Abstract:
We show that energy and certain others characteristics of a friction controlled slide of a body excited by random motions of a foundation can be treated in an analytic manner. Assuming the random excitation is switched off at some time, we derive the moments of the displacement and of the total distance traveled by the body and calculate an average energy loss due to friction. To accomplish that we utilize the Pugachev-Sveshnikov equation for the characteristic function of a continuous random process, which is solved by reduction to the parametric Riemann boundary value problem.

Abstract:
This
paper presents an array pattern synthesis algorithm for arbitrary arrays based
on coordinate descent method (CDM). With this algorithm, the complex element
weights are found to minimize a weighted L_{2} norm of the difference between desired and achieved pattern. Compared with
traditional optimization techniques, CDM is easy to implement and efficient to
reach the optimum solutions. Main advantage is the flexibility. CDM is suitable
for linear and planar array with arbitrary array elements on arbitrary
positions. With this method, we can configure arbitrary beam pattern, which
gives it the ability to solve variety of beam forming problem, e.g. focused
beam, shaped beam, nulls at arbitrary direction and with arbitrary beam width.
CDM is applicable for phase-only and amplitude-only arrays as well, and
furthermore, it is a suitable method to treat the problem of array with element
failures.

Abstract:
Recent studies show that in interdependent networks a very small failure in one network may lead to catastrophic consequences. Above a critical fraction of interdependent nodes, even a single node failure can invoke cascading failures that may abruptly fragment the system, while below this "critical dependency" (CD) a failure of few nodes leads only to small damage to the system. So far, the research has been focused on interdependent random networks without space limitations. However, many real systems, such as power grids and the Internet, are not random but are spatially embedded. Here we analytically and numerically analyze the stability of systems consisting of interdependent spatially embedded networks modeled as lattice networks. Surprisingly, we find that in lattice systems, in contrast to non-embedded systems, there is no CD and \textit{any} small fraction of interdependent nodes leads to an abrupt collapse. We show that this extreme vulnerability of very weakly coupled lattices is a consequence of the critical exponent describing the percolation transition of a single lattice. Our results are important for understanding the vulnerabilities and for designing robust interdependent spatial embedded networks.

Abstract:
Two different ways of quantizing the relativistic Hamiltonian for radial motion in the field of Coulomb-like potential are compared. The results depend slightly on choice of time. In the case of Lorentzian time a Sommerfeld spectrum is recovered. Application to quantum black holes gives a sqrt{n} mass spectrum with about the same numerical factors.

Abstract:
The global geometries of bulk vacuum space-times in the brane-universe models are investigated and classified in terms of geometrical invariants. The corresponding Carter-Penrose diagrams and embedding diagrams are constructed. It is shown that for a given energy-momentum induced on the brane there can be different types of global geometries depending on the signs of a bulk cosmological term and surface energy density of the brane (the sign of the latter does not influence the internal cosmological evolution). It is shown that in the Randall-Sundrum scenario it is possible to have an asymmetric hierarchy splitting even with a $Z_2$-symmetric matching of "our" brane to the bulk.

Abstract:
The model is constructed, some features of which comes from quantum thin dust shells and is, in fact, an extension of the "no hair" property of classical black hole on a quantum level. It appears that the proposed classical analog of quantum black hole is heated, the temperature being exactly the Hawking's temperature.

Abstract:
The model is built in which the main global properties of classical and quasi-classical black holes become local. These are the event horizon, "no-hair", temperature and entropy. Our construction is based on the features of a quantum collapse, discovered while studying some quantum black hole models. But it is purely classical, and this allows to use the Einstein equations and classical (local) thermodynamics and explain in this way the "log(3)" - puzzle.

Abstract:
In the present paper we consider, using our earlier results, the process of quantum gravitational collapse and argue that there exists the final quantum state when the collapse stops. This state, which can be called the ``no-memory state'', reminds the final ``no-hair state'' of the classical gravitational collapse. Translating the ``no-memory state'' into classical language we construct the classical analogue of quantum black hole and show that such a model has a topological temperature which equals exactly the Hawking's temperature. Assuming for the entropy the Bekenstein-Hawking value we develop the local thermodynamics for our model and show that the entropy is naturally quantized with the equidistant spectrum S + gamma_0*N. Our model allows, in principle, to calculate the value of gamma_0. In the simplest case, considered here, we obtain gamma_0 = ln(2).

Abstract:
The aim of this Letter is rather pedagogical. We considered the static spherically symmetric ensemble of observers, having finite bare mass and trying to measure geometrical and physical properties of the environmental static (Schwarzschild) space-time. It is shown that, using the photon rockets (which the mass together with the mass of their fuel is also taken into account) they can managed to keep themselves on the fixed value of radius. The process of diminishing the total bare mass up to zero lasts infinitely long time. It is important that the problem is solved self-consistently, i.e., with full account for the back reaction of both bare mass and radiation from rockets on the space-time geometry.