The Kinetics of Sorption–Desorption Phenomena: Local and Non-Local Kinetic Equations

The kinetics of adsorption phenomena are investigated in terms of local and non-local kinetic equations of the Langmuir type. The sample is assumed in the shape of a slab, limited by two homogeneous planar-parallel surfaces, in such a manner that the problem can be considered one-dimensional. The local kinetic equations in time are analyzed when both saturation and nonsaturation regimes are considered. These effects result from an extra dependence of the adsorption coefficient on the density of adsorbed particles, which implies the consideration of nonlinear balance equations. Non-local kinetic equations, arising from the existence of a time delay characterizing a type of reaction occurring between a bulk particle and the surface, are analyzed and show the existence of adsorption effects accompanied by temporal oscillations

Two-parameter deformations of logarithm, exponential, and entropy: A consistent framework for generalized statistical mechanics

A consistent generalization of statistical mechanics is obtained by applying the maximum entropy principle to a trace-form entropy and by requiring that physically motivated mathematical properties are preserved. The emerging differential-functional equation yields a two-parameter class of generalized logarithms, from which entropies and power-law distributions follow: these distributions could be relevant in many anomalous systems. Within the specified range of parameters, these entropies possess positivity, continuity, symmetry, expansibility, decisivity, maximality, concavity, and are Lesche stable. The Boltzmann-Shannon entropy and some one parameter generalized entropies already known belong to this class. These entropies and their distribution functions are compared, and the corresponding deformed algebras are discussed.Comment: Version to appear in PRE: about 20% shorter, references updated, 13 PRE pages, 3 figure

Rigid rotators and diatomic molecules via Tsallis statistics

We obtain an analytic expression for the specific heat of a system of N rigid rotators exactly in the high temperature limit, and via a pertubative approach in the low temperature limit. We then evaluate the specific heat of a diatomic gas with both translational and rotational degrees of freedom, and conclude that there is a mixing between the translational and rotational degrees of freedom in nonextensive statistics.Comment: 12 page

The relativistic statistical theory and Kaniadakis entropy: an approach through a molecular chaos hypothesis

We have investigated the proof of the $H$ theorem within a manifestly covariant approach by considering the relativistic statistical theory developed in [G. Kaniadakis, Phy. Rev. E {\bf 66}, 056125, 2002; {\it ibid.} {\bf 72}, 036108, 2005]. As it happens in the nonrelativistic limit, the molecular chaos hypothesis is slightly extended within the Kaniadakis formalism. It is shown that the collisional equilibrium states (null entropy source term) are described by a $\kappa$ power law generalization of the exponential Juttner distribution, e.g., $f(x,p)\propto (\sqrt{1+ \kappa^2\theta^2}+\kappa\theta)^{1/\kappa}\equiv\exp_\kappa\theta$, with $\theta=\alpha(x)+\beta_\mu p^\mu$, where $\alpha(x)$ is a scalar, $\beta_\mu$ is a four-vector, and $p^\mu$ is the four-momentum. As a simple example, we calculate the relativistic $\kappa$ power law for a dilute charged gas under the action of an electromagnetic field $F^{\mu\nu}$. All standard results are readly recovered in the particular limit $\kappa\to 0$.Comment: 7 pages; to be published in EPJ

The HH-theorem in κ\kappa-statistics: influence on the molecular chaos hypothesis

We rediscuss recent derivations of kinetic equations based on the Kaniadakis' entropy concept. Our primary objective here is to derive a kinetical version of the second law of thermodynamycs in such a $\kappa$-framework. To this end, we assume a slight modification of the molecular chaos hypothesis. For the $H_{\kappa}$-theorem, it is shown that the collisional equilibrium states (null entropy source term) are described by a $\kappa$-power law extension of the exponential distribution and, as should be expected, all these results reduce to the standard one in the limit $\kappa\to 0$.Comment: 4 pages, eqs. (18) and (22) have been corrected, to appear in Phys. Lett.

Nuclear electron capture rate in stellar interiors and the case of 7Be

Nuclear electron capture rate from continuum in an astrophysical plasma environment (like solar core) is calculated using a modified Debye-Huckel screening potential and the related non-Gaussian q-distribution of electron momenta. For q=1 the well-known Debye-Huckel results are recovered. The value of q can be derived from the fluctuation of number of particles and temperature inside the Debye sphere. For 7Be continuum electron capture in solar core, we find an increase of 7 -- 10 percent over the rate calculated with standard Debye-Huckel potential. The consequence of this results is a reduction of the same percentage of the SSM 8B solar neutrino flux, leaving unchanged the SSM 7Be flux.Comment: 8 pages, 1 figure, IOP macro style, submitted to JP

Numerical study of the application of capillary barrier systems for prevention of rainfall-induced slope instabilities

Slope instability is often caused by decreases in suction due to heavy and prolonged rainfall. In this study, the application of capillary barrier systems (CBSs) for suction control and slope stabilization purposes (i.e. reducing the risk of rainfall-induced slope instabilities) is analysed, due to their capacity to limit the percolation of water into the underlying soil. The behaviour of two slopes was studied numerically: a bare slope made of fine-grained soil and the same slope covered by a capillary barrier system. The time evolution of suction in the slopes subjected to realistic atmospheric conditions was studied by performing numerical finite element analyses with Code_Bright. In particular, multi-phase multi-physics thermo-hydraulic analyses were performed, modelling the soil-atmosphere interaction over periods of many years. Suction and degree of saturation distributions obtained from these analyses were then exported to the software LimitState GEO, which was used to perform limit analysis to assess the stability of the slopes. The CBS was able to limit the percolation of water into the slope and was shown to be effective in increasing the minimum values of suction attained in the underlying ground, resulting in improved stability of the slope

Entanglement in composite bosons realized by deformed oscillators

Composite bosons (or quasibosons), as recently proven, are realizable by deformed oscillators and due to that can be effectively treated as particles of nonstandard statistics (deformed bosons). This enables us to study quasiboson states and their inter-component entanglement aspects using the well developed formalism of deformed oscillators. We prove that the internal entanglement characteristics for single two-component quasiboson are determined completely by the parameter(s) of deformation. The bipartite entanglement characteristics are generalized and calculated for arbitrary multi-quasiboson (Fock, coherent etc.) states and expressed through deformation parameter.Comment: 5 pages; v2: abstract and introduction rewritten, references adde

Capillary barriers during rainfall events in pyroclastic deposits of the vesuvian area

In the present paper, the capillary barrier formation at the interface between soil layers, which is characterized by textural discontinuities, has been analyzed. This mechanism has been investigated by means of a finite element model of a two-layer soil stratification. The two considered formations, belonging to the pyroclastic succession of the “Pomici di Base” Plinian eruption (22 ka, Santacroce et al., 2008) of the Somma–Vesuvius volcano, are affected by shallow instability phenomena likely caused by progressive saturation during the rainfall events. This mechanism could be compatible with the formation of capillary barriers at the interface between layers of different grain size distributions during infiltration. One-dimensional infiltration into the stratified soil was parametrically simulated considering rainfall events of increasing intensity and duration. The variations in the suction and degree of saturation over time allowed for the evaluation of stability variations in the layers, which were assumed as part of stratified unsaturated infinite slopes

Cole-Hopf Like Transformation for Schr\"odinger Equations Containing Complex Nonlinearities

We consider systems, which conserve the particle number and are described by Schr\"odinger equations containing complex nonlinearities. In the case of canonical systems, we study their main symmetries and conservation laws. We introduce a Cole-Hopf like transformation both for canonical and noncanonical systems, which changes the evolution equation into another one containing purely real nonlinearities, and reduces the continuity equation to the standard form of the linear theory. This approach allows us to treat, in a unifying scheme, a wide variety of canonical and noncanonical nonlinear systems, some of them already known in the literature. pacs{PACS number(s): 02.30.Jr, 03.50.-z, 03.65.-w, 05.45.-a, 11.30.Na, 11.40.DwComment: 26 pages, no figures, to be appear in J. Phys. A: Math. Gen. (2002