arXiv subjects

Charles Emmett Maher

Publications and source records attributed to Charles Emmett Maher.

12 recordsLinked to original sources

arXiv2026

Local Geometric and Transport Properties of Networks that are Generated from Hyperuniform Point Patterns

Hyperuniformity, which is a type of order that is characterized by the suppression of long-range density fluctuations in comparison to the fluctuations in standard disordered systems, has emerged as a powerful concept in many natural and engineered phenomena. In this paper, we harness hyperuniform point patterns to generate disordered, spatially-embedded networks that are distinct from both perfectly ordered lattices and uniformly random spatial networks. We refer to this class of disordered networks as \emph{hyperuniform-point-pattern-induced (HuPPI) networks}, and we compare them to counterpart \emph{Poisson-point-pattern-induced (PoPPI) networks} and networks that we generate from random-sequential-adsorption (RSA) packings (which have local order but are not hyperuniform). We examine HuPPI, PoPPI, and RSA networks that we generate using Gabriel, Delaunay, Delaunay-centroidal, and Voronoi network-generation methods. We show that HuPPI networks have smaller mean normalized total effective resistances (TERs) than PoPPI networks in Gabriel, Delaunay-centroidal, and Voronoi networks and have shorter mean random-walk mixing times than PoPPI networks in Gabriel, Delaunay, and Delaunay-centroidal networks. For all four network-generation methods and for both HuPPI and PoPPI networks, we find that the Ollivier--Ricci curvature (ORC) of an edge is negatively correlated with its TER edge contribution (i.e., the increase in TER that results from removing that edge). Collectively, our results (1) illustrate how the local network geometry that ORC measures is related to transport and network connectivity and (2) demonstrate that the network-generation method provides an additional design lever for spatial networks beyond the choice of their underlying point pattern. [This abstract is abridged significantly from the full abstract.]

cond-mat.dis-nn↗

arXiv2026

Mechanism of Band Gap Formation in Beam Networks

Band gaps are commonly attributed to Bragg scattering or local resonance, yet it remains unclear whether these mechanisms govern band gap formation in beam networks. In this work, we explain band gap formation in beam networks in terms of a new mechanism, geometry-induced coupling between deformation modes. Specifically, band gap onset arises from axial-bending coupling at lattice nodes and scales with the axial cutoff frequency of a one-dimensional periodic beam, whereas band gap termination is primarily governed by high-frequency rotational branches associated with beam geometry. This mechanism holds for both periodic and disordered beam networks. In periodic lattices, it manifests through beam orientations at lattice nodes, whereas in disordered networks it manifests through short-beam statistics arising from variations in beam length. Together, these results establish a unified mechanism for band gap formation across both periodic and disordered beam networks, providing new insight into the physical origin of band gaps in beam-network materials.

cond-mat.mtrl-sci↗

arXiv2026

Effect of Local Topological Changes on Resistance in Spatially-Embedded Disordered Networks

Disordered materials occur naturally and also provide a broader design space than ordered or crystalline structures. We investigate a two-dimensional disordered network metamaterial constructed from a Delaunay triangulation of an underlying point cloud. Small perturbations in the point cloud induce discrete topological changes. One such change we identify is a Delaunay flip, in which two neighboring Delaunay triangles that form a convex quadrilateral structure with their common edge being one of the two quadrilateral diagonals exchange this diagonal for the other diagonal. These topological changes can cause substantial jumps in the effective resistance measured diagonally across the network, when the change is located near the source or the sink node. The jumps are explained analytically by showing that the change in effective resistance from edge removal or addition depends on the voltage drop across that edge. However, Delaunay flips have less impact on global resistance measurements and in larger networks. These local topological changes are relevant for finite-sized samples and experimentally-measurable properties such as electrical transport. Global characterizations of the network disorder or topology lack the location-specificity of our observed effects on network transport, and thus may be inadequate for predicting certain experimentally measurable transport properties in disordered network metamaterials, highlighting the importance of localized regions in material design.

cond-mat.dis-nn↗

arXiv2026

Probing the influence of topological and geometric disorder on the spectrum of the differential Laplacian operator on networks

Metric networks are network-shaped, one-dimensional structures on which one can solve differential equations to simulate a wide range of physical systems including conjugated molecules, photonic crystals, quantum mechanics in waveguide networks, and acoustic metamaterials. More concretely, a metric network is a network whose edges are each assigned a notion of length and a coordinate describing position. One can then define function spaces and differential operators on these objects to model the aforementioned systems. Recent software advancements have made it feasible to analyze partial differential equations on large, compact metric networks with a vast array of structures. Here, we generate compact metric network structures using the spatial tessellations of two-dimensional hyperuniform point patterns, which have suppressed large-scale density fluctuations relative to typical disordered point patterns. This choice of structure is inspired by the exotic physical properties of network materials with these structures in other contexts. Then, we characterize the eigenvalue spectrum structure of the differential Laplace operator on these networks. In particular, we find that gaps can form in the eigenvalue spectra of these networks whose widths increase when the distribution of edge lengths is narrow and as the number of triangular faces increases. Importantly, many of the structures we consider are realizable in Euclidean space, meaning they are well-suited for practical applications in, e.g., metamaterial design. This work can thus be used to inform the design of metric network-based systems with spectral gaps with tunable widths and locations.

cond-mat.dis-nn↗

arXiv2025

Comparing dragonfly wings to jars of marbles through the lens of hyperuniformity

When we look at the world around us, we see both organized (also called ordered) and disorganized (also called disordered) arrangements of things. Carefully-tiled floors and brick walls have organized and repeating patterns, but the stars in the sky and the trees in a forest look like they're arranged in a disordered way. We also see objects, like jars of marbles and the lacy wings of insects, that lie between ordered and disordered extremes. Although the marbles in a jar don't sit on a regular grid like carefully-arranged tiles, the collection of marbles does have some consistent features, such as the typical size and spacing between them. However, the positions of the marbles are much less random than the positions of the stars in the sky. To help understand and classify these patterns, mathematicians and physicists use the term hyperuniform to help them describe the situations of being perfectly organized or being disorganized in an organized way. In this article, we discuss various fascinating properties of hyperuniform patterns. We explore where they occur in the natural world and how engineers are using them to build new structures.

math.HO↗

arXiv2025

Characterizing the Hyperuniformity of Disordered Network Metamaterials

Advancements in materials design and manufacturing have allowed for the production of ordered and disordered metamaterials with diverse and novel properties. Hyperuniform two-phase heterogeneous materials, which anomalously suppress density fluctuations on large length scales compared to typical disordered systems, and network materials are two classes of metamaterial that have desirable physical properties. Recent focus has been placed on the design of disordered hyperuniform network metamaterials that inherit the desirable properties of both of these metamaterial classes. In this work, we focus on determining the extent to which network structures derived from the spatial tessellations of hyperuniform point patterns inherit the hyperuniformity of the progenitor point patterns. In particular, we examine the Delaunay, Voronoi, Delaunay-Centroidal, and Gabriel tessellations of nonhyperuniform and hyperuniform point patterns in two- and three-dimensional Euclidean space. We use the spectral density to characterize the density fluctuations of two-phase media created by thickening the edges of these tessellations in two dimensions and introduce a novel variance-based metric to characterize the network structures directly in two and three dimensions. We find that, while none of the tessellations completely inherit the hyperuniformity of the progenitor point pattern, the degree to which the hyperuniformity is inherited is sensitive to the tessellation scheme and the short- and long-range translational disorder in the point pattern, but not to the choice of beam shape when mapping the networks into two-phase media.

cond-mat.soft↗

arXiv2025

Local order metrics for many-particle systems across length scales

Formulating order metrics that sensitively quantify the degree of order/disorder in many-particle systems in $d$-dimensional Euclidean space $\mathbb{R}^d$ across length scales is an outstanding challenge in physics, chemistry, and materials science. Since an infinite set of $n$-particle correlation functions is required to fully characterize a system, one must settle for a reduced set of structural information, in practice. We initiate a program to use the local number variance $σ_N^2(R)$ associated with a spherical sampling window of radius $R$ (which encodes pair correlations) and an integral measure derived from it $Σ_N(R_i,R_j)$ that depends on two specified radial distances $R_i$ and $R_j$. Across the first three space dimensions ($d = 1,2,3$), we find these metrics can sensitively describe and categorize the degree of order/disorder of 41 different models of antihyperuniform, nonhyperuniform, disordered hyperuniform, and ordered hyperuniform many-particle systems at a specified length scale $R$. Using our local variance metrics, we demonstrate the importance of assessing order/disorder with respect to a specific value of $R$. These local order metrics could also aid in the inverse design of structures with prescribed length-scale-specific degrees of order/disorder that yield desired physical properties. In future work, it would be fruitful to explore the use of higher-order moments of the number of points within a spherical window of radius $R$ [S. Torquato {\it et al}., Phys. Rev. X, \textbf{11}, 021028 (2021)] to devise even more sensitive order metrics.

cond-mat.stat-mech↗

arXiv2024

Hyperuniformity scaling of maximally random jammed packings of two-dimensional binary disks

Jammed (mechanically rigid) polydisperse circular-disk packings in two dimensions (2D) are popular models for structural glass formers. Maximally random jammed (MRJ) states, which are the most disordered packings subject to strict jamming, have been shown to be hyperuniform. The characterization of the hyperuniformity of MRJ circular-disk packings has covered only a very small part of the possible parameter space for the disk-size distributions. Hyperuniform heterogeneous media are those that anomalously suppress large-scale volume-fraction fluctuations compared to those in typical disordered systems, i.e., their spectral densities $\tildeχ_{_V}(\mathbf{k})$ tend to 0 as the wavenumber $k\equiv|\mathbf{k}|$ tends to 0 and are described by the power-law $\tildeχ_{_V}(\mathbf{k})\sim k^α$ as $k\rightarrow0$ where $α$ is the hyperuniformity scaling exponent. In this work, we generate and characterize the structure of strictly jammed binary circular-disk packings with disk-size ratio $β$ and a molar ratio of 1:1. By characterizing the rattler fraction, the fraction of isostatic configurations in an ensemble with fixed $β$, and the $n$-fold orientational order metrics of ensembles of packings with a wide range of $β$, we show that size ratios $1.2\lesssim β\lesssim 2.0$ produce MRJ-like states, which we show are the most disordered packings according to several criteria. Using the large-length-scale scaling of the volume fraction variance, we extract $α$ from these packings, and find the function $α(β)$ is maximized at $β$ = 1.4 (with $α= 0.450\pm0.002$) within the range $1.2\leqβ\leq2.0$, and decreases rapidly outside of this range. The results from this work can inform the experimental design of disordered hyperuniform thin-film materials with tunable degrees of orientational and translational disorder. (abridged)

cond-mat.soft↗

arXiv2024

Hyperuniformity Classes of Quasiperiodic Tilings via Diffusion Spreadability

Hyperuniform point patterns can be classified by the hyperuniformity scaling exponent $α> 0$, that characterizes the power-law scaling behavior of the structure factor $S(\mathbf{k})$ as a function of wavenumber $k\equiv|\mathbf{k}|$ in the vicinity of the origin, e.g., $S(\mathbf{k})\sim|\mathbf{k}|^α$ in cases where $S(\mathbf{k})$ varies continuously with $k$ as $k\rightarrow0$. In this paper, we show that the spreadability is an effective method for determining $α$ for quasiperiodic systems where $S(\mathbf{k})$ is discontinuous and consists of a dense set of Bragg peaks. We first transform quasiperiodic and limit-periodic point patterns into two-phase media by mapping them onto packings of identical nonoverlapping disks, where space interior to the disks represents one phase and the space in exterior to them represents the second phase. We then compute the spectral density of the packings, and finally compute and fit the long-time behavior of their excess spreadabilities. Specifically, we show that the excess spreadability can be used to accurately extract $α$ for the 1D limit-periodic period doubling chain and the 1D quasicrystalline Fibonacci chain to within $0.02\%$ of the analytically known exact results. Moreover, we obtain a value of $α= 5.97\pm0.06$ for the 2D Penrose tiling, which had not been computed previously. We also show that one can truncate the small-$k$ region of the scattering information used to compute the spreadability and still obtain an accurate value of $α$. The methods described here offer a simple way to characterize the large-scale translational order present in quasicrystalline and limit-periodic media in any space dimension that are self-similar. Moreover, the scattering information extracted from these two-phase media encoded in the spectral density can be used to estimate their physical properties. (abridged)

cond-mat.stat-mech↗

arXiv2023

Hyperuniformity of Maximally Random Jammed Packings of Hyperspheres Across Spatial Dimensions

The maximally random jammed (MRJ) state is the most random configuration of strictly jammed (mechanically rigid) nonoverlapping objects. MRJ packings are hyperuniform, meaning their long-wavelength density fluctuations are anomalously suppressed compared to typical disordered systems, i.e., their structure factors $S(\mathbf{k})$ tend to zero as the wavenumber $|\mathbf{k}|$ tends to zero. Here, we show that generating high-quality strictly jammed states for space dimensions $d = 3,4,$ and $5$ is of paramount importance in ensuring hyperuniformity and extracting precise values of the hyperuniformity exponent $α> 0$ for MRJ states, defined by the power-law behavior of $S(\mathbf{k})\sim|\mathbf{k}|^α$ in the limit $|\mathbf{k}|\rightarrow0$. Moreover, we show that for fixed $d$ it is more difficult to ensure jamming as the particle number $N$ increases, which results in packings that are nonhyperuniform. Free-volume theory arguments suggest that the ideal MRJ state does not contain rattlers, which act as defects in numerically generated packings. As $d$ increases, we find that the fraction of rattlers decreases substantially. Our analysis of the largest truly jammed packings suggests that the ideal MRJ packings for all dimensions $d\geq3$ are hyperuniform with $α= d - 2$, implying the packings become more hyperuniform as $d$ increases. The differences in $α$ between MRJ packings and recently proposed Manna-class random close packed (RCP) states, which were reported to have $α= 0.25$ in $d=3$ and be nonhyperuniform ($α= 0$) for $d = 4$ and $d = 5$, demonstrate the vivid distinctions between the large-scale structure of RCP and MRJ states in these dimensions. Our work clarifies the importance of the link between true jamming and hyperuniformity and motivates the development of an algorithm to produce rattler-free three-dimensional MRJ packings.

cond-mat.soft↗

arXiv2022

Characterization of Void Space, Large-Scale Structure, and Transport Properties of Maximally Random Jammed Packings of Superballs

Dense, disordered packings of particles are useful models of low-temperature amorphous phases of matter, biological systems, granular media, and colloidal systems. The study of dense packings of nonspherical particles enables one to ascertain how rotational degrees of freedom affect packing behavior. Here, we study superballs, a large family of deformations of the sphere, defined in three dimensions by $|x_1|^{2p}+|x_2|^{2p}+|x_3|^{2p}\leq1$, where $p>0$ is a deformation parameter indicating to what extent the shape deviates from a sphere. As $p$ increases from the sphere point ($p=1$), the superball attains cubic symmetry, and attains octahedral symmetry when $p<1$. Previous characterization of superball packings has shown that they have a maximally random jammed (MRJ) state, whose properties (e.g., packing fraction $ϕ$) vary nonanalytically as $p$ diverges from unity. Here, we use an event-driven molecular dynamics algorithm to produce MRJ superball packings. We characterize their large-scale structure by examining the small-$Q$ behavior of their structure factors and spectral densities, which indicate these packings are effectively hyperuniform. We show that the mean width $\bar{w}$ is a useful length scale to make distances dimensionless in order to compare systematically superballs of different shape. We also compute the complementary cumulative pore-size distribution $F(δ)$ and find the pore sizes tend to decrease as $|1-p|$ increases. From $F(δ)$, we estimate the fluid permeability, mean survival time, and principal diffusion relaxation time of the packings. Additionally, we compute the diffusion spreadability and find the long-time power-law scaling indicates these packings are hyperuniform. Our results can be used to help inform the design of granular materials with targeted densities and transport properties.

cond-mat.soft↗

arXiv2021

Kinetic Frustration Effects on Dense Two-Dimensional Packings of Convex Particles and Their Structural Characteristics

The study of hard-particle packings is of fundamental importance in physics, chemistry, cell biology, and discrete geometry. Much of the previous work on hard-particle packings concerns their densest possible arrangements. By contrast, we examine kinetic effects inevitably present in both numerical and experimental packing protocols. Specifically, we determine how changing the compression/shear rate of a two-dimensional packing of noncircular particles causes it to deviate from its densest possible configuration, which is always periodic. The adaptive shrinking cell (ASC) optimization scheme maximizes the packing fraction of a hard-particle packing by first applying random translations and rotations to the particles and then isotropically compressing and shearing the simulation box repeatedly until a possibly jammed state is reached. We use a stochastic implementation of the ASC optimization scheme to mimic different effective time scales by varying the number of particle moves between compressions/shears. We generate dense, effectively jammed, monodisperse, two-dimensional packings of obtuse scalene triangle, rhombus, curved triangle, lens, and "ice cream cone" (a semicircle grafted onto an isosceles triangle) shaped particles, with a wide range of packing fractions and degrees of order. To quantify these kinetic effects, we introduce the kinetic frustration index $K$, which measures the deviation of a packing from its maximum possible packing fraction. To investigate how kinetics affect short- and long-range ordering in these packings, we compute their spectral densities and characterize their contact networks. We find that kinetic effects are most significant when the particles have greater asphericity, less curvature, and less rotational symmetry. This work may be relevant to the design of laboratory packing protocols.

cond-mat.soft↗