Gauss’ law of error revisited in the framework of Sharma-Taneja-Mittal information measure

We reformulate the Gauss’ law of error in presence of correlations which are taken into account by means of a deformed product arising in the framework of the Sharma-Taneja-Mittal measure. Having reviewed the main proprieties of the generalized product and its related algebra, we derive, according to the Maximum Likelihood Principle, a family of error distributions with an asymptotic power-law behavior.      

An econophysics approach to analyse uncertainty in financial markets: an application to the Portuguese stock market

In recent years there has been a closer interrelationship between several scientific areas trying to obtain a more realistic and rich explanation of the natural and social phenomena. Among these it should be emphasized the increasing interrelationship between physics and financial theory. In this field the analysis of uncertainty, which is crucial in financial analysis, can be made using measures of physics statistics and information theory, namely the Shannon entropy. One advantage of this approach is that the entropy is a more general measure than the variance, since it accounts for higher order moments of a probability distribution function. An empirical application was made using data collected from the Portuguese Stock Market.     

Angular auto-correlation functions in molecular crystals and liquids: application to incoherent neutron scattering law

The effect of the local hindered molecular motion in the incoherent neutron scattering spectra in crystals and liquids is studied theoretically on the basis of the angular auto-correlation functions symmetrized on the dynamical point groups. The extended angular jump model simulates the motion. The microscopic properties of the matter, the time scale and the point symmetry of the molecule motion as well as the site symmetry of the molecule, are taken into account with the help of the dynamical variables of the model. The incoherent neutron scattering function is anisotropic in a monocrystalline sample. The scattering function consists of elastic plus quasi-elastic components. The shape of the quasi-elastic scattering spectrum is expressed by the sum of the weighted Lorentzian curves symmetrized with respect to the non-identical irreducible representations of the molecule motion point symmetry group. The elastic part of the intensity is increased by the contribution arising from the molecule motion of the identity representation symmetry. The scattering expression related to the molecule motion symmetry of a perfect cubic group is similar to the well-known expression derived for the scattering from the spherical top molecules exhibiting rotation diffusion.     

Informational analysis of seismic sequences by applying the Fisher Information Measure and the Shannon entropy: An application to the 2004–2010 seismicity of Aswan area (Egypt)

The interevent-time (IET) and interevent-distance (IED) series of seismic events occurred at Aswan area (Egypt) from 2004 to 2010 were investigated by means of the Fisher Information Measure and the Shannon entropy. The analysis was performed varying the depth and the magnitude thresholds. The results point out to an increase of level of organization and order with the decrease of magnitude threshold and the increase of depth threshold for the IET series, while the IED series are characterized by a level of uncertainty approximately constant with the threshold magnitude. The complexity measure, calculated as the product of the Fisher Information Measure and the Shannon entropy power, presents very similar pattern for both the types of seismic series, indicating an increasing complexity with the decrease of the threshold magnitude and the increase of the threshold depth.     

物理力学公式、定律在"和平号"空间站坠毁过程中的运用

利用物理力学定律对“和平号”空间站坠毁过程作了比较详细的计算和描述，旨在使读者在航天器有关知识有更多了解。     

Speed-Dependent Weighting of the Maxwellian Distribution in Rarefied Gases: A Second-Law Paradox?

We show that the velocity distribution in rarefied (i.e., Knudsen) gases is spontaneously weighted in favor of small speeds away from the Maxwellian distribution corresponding to the temperature of the container walls—despite thermodynamic equilibrium with the walls. The consequent paradox concerning the second law of thermodynamics is discussed.     

Entanglement dynamics in atom-field interaction in the presence of noise: a special application of the Burshtein equation

The entanglement dynamics in a system of the interaction of an atom with a single-mode thermal field in the presence of noise is studied by the Jaynes-Cummings model. Two-state random phase telegraph noise is considered as the noise in the interaction and an exact solution to the model under this noise is obtained by the Burshtein equation. Although the Burshtein equation is applicable for laser-atom interactions, it is shown that it can be applied to atom-thermal field system as a special case. The solution is used to investigate the entanglement dynamics of the atom-field interaction by calculating a lower bound on concurrence. It is found that the entanglement is a non monotonic function of the intensity of the noise. The degree of the entanglement decreases to a minimum value for an optimal intensity of the noise and then increases for a sufficiently large intensity. Moreover, intense noise may generate stronger entanglement compared with the absence of noise.     

A model for the enzyme activity in systems with large composition fluctuations. An application to the unusual kinetics of phospholipase A2

A non-equilibrium thermodynamics based model is proposed in order to describe the role of large concentration fluctuations of enzymes, reactants and products in modulating the macroscopic time evolution of chemical kinetics. The encounter probabilities between reactants and enzyme depend on their local concentration. Fluctuations modify the bimolecular encounter probability. Since, in turn, the amplitude of fluctuations depends itself on the instantaneous composition of the reacting mixture, the time-varying chemical composition acts as a positive feedback mechanism for the reactive fluid mixture near the critical temperature for phase separation. The model is applied to rationalize the unusual features of phospholipase kinetics, an enzyme which catalyzes the hydrolisis of membrane forming phospholipids, yielding products which are still soluble in the lipid matrix. A typical feature of the enzyme reaction is the long induction time prior to a ”burst” of activity. This effect is well reproduced by the theory, together with the dependence of the induction time on the exogeneous addition of products or other liposoluble substances, the effects of enzyme and substrate concentration, and the temperature dependence of the enzyme activation. All these properties emerge as a consequence of the coupling between enconter probability and time-varying bilayer heterogeneity. A good qualitative agreement between theoretical results and the available experimental results has been generally found. Received: 25 June 1996 / Revised: 17 April 1997 / Accepted: 26 November 1997     

Free energy landscape from path-sampling: application to the structural transition in LJ38

We introduce a path-sampling scheme that allows equilibrium state-ensemble averages to be computed by means of a biased distribution of non-equilibrium paths. This non-equilibrium method is applied to the case of the 38-atom Lennard-Jones atomic cluster, which has a double-funnel energy landscape. We calculate the free energy profile along the Q₄ bond orientational order parameter. At high or moderate temperature the results obtained using the non-equilibrium approach are consistent with those obtained using conventional equilibrium methods, including parallel tempering and Wang-Landau Monte Carlo simulations. At lower temperatures, the non-equilibrium approach becomes more efficient in exploring the relevant inherent structures. In particular, the free energy agrees with the predictions of the harmonic superposition approximation.