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The knowledge of stellar evolution is evolving quickly thanks to an increased number of opportunities to scrutinize the stellar internal plasma properties by stellar seismology and by 1D and 3D simulations. These new tools help us to…
The Carnot theory is unique among the theories of heat developed before the emergence of thermodynamics because it considers the relationship between heat and work. The theory is contained in Carnot's book published in 1824, which includes…
Cosmic rays represent one of the most fascinating research themes in modern astronomy and physics. After almost a century since their discovery, a huge amount of scientific literature has been written on this topic and it is not always easy…
Fitting the multi-wavelength spectral energy distributions (SEDs) of galaxies is a widely used technique to extract information about the physical properties of galaxies. However, a major difficulty lies in the numerous uncertainties…
If we prepare an isolated, interacting quantum system in an eigenstate and perturb a local observable at an initial time, its expectation value will relax towards a thermal expectation value, even though the time evolution of the system is…
We establish global well-posedness and scattering for wave maps from $d$-dimensional hyperbolic space into Riemannian manifolds of bounded geometry for initial data that is small in the critical Sobolev space for $d \geq 4$. The main…
These notes present the fundamentals of Fermi acceleration at shocks, with a special attention to the role that supernova remnants have in producing Galactic cosmic rays. Then, the recent discoveries in the theory of diffusive shock…
Important gaps remain in our understanding of the thermodynamics and statistical physics of self-gravitating systems. Using mean field theory, here we investigate the equilibrium properties of several spherically symmetric model systems…
The Dulong-Petit limiting law for the specific heats of solids, one of the first general results in thermodynamics, has provided Mendeleev with a powerful tool for devising the periodic table and gave an important support to Boltzmann's…
Mathematicians have long been fascinated by the resolution of algebraic and Diophantine equations in search of integer or rational solutions. This article presents a list of thirty-three open problems in number theory, posed in the 13th…
Diffusive shock acceleration operating at expanding supernova remnant shells is by far the most popular model for the origin of galactic cosmic rays. Despite the general consensus received by this model, an unambiguous and conclusive proof…
This review article provides the basics and discusses some important applications of thermal field theory, namely the combination of statistical mechanics and relativistic quantum field theory. In a first part the fundamentals are covered:…
A one dimensional radiative transfer code is developed to track the ionization and heating pattern around the first miniquasars and Population III stars. The code follows the evolution of the ionization of the species of hydrogen and helium…
Using a criterion proposed by Salpeter,and standard solid state physics,we have determined the Debye temperature of a solid in equilibrium with the electron gas surrounding it.The results obtained can have implications in studies of the…
The origin of galactic cosmic rays is one of the most interesting unsolved problems in astroparticle physics. Experimentally, the problem is attacked by a multi-disciplinary effort, namely by direct measurements of cosmic rays above the…
Inspired by the method of smoothed asymptotics developed by Terence Tao, we introduce a new ultra-violet regularisation scheme for loop integrals in quantum field theory which we call $\eta$ regularisation. This allows us to reveal a…
The discovery of connections between the distribution of energy levels of heavy nuclei and spacings between prime numbers has been one of the most surprising and fruitful observations in the twentieth century. The connection between the two…
Many of the basic problems in the astrophysics of charged Cosmic Rays remain on principle unresolved by in situ observations in the Solar System due to the chaotic nature of the propagation of these particles in Interstellar space. This…
We obtain, by starting from the balance laws of a continuum endowed with a vectorial microstructure and with a suitable thermodynamics, the evolution equation for the excitation carriers in scintillating crystals. These equations, coupled…
In 1925 Sir James Jeans calculated that a star made up of an ideal gas, generating energy as a moderately positive function of temperature and density, could not exist. Such stars would be unstable to oscillations of increasing size. It…