Exterior problem for the two-dimensional compressible Euler equation

In this paper we show the existence of a solution, on any time intervals, in suitable Sobolev spaces for the 2D compressible Euler equation in the exterior domain, when the Mach number is sufficiently small. We shall extend results obtained in [8] in the case of an infinity velocity different from zero.

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Sunto In questo lavoro proviamo l'esistenza di una soluzione, su ogni intervallo temporale, in opportuni spazi di Sobolev per le equazioni di Eulero 2D comprimibili in un dominio esterno, quando il numero di Mach è sufficientemente piccolo. Estenderemo i risultati ottenuti in [8] al caso di velocità all'infinito diversa da zero.

     

Positive solutions of $\Delta u+u^p = 0$ whose singular set is a manifold with boundary

The aim of this paper is to prove the existence of weak solutions to the equation , with , which are positive in a domain and which are singular along a k-dimensional submanifold with smooth boundary. Here, the exponent p is required to lie in the interval , where is the dimension of the singular set. In the particular case where and , solutions correspond to solutions of the singular Yamabe problem. Received: 7 October 2001 / Accepted: 7 March 2002 / Published online: 6 August 2002     

Nature of physical phenomena in ferroelectric relaxors

The nature of physical phenomena in ferroelectric relaxors, i.e., ferroelectrics undergoing smeared phase transitions, is discussed. These phenomena are closely related to the dynamics of polar regions (PRs), in which thermal fluctuations cause relaxation processes that control the crystal properties. The PRs interact with one another not only via electrical but also via mechanical interactions, and the deformed paraelectric interlayers between PRs play an important role in the transition to a macrodomain state.     

Electrical conduction in binary macrosystems: General rules

The conductivity of a macroscopically disordered graphite-paraffin system as a function of the graphite content and temperature is studied. It is shown that the properties of the heterosystem differ essentially from those of its components. Experimental data obtained are explained in terms of the percolation theory and concepts of fractal-structure objects.     

Subgame Consistent Cooperative Solutions in Stochastic Differential Games

Subgame consistency is a fundamental element in the solution of cooperative stochastic differential games. In particular, it ensures that: (i) the extension of the solution policy to a later starting time and to any possible state brought about by the prior optimal behavior of the players would remain optimal; (ii) all players do not have incentive to deviate from the initial plan. In this paper, we develop a mechanism for the derivation of the payoff distribution procedures of subgame consistent solutions in stochastic differential games with transferable payoffs. The payoff distribution procedure of the subgame consistent solution can be identified analytically under different optimality principles. Demonstration of the use of the technique for specific optimality principles is shown with an explicitly solvable game. For the first time, analytically tractable solutions of cooperative stochastic differential games with subgame consistency are derived.     

Focusing of parametric X-ray radiation

The possibility of focusing parametric x rays (PXRs) without x-ray optics has been shown. Parametric x rays are emitted by channeled relativistic charged particles moving along a bent crystal. Parametric x rays emitted from the entire length of the bent crystal are focused at two points on the bending axis of the crystal. The Huygens picture of formation of focused PXRs is given. The width of the spectral peak of this radiation has been estimated. Certain properties of focused PXRs are estimated for typical experimental conditions, and possibilities for the application of focused PXRs are discussed. An experiment for the observation of focused PXRs has been proposed. It has been shown that focused PXRs can be observed for a proton energy of several tens of GeVs or higher.     

Optical investigation of cavitation erosion by laser-induced bubble collapse

By means of a new force sensor based on optical beam deflection (OBD), the mechanical effects of laser-matter interaction underwater at different incident laser energy are investigated in detail. The experimental results show that a target underwater is impacted in turn by laser-plasma ablation force and high-speed liquid-jet impulse induced by bubbles collapse in the vicinity of a solid boundary. Furthermore, the amplitudes of the two forces increase monotonously with laser energy. According to the ablation force detected by the experiment and the theoretical relationship between laser intensity and ablation pressure, the value of liquid-jet impact against a solid boundary can be easily obtained. In addition, based on the model of a collapsing bubble, some characteristic parameters, such as the liquid-jet impact velocity, the maximum bubble radius, the bubble energy can also be obtained at different laser energy, which are valuable in the corresponding research fields.