Second Type Of Solution Research Articles

Vortices associated with toroidal ion-temperature-gradient-driven fluctuations

The three nonlinear hydrodynamic equations for potential, parallel ion velocity and ion pressure used in simulations of the toroidal ion-temperature-gradient-driven fluctuations and transport in a shear magnetic field are analyzed for coherent vortex structures. Two types of vortex structures are found: one type for weak shear that is a generalization of the usual modon vortex construction and the second type of solution for strong magnetic shear where the convective nonlinearity in the parallel velocity field generates a cubic trapping nonlinearity in the vorticity equation. These vortex structures show the possibility of explaining the saturated states observed in the numerical simulations as self-organized nonlinear states in contrast to wave turbulence.

La rue et l'immeuble, mobilité quotidienne et formes urbaines

The rise of daily mobility in European towns has introduced a series of problems as yet unresolved by planning. Congestion and noise are the most obvious signs. On a larger scale the relationship between areas of circulation and more private spaces has been affected. One type of solution is based on strict functional divisions. This solution more or less favours traffic flow. Space is badly adapted to the cultural codes of customs. The second type of solution tends to keep classical morphologies by using various technical means to treat traffic. This type of solution seems to be more interesting.

Electromagnetic solitary vortices in a rotating plasma

The nonlinear equations describing drift-Alfvén solitary vortices in a low β, rotating plasma are derived. Two types of solitary vortex solutions along with their corresponding nonlinear dispersion relations are obtained. Both solutions have the localized coherent dipolar structure. The first type of solution belongs to the family of the usual Rossby or drift wave vortex, while the second type of solution is intrinsic to the electromagnetic perturbation in a magnetized plasma and is a complicated structure. While the first type of vortex is a solution to a second-order differential equation the second one is the solution of a fourth-order differential equation intrinsic to the electromagnetic problem. The fourth-order vortex solution has two intrinsic space scales in contrast to the single space scale of the previous drift vortex solution. With the second short scale length the parallel current density at the vortex interface becomes continuous. As special cases the rotational electron drift vortex and the rotational ballooning vortex also are given.

High- Z liquid scintillators containing tin

Two series of high- Z liquid scintillators have been developed and found to be useful for detection of X-rays and gamma rays in the energy range of about 4–200 keV. One type of solution is composed of pseudocumene (PC) as the solvent, 4,4″-di(5-tridecyl)-p-terphenyl as the scintillating solute, and tetramethyltin as the heavy-atom compound. A second type of solution contains a much faster but lower-yield solute, 4-bromo-4″-(5-hexadecyl)-p-terphenyl; the other components are the same. A tin loading of 22 weight percent in either of these solutions increases its sensitivity to 8 keV X-rays by a factor of 2.5 for a sample thickness of 1 mm. Well-resolved photopeaks were recorded for 122 keV gamma rays from 57Co using solutions containing 28 and 49 weight percent tin. Several pulse parameters i.e., rise time, decay time, etc., of the radiation from solutions with and without added tin have been measured by exciting the solutions with pulsed electrons from a linac. The decrease in scintillation yield with increased tin loading was found to be proportional to dilution of the PC solvent. Moreover, decay times of the solutions were not affected by addition of tetramethyltin. Therefore, it is concluded that the heavy atoms do not actively quench the fluorescence from these solutions.

The evaporation of spherical clouds in a hot gas. III - Suprathermal evaporation

We develop a steady-state model for the thermal evaporation of isolated spherical clouds in the limit where the collisional mean free path of the hot ambient electrons is very much larger than the characteristic length scale associated with the evaporative outflow. This process is referred to as suprathermal evaporation. The energy equation used includes both the effects of direct Coulomb collisions between the suprathermal particles and the thermal gas of the evaporative outflow as well as flux-limited conductive heating of the outflow. The fluid dynamical equations for the flow allow two categories of solution: one in which conductive heating dominates near the cloud, the other in which Coulomb heating dominates. In the first type of solution the mass loss rate is found to be an eigenvalue of the equations; in the second type of solution, the effects of the radiative losses in the cloud interior must be considered to determine the mass loss rate. Both solutions are transonic and display the same asymptotic form at large distances from the cloud. The confinement pressure at the cloud surface may greatly exceed the ambient pressure in suprathermal evaporation.

Stationary Solutions to Nonlinear Partial Differential Equations for the Classical Continuous Isotropic Heisenberg Model

Stationary solutions to nonlinear partial differential equations obeyed by two angles of rotation, e and cp, of spins for the classical continuous isotropic Heisenberg model are studied. By paying attention to particular solutions for which cp satisfies the Laplace equation, three types of solutions of physical interest describing nonlinear excitations in the system are studied. These are cylindrical symmetric or vortex string type solutions, axisymmetric solutions and uniform·flow solutions, for each of which an equation obeyed by e takes the form of the sine· Gordon equation having the corresponding symmetry. For the first type multi-vortex string solutions are obtained in terms of the Jacobi elliptic functions with argument given by a stream function for vortices. The second type of solutions is written in terms of the Painleve trans­ cendents of the third kind. Here solutions of another type are also obtained in close similarity to solutions to the Ernst equation for the axisymmetric gravitational field problem. The third type of solutions is given as solutions to the conventional static two-dimensional sine-Gordon equation for which multi-kink solutions exist.

Deformation of Supercritically Stable Waves on a Viscous Liquid Film down an Inclined Plane Wall with the Decrease of Wave Number

The deformation of supercritically stable monochromatic waves on a viscous liquid film down an inclined plane wall with the decrease of wave number from that for the neutral stability is studied on the basis of a weakly nonlinear surface height equation. The equation is solved by using a two-amplitudes expansion technique to obtain two types of supercritically stable wave solutions and to examine their stability. It is found that the well-known first type of solution becomes unstable for the wave number smaller than a certain critical value, and the second type of solution becomes stable to be realized in place of the first type. With the further decrease of wave number, the second type of supercritically stable wave is transformed again into the first type with the wave number twice that of the sinusoidal disturbance imparted initially.

Millennialism in Relation to Buddhism

Weber, in his comparative studies of religion, characterized millennial eschatologies (embodying beliefs in a just redistribution of fortune through a future revolution in this world) as one possible type of solution to a problem of meaning which he considered central to all religious traditions—the problem of explaining the world's imperfections. Taking this type of solution as his point of departure, he arranged the other types in a logical order. Thus when the supervention of the messianic kingdom in this world appeared to be unduly delayed, a second type of solution became necessary and possible, a solution in terms of other-worldly expectations of heaven and hell. This second solution itself entailed difficulties of its own: when heaven and hell were conceived as intermediate realms of existence, there still remained problems regarding the eternity of salvation (and damnation); and, when they were conceived as eternal realms of existence, there arose, especially in the context of theistic beliefs, the difficulty of reconciling the punishment of human errors with the conception of a benevolent and powerful creator of the world who would ultimately be responsible for these human actions himself. The third, fourth and fifth types of solutions were seen as responses to this problem, a problem which in Christian theology came to be known as ‘theodicy’ or the problem of reconciling the two fundamental attributes of God, universal benevolence and omnipotence, in view of the existence of evil. The third type of solution, best exemplified in the Protestant doctrine of predestination, preserved God's omnipotence and resolved his lack of benevolence by placing him beyond the ethical claims of his creatures.

Properties of Vortex Lines in Superconducting Barriers

There are two qualitatively different types of solution to the Josephson barrier equations. The first type corresponds to vortex lines in the barriers. For small damping, a rather complete picture of vortex line motion can be obtained including inertial and dissipative effects. The second type of solution corresponds to plasma oscillations. The stability of the solutions is investigated and results are obtained for the collective modes of the vortex lines and the propagation of plasma oscillations in a magnetic field.