A number of microorganisms leave persistent trails while moving along surfaces. For single-cell organisms, the trail-mediated self-interaction will influence its dynamics. It has been discussed recently [Kranz textit{et al.} Phys. Rev. Lett. textbf{1
17}, 8101 (2016)] that the self-interaction may localize the organism above a critical coupling $chi_c$ to the trail. Here we will derive a generalized active particle model capturing the key features of the self-interaction and analyze its behavior for smaller couplings $chi < chi_c$. We find that fluctuations in propulsion speed shift the localization transition to stronger couplings.
We discuss the uniform shear flow of a fluidized granular bed composed of monodisperse Hertzian spheres. Considering high densities around the glass transition density of inelastic Hertzian spheres, we report kinetic theory expressions for the Newton
ian viscosity as well as the Bagnold coefficient. We discuss the dependence of the transport coefficients on density and coefficient of restitution.
We compute the rheological properties of inelastic hard spheres in steady shear flow for general shear rates and densities. Starting from the microscopic dynamics we generalise the Integration Through Transients (textsc{itt}) formalism to a fluid of
dissipative, randomly driven granular particles. The stress relaxation function is computed approximately within a mode-coupling theory---based on the physical picture, that relaxation of shear is dominated by slow structural relaxation, as the glass transition is approached. The transient build-up of stress in steady shear is thus traced back to transient density correlations which are computed self-consistently within mode-coupling theory. The glass transition is signalled by the appearance of a yield stress and a divergence of the Newtonian viscosity, characterizing linear response. For shear rates comparable to the structural relaxation time, the stress becomes independent of shear rate and we observe shear thinning, while for the largest shear rates Bagnold scaling, i.e., a quadratic increase of shear stress with shear rate, is recovered. The rheological properties are qualitatively similar for all values of $varepsilon$, the coefficient of restitution; however, the magnitude of the stress as well as the range of shear thinning and thickening show significant dependence on the inelasticity.
Considering a granular fluid of inelastic smooth hard spheres we discuss the conditions delineating the rheological regimes comprising Newtonian, Bagnoldian, shear thinning, and shear thickening behavior. Developing a kinetic theory, valid at finite
shear rates and densities around the glass transition density, we predict the viscosity and Bagnold coefficient at practically relevant values of the control parameters. The determination of full flow curves relating the shear stress $sigma$ to the shear rate $dotgamma$, and predictions of the yield stress complete our discussion of granular rheology derived from first principles.
Like ants, some microorganisms are known to leave trails on surfaces to communicate. We explore how trail-mediated self-interaction could affect the behavior of individual microorganisms when diffusive spreading of the trail is negligible on the time
scale of the microorganism using a simple phenomenological model for an actively moving particle and a finite-width trail. The effective dynamics of each microorganism takes on the form of a stochastic integral equation with the trail interaction appearing in the form of short-term memory. For moderate coupling strength below an emergent critical value, the dynamics exhibits effective diffusion in both orientation and position after a phase of superdiffusive reorientation. We report experimental verification of a seemingly counterintuitive perpendicular alignment mechanism that emerges from the model.
I derive a mode-coupling theory for the velocity autocorrelation function, psi(t), in a fluid of randomly driven inelastic hard spheres far from equilibrium. With this, I confirm a conjecture from simulations that the velocity autocorrelation functio
n decays algebraically, psi(t) ~ t^{-3/2}, if momentum is conserved. I show that the slow decay is due to the coupling to transverse currents.
We investigate the dynamics of a driven system of dissipative hard spheres in the framework of mode-coupling theory. The dissipation is modeled by normal restitution, and driving is applied to individual particles in the bulk. In such a system, a gla
ss transition is predicted for a finite transition density. For increasing inelasticity, the transition shifts to higher densities. Despite the strong driving at high dissipation, the transition persists up to the limit of totally inelastic normal restitution.
A highly polydisperse granular gas is modeled by a continuous distribution of particle sizes, a, giving rise to a corresponding continuous temperature profile, T(a), which we compute approximately, generalizing previous results for binary or multicom
ponent mixtures. If the system is driven, it evolves towards a stationary temperature profile, which is discussed for several driving mechanisms in dependence on the variance of the size distribution. For a uniform distribution of sizes, the stationary temperature profile is nonuniform with either hot small particles (constant force driving) or hot large particles (constant velocity or constant energy driving). Polydispersity always gives rise to non-Gaussian velocity distributions. Depending on the driving mechanism the tails can be either overpopulated or underpopulated as compared to the molecular gas. The deviations are mainly due to small particles. In the case of free cooling the decay rate depends continuously on particle size, while all partial temperatures decay according to Haffs law. The analytical results are supported by event driven simulations for a large, but discrete number of species.
