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The Darwin model of electromagnetic interaction is presented as a self-consistent theory, and is shown to be an excellent approximation to the Maxwell theory for slow electromagnetic waves. Since the fast waves of the Maxwell theory are absent, it is convenient for use in the computer simulation of the electromagnetic dynamics of nonrelativistic plasma.
Data obtained from a numerical solution of the Boltzmann equation for shock-wave structure are used to test the accuracy of accepted approximate expressions for the two moments of the collision integral Delta (Q) for general intermolecular potentials in systems with a large translational nonequilibrium. The accuracy of the numerical scheme is established by comparison of the numerical results with exact expressions in the case of Maxwell molecules. They are then used in the case of hard-sphere molecules, which are the furthest-removed inverse power potential from the Maxwell molecule; and the accuracy of the approximate expressions in this domain is gauged. A number of approximate solutions are judged in this manner, and the general advantages of the numerical approach in itself are considered.
The quantum principles that establish the energy levels and degeneracies needed to evaluate the partition functions are explored. The uncertainty principle is associated with the dual wave-particle nature of the model used to describe quantized gas particles. The Schroedinger wave equation is presented as a generalization of Maxwell's wave equation; the former applies to all particles while the Maxwell equation applies to the special case of photon particles. The size of the quantum cell in phase space and the representation of momentum as a space derivative operator follow from the uncertainty principle. A consequence of this is that steady-state problems that are space-time dependent for the classical model become only space dependent for the quantum model and are often easier to solve. The partition function is derived for quantized free particles and, at normal conditions, the result is the same as that given by the classical phase integral. The quantum corrections that occur at very low temperatures or high densities are derived. These corrections for the Einstein-Bose gas qualitatively describe the condensation effects that occur in liquid helium, but are unimportant for most practical purposes otherwise. However, the corrections for the Fermi-Dirac gas are important because they quantitatively describe the behavior of high-density conduction electron gases in metals and explain the zero point energy and low specific heat exhibited in this case.
The paper discusses a new radar image of the visible face of Venus, with particular reference to the relative backscattered power between latitudes 46 and 75 deg and covering the approximate longitude range from 290 to 10 deg, with an approximate resolution of 20 km. Two features seem to dominate this region: one is a large low-contrast area with a well-defined rim on its southern side and with two high-contrast features forming its northern and northwestern edges, and the other consists of the same two small high-contrast features on the northern edge of the basin and a large very high contrast feature straddling the zero-deg meridian and extending from 60 to 70 latitude, the last feature being previously named Maxwell. It is shown that Maxwell and the two high-contrast features are likely to indicate tectonic activity. Their probable high degree of surface roughness, well-defined boundaries, and irregular shapes make an origin based on the impact history of the planet hard to conceive.
Observations of radio emission at 3.3 mm wavelength associated with magnetic fields in active regions are reported. Results of more than 200 regions during the years 1967-1968 show a strong correlation between peak enhanced millimeter emission, total flux of the longitudinal component of photospheric magnetic fields and the number of flares produced during transit of active regions. For magnetic flux greater than (10 to the 21st power) maxwells flares will occur and for flux of (10 to the 23rd power) maxwells the sum of the H-alpha flare importance numbers is about 40. The peak millimeter enhancement increases with magnetic flux for regions which subsequently flared. Estimates of the magnetic energy available and the correlation with flare production indicate that the photospheric fields and probably chromospheric currents are responsible for the observed pre-flare heating and provide the energy of flares.
In order to study the interaction with the surface, a Monte Carlo program is developed to determine the distribution with altitude as well as the global distribution of density at the surface in a single operation. The analysis presented shows that the appropriate source distribution should be Maxwell-Boltzmann flux if the particles in the distribution are to be treated as components of flux. Monte Carlo calculations with a Maxwell-Boltzmann flux source are compared with Mariner 10 UV spectrometer data. Results indicate that the presently operating models are not capable of fitting the observed Mercury exosphere. It is suggested that an atmosphere calculated with a barometric source distribution is suitable for more realistic future exospheric models.
The lepton self-mass problem is examined within the framework of the quantum theory of electromagnetism and gravity. Consideration is given to the Reissner-Nordstrom solution to the Einstein-Maxwell classical field equations for an electrically charged mass point, and the WKB theory for a semiclassical system with total energy zero is used to obtain an expression for the Einstein-Maxwell action factor. The condition obtained is found to account for the observed mass values of the three charged leptons, and to be in agreement with the correspondence principle.
The deformation of the Earth following a dip-slip earthquake is calculated using a three layer rheological model and finite element techniques. The three layers are an elastic upper lithosphere, a standard linear solid lower lithosphere, and a Maxwell viscoelastic asthenosphere-a model previously analyzed in the strike-clip case (Cohen, 1981, 1982). Attention is focused on the magnitude of the postseismic subsidence and the width of the subsidence zone that can develop due to the viscoelastic response to coseismic reverse slip. Detailed analysis for a fault extending from the surface to 15 km with a 45 deg dip reveals that postseismic subsidence is sensitive to the depth to the asthenosphere but is only weakly dependent on lower lithosphere depth. The greatest subsidence occurs when the elastic lithosphere is about 30 km thick and the asthenosphere lies just below this layer (asthenosphere depth = 2 times the fault depth). The extremum in the subsidence pattern occurs at about 5 km from the surface trace of the fault and lies over the slip plane. In a typical case after a time t = 30 tau (tau = Maxwell time) following the earthquake the subsidence at this point is 60% of the coseismic uplift. Unlike the horizontal deformation following a strike slip earthquake, significant vertical deformation due to asthenosphere flow persists for many times tau and the magnitude of the vertical deformation is not necessarily enhanced by having a partially relaxing lower lithosphere.
A detailed treatment of the kinematics of relativistic systems of particles and photons is presented. In the case of a relativistic Maxwell-Boltzmann distribution of particles, the reaction rate and luminosity are written as single integrals over the invariant cross section, and the production spectrum is written as a double integral over the cross section differential in the energy of the produced particles (or photons) in the center-of-momentum system of two colliding particles. The results are applied to the calculation of the annihilation spectrum of a thermal electron-positron plasma, confirming previous numerical and analytic results. Relativistic thermal electron-ion and electron-electron bremsstrahlung are calculated exactly to lowest order, and relativistic thermal electron-positron bremsstrahlung is calculated in an approximate fashion. An approximate treatment of relativistic Comptonization is developed. The question of thermalization of a relativistic plasma is considered. A formula for the energy loss or exchange rate from the interaction of two relativistic Maxwell-Boltzmann plasmas at different temperatures is derived. Application to a stable, uniform, nonmagnetic relativistic thermal plasma is made. Comparison is made with other studies.
A macroscopic Lagrangian is derived which includes a pressure tensor, heat conduction, and elastic collisions. Its Euler-Lagrange equations are shown to be the Maxwell equations and the macroscopic force law. The corresponding Hamiltonian is derived, and Hamilton's canonical equations are also demonstrated to lead to the Maxwell equations and the macroscopic force law. The treatment is facilitated by working in a mixture of Eulerian coordinates (for the fields) and Lagrangian coordinates (for the particle motions), and the introduction of a macroscopic potential expressed in terms of the plasma thermal energy and the energy losses by heat conduction.
The deformation of the earth following a dip-slip earthquake is calculated using a three layer rheological model and finite element techniques. The three layers are an elastic upper lithosphere, a standard linear solid lower lithosphere, and a Maxwell viscoelastic asthenosphere - a model previously analyzed in the strike-clip case (Cohen, 1981, 1982). Attention is focused on the magnitude of the postseismic subsidence and the width of the subsidence zone that can develop due to the viscoelastic response to coseismic reverse slip. Detailed analysis for a fault extending from the surface to 15 km with a 45 deg dip reveals that postseismic subsidence is sensitive to the depth to the asthenosphere but is only weakly dependent on lower lithosphere depth. The greatest subsidence occurs when the elastic lithosphere is about 30 km thick and the asthenosphere lies just below this layer (asthenosphere depth = 2 times the fault depth). The extremum in the subsidence pattern occurs at about 5 km from the surface trace of the fault and lies over the slip plane. In a typical case after a time t = 30 tau (tau = Maxwell time) following the earthquake, the subsidence at this point is 60 percent of the coseismic uplift. Unlike the horizontal deformation following a strike slip earthquake, significant vertical deformation due to asthenosphere flow persists for many times tau and the magnitude of the vertical deformation is not necessarily enhanced by having a partially relaxing lower lithosphere. Previously announced in STAR as N83-13683
An isotropic, heterogeneous, viscous thermoplastic model of the uniaxially shock-compressed state in transparent solids is examined with a view to determining the conditions under which this radiation may be nominally thermal or nonthermal. Regions of locally high temperatures producing thermal radiation may develop only where the local viscosity is low and the Maxwell time is short; alternatively, regions of low elastic moduli and long Maxwell time could experience sustained elastic deformation, leading to microfracture and triboluminescence. Attention is given to the cases of MgO and SiO2.
The main part of the Ishtar Terra east of the Maxwell Montes is covered with systems of areal dislocations of several directions, which are called Parquet. According to the structural patterns these may be divided into: (1) the central stable block; (2) the lesser peripheral blocks separated from the central one by gaps and grabens; (3) the zones of mobilized parquet, whose substance flowed downward at an incline in the directions away from the central block in the form of plastic flows; and (4) the partially parqueted lava sheets. The Maxwell Montes were formed as a result of the collision between the central parquet block and the Lakshmi Planum.
Moving from the Maxwell Montes to the eastern edge of Ishtar Terra there is a gradual shift in submeridional meandering folded ranges in the western section of the area to straight intersecting disjunctive systems of connected faults and sublatitudinal shifts. These disjunctive systems evidently transform older structures; the major axis of the stresses created by them is primarily oriented sublatitudinally. Relative to younger structures, in the western they occupy a higher hypsometric position. The reason for the formation of this entire system may be a large astenospheric flow wihch rise in the region of Lakashmi Planum and Maxwell Montes and which spreads and plunges in an easterly direction, taking with it deformed blocks of the lithosphere.
There are no large-scale sedimentation and erosion processes on Venus, therefore the observed deformation must be formed on the surface or close to it, and in the ellipsoids of stresses one of the main axes must be perpendicular to the surface. According to the deformation visible on photography from Venera-15, 16, the orientations of the ellipsoids of stresses are established in the different sections of the Montes Maxwell and the northern parquet. A geological model is established, according to which the Montes Maxwell is an arched vault and the region to the south a conjugate bend, separated by a shift zone.
The effect of transient creep on the inference of long-term mantle viscosity is investigated using theoretical predictions from self-gravitating, layered earth models with Maxwell, Burgers' body, and standard linear solid rheologies. The interaction between transient and steady-state rheologies is studied. The responses of the standard linear solid and Burgers' body models to transient creep in the entire mantle, and of the Burgers' body and Maxwell models to creep in the lower mantle are described. The models' responses are examined in terms of the surface displacement, free air gravity anomaly, wander of the rotation pole, and the secular variation of the degree 2 zonal coefficient of the earth's gravitational potential field. The data reveal that transient creep cannot operate throughout the entire mantle.
The solution of filtered Vlasov-Maxwell equations, rather than the Vlasov-Maxwell equations themselves, is shown to ameliorate the velocity space filamentation problem in collisionless plasma models. Exact field solutions and filtered velocity distribution functions are obtained without introducing errors. Proper selection of the filter width is demonstrated to inhibit development of velocity space filamentation and, it is conjectured, position space filamentation. The results of sample calculations of both filtered and nonfiltered field solutions illustrate a high degree of agreement between both solutions, with significant savings in computational time and memory requirements with the filtered solutions.
The motion of charged, conducting droplets present in an insulating fluid medium is analyzed under the action of an electric field, in microgravity. Previous analyses of this problem have considered the Maxwell stresses as the only driving force. In the present study, arguments from macroscopic thermodynamics and the molecular theory of surface tension are used to show that the surface tension gradients can be induced due to the variation of the electric potential on the interface. In the limit of Reynolds numbers small compared to unity, the terminal velocity of migration of the droplet is calculated under the combined action of the Maxwell stresses and the surface tension gradients. The results show that there are no surface tension gradients (i.e., no electric potential variation at the interface) in a case that is due to the convection of the surface charges, surface tension gradients do exist and tend to reduce the terminal velocity of the droplet. The shape of the droplet altered by the motion was also calculated, when the deformations from the spherical shape are small.