Academic Year 2018
- Physics of the jamming transition (lecture)
- Speaker: Atsushi Ikeda (The University of Tokyo)
- Date: 2019/02/14 — 2019/02/15
- Place: Lecture room no.111, 1st floor, RIMS, Kyoto U.
- Abstract:
Many of hard and soft condensed matters in our world are disordered.
Examples include inorganic and metallic glasses, colloids, pastes,
foams and granular materials. Recently, it has been established that
some of these glassy systems have a critical point in their phase
diagram, which is called the jamming transition.
In this lecture, I will discuss the physics of glasses with special
focus on the jamming transition. I will give a brief introduction to
the physics of glasses, and then discuss what the jamming transition
is and why it is relevant to the glasses. Next, I will introduce
several basic concepts of the rigidity of floppy networks, which is
useful to study the jamming transition. Based on these introductory
discussions, we look into several successful theoretical ideas/tools
to understand the jamming transition. Finally, we discuss important
questions on the stability of these systems which are still
unanswered. The lectures will be given on the blackboard with
occasional use of slides.
Feb.14, 10:30-12:00, 13:30-15:00, 15:30-17:00
1.Introduction
2.Jamming transition
3.Floppy networks
Feb.15, 10:30-12:00, 13:30-15:00, 15:30-17:00
1.Variational arguments
2.Effective medium theory
3.Stability of amorphous solid
- Particle flows around a spherical intruder
- Speaker: Satoshi Takada (The University of Tokyo)
- Date: 2019-02-13 (Wed.) 15:15 –
- Place: Seminar room (1st floor), Koboyashi-Masukawa Building, Kyoto U.
- Abstract:
We try to characterize particle flows around an intruder by performing simulations. The beam particles move toward the intruder and collide each other. We find that the drag law changes depending on the ratio of the speed to the thermal velocity. The high speed regime shows the quadratic dependence while the linear dependence is observed in the low speed regime. These asymptotic behavior can be understood by a simple collision model considering the momentum change between the intruder and the beam particles. In the high speed regime, a vortex structure is observed behind an intruder. We also analyze the inverse problem about the scattering process and investigate the information on the internal state of the beam particle.
- Stress relaxation above and below the jamming transition
- Speaker: Kuniyasu Saitoh (Tohoku University)
- Date: 2019-02-13 (Wed.) 13:30 –
- Place: Seminar room (1st floor), Koboyashi-Masukawa Building, Kyoto U.
- Abstract:
We numerically investigate stress relaxation in soft athermal disks and predict critical divergence of relaxation time near the jamming transition by viscoelastic theory. We observe critical slowing down of time-dependent shear modulus when the system approaches the critical point from both above and below jamming, while critical exponents for the relaxation time are different on both sides. The relaxational density of states, which is a key ingredient of the viscoelastic theory, also exhibits a qualitative difference; an extra slow relaxational mode emerges below jamming. Implementing the extra mode in the theory, we explain the critical exponents of relaxation time.
- Avalanche Interpretation of the Power-Law Energy Spectrum in Three-Dimensional Dense Granular Flow
- Speaker: Norihiro Oyama (Tohoku University)
- Date: 2019-02-13 (Wed.) 10:30 –
- Place: Seminar room (1st floor), Koboyashi-Masukawa Building, Kyoto U.
- Abstract:
Molecular dynamics simulations on dense granular packings under a very slow simple shear flow have revealed that the statistical properties of the non-affine velocity field are consistent with those of classical turbulence of viscous fluid. However, such observations have been limited to two-dimensional systems and knowledge about three dimensional systems is still missing[1]. In this work[2], we conducted direct numerical simulations on three-dimensional dense granular flow and found that the statistical property is not turbulent-like in three dimension. We propose a new understanding from the perspective of avalanche dynamics. This interpretation can explain the power law behavior of energy spectra both in two and three dimension, although the turbulent- like interpretation is valid only in two dimension. Furthermore, we analyzed the spatial structures of collectively moving particles by looking at the vorticity field. Although the system does not show the turbulent-like behavior in three dimension, the structural analysis based on the vorticity field allows us to extract a diverging length scale which a conventional simple spatial correlation function cannot detect.
- References
[1] F. Radjai, and S. Roux, Phys. Rev. Lett. 89, 064302 (2002).
K. Saitoh, and H. Mizuno, Soft Matter 12, 1360 (2016).
[2] N. Oyama, H. Mizuno, and K. Saitoh, arXiv: 1805.05449 (2018).
- Interaction between two intruders in granular flow
- Speaker: Takahiro Tanabe (Meiji University)
- Date: 2019-01-30 (Wed.) 16:00 –
- Place: Y206, Main Building, Yukawa Institute, Kyoto U.
- Abstract:
There are various effective interactions in nonequilibrium situations, for examples, depletion force, which is an attractive force between suspending large colloidal particles in a dilute solution, and Casimir-like force in jammed-granular system, which shows both the attractive and repulsive interactions due to long-ranged fluctuations [1, 2]. Although there are variety of interactions depending on the environments, we focus on the interactions in two-dimensional granular media. Since granular materials are of significant for our daily life and industrial applications, it is one of the important themes to understand the behavior of the interaction in the granular flow. Recently, the studies of the drag forces for one-intruder in the granular media have been proposed, nevertheless, there are few studies of the interactions between intruders in granular media [3]. In this presentation, we consider the interactions between two intruders surrounded by granular disks on a plane under a uniform flow and oscillatory flow based on discrete element method (DEM) simulations. The interaction is repulsive under uniform granular disks flow. The overlap of high-density region in front of the intruders effects this interaction, therefore, the interaction vanishes away when two intruders take enough distance. By contrast, the interaction shows both attractive and non-attractive interactions under oscillatory flow depending on their oscillation conditions. In the case of the optimal condition, the disks at channel region show high granular temperature and they move out of the region. This hot dilute region makes the intruders approach each other.
- References
[1] S. Asakura and F. Oosawa, J. Chem. Phys., 22, 1255, (1954).
[2] Juan-Jose Lietor-Santos and Justin C. Burton, Soft Matter, 13, 1142-1155, (2017).
[3] Y. Takehara and K. Okumura, Phys. Rev. Lett., 112, 1 (2014).
- Collective Motion without Activity: Becoming a cool bird out of frustration
- Speaker: Mathias Casiulis (Sorbonne University)
- Date: 2018-12-21 (Fri.) 18:00 –
- Place: K202, Main Building, Yukawa Institute, Kyoto U.
- Abstract:
Collective motion (the macroscopic ordering of velocities) is a common feature in systems of active particles where ordering typically happens at low noise and high enough density. Examples that come to mind are flocks of birds, schools of fish, human crowds or bacterial suspensions. However, unlike some other features of active matter, collective motion is not necessarily a direct consequence of activity and is, rather, a side effect of the breaking of Galilean invariance. In my talk, I will prove this point by presenting an equilibrium model that features collective motion, and discuss its phase diagram and how finite size effects affect it.
- Twist-induced snapping in a bent elastic ribbon
- Speaker: Tomohiko Sano (Ritsumeikan University)
- Date: 2018-11-7 (Wed.) 16:00 –
- Place: K202, Main Building, Yukawa Institute, Kyoto U.
- Abstract:
Snapping a slender structure is utilized in a wide range of natural and man-made systems, mostly to achieve rapid movement without relying on muscle-like elements [1-4]. Although several mechanisms for elastic energy storage and rapid release have been studied in detail, a general understanding of the approach to design such a kinetic system is a key challenge in mechanics. Here we study a twist-driven buckling and fast flip dynamics of a geometrically constraint ribbon by combining experiments, numerical simulations, and analytical theory[5]. We identify two distinct types of shape transitions; a narrow ribbon snaps, whereas a wide ribbon forms a pair of localized helices. We construct a phase diagram and explain the origin of the boundary, which is determined only by geometry. We quantify effects of gravity and clarify time scale dictating the rapid flipping. Our study reveals the unique role of geometric twist-bend coupling on the fast dynamics of a thin constrained structure, which has implications for a wide range of biophysical and applied physical problems.
- References
[1] J. Dumais and Y. Forterre, Annu. Rev. Fluid Mech. 44, 453 (2012).
[2] Y. Forterre, J. M. Skotheim, J. Dumais, and L. Mahadevan, Nature 433, 421 (2005).
[3] X. Noblin, N. O. Rojas, J. Westbrook, C. Llorens, M. Argentina, and J. Dumais, Science 335, 1322 (2012).
[4] P. M. Reis, J. Appl. Mech. 82, 111001 (2015).
[5] T. G. Sano and H. Wada, arXiv:1809.05816
- The 2nd law-type work relation in non-equilibrium steady states in infinite quantum systems
- Speaker: Kazuki Yamaga (Kyoto University)
- Date: 2018-10-31 (Wed.) 16:00 –
- Place: K202, Main Building, Yukawa Institute, Kyoto U.
- Abstract:
“Operation” and “work” are fundamental elements in thermodynamics and there is a strong relation between them, “the 2nd law of thermodynamics”, which tells one cannot extract any work by cyclic operations from the system in equilibrium. It is known that one can reproduce this law from quantum theory using equilibrium quantum statistical mechanics. Although the properties of equilibrium systems are well investigated from both macroscopic and microscopic standpoint, we know little about non-equilibrium systems. In this work, we considered a non-equilibrium steady state (NESS) produced by two infinite quantum thermal reservoirs at different temperatures. Under some assumptions we obtained a generalized form of the 2nd law-type inequality in this NESS. This inequality gives the upper bound of the work extracted by cyclic operations and is continuously connected to the original 2nd law of thermodynamics. In the seminar, first I will explain this 2nd law-type inequality in general models and then I will consider work density in 1-dimensional quantum lattice systems.
- The emergence of collective modes, ecological collapse and directed percolation at the laminar-turbulence transition in pipe flow
- Speaker: Nigel Goldenfeld (NASA Astrobiology Institute for Universal Biology at UIUC)
- Date: 2018-09-05 (Wed.) 16:00 –
- Place: K206, Main Building, Yukawa Institute, Kyoto U.
- Abstract:
How do fluids become turbulent as their flow velocity is increased? In
recent years, careful experiments in pipes and Taylor-Couette systems have
revealed that the lifetime of transient turbulent regions in a fluid appears to
diverge with flow velocity just before the onset of turbulence, faster than any
power law or exponential function. I show how this superexponential scaling of
the turbulent lifetime in pipe flow is reminiscent of extreme value statistics,
and a manifestation of a mapping between transitional turbulence and the
statistical mechanics model of directed percolation. This mapping itself arises
from a further surprising and remarkable connection: laminar and turbulent
regions in a fluid behave as a predator-prey ecosystem. I explain the evidence
for this mapping, and propose how a unified picture of the transition to
turbulence emerges in systems ranging from turbulent convection to
magnetohydrodynamics.
- References
[1] Nigel Goldenfeld, N. Guttenberg and G. Gioia. Extreme fluctuations and the
finite lifetime of the turbulent state. Phys. Rev. E Rapid Communications 81,
035304 (R):1-3 (2010)
[2] Maksim Sipos and Nigel Goldenfeld. Directed percolation describes lifetime
and growth of turbulent puffs and slugs. Phys. Rev. E Rapid Communications 84,
035305 (4 pages) (2011).
[3] Hong-Yan Shih, Tsung-Lin Hsieh and Nigel Goldenfeld. Ecological collapse and
the emergence of travelling waves at the onset of shear turbulence. Nature
Physics 12, 246-248 (2016)
[4] Nigel Goldenfeld and Hong-Yan Shih. Turbulence as a problem in
non-equilibrium statistical mechanics. J. Stat. Phys. 167, 575-594 (2017).
- Heating in integrable time-periodic systems
- Speaker: Takashi Ishii (University of Tokyo)
- Date: 2018-07-11 (Wed.) 16:00 –
- Place: K202, Main Building, Yukawa Institute, Kyoto U.
- Abstract:
Time-periodic systems gather attention both experimentally and
theoretically because of its potential of realizing novel physical phases, such as
topological phases by using simple time-dependent Hamiltonians [1,2]. It is an
important quesion to clarify to what extent the system absorbs energy from the
driving because the heating may break down the nontrivial quantum phases. In
nonintegrable time-periodic systems, heating to the infinite temperature
is expected to occur in the infinite-time scale [3]. In this talk, we
present our results [4] on a heating phenomenon in integrable time-periodic systems
that can be mapped to free-fermion models. We find that heating to the high-
temperature state can also appear in integrable time-periodic systems.
We obtain the asymptotic behavior L^{-1} and T^{-2} as to how the steady state approaches
the infinite-temperature state as the system size L and the driving period T increase.
- References
[1] N. Lindner, G. Rafael, and V. Galitski, Nat. Phys. 7, 490 (2011)
[2] A. G. Grushin, A. Gómez-León, and T. Neupert, PRL 112, 156801 (2014)
[3] L. D’Alessio and M. Rigol, PRX 4, 041048 (2014)
[4] T. Ishii, T. Kuwahara, T. Mori, and N. Hatano, PRL 120, 220602 (2018)
- Shear Jamming of Granular Materials under Oscillatory Shear
- Speaker: Michio Otsuki (Osaka University)
- Date: 2018-05-16 (Wed.) 16:00 –
- Place: K206, Main Building, Yukawa Institute, Kyoto U.
- Abstract:
Granular materials have rigidity above a critical density [1]. It is
well-known that frictionless grains under small strain exhibit a continuous
transition of the shear modulus G, while recent studies have revealed that G of
frictional grains with harmonic repulsive interaction discontinuously emerges at
the critical density [2].
In this seminar, we present our recent numerical
results on the shear modulus of frictional grains under oscillatory shear. It is
confirmed that the shear modulus depends on the amplitude of the initial
oscillatory shear before the measurement. Even at densities below the transition
point, where isotropic jamming occurs without shear, the initial oscillatory
shear can induce the finite shear modulus. This behavior is consistent with a
transition known as shear jamming (SJ) [3]. It is also found that the viscosity
of grains increases discontinuously as the initial shear increases, which is
similar to the discontinuous shear thickening (DST). We discuss the relationship
between SJ and DST.
- References
[1] M. van Hecke, J. Phys.: Condens. Matter 22, 033101 (2009).
[2] M. Otsuki and H. Hayakawa, Phys. Rev. E 95, 062902 (2017).
[3] D. Bi, J. Zhang, B. Chakraborty, and R. Behringer, Nature (London) 480, 355 (2011).
- Rheology and fluid mechanics of dense suspensions
- Speaker: Ryohei Seto (Kyoto University)
- Date: 2018-04-25 (Wed.) 16:00 –
- Place: K206, Main Building, Yukawa Institute, Kyoto U.
- Abstract:
Suspension, an effective fluid made up of particles suspended in a
viscous liquid, is a common form of materials in nature and industrial
processes. The flowing behavior of suspensions is not usually captured
by the Newtonian model or its simple extensions, such as generalized
Newtonian model. Flow-induced microstructure brings complex flow
properties. Thus, although computational fluid dynamics (CFD) becomes
more and more important tool to design and optimize processes of fluid
flows in industry, no widely-accepted CFD method is available to
handle suspensions. Formulating constitutive equations for complex
fluids has a long history, especially for viscoelastic polymer fluids,
but much less for suspensions so far. Our understanding of dense
suspension rheology, however, has significantly progressed for last
five years. The local rheology of dense suspensions, such as shear
thickening—a counterintuitive non-Newtonian behavior, is mostly
understood through particle-dynamics simulations [1, 2] and a recent
theoretical argument by Wyart and Cates [3]. Also, some concepts
appeared in studies of granular materials, such as “macroscopic
friction” rheology [4] and nonlocal rheology [5], are giving impact on
suspension rheology as well. In this seminar, I will provide a brief
overview of suspension rheology studies and introduce our works on the
extensional rheology of dense suspensions [6, 7]. I also plan to
discuss on physical aspects which may cause the gap between microscale
rheology and macroscale fluid mechanical modeling.
- References
[1] R. Seto, R. Mari, J. F. Morris, and M. M. Denn. Discontinuousshear thickening of frictional hard-sphere suspensions. Phys. Rev.Lett., 111:218301, Nov 2013.
[2] R. Mari, R. Seto, J. F. Morris, and M. M. Denn. Shear thickening,frictionless and frictional rheologies in non-Brownian suspensions. J.Rheol., 58(6):1693– 1724, 2014.
[3] M. Wyart and M. E. Cates. Discontinuous shear thickening withoutinertia in dense non-brownian suspensions. Phys. Rev. Lett.,112:098302, Mar 2014.
[4] F. Boyer, É. Guazzelli, and Olivier Pouliquen. Unifying suspensionand granular rheology. Phys. Rev. Lett., 107:188301, 2011.
[5] O. Pouliquen and Y. Forterre. A non-local rheology for dense granular flows.Philosophical Transactions of the Royal Society of London A:Mathematical, Physical and Engineering Sciences, 367(1909):5091–5107,2009.
[6] R. Seto, G. G. Giusteri, and Antonio Martiniello. Microstructureand thickening of dense suspensions under extensional and shear flows.J. Fluid Mech., 825:R3, 2017.
[7] G. G. Giusteri and R. Seto. A theoretical framework forsteady-state rheometry in generic flow conditions, 2017.
- Near-wall Dynamics of Passive and Active Particles at Low Reynolds Number
- Speaker: Takuya Ohmura (Kyoto University)
- Date: 2018-04-11 (Wed.) 16:00 –
- Place: K206, Main Building, Yukawa Institute, Kyoto U.
- Abstract:
Moving particles at low Reynolds number are categorized into two types.
The first are passive particles driven by an external force.
The second are active particles which exchange energy for kinetic motion
and are self-driven. Such as red blood cells driven by flow in a capillary
vessel and aquatic microorganisms living at bottoms, the passive and active
particles moving close to a solid-fluid interface exist in nature. Even if
considering only hydrodynamic effects, the “near-wall” dynamics of such
actual particles tends to be complex and unpredictable. Our aim is to
extract essential elements that govern the actual systems by using
quantitative experiments and simple numerical calculations.
As the motions of the passive particles, we studied the oscillation and
dynamic clustering of heterogeneous microfluidic droplets aligned in one
line in a microchannel. The experiments and hydrodynamic numerical
calculations by Lattice Boltzmann Method and Immersed Boundary Method
revealed that the phenomena of the droplets were caused by a 3-dimensional
flow effect. That flow was generated in a space surrounded by the top-bottom
channel walls and the two large droplets and similar to the “bolus flow” in
a capillary blood flow [1]. As the motion of the active particle, we
investigated the non-trivial sliding motion of the swimming microorganism on
a wall. By comparison of the experiments with the hydrodynamic numerical
calculations by Boundary Element Method, we identified that the sliding motion
could be explained by two simple physical factors; the asymmetricity of swimming
thrust force and the anisotropic shape of the cell body. In addition, this study
described the mechanism of an intrinsic habit for the microorganism to accumulate
near a wall for survival [2]. I also would like to talk about our recent
research on the motion of the swimming microorganism under a shear flow
in a microchannel.
- References:
[1] T. Ohmura, M. Ichikawa, K. Kamei and Y. T. Maeda, Appl. Phys. Lett. 107(7), 074102 (2015).
[2] T. Ohmura, Y. Nishigami, A. Taniguchi, S. Nonaka, J. Manabe, T. Ishikawa and M. Ichikawa, Proc. Nat. Acad. Sci. USA, 115(13), 3231-3236 (2018).