1st Regular Kakenhi Meeting
Date: Dec. 3rd, 2021
Hybrid meeting: onsite (K206, YITP, Kyoto Univ.) & online

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Presentation Time Speaker
09:30—10:15 Hisao Hayakawa† (YITP, Kyoto Univ.)
"Geometrical Quantum Chemical Engine"
(abstract) We propose a chemical engine in an adiabatic (Thouless) pumping process for a quantum dot connected to external reservoirs under an isothermal condition. Thanks to the existence of a Berry-phase-like variable in this process, we can extract work by controlling the chemical potentials in the reservoirs without time averaged bias. Through the theoretical analysis of the quantum master equation for the Anderson model of a quantum dot within the wide band approximation, we illustrate the explicit values of the work, thermodynamic length and effective efficiency of the engine as functions of the phase difference of the controlled chemical potentials. This talk is based on the collaboration with Ryosuke Yoshii and Ville M. M. Paasonen.
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10:15—10:45 Kiyoshi Kanazawa† (Tsukuba Univ.)
"Field master equation for non-Markovian stochastic processes and its application to linear and nonlinear Hawkes processes"
(abstract) Non-Markovian stochastic processes are ubiquitous in all disciplines across natural and social sciences. However, the current mathematical framework mainly focuses on the Markovian stochastic processes, and it is technically not accessible to address such non-Markovian systems in general. In this talk, we have solved this technical problem by developing the Markov embedding approach and deriving the field master equation for non-Markovian processes [1-4]. In particular, we focus on the linear [1,2] and nonlinear [3,4] Hawkes processes, popular non-Markovian models for complex systems. The Hawkes processes are designed to capture the positive-feedback loop due to historical events and have broad applications to various complex systems, such as seismology, financial modelling, and social dynamics. We have provided various asymptotic solutions for linear and nonlinear Hawkes processes by solving the field master equations. We finally find that various power laws are ubiquitously observed for linear and nonlinear Hawkes processes regarding the intensity probability density function.

References:
1. K. Kanazawa and D. Sornette, Phys. Rev. Lett. 125, 138301 (2020).
2. K. Kanazawa and D. Sornette, Phys. Rev. Research 2, 033442 (2020).
3. K. Kanazawa and D. Sornette, Phys. Rev. Lett. 127, 188301 (2021).
4. K. Kanazawa and D. Sornette, arXiv:2110.01523.
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10:45—11:00 break
11:00—12:15 Amit Kumar Chatterjee† (YITP, Kyoto Univ.)
"Stochastic finite range processes: non-equilibrium steady state and observables"
(abstract) We consider a generic class of non-equilibrium stochastic processes on one dimensional periodic lattices, where particle from a randomly chosen lattice site can hop to its nearest neighbors. The hop-rates however, in general, can depend on the departure and arrival lattice sites as well as a finite number of neighboring lattice sites. These stochastic processes, generalizing the interaction range from nearest or next nearest neighbors to a general finite number of neighbors, is thereby named as finite range processes [1]. Inspired by the detailed balance condition leading to equilibrium Gibbs-Boltzmann distribution, we will show how generalized techniques like pairwise balance condition [1], h-balance condition [2] etc. can exactly solve the non-trivial non-equilibrium steady state probability distributions of finite range processes. Consequently, one can analytically calculate observables e.g. spatial correlations, particle current etc. for these non-equilibrium steady states. Interestingly, for specific choice of the hop-rates, we will discuss how the stochastic finite range processes exhibit phenomena like negative differential mobility (decreasing current with increasing bias) [2], zero-current non-equilibrium states [2] and condensation (accumulation of macroscopic number of particles at a single lattice site) [1].

References:
1. Physical Review E 92, 032103 (2015).
2. Physical Review E 98, 062134 (2018).
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12:15—13:15 lunch break
13:15—13:45 Kuniyasu Saitoh‡ (Kyoto Sangyo Univ.)
"Sound damping near jamming"
(abstract) Sound characteristics of soft athermal particles are closely related to their mechanical properties near jamming. For example, the speed of transverse sound is proportional to the square-root of shear modulus which eventually vanishes at the onset of unjamming such that the transverse sound does not exist in a liquid state. Employing numerical simulations, we investigate sound characteristics of two-dimensional soft athermal particles. Based on our recent study [K. Saitoh and H. Mizuno, Soft Matter 17, 4204 (2021)], we show that viscous forces between the particles in contact strongly affect both the speed and attenuation of sound, where a characteristic dip in the sound speed disappears and the Rayleigh law of sound scattering exhibits a crossover to the quadratic scaling with the increase of viscous forces. We also find that critical scaling of the sound speeds and attenuation coefficients can be explained by the rheological properties of soft athermal particles, i.e. the storage and loss moduli, where our numerical results with different packing fraction are nicely collapsed by the proximity to jamming.
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13:45—14:15 Michio Otsuki‡ (Osaka Univ.)
"Softening and residual loss modulus of jammed grains under oscillatory shear"
(abstract) Dense disordered materials, such as granular materials, emulsions, and colloidal suspensions, behave like solids when the packing fraction exceeds the jamming point. Under a small shear strain, the shear stress is proportional to the shear strain, while the mechanical response becomes nonlinear as the strain increases. The nonlinear response is believed to result from the yielding transition associated with plastic deformation. However, recent studies have indicated that the mechanical response becomes nonlinear even below the yielding point [1]. Such a response is called softening, where the storage modulus under oscillatory shear decreases as the strain amplitude increases.

In this study, we numerically investigate jammed materials comprising frictionless particles under oscillatory shear to clarify the origin of softening [2]. We find the storage modulus exhibits softening, and the loss modulus remains finite even below the yielding point. With the aid of Fourier analysis of the particle trajectories, we theoretically reveal the role of Fourier components for the storage and loss moduli.

In addition, we also study frictional granular materials and find that the softening and the residual loss modulus depend on the friction coefficients [3]. An analysis of a simplified model predicts a scaling law for the mechanical response depending on the friction coefficients, which is consistent with our numerical results.

[1] J. Boschan, D. Vågberg, E. Somfai, and B. P. Tighe, Soft Matter 12, 5450 (2016).
[2] M. Otsuki and H. Hayakawa, arXiv:2101.07473.
[3] M. Otsuki and H. Hayakawa, Eur. Phys. J. E 44, 70 (2021).
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14:15—14:45 Satoshi Takada‡ (Tokyo Univ. Agri. Tech.)
"Discontinuous shear thickening of a moderately dense inertial suspension composed of frictionless soft-core particles"
(abstract) We investigate the rheology of a moderately dense inertial suspension composed of frictionless soft-core particles. Based on our previous work for a dilute system [1], we develop the kinetic theory of this system to denser systems. Contrary to a hard-core system [2], the discontinuous shear thickening is observed even when the packing fraction becomes finite. We also perform Langevin simulations to validate the theoretical treatment, which shows good agreement with each other. This talk is based on the collaboration with Kazuhiro Hara and Hisao Hayakawa.

[1] S. Sugimoto and S. Takada, J. Phys. Soc. Jpn. 89, 084803 (2020).
[2] H. Hayakawa, S. Takada, and V. Garzó, Phys. Rev. E 96, 042903 (2017), [Erratum] 101, 069904 (2020).
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14:45—15:05 break
15:05—15:50 Takeshi Kawasaki‡ (Nagoya Univ.)
"Nonlinear rheology in jammed frictionless athermal systems"
(abstract) We investigate criticality near the jamming transition density in both quiescent systems and those under shear flow by considering the effect of mechanical training on the jamming transition and nonlinear rheology. We simulate frictionless soft particles undergoing athermal quasi-static shear flow using initial configurations trained with athermal quasi-static cyclic volume deformations. The jamming transition density of the initial configuration is systematically changed by tuning the ``depth'' of mechanical training. We exert a steady shear flow on these configurations and observe either shear jamming (gain of stiffness due to shear flow) or shear melting (loss of stiffness due to shear flow), depending on the depth of training and proximity to the jamming transition density. We also observe that the characteristic strains at which shear jamming or melting occurs diverge at a unique density. Finally, we thoroughly investigate nonlinear rheology near the jamming transition density, and contrary to previous work, we find a nonlinear ``softening'' occurs below the jamming transition density as well as above it.
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15:50—16:20 Pradipto† (YITP, Kyoto Univ.)
"Viscoelastic response of the impact process on dense suspensions"
(abstract) We numerically study impact processes on dense suspensions using the lattice Boltzmann method to elucidate the connection between the elastic rebound of an impactor and relations among the impact speed, the maximum force acting on the impactor and elapsed time to reach the maximum force. We find that the maximum force emerges in the early stage of the impact, while the rebound process takes place in the late stage. We find a crossover of the maximum force from speed independent regime for low impact speed to a power-law regime for high impact speed. We then propose a floating + force chain model, where the rebound process is caused by an elastic term that is proportional to the number of the connected force chains from the impactor to the bottom plate. This phenomenology predicts the power-law relations and also recovers the behavior of the impactor quantitatively.
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16:20—16:50 Daisuke Ishima† (YITP, Kyoto Univ.)
"Jacobian analysis for frictional amorphous solids under quasistatic shear"
(abstract) In this study, we investigate the frictional amorphous solids under quasi-static shear using the dynamical matrix (Jacobian). We obtained the other expression of the rigidity using the Jacobian in the linear region. In addition, it has been found that when the density of states was measured in the frictional amorphous solids, an isolated band is generated at low frequency. Furthermore, to study the stability of the configuration with viscous drag, we analyzed the stability of the frictional amorphous solids under quasi-static shear using the eigenvalues of the dynamical matrix which includes the viscous drag. We confirmed that there is an oscillatory instability consistent with Ref. [1] when we neglect the viscous term. However, when we use the dynamical matrix which includes the viscous drag, as in Ref. [2] we cannot obtain the oscillatory instability.

[1] J. Chattoraj, O. Gendelman, M. P. Ciamarra, and I. Procaccia, Phys. Rev. Lett. 123, 098003 (2019).
[2] J. Chattoraj, O. Gendelman, M. P. Ciamarra, and I. Procaccia, Phys. Rev. E 100, 042901 (2019).
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16:50—17:10 break
17:10—17:40 Kiwamu Yoshii† (Osaka Univ.)
"Rheology of dense wet granular materials"
(abstract) Athermal assemblies of particles, such as granular materials, emulsions, foams, and colloids, turn into jammed solids above the jamming point. Previous studies have numerically investigated the rheological properties of jammed solids near the jamming point by assuming only purely repulsive contact force, but cohesiveness between particles is nonnegligible in many realistic situations. For example, small amounts of liquid induce cohesive interaction by capillary bridges between particles. However, the effect of cohesiveness on the rheological properties remains unclear.

In this study, we numerically study the rheological properties of wet granular materials at constant volume. Wet granular materials under oscillatory shear behave like solids with finite shear modulus even below the jamming point of dry grains and exhibit critical scaling laws with different critical exponents. We also discuss the rheological properties of wet granular materials under steady shear depending on the shear rate.
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17:40—18:10 Sadato Yamanaka‡ (Kyoto Sangyo Univ.)
"Vibrational modes and mechanical responses of deformable bubbles at the jamming transition"
(abstract) Soft particles, such as bubbles and emulsions, display jamming transition, in which e.g. confining pressure, excess contact number, and shear modulus have finite value upon the jamming and obey logarithmic scaling laws as a function of the distance to the jamming. These systems are usually modelled by undeformable particles which interact with soft-core potentials and overlap when they are in touch. The prediction for the scaling of shear modulus in the model, however, differ from experiments in emulsions. This implies deformability of particles would be a missing link because the deformability can modify mechanical responses even just above the jamming onset. We investigated the role of particle deformability on the jamming transition with respect to scaling laws, mechanical responses, and vibrational properties by using Morse-Witten model.
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† onsite presentation / ‡ online presentation