Academic Year 2020
- “Roll” of Friction and Constitutive Model of Dense Frictional Suspensions【Zoom】
- Abhinendra Singh (James Franck Institute and Pritzker School of Molecular Engineering, University of Chicago)
- Date: 2020/07/21 10:00 --
- Place: ZOOM*
*People interested in attending the seminar should register with
google form.
- Abstract:
The mechanism of shear thickening in dense suspensions has been shown to be consistent with a transition from an unconstrained “frictionless (lubricated) rheology”, where close interactions between suspended particles take place through a thin liquid film, to a constrained “frictional rheology”, wherein particles experience frictional contacts. Particle simulations that led to this concept have been successful in quantitatively reproducing the non-Newtonian shear behavior of discontinuous shear thickening suspensions [1].
As a step towards developing a constitutive model for such materials, an extension of Wyart-Cates model [2] for lubricated and frictional rheologies is made to both shear and normal stresses for non-colloidal suspensions and demonstrate the agreement between such a model and the simulation results [3]. Finally, the role of stress-activated constraints, with an emphasis on resistance to gear-like rolling will be presented. Rolling friction decreases the volume fraction required for DST and SJ, in quantitative agreement with real-life suspensions with adhesive surface chemistries and "rough" particle shapes. It sets a distinct structure of the frictional force network compared to only sliding friction, and from a dynamical perspective leads to an increase in the velocity correlation length, in part responsible for the increased viscosity. Finally, I will show that the physics of rolling friction is a key element in achieving a comprehensive understanding of strongly shear-thickening materials [4].
- Reference
[1] Mari, R., Seto, R., Morris, J.F. and Denn, M.M., 2015. Discontinuous shear thickening in
Brownian suspensions by dynamic simulation. Proceedings of the National Academy of
Sciences, 112(50), pp.15326-15330.
[2] Wyart, M. and Cates, M.E., 2014. Discontinuous shear thickening without inertia in dense
non-Brownian suspensions. Physical Review Letters, 112(9), p.098302.
[3] Singh, A., Mari, R., Denn M.M. and Morris, J.F., 2018. A constitutive model for simple shear
of dense frictional suspensions. Journal of Rheology, 62(2), pp.457-468.
[4] Singh, A., Ness C., Seto R., de Pablo J.J., Jaeger H.M., Shear thickening and jamming of
dense suspensions: the roll of friction. arXiv preprint arXiv:2002.10996.
- Markov embedding approach and field master equation for Non-Markovian Hawkes processes【Zoom】
- Kiyoshi Kanazawa (University of Tsukuba)
- Date: 2020/07/08 16:00 --
- Place: ZOOM*
*People interested in attending the seminar should register with
google form.
- Abstract:
The Hawkes process is a stochastic model of endogenous bursty dynamics
and has been applied to various complex systems, such as financial,
seismic, and social sciences.
One of the key features of the Hawkes process is that it is
essentially a non-Markovian model since the intensity of burst is
under strong influence of historical bursts.
Because non-Markovian stochastic processes are not
analytically-tractable easily in general, the analytical characters of
the Hawkes processes have not been fully revealed yet.
In this seminar, we report an analytical solution to the Hawkes
process by applying Markov embedding and field master equations
according to Refs. [1,2].
We first show that the Hawkes process can be converted into an
stochastic partial differential equation (SPDE) that is Markovian by
adding sufficient number of auxiliary variables.
This technique is called Markov embedding in mathematics to map the
original non-Markovian dynamics to Markovian field dynamics.
We then derive the master equation on the auxiliary field stochastic
variables governed by the SPDE to solve the steady intensity
distribution.
We finally find that the intensity distribution has a power-law tail
as intermediate asymptotics near criticality,
which is in contrast to the common wisdom that the Hawkes process
cannot produce large fluctuation.
Our theoretical approach can be generalized for the nonlinear Hawkes
process and thus provides a useful toolkit for various non-Markovian
stochastic processes.
- Reference
[1] K. Kanazawa and D. Sornette, arXiv:2001.01197
[2] K. Kanazawa and D. Sornette, arXiv:2001.01195
- Enskog kinetic theory of rheology for a moderately dense inertial suspension【Zoom】
- Satoshi Takada (Institute of Engineering, Tokyo University of Agriculture and Technology)
- Date: 2020/05/25 16:30 --
- Place: ZOOM
- Abstract:
The Enskog kinetic theory for moderately dense inertial suspensions under simple shear flow is considered as a model to analyze the rheological properties of the system. The influence of the background fluid on suspended particles is modeled via a viscous drag force plus a Langevin-like term defined in terms of the background temperature. Grad's moment method with the aid of a linear shear-rate expansion was employed to obtain a theory which gave good agreement with the results of event-driven Langevin simulations of hard spheres for low densities and/or small shear rates [1]. Nevertheless, the previous approach had a limitation of applicability to the high shear-rate regime. Thus, in the present study [2], we extend the previous work and develop Grad's theory including higher order terms in the shear rate. This improves significantly the theoretical predictions, a quantitative agreement between theory and simulation being found in the high-density region (volume fractions smaller than or equal to 0.4).
- Reference
[1] H. Hayakawa, S. Takada, and V. Garzó, Phys. Rev. E 96, 042903 (2017).
[2] S. Takada, H. Hayakawa, A. Santos, and V. Garzó, arXiv:2005.05969.