High-Speed Scattering of Charged and Uncharged Particles in General Relativity

After a brief consideration of the high-speed scattering of two point charges we thoroughly discuss high-speed scattering for a charged particle by a fixed mass and of two uncharged particles of comparable masses. We use perturbation technique over Minkowski spacetime in the de Donder gauge and solve the field equations and the resulting equations of motion (which take the reaction of the particles' quasistatic self-field into account) by iteration. The obtained energy-momentum conservation laws allow the computation of second-order corrections for the scattering angle and the cross section. The asymptotic structure of the far-field indicates synchrotron radiation (electromagnetic and gravitational, respectively) which causes an energy loss whose reaction on the motion is briefly considered in the low-velocity limit including bound motion. (For neutral particles this is a third-order effect).     

Effect of electron-neutral collisions on the satellites of the Thomson scattering spectrum in arc plasmas

The effect of electron-neutral collisions on the high frequency spectrum of laser radiation scattered by the free electrons of a plasma is investigated for a partially ionized H₂ are plasma at atmospheric pressure. The calculations are carried out along Gorog's theory solving the linearized Boltzmann equation for electrons with a collision term. The collision integral is approximated by a Krook relaxation model with the collision frequency determined from experimental electron-atom scattering data. The collisions influence size, half width, and position of the high frequency satellites. In a H₂ arc plasma, the change of the satellites' position is negligible as well as the change in half width within experimentally attainable error limits. The change of size is of minor importance, since the general evaluation procedure uses only normalized scattering intensities. Thus, for laser scattering experiments in are plasmas the collision-free theory can be applied.     

On Rosen's bi-metric theory of gravitation

The field equations of Rosen's bi-metric theory of gravitation [1] are solved exactly. The solutions are the same as in the author's theory of gravitation [2]. These solutions are, however, incompatible with Rosen's conservation laws and his second (flat) metric. Incompatibility with the conservation laws arises in second order. Incompatibility with the flat metric arises in first order but only for time-dependent fields. Rosen's theory is defensible only as a static first order theory and predicts the red shift light deflection and time-delay correctly.     

激波风洞设施中的等离子体包覆目标电磁散射实验研究

利用JF10高焓激波风洞设施, 进行了等离子鞘包覆目标的电磁散射测量实验. 基于矢量网络仪的步进扫频体制, 在C波段进行实验, 观测到等离子鞘对目标雷达散射截面(radar cross section, RCS)的影响. 并且, 目标散射测量值中直接体现了激波风洞的高速气流状态信息: 气流前段会造成散射回波的剧烈变化且稳定性差, 持续0.5–1 ms; 激发的等离子鞘有效持续时间仅约为2 ms, 衰减了目标RCS回波.     

Scattering off of an instanton

We consider the scattering of a classical colored particle off an instanton. That is, we investigate Wong's equations (or equivalently, the Kaluza-Klein geodesic equations) for a colorSU(2) particle under the influence of a Euclidean instanton. We solve the equations in the limit in which the instanton becomes singular. Our main result is that particles with head-on trajectories scatter off the instanton with a scattering angle of π/3. This angle is independent of the magnitude of the color charge and velocity of the particle as long as both are nonzero. The plane in which the scattering takes place is determined by the particle's initial position and color charge. We also solve for the geodesics for the corresponding (singular) Kaluza-Klein metric onS ⁷.     

Theory of electron-electron interaction and superconductivity in dilute magnetic alloys above the Kondo temperature

The effective electron-electron interaction resulting from the virtual polarization of the impurity spin is investigated. Abrikosov's pseudofermion representation of spin operators has been applied. It is pointed out that the effective electron-electron interaction consists of two parts: 1) elastic scattering; 2) inelastic scattering. The second part shows a singularity of new type as (ω-ω′)^?1, whereω-ω′ is the energy transfer between the two electrons. Both parts have been calculated in logarithmic approximation. Inspite of the fact that the second one is found to be lower by one order of the typical logarithmic Kondo terms than the first one, both terms can be of the same order of magnitude. Studying the superconducting transition temperature Abrikosov and Gor'kov's calculation is extended to include these interactions in any order of perturbation theory keeping the leading logarithmic terms. Our results are restricted to the temperature region well above the Kondo temperature. Considering the decrease of the superconducting transition temperature due to the magnetic impurities in the antiferromagnetic case the effect of the elastic scattering can be essentially reduced by the inelastic one.     

Rotating bodies in general relativity

Synge's approximation method is used in order to obtain the gravitational field of a massive body with an axis of symmetry around which it is rotating steadily. The method is carried out to include the second approximation. This means that terms of orderm ² are retained as significant, and there is an error of orderm ³ in the field equations,m being the mass of the body.     

Planck's Orders of Magnitude and the Limits of the Quantum Gravity Conception

Considering gravitational Euler scattering and energy fluctuations of gravitational Planck radiation it is shown that - due to the nonlinearity of Einstein's equations - there arise effective cut-of lengths preventing the measurability of quantum vacuum effects near Planck's length.     

Compton 散射对线偏光在相对论等离子体中调制不稳定性的影响

应用多光子非线性Compton 散射模型、电磁波非线性色散方程和Karpman 方法,研究了 Compton 散射对线偏光在相对论等离子体中调制不稳定性的影响,给出了等离子体的非线性色散、控制和调制不稳定性增 长率的修正方程,并进行了数值模拟。结果表明：与散射前相比,随无量纲化频率值减小,即趋于等离子体临界面处,散射使相同扰动波数引起的调制不稳定性增长率更大,使等离子体临界面处的调制不稳定性增长率较其余位置尤为显著。这是由于散射光使等离子体非线性增强,形成了激光场自聚焦和自成丝的缘故。     

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By using the model of multi-photon nonlinear Compton scattering, the nonlinear dispersion relation and Karpman’s model, the influences of the modulation instability on Compton scattering to the linear polarized light in relativistic plasma were studied, the revised equations on the nonlinear dispersion, the control and the growth rate of the modulation instability were given out, and these equations are simulated. The results show that under the same perturbation wave numbers, the even big rate of the modulation instability near the plasma surface are taken place by Compton scattering along with the decreasing of the numbers of the no gauge frequency than before Compton scattering, and the even marked growth rate of the modulation instability near the plasma surface are taken place near the plasma surface than other places. Because the plasma nonlinear is increased by the scattering, the self-focusing and self-turned fine silk are formed.     

Multi-kHz mixture fraction imaging in turbulent jets using planar Rayleigh scattering

In this study, we describe the development of two-dimensional, high repetition-rate (10-kHz) Rayleigh scattering imaging as applied to turbulent flows. In particular, we report what we believe to be the first sets of high-speed 2D Rayleigh scattering images in turbulent non-reacting jets, yielding temporally correlated image sequences of the instantaneous mixture fraction field. Results are presented for turbulent jets of propane issuing into a low-speed co-flow of air at jet-exit Reynolds numbers of 10,000, 15,000, and 30,000 at various axial positions downstream of the jet exit. The quantitative high-speed mixture fraction measurements are facilitated by the use of a calibrated, un-intensified, high-resolution CMOS camera in conjunction with a unique high-energy, high-repetition rate pulse-burst laser system (PBLS) at Ohio State, which yields output energies of ∼200 mJ/pulse at 532 nm with 100-μs laser pulse spacing. The quality, accuracy, and resolution of the imaging system and the resulting image sets are assessed by (1) comparing the mean mixture fraction results to known scaling laws for turbulent jets, (2) comparing instantaneous images/mixture fraction profiles acquired simultaneously with the high-speed CMOS camera and a well-characterized, high-quantum efficiency CCD camera, and (3) comparing statistical quantities such as the probability density function of the mixture fraction results using the high-speed CMOS camera and the CCD camera. Results indicate accurate mixture fraction measurements and a high potential for accurately measuring mixture fraction gradients in both time and space.     

Depolarized light scattering,flow birefringence and local order in molecular liquids

We propose a generalization of De Gennes' theory of flow birefringence [3] to the case of two distinct local anisotropy variables and also some extensions to the existing three variable theories of light scattering spectra. We show that the application of the theories with one or with two local anisotropy variables to analyse flow birefringence and light scattering spectra give numerically different results. We also show that it is possible to determinewhether the second local anisotropy variable is a primary or a secondary variable.

The VH and HH light scattering spectra of a number of symmetric top molecules are analysed. They show an unambiguous ‘shear mode coupling’ down to very small values of (q ²η/ρΦ). These results are discussed and compared to flow birefringence experiments in the light of our theoretical considerations. The three variable correction is shown to be small and within experimental error for all liquids studied except one (pyridine). The flow birefringence coefficient for CCl₄ is measured and found to be negative as predicted by our theory. Limitations to the formalism of generalized hydrodynamics are also discussed briefly.     

Electromagnetic and Force Field Equations

In classical physics the electromagnetic equations are described by Maxwell's equations. Maxwell's equations proved to be invariant under gauge, or Lorentz transformations. Also, Einstein's equations of the special theory of relativity are invariant under Lorentz transformations. On the other hand classical mechanics and quantum mechanics laws are invariant under Galilean transformations. This means that, there are two different dynamical structures describing our universe. Einstein's unified field theory failled in putting our universe in one dynamical structure. New electromagnetic and force field equations are going to be derived. They have the same shape like Maxwell's equations, but with different dynamical structure. Those equations are invariant under Galilean transformations and in the density matrix formalism of quantum mechanics.     

Coulomb forces in the three-body problem with application to direct nuclear reactions

Faddeev equations are considered in the case of three charged particles interacting with both separable nuclear two-body interactions and also including Coulomb forces. Modified Faddeev equations with Coulomb Green's functions are introduced. The three-body amplitudes are given into pure Coulomb and distorted-Coulomb amplitudes. Introducing a decomposition in the angular momentum states, a set of three-body integral equations is obtained. The effect of pure coulomb amplitudes is studied in direct nuclear reactions and found to give a large contribution to the cross sections. The three-body integral equations obtained are applied for direct nuclear reactions. The angular distributions for¹²C(⁶Li,d)¹⁶O,¹⁶O(⁶Li,d)²⁰Ne, and¹²C(⁶Li,α)¹⁴N transfer reactions are calculated as well as for the⁶Li elastic scattering on¹²C. From the good agreement between the theoretically calculated and experimental data, better spectroscopic factors are extracted. The effect of including Coulomb forces in the three-body problem is found to improve the results by about 16.26%.     

Foundations of the unified theory of gravitational,electromagnetic, and scalar fields

A particular case of bimetrical unified field theory is considered, which is based on Hilbert's proposal of obtaining a complete system of independent equations for unified theory. The action depends on two symmetrical tensors g_μν and g _μν ^° , the second leading to a zero curvature tensor, which results in the theory being invariant under the Poincaré group, and in ten conservation laws. The field equations obtained when varying the action with respect to g_μν have the form of Einstein equations whose righthand side is not defined independently, but is rather a function of g_μν and g _μν ^° . The vector and scalar gauge transformations corresponding to variations δS of special form are defined. With the aid of these transformations, the electromagnetic and scalar fields are introduced within the framework of the unified theory. The basic equations of the theory under consideration contain a new dimensional physical constant, which connects gravitation and electromagnetism. A numerical estimate of this constant is given.     

Simultaneous high-speed planar imaging of mixture fraction and velocity using a burst-mode laser

Simultaneous high-speed quantitative imaging of mixture fraction and velocity is demonstrated using the fourth- and second-harmonic outputs, respectively, of a burst-mode Nd:YAG laser. A tenfold increase in the record length and 16-fold increase in per-pulse energy are achieved compared with previous measurements of mixture fraction using burst-mode and continuously pulsed diode-pumped solid-state lasers, respectively. The high output energy is used for quantitative, high-speed mixture-fraction imaging with acetone planar laser-induced fluorescence, which also enables simultaneous particle-based velocimetry without interference from particle scattering. A semiquantitative model is used to determine the limitations on fourth-harmonic output energy due to the effects of transient absorption and thermal phase mismatch over a range of repetition rates. Data are presented for mixing within a turbulent jet (Reynolds number of 15,000) and are validated by comparisons with known turbulent mixing laws and previously published data.     

Hydrodynamic analogies between the equations of classical hydrodynamics and electrodynamics in electrochemistry

It is shown that the use of equations of hydrodynamics of an incompressible and compressible fluid gives similar results for a number of experimental data from the field of classical electrodynamics used in electrochemistry. The analogue of electric current in wires is a stream that creates around itself a flow of a fluid. The analogue of electric field is the acceleration of a flow, whereas the analogue of magnetic induction is the frequency of a rotational motion of the fluid. Ampere’s law in hydrodynamics describes the interaction of flows with real bodies in terms of the Zhukovsky equation. The power laws in the fluid are similar, with some distinctions, to Maxwell equations. The expansion of the equations of conservation of momentum and mass in a series in perturbations leads to wave equations also similar to the Maxwell equations for the propagation of electromagnetic waves.     

CONSERVATION LAWS FOR HEATED LAMINAR RADIAL LIQUID AND FREE JETS

The conserved quantities for the heated radial liquid jet and the heated radial free jet are established by using conservation laws. The flow in a heated radial jet is described by Prandtl's momentum boundary layer equation, the continuity equation and the energy equation. Viscous dissipation is neglected. The multiplier approach is used to derive the conservation laws for the system of three equations for the velocity components and the temperature and three conserved vectors are obtained. The conservation laws for the system of two partial differential equations for the stream function formulation are also computed by the multiplier approach and three conserved vectors are obtained. One of these is a non-local conserved vector for the system. The conserved quantities for the heated radial liquid jet and the heated radial free jet, emitted into a stationary fluid of uniform temperature θ_∞, are derived by integrating the conservation laws across the jet.     

Calculation of the imaginary part of the nucleon-nucleus optical-model potential

The imaginary part of the optical-model potential for the scattering of nucleons by nuclei is studied in the frame of the shell-model approach to nuclear reactions. Special attention is paid to the one-hole target nuclei. The imaginary part of the optical-model potential in the second order in the nucleon-nucleus interaction is divided into two parts. The first corresponds to the average resonant scattering. The second corresponds to the inelastic scattering leading to the non-collective states of the target nuclei. A local potential equivalent to the non-local theoretical one is constructed in order to facilitate comparison with experiment. Numerical calculations concern the scattering of 14.5 MeV protons by ³⁹K. It is found that the imaginary part depends upon the angular momentum and that its radial variation is governed by strong shell effects. The predicted absorption is approximately 60% of the experimental one. The average resonant scattering contributes to the imaginary part of the optical-model potential as much as the inelastic non-collective excitations of the target.