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W. Till Kranz

Publications and source records attributed to W. Till Kranz.

17 recordsLinked to original sources
arXiv2026

Time-state superposition in non-equilibrium fluidized granular matter

Despite being intrinsically athermal and strongly driven, granular materials can exhibit remarkably glass-like dynamics. Whether their rheology can be described by the same scaling concepts remains an open question. Here, we investigate the linear viscoelastic response of an air-fluidized granular bed using small-amplitude oscillatory shear over a broad range of fluidization states. We show that the frequency-dependent spectra collapse onto a single master curve when shifted by a state-dependent relaxation time, establishing a time-state superposition principle analogous to time-temperature superposition in molecular glasses. The master curve spans more than five decades in relaxation time and is quantitatively described by a Cole-Davidson relaxation spectrum. By comparison with continuous shear measurements, we identify tribocharging as the origin of history-dependent deviations from universal scaling. Our results demonstrate that fluidization primarily rescales a single structural relaxation time while preserving the underlying relaxation spectrum, establishing a direct connection between the rheology of driven granular matter and molecular glass-forming liquids.

cond-mat.soft↗
arXiv2025

Rheological regimes in agitated granular media under shear

Agitated granular media have a rich rheology: they exhibit Newtonian behavior at low shear rate and density, develop a yield stress at high density, and cross over to Bagnoldian shear thickening when sheared rapidly -- making them challenging to encompass in one theoretical framework. We measure the rheology of air-fluidized glass particles, spanning five orders of magnitude in shear rate. By comparing fluidization-induced to Brownian agitation, we show that all rheological regimes can be delineated by two dimensionless numbers -- the Peclet number, $\Pe$, and the ratio of shear-to-fluidization power, $Π$ -- and propose a constitutive relation that captures all flow behaviors, qualitatively and quantitatively, in one unified framework.

cond-mat.soft↗
arXiv2023

The manifold rheology of fluidized granular media

Fluidized granular media have a rich rheology: measuring shear stress $σ$ as a function of shear rate $\dotγ$, they exhibit Newtonian behavior $σ\sim\dotγ$ for low densities and shear rates, develop a yield stress for intermediate shear rates and densities approaching the granular glass transition, and finally, cross over to shear-thickening Bagnold scaling, $σ\sim\dotγ^2$. This wealth of flow-behaviors makes fluidized beds a fascinating material, but also one that is challenging to encompass into a global theory, despite its relevance for optimizing industrial processes and predicting natural hazards. We provide careful measurements spanning eight orders of magnitude in shear rate, and show that all these rheological regimes can be described qualitatively and quantitatively using the granular integration through transient formalism, a theory for glassy dynamics under shear adapted to granular fluids.

cond-mat.soft↗
arXiv2022

Granular piston-probing in microgravity: powder compression, from densification to jamming

The macroscopic response of granular solids is determined by the microscopic fabric of force chains, which, in turn, is intimately linked to the history of the solid. To query the influence of gravity on powder flow-behavior, a granular material is subjected to compression by a piston in a closed container, on-ground and in microgravity. Results show that piston-probing densifies the packing, eventually leading to jamming of the material compressed by the piston, regardless of the gravitational environment. The onset of jamming is found to appear at lower packing fraction in microgravity ($φ^{\textrm{$μ$-g}}_J = 0.567 \pm 0.014$) than on-ground ($φ^{\text{gnd}}_J = 0.579 \pm 0.014 $). We interpret these findings as the manifestation of a granular fabric altered by the gravitational force field: in absence of a secondary load (due to gravitational acceleration) to stimulate reorganization in a different direction to the major compression stress, the particles' configuration becomes stable at lower density, as the particles have no external drive to promote reorganization into a denser packing. This is coupled with a change in interparticular force balance which takes place under low gravity, as cohesive interactions become predominant. We propose a combination of microscopic and continuum arguments to rationalize our results.

cond-mat.soft↗
arXiv2021

A gravity-independent powder-based additive manufacturing process tailored for space applications

The future of space exploration missions will rely on technologies increasing their endurance and self-sufficiency, including for manufacturing objects on-demand. We propose a process for handling and additively manufacturing powders that functions independently of the gravitational environment and with no restriction on feedstock powder flowability. Based on a specific sequence of boundary loads applied to the granular packing, powder is transported to the printing zone, homogenized and put under compression to increase the density of the final part. The powder deposition process is validated by simulations that show the homogeneity and density of deposition to be insensitive to gravity and cohesion forces within the DEM model. We further provide an experimental proof of concept of the process by successfully 3D printing parts on-ground and in weightlessness, on parabolic flight. Powders exhibiting high and low flowability are used as model feedstock material to demonstrate the versatility of the process, opening the way for additive manufacturing of recycled material.

cond-mat.mtrl-sci↗
arXiv2020

Integration through transients for inelastic hard sphere fluids

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.

cond-mat.soft↗
arXiv2019

Trail-Mediated Self-Interaction

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{117}, 8101 (2016)] that the self-interaction may localize the organism above a critical coupling $χ_c$ 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 $χ< χ_c$. We find that fluctuations in propulsion speed shift the localization transition to stronger couplings.

physics.bio-ph↗
arXiv2019

Asymptotically Exact Solution of the Fredrickson-Andersen Model

The Fredrickson-Andersen (FA) model---a kinetically constrained lattice model---displays an ergodic to non-ergodic transition with a slow two-step relaxation of dynamical correlation functions close to the transition point. We derive an asymptotically exact solution for the dynamical occupation correlation function of the FA model on the Bethe lattice by identifying an exact expression for its memory kernel. The exact solution fulfills a scaling relation between critical exponents and allows to calculate the exponents explicitly. In addition, we propose an approximate dynamics that describes numerical data away from the critical point over many decades in time.

cond-mat.stat-mech↗
arXiv2018

Rheology of inelastic hard spheres at finite density and shear rate

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 $σ$ to the shear rate $\dotγ$, and predictions of the yield stress complete our discussion of granular rheology derived from first principles.

cond-mat.soft↗
arXiv2017

Kinetic theory for strong uniform shear flow of granular media at high density

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 Newtonian viscosity as well as the Bagnold coefficient. We discuss the dependence of the transport coefficients on density and coefficient of restitution.

cond-mat.soft↗
arXiv2016

Multicellular self-organization of P. aeruginosa due to interactions with secreted trails

Guided movement in response to slowly diffusing polymeric trails provides a unique mechanism for self-organization of some microorganisms. To elucidate how this signaling route leads to microcolony formation, we experimentally probe the trajectory and orientation of Pseudomonas aeruginosa that propel themselves on a surface using type IV pili motility appendages, which preferentially attach to deposited exopolysaccharides. We construct a stochastic model by analyzing single-bacterium trajectories, and show that the resulting theoretical prediction for the many-body behavior of the bacteria is in quantitative agreement with our experimental characterization of how cells explore the surface via a power law strategy.

q-bio.CB↗
arXiv2016

Effective dynamics of microorganisms that interact with their own trail

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 timescale 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.

physics.bio-ph↗
arXiv2013

A classical long-time tail in a driven granular fluid

I derive a mode-coupling theory for the velocity autocorrelation function, ψ(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 function decays algebraically, ψ(t) ~ t^{-3/2}, if momentum is conserved. I show that the slow decay is due to the coupling to transverse currents.

cond-mat.soft↗
arXiv2010

Glass Transition for Driven Granular Fluids

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 glass 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.

cond-mat.soft↗
arXiv2009

Partitioning of energy in highly polydisperse granular gases

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 multicomponent 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 Haff's law. The analytical results are supported by event driven simulations for a large, but discrete number of species.

cond-mat.soft↗
arXiv2006

Translations and Rotations are correlated in Granular Gases

In a granular gas of rough particles the axis of rotation is shown to be correlated with the translational velocity of the particles. The average relative orientation of angular and linear velocities depends on the parameters which characterise the dissipative nature of the collision. We derive a simple theory for these correlations and validate it with numerical simulations for a wide range of coefficients of normal and tangential restitution. The limit of smooth spheres is shown to be singular: even an arbitrarily small roughness of the particles gives rise to orientational correlations.

cond-mat.stat-mech↗