2nd Regular Kakenhi Meeting
"Theoretical studies of non-equilibrium driven-dissipative systems"

Date: Nov. 1st, 2022
Hybrid meeting: onsite (K206, YITP, Kyoto Univ.) & online

Registration form

Presentation Time	Speaker
09:30—09:35	Hisao Hayakawa† (YITP, Kyoto Univ.) Opening remarks
09:35—10:00	Michio Otsuki† (Osaka Univ.) "Three-particle model for the complex shear modulus of frictional granular materials" (abstract) We propose a simple model consisting of three particles to study the mechanical properties of frictional granular materials under oscillatory shear. Thanks to the introduction of the simple model, we can obtain an exact and analytic expression of the complex shear modulus, which satisfies a scaling law for a small strain amplitude in the vicinity of the jamming point. These expressions perfectly reproduce the shear modulus of many-body systems composed of identical circular disks with the initial configuration on a triangular lattice. Even for disordered systems, the model reproduces the results of many-body systems by introducing one fitting parameter. slide (open)
10:00—10:25	Daisuke Ishima† (YITP, Kyoto Univ.) "Theoretical determination of stress-strain curve of two-dimensional amorphous solids of dispersed frictional grains with finite shear strain" (abstract) The rigidity of frictionless grains is determined by the eigenvalue analysis of Hessian which is obtained from the configuration of grains [1]. However, frictional force between grains cannot be ignored in physical situations. In this talk I would like to report the theoretical expression of two-dimensional amorphous solids consisting of frictional dispersed grains which are interacted with a harmonic potential with finite shear strain, in which we ignore the dynamical friction caused by the slip processes of contact points. This research is a natural extension of our recent paper in the linear response regime [2]. With the aid of eigenvalue analysis of Hessian matrix, we theoretically determine the rigidity. The theoretical rigidity agrees with that obtained by molecular dynamics simulations except for the yielding point at which stress drops take place. [1] C. Maloney and A. Lemaître, Phys. Rev. E 74, 016118 (2006). [2] D. Ishima, K. Saitoh, M. Otsuki and H. Hayakawa, arXiv:2207.06632. slide (open)
10:25—10:40	break
10:40—11:10	Norihiro Oyama† (Toyota Central R&D Labs.) "Machine Learning Structural Orders of Glasses" (abstract) Glass transition, a solidification of liquids upon fast cooling with its structures remaining random, is observed quite universally in both natural and industrial scenes. This phenomenon has challenged statistical physicists for more than 100 years as the deepest and most interesting unsolved problem in solid state theory. One puzzling feature is that the two-body density correlation function, a typical measure of structures, does not exhibit a major change at the transition while the viscosity changes by more than 15 decades. On the other hand, detailed analyses on the dynamics of glassy, supercooled liquids elucidated that the readily mobile regions are spatially correlated and the resulting displacement fields are heterogeneous. Although recently-invented several multi-body structural indicators successfully explained this dynamical heterogeneity purely in terms of static structural information, the examples are limited to specific classes of glass formers. In particular, no indicator has been proposed for a widely-used typical glass former, the Kob-Andersen model. In general, finding the structural indicator requires trials-and-errors approach depending on the system details and thus is troublesome and time-consuming. This situation naturally evoked the machine learning-based exploration of the structural indicators that can explain the glassy dynamics in the Kob-Andersen model. In this talk, we introduce a new deep learning scheme for this purpose. We first conduct supervised learning using a convolutional neural network on a classification task of liquids and glasses. The structural orders of glasses are then extracted by asking the ground for the decision made for the classification by means of the gradient-weighted class activation mapping. Although no information about the dynamics is provided, the obtained structures in this way showed a strong correlation with the long-time displacement fields (the Pearson's coefficient becomes more than 0.9). slide
11:10—11:55	Hirokazu Maruoka† (JAMSTEC) "A framework for crossover of scaling law using a self-similar solution : dynamical impact of the solid sphere onto the viscoelastic PDMS board" (abstract) In this research, I propose a framework of crossover of scaling law based on self-similarity. A crossover of scaling law is the transition of the power-law behavior by the variation of parameters. Here I show that this process can be described continuously as the interference between two similarity parameters which constitutes a self-similar solution. Based on the framework, the procedure to identify the self-similar solution is proposed, then is applied to a problem of the dynamical impact of the solid sphere onto the viscoelastic board. Finally I succeeded in obtaining the self-similar solution of the second kind which bridges the gap between elastic impacts and viscoelastic impacts and the perturbation solution describing the crossover, from the Maxwell viscoelastic foundation model. slide (open)
11:55—12:20	Kuniyasu Saitoh† (Kyoto Sangyo Univ.) "Sound damping near jamming" (abstract) We study sound properties of soft athermal particles near jamming. Numerically demonstrating elastic waves in particulate media, we show that time correlations of particle velocities are suppressed by disordered configuration of the particles and dissipation of kinetic energy. We extract sound characteristics, i.e. dispersion relations, sound speeds, and sound attenuation coefficients, from the results of velocity auto-correlation functions and find that these are strongly dependent on the proximity to the jamming transition. Employing non-local viscoelasticity, we connect the sound speeds and attenuation coefficients to complex moduli of soft athermal particles. Furthermore, we use the critical scaling of complex moduli to collapse the data of sound speeds and attenuation coefficients near jamming. slide (open)
12:20—13:30	lunch break
13:30—15:00	Ryo Hanai† (YITP, Kyoto Univ. / APCTP) "Non-reciprocal many-body physics: phase transitions and frustration physics" (abstract) In equilibrium, the system typically dissipates toward its minimum free-energy state. This implies that the interaction is always reciprocal (like in Newton's third law). However, once driven out of equilibrium, this action-reaction symmetry is often broken. In fact, they appear ubiquitously in Nature in a wide discipline of science, ranging from open quantum systems, active matter, ecology, social science, neuroscience, to robotics. In this talk, I will introduce the following two classes of collective phenomena that arise due to non-reciprocity in driven many-body systems. In the first part of the talk, I will introduce a novel class of nonequilibrium phase transitions [1-2] and critical phenomena [3] that can only occur in the presence of macroscopic non-reciprocity, by generalizing the Ginzburg-Landau theory to driven systems. Remarkably, the discovered phase transition is controlled by spectral singularity called exceptional points that can only occur by breaking the detailed balance and therefore has no equilibrium counterparts. The emergent collective phenomena range from active time (quasi)crystals, hysteresis, to anomalous critical phenomena that exhibit anomalously large phase fluctuations that diverge at d≤4 [3]. These phenomena occur in a broad class of many-body interacting nonequilibrium systems both in quantum and classical matter, where examples include exciton-polariton condensates [2], pattern formation [1], flocking [1], and synchronization [1]. In the second part of the talk, I will view non-reciprocal interacting many-body systems from the perspective of frustration physics. I argue that there is a direct analogy between geometrical frustration and non-reciprocity-induced frustration physics [4], by pointing out the marginal orbits that emerge in anti-symmetric coupled non-reciprocal matter that can be regarded as the dynamical counterpart of accidental degeneracy. I will show that the dynamical counterpart of order-by-disorder phenomena and spin glass occurs due to non-reciprocal frustration. These frameworks lay the foundation of the general theory of critical phenomena and frustration physics in systems whose dynamics are not governed by an optimization principle. [1] M. Fruchart*, R. Hanai*, P. B. Littlewood, and V. Vitelli, Nature 592, 363 (2021). [2] R. Hanai, et al, Phys. Rev. Lett. 122, 185301 (2019). [3] R. Hanai and P. B. Littlewood, Phys. Rev. Res. 2, 033018 (2020). [4] R. Hanai, arXiv:2208.08577. slide
15:00—15:20	break
15:20—15:45	Ryosuke Yoshii† (Sanyo-Onoda City Univ.) "Demon driven by geometrical phase" (abstract) We theoretically study an entropy production and a work extracted from a system connected to two reservoirs by periodic modulations of chemical potentials of the reservoirs and one parameter in the system Hamiltonian under an isothermal condition [1,2]. We find that the modulation of parameters can drive the geometrical state, which is away from nonequilibrium steady state. As a result, the driven system cannot reach the nonequilibrium steady state at which the relative entropy takes the minimum value. With the aid of this property, we construct Maxwell's demon in which the relative entropy increases with time, and we can extract the work, if we begin with the nonequilibrium steady state without modulations of parameters. We employ the Anderson model to demonstrate that the relative entropy can increase with time. [1] H. Hayakawa, V.M.M. Paasonen, and R.Yoshii, arXiv:2112.12370, 2021. [2] R. Yoshii and H. Hayakawa, arXiv:2205.15193, 2022. slide (open)
15:45—16:10	Amit Kumar Chatterjee† (YITP, Kyoto Univ.) "Multi species ASEP with impurities: matrix product state, negative mobility and clustering" (abstract) The asymmetric simple exclusion process (ASEP) is broadly regarded as a paradigmatic model for non-equilibrium transport processes. Motivated by a simplistic description of multi lane traffic flow, we present a multi species generalization of ASEP along with impurities where the impurities can activate flips between species, imitating the lane change dynamics in multi lane traffic flow. This model, being disordered and non-ergodic, is of intrinsic interest. The exact non-equilibrium steady state probability distribution is obtained using the technique of matrix product ansatz [1]. For special choices of the microscopic dynamics, the model exhibits (i) negative differential mobility where current can decrease with increasing bias [1], (ii) cluster formation as a result of counter-flow of different species [2]. [1] A. K. Chatterjee and H. Hayakawa, arXiv:2205.03082 (2022). [2] A. K. Chatterjee and H. Hayakawa, arXiv:2208.03297 (2022). slide (open)
16:10—16:35	Takeshi Kawasaki† (Nagoya Univ.) "Emergent elasticity and topological phase transitions controlled via molecular chirality and steric anisotropy" (abstract) Topological phase transitions into skyrmion and half-skyrmion (meron) phases are widely observed in condensed matter such as chiral magnets [1] and liquid crystals [2]. They are utilized to design magnetoelectric, optical, and mechanoresponsive materials by controlling such topological phases. However, the role of the elastic field in non-uniform topological phases is elusive, though the essential role of crystal elasticity in uniform ordered crystal phase has been recognized. To elucidate this problem, we construct a new model describing chiral molecules and colloids in quasi two-dimensional molecular crystals, which incorporates intermolecular chiral twisting and spheroidal steric interactions. Here we reveal that emergence of the elastic fields from the competition between steric anisotropy and intermolecular twisting is a key to control uniform, helical, and half-skyrmion structures. By utilizing the coupling between the spheroidal orientations and the elastic fields, these topological phases are switched by temperature, external electromagnetic fields, and anisotropic stresses, where a novel re-entrant phase transition between the helical and the half-skyrmion phases is discovered. Our results imply that controlling the emergent elastic fields is crucial for obtaining a fundamental physical principle for controlling topological phases using chiral molecular and colloidal crystals [3]. [1] N. Nagaosa and Y. Tokura, Nat. Nanotech. 8, 899 (2013). [2] Ji. Fukuda, S. Žumer, Nat. Commun. 2, 246 (2011). [3] K. Takae and T. Kawasaki, Proc. Natl. Acad. Sci. USA 119, e2118492119 (2022). slide
16:35—16:50	break
16:50—17:15	Pradipto† (Tokyo Univ. Agri. Tech.) "Role of the dynamically jammed region in the impact-induced hardening of dense suspensions" (abstract) People are able to run on top of suspension due to the impact-induced hardening property of dense suspensions. Under impact, a localized solid-like rigid region emerges inside the suspensions and it is called the dynamically jammed region (DJR). By coarse-graining the Lattice Boltzmann Method-Discrete Element Method (LBM-DEM) simulation data of the impact by a free-falling spherical impactor, such DJR can be delineated. We propose a data-assisted model for the motion of the impactor using the effective viscosity and elasticity of the DJR. The results are then compared with a simple 1-D toy model of growing DJR. slide (open)
17:15—17:40	Satoshi Takada† (Tokyo Univ. Agri. Tech.) "Stress propagation in a two-dimensional elastic circular disk under diametric loads" (abstract) We study the stress propagation in a two-dimensional elastic circular disk when diametric loads act on the disk. We derive the displacement and stress under both the initial and boundary conditions. The solutions are expressed in terms of the scalar and vector potentials, which are the sums of the Bessel functions. We find that these solutions correspond to the primary and secondary waves, respectively. We also show that the surface wave is included in these solutions. slide (open)
17:40—18:05	Kiwamu Yoshii† (Osaka Univ.) "Jamming in channel flow of granular materials" (abstract) Dense disordered materials, such as granular materials, emulsions, and colloidal suspensions, behave like solids with rigidity above the jamming point. This transition, known as the jamming transition, has been extensively studied for years. Critical behaviors near the jamming point have been revealed in previous studies. Most previous studies have focused on uniform systems with a constant shear rate. However, jamming is also observed in non-uniform systems, such as sand piles, ball mills, and pipe flow. It is unclear whether similar critical behaviors are observed in these non-uniform systems. In this study, we investigate the flow of granular materials between two parallel plates driven by an external force. We derive solutions for the velocity profile and mass flux based on a continuum model. The flow with non-zero mass flux occurs only when the external force exceeds a critical force, which depends on the packing fraction, pressure, and system size. We predict scaling laws for the critical force and the mass flux, which are verified by our DEM simulation. We also discuss the effect of cohesiveness between particles on the flow. slide (open)

† onsite presentation / ‡ online presentation