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Dynamics of atoms near the glass transition of simple classical liquids is studied on the basis of the mesoscopic stochastic-trapping diffusion model recently developed by Odagaki [J. Phys. A 20, 6455 (1987); Phys. Rev. B. 38, 9044 (1988)]. The jump rate of an atom {tracer) is assumed to have a distribution following a power-law function with exponent p, where p is a phenomenological parameter. A sharp transition is predicted at p=0, that is, the self-diffusion vanishes when p &0 and takes a nonzero finite value when p) 0. This transition is identified as the glass transition. With use of the coherent-medium approximation, the mean-square displacement is shown to exhibit a powerlaw dependence on time with exponent less than unity, and hence the incoherent scattering function for small wave vectors shows stretched exponential decay when p & 0. The non-Gaussian parameter at time t = 00 is shown to be nonzero in the glassy state (p &0) and vanishes in the fluid state (p) 0), indicating that this quantity may be used as an order parameter of the glass transition. The meansquare displacement and the non-Gaussian parameter are obtained in the intermediate time scale as well from the frequency-dependent diffusion constant. The apparent diffusion constant determined by the derivative of the mean-square displacement at an imtermediate time shows a smooth transition instead of the sharp one, which coincides with observations in molecular dynamics studies.The incoherent scattering function in the intermediate time scale agrees qualitatively with experiments and the exponent of its stretched exponential decay deviates from unity before the glass transition takes place, in agreement with observations made via computer experiments.

The SIQR model is exploited to analyze the outbreak of COVID-19 in Japan where the number of the daily confirmed new cases is explicitly treated as an observable. It is assumed that the society consists of four compartments; susceptible individuals (S), infected individuals at large (I), quarantined patients (Q) and recovered individuals (R), and the time evolution of the pandemic is described by a set of ordinary differential equations. It is shown that the quarantine rate can be determined from the time dependence of the daily confirmed new cases, from which the number of infected individuals can be estimated. The infection rate and quarantine rate are determined for the period from mid-February to mid-April in Japan and transmission characteristics of the initial stages of the outbreak in Japan are analyzed in connection with the policies employed by the government. The effectiveness of different measures is discussed for controlling the outbreak and it is shown that identifying patients through PCR (Polymerase Chain Reaction) testing and isolating them in a quarantine is more effective than lockdown measures aimed at inhibiting social interactions of the general population. An effective reproduction number for infected individuals at large is introduced which is appropriate to epidemics controlled by quarantine measures.

%e study the properties of one-dimensional quasilattices numerically and analytically. The geometrical properties of general one-dimensional quasilattices are discussed. The Ising model on these lattices is studied by a decimation transformation:The critical temperature and critical exponents do not differ from those for a regular periodic chain. The vibrational spectrum in the harmonic approximation is analyzed numerically. The system exhibits characteristics of both a regular periodic system and a disordered system. In the low-frequency region, the system behaves as a regular periodic system; wave functions appear extended. In the high-frequency region, the spectrum is self-similar and there is no unique behavior for the wave functions. The spectrum shows many gaps and Van Hove singularities. The gaps in the spectrum are also obtained analytically by examining the convergence of a continued-fraction expansion plus decimation transformation. The energy spectrum of a tight-binding electron Hamiltonian on the Fibonacci chain is also analyzed; it shows similar characteristics to those of the lattice vibration spectrum.