In this study, we developed a fragment–asperity interaction model for earthquakes. Based on Tsallis entropy, this model can provide mathematical expression for the non-extensive entropy of fragments ...and asperities in the gouge area. From a statistical physics perspective, we hypothesized that non-extensive entropy decreases with energy relaxation after crustal rupture (i.e., following an earthquake). By using a windowing process, the non-extensive entropy value was monitored for three relatively recent earthquakes: the 2009 M6.1 L’Aquila (Italy) earthquake, 2011 M9.0 Tohoku (Japan) megathrust earthquake, and 2016 M7.8 Kaikoura (New Zealand) earthquake. The results support our hypothesis and suggest that the non-extensive entropy formula obtained in this study can provide a good characterization of seismicity for a given area.
•Fragment–asperity interaction model gives non-extensive entropy (S) in fault gauge.•Entropy values for earthquake catalogues depend on the q non-extensive parameter.•S indicates the equilibrium state of seismically active regions.•Abrupt falls in S marked the 2009 L’Aquila, 2011 Tohoku & 2016 Kaikoura events.•Classic physics concepts are exportable to non-linear phenomena.
Graphene has proven to be an ideal system for exotic transport phenomena. In this work, we report another exotic characteristic of the electron transport in graphene. Namely, we show that the ...linear-regime conductance can present self-similar patterns with well-defined scaling rules, once the graphene sheet is subjected to Cantor-like nanostructuring. As far as we know the mentioned system is one of the few in which a self-similar structure produces self-similar patterns on a physical property. These patterns are analysed quantitatively, by obtaining the scaling rules that underlie them. It is worth noting that the transport properties are an average of the dispersion channels, which makes the existence of scale factors quite surprising. In addition, that self-similarity be manifested in the conductance opens an excellent opportunity to test this fundamental property experimentally.
A physical model for dementia Sotolongo-Costa, O.; Gaggero-Sager, L.M.; Becker, J.T. ...
Physica A,
04/2017, Letnik:
472
Journal Article
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Odprti dostop
Aging associated brain decline often result in some kind of dementia. Even when this is a complex brain disorder a physical model can be used in order to describe its general behavior. A ...probabilistic model for the development of dementia is obtained and fitted to some experimental data obtained from the Alzheimer’s Disease Neuroimaging Initiative. It is explained how dementia appears as a consequence of aging and why it is irreversible.
•A thermodynamical model for relating brain networks with energy is proposed.•A Langevin equation is obtained and its Fokker–Planck equation is solved.•The model is successfully compared with the known experimental data.•The cusp model used gives a new probabilistic interpretation to the dementia onset.•Results support known facts of dementia and shed light on issues of related diseases.
Using nonlinear mathematical models and experimental data from laboratory and clinical studies, we have designed new combination therapies against COVID-19.
We derive a universal function for the kinetics of complex systems characterized by stretched exponential and/or power-law behaviors. This kinetic function unifies and generalizes previous ...theoretical attempts to describe what has been called “fractal kinetic”.
The concentration evolutionary equation is formally similar to the relaxation function obtained in the stochastic theory of relaxation, with two exponents
α
and
n. The first one is due to memory effects and short-range correlations and the second one finds its origin in the long-range correlations and geometrical frustrations which give rise to ageing behavior. These effects can be formally handled by introducing adequate probability distributions for the rate coefficient. We show that the distribution of rate coefficients is the consequence of local variations of the free energy (energy landscape) appearing in the exponent of the Arrhenius formula.
The fractal
(
n
,
α
)
kinetic has been applied to a few problems of fundamental and practical importance in particular the sorption of dissolved contaminants in liquid phase. Contrary to the usual practice in that field, we found that the exponent
α
, which is implicitly equal to 1 in the traditional analysis of kinetic data in terms of first- or second-order reactions, is a relevant and useful parameter to characterize the kinetics of complex systems. It is formally related to the system energy landscape which depends on physical, chemical and biological internal and external factors.
We discuss briefly the relation of the
(
n
,
α
)
kinetic formalism with the Tsallis theory of non-extensive systems.
Graphene Superlattices (GSs) have attracted a lot of attention due to its peculiar properties as well as its possible technological implications. Among these characteristics we can mention: the extra ...Dirac points in the dispersion relation and the highly anisotropic propagation of the charge carriers. However, despite the intense research that is carried out in GSs, so far there is no report about the angular dependence of the Transmission Gap (TG) in GSs. Here, we report the dependence of TG as a function of the angle of the incident Dirac electrons in a rather simple Electrostatic GS (EGS). Our results show that the angular dependence of the TG is intricate, since for moderated angles the dependence is parabolic, while for large angles an exponential dependence is registered. We also find that the TG can be modulated from meV to eV, by changing the structural parameters of the GS. These characteristics open the possibility for an angle-dependent bandgap engineering in graphene.
A model for earthquake dynamics consisting of two rough profiles interacting via fragments filling the gap is introduced, the fragments being produced by the local breakage due to the interaction of ...the local plates. The irregularities of the fault planes can interact with the fragments between them to develop a mechanism for triggering earthquakes. The fragment size distribution function comes from a nonextensive formulation, starting from first principles. An energy distribution function, which gives the Gutenberg-Richter law as a particular case, is analytically deduced.
Several radiobiological models mimic the biologic effect of one single radiation dose on a living tissue. However, the actual fractionated radiotherapy requires accounting for a new magnitude, i.e., ...time. Here, we explore the biological consequences posed by the mathematical prolongation of a previous single radiation model to fractionated treatment. The survival fraction is obtained, together with the equivalent physical dose, in terms of a time dependent factor (similar to a repair coefficient) describing the tissue trend to recovering its radioresistance. The model describes how dose fractions add up to obtain the equivalent dose and how the repair coefficient poses a limit to reach an equivalent dose equal to the critical one that would completely annihilate the tumor. On the other hand, the surrounding healthy tissue is a limiting factor to treatment planning. This tissue has its own repair coefficient and thus should limit the equivalent dose of a treatment. Depending on the repair coefficient and the critical dose of each tissue, unexpected results (failure to fully remove the tumor) can be obtained. To illustrate these results and predictions, some realistic example calculations will be performed using parameter values within actual clinical ranges. In conclusion, the model warns about treatment limitations and proposes ways to overcome them.
We have derived a general two-power-law relaxation function for heterogeneous materials using the maximum entropy principle for nonextensive systems. The power law exponents of the relaxation ...function are simply related to a global fractal parameter
α
and for large time to the entropy nonextensivity parameter
q. For intermediate times the relaxation follows a stretched exponential behavior. The asymptotic power law behaviors both in the time and the frequency domains coincide with those of the Weron generalized dielectric function derived in the stochastic theory from an extension of the Lévy central limit theorem. These results are in full agreement with the Jonscher universality principle and trace the origin of the large
t power law universality (with system dependent exponent
α
and
q
) to the scaling behavior of the extreme value distribution function of the effective macroscopic waiting time and the fluctuation of the number of relaxing entities.
The biological effect of one single radiation dose on a living tissue has been described by several radiobiological models. However, the fractionated radiotherapy requires to account for a new ...magnitude: time. In this paper we explore the biological consequences posed by the mathematical prolongation of a previous model to fractionated treatment. Nonextensive composition rules are introduced to obtain the survival fraction and equivalent physical dose in terms of a time dependent factor describing the tissue trend towards recovering its radioresistance (a kind of repair coefficient). Interesting (known and new) behaviors are described regarding the effectiveness of the treatment which is shown to be fundamentally bound to this factor. The continuous limit, applicable to brachytherapy, is also analyzed in the framework of nonextensive calculus. Here a coefficient that rules the time behavior also arises. All the results are discussed in terms of the clinical evidence and their major implications are highlighted.
► The radiobiological Tsallis MaxEnt model is extended to dose fractionation. ► The mathematical constraints lead to a tissue radioresistance recovery factor. ► This factor determines whether fractionated radiotherapy can be successful. ► The continuous irradiation limit is also obtained from nonextensive calculus. ► The model biological interpretation is simpler than others currently accepted.
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