Radiation damping in closed expanding universes

The dynamics of a coupled model (harmonic oscillator-relativistic scalar field) in Conformal Robertson-Walker (k = +1) spacetimes is investigated. The exact radiation-reaction equation of the source-including the retarded radiation terms due to the closed space geometry – is obtained and analyzed. A suitable family of Lyapunov functions is constructed to show that, if the spacetime expands monotonely, then the source's energy damps. A numerical simulation of this equation for expanding Universes, with and without Future Event Horizon, is performed.     

Cohomogeneity One Einstein-Sasaki 5-Manifolds

We consider hypersurfaces in Einstein-Sasaki 5-manifolds which are tangent to the characteristic vector field. We introduce evolution equations that can be used to reconstruct the 5-dimensional metric from such a hypersurface, analogous to the (nearly) hypo and half-flat evolution equations in higher dimensions. We use these equations to classify Einstein-Sasaki 5-manifolds of cohomogeneity one.     

Cosmological Two-Fluid Thermodynamics

We reveal unifying thermodynamic aspects of so different phenomena as the cosmological electron-positron annihilation, the evaporation of primordial black holes with a narrow mass range, and the "deflationary" transition from an initial de Sitter phase to a subsequent standard Friedmann–Lemaître–Robertson–Walker (FLRW) behavior.     

On the Singular Effects in the Relativistic Landau Levels in Graphene with a Disclination

The effect of a pseudo Aharonov-Bohm (AB) magnetic field generated by a disclination on a two-dimensional electron gas in graphene is addressed in the continuum limit within the geometric approach. The influence of the coupling between the spinor fields and the singular conical curvature is investigated, which shows that singularities have pronounced impact in the Hall conductivity. Moreover, the degeneracy related to the Dirac valleys is broken for negative values of the angular momentum quantum numbers, l, includingl ≡ 0. In this case, a Hall plateau develops at the null filling factor. Obtaining the Hall conductivity by summing over the positive and the negative l's, the null Landau level is recovered and the plateau at the null filling factor disappears. In any case, the standard plateaus, which are seen in a flat graphene are not obtained with these curvature and singular effects.     

Mean value formulas for classical solutions to uniformly parabolic equations in the divergence form with non-smooth coefficients

We prove surface and volume mean value formulas for classical solutions to uniformly parabolic equations in the divergence form with low regularity of the coefficients. We then use them to prove the parabolic strong maximum principle and the parabolic Harnack inequality. We emphasize that our results only rely on the classical theory, and our arguments follow the lines used in the original theory of harmonic functions. We provide two proofs relying on two different formulations of the divergence theorem, one stated for sets with almost C¹-boundary, the other stated for sets with finite perimeter.     

Spectrum comparison on free boundary minimal submanifolds of Euclidean domains

In this paper, using ideas of Simons, Ros, and Savo, we prove a comparison between the spectrums of the stability operator and the Hodge–Laplacian acting on differential 1-forms on a compact minimal submanifold immersed into a Euclidean domain.     

Scalar Quantum Electrodynamics on the lattice as classical statistical mechanics

Wilson's lattice approximation allows us to apply classical statistical mechanics ideas to the study of Scalar Quantum Electrodynamics. Our main tools are Griffiths-Kelly-Sherman inequalities, the transfer matrix formalism and exponential bounds. Our main result is the existence of the infinite volume limit for every value of the coupling parameters.     

On cardinal characteristics of Yorioka ideals

Yorioka introduced a class of ideals (parametrized by reals) on the Cantor space to prove that the relation between the size of the continuum and the cofinality of the strong measure zero ideal on the real line cannot be decided in . We construct a matrix iteration of c.c.c. posets to force that, for many ideals in that class, their associated cardinal invariants (i.e., additivity, covering, uniformity and cofinality) are pairwise different. In addition, we show that, consistently, the additivity and cofinality of Yorioka ideals does not coincide with the additivity and cofinality (respectively) of the ideal of Lebesgue measure zero subsets of the real line.     

The role of nanocellulose fibers, starch and chitosan on multipolysaccharide based films

Thin nanocomposite films of thermoplastic starch, chitosan and cellulose nanofibers (bacterial cellulose or nanofibrillated cellulose) were prepared for the first time by solvent casting of water based suspensions of the three polysaccharides. The role of the different bioploymers on the final properties (thermal stability, transparency, mechanical performance and antimicrobial activity) of the films was related with their intrinsic features, contents and synergic effects resulting from the establishment of interactions between them. Thermoplastic starch displays an important role on the thermal stability of the films because it is the most stable polysaccharide; however it has a negative impact on the mechanical performance and transparency of the films. The addition of chitosan improves considerably the transparency (up to 50 % transmittance for 50 % of chitosan, in respect to the amount of starch), mechanical performance and antimicrobial properties (at least 25 % of chitosan and no more than 10 % of cellulose nanofibers are required to observe bacteriostatic or bactericidal activity) but decrease their thermal stability. The incorporation of cellulose nanofibers had the strongest positive impact on the mechanical properties of the materials (increments of up to 15 and 30 MPa on the Young′s modulus and Tensile strength, respectively, for films with 20 % of BC or NFC). Nonetheless, the impact in thermal stability and mechanical performance of the films, promoted by the addition of chitosan and cellulose nanofibres, respectively, was higher than the expected considering their percentage contents certainly because of the establishment of strong and complex interactions between the three polysaccharides.