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Tetsuro Konishi

Publications and source records attributed to Tetsuro Konishi.

At least 19 recordsLinked to original sources
arXiv2022

Dynamically induced conformation depending on excited normal modes of fast oscillation

We present dynamical effects on conformation in a simple bead-spring model consisting of three beads connected by two stiff springs. The conformation defined by the bending angle between the two springs is determined not only by a given potential energy function depending on the bending angle, but also fast motion of the springs which constructs the effective potential. A conformation corresponding with a local minimum of the effective potential is hence called the dynamically induced conformation. We develop a theory to derive the effective potential by using multiple-scale analysis and the averaging method. A remarkable consequence is that the effective potential depends on the excited normal modes of the springs and amount of the spring energy. Efficiency of the obtained effective potential is numerically verified.

nlin.CD↗
arXiv2021

Multiple pendulum and nonuniform distribution of average kinetic energy

Multiple pendulums are investigated numerically and analytically to clarify the nonuniformity of average kinetic energies of particles. The nonuniformity is attributed to the system having constraints and it is consistent with the generalized principle of the equipartition of energy. With the use of explicit expression for Hamiltonian of a multiple pendulum, approximate expressions for temporal and statistical average of kinetic energies are obtained, where the average energies are expressed in terms of masses of particles. In a typical case, the average kinetic energy is large for particles near the end of the pendulum and small for those near the root. Moreover, the exact analytic expressions for the average kinetic energy of the particles are obtained for a double pendulum.

nlin.CD↗
arXiv2021

Exact expression for average kinetic energy of 2-dimensional freely jointed chain and a related model

For a 2-dimensional freely jointed chain with 3 particles and a related model, the average and variance of the kinetic energies of each particle in thermal equilibrium are exactly obtained. The same is done for a related model. The excess of average kinetic energies near the chain ends, previously observed by numerical simulation, is analytically confirmed. The non-uniformity of the average kinetic energy results from the generalized principle of equipartition of energy. The non-uniformity also depends on temperature for a model that has intra-chain potential, and we can control it from outer-energetic to inner-energetic by decreasing the temperature.

cond-mat.stat-mech↗
arXiv2021

Emergence of Quasi-equilibrium State and Energy Distribution for the Beads-spring Molecule Interacting with a Solvent

We study the energy distribution during the emergence of a quasi-equilibrium (QE) state in the course of relaxation to equipartition in slow-fast Hamiltonian systems. A bead-spring model where beads (masses) are connected by springs is considered, and it is used as a model of polymers. The QE lasts for a long time because the energy exchange between the high-frequency vibrational and other motions is prevented when springs in the molecule become stiff. We numerically calculated the time-averaged kinetic energy and found that the kinetic energy of the solvent particles was always higher than that of the bead in a molecule. This is explained by adapting the equipartition theorem in QE, and it agrees well with the numerical results. The energy difference can help determine how far the system is from achieving equilibrium, and it can be used as an indicator of the number of frozen or inactive degrees exist in the molecule.

cond-mat.soft↗
arXiv2010

Slow relaxation to equipartition in spring-chain systems

In this study, one-dimensional systems of masses connected by springs, i.e., spring-chain systems, are investigated numerically. The average kinetic energy of chain-end particles of these systems is larger than that of other particles, which is similar to the behavior observed for systems made of masses connected by rigid links. The energetic motion of the end particles is, however, transient, and the system relaxes to thermal equilibrium after a while, where the average kinetic energy of each particle is the same, that is, equipartition of energy is achieved. This is in contrast to the case of systems made of masses connected by rigid links, where the energetic motion of the end particles is observed in equilibrium. The timescale of relaxation estimated by simulation increases rapidly with increasing spring constant. The timescale is also estimated using the Boltzmann-Jeans theory and is found to be in quite good agreement with that obtained by the simulation.

nlin.CD↗
arXiv2008

Apparent violation of equipartition of energy in constrained dynamical systems

We propose a planar chain system, which is a simple mechanical system with a constraint. It is composed of $N$ masses connected by $N-1$ light links. It can be considered as a model of a chain system, e.g., a polymer, in which each bond is replaced by a rigid link. The long time average of the kinetic energies of the masses in this model is numerically computed. It is found that the average kinetic energies of the masses are different and masses near the ends of the chain have large energies. We explain that this result is not in contradiction with the principle of equipartition. The apparent violation of equipartition is observed not only in the planar chain systems but also in other constrained systems. We derive an approximate expression for the average kinetic energy, which is in qualitative agreement with the numerical results.

cond-mat.stat-mech↗
arXiv2007

1/f fluctuations in spinning-particle motions around Schwarzschild black hole

We study the properties of chaos in the motions of a spinning test particle in Schwarzschild spacetime. We characterize the chaos using the power spectrum of the time series of $z$ components of the particle's position. It is found that the pattern of the power spectrum shows not only white noise but also $1/f$-type fluctuation, depending on the value of the total angular momentum $J$ and the spin $S$ of the test particle. Therefore we succeed in classifying the chaotic motions, which have been classified as simply chaotic ones in former works, into the two distinct types. One is $1/f$, and the other is white noise. Based on this classification, we plot, in the two-dimensional parameter space $(J,S)$, the phase diagram for the properties of the chaos. This phase diagram enables us in principle to guess the properties of the system $(J,S)$ by observing the dynamics of the test particle, even if the motion is chaotic. Furthermore, we detect that the origin of the $1/f$ fluctuation is that the particle motion stagnates around regular orbits (tori), while traveling back and forth between them, which is called ``stagnant motion'' or ``sticky motion'' in Hamiltonian dynamical systems. The point is that the difference of the property of the chaos or the power spectra is due to the topological structure of the phase space, which in turn is governed by the physical parameter set $(J,S)$ of the system. From this point of view, the chaos we found in this system is not always merely random.

gr-qc↗
arXiv2006

Clusters die hard: Time-correlated excitation in the Hamiltonian Mean Field model

The Hamiltonian Mean Field (HMF) model has a low-energy phase where $N$ particles are trapped inside a cluster. Here, we investigate some properties of the trapping/untrapping mechanism of a single particle into/outside the cluster. Since the single particle dynamics of the HMF model resembles the one of a simple pendulum, each particle can be identified as a high-energy particle (HEP) or a low-energy particle (LEP), depending on whether its energy is above or below the separatrix energy. We then define the trapping ratio as the ratio of the number of LEP to the total number of particles and the ``fully-clustered'' and ``excited'' dynamical states as having either no HEP or at least one HEP. We analytically compute the phase-space average of the trapping ratio by using the Boltzmann-Gibbs stable stationary solution of the Vlasov equation associated with the $N \to \infty$ limit of the HMF model. The same quantity, obtained numerically as a time average, is shown to be in very good agreement with the analytical calculation. Another important feature of the dynamical behavior of the system is that the dynamical state changes transitionally: the ``fully-clustered'' and ``excited'' states appear in turn. We find that the distribution of the lifetime of the ``fully-clustered'' state obeys a power law. This means that clusters die hard, and that the excitation of a particle from the cluster is not a Poisson process and might be controlled by some type of collective motion with long memory. Such behavior should not be specific of the HMF model and appear also in systems where {\it itinerancy} among different ``quasi-stationary'' states has been observed. It is also possible that it could mimick the behavior of transient motion in molecular clusters or some observed deterministic features of chemical reactions.

nlin.CD↗
arXiv2005

Formation of fractal structure in many-body systems with attractive power-law potentials

We study the formation of fractal structure in one-dimensional many-body systems with attractive power-law potentials. Numerical analysis shows that the range of the index of the power for which fractal structure emerges is limited. Dependence of the growth rate on wavenumber and power-index is obtained by linear analysis of the collisionless Boltzmann equation, which supports the numerical results.

nlin.PS↗
arXiv1999

Direct measurement of intersection angle of invariant manifolds for area preserving mappings

Intersection angles of stable and unstable manifolds for area preserving mappings are numerically calculated by extremely accurate computation. With the use of multiprecision library the values of angle as small as 10^{-400} are obtained. The singular dependence of the angle on the magnitude of hyperbolicity is confirmed. The power-law type prefactor with Stokes constant is also in good agreement with analytical estimation.

chao-dyn↗
arXiv1999

The Intersection Angles between N-Dimensional Stable and Unstable Manifolds in 2N-Dimensional Symplectic Mappings

We asymptotically compute the intersection angles between N-dimensional stable and unstable manifolds in 2N-dimensional symplectic mappings. There exist particular 1-dimensional stable and unstable sub-manifolds which experience exponentially small splitting of separatrix in our models. We show that the angle between the sub-manifolds is exponentially small with respect to the perturbation parameter $ε$, and the other angles are $O(ε^2)$.

chao-dyn↗
arXiv1998

Asymptotic expansion of 1-dimensional sub-manifolds of stable and unstable manifolds in a 4-dimensional symplectic mapping

We analytically compute asymptotic expansions of a 1-dimensional sub-manifold of stable and unstable manifolds in a 4-dimensional symplectic mapping by using the method called asymptotic expansions beyond all orders. This method enables us to capture exponentially small splitting of separatrices and also to obtain explicit functional approximations of the sub-manifolds. In addition, we show the condition with which homoclinic structure caused by crossing between the stable and unstable sub-manifolds is regarded as a direct product of 2-dimensional mappings.

chao-dyn↗
arXiv1996

Chaotic itinerancy and thermalization in one-dimensional self-gravitating systems

This is the third paper of the series of our studies of the one-dimensional self-gravitating many-body systems. In this paper, we thus study the transition phenomena after the first transition from a quasiequilibrium. We found that irrespective of the initial conditions, the system wanders between many states which yield the same properties of the quasiequilibrium as the water-bag. This itinerancy is most prominent in the time scale $t\sim 10^5 \sim 10^6 t_c$. In the midway between two succeeding quasiequilibria, the system experiences a transient state, where one particle keeps exclusive high energy and its motion decouples with the others. Though the transient state is not the thermally relaxed equilibrium, its distribution quite resembles the isothermal distribution. Thus the macroscopic relaxation we discussed in the previous papers corresponds to the transition from one of quasiequilibria to a transient state. Averaging the behavior over a time scale much longer than the macroscopic relaxation time gives the isothermal distribution. Distribution of lifetime $τ$ of the transient states yields a power-law distribution of $τ^{-2}$. The transient state gives a clear example of chaotic itinerancy in conserved dynamical systems. The mechanism of the onset of itinerancy is examined.

astro-ph↗