with a large particle only for a short time, after which the particle escapes to infinity and new particles start interacting with the large particles. Thus, the initial spatial independence of the small particles causes independence in the time increments of the velocities of the large particles. Therefore, as the friction of the large particles and the speed of the small particles tend to infinity in this scaling limit, the positions of the large particles become the positions of spatially correlated Brownian motions whose correlations can be computed from the interaction force. A similar result holds for a system without friction, where the velocities of the large particles become spatially correlated Brownian motions.

Few-cycle relativistic solitons in plasmas

A set of exact one-dimensional solutions to coupled nonlinear equations describing the propagation of a relativistic ultrashort circularly polarized laser pulse in a cold collisionless and bounded plasma where electrons have an initial velocity in the laser propagating direction is presented. The solutions investigated here are in the form of quickly moving envelop solitons at a propagation velocity comparable to the light speed. The features of solitons in both underdense and overdense plasmas with electrons having different given initial velocities in the laser propagating direction are described. It is found that the amplitude of solitons is larger and soliton width shorter in plasmas where electrons have a larger initial velocity. In overdense plasmas, soliton duration is shorter, the amplitude higher than that in underdense plasmas where electrons have the same initial velocity.

Anomalous quantum diffusion over a saddle point and application to fusion of massive nuclei

Abstract The quantal diffusion of a particle with an initial velocity coupled to a non-Ohmic environment passing over a potential top is considered. It is shown that sub- and super-diffusions hinder the directional motion of the particle in two different ways. The former makes the particle have a strong memory to its initial position rather than initial velocity and the latter increases the randomness of motion. The quantum fluctuation helps the particle with a small initial velocity to cross the saddle point, however, it is harmful to the directional motion of the particle with a large initial velocity. The present model is applied to calculate the fusion probability of massive nuclei and the fusion probability curve increases slowly with the center-of-mass energy. This is in agreement with the experimental fact.

Understanding B-type supergiants in the low metallicity environment of the SMC

Spectroscopic analyses of 7 SMC B-type supergiants and 1 giant have been undertaken using high resolution optical data obtained on the VLT with UVES. FASTWIND, a non-LTE, spherical, line-blanketed model atmosphere code was used to derive atmospheric and wind parameters of these stars as well as their absolute abundances. Mass-loss rates, derived from H α profiles, are in poor agreement with metallicity dependent theoretical predictions. Indeed the wind-momenta of the SMC stars appear to be in good agreement with the wind-momentum luminosity relationship (WLR) of Galactic B-type stars, a puzzling result given that line-driven wind theory predicts a metallicity dependence. However the galactic stars were analysed using unblanketed model atmospheres which may mask any dependence on metallicity. A mean nitrogen enhancement of a factor of 14 is observed in the supergiants whilst only an enrichment of a factor of 4 is present in the giant, AV216. Similar excesses in nitrogen are observed in O-type dwarfs and supergiants in the same mass range, suggesting that the additional nitrogen is produced while the stars are still on the main-sequence. These nitrogen enrichments can be reproduced by current stellar evolution models, which include rotationally induced mixing, only if large initial rotational velocities of 300 km s -1 are invoked. Such large rotational velocities appear to be inconsistent with observed ν sin i distributions for O-type stars and B-type supergiants, Hence it is suggested that the currently available stellar evolution models require more efficient mixing for lower rotational velocities.

The influence of terrestrial processes on meteorite magnetic records

In early solar system history there are several electromagnetic processes (electric discharges, pressure shock waves, electric discharges and currents) capable of magnetizing the primitive solid particles condensating from the solar nebula. The record of these magnetic events is the main objective of rock magnetic laboratory studies of meteorites found on the Earth. However, terrestrial environment can affect the magneto-mineralogy, can cause changes in magnetic parameters and can overprint the primary magnetic record. The entry of a meteorite into the terrestrial atmosphere causes surface heating and pressure effects due to large initial velocity. The effect of surface heating was the subject of the study with the CM2 Murchison meteorite. Results show the remagnetised zone to be at least 6 mm thick. On CM3, Allende meteorite we studied an effect of pressure during the atmospheric entry. According to our results the pressure does not seem to be a source responsible for meteorite remagnetization. Some meteorites are found several days after the fall, some are deposited in a desert or on the Antarctic ice for thousands of years. Most of them contain visible traces of terrestrial oxidation and weathering. We used the sample of an L6 chondrite DaG 979 found in the Libya desert, sample of the iron meteorite Campo del Cielo (found in Argentina 5000 years after the fall), and sample of the H5 Zebrak meteorite (found several days after the fall) for weathering simulations. Weathering plays an important role in the meteorite terrestrial history and is capable of complete remagnetization of the meteoritic material. To document the terrestrial processes that influence meteorite magnetism we monitored changes in magnetic remanence and magnetic hysteresis parameters. Our results indicate that the terrestrial processes are capable of changing magnetic properties and can overprint the primary magnetic record. Therefore, an extreme care is required when selecting the meteorite samples for primary magnetic component study.

Density-dependent incompressible viscous fluids in critical spaces

We study the unique solvability of density-dependent incompressible Navier-Stokes equations in the whole space RN (N ≥ 2). The celebrated results by Fujita and Kato devoted to the constant density case are generalized to the case when the initial density is close to a constant: we find local well posedness for large initial velocity, and global well posedness for initial velocity small with respect to the viscosity. Our functional setting is very close to the one used by Fujita and Kato.

Moon‐related nonthermal ions observed by Nozomi: Species, sources, and generation mechanisms

The 3‐D velocity distribution functions of nonthermal ions observed in the vicinity of the Moon have been analyzed to understand the interaction between the solar wind and the Moon. The observation was made during the lunar swing‐by of the Nozomi spacecraft, and the closest approach was about 1.6 RL from the Moon's surface. Both Nozomi and the Moon were located in the solar wind, and nonthermal ions were observed only when the spacecraft was very close to the Moon. The nonthermal ions were measured by a Particle Spectrum Analyzer/Ion Spectrum Analyzer (PSA/ISA) on board the Nozomi. After analyses and careful examination of the 3‐D velocity distribution of the nonthermal ions, the characteristics of the nonthermal ions were revealed as follows: The nonthermal ions have a partial ring structure in the phase space, they are protons, their source location is the dayside of the Moon, and they have large velocities when they are generated. We propose the following scenario of a solar wind interaction with the Moon: The electromagnetic field in the vicinity of the Moon must have a dynamic structure, possibly a miniature bow shock associated with a local magnetic anomaly, where some of the solar wind protons are deflected violating their first adiabatic invariant. After the deflection, they move under the force of the convection electric field and gyrate around the magnetic field in the solar wind. This motion forms a partial ring structure with large initial velocities in the velocity phase space.

Edge imaging in intense beams

The appearance of rings of charge observed near the edge of beams from high-perveance guns is described with a simple ray tracing technique inspired by the particle-core model. We illustrate the technique, which has no analog in light optics, with examples from experiments employing solenoid focusing of an electron beam. The rings of charge result from the combined effects of external focusing and space-charge forces acting on paraxial fringe particles with relatively large initial transverse velocities. The model is independent of the physical mechanisms responsible for the fringe particles. Furthermore, the focal length for edge imaging in a uniform focusing channel is derived using a linearized trajectory equation for the motion of fringe particles. Counterintuitively, the focal length decreases as the beam current increases.

Analysis of the motion of a flat jet in a direct strip casting feeding system

The motion and shape of a vertically falling flat rectangular jet of liquid metal issuing from an inclined plane is analysed numerically and analytically. The jet is affected by surface tension and gravity. The main interest in this problem originates from the technological application of the direct strip casting process, which is a novel process to cast steel strips in a thickness range from 2 to 15 mm with a minimum or no hot‐rolling. In this process the liquid metal is fed onto a single endless horizontal belt that runs between two rollers. The bottom of the belt is cooled by water. One of the techniques to feed the liquid metal is down an inclined plane. Due to disturbances in the flow, for instance slag in the liquid metal, the jet issuing from the inclined plane may split into two or several jets. The large convergence of the individual jets causes an unfavourable non uniform distribution of the liquid metal over the belt.In the analysis of the present paper it is shown, using an expansion in the inverse Froude number, that the convergence of a single jet depends to zero order on the inverse square root of the Weber number We−1/2 = (γl(ρw02 h0))1/2. Small convergence of the jet is found for large Weber numbers, which can be accomplished with a large initial velocity w0.