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  1. Article: Some fractal thoughts about the COVID-19 infection outbreak

    Materassi, Massimo

    Abstract: Some ideas are presented about the physical motivation of the apparent capacity of generalized logistic equations to describe the outbreak of the COVID-19 infection, and in general of quite many other epidemics. The main focuses here are: the complex, ... ...

    Abstract Some ideas are presented about the physical motivation of the apparent capacity of generalized logistic equations to describe the outbreak of the COVID-19 infection, and in general of quite many other epidemics. The main focuses here are: the complex, possibly fractal, structure of the locus describing the"contagion event set"; what can be learnt from the models of trophic webs with"herd behaviour".
    Keywords covid19
    Publisher ArXiv
    Document type Article
    Database COVID19

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  2. Book ; Online: Some fractal thoughts about the COVID-19 infection outbreak

    Materassi, Massimo

    2020  

    Abstract: Some ideas are presented about the physical motivation of the apparent capacity of generalized logistic equations to describe the outbreak of the COVID-19 infection, and in general of quite many other epidemics. The main focuses here are: the complex, ... ...

    Abstract Some ideas are presented about the physical motivation of the apparent capacity of generalized logistic equations to describe the outbreak of the COVID-19 infection, and in general of quite many other epidemics. The main focuses here are: the complex, possibly fractal, structure of the locus describing the "contagion event set"; what can be learnt from the models of trophic webs with "herd behaviour".
    Keywords Quantitative Biology - Populations and Evolution ; Mathematics - Dynamical Systems ; Physics - Biological Physics ; covid19
    Publishing date 2020-04-08
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  3. Article ; Online: Some fractal thoughts about the COVID-19 infection outbreak

    Massimo Materassi

    Chaos, Solitons & Fractals: X, Vol 4, Iss , Pp 100032- (2019)

    2019  

    Abstract: Some ideas are presented about a geometric motivation of the apparent capacity of generalized logistic equations to describe the outbreak of quite many epidemics, possibly including that of the COVID-19 infection. This interpretation pivots on the ... ...

    Abstract Some ideas are presented about a geometric motivation of the apparent capacity of generalized logistic equations to describe the outbreak of quite many epidemics, possibly including that of the COVID-19 infection. This interpretation pivots on the complex, possibly fractal, structure of the locus describing the “contagion event set”, and on what can be learnt from the models of trophic webs with “herd behaviour”.Under the hypothesis that the total number of cases, as a function of time, is fitted by a solution of the Generalized Richards Model, it is argued that the exponents appearing in that differential equation, usually determined empirically, represent the geometric signature of the non-space filling, network-like locus on which contagious contacts take place.
    Keywords COVID-19 outbreak ; Generalized Richards Model ; Herd behaviour ; Population dynamics ; Fractal dimension ; Physics ; QC1-999 ; Mathematics ; QA1-939 ; covid19
    Language English
    Publishing date 2019-12-01T00:00:00Z
    Publisher Elsevier
    Document type Article ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  4. Article ; Online: Some fractal thoughts about the COVID-19 infection outbreak

    Materassi, Massimo

    Chaos, Solitons & Fractals: X

    2019  Volume 4, Page(s) 100032

    Keywords covid19
    Language English
    Publisher Elsevier BV
    Publishing country us
    Document type Article ; Online
    ISSN 2590-0544
    DOI 10.1016/j.csfx.2020.100032
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  5. Article: Some fractal thoughts about the COVID-19 infection outbreak

    Materassi, Massimo

    Chaos Solitons Fractals X

    Abstract: Some ideas are presented about a geometric motivation of the apparent capacity of generalized logistic equations to describe the outbreak of quite many epidemics, possibly including that of the COVID-19 infection. This interpretation pivots on the ... ...

    Abstract Some ideas are presented about a geometric motivation of the apparent capacity of generalized logistic equations to describe the outbreak of quite many epidemics, possibly including that of the COVID-19 infection. This interpretation pivots on the complex, possibly fractal, structure of the locus describing the “contagion event set”, and on what can be learnt from the models of trophic webs with “herd behaviour”. Under the hypothesis that the total number of cases, as a function of time, is fitted by a solution of the Generalized Richards Model, it is argued that the exponents appearing in that differential equation, usually determined empirically, represent the geometric signature of the non-space filling, network-like locus on which contagious contacts take place.
    Keywords covid19
    Publisher WHO
    Document type Article
    Note WHO #Covidence: #343076
    Database COVID19

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  6. Article ; Online: Metriplectic Structure of a Radiation-Matter-Interaction Toy Model.

    Materassi, Massimo / Marcucci, Giulia / Conti, Claudio

    Entropy (Basel, Switzerland)

    2022  Volume 24, Issue 4

    Abstract: A dynamical system defined by a metriplectic structure is a dissipative model characterized by a specific pair of tensors, which defines a Leibniz bracket; and a free energy, formed by a "Hamiltonian" and an entropy, playing the role of dynamics ... ...

    Abstract A dynamical system defined by a metriplectic structure is a dissipative model characterized by a specific pair of tensors, which defines a Leibniz bracket; and a free energy, formed by a "Hamiltonian" and an entropy, playing the role of dynamics generator. Generally, these tensors are a Poisson bracket tensor, describing the Hamiltonian part of the dynamics, and a symmetric metric tensor, that models purely dissipative dynamics. In this paper, the metriplectic system describing a simplified two-photon absorption by a two-level atom is disclosed. The Hamiltonian component is sufficient to describe the free electromagnetic radiation. The metric component encodes the radiation-matter coupling, driving the system to an asymptotically stable state in which the excited level of the atom is populated due to absorption, and the radiation has disappeared. First, a description of the system is used, based on the real-imaginary decomposition of the electromagnetic field phasor; then, the whole metriplectic system is re-written in terms of the phase-amplitude pair, named Madelung variables. This work is intended as a first result to pave the way for applying the metriplectic formalism to many other irreversible processes in nonlinear optics.
    Language English
    Publishing date 2022-04-04
    Publishing country Switzerland
    Document type Journal Article
    ZDB-ID 2014734-X
    ISSN 1099-4300 ; 1099-4300
    ISSN (online) 1099-4300
    ISSN 1099-4300
    DOI 10.3390/e24040506
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  7. Article: A stretched logistic equation for pandemic spreading.

    Consolini, Giuseppe / Materassi, Massimo

    Chaos, solitons, and fractals

    2020  Volume 140, Page(s) 110113

    Abstract: In this brief work we present a novel approach to the logistic dynamics of populations and epidemic spreading that can take into account of the complex nature of such a process in several real situations, where due to different agents the dynamics is no ... ...

    Abstract In this brief work we present a novel approach to the logistic dynamics of populations and epidemic spreading that can take into account of the complex nature of such a process in several real situations, where due to different agents the dynamics is no longer characterized by a single characteristic timescale, but conversely by a distribution of time scales, rendered via a time-dependent growth rate. In detail, a differential equation containing a power-law time dependent growth rate is proposed, whose solution, named
    Keywords covid19
    Language English
    Publishing date 2020-07-22
    Publishing country England
    Document type Journal Article
    ZDB-ID 2003919-0
    ISSN 1873-2887 ; 0960-0779
    ISSN (online) 1873-2887
    ISSN 0960-0779
    DOI 10.1016/j.chaos.2020.110113
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  8. Article ; Online: Entropy as a Metric Generator of Dissipation in Complete Metriplectic Systems

    Massimo Materassi

    Entropy, Vol 18, Iss 8, p

    2016  Volume 304

    Abstract: This lecture is a short review on the role entropy plays in those classical dissipative systems whose equations of motion may be expressed via a Leibniz Bracket Algebra (LBA). This means that the time derivative of any physical observable f of the system ...

    Abstract This lecture is a short review on the role entropy plays in those classical dissipative systems whose equations of motion may be expressed via a Leibniz Bracket Algebra (LBA). This means that the time derivative of any physical observable f of the system is calculated by putting this f in a “bracket” together with a “special observable” F, referred to as a Leibniz generator of the dynamics. While conservative dynamics is given an LBA formulation in the Hamiltonian framework, so that F is the Hamiltonian H of the system that generates the motion via classical Poisson brackets or quantum commutation brackets, an LBA formulation can be given to classical dissipative dynamics through the Metriplectic Bracket Algebra (MBA): the conservative component of the dynamics is still generated via Poisson algebra by the total energy H, while S, the entropy of the degrees of freedom statistically encoded in friction, generates dissipation via a metric bracket. The motivation of expressing through a bracket algebra and a motion-generating function F is to endow the theory of the system at hand with all the powerful machinery of Hamiltonian systems in terms of symmetries that become evident and readable. Here a (necessarily partial) overview of the types of systems subject to MBA formulation is presented, and the physical meaning of the quantity S involved in each is discussed. Here the aim is to review the different MBAs for isolated systems in a synoptic way. At the end of this collection of examples, the fact that dissipative dynamics may be constructed also in the absence of friction with microscopic degrees of freedom is stressed. This reasoning is a hint to introduce dissipation at a more fundamental level.
    Keywords dissipative systems ; metriplectic dynamics ; Leibniz algebra ; Science ; Q ; Astrophysics ; QB460-466 ; Physics ; QC1-999
    Subject code 531
    Language English
    Publishing date 2016-08-01T00:00:00Z
    Publisher MDPI AG
    Document type Article ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  9. Article ; Online: Chaos and Predictability in Ionospheric Time Series.

    Materassi, Massimo / Alberti, Tommaso / Migoya-Orué, Yenca / Radicella, Sandro Maria / Consolini, Giuseppe

    Entropy (Basel, Switzerland)

    2023  Volume 25, Issue 2

    Abstract: Modelling the Earth's ionosphere is a big challenge, due to the complexity of the system. Different first principle models have been developed over the last 50 years, based on ionospheric physics and chemistry, mostly controlled by Space Weather ... ...

    Abstract Modelling the Earth's ionosphere is a big challenge, due to the complexity of the system. Different first principle models have been developed over the last 50 years, based on ionospheric physics and chemistry, mostly controlled by Space Weather conditions. However, it is not understood in depth if the residual or mismodelled component of the ionosphere's behaviour is predictable in principle as a simple dynamical system, or is conversely so chaotic to be practically stochastic. Working on an ionospheric quantity very popular in aeronomy, we here suggest data analysis techniques to deal with the question of how chaotic and how predictable the local ionosphere's behaviour is. In particular, we calculate the correlation dimension D2 and the Kolmogorov entropy rate K2 for two one-year long time series of data of vertical total electron content (vTEC), collected on the top of the mid-latitude GNSS station of Matera (Italy), one for the year of Solar Maximum 2001 and one for the year of Solar Minimum 2008. The quantity D2 is a proxy of the degree of chaos and dynamical complexity. K2 measures the speed of destruction of the time-shifted self-mutual information of the signal, so that K2-1 is a sort of maximum time horizon for predictability. The analysis of the D2 and K2 for the vTEC time series allows to give a measure of chaos and predictability of the Earth's ionosphere, expected to limit any claim of prediction capacity of any model. The results reported here are preliminary, and must be intended only to demonstrate how the application of the analysis of these quantities to the ionospheric variability is feasible, and with a reasonable output.
    Language English
    Publishing date 2023-02-17
    Publishing country Switzerland
    Document type Journal Article
    ZDB-ID 2014734-X
    ISSN 1099-4300 ; 1099-4300
    ISSN (online) 1099-4300
    ISSN 1099-4300
    DOI 10.3390/e25020368
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  10. Article ; Online: Metriplectic Structure of a Radiation–Matter-Interaction Toy Model

    Massimo Materassi / Giulia Marcucci / Claudio Conti

    Entropy, Vol 24, Iss 506, p

    2022  Volume 506

    Abstract: A dynamical system defined by a metriplectic structure is a dissipative model characterized by a specific pair of tensors, which defines a Leibniz bracket; and a free energy, formed by a “Hamiltonian” and an entropy, playing the role of dynamics ... ...

    Abstract A dynamical system defined by a metriplectic structure is a dissipative model characterized by a specific pair of tensors, which defines a Leibniz bracket; and a free energy, formed by a “Hamiltonian” and an entropy, playing the role of dynamics generator. Generally, these tensors are a Poisson bracket tensor, describing the Hamiltonian part of the dynamics, and a symmetric metric tensor, that models purely dissipative dynamics. In this paper, the metriplectic system describing a simplified two-photon absorption by a two-level atom is disclosed. The Hamiltonian component is sufficient to describe the free electromagnetic radiation. The metric component encodes the radiation–matter coupling, driving the system to an asymptotically stable state in which the excited level of the atom is populated due to absorption, and the radiation has disappeared. First, a description of the system is used, based on the real–imaginary decomposition of the electromagnetic field phasor; then, the whole metriplectic system is re-written in terms of the phase–amplitude pair, named Madelung variables. This work is intended as a first result to pave the way for applying the metriplectic formalism to many other irreversible processes in nonlinear optics.
    Keywords two-photon absorption ; metriplectic systems ; dissipative systems ; asymptotically stable equilibrium ; Madelung variables ; Science ; Q ; Astrophysics ; QB460-466 ; Physics ; QC1-999
    Subject code 531
    Language English
    Publishing date 2022-04-01T00:00:00Z
    Publisher MDPI AG
    Document type Article ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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