We critically analyze the models of a main-sequence star based on polytropic gases. First, we put in evidence that the hypothesis of polytropic gas is compatible with the constitutive equation of an ideal gas if the transformations inside... more
We critically analyze the models of a main-sequence star based on polytropic gases. First, we put in evidence that the hypothesis of polytropic gas is compatible with the constitutive equation of an ideal gas if the transformations inside the star are adiabatic. Then, neither the mono- or the polyphasic models of an ideal gas can be applied inside the stellar core for the existence in this region of nuclear reactions. Moreover, we prove that polyphasic models doesn’t allow the existence of C1solutions of the stationary hydrodynamic equations.
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The potential impact of cyanobacteria and microalgae on the weathering of calcareous tesserae from a Roman mosaic of the II Century CE has been followed through in vitro experiments. Laboratory tests were carried out by inoculating mosaic... more
The potential impact of cyanobacteria and microalgae on the weathering of calcareous tesserae from a Roman mosaic of the II Century CE has been followed through in vitro experiments. Laboratory tests were carried out by inoculating mosaic tiles with single strains of Cyanobacteria or Chlorophyta to evaluate the roles of pioneer phototrophic microrganism on the resulting architecture of biofilms. The interaction between tesserae and strains was assessed at the whole substratum and micrometer scales, by image analysis and Confocal Laser Scanning (CLS) microscopy, respectively. The biofilm surface coverage on each tessera varied from 19% (Fischerella ambigua) to 97% (Microcoleus autumnalis). Cyanobacteria showed a better growth on calcareous tesserae, whereas the only green alga attaining a superficial coverage higher than 50% was Coelastrella rubescens. CLS microscopy evidenced two different types of spatial arrangement of the phototrophic organisms on the tesserae, that were defined as compact or porous, respectively. In the first one was measured a reduced number of empty spaces between cells or filaments, whereas in the second type, a reticulate texture allowed the presence of numerous empty volumes. The colonization processes observed are an intrinsic characteristic of each strain. We have proposed a colonization index I C as a sensible tool to describe, in a quantitative way, the pioneering attitude of each photosynthetic microorganism to colonize lithic substrates under laboratory conditions.
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Research Interests: Mathematics, Analytical dynamics, Symplectic geometry, Geometric Mechanics, Port Hamiltonian system, and 7 moreVector Calculus, Rigid Body, Euclidean space, Lagrangian Mechanics, Reaserch In a Field of Applied Mathematics and Mathematical Physics, Lagrangian & Hamiltonian Mechanics, and Springer Ebooks
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Statistical mechanics is an important part of mechanics. Its origin can be found in the old Greek dream of describing the macroscopic behavior of real bodies starting from the properties of the elementary constituents of matter: the atoms... more
Statistical mechanics is an important part of mechanics. Its origin can be found in the old Greek dream of describing the macroscopic behavior of real bodies starting from the properties of the elementary constituents of matter: the atoms (Democritus). If this approach were practicable, it would be possible to reduce the variety of macroscopic properties of real bodies to the few properties of the elementary components of matter. However, this point of view exhibits some apparently insuperable difficulties related to the huge number of atoms composing macroscopic bodies. These difficulties justify the opposite approach undertaken by continuum mechanics, which will be partially described in Chap. 23, devoted to fluid mechanics.
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Understanding how different sources of concern interact in people’s mind is a question that has entertained generations of scholars. The finite-pool-of-worry (FPW) hypothesis states that humans have limited resources to worry, thus when... more
Understanding how different sources of concern interact in people’s mind is a question that has entertained generations of scholars. The finite-pool-of-worry (FPW) hypothesis states that humans have limited resources to worry, thus when they are worried about one issue they become less worried about other issues. Instead, the affect generalization theory (AGT) posits that an increased level of worry about one threat increases concerns about related threats. To this end, we adopt a Lotka–Volterra model to detect instances of AGT and FPW among worries for the environment, economy, safety, social issues and immigration in 31 European countries between 2012 and 2019 (Eurobarometer data). Consistently with AGT, we find that an increase in the concern for the environment often favors the growth of concerns for the economy. Meanwhile, consistently with FPW, an increase in the concerns for the economy and for other sources of worry, often pushes down concerns for the environment. Building on our results, we hypothesize the existence of a pyramid of worries. At the bottom of the pyramid lie worries like concerns for the economy, which generally predate other worries. Concerns for the environment lie at the very top of the pyramid as they are generally predated by other worries. Last, we find that AGT and FPW can coexist not only over time and across countries, but also as a result of an asymmetric interaction.
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... R. Caccioppoli” Universit`a degli Studi di Napoli “Federico II” via Cintia 80126 Napoli Italy antroman@unina.it Addolorata Marasco Dipartimento di Matematica e Applicazioni “R. Caccioppoli” Universit`a degli Studi di Napoli “Federico... more
... R. Caccioppoli” Universit`a degli Studi di Napoli “Federico II” via Cintia 80126 Napoli Italy antroman@unina.it Addolorata Marasco Dipartimento di Matematica e Applicazioni “R. Caccioppoli” Universit`a degli Studi di Napoli “Federico II” via ... 125 4.7 Wulff's Construction . . . . ...
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Starting from integral balance laws, a model based on nonlinear ordinary differential equations (ODEs) describing the evolution of Phosphorus cycle in a lake is proposed. After showing that the usual homogeneous model is not compatible... more
Starting from integral balance laws, a model based on nonlinear ordinary differential equations (ODEs) describing the evolution of Phosphorus cycle in a lake is proposed. After showing that the usual homogeneous model is not compatible with the mixture theory, we prove that an ODEs model still holds but for the mean values of the state variables provided that the nonhomogeneous involved fields satisfy suitable conditions. In this model the trophic state of a lake is described by the mean densities of Phosphorus in water and sediments, and phytoplankton biomass. All the quantities appearing in the model can be experimentally evaluated. To propose restoration programs, the evolution of these state variables toward stable steady state conditions is analyzed. Moreover, the local stability analysis is performed with respect to all the model parameters. Some numerical simulations and a real application to lake Varese conclude the paper.
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In the preceding chapters we analyzed some properties of a vector space E\(_{\textit{n}}\). In this chapter we introduce into E\(_{\textit{n}}\) two other operations: the scalar product and the antiscalar product. A vector space equipped... more
In the preceding chapters we analyzed some properties of a vector space E\(_{\textit{n}}\). In this chapter we introduce into E\(_{\textit{n}}\) two other operations: the scalar product and the antiscalar product. A vector space equipped with the first operation is called a Euclidean vector space, whereas when it is equipped with the second operation, it is said to be a symplectic vector space. These operations allow us to introduce into E\(_{\textit{n}}\) many other geometric and algebraic concepts such as length of a vector, orthogonality between two vectors, etc. Further, eigenvalues and eigenvectors of a linear map are analyzed together with orthogonal transformations of \(E_n\). Finally, symplectic vector spaces are introduced and some their properties studied.
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Celestial mechanics is one of the most interesting applications of classical mechanics. This topic answers one of the oldest questions of facing humankind: what forces govern the motion of celestial bodies? How do celestial bodies move... more
Celestial mechanics is one of the most interesting applications of classical mechanics. This topic answers one of the oldest questions of facing humankind: what forces govern the motion of celestial bodies? How do celestial bodies move under the action of these forces? In this chapter we discuss the foundations of this subject. We first recall the two-body problem and introduce the orbital elements. Then, we analyze the restricted three-body problem in which the third body has a very small mass compared with the masses of the other two bodies. In particular, we describe the Lagrange equilibrium positions and their stability. Then, we consider the N–body problem showing that the Hamiltonian of this system is obtained by adding the Hamiltonian of the two-body problem, that describes a completely integrable system, to another term that can be regarded as a perturbation term. In the remaining part of the chapter, we show how the gravitation law for mass points can be extended to continu...
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Research Interests: Neuroscience and ODOR
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Statistical mechanics is an important part of mechanics. Its origin can be found in the old Greek dream of describing the macroscopic behavior of real bodies starting from the properties of the elementary constituents of matter: the atoms... more
Statistical mechanics is an important part of mechanics. Its origin can be found in the old Greek dream of describing the macroscopic behavior of real bodies starting from the properties of the elementary constituents of matter: the atoms (Democritus). If this approach were practicable, it would be possible to reduce the variety of macroscopic properties of real bodies to the few properties of the elementary components of matter. However, this point of view exhibits some apparently insuperable difficulties related to the huge number of atoms composing macroscopic bodies. These difficulties justify the opposite approach undertaken by continuum mechanics, which will be partially described in Chap. 23, devoted to fluid mechanics.
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In this chapter, a brief introduction to one-dimensional continuous systems is presented. First, the balance equations relative to these systems are formulated: the mass conservation and the balance of momentum and angular momentum. Then,... more
In this chapter, a brief introduction to one-dimensional continuous systems is presented. First, the balance equations relative to these systems are formulated: the mass conservation and the balance of momentum and angular momentum. Then, these equations are applied to describe the behavior of Euler’s beam. Further, the simplified model of wires is introduced to describe the suspension bridge and catenary. Finally, the equation of vibrating strings is derived and the corresponding Sturm–Liouville problem is analyzed. In particular, the homogeneous string is studied by D’Alembert solution.