arXiv subjects

Takashi Odagaki

Publications and source records attributed to Takashi Odagaki.

18 recordsLinked to original sources

arXiv2025

Aging of glass-forming materials following a temperature jump

Physical aging is one of the non-equilibrium phenomena where physical properties change over time due to structural relaxation. Aging in spin glass systems has been explained by a trap model on the temperature-independent energy landscape. Meanwhile, in the free energy landscape (FEL) approach to aging phenomena, it is assumed that the FEL responds to temperature changes with a time delay. In this paper, aging in a glass forming model in which both the trapping effect and the delayed response of the FEL exist is studied after the temperature is changed. It is confirmed that the trapping effect gives rise to Type-I aging where the relaxation time increases with waiting time regardless of the direction of temperature change, and that the delayed response of the FEL produces Type-II aging where the waiting-time dependence of the relaxation time depends on the direction of temperature change. When both effects exist and the response time of the FEL is appropriate, these effects can be differentiated in the short-time behavior of the temporal relaxation time. It is argued that the material time or the internal clock and the fictive temperature introduced phenomenologically are understood as the concepts describing the delayed response of the FEL to temperature change.

cond-mat.stat-mech↗

arXiv2021

Variable range random walk

Exploiting the coherent medium approximation, random walk among sites distributed randomly in space is investigated when the jump rate depends on the distance between two adjacent sites. In one dimension, it is shown that when the jump rate decays exponentially in the long distance limit, a non-diffusive to diffusive transition occurs as the density of sites is increased. In three dimensions, the transition exists when the jump rate has a super Gaussian decay.

cond-mat.stat-mech↗

arXiv2021

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 $λ$ of change of the number of infected individuals $I$ is given by an ellipse in the $λ$-$I$ plane which is supported in $[I_{\ell}, I_h]$. With $a \equiv (I_h - I_{\ell})/(I_h + I_{\ell})$, it is shown that (1) when $a < 1$ or $I_{\ell} >0$, oscillation of the infection curve is self-organized and the period of the oscillation is in proportion to the ratio of the difference $ (I_h - I_{\ell})$ and the geometric mean $\sqrt{I_h I_{\ell}}$ of $I_h$ and $I_{\ell}$, (2) when $a = 1$, the infection curve shows a critical behavior where it decays obeying a power law function with exponent $-2$ in the long time limit after a peak, and (3) when $a > 1$, 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 $I_{\ell} < 0$.

q-bio.PE↗

arXiv2020

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.

q-bio.PE↗

arXiv2020

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. On the basis of the expected utility theory, a theoretical framework to find out an optimum strategy in the space of lockdown measure and quarantine measure is proposed for minimizing the maximum number of infected and for controlling the outbreak of pandemic at its early stage.

physics.soc-ph↗

arXiv2010

Dynamics of particle flips in two-dimensional quasicrystals

The dynamics of quasicrystals is more complicated than the dynamics of periodic solids and difficult to study in experiments. Here, we investigate a decagonal and a dodecagonal quasicrystal using molecular dynamics simulations of the Lennard-Jones-Gauss interaction system. We observe that the short time dynamics is dominated by stochastic particle motion, so-called phason flips, which can be either single-particle jumps or correlated ring-like multi-particle moves. Over long times, the flip mechanism is efficient in reordering the quasicrystals and can generate diffusion. The temperature dependence of diffusion is described by an Arrhenius law. We also study the spatial distribution and correlation of mobile particles by analyzing the dynamic propensity.

cond-mat.mtrl-sci↗

arXiv2009

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 temperature 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 Tm at several cooling rates to produce an amorphous state. Various thermodynamic quantities are measured as a function of temperature while the system is heated at a constant rate. The glass transiton is observed by a sudden increase of the energy and Tg is shown to be an increasing function of the cooling rate in the preparation process of the amorphous state. In a relatively-high temperature region, the system gradually transforms into crystals, and the time-temperature-transformation(TTT) curve shows a typical nose shape. It is found that the transformation time to a crystalline state is the shortest at a temperature 14~15% below the melting temperature Tm and that at sufficiently low temperatures the transformation time is much longer than the available CPU time. This indicates that a long-lived glassy state is realized.

cond-mat.dis-nn↗

arXiv2009

Vitrification of a monatomic 2D simple liquid

A monatomic simple liquid in two dimensions, where atoms interact isotropically through the Lennard-Jones-Gauss potential [M. Engel and H.-R. Trebin, Phys. Rev. Lett. 98, 225505 (2007)], is vitrified by the use of a rapid cooling technique in a molecular dynamics simulation. Transformation to a crystalline state is investigated at various temperatures and the time-temperature-transformation (TTT) curve is determined. It is found that the transformation time to a crystalline state is the shortest at a temerature 14% below the melting temperature Tm and that at temperatures below Tv = 0.6 Tm the transformation time is much longer than the available CPU time. This indicates that a long-lived glassy state is realized for T < Tv.

cond-mat.dis-nn↗

arXiv2008

Molecular dynamics studies on spatial scale of low energy excitation in a simple polymer system

A molecular dynamics simulation is performed to investigate spatial scale of low energy excitation (LEE) in a single linear chain of united atoms. The self part of the dynamic structure function, $S_\mathrm{S}(q,ω)$, is obtained in a wide range in frequency space ($ω$) and reciprocal space ($q$). A broad peak corresponding to the LEE is detected at $ω/2π=2.5 \times 10^{11} \mathrm{s^{-1}}$ ($\equiv ω_{\mathrm{LEE}}/2π$) on the contour maps of $S_\mathrm{S}(q,ω)$, near and below the glass transition temperature ($T_{\mathrm{g}}$=230 K). The $S_\mathrm{S}(q,ω_{\mathrm{LEE}})$ is symmetric around a maximum along the logarithm of $q$. The inverse of $q_{\mathrm{max}}$, giving the maximum position of $S_\mathrm{S}(q,ω_{\mathrm{LEE}})$, depends on temperature as $2π/q_{\mathrm{max}}\sim T^{0.52}$ for $60 \mathrm{K}<T<T_{\mathrm{g}}$ and $2π/q_{\mathrm{max}}\sim T^{0.97}$ for $T_{\mathrm{g}}<T<600 \mathrm{K}$, which is the spatial scale of the motion corresponding to the LEE at low temperatures. Based on a Gaussian approximation for the displacements of monomer groups which give rise to the motion relevant to the LEE, it is found that the number of monomers contained in a group is about 6.

cond-mat.mtrl-sci↗

arXiv2007

Nonlinear Energy Response of Glass Forming Materials

A theory for the nonlinear energy response of a system subjected to a heat bath is developed when the temperature of the heat bath is modulated sinusoidally. The theory is applied to a model glass forming system, where the landscape is assumed to have 20 basins and transition rates between basins obey a power law distribution. It is shown that the statistics of eigenvalues of the transition rate matrix, the glass transition temperature $T_g$, the Vogel-Fulcher temperature $T_0$ and the crossover temperature $T_x$ can be determined from the 1st- and 2nd-order ac specific heats, which are defined as coefficients of the 1st- and 2nd-order energy responses. The imaginary part of the 1st-order ac specific heat has a broad peak corresponding to the distribution of the eigenvalues. When the temperature is decreased below $T_g$, the frequency of the peak decreases and the width increases. Furthermore, the statistics of eigenvalues can be obtained from the frequency dependence of the 1st-order ac specific heat. The 2nd-order ac specific heat shows extrema as a function of the frequency. The extrema diverge at the Vogel-Fulcher temperature $T_0$. The temperature dependence of the extrema changes significantly near $T_g$ and some extrema vanish near $T_x$.

cond-mat.stat-mech↗

arXiv2006

Self-organizing social hierarchy and villages in a challenging society

We show by Monte Calro (MC) simulation that the hierarchy and villages emerge simultaneously in a challenging society when the population density exceeds a critical value. Our results indicate that among controlling processes of diffusion and fighting of individuals and relaxation of wealth, the trend of individuals challeninging to stronger neighbors plays the pivotal role in the self-organization of the hierarchy and villages.

physics.soc-ph↗

arXiv2005

Packing and percolation of poly-disperse discs and spheres

For the binary discs packed in two dimensions, the packing fraction of disc assembly becomes lower than that of the monodisperse system when the size ratio is close to unity. We show that the suppressed packing fraction is caused by an increase of the adjacent neighbours with long bonds where the adjacent neighbours is defined on the basis of the Laguerre (radical) tessellation. For the poly-disperse systems in two and three dimensions, the packing fraction is shown to have a minimuma as a function of the poly-dispersity. Percolation process in the densely packed discs and spheres is also studied. The critical area (volume) fraction in two (three) dimensions is shown to be a monotonically increasing (decreasing) function of the poly-dispersity.

cond-mat.dis-nn↗

arXiv2005

Self-organizing social hierarchies in a timid society

Emergence of hierarchies is investigated by Monte Carlo simulation in a timid society where all individuals are pacifist. The self-organiztion of hierarchies is shown to occur in two steps as the population is increased, i.e. there are three states, one egalitarian and two hierarchical states;the transition from the egalitarian to the first hierarchical state is continuous and the transition from the first hierachical state to the second one is discontinuous. In the first hierarchical society, all individuals belong to either middle class or losers and no winners appear. In the second hierarchical society, many winners emerge and the population of the middle class is reduced. The hierarchy in the second hierarchical society is stronger than the hierachy in a no-preference society studied by Bonabeau et al [ Physica A{\bf 217}, 373 (1995)]

physics.soc-ph↗

arXiv2005

Construction of the free energy landscape by the density functional theory

On the basis of the density functional theory, we give a clear definition of the free energy landscape. To show the usefulness of the definition, we construct the free energy landscape for rearrangement of atoms in an FCC crystal of hard spheres. In this description, the cooperatively rearranging region (CRR) is clealy related to the hard spheres involved in the saddle between two adjacent basins. A new concept of the simultaneously rearranging region (SRR) emerges naturally as spheres defined by the difference between two adjacent basins. We show that the SRR and the CRR can be determined explicitly from the free energylandscape.

cond-mat.stat-mech↗

arXiv2003

Absence of self-averaging in the complex admittance for transport through disordered media

Random walk models in one-dimensional disordered media with an oscillatory input current are investigated theoretically as generic models of the boundary perturbation experiment. It is shown that the complex admittance obtained in the experiment is not self-averaging when the jump rates $w_i$ are random variables with the power-law distribution $ρ(w_i)\sim {w_i}^{α-1} (0 < α\leq 1)$. More precisely, the frequency-dependence of the disorder-averaged admittance $<χ>$ disagrees with that of the admittance $χ$ of any sample. It implies that the Cole-Cole plot of $<χ>$ shows a different shape from that of the Cole-Cole plots of $χ$ of each sample. The condition for absence of self-averaging is investigated with a toy model in terms of the extended central limit theorem. Higher dimensional media are also investigated and it is shown that the complex admittance for two-dimensional or three-dimensional media is also non-self-averaging.

cond-mat.dis-nn↗

arXiv2002

Anomalous thermal conductivity and local temperature distribution on harmonic Fibonacci chains

The harmonic Fibonacci chain, which is one of a quasiperiodic chain constructed with a recursion relation, has a singular continuous frequency-spectrum and critical eigenstates. The validity of the Fourier law is examined for the harmonic Fibonacci chain with stochastic heat baths at both ends by investigating the system size N dependence of the heat current J and the local temperature distribution. It is shown that J asymptotically behaves as (ln N)^{-1} and the local temperature strongly oscillates along the chain. These results indicate that the Fourier law does not hold on the harmonic Fibonacci chain. Furthermore the local temperature exhibits two different distribution according to the generation of the Fibonacci chain, i.e., the local temperature distribution does not have a definite form in the thermodynamic limit. The relations between N-dependence of J and the frequency-spectrum, and between the local temperature and critical eigenstates are discussed.

cond-mat.stat-mech↗

arXiv2001

Binary self-similar one-dimensional quasilattices: Mutual local-derivability classification and substitution rules

Self-similar binary one-dimensional (1D) quasilattices (QLs) are classified into mutual local-derivability (MLD) classes. It is shown that the MLD classification is closely related to the number-theoretical classification of parameters which specify the self-similar binary 1D QLs. An algorithm to derive an explicit substitution rule, which prescribes the transformation of a QL into another QL in the same MLD class, is presented. An explicit inflation rule, which prescribes the transformation of the self-similar 1D QL into itself, is obtained as a composition of the explicit substitution rules. Symmetric substitution rules and symmetric inflation rules are extensively discussed.

cond-mat↗

arXiv2000

Absence of self-averaging in the complex admittance for transport through random media

A random walk model in a one dimensional disordered medium with an oscillatory input current is presented as a generic model of boundary perturbation methods to investigate properties of a transport process in a disordered medium. It is rigorously shown that an admittance which is equal to the Fourier-Laplace transform of the first-passage time distribution is non-self-averaging when the disorder is strong. The low frequency behavior of the disorder-averaged admittance, $<χ> -1 \sim ω^μ$ where $μ< 1$, does not coincide with the low frequency behavior of the admittance for any sample, $χ- 1 \sim ω$. It implies that the Cole-Cole plot of $<χ>$ appears at a different position from the Cole-Cole plots of $χ$ of any sample. These results are confirmed by Monte-Carlo simulations.

cond-mat.dis-nn↗