This also gives an affirmative answer to an open problem presented by Rass and Radcliffe (2003 Spatial Deterministic Epidemics (Mathematical Surveys and Monographs vol 102) (Providence, RI: American Mathematical Society)) in the case of discrete spatial habitat By appealing to the theory of spreading speeds and travelling waves for monotonic semiflows, we establish the existence of asymptotic speed of spread and show that it coincides with the minimal wave speed for monotonic travelling waves. ![]() This paper is devoted to the study of the asymptotic speed of spread and travelling waves for a spatially discrete SIS epidemic model. International Nuclear Information System (INIS) Spreading speed and travelling waves for a spatially discrete SIS epidemic model And for the CV model with a non-Fourier medium, the interval of group speed is also bounded and the maximum value can be obtained when the logarithmic heating rate is infinite. For the finite relaxation model with non-Fourier media, the interval of group speed is bounded and the maximum speed can be obtained when the logarithmic heating rate is exactly the reciprocal of relaxation time. For the model media that follow Fourier's law and correspond to the positive heat rate of heat conduction, the propagation mode is also considered the propagation of a group of heat waves because the group speed has no upper bound. These features show that propagation accelerates when heated and decelerates when cooled. The latter indicates that the spatial distribution of temperature, which follows the exponential function law, decays with time. The total speed of all the possible heat waves can be combined to form the group speed of the wave propagation. The former shows that a group of heat waves whose spatial distribution follows the exponential function law propagates at a group speed the speed of propagation is related to the logarithmic heating rate. Results show that the general form of the time spatial distribution of temperature for the three media comprises two solutions: those corresponding to the positive and negative logarithmic heating rates. Independent variable translation is applied to solve the partial differential equation. In view of the finite relaxation model of non-Fourier's law, the Cattaneo and Vernotte (CV) model and Fourier's law are presented in this work for comparing wave propagation modes. Wave propagation model of heat conduction and group speed We find these results: the whole system for the determination of the wave speeds can be divided into independent subsystems which are expressed by linear combinations, through scalar coefficients, of tensors all of the same order some wave speeds, but not all of them, are expressed by square roots of rational numbers finally, we prove that these wave speeds for the macroscopic model are the same of those furnished by the kinetic model. This model is already present in literature it deals with an arbitrary number of moments and it was proposed in the context of exact macroscopic approaches in Extended Thermodynamics. Matematica, Università di Cagliari, Via Ospedale 72, 09124 Cagliari (Italy)Įquations determining wave speeds for a model of ultrarelativistic gases are investigated. Matematica, Università di Cagliari, Viale Merello 92, 09123 Cagliari (Italy) Pennisi, S., E-mail: [Dip. Matematica e Informatica, Università di Cagliari, Via Ospedale 72, 09124 Cagliari (Italy) Demontis, F., E-mail: [Dip. It is not working: Function elipticity_calculation(rotation, elipticity, energy, calculated_elipticity)ĭelta = (kve*1.69508759865*100000+2.Wave speeds in the macroscopic extended model for ultrarelativistic gasesĮnergy Technology Data Exchange (ETDEWEB)īorghero, F., E-mail: [Dip. However, this code create new waves for every calculated point and also create wave wOut empty. WOut = (elipticity-rotation*cos(delta))/sin(delta) ![]() elipticity_calculation(wave1, wave2, wave3, "calculated_elipticity") However, when I put the function in the command window (see below), it gives me an syntax error:Įxpected wave name. WOut = (elipticity-rotation*cos(delta)/sin(delta)) The procedure look like this: Function elipticity_calculation(rotation, elipticity, energy, calculated_elipticity)ĭuplicate/O rotation, $calculated_elipticity I wrote a procedure for making a wave out of another with some calculations.
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