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The processes of heat transfer occurring between the Earth's asthenosphere and lithosphere are responsible for partial melting of rocks, leading to the magma generation and its migration and segregation in the crust and, possibly, to volcanoes generation at the surface. Convection is the dominant mechanism regulating the heat transfer from the asthenosphere to the lithosphere, although many aspects of the whole process are not yet clear. Therefore, the knowledge of the physical processes leading to the melting of the lithospheric rocks has important consequences in understanding the interior Earth dynamics, the surface volcanic dynamics, and its related hazards. Rock melting occurs when the temperature gradient meets the rock solidus. Here, we propose a nonlinear convective 1D analytical model (representing an approximation of more 3D complex models). The steady-state solution of our equation is in good agreement with the estimated geotherms of the asthenosphere. A perturbative approach leads to a heat swelling at the boundary between asthenosphere and lithosphere able to determine its melting and the birth of a volcano. [ABSTRACT FROM AUTHOR]

Pd(0) is able to catalyze oxygen-involving reactions because of its capability to convert molecular oxygen to the very reactive atomic form. Consequently, the embedding of a little amount of Pd(0) clusters in polymeric phases can be technologically exploited to enhance the incineration kinetic of these polymers. The effect of nanostructuration on the Pd(0) catalytic activity in the polymer incineration reaction has been studied using poly( N-vinyl-2-pyrrolidone) ( $$ \overline{Mw} $$ = 10,000 gmol) as polymeric model system. A change in the PVP incineration kinetic mechanism with significant increase in the reaction rate was experimentally found. The kinetic of the Pd(0)-catalyzed combustion has been studied by isothermal thermogravimetric analysis. After a short induction time, the combustion in presence of Pd(0) clusters shifted to a zero-order kinetic from a second-order kinetic control, which is operative in pure PVP combustion reaction. In addition, the activation energy resulted much lowered compared to the pure PVP incineration case (from 300 to 260 kJ/mol). [ABSTRACT FROM AUTHOR]

On the basis of recent investigations, a newly developed analytical procedure is used for constructing a wide class of localized solutions of the controlled three-dimensional (3D) Gross-Pitaevskii equation (GPE) that governs the dynamics of Bose-Einstein condensates (BECs) in the presence of a spatio-temporally varying external potential. The controlled 3D GPE is decomposed into a two-dimensional (2D) linear Schrödinger equation (called the `transverse equation’) and a one-dimensional (1D) nonlinear Schrödinger equation (called the `longitudinal equation’), constrained by a variational condition for the controlling potential. The latter corresponds to the requirement for the minimization of the control operation in the transverse plane. Then, the above class of localized solutions are constructed as the product of the solutions of the transverse and longitudinal equations. A consistency condition between the transverse and longitudinal solutions yields a relationship between the transverse and longitudinal restoring forces produced by the external trapping potential well through a `controlling parameter’ (i.e. the average, with respect to the transverse profile, of the nonlinear inter-atomic interaction term of the GPE). It is found that the longitudinal profile supports localized solutions in the form of bright, dark or grey solitons with time-dependent amplitudes, widths and centroids. The related longitudinal phase is varying in space and time with time-dependent curvature radius and wavenumber. In turn, all the above parameters (i.e. amplitudes, widths, centroids, curvature radius and wavenumbers) can be easily expressed in terms of the controlling parameter. It is also found that the transverse profile has the form of Hermite-Gauss functions (depending on the transverse coordinates), and the explicit spatio-temporal dependence of the controlling potential is self-consistently determined. On the basis of these exact 3D analytical solutions, a stability analysis is carried out, focusing our attention on the physical conditions for having collapsing or non-collapsing solutions. [ABSTRACT FROM AUTHOR]

A correspondence between the families of generalized nonlinear Schrödinger (NLS) equations and generalized KdV equations was recently found using a Madelung fluid description. We similarly consider a special derivative NLS equation. We find a number of solitary waves and periodic solutions (expressed in terms of elliptic Jacobi functions) for a motion with a stationary profile current velocity. We study the stability of a bright solitary wave (ground state) by conjecturing that the Vakhitov-Kolokolov criterion is applicable. [ABSTRACT FROM AUTHOR]

We present one-dimensional (1D) stability analysis of a recently proposed method to filter and control localized states of the Bose–Einstein condensate (BEC), based on novel trapping techniques that allow one to conceive methods to select a particular BEC shape by controlling and manipulating the external potential well in the three-dimensional (3D) Gross–Pitaevskii equation (GPE). Within the framework of this method, under suitable conditions, the GPE can be exactly decomposed into a pair of coupled equations: a transverse two-dimensional (2D) linear Schrödinger equation and a one-dimensional (1D) longitudinal nonlinear Schrödinger equation (NLSE) with, in a general case, a time-dependent nonlinear coupling coefficient. We review the general idea how to filter and control localized solutions of the GPE. Then, the 1D longitudinal NLSE is numerically solved with suitable non-ideal controlling potentials that differ from the ideal one so as to introduce relatively small errors in the designed spatial profile. It is shown that a BEC with an asymmetric initial position in the confining potential exhibits breather-like oscillations in the longitudinal direction but, nevertheless, the BEC state remains confined within the potential well for a long time. In particular, while the condensate remains essentially stable, preserving its longitudinal soliton-like shape, only a small part is lost into “radiation”. [ABSTRACT FROM AUTHOR]

Using the tomographic probability distribution (symplectic tomogram) describing the quantum state (instead of the wave function or density matrix) and properties of recently introduced tomographic entropy associated with the probability distribution, the new uncertainty relation for the tomographic entropy is obtained. Examples of the entropic uncertainty relation for squeezed states and solitons of the Bose-Einstein condensate are considered. [ABSTRACT FROM AUTHOR]

We introduce a new type of tomographic probability distribution containing complete information about the density matrix (wave function) related to the Fresnel transform of the complex wave function. We elucidate the relation to the symplectic tomographic probability distribution. We present a multimode generalization of the Fresnel tomography and give examples of applications of the present approach. [ABSTRACT FROM AUTHOR]

We present a controlling potential method for solving the three-dimensional Gross–Pitaevskii equation (GPE), which governs the nonlinear dynamics of the Bose–Einstein condensates (BECs) in an inhomogeneous potential trap. Our method allows one to construct ground and excited matter wave states whose longitudinal profiles can have bright solitons. This method provides the confining potential that filters and controls localized BECs. Moreover, it is predicted that, while the BEC longitudinal soliton profile is controlled and kept unchanged, the transverse profile may exhibit oscillatory breathers (the unmatched case) or move as a rigid body in the form of either coherent states (performing the Lissajous figures) or a Schrödinger cat state (matched case). © 2004 MAIK “Nauka / Interperiodica”. [ABSTRACT FROM AUTHOR]

Experimental results concerning the synthesis of gold nanoparticles prepared by alcoholic reduction of Au(III) ions in presence of a polymeric stabilizer, and UV-visible spectroscopic characterization is presented. Optical spectroscopic data have been correlated tooff-linesize measurements obtained analysing transmission electron micrographs. The gold cluster size, coming from both TEM micrographs and absorbance cubic root, behaved linearly with time above a threshold temperature (70C) according to a deposition-controlled growth mechanism. The plasmon peak halfwidth behaved linearly with inverse particle radius (obtained by TEM), thus proving the hypothesized mechanism growth. The spectroscopic approach allows anon-linegold cluster measurement with possibility to fine control particle size also in the case of a fast process. [ABSTRACT FROM AUTHOR]

Tomographic-probability representation for soliton solutions of Gross-Pitaevskii equation is introduced. Tomograms of the wavefunction describing bright soliton states of Bose-Einstein condensate are obtained in the presence of a quadratic external potential. [ABSTRACT FROM AUTHOR]