arXiv subjects

Alex Dixon

Publications and source records attributed to Alex Dixon.

5 recordsLinked to original sources

arXiv2026

Rheology of dense suspensions of granular spherocylinders by particle-based simulation

Dense suspensions of rod-shaped granular particles are widespread in nature and manufacturing, where their fluid mechanical properties are often paramount. We have developed a particle-based simulation that models such suspensions under simple shear flow, providing predictions of the viscosity and microstructure for a given solids volume fraction and particle aspect ratio. The model tracks the trajectories of spherocylindrical rods under the action of short-range frictional contact and hydrodynamic forces, inspired by similar tools that have generated new insight into suspensions of granular spheres. It incorporates new schemes for the computation of lubrication forces between spherocylinders and the dynamic determination of the timestep. For aspect ratios up to 20, the model predicts a viscosity spike at shear start-up, giving way to steady state viscosities that increase systematically with volume fraction and aspect ratio. Likewise, particle alignment increases with volume fraction up to an aspect-ratio-dependent critical point. Our model corroborates the limited experimental rheology data available for suspensions of granular rods, and offers a tool for fundamental exploration of the fluid mechanics, microstructure and rheology of this widespread material.

cond-mat.soft↗

arXiv2023

Saturating automata for game semantics

Saturation is a fundamental game-semantic property satisfied by strategies that interpret higher-order concurrent programs. It states that the strategy must be closed under certain rearrangements of moves, and corresponds to the intuition that program moves (P-moves) may depend only on moves made by the environment (O-moves). We propose an automata model over an infinite alphabet, called saturating automata, for which all accepted languages are guaranteed to satisfy a closure property mimicking saturation. We show how to translate the finitary fragment of Idealized Concurrent Algol (FICA) into saturating automata, confirming their suitability for modelling higher-order concurrency. Moreover, we find that, for terms in normal form, the resultant automaton has linearly many transitions and states with respect to term size, and can be constructed in polynomial time. This is in contrast to earlier attempts at finding automata-theoretic models of FICA, which did not guarantee saturation and involved an exponential blow-up during translation, even for normal forms.

cs.PL↗

arXiv2021

Leafy Automata for Higher-Order Concurrency

Finitary Idealized Concurrent Algol (FICA) is a prototypical programming language combining functional, imperative, and concurrent computation. There exists a fully abstract game model of FICA, which in principle can be used to prove equivalence and safety of FICA programs. Unfortunately, the problems are undecidable for the whole language, and only very rudimentary decidable sub-languages are known. We propose leafy automata as a dedicated automata-theoretic formalism for representing the game semantics of FICA. The automata use an infinite alphabet with a tree structure. We show that the game semantics of any FICA term can be represented by traces of a leafy automaton. Conversely, the traces of any leafy automaton can be represented by a FICA term. Because of the close match with FICA, we view leafy automata as a promising starting point for finding decidable subclasses of the language and, more generally, to provide a new perspective on models of higher-order concurrent computation. Moreover, we identify a fragment of FICA that is amenable to verification by translation into a particular class of leafy automata. Using a locality property of the latter class, where communication between levels is restricted and every other level is bounded, we show that their emptiness problem is decidable by reduction to Petri net reachability.

cs.FL↗

arXiv2009

Anomalously slow attrition times for asymmetric populations with internal group dynamics

The many-body dynamics exhibited by living objects include group formation within a population, and the non-equilibrium process of attrition between two opposing populations due to competition or conflict. We show analytically and numerically that the combination of these two dynamical processes generates an attrition duration T whose nonlinear dependence on population asymmetry x is in stark contrast to standard mass-action theories. A minority population experiences a longer survival time than two equally balanced populations, irrespective of whether the majority population adopts such internal grouping or not. Adding a third population with pre-defined group sizes allows T(x) to be tailored. Our findings compare favorably to real-world observations.

cond-mat.soft↗

arXiv2009

Internal network dynamics prolong a losing battle

Fights-to-the-death occur in many natural, medical and commercial settings. Standard mass action theory and conventional wisdom imply that the minority (i.e. smaller) group's survival time decreases as its relative initial size decreases, in the absence of replenishment. Here we show that the opposite actually happens, if the minority group features internal network dynamics. Our analytic theory provides a unified quantitative explanation for a range of previously unexplained data, and predicts how losing battles in a medical or social context might be extended or shortened using third-party intervention.

physics.soc-ph↗