arXiv subjects

Varda F. Hagh

Publications and source records attributed to Varda F. Hagh.

16 recordsLinked to original sources

arXiv2026

Spatiotemporal Disk Packing for Directed Growth of Complex Geometries

Growing complex shapes requires control over both where growth begins and how it evolves in time. Here, we introduce a geometric framework for growing prescribed 2D shapes using a disk packing algorithm. In this approach, a target geometry is filled by disks whose centers define where growth is initiated and whose radii define how long each region is allowed to grow. The allowed disk sizes are constrained by the physics of the process, including the growth velocity, the time required to initiate each growth event, and the number of initiations that can occur in parallel. To generate physically realizable packings, we introduce the Largest Gap Algorithm (LGA), which sequentially fills the largest remaining gaps in a target shape with the largest disk that satisfies both geometric and kinetic constraints. We show that this method produces high coverage packings for a variety of geometries and that the resulting packings can be directly converted into spatiotemporal packing instructions. We then demonstrate that these instructions can be realized experimentally using multi-point initiation of frontal polymerization in viscosified dicyclopentadiene (DCPD) resin using CO$_2$ laser. Our results show that complex shapes can be grown by programming a small number of local initiation events, providing a simple connection between geometry and dynamics of growth.

cond-mat.soft↗

arXiv2026

Basin-volume distributions in monodisperse particle packings -- the soul of memory

Mechanically stable packings of $N$ particles in $d$ dimensions lie at the minima of an $Nd$-dimensional potential energy landscape. Starting from random initial particle positions, the system can relax using gradient-based optimization until it arrives at one of the equilibrium states; all initial conditions that end at the same minimum belong to the same catchment basin. We measure the distribution of the catchment basin volumes for indistinguishable monodisperse soft spheres in both $d=2$ and $d=3$. Ordering the basins at each system size, $N$, according to their volume, $P_N(n)$, from the largest at $n=1$ to smaller at larger $n$, we find a very wide distribution of volumes which is similar in both dimensions: $P_N(n) \approx A_Nn^{-α}$ with $α\approx 1$ which, in our most favorable cases, extends over $7$ decades. We explore aspects of the connectivity of the basins, show that their structure is highly contorted, and demonstrate how these results may be used to understand the imprinting of memories in cyclic strain studies of solids.

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arXiv2026

Local Rules for Directing the Emergence of Global Properties in Complex Structures

From ants to caterpillars, many biological systems composed of simple builders have been observed to construct complex, adaptive, and functional architectures without requiring complete access to the global state of the structure. In these systems, global function emerges from the accumulation of local actions, as individual builders follow local rules to manipulate, modify, and deposit material in response to local environmental stimuli. This raises the question of how local rules can be selected for simple builders so that desired functions reliably emerge as a natural consequence of their interactions with their environment. We propose a systematic framework for determining such rules and demonstrate its effectiveness using a minimal model inspired by tent caterpillars and their silk networks. Using our framework, we show that local rules can be designed so that when simple builders follow them during network construction, the values of several emergent properties including area coverage, mean line density, and front curvature can be directed toward specific target values. We use a statistical approach to determine how rules can be modified to increase the probability that a useful local change occurs, the magnitude of that change, or both, so that the target property can be achieved reliably. Our results demonstrate a general strategy for linking local rules to emergent global properties in complex structures. This strategy offers a step toward fabricating functional structures using simple builders in uncertain environments where global information, precise control, and sustained human supervision are infeasible.

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arXiv2025

Deterministic Interrelation Between Elastic Moduli in Critically Elastic Materials

Critically elastic materials - those that are rigid with a single state of self-stress - can be generated from parent systems with two states of self-stress by the removal of one of many constraints. We show that the elastic moduli of the resulting homogeneous and isotropic daughter systems are interrelated by a universal functional form parametrized by properties of the parent. In simulations of both spring networks and packings of soft spheres, judicious choice of parent systems and bond removal allows for the selection of a wide variety of moduli and Poisson's ratios in the critically elastic systems, providing a framework for versatile deterministic selection of mechanical properties.

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arXiv2024

Order in disordered packings with and without permutation symmetry

A disordered solid, such as an athermal jammed packing of soft spheres, exists in a rugged potential-energy landscape in which there are a myriad of stable configurations that defy easy enumeration and characterization. Nevertheless, in three-dimensional monodisperse particle packings, we demonstrate an astonishing regularity in the distribution of basin volumes. The probability of landing randomly in a basin is proportional to its volume. Ordering the basins according to their probability, $P(n)$, from the largest at $n=1$ to smaller at larger $n$, we find approximately: $P(n) \propto n^{-1}$. This order, persisting up to the largest systems for which we can collect sufficient data, has implications for the dynamics of a system as it evolves under perturbations. In monodisperse packings there is ``permutation symmetry'' since identical particles can always be interchanged without affecting the system or its properties. Introducing any distribution of radii breaks this symmetry and leads to a proliferation of distinct configurations. We present an algorithm that partially restores permutation symmetry to such polydisperse packings.

cond-mat.soft↗

arXiv2022

Competition between energy and dynamics in memory formation

Bi-stable objects that are pushed between states by an external field are often used as a simple model to study memory formation in disordered materials. Such systems, called hysterons, are typically treated quasistatically. Here, we generalize hysterons to explore the effect of dynamics in a simple spring system with tunable bistability and study how the system chooses a minimum. Changing the timescale of the forcing allows the system to transition between a situation where its fate is determined by following the local energy minimum to one where it is trapped in a shallow well determined by the path taken through configuration space. Oscillatory forcing can lead to transients lasting many cycles, a behavior not possible for a single quasistatic hysteron.

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arXiv2022

Emergence of zero modes in disordered solids under periodic tiling

In computational models of particle packings with periodic boundary conditions, it is assumed that the packing is attached to exact copies of itself in all possible directions. The periodicity of the boundary then requires that all of the particles' images move together. An infinitely repeated structure, on the other hand, does not necessarily have this constraint. As a consequence, a jammed packing (or a rigid elastic network) under periodic boundary conditions may have a corresponding infinitely repeated lattice representation that is not rigid or indeed may not even be at a local energy minimum. In this manuscript, we prove this claim and discuss ways in which periodic boundary conditions succeed to capture the physics of repeated structures and where they fall short.

cond-mat.soft↗

arXiv2022

rigidPy: Rigidity Analysis in Python

rigidPy is a Python package that provides a set of tools necessary for studying rigidity and mechanical response in spring networks. It also includes suitable modules for generating new realizations of networks with applications in glassy systems and protein structures. rigidPy is available freely on GitHub and can be installed using Python Package Index (PyPi). The detailed setup information is provided in this paper, along with an overview of the mathematical framework that has been used in developing the package.

cond-mat.soft↗

arXiv2021

Free-then-freeze: transient learning degrees of freedom for introducing function in materials

The introduction of transient learning degrees of freedom into a system can lead to novel material design and training protocols that guide a system into a desired metastable state. In this approach, some degrees of freedom, which were not initially included in the system dynamics, are first introduced and subsequently removed from the energy minimization process once the desired state is reached. Using this conceptual framework, we create stable jammed packings that exist in exceptionally deep energy minima marked by the absence of low-frequency quasilocalized modes; this added stability persists in the thermodynamic limit. The inclusion of particle radii as transient degrees of freedom leads to deeper and much more stable minima than does the inclusion of particle stiffnesses. This is because particle radii couple to the jamming transition whereas stiffnesses do not. Thus different choices for the added degrees of freedom can lead to very different training outcomes.

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arXiv2021

Marginal Stability Enables Memory Training in Jammed Solids

Memory encoding by cyclic shear is a reliable process to store information in jammed solids, yet its underlying mechanism and its connection to the amorphous structure are not fully understood. When a jammed sphere packing is repeatedly sheared with cycles of the same strain amplitude, it optimizes its mechanical response to the cyclic driving and stores a memory of it. We study memory by cyclic shear training as a function of the underlying stability of the amorphous structure in marginally stable and highly stable packings, the latter produced by minimizing the potential energy using both positional and radial degrees of freedom. We find that jammed solids need to be marginally stable in order to store a memory by cyclic shear. In particular, highly stable packings store memories only after overcoming brittle yielding and the cyclic shear training takes place in the shear band, a region which we show to be marginally stable.

cond-mat.soft↗

arXiv2021

Energetic rigidity I: A unifying theory of mechanical stability

Rigidity regulates the integrity and function of many physical and biological systems. This is the first of two papers on the origin of rigidity, wherein we propose that "energetic rigidity," in which all non-trivial deformations raise the energy of a structure, is a more useful notion of rigidity in practice than two more commonly used rigidity tests: Maxwell-Calladine constraint counting (first-order rigidity) and second-order rigidity. We find that constraint counting robustly predicts energetic rigidity only when the system has no states of self stress. When the system has states of self stress, we show that second-order rigidity can imply energetic rigidity in systems that are not considered rigid based on constraint counting, and is even more reliable than shear modulus. We also show that there may be systems for which neither first nor second-order rigidity imply energetic rigidity. The formalism of energetic rigidity unifies our understanding of mechanical stability and also suggests new avenues for material design.

cond-mat.soft↗

arXiv2021

Energetic rigidity II: Applications in examples of biological and underconstrained materials

This is the second paper devoted to energetic rigidity, in which we apply our formalism to examples in two dimensions: underconstrained random regular spring networks, vertex models, and jammed packings of soft particles. Spring networks and vertex models are both highly underconstrained, and first-order constraint counting does not predict their rigidity, but second-order rigidity does. In contrast, spherical jammed packings are overconstrained and thus first-order rigid, meaning that constraint counting is equivalent to energetic rigidity as long as prestresses in the system are sufficiently small. Aspherical jammed packings on the other hand have been shown to be jammed at hypostaticity, which we use to argue for a modified constraint counting for systems that are energetically rigid at quartic order.

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arXiv2021

Realizations of Isostatic Material Frameworks

This paper studies the set of equivalent realizations of isostatic frameworks in two dimensions, and algorithms for finding all such realizations. We show that an isostatic framework has an even number of equivalent realizations that preserve edge lengths and connectivity. We enumerate the complete set of equivalent realizations for a toy framework with pinned boundary in two dimensions and study the impact of boundary length on the emergence of these realizations. To ameliorate the computational complexity of finding a solution to a large multivariate quadratic system corresponding to the constraints; alternative methods - based on constraint reduction and distance-based covering map or Cayley parameterization of the search space - are presented. The application of these methods is studied on atomic clusters, a model two-dimensional glasses, and jamming.

cond-mat.dis-nn↗

arXiv2018

Disordered auxetic networks with no re-entrant polygons

It is widely assumed that disordered auxetic structures (i.e. structures with a negative Poisson's ratio) must contain re-entrant polygons in $2$D and re-entrant polyhedra in $3$D. Here we show how to design disordered networks in $2$D with only convex polygons. The design principles used allow for any Poisson ratio $-1 < ν< 1/3$ to be obtained with a prescriptive algorithm. By starting from a Delaunay triangulation with a mean coordination $ \simeq 6$ and $ν\simeq 0.33$ and removing those edges that decrease the shear modulus by the least without creating any re-entrant polygons, the system evolves monotonically towards the isostatic point with $ \simeq 4$ and $ν\simeq -1$.

cond-mat.dis-nn↗

arXiv2018

Jamming in Perspective

Jamming occurs when objects like grains are packed tightly together (e.g. grain silos). It is highly cooperative and can lead to phenomena like earthquakes, traffic jams, etc. In this Letter we point out the paramount importance of the underlying contact network for jammed systems; the network must have one contact in excess of isostaticity and a finite bulk modulus. Isostatic means that the number of degrees of freedom are exactly balanced by the number of constraints. This defines a large class of networks that can be constructed without the necessity of packing particles together compressively (either in the lab or computationally). One such construction, which we explore here, involves setting up the Delaunay triangulation of a Poisson disk sampling and then removing edges to maximize the bulk modulus until the isostatic plus one point is reached. This construction works in any dimensions and here we give results in 2D where we also show how such networks can be transformed into a disk pack.

cond-mat.dis-nn↗

arXiv2015

Rigidity Loss in Disordered Systems: Three Scenarios

We reveal significant qualitative differences in the rigidity transition of three types of disordered network materials: randomly diluted spring networks, jammed sphere packings, and stress-relieved networks that are diluted using a protocol that avoids the appearance of floppy regions. The marginal state of jammed and stress-relieved networks are globally isostatic, while marginal randomly diluted networks show both overconstrained and underconstrained regions. When a single bond is added to or removed from these isostatic systems, jammed networks become globally overconstrained or floppy, whereas the effect on stress-relieved networks is more local and limited. These differences are also reflected in the linear elastic properties and point to the highly effective and unusual role of global self-organization in jammed sphere packings.

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