New compartment model for COVID-19.

The SIR or susceptible-infected-recovered model is the standard compartment model for understanding epidemics and has been used all over the world for COVID-19. While the SIR model assumes that infected patients are identical to symptomatic and infectious patients, it is now known that in COVID-19 pre-symptomatic patients are infectious and there are significant number of asymptomatic patients who are infectious. In this paper, population is separated into five compartments for COVID-19; susceptible individuals (S), pre-symptomatic patients (P), asymptomatic patients (A), quarantined patients (Q) and recovered and/or dead patients (R).

Waiting time dependence of aging.

Aging phenomena have been observed in many non-equilibrium systems such as polymers and glasses, where physical properties depend on the waiting time between the starting time of observation and the time when the temperature is changed. The aging is classified into two types on the basis of the waiting time dependence of an instantaneous relaxation time: When the relaxation time is always an increasing function of the waiting time, the aging is called Type I and when it depends on the protocol of the temperature change, the aging is called Type II. Aging of a random walk in three dimensions is investigated when the free energy landscape controlling the jump rate responds to temperature change with a delay.

Self-organization of oscillation in an epidemic model for COVID-19.

On the basis of a compartment model, the epidemic curve is investigated when the net rate of change of the number of infected individuals is given by an ellipse in the - plane which is supported in . With , it is shown that (1) when , oscillation of the infection curve is self-organized and the period of the oscillation is in proportion to the ratio of the difference and the geometric mean of and , (2) when , the infection curve shows a critical behavior where it decays obeying a power law function with exponent in the long time limit after a peak, and (3) when , the infection curve decays exponentially in the long time limit after a peak. The present result indicates that the pandemic can be controlled by a measure which makes .

Self-organized wavy infection curve of COVID-19.

Exploiting the SIQR model for COVID-19, I show that the wavy infection curve in Japan is the result of fluctuation of policy on isolation measure imposed by the government and obeyed by citizens. Assuming the infection coefficient be a two-valued function of the number of daily confirmed new cases, I show that when the removal rate of infected individuals is between these two values, the wavy infection curve is self-organized. On the basis of the infection curve, I classify the outbreak of COVID-19 into five types and show that these differences can be related to the relative magnitude of the transmission coefficient and the quarantine rate of infected individuals.

Exact properties of SIQR model for COVID-19.

The SIQR model is reformulated where compartments for infected and quarantined are redefined so as to be appropriate to COVID-19, and exact properties of the model are presented. It is shown that the maximum number of infected at large depends strongly on the quarantine rate and that the quarantine measure is more effective than the lockdown measure in controlling the pandemic. The peak of the number of quarantined patients is shown to appear some time later than the time that the number of infected becomes maximum.

Analysis of the outbreak of COVID-19 in Japan by SIQR model.

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.

Critical nucleus size for crystallization of supercooled liquids in two dimensions.

Using molecular dynamics simulations, we study the crystallization of supercooled liquids in two dimensions in which particles interact with other particles via the Lennard-Jones-Gauss potential. We first prepare supercooled liquids at various temperatures by rapid quenching from the melt. The simulations are performed with a crystalline seed inserted at the center of the initial system.

New Scenario of Dynamical Heterogeneity in Supercooled Liquid and Glassy States of 2D Monatomic System.

Via analysis of spatiotemporal arrangements of atoms based on their dynamics in supercooled liquid and glassy states of a 2D monatomic system with a double-well Lennard-Jones-Gauss (LJG) interaction potential, we find a new scenario of dynamical heterogeneity. Atoms with the same or very close mobility have a tendency to aggregate into clusters. The number of atoms with high mobility (and size of their clusters) increases with decreasing temperature passing over a maximum before decreasing down to zero.

Solid phase stability of a double-minimum interaction potential system.

We study phase stability of a system with double-minimum interaction potential in a wide range of parameters by a thermodynamic perturbation theory. The present double-minimum potential is the Lennard-Jones-Gauss potential, which has a Gaussian pocket as well as a standard Lennard-Jones minimum. As a function of the depth and position of the Gaussian pocket in the potential, we determine the coexistence pressure of crystals (fcc and bcc).

Glass formation and thermodynamics of supercooled monatomic liquids.

Atomic mechanism of glass formation of a supercooled simple monatomic liquid with Lennard-Jones-Gauss (LJG) interatomic potential is studied by molecular dynamics (MD) simulation. Supercooled and glassy states are obtained by cooling from the melt. Glassy state obtained at low temperatures is annealed for very long time, on the order of microsecond, and we find that glassy state remains unchanged and that the long-lived glassy state of a simple monatomic system in three dimensions is realized.

Glass formation and crystallization of a simple monatomic liquid.

A simple monatomic system in two dimensions with a double-well interaction potential is investigated in a wide range of temperatures by molecular-dynamics simulation. The system is melted and equilibrated well above the melting temperature, and then it is quenched to a temperature 88% below the melting temperature at several cooling rates to produce an amorphous state. Various thermodynamic quantities are measured as functions of temperature while the system is heated at a constant rate.

Free-energy landscape for a tagged particle in a dense hard-sphere fluid.

Exploiting the thermodynamic potential functional provided by density functional theory, we determine analytically the free-energy landscape (FEL) in a hard-sphere fluid. The FEL is represented in the three-dimensional coordinate space of the tagged particle. We also analyze the distribution of the free-energy barrier between adjacent basins and show that the most provable value and the average of the free-energy barrier are increasing functions of the density.

Geometrical percolation of hard-core ellipsoids of revolution in the continuum.

The percolation threshold of hard prolate ellipsoids of revolution dispersed in a continuum is obtained as a function of the aspect ratio. First random close packing of ellipsoids is produced by a dropping-and-shaking protocol. Two ellipsoids are regarded as connected when they come sufficiently close.

Storage capacity and retrieval time of small-world neural networks.

To understand the influence of structure on the function of neural networks, we study the storage capacity and the retrieval time of Hopfield-type neural networks for four network structures: regular, small world, random networks generated by the Watts-Strogatz (WS) model, and the same network as the neural network of the nematode Caenorhabditis elegans. Using computer simulations, we find that (1) as the randomness of network is increased, its storage capacity is enhanced; (2) the retrieval time of WS networks does not depend on the network structure, but the retrieval time of C. elegans's neural network is longer than that of WS networks; (3) the storage capacity of the C.

Mean-field analysis of phase transitions in the emergence of hierarchical society.

Emergence of hierarchical society is analyzed by use of a simple agent-based model. We extend the mean-field model of Bonabeau et al. [Physica A 217, 373 (1995)] to societies obeying complex diffusion rules where each individual selects a moving direction following their power rankings.

Free energy landscape and cooperatively rearranging region in a hard sphere glass.

Exploiting the density functional theory, we calculate the free energy landscape (FEL) of the hard sphere glass in three dimensions. From the FEL, we estimate the number of the particles in the cooperatively rearranging region (CRR). We find that the density dependence of the number of the particles in the CRR is expressed as a power law function of the density.

Effects of superspreaders in spread of epidemic.

Within the standard SIR model with spatial structure, we propose two models for the superspreader. In one model, superspreaders have intrinsically strong infectiousness. In other model, they have many social connections.

Dissipative process under a boundary perturbation.

A dissipative process in systems subjected to a boundary perturbation is analyzed on the basis of quantum mechanics. We show that the response of the system to the perturbation can be expressed in terms of the first-passage time defined appropriately by quantum mechanics. In other words, the first-passage-time distribution plays the role of the response function in the linear response theory.

Resonant transmission of a soliton across an interface between two Toda lattices.

The transmission of a single soliton is investigated numerically across an interface between two Toda lattices which are connected by a harmonic spring. We find that a resonant transmission of the soliton occurs when the spring constant of the harmonic spring is adjusted properly. Furthermore, when the amplitude of the incident soliton is large, the soliton transmission coefficient exhibits a local minimum which is due to an emergence of localized waves around the harmonic spring.

Numerical study of soliton scattering in inhomogeneous optical fibers.

Using a variable-coefficient nonlinear Schrödinger equation, transmission profile of a single soliton in the optical fiber with an inhomogeneous region is studied numerically. It is found that the transmitted wave contains two solitons which form a bound state when the difference of the dispersion coefficient between the inhomogeneous and the homogeneous regions is large enough. When the amplitude of the transmitted wave is small, the transmitted wave is apt to contain a bound state soliton.

Specific heat in a nonequilibrium system composed of Einstein oscillators.

In order to understand the behavior of thermodynamic quantities near the glass transition temperature, we put the energy landscape picture and the particle's jump motion together and calculate the specific heat of a nonequilibrium system. Taking the finite observation time into account, we study the observation time dependence of the specific heat. We assume the Einstein oscillators for the dynamics of each basin in the landscape structure of phase space and calculate the specific heat of a system with 20 basins.