Martin Depken

Continuum approach to wide shear zones in quasistatic granular matter.

Slow and dense granular flows often exhibit narrow shear bands, making them ill suited for a continuum description. However, smooth granular flows have been shown to occur in specific geometries such as linear shear in the absence of gravity, slow inclined plane flows and, recently, flows in split-bottom Couette geometries. The wide shear regions in these systems should be amenable to a continuum description, and the theoretical challenge lies in finding constitutive relations between the internal stresses and the flow field. We propose a set of testable constitutive assumptions, including rate independence, and investigate the additional restrictions on the constitutive relations imposed by the flow geometries. The wide shear layers in the highly symmetric linear shear and inclined plane flows are consistent with the simple constitutive assumption that, in analogy with solid friction, the effective-friction coefficient (ratio between shear and normal stresses) is a constant. However, this standard picture of granular flows is shown to be inconsistent with flows in the less symmetric split-bottom geometry--here the effective friction coefficient must vary throughout the shear zone, or else the shear zone localizes. We suggest that a subtle dependence of the effective-friction coefficient on the orientation of the sliding layers with respect to the bulk force is crucial for the understanding of slow granular flows.

Nonlinear viscoelasticity of actin transiently cross-linked with mutant α-actinin-4.

Filamentous actin and associated actin binding proteins play an essential role in governing the mechanical properties of eukaryotic cells. They can also play a critical role in disease; for example, mutations in α-actinin-4 (Actn4), a dynamic actin cross-linking protein, cause proteinuric disease in humans and mice. Amino acid substitutions strongly affect the binding affinity and protein structure of Actn4. To study the physical impact of such substitutions on the underlying cytoskeletal network, we examine the bulk mechanical behavior of in vitro actin networks cross-linked with wild-type and mutant Actn4. These networks exhibit a complex viscoelastic response and are characterized by fluid-like behavior at the longest timescales, a feature that can be quantitatively accounted for through a model governed by dynamic cross-linking. The elastic behavior of the network is highly nonlinear, becoming much stiffer with applied stress. This nonlinear elastic response is also highly sensitive to the mutations of Actn4. In particular, we observe that actin networks cross-linked with Actn4 bearing the disease-causing K255E mutation are more brittle, with a lower breaking stress in comparison to networks cross-linked with wild-type Actn4. Furthermore, a mutation that ablates the first actin binding site (ABS1) in Actn4 abrogates the networks ability to stress-stiffen is standard nomenclature. These changes in the mechanical properties of actin networks cross-linked with mutant Actn4 may represent physical determinants of the underlying disease mechanism in inherited focal segmental glomerulosclerosis.

Exact probability function for bulk density and current in the asymmetric exclusion process

We examine the asymmetric simple exclusion process with open boundaries, a paradigm of driven diffusive systems, having a nonequilibrium steady-state transition. We provide a full derivation and expanded discussion and digression on results previously reported briefly in M. Depken and R. Stinchcombe, Phys. Rev. Lett. 93, 040602 (2004). In particular we derive an exact form for the joint probability function for the bulk density and current, both for finite systems, and also in the thermodynamic limit. The resulting distribution is non-Gaussian, and while the fluctuations in the current are continuous at the continuous phase transitions, the density fluctuations are discontinuous. The derivations are done by using the standard operator algebraic techniques and by introducing a modified version of the original operator algebra. As a by-product of these considerations we also arrive at a very simple way of calculating the normalization constant appearing in the standard treatment with the operator algebra. Like the partition function in equilibrium systems, this normalization constant is shown to completely characterize the fluctuations, albeit in a very different manner.

Exact joint density-current probability function for the asymmetric exclusion process.

We study the asymmetric simple exclusion process with open boundaries and derive the exact form of the joint probability function for the occupation number and the current through the system. We further consider the thermodynamic limit, showing that the resulting distribution is non-Gaussian and that the density fluctuations have a discontinuity at the continuous phase transition, while the current fluctuations are continuous. The derivations are performed by using the standard operator algebraic approach and by the introduction of new operators satisfying a modified version of the original algebra.