A unified IMEX Runge-Kutta approach for hyperbolic systems with multiscale relaxation

In this paper we consider the development of Implicit-Explicit (IMEX) Runge-Kutta schemes for hyperbolic systems with multiscale relaxation. In such systems the scaling depends on an additional parameter which modifies the nature of the asymptotic behavior which can be either hyperbolic or parabolic. Because of the multiple scalings, standard IMEX Runge-Kutta methods for hyperbolic systems with relaxation loose their efficiency and a different approach should be adopted to guarantee asymptotic preservation in stiff regimes. We show that the proposed approach is capable to capture the correct asymptotic limit of the system independently of the scaling used. Several numerical examples confirm our theoretical analysis

The Influence of Colour on Radiometric Performances of Agricultural Nets

The whole construction parameters of the net, combined with the shape of the structure, the position of the sun and the sky conditions affect the radiometric performance of the permeable covering system. The radiometric properties of the permeable membrane influence the quality of the agricultural production and the aesthetic characteristics of the netting system. Moreover, the colour of the material and the light reflection- especially of the wavelengths visible for the human eye (VIS, 380-760nm)- is an interesting criterion to determine the aesthetic value of the net structure and its environmental impact. In order to investigate the influence of the threads colour on the radiometric properties of the net, a set of field tests were performed by means of a spectroradiometer in combination with an experimental setup 120x120x50cm covered with membranes formed by threads with different colour. A second set of experiments were performed, on the same kind of nets, in laboratory by means of a combination of a large integrating sphere and a small one: the transmissivity from a direct (tauDIR) and diffuse ((tauDIF) source and the reflectivity from diffuse source (¿) of 50x50cm samples were measured in the PAR range. The evaluation of the transmissivity values shows that the colour of a net influence spectral distribution of the radiation passing through the net absorbing their complementary colours. The transmissivity of black nets is almost constant in the visible range and the reduction of the incoming radiation is proportional to the solidity of the net. In the PAR range transparent and black nets doesn¿t cause an alteration of the spectrum of solar radiation and transmittance is almost constant with a slight growth in nets having lower porosity

Implicit-Explicit Runge-Kutta schemes for hyperbolic systems and kinetic equations in the diffusion limit

We consider Implicit-Explicit (IMEX) Runge-Kutta (R-K) schemes for hyperbolic systems with stiff relaxation in the so-called diffusion limit. In such regime the system relaxes towards a convection-diffusion equation. The first objective of the paper is to show that traditional partitioned IMEX R-K schemes will relax to an explicit scheme for the limit equation with no need of modification of the original system. Of course the explicit scheme obtained in the limit suffers from the classical parabolic stability restriction on the time step. The main goal of the paper is to present an approach, based on IMEX R-K schemes, that in the diffusion limit relaxes to an IMEX R-K scheme for the convection-diffusion equation, in which the diffusion is treated implicitly. This is achieved by an original reformulation of the problem, and subsequent application of IMEX R-K schemes to it. An analysis on such schemes to the reformulated problem shows that the schemes reduce to IMEX R-K schemes for the limit equation, under the same conditions derived for hyperbolic relaxation. Several numerical examples including neutron transport equations confirm the theoretical analysis

Cosmological string models from Milne spaces and SL(2,Z) orbifold

The $n+1$-dimensional Milne Universe with extra free directions is used to construct simple FRW cosmological string models in four dimensions, describing expansion in the presence of matter with $p=k \rho$, $k=(4-n)/3n$. We then consider the n=2 case and make SL(2,Z) orbifold identifications. The model is surprisingly related to the null orbifold with an extra reflection generator. The study of the string spectrum involves the theory of harmonic functions in the fundamental domain of SL(2,Z). In particular, from this theory one can deduce a bound for the energy gap and the fact that there are an infinite number of excitations with a finite degeneracy. We discuss the structure of wave functions and give examples of physical winding states becoming light near the singularity.Comment: 14 pages, harvma

Soluble models in 2d dilaton gravity

A one-parameter class of simple models of two-dimensional dilaton gravity, which can be exactly solved including back-reaction effects, is investigated at both classical and quantum levels. This family contains the RST model as a special case, and it continuously interpolates between models having a flat (Rindler) geometry and a constant curvature metric with a non-trivial dilaton field. The processes of formation of black hole singularities from collapsing matter and Hawking evaporation are considered in detail. Various physical aspects of these geometries are discussed, including the cosmological interpretation.Comment: 15 pages, harvmac, 3 figure

Model of black hole evolution

From the postulate that a black hole can be replaced by a boundary on the apparent horizon with suitable boundary conditions, an unconventional scenario for the evolution emerges. Only an insignificant fraction of energy of order $(mG)^{-1}$ is radiated out. The outgoing wave carries a very small part of the quantum mechanical information of the collapsed body, the bulk of the information remaining in the final stable black hole geometry.Comment: 9 pages, harvmac, 3 figures, minor addition

Model of black hole evolution

From the postulate that a black hole can be replaced by a boundary on the apparent horizon with suitable boundary conditions, an unconventional scenario for the evolution emerges. Only an insignificant fraction of energy of order $(mG)^{-1}$ is radiated out. The outgoing wave carries a very small part of the quantum mechanical information of the collapsed body, the bulk of the information remaining in the final stable black hole geometry.Comment: 9 pages, harvmac, 3 figures, minor addition

Use of phytotherapics in dogs and cats.

Phytotherapy is one of the most utilized non conventional medicines (NCM) both in human and veterinary medicine. It can be used to mitigate and prevent slight diseases and to support conventional medicine using allopathic drugs. In this paper the Authors report the phytoterapeutics most utilized in both dogs and cats, in which the use of phytotherapics is increasing, despite the prejudices of the academic world and of the veterinary practitioners. Laws regarding the use of non conventional medicines in veterinary practises are lacking in Italy, despite many other countries in Europe; yet National Federation of Italian Veterinaries (F.N.O.V.I.) asserted that the use of NCM has to be considered a veterinary practise at all. At the end of this paper, the Authors provided many examples of phytotheapic prescriptions to control different illness in both dogs and cats