Über ein weiteres Variationsprinzip im Zusammenhang mit kraftfreien Magnetfeldern

Im Anschluß an ein von Woltjer [1] diskutiertes Variationsproblem wird gezeigt: Die Euler-Lagrange-Gleichungen des Variationsproblems mit der Nebenbedingung wo H = rot A gesetzt ist, sind die Differentialgleichungen der kraftfreien Magnetfelder mit variablem α. Die Nebenbedingung läßt sich für alle Felder H erfüllen, die keinen singulären Punkt mit H = 0 in dem betrachteten Volumen V haben. In persuance of a variational principle discussed by Woltjer [1] it is shown that the Euler-Lagrange-equations of the variational problem with the secondary condition where H = rot A are the differential equations of the force-free magnetic fields with a variable scalar α. The secondary condition can be accomplished for all magnetic fields which do not contain singular points with H = 0 in the volume V under consideration.     

Parametric Excitation of Electron-Acoustic Mode in a Plasma of Two-Temperature Electrons

Using hydrodynamical model of the two-electron-temperatere plasma, the analytical investigation of parametric instability of electron-acoustic wave has been made. It is found that the growth rate decreases with increasing concentration ratio of the hot to the total electrons n_h0/n₀. The growth rate is found to be more for      

Zur O2-Dissoziation in der Gleichstromglimmentladung. Teil I Bestimmung des Dissoziationsgrades mittels der O3-Bildung an gekühlten Oberflächen

The synthesis of ozone on the surface S cooled with liquid nitrogen O + O₂·S→O₃·S[1] was used to measure the concentration of atoms in a flow tube downstream of a d.c. discharge. The flow tube was constructed in the form of a U-tube. The ozone was deposited as a blue liquid film in the neighbourhood of the surface of the liquid nitrogen on the walls of the part of the U-tube, which was connected with the discharge tube. The oxygen atom decay in the U-tube was observed by measuring the production of ozone as the distance between the discharge tube (diameter: 5,2 cm) and the surface of the liquid nitrogen was varied. The decay is first order in atom concentration for the pressures p > 1 torr. But for the pressures below p = 1 torr near by the discharge tube we observed deviations from the law of decay In [O]₀/[O] = k·t for the currents of about i = 100 mA. This effect was attributed to the process From the extrapolation of an ozone production curve atom concentrations in the discharge have been obtained. The transition from the ?H”? form to the ?T”? form (striated, low average electric field) of the discharge [2] caused the dissociation to decrease rapidly. The highest dissociation (10%) was obtained in the ?H”? form at high currents (i = 120 mA) and low pressures (p = 0,60 torr). The yield of atomic oxygen per kilowatt hour of energy was measured as functions of pressure and gas flow rate for i = 100 mA and i = 50 mA.     

The Thermo-Field Emission of Electrons in Arc Discharges

Starting from the conventional theory of thermo-field emission of electrons from metal surfaces, the range of validity and the errors of several approximate emission formulae are examined that are additive or harmonic combinations of the limiting thermionic (Richardson) and field emission (Fowler—Nordheim) equations. An optimization of such kinds of equations results in the simple dependence (for example) (iTF electron current density, T temperature, F field strength, k, A, B etc. are constants), or (dependent on only one variable Y = T + β′F β′ = const.). If the emission equations are applied to arc cathodes, both T and F must be expressed as functions of the ion current (I_i) and the ion current density (j_i); a simple interpolating formula of the electron current density j_e adapted to numerical results in the case of Cu cathodes becomes (ā, B?, C?: constants).     

Über stationäre,rotierende, inkompressible Plasmen mit minimalen inneren Verlusten

The condition that the Ohmic and the friction losses are minimized leads to the assumption that both the magnetic field H and the velocity field v are Trkal-fields. . In the rotationally symmetric, stationary case the boundary conditions and the condition that the toroidal part of v and H should vanish on the boundary, lead to a linear eigenvalue problem for α, β which in case of a rectangular domain easily can be resolved. It follows: .     

Die Zurückführung der Gleichungen eines rotationssymetrischen,statischen, inkompressiblen Plasmas von unendlicher Leitfähigkeit auf ein Randwertproblem

The equations of a rotationally symmetric, static, incompressible plasma with infinite conductivity are equivalent to an elliptic differential equation for the function where p means the pressure, ? the density, and Φ the potential of the external forces. Moreover this differential equality contains two arbitrary functions of ξ. When ξ_?² + ξ_?² < 0, both arbitrary functions can be computed from the boundary values of Hφ und H⊥ (the component of H , which is perpendicular to the boundary).     

Dynamische Äquivalenz,GAUSSsche Konstante und Zeit-Skala für die nach-NEWTONschen Näherungen klassischer und relativistischer Gravitationstheorien

The post-NEWTON ian approximation of the gravo-dynamics of planetary motions is given by a LAGRANG ian . For ε = 1/8, β = 3/2 und γ = ?1/2 this LAGRANG ian is the well-know function for EINSTEIN 's geodesic motion in an isotropic SCHWARZSCHILD metric. The perihel motion is given by TISSERAND 's formula      

Zur unitarisierten Gravitationstheorie mit lang- und kurzrechweitigen Termen (mit ruhmasselosen und schweren Gravitonen)

In our papers, TREDER [1, 2] we have formulated a unified electrodynamics of the fourth order with bi-wave equations for the vector potential A. In this electrodynamics EINSTEIN ian photon and heavy W-mesons are the field quanta. In correspondence to this field theory we are able to formulate a unified theory of gravitation, too. The field equations for the gravitational metrics grr in this theory are corresponding with the EINSTEIN equations of General Relativity in the same way like the electromagnetic bi-wave equations are corresponding with the MAXWELL equations. The metric g_μν is a linear functional of an EINSTEIN ian long-range potential g_μν and of a subatomic short-range potential definierte Materie-Tensor die gemeinsame Quelle für alle drei Felder ist. Dann ist g1_μν, g2_μν und g_μν und es gelten die Funktional-Bedingungen wobei hier g2_μν Feldgleichungen vom “kosmologischen Typ” befriedigt. By these conditions, the short-range interaction becomes a repulsive force and the action of the NEWTON -EINSTEIN ian attraction and of the subatomic repulsion makes the matter point-like (as in the E.-I.-H.-method) but self-consistent. The gravitational metrics g2_μν become regulary. P. e., in the EINSTEIN approximation the field of a point-like mass M is given by a SCHWARZSCHILD     

Cosmic Antiproton Spectrum at the Top of the Atmosphere Derived from the New Scaling Model

The new scaling variable model explains the scaling behavior of p + p → p + X inclusive reactions at ISR energies. The cosmic antiproton spectrum has been derived from this model using the primary proton spectrum of RYAN et al. The derived antiproton-proton flux ratio lies within the upper limit value of BOGOMOLOV et al. and CHEN. The estimated antiproton spectrum follows the relation where the antiproton energy E_p is expressed in GeV and the intensity in units (cm² sec sr GeV)^?1.     

On the Nuclear Energy Generation Rate in a Simple Analytic Stellar Model

This paper is concerned with the hydrostatic equilibrium of a purely gaseous star generating energy at a rate . By the common technique of integration theory of special functions the total net rate of nuclear energy generation is evaluated analytically for a linear density distribution function assumed for a simple stellar model.     

Gravitationskollaps und Lichtgeschwindigkeit im Gravitationsfeld

An elementary criterion of the stability of a matter sphere against gravitational collapse is given by the circular velocity condition of POINCARÉ : In a space with a spherically symmetric gravitation potential ? (r) and with a spherically symmetric metric gik (e.g., a SCHWARZSCHILD space time) the circular velocity V^* of a particle on the surface r = R of the matter-sphere must be (This condition is a consequence of the virial theorem and of the POINCARÉ theorem.) - However, EINSTEIN 's axiom of causality implies that this velocity V^* must be smaller than the local velocity of light v: V^*2 < v². And this local velocity v is a function of the gravitation potential ?, too: v = v [?]. In the case of NEWTON 's or EINSTEIN 's theory the spherically symmetric gravitation potential is given by the NEWTON ian function ? = fM/r. In the special theory of relativity, we would have v = c (c = EINSTEIN 's fundamental velocity) and grr = 1. Therefore, the specialrelativistic stability condition is R > fMc^?2. - But in the NEWTON ian theory v is depending of the gravitation potential and depends of the boundary condition for the light propagation, also. According to the ansatz of LAPLACE (1799) we have: (emanation-theory of light). But, according to SOLDNER (1801), we have Therefore, we are finding in the case of LAPLACE the same condition R > fMc^?2 as in the SRT. But, in the case of SOLDER 's ansatz non condition for stability is resulting. - In the general relativistic theories the local velocity of light is given by EINSTEIN 's expression According to EINSTEIN 's theory of “static gravitation” (1911/12) we have grr = 1 and therefore the formula and according to the GRT (with - g_ω = grr^?1) we have the formula Therefore, the Hilbert-Laue condition r= R > 3fMc^?2 results as stability condition. From the gravo-optical point of view, in GRT and for the classical ansatz of LAPLACE “black-holes” with bounding states of light result for R ≤ 2fM^?2. But, no “black-holes” are existing according to SOLDNER 's ansatz. However, in GRT each black-hole must be a “collapsar”. But according to the classical theory of LAPLACE we have uncollapsed “black- holes” for the domain .     

Nachweis von radikalischen Zersetzungsprodukten in CCl4-Entladungen mit der EPR-Spektroskopie

Among the dissociation products of a r.f. discharge in CCl₄-vapour the radicals CCl₃ and Cl₂- have been identified by EPR-spectroscopy after condensation at 80 K. The gas-phase reaction CCl₃ + O₂ → CCl₃OO has been used to estimate the CCl₃ concentration to be approximately 5 · 10¹³ radicals/cm³ at p = 55 Pa. The life-time of CCl₃-radicals is governed by the rate of desactivation of some exited species (eg. CCl₄*) via . At a pressure p = 55 Pa a half-life of CCl₃-radicals of τ1/2 = 80 ms has been found.     

Secondary Neutral Pion-nucleon Flux Ratio at the Top of the Atmosphere

The CERN Intersecting Storage Ring data on the inclusive reaction p + p → π° + X has been fitted with a phenomenological form where W_c(a,b,z) is the generalized confluent function defined by . M(a, b, z) being the well known Kummer's function. Using this form and primary proton spectrum of Goddard Space Flight Center Group the secondary neutral pion-nucleon flux ratio at the top of the atmosphere has been estimated. The derived result has been compared with those expected from p + p → π^± + X data, via different models.     

Gibt es Plancksche Sekunden des Kosmos?

On Planckian Seconds of the Universe According to the Planckian limites for quantum energies the cosmological scenaria break-down for space dimensions (or for life times of the universe) and for Planckian lengths, not till.     

Comments on the Pressure Dissociation of Deuterium as Related to the Nova Laser Hugoniot

The recent Nova laser experimental Hugoniot for deuterium can be justified by a simple model which involves only very general properties of this material and which highlights the role of the molecular dissociation. The region of maximal compression along the principal Hugoniot is characterized by , , , where E_B is the binding energy of a molecule, and ρ_o is the initial density.     

The metal‐insulator transitions of VO2: A band theoretical approach

The results of first principles electronic structure calculations for the metallic rutile and the insulating monoclinic phase of vanadium dioxide are presented. In addition, the insulating phase is investigated for the first time. The density functional calculations allow for a consistent understanding of all three phases. In the rutile phase metallic conductivity is carried by metal orbitals, which fall into the one‐dimensional band, and the isotropically dispersing bands. Hybridization of both types of bands is weak. In the phase splitting of the band due to metal‐metal dimerization and upshift of the bands due to increased p‐d overlap lead to an effective separation of both types of bands. Despite incomplete opening of the optical band gap due to the shortcomings of the local density approximation, the metal‐insulator transition can be understood as a Peierls‐like instability of the band in an embedding background of electrons. In the phase, the metal‐insulator transition arises as a combined embedded Peierls‐like and antiferromagnetic instability. The results for VO₂ fit into the general scenario of an instability of the rutile‐type transition‐metal dioxides at the beginning of the d series towards dimerization or antiferromagnetic ordering within the characteristic metal chains. This scenario was successfully applied before to MoO₂ and NbO₂. In the compounds, the and bands can be completely separated, which leads to the observed metal‐insulator transitions.     

Far-infrared spectrum and the soft mode of ferroelectric betaine phosphite

The far-infrared reflection spectra of betaine phosphite single crystals in the three crystallographic directions are investigated in the range from 5 to 600 cm^?1 at temperatures between 203 and 323 K using a dispersive Fourier spectrometer. The dielectric function is evaluated from the complex amplitude reflection coefficient measured. In the spectrum polarized along the ferroelectric direction a soft mode of relaxation type is observed which accounts for a large part of the relevant static dielectric constant at T_c = 210 K. Among the oscillator modes, which generally exhibit normal temperature dependence, there is a heavily overdamped mode at 58 cm^?1, polarized along the crystallographia a₁ axis, with anomalous damping behaviour. The damping constant decreases nearly linearly with temperature up to 323 K which is close to T = 355 K where a second phase transition is known to exist.     

Einsteins hermitesche Relativitätstheorie als Unifikation von Gravo- und Chromodynamik

Einstein's Hermitian Theory of Relativity as Unification of Gravo- and Chromodynamics Einstein's Hermitian unified field theory is the continuation of the Riemannian GRG to complexe values with a Hermitian fundamental tensor gμ_v = g_v*μ This complexe continuation of GRG implies the possibility of matter and anti matter with a sort of CPT theorem. — Einstein himself has interpreted his theory as a unification and generalization of the Einstein and Maxwell theory, th. i. of gravodynamics and of electrodynamics. However — according the EIH approximation —, from Einstein's equations no Coulomb-like forces between the charges are resulting (INFELD, 1950). But, the forces between two charges ?_A and ?_B have the form (Treder 1957) It is interesting that such forces are postulated in the classical models of the chromodynamics of the interactions between quarks (for the confinement of their motions. If we interprete the purely imaginary part gμ_v of the hermitian metrics gμ_v=gμ_v+gμ_v as the dual of the field of gluons then, all peculiarities of Einstein's theory become physically meaningful. — Einstein's own interpretation suggests that the both long-range fields, gravitation and electromagnetism, must be unified in a geometrical field theory. However, the potential α/r + ε/2 has a “longer range” than the Coulomb potential ～1, and such an asymptotical potential ～ ε/2 is resulting from Einstein's equations (TREDER 1957). In Einstein's theory there are no free charges with \documentclass{article}\pagestyle{empty}\begin{document}$ \sum\limits_A^n {\varepsilon A} $\end{document}. (Wyman 1950) because the field mass of a charged particle becomes infinite asymptotically: That means, in a chromodynamics we dont's have free quarks. The same divergence are resulting from one-particle systems with non-vanishing total charges: M～ε²r. However, if the total charges vanish because in a domain ～L³ the positive sources are compensated by negative sources, the field masses of the n-charge systems become finite. From the gravitational part of Einstein's equations we get field masses which are the masses measured by observers in distances r ? L. That means, the masses of quark systems with the colour condition \documentclass{article}\pagestyle{empty}\begin{document}$ \sum\limits_A^n {\varepsilon A} $\end{document} are proportional to the linear dimension L of the system.     

Vakuum-Lichtgeschwindigkeit und differentielle Aberration

Vacuum Light Velocity and Differential Abberation In the frame work of Newton's theories of gravity and of light Laplace (1796) has deduced that the effective velocity c* of light is dependent on the gravitational potential of its source: Laplace, Olbers, a. o. have demonstrated that this effect implies differential aberrations of the light of different cosmisc sources. - But, Einstein's principles of relativity imply the independence of the velocity of light on its sources. This assertion is the fundamental principle of the Einsteinian theories of relativity. However, there seems to be no direct experimental facts disproving Laplace's formula, till today.     

On Static Asymptotically Flat Solutions of Fourth Order Gravitational Field Equations

It is shown that each non-flat regular static asymptotically flat solution of the gravitational field equation following from the Lagrangian has in a certain sense positive energy. Further, for a set of parameters including the BACH -EINSTEIN theory some results concerning the full nonlinear behaviour of the solutions of the field equation will be given.