arXiv subjects

Abram H. Clark

Publications and source records attributed to Abram H. Clark.

At least 19 recordsLinked to original sources

arXiv2026

Proximity to Jamming Governs Acoustic Attenuation in Damped Packings

We use particle-based numerical simulations to address a longstanding question regarding the origins of the linear frequency dependence of attenuation in fluid-saturated granular media. We study both the acoustic modes and wave propagation in damped, disordered particle packings. We calculate the damped vibrational modes of packings as a function of frequency, pressure, and grain-contact dissipation. The spatial structure and dissipation of these modes show a clear transition at a pressure-dependent critical frequency from viscous-like continuum behavior to more localized, scattering modes. We also measure how wavespeed and spatial attenuation rate depend on these same parameters. At the same critical frequency, wave propagation also shifts from coherent motion, where attenuation scales quadratically with frequency and linearly with contact damping, to much more incoherent particle-scale motion, where attenuation scales linearly with frequency and sublinearly with contact damping. All of these features, including the transition frequency, are consistent with a large collection of experimental data, which has not been explained by any framework based on grain-scale physics. We refer to this approach as ``Jammed-Network Scattering'' (JNS), and propose it as a grain-scale framework for understanding the acoustics of fluid-saturated granular media.

cond-mat.soft↗

arXiv2026

Scaling and Trade-offs in Multi-agent Autonomous Systems

Designing autonomous drone swarms is hampered by a vast design space spanning platform, algorithmic, and numerical-strength choices. We perform large-scale agent-based simulations in three canonical scenarios: swarm-on-swarm battle, cooperative area search with attrition, and pursuit of scattering targets. We demonstrate how dimensional-analysis and data-scaling can be leveraged to collapse performance data onto scaling functions that are mathematically simple, yet counterintuitive and therefore difficult to predict a priori. These scaling laws reveal success-failure boundaries, including sharp break points which we show can be framed as an ``effective swarm size.'' Additionally, we show how this technique can be used to quantify trade-offs between agent count and platform parameters such as velocity, sensing or weapon range, and attrition rate. Furthermore, we show the benefits of embedding an optimal path planning loop within this framework, which can qualitatively improve the scaling laws that govern the outcome. The methods we demonstrate are highly flexible and would enable rapid, budget-aware sizing and algorithm selection for large autonomous swarms.

eess.SY↗

arXiv2026

Modeling Large-Scale Adversarial Swarm Engagements using Optimal Control

We study optimal control of large-scale autonomous systems under adversarial conditions in which agents may be probabilistically destroyed during an engagement. Because attrition changes the population that generates the spatial interaction dynamics, treating survival and motion independently can produce physically inconsistent solutions. We formulate a stochastic variable-population benchmark and examine three deterministic approximations that propagate agent survival probabilities from relative geometry. The models are applied to defense of a high-value unit against an attacking swarm and solved using direct optimal-control methods. Monte Carlo realizations of the stochastic benchmark show that deterministic models can reproduce engagement outcomes when attrition is coupled to spatial influence, whereas a decoupled formulation can exploit effectively destroyed defenders that continue to repel attackers, a failure mode we term ``ghost herding.'' Large-scale simulations and defender-number sweeps further show that this modeling choice can substantially alter predicted high-value-unit survival and inferred defensive resource requirements. The results provide a tractable framework for attrition-aware trajectory optimization and resource--survival analysis in adversarial autonomous systems.

math.OC↗

arXiv2026

Saddle Point Evasion via Curvature-Regularized Gradient Dynamics

Nonconvex optimization underlies many modern machine learning and control tasks, where saddle points pose the dominant obstacle to reliable convergence in high-dimensional settings. Escaping these saddle points deterministically using continuous-time optimization remains an open challenge: gradient descent is blind to curvature, stochastic perturbation methods lack deterministic guarantees, and Newton-type approaches suffer from Hessian singularity. Adopting the perspective of viewing optimization algorithms as dynamical systems, we present Curvature-Regularized Gradient Dynamics (CRGD), which augments the objective with a smooth penalty on the negative Hessian eigenvalues, yielding an augmented cost that serves as an optimization Lyapunov function with user-selectable convergence rates to second-order stationary points. Numerical experiments confirm that CRGD converges to second-order stationary points, even in regimes where gradient descent fails.

math.OC↗

arXiv2026

Prescribed-Time Distributed Generalized Nash Equilibrium Seeking

Safety-critical multi-agent systems, from cooperative guidance to collision avoidance, must often reach a coordinated decision by a hard deadline rather than merely converge to one eventually. This paper proposes the first fully distributed algorithm that solves the generalized Nash equilibrium (GNE) problem, a non-cooperative game with shared coupling constraints and general cost coupling, at a user-prescribed time $T$ independent of initial conditions. The foundation is a centralized, prescribed-time result built on the optimization Lyapunov function framework and implemented via unnormalized Hessian-gradient feedback, chosen because, unlike the Newton and normalized Hessian-gradient realizations, it naturally splits into per-agent computations. Distributing this feedback requires each agent to run three coupled processes simultaneously: a prescribed-time observer of the global state, a local optimization law, and a dual-consensus mechanism that enforces the shared multipliers of the variational GNE. Their simultaneous operation is the core difficulty, as the optimization continually displaces the states the observers track, while estimation errors corrupt the gradients that drive the optimization. We resolve this coupling with a multi-rate gain schedule whose observer and dual-consensus layers contract strictly faster than the optimization layer, so that every error component vanishes exactly at $T$. A Fischer-Burmeister reformulation keeps the design projection-free while enforcing the constraints at the deadline. Numerical results for a Cournot game and a time-critical sensor-coverage problem validate the approach and demonstrate its use as a solver-in-the-loop for time-critical autonomy.

math.OC↗

arXiv2026

Optimization via a Control-Centric Framework

Optimization plays a central role in intelligent systems and cyber-physical technologies, where speed and reliability of convergence directly impact performance. In control theory, optimization is the foundation of widely-used design methodologies such as linear quadratic regulation, $H_\infty$ control, and model predictive control. In contrast, this paper develops a control-centric framework for optimization itself, where algorithms are constructed directly from Lyapunov stability principles rather than being proposed first and analyzed afterward. A key element is the stationarity vector, which encodes first-order optimality conditions and enables Lyapunov-based convergence analysis. By pairing a Lyapunov function with a selectable decay law, we obtain continuous-time dynamics with guaranteed exponential, finite-time, fixed-time, or prescribed-time convergence. Within this framework, we introduce three feedback realizations of increasing restrictiveness: the Hessian-gradient, Newton, and gradient dynamics. Each realization shapes the decay of the stationarity vector to achieve the desired rate. These constructions unify unconstrained optimization, extend to constrained problems via Lyapunov-consistent primal-dual dynamics, and broaden results for minimax and generalized Nash equilibrium seeking problems beyond exponential stability. In total, the framework spans six problem classes and four convergence regimes, yielding a unified design recipe across twenty-four combinations, nine of which, to the best of our knowledge, have no direct continuous-time counterpart in the prior literature. The framework provides systematic design tools for optimization algorithms in control and game-theoretic problems.

math.OC↗

arXiv2024

Granular temperature controls local rheology of vibrated granular flows

We use numerical simulations to demonstrate a local rheology for sheared, vibrated granular flows. We consider a granular assembly that is subjected to simple shear and harmonic vibration at the boundary. This configuration allows us to isolate the effects of vibration, as parameterized by granular temperature. We find that friction is reduced due to local velocity fluctuations of grains. All data obey a local rheology that relates the material friction coefficient, the granular temperature, and the dimensionless shear rate. We also observe that reduction in material friction due to granular temperature is associated with reduction in fabric anisotropy. We demonstrate that the temperature can be modeled by a heat equation with dissipation with appropriate boundary conditions, which provides complete closure of the system and allows a fully local continuum description of sheared, vibrated granular flows. This success suggests local rheology based on temperature, as suggested previously, combined with the new, empirical heat diffusion equation may provide a general strategy for dense granular flows.

cond-mat.soft↗

arXiv2024

An explicit granular-mechanics approach to marine sediment acoustics

Here we theoretically and computationally study the frequency dependence of phase speed and attenuation for marine sediments from the perspective of granular mechanics. We leverage recent theoretical insights from the granular physics community as well as discrete-element method simulations, where the granular material is treated as a packing of discrete objects that interact via pairwise forces. These pairwise forces include both repulsive contact forces as well as dissipative terms which may include losses from the fluid as well as losses from inelasticity at grain-grain contacts. We show that the structure of disordered granular packings leads to anomalous scaling laws for frequency-dependent phase speed and attenuation that do not follow from a continuum treatment. Our results demonstrate that granular packing structure, which is not explicitly considered in existing models, may play a crucial role in a complete theory of sediment acoustics. While this simple approach does not explicitly treat sound propagation or inertial effects in the interstitial fluid, it provides a starting point for future models that include these and other more complex features.

cond-mat.soft↗

arXiv2023

Frictional weakening of vibrated granular flows

We computationally study the frictional properties of sheared granular media subjected to harmonic vibration applied at the boundary. Such vibrations are thought to play an important role in weakening flows, yet the independent effects of amplitude, frequency, and pressure on the process have remained unclear. Based on a dimensional analysis and DEM simulations, we show that, in addition to a previously proposed criterion for peak acceleration that leads to breaking of contacts, weakening requires the absolute amplitude squared of the displacement is sufficiently large relative to the confining pressure. The analysis provides a basis for predicting flows subjected to arbitrary external vibration and demonstrates that a previously unrecognized second process that is dependent on dissipation contributes to shear weakening under vibrations.

cond-mat.soft↗

arXiv2021

Modeling and Control of Large-Scale Adversarial Swarm Engagements

We theoretically and numerically study the problem of optimal control of large-scale autonomous systems under explicitly adversarial conditions, including probabilistic destruction of agents during the simulation. Large-scale autonomous systems often include an adversarial component, where different agents or groups of agents explicitly compete with one another. An important component of these systems that is not included in current theory or modeling frameworks is random destruction of agents in time. In this case, the modeling and optimal control framework should consider the attrition of agents as well as their position. We propose and test three numerical modeling schemes, where survival probabilities of all agents are smoothly and continuously decreased in time, based on the relative positions of all agents during the simulation. In particular, we apply these schemes to the case of agents defending a high-value unit from an attacking swarm. We show that these models can be successfully used to model this situation, provided that attrition and spatial dynamics are coupled. Our results have relevance to an entire class of adversarial autonomy situations, where the positions of agents and their survival probabilities are both important.

math.OC↗

arXiv2021

Darcy-Reynolds forces during intrusion into granular-fluid beds

We experimentally study intrusion into fluid-saturated granular beds by a free-falling sphere, varying particle size and fluid viscosity. We test our results against Darcy-Reynolds theory, where the deceleration of the sphere is controlled by Reynolds dilatancy and the Darcy flow resistance. We find the observed intruder dynamics are consistent with Darcy-Reynolds theory for varied particle size. We also find that our experimental results for varied viscosity are consistent with Darcy-Reynolds theory, but only for a limited range of the viscosity. For large viscosities, observed forces begin to decrease with increasing viscosity, in contrast with the theoretical prediction.

cond-mat.soft↗

arXiv2021

Viscous-like forces control the impact response of shear-thickening dense suspensions

We experimentally and theoretically study impacts into dense cornstarch and water suspensions. We vary impact speed as well as intruder size, shape, and mass, and we characterize the resulting dynamics using high-speed video and an onboard accelerometer. We numerically solve previously proposed models, most notably the added-mass model as well as a class of {viscous-like} models. In the {viscous-like models}, the intruder dynamics are dominated by {large, viscous-like forces} at the boundary of the jammed front {where large shear rates and accompanying large viscosities are present.} We find that our experimental data are consistent with this class of models and inconsistent with the added mass model. Our results strongly suggest that the added-mass model, which is the dominant model for understanding the dynamics of impact into shear-thickening dense suspensions, should be updated to include these viscous-like forces.

cond-mat.soft↗

arXiv2020

Power law scaling of early-stage forces during granular impact

We experimentally and computationally study the early-stage forces during intruder impacts with granular beds in the regime where the impact velocity approaches the granular force propagation speed. Experiments use 2D assemblies of photoelastic disks of varying stiffness, and complimentary discrete-element simulations are performed in 2D and 3D. The peak force during the initial stages of impact and the time at which it occurs depend only on the impact speed, the intruder diameter, the mass density of the grains, and the elastic modulus of the grains according to power-law scaling forms that are not consistent with Poncelet models, granular shock theory, or added-mass models. The insensitivity of our results to many system details suggest that they may also apply to impacts into similar materials like foams and emulsions.

cond-mat.soft↗

arXiv2020

The physics of sediment transport initiation, cessation, and entrainment across aeolian and fluvial environments

Predicting the morphodynamics of sedimentary landscapes due to fluvial and aeolian flows requires answering the following questions: Is the flow strong enough to initiate sediment transport, is the flow strong enough to sustain sediment transport once initiated, and how much sediment is transported by the flow in the saturated state (i.e., what is the transport capacity)? In the geomorphological and related literature, the widespread consensus has been that the initiation, cessation, and capacity of fluvial transport, and the initiation of aeolian transport, are controlled by fluid entrainment of bed sediment caused by flow forces overcoming local resisting forces, whereas aeolian transport cessation and capacity are controlled by impact entrainment caused by the impacts of transported particles with the bed. Here the physics of sediment transport initiation, cessation, and capacity is reviewed with emphasis on recent consensus-challenging developments in sediment transport experiments, two-phase flow modeling, and the incorporation of granular physics' concepts. Highlighted are the similarities between dense granular flows and sediment transport, such as a superslow granular motion known as creeping (which occurs for arbitrarily weak driving flows) and system-spanning force networks that resist bed sediment entrainment; the roles of the magnitude and duration of turbulent fluctuation events in fluid entrainment; the traditionally overlooked role of particle-bed impacts in triggering entrainment events in fluvial transport; and the common physical underpinning of transport thresholds across aeolian and fluvial environments. This sheds a new light on the well-known Shields diagram, where measurements of fluid entrainment thresholds could actually correspond to entrainment-independent cessation thresholds.

physics.geo-ph↗

arXiv2019

A real-space renormalization group for jamming

Jamming occurs in granular materials, as well as in emulsions, dense suspensions, and other amorphous, particulate systems. When the packing fraction $ϕ$, defined as the ratio of particle volume to system volume, is increased past a critical value $ϕ_c$, a liquid-solid phase transition occurs, and grains are no longer able to rearrange. Previous studies have shown evidence of spatial correlations that diverge near $ϕ= ϕ_c$, but there has been no explicit spatial renormalization group (RG) scheme that has captured this transition. Here, I present a candidate for such a scheme, using a block-spin-like transformation of a randomly vacated lattice of grains. I define a real-space RG transformation based on local mechanical stability. This model displays a critical packing fraction $ϕ_c$ and gives estimates of critical exponents in two and three dimensions.

cond-mat.soft↗

arXiv2019

Critical scaling for yield is independent from distance to isostaticity

Using discrete element simulations, we demonstrate that critical behavior for yielding in soft disk and sphere packings is independent of distance to isostaticity over a wide range of dimensionless pressures. Jammed states are explored via quasistatic shear at fixed pressure, and the statistics of the dimensionless shear stress $μ$ of these states obey a scaling description with diverging length scale $ξ\propto |μ-μ_c|^{-ν}$. The critical scaling functions and values of the scaling exponents are nearly independent of distance to isostaticity despite the large range of pressures studied. Our results demonstrate that yielding of jammed systems represents a distinct nonequilibrium critical transition from the isostatic critical transition which has been demonstrated by previous studies. Our results may also be useful in deriving nonlocal rheological descriptions of granular materials, foams, emulsions, and other soft particulate materials.

cond-mat.soft↗

arXiv2018

Vibration can enhance stick-slip behavior for granular friction

We experimentally study the frictional behavior of a two-dimensional slider pulled slowly over a granular substrate comprised of photoelastic disks. The slider is vibrated at frequencies ranging from 0 to 30 Hz in a direction parallel to sliding. The applied vibrations have constant peak acceleration, which results in constant average friction levels. Surprisingly, we find that stick-slip behavior, where stress slowly builds up and is released in intermittent slips, is enhanced as the frequency of vibration is increased. Our results suggest that increasing the frequency of vibration may help to combine many smaller rearrangements into fewer, but larger, avalanche-like slips, a mechanism unique to granular systems. We also examine the manner in which the self affine character of the force curves evolves with frequency, and we find additional support for this interpretation.

cond-mat.soft↗

arXiv2018

Critical scaling near the yielding transition in granular media

We show that the yielding transition in granular media displays second-order critical-point scaling behavior. We carry out discrete element simulations in the low inertial number limit for frictionless, purely repulsive spherical grains undergoing simple shear at fixed nondimensional shear stress $Σ$ in two and three spatial dimensions. To find a mechanically stable (MS) packing that can support the applied $Σ$, isotropically prepared states with size $L$ must undergo a total strain $γ_{\rm ms}(Σ,L)$. The number density of MS packings ($\propto γ_{\rm ms}^{-1}$) vanishes for $Σ> Σ_c \approx 0.11$ according to a critical scaling form with a length scale $ξ\propto |Σ- Σ_c|^{-ν}$, where $ν\approx 1.7-1.8$. Above the yield stress ($Σ>Σ_c$), no MS packings that can support $Σ$ exist in the large system limit, $L/ξ\gg 1$. MS packings generated via shear possess anisotropic force and contact networks, suggesting that $Σ_c$ is associated with an upper limit in the degree to which these networks can be deformed away from those for isotropic packings.

cond-mat.soft↗