arXiv subjects

Christopher Harper

Publications and source records attributed to Christopher Harper.

4 recordsLinked to original sources

arXiv2026

Geometric Origin of Macroscopic Alignment in Granular Flows

Predicting the nematic alignment of nonspherical particles in sheared granular flows is essential for understanding the rheology, packing, and constitutive response of dense particulate media. While macroscopic fabric is typically attributed to complex multibody interactions, stress transmission, and dissipative collisions, empirical observations reveal that the steady-state nematic order parameter $S_2$ depends primarily on particle aspect ratio and remains remarkably insensitive to shear rate and interparticle friction. Here, we show that this leading-order alignment emerges directly from single-particle boundary geometry without resolving dynamical equations of motion. Assuming uniform contact probability along a particle perimeter, we derive an analytical transform linking local boundary curvature $κ(θ)$ to the distribution of contact normals, $P(θ) \propto 1/κ(θ)$, which in turn geometrically constrains the phase space of admissible particle orientations. This minimal framework accurately predicts the magnitude of $S_2$ across the full continuum of aspect ratios for smooth ellipsoids as well as the singular limit of faceted rectangles and cylinders. Our analytical predictions capture the envelope of three-dimensional discrete element simulations and match laboratory measurements on sheared rice grains and glass cylinders across decadal variations in shear rate. By identifying particle geometry as the primary control parameter for granular alignment, this work provides a first-principles physical foundation for geometric saturation at the critical state, establishing a universal baseline upon which dynamical and frictional effects act as secondary modulations.

cond-mat.soft↗

arXiv2024

The role of compressional dynamics in setting the scale-dependent rheology of granular flows: Application to the emergence of thin layer stability

One great challenge of modeling granular systems lies in capturing the rheologic dependencies on scale. For example, there are marked differences between quasi-static, intermediate, and rapid flow regimes. In this study, we demonstrate that assumptions for infinite stiffness of rigid particles, an assumption upon which the state-of the-art ($μ(I)$-rheology) modeling approaches are constructed, must be relaxed in order to recover the physical mechanisms behind many scale-dependent and non-local rheological effects. Any relaxation of the infinite stiffness assumption allows for particles to compress in series, whereby the number of simultaneously compressed particles controls the extent to which end-member particles experience a modified coefficient of effective friction, analogous to reduced stiffness for springs in series. To demonstrate the importance of such a mechanism in setting the dynamics for dense rigid granular systems, we show that modifying simple models to include the kinematics introduced by compression in series captures the emergence of thin layer stability, a widely observed yet incompletely explained non-local granular phenomenon. We also discuss, in general, how knowledge of the contact network and softness provides a potential physical basis for the diffusion of granular temperature.

cond-mat.soft↗

arXiv2022

Integrating Formal Verification and Simulation-based Assertion Checking in a Corroborative V&V Process

Automated Vehicles (AVs) are rapidly maturing in the transportation domain. However, the complexity of the AV design problem is such that no single technique is sufficient to provide adequate validation of key properties such as safety, reliability or trustworthiness. In this vision paper, a combination of a spatial traffic logic and agent-based verification methods with a validation method that uses assertion checking of simulations is proposed. We sketch how to integrate the respective approaches within a methodological framework called Corroborative Verification and Validation (V&V).The Corroborative V&V framework identifies three different verification and validation levels for AVs (formal verification, simulation-based testing, real-world experiments) and specifies connections and evidence between these levels. We define specifications for the formal relationships that must be established between processes, system models and requirements models for the evidence from formal design verification and simulation-based testing to corroborate each other and enhance assurance confidence from verification and validation.

cs.SE↗

arXiv2022

Safety Validation of Autonomous Vehicles using Assertion Checking

Safety and mission performance validation of autonomous vehicles (AVs) is a major challenge. In this paper we describe a methodology for constructing and applying assertion checks to validate the behaviour of an AV operating either in simulation or in the real world. We have identified a taxonomy of assertion types and the general format of their specification, and we have developed procedures for translating driving codes of practice to yield formal logical expressions that can be monitored automatically by computer, either by direct translation or by physical modelling. We have developed examples of assertions derived from the UK Highway Code (UKHC), as an example of a code of practice. We illustrate the approach with an example of assertion checking for vehicle overtaking, using a geospatial information system in an SQL database for validation and performance assessment. We present initial simulation and runtime monitoring experiments that apply assertions relevant in this overtaking scenario together with an analysis of the safety and mission performance characteristics measured.

cs.DB↗