arXiv subjects

Luke K. Davis

Publications and source records attributed to Luke K. Davis.

8 recordsLinked to original sources

arXiv2026

A solid-state theory for dense cylindrical packings of balls

We develop an analytical theory for the dense packing of hard spheres in cylinders. Physically, our theory consists of a finite cylindrical masking of a close-packed three-dimensional solid and covers the entire range of cylinder aspect ratios, thus going beyond efforts that are focused on very tall cylinders in a narrow range of widths. We explicitly derive an exact equation for resulting packing fractions, valid for any regular lattice, and it provides a basis to understand the oscillations and scaling of volume fractions that have appeared in previous works. Our analytical relation serves as a rigorous lower bound and to tighten it we derive, and implement, an efficient mathematical procedure to optimize the orientation of the cylinder. Furthermore, we suggest simple techniques to improve on the predicted packings. Overall, we provide a general theoretical foundation for the packing of balls in cylinders, valid for all container sizes.

cond-mat.soft↗

arXiv2026

Geometric decomposition of the $d$-dimensional hard-sphere partition function

We introduce a geometric decomposition of the hard-sphere partition function. Using a close-packing-inspired geometric bound on the available insertion volume, made rigorous when a corresponding local density certificate is available, we establish a reference upper bound $Q^\ast$ on the configurational integral. Factoring this upper bound out of the statistical geometric partition function of Speedy yields a new form for the $d$-dimensional partition function, $Q(N,V,T)=Q^\ast \exp(-N \mathcal{J})$, where $\mathcal{J}$ depends strictly on the boundary-to-volume ratio of the voids and the close-packing density. Overall, this work deepens our statistical geometric understanding of the hard-sphere system.

cond-mat.stat-mech↗

arXiv2026

Optimal multi-parameter control of trapped active matter

The realization of efficient micro-machines built from active matter requires precise thermodynamic control far from equilibrium. Despite theoretical progress, the focus on single-parameter driving, coupled with strict theoretical assumptions, limits efforts to capture modern multi-parameter control experiments. Here, guided by careful theoretical considerations, we develop a transparent computational framework based on exact-gradient descent via automatic differentiation. We derive optimal protocols for a wide range of multi-parameter problems -- involving trap stiffness, trap center, and particle activity -- to minimize the thermodynamic work or heat. We demonstrate that smoothed, experimentally plausible protocols -- obtained by assigning kinetic costs to the controls -- achieve near-optimal efficiencies comparable to discontinuous ``bang-bang'' solutions. By exploring both open- and closed-loop control, we find the dynamical coupling between parameters leads to genuinely new strategies, including symmetry breaking in optimal activity cycles and non-monotonic trap stiffness controls. Further, we identify regimes where initial measurement and multi-parameter flexibility combine to improve efficiency. Finally, we reveal that the naive simultaneous execution of independently optimized controls incurs only slightly more work than the full multi-parameter solutions. Taken together, our work elucidates the non-equilibrium physics of multi-parameter control and provides robust, scalable strategies for controlling active matter.

cond-mat.soft↗

arXiv2026

Reentrance in a Hamiltonian flocking model

The clustering of self-motile and repulsive particles, so-called motility-induced phase separation (MIPS), is one of the clearest signatures of active physics. Typically, increasing the amplitude of self-motility increases the degree of clustering, however for high enough self-motility the homogeneous phase is reentered. Here, we report that such reentrance naturally emerges in a Hamiltonian (conservative) model known to recapitulate properties of (active) bird flocks, and exhibits clustering behaviour reminiscent of MIPS. We numerically demonstrate the reentrance of the homogeneous phase and identify the underlying mechanism as a competition between the amplitude of a spin-velocity coupled drive and mobility-limited kinetic frustration. Specifically, we reveal that strong spin-velocity coupling suppresses transverse diffusion, thereby leading the system into an arrest that closes the window for phase separation. Overall, our work offers a Hamiltonian, conservative, bridge between reentrant physics across equilibrium and non-equilibrium materials.

cond-mat.soft↗

arXiv2025

Insertion space in repulsive active matter

For equilibrium hard spheres, the statistical geometry of the insertion space, the room to accommodate another sphere, relates exactly to the equation of state. We begin to extend this idea to active matter, analyzing the insertion space for repulsive active particles in one and two dimensions using both on- and off-lattice models. In one dimension, we derive closed-form expressions for the mean insertion cavity size, cavity number, and total insertion volume, all in excellent agreement with simulations. Strikingly, activity increases the total insertion volume and tends to keep the insertion space more connected. We also find that insertion space metrics contain signatures of collective phase behaviors occurring at previously predicted packing fractions. Taken together, our work provides the first quantitative foundation for the statistical geometry of active matter.

cond-mat.soft↗

arXiv2025

Force and geometric signatures of the creep-to-failure transition in a granular pile

Granular creep is the slow, sub-yield movement of constituents in a granular packing due to the disordered nature of its grain-scale interactions. Despite the ubiquity of creep in disordered materials, it is still not understood how to best predict the creep-to-failure regime based on the forces and interactions among constituents. To address this gap, we perform experiments to explore creep and failure in quasi two-dimensional piles of photoelastic disks, allowing the quantification of both grain movements and grain-scale contact force networks. Through controlled external disturbances, we investigate the emergence and evolution of grain rearrangements, force networks, and voids to illuminate signatures of creep and failure. Surprisingly, the force chain structure remains dynamic even in the absence of observable particle motion. We find that shifts in force chains provide an indication to larger, avalanche-scale disruptions. We connect these force signatures with the geometry of the voids in the pile. Overall, our novel experiments and analyses deepen our mechanical and geometric understanding of the creep-to-failure transition in granular systems.

cond-mat.soft↗

arXiv2025

Mesoscopic heterogeneity in biomolecular condensates from sequence patterning

Biomolecular condensates composed of intrinsically disordered proteins (IDPs) are vital for proper cellular function, and their dysfunction is associated with diseases including neurodegeneration and cancer. Despite their biological importance, the precise physical mechanisms underlying condensate (dys)function are unclear, in part owing to the difficulties in understanding how biomolecular sequence patterns influence emergent condensate behaviours across relevant length and timescales. Here, through minimal physical modelling, we explain how IDP sequence patterning gives rise to nano-scale organisational heterogeneities in condensates. By applying our coarse-grained molecular-dynamics polymer model, which accounts for steric, attractive, and electrostatic interactions, we systematically quantify and map out the emergent morphological phases resulting from a wide range of sequence patterns. We demonstrate how sequences that enable local coil-to-globule transitions within regions of single polymers - driven by a competition between the preferred crowding densities of different regions in the sequence - also exhibit cluster formation in condensates. Overall, our work provides a conceptual framework to understand how sequence properties determine mesoscopic organisation within biomolecular condensates.

cond-mat.soft↗

arXiv2024

Active matter under control: Insights from response theory

Active constituents burn fuel to sustain individual motion, giving rise to collective effects that are not seen in systems at thermal equilibrium, such as phase separation with purely repulsive interactions. There is a great potential in harnessing the striking phenomenology of active matter to build novel controllable and responsive materials that surpass passive ones. Yet, we currently lack a systematic roadmap to predict the protocols driving active systems between different states in a way that is thermodynamically optimal. Equilibrium thermodynamics is an inadequate foundation to this end, due to the dissipation rate arising from the constant fuel consumption in active matter. Here, we derive and implement a versatile framework for the thermodynamic control of active matter. Combining recent developments in stochastic thermodynamics and nonequilibrium response theory, our approach shows how to find the optimal control for either continuous- or discrete-state active systems operating arbitrarily far from equilibrium. Our results open the door to designing novel active materials which are not only built to stabilize specific nonequilibrium collective states, but are also optimized to switch between different states at minimum dissipation.

cond-mat.stat-mech↗