Black-hole horizon and metric singularity at the brane separating two sliding superfluids

An analogue of a black hole can be realized in the low-temperature laboratory. The horizon can be constructed for “relativistic” ripplons (surface waves) living on the brane. The brane is represented by the interface between two superfluid liquids, ³He-A and ³He-B, sliding along each other without friction. A similar experimental arrangement was recently used for the observation and investigation of the Kelvin-Helmholtz type of instability in superfluids [1]. The shear-flow instability in superfluids is characterized by two critical velocities. The lowest threshold measured in recent experiments [1] corresponds to the appearance of the ergoregion for ripplons. In the modified geometry, this will give rise to the black-hole event horizon in the effective metric experienced by ripplons. In the region behind the horizon, the brane vacuum is unstable due to interaction with the higher-dimensional world of bulk superfluids. The time of the development of instability can be made very long at low temperature. This will allow us to reach and investigate the second critical velocity—the proper Kelvin-Helmholtz instability threshold. The latter corresponds to the singularity inside the black hole, where the determinant of the effective metric becomes infinite.     

The study of the weibel electromagnetic instability growth rate in the presence of the body stress

Body stress flow can be expected in the fast ignition imploding of the inertial fusion process that strongly damps small‐scale velocity structures. The Weibel instability is one of the plasma instabilities that require anisotropy in the distribution function. The body stress effect was neglected in the calculation of the Weibel instability growth rate. In this article, the propagation condition of impinging waves and the growing modes of the Weibel instability on the plasma density gradient of the fuel fusion with the body stress flow are investigated. Calculations show that the minimum value of the body stress rate threshold in the linear polarization is about 2.96 times greater than that of the circular polarization. Increasing 10 times of the density gradient and decreasing 2 times of the wavelength in the linear polarization and the circular polarization, respectively, lead to about 1.78 × 10⁶ times increment and 0.019 times decrement in the maximum of the Weibel instability growth rate. Also, the Weibel instability growth rate maximum in the circular polarization is about 10⁷ times greater than that of the linear polarization. The body stress flow and the density gradient tend to stabilize the Weibel instability in the circular polarization and act as a destabilizing source in the linear polarization. Therefore, by increasing steps of the density gradient plasma near the relativistic electron beam‐emitting region, in the circular polarization, the Weibel instability occurs at a higher stress flow.     

On the Kelvin-Helmholtz instability in superfluids

The Kelvin-Helmholtz instability in superfluids is discussed on the basis of the first experimental observation of such an instability at the interface between superfluid ³He-A and superfluid ³He-B (R. Blaauwgeers, V. B. Eltsov, G. Eska et al., cond-mat/0111343). We discuss why the Kelvin-Helmholtz criterion, the Landau critical velocity for nucleation of ripplons, and the free-energy consideration all give different values for the instability threshold.     

Electron-nucleon interaction in quasi-free scattering: (II). Non-relativistic Hamiltonian through fourth order

The interaction of non-relativistic nucleons with relativistic electrons can be expressed by a Hamiltonian expanded in a power series of the recoil nucleon velocity. In this paper third- and fourth-order terms are calculated. Free electron-nucleon-scattering and quasi-free electron scattering on ¹²C are studied and results through various orders are compared with the relativistic formulae. A different off-shell behaviour of the relativistic approach is found, which is independent of the higher-order terms and seems responsible for the different results of knock-out reactions.     

Relationships between a roller and a dynamic pressure distribution in circular hydraulic jumps

We investigated numerically the relation between a roller and the pressure distribution to clarify the dynamics of the roller in circular hydraulic jumps. We found that a roller which characterizes a type II jump is associated with two high pressure regions after the jump, while a type I jump (without the roller) is associated with only one high pressure region. Our numerical results show that building up an appropriate pressure field is essential for a roller.     

Ideal hydrodynamics outside and inside a black hole: Hamiltonian description in Painlevé-Gullstrand coordinates

We show that when the Painlevé-Gullstrand coordinates are used in their Cartesian version, the Hamiltonian of relativistic ideal hydrodynamics in the vicinity of a nonrotating black hole differs by only one simple term from the corresponding Hamiltonian in a flat spacetime. The interior region of the black hole is also described in a unified way, because there is no singularity on the event horizon in Painlevé-Gullstrand coordinates. We present the exact solution describing the steady accretion of extremely hard matter (? ∝ n ²) onto a moving black hole up to the central singularity. In the local induction approximation, we derive the equation of motion for a thin vortex filament against the background of such an accretion flow. We explicitly calculate the Hamiltonian for a fluid with an ultrarelativistic equation of state, ? ∝ n ^4/3, and solve the problem of a centrally symmetric steady flow of such matter.     

A relativistic correction to semiclassical charmonium

It is shown that the relativistic linear potentials, introduced by the author within the particle à la Wheeler-Feynman direct-interaction (AAD) theory, applied to the semiclassically quantized charmonium, yield energy spectrum comparable to that of some known models. Using the expansion of the relativistic linear AAD potentials in powers ofc ^–1, the charmonium spectrum, given as a rule by Bohr-Sommerfeld quantization of circular orbits, is extended up to the second order of relativistic corrections.     

Relativistic palladium electronic structure

We report here an “ab initio” relativistic KKR⁽¹⁾ electronic structure calculation for Pd metal in the fcc phase. The energies were evaluated in 89 points in the 1/48 wedge of the Brillouin Zone. The present results are in agreement with those obtained by Mueller et al⁽²⁾ who treated the spin-orbit coupling as the principal relativistic effect. As it is explained below we have solved the full Dirac equation in the interior of the “muffin-tin” spheres. At the same time we have made use of the symmetry in order to reduce the calculation time. The relativistic version of the KKR method has proved to be a very efficient tool for investigating the band structure since energies are calculated by solving very small secular determinants.     

A theoretical prediction of rotating waves in Type-I hydraulic jumps

The rotation of polygons in a Type-II hydraulic jump prompts us to look for a rotational feature in the Type-I hydraulic jump. Coupling the radial and azimuthal flows breaks the azimuthal symmetry of the shallow-water circular jump. An unstable rotating wave along the circumference of the jump is possible with a kinematic viscosity of very small order, whose upper threshold value is less than the kinematic viscosity of water.     

Some problems in relativistic thermodynamics

The relativistic equations of state for ideal and real gases, as well as for various interface regions, have been derived. These dependences help to eliminate some controversies in the relativistic thermodynamics based on the special theory of relativity. It is shown, in particular, that the temperature of system whose velocity tends to the velocity of light in vacuum varies in accordance with the Ott law T = T ₀/√1 ? v ²/c ². Relativistic dependences for heat and mass transfer, for Ohm’s law, and for a viscous flow of a liquid have also been derived.     

Dissipation of ripplon flow at the surface of superfluid <Superscript>4</Superscript>He

Within the framework of quantum hydrodynamics of a superfluid helium surface, the momentum relaxation rate caused by the annihilation of two ripplons with phonon creation, inelastic phonon scattering with ripplon annihilation, and in the case of helium films one-particle ripplon scattering from the surface-level inhomogeneities introduced by the substrate roughness (new relaxation mechanism) was obtained for a ripplon gas at T?0.25 K. The contribution from the inelastic phonon scattering is negligible at these temperatures. For a film at T≤0.15 K, one-particle scattering dominates, leading to a temperature dependence of the form K∝T^5/3 for the convective thermal conductance.At higher temperatures, phonon creation with annihilation of two ripplons is the dominant mechanism, giving K∝T^?3. These results are in quantitative agreement with the available experimental data.     

用负温度高能离子束的相对论多普勒效应实现从红外到X射线连续调谐激光器

利用负温度高能离子束的相对论多普勒效应,可能实现从红外到X射线连续调谐激光器。调谐范围△ν_T=2ν₀βγ。离子束从零到c调速时,激光频率为0—∞。本文给出了激光参数的相对论变换式,计算了负温度相对论离子束激光器的增益、阈值和输出特性,提出了用激光束对相对论离子束进行共振激发的方法,并讨论了He⁺离子束及Ar⁺离子束激光器的设计参数。 关键词：     

Reentrant violation of special relativity in the low-energy corner

In the effective relativistic quantum field theories, the energy region in which special relativity holds can be sandwiched from both the high-and low-energy sides by domains where special relativity is violated. An example is provided by ³He-A, where the relativistic quantum field theory emerges as the effective theory. The reentrant violation of special relativity in the ultralow-energy corner is accompanied by the redistribution of the momentum-space topological charges among the fermionic flavors. At this ultralow energy, an exotic massless fermion with topological charge N ₃=2 arises whose energy spectrum mixes classical and relativistic behaviors. This effect can lead to neutrino oscillations, if neutrino flavors are still massless on this energy scale.     

Drift theory of charged-particle motion for a strong electric field in a weakly relativistic approximation

Drift equations of motion are derived for a charged particle in the case of a strong electric field with allowance for relativistic effects of order v²/c². The role of these effects is discussed along with the effects of a high-frequency field. The cases of weak and strong electric fields are distinguished [2] in the drift theory of the motion of charged particles in weakly inhomogeneous magnetic and electric fields. In the case of a weak electric field, the electric-drift velocity is v_E v, where v is the characteristic velocity of the particle. For a strong electric field,v _Ev.The drift theory has now been reasonably well developed for the case of weak electric fields in the classical and relativistic cases, for the absence of high-frequency fields and for the presence of these [1–3], Extension of the theory to strong electric fields involves considerable mathematical difficulties, and this has been done only in the classical approximation with and without hf fields [2–4], Here we consider the drift theory of charged-particle motion for the case of a strong electric field in the weakly relativistic approximation, incorporating terms of order v²/c², where c is the velocity of light. Also hf fields may be present.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 7–9, September, 1981.     

Laser-induced fluorescence measurements of velocity within a Hall discharge

The results of a study of laser-induced fluorescence velocimetry of neutral and singly ionized xenon in the plume and interior portions of the acceleration channel of a Hall thruster plasma discharge operating at powers ranging from 250 to 725 W are described. Axial ion and neutral velocity profiles for four discharge voltage conditions (100 V, 160 V, 200 V, 250 V) are measured as are radial ion velocity profiles in the near-field plume. Ion velocity measurements of axial velocity both inside and outside the thruster as well as radial velocity measurements outside the thruster are performed using laser-induced fluorescence with nonresonant signal detection on the xenon ion 5d[4]_7/2–6p[3]_5/2 excitation transition while monitoring the signal from the 6s[2]_3/2–6p[3]_5/2transition. Neutral axial velocity measurements are similarly performed in the interior of the Hall thruster using the 6s[3/2]⁰ ₂–6p[3/2]₂transition with resonance fluorescence collection. Optical access to the interior of the Hall thruster is provided by a 1-mm-wide axial slot in the insulator outer wall. While the majority of the ion velocity measurements used partially saturated fluorescence to improve the signal-to-noise ratio, one radial trace of the ion transition was taken in the linear fluorescence region and yields a xenon ion translational temperature between 400 and 800 K at a location 13 mm into the plume. Received: 27 September 2000 / Revised version: 2 March 2001 / Published online: 9 May 2001     

Exact inclusion of the Coulomb field in the photobeta decay of a nucleus and problem of bypassed elements

The probability of the endothermic β^? decay of nuclei that is stimulated by an electromagnetic field of Planck frequency spectrum (photobeta decay) is calculated, the effect of the Coulomb field on a relativistic electron and a virtual relativistic positron being exactly taken into account in this calculation. It is shown that the inclusion of Coulomb effects is of paramount importance and that the results of the calculations may differ by an order of magnitude from those that were obtained previously in the plane-wave approximation, depending on the energy range being considered. A model for the synthesis of bypassed elements in the interior of massive stars is proposed on the basis of the mechanism of the photobeta decay of stable elements that originate from s and r processes.     

Fermi Acceleration in driven relativistic billiards

We show numerical experiments of driven billiards using special relativity. We have the remarkable fact that for the relativistic driven circular and annular concentric billiards, depending on initial conditions and parameters, we observe Fermi Acceleration, absent in the Newtonian case. The velocity for these cases tends to the speed of light very quickly. We find that for the annular eccentric billiard the initial velocity grows for a much longer time than the concentric annular billiard until it asymptotically reach c.     

原子内壳层双光子衰变的相对论效应和屏蔽效应

本文系统地计算了H原子,类H-Xe离子及Xe原子内壳层的双光子衰变速率。阐明其相对论效应和电子屏蔽效应。并与最新的实验结果和他人的理论计算结果进行了比较和分析讨论。 关键词：     

Shock modon: a new type of coherent structure in rotating shallow water

We show that a new type of coherent structure, a shock modon, exists in a rotating shallow water model at large Rossby numbers. It is a combination of an asymmetric vortex dipole with a stationary hydraulic jump. The structure is long living, despite the energy dissipation by the hydraulic jump, and moving along a circular path. Collisions of shock modons can be elastic, or lead to formation of shock tripoles.