Kinetic theory of discontinuous rheological phase transition for a dilute inertial suspension

A kinetic theory for a dilute inertial suspension under a simple shear is developed. With the aid of the corresponding Boltzmann equation, it is found that the flow curves (the relations between the stress and the strain rate) exhibit the crossovers from the Newtonian to the Bagnoldian for a granular suspension and from the Newtonian to a fluid having a viscosity proportional to the square of the shear rate for a suspension consisting of elastic particles, respectively. The existence of the negative slope in the flow curve directly leads to a discontinuous shear thickening (DST). This DST corresponds to the discontinuous transition of the kinetic temperature between a quenched state and an ignited state. The results of the event-driven Langevin simulation of hard spheres perfectly agree with the theoretical results without any fitting parameter. The introduction of an attractive interaction between particles is also another source of the DST in dilute suspensions. Namely, there are two discontinuous jumps in the flow curve if the suspension particles have the attractive interaction.

Comparative study of the crowding-induced collapse effect in hard-sphere, flexible polymer and rod-like polymer systems

A systematic Langevin simulation is performed to study the crowding-induced collapse effect on a probed chain in three typical systems: hard sphere (HS), flexible polymer and rod-like polymer.

Complex Langevin simulation of QCD at finite density and low temperature using the deformation technique

We study QCD at finite density and low temperature by using the complex Langevin method. We employ the gauge cooling to control the unitarity norm and intro-duce a deformation parameter in the Dirac operator to avoid the singular-drift problem. The reliability of the obtained results are judged by the probability distribution of the magnitude of the drift term. By making extrapolations with respect to the deformation parameter using only the reliable results, we obtain results for the original system. We perform simulations on a 43 × 8 lattice and show that our method works well even in the region where the reweighing method fails due to the severe sign problem. As a result we observe a delayed onset of the baryon number density as compared with the phase-quenched model, which is a clear sign of the Silver Blaze phenomenon.

Surface diffusion of a Brownian particle subjected to an external harmonic noise

Langevin simulation is performed to investigate the diffusion coefficient of a Brownian particle subjected to an external harmonic noise in a two-dimensional coupled periodic potential. Resonant diffusion phenomenon is observed as a result of the coupling between the central frequency of the spectral density of the harmonic noise and the frequency of the potential well bottom. The diffusion coefficient presents approximately linear functions of the strengths of the internal and external noises for low values of the strengths, these functions can be understood by the local linearization approximation of the potential force. The damping coefficient dependence of the diffusion coefficient in lower damping is well fitted by a negative power function, as an internal Gaussian white noise case does, but with a power whose absolute value is larger than 1.