arXiv subjects

Salvatore Torquato

Publications and source records attributed to Salvatore Torquato.

At least 55 records · Page 3Linked to original sources

arXiv2023

Designer Pair Statistics of Disordered Many-Particle Systems with Novel Properties

Knowledge of exact analytical functional forms for the pair correlation function $g_2(r)$ and its corresponding structure factor $S(k)$ of disordered many-particle systems is limited. For fundamental and practical reasons, it is highly desirable to add to the existing data base of analytical functional forms for such pair statistics. Here, we design a plethora of such pair functions in direct and Fourier spaces across the first three Euclidean space dimensions that are realizable by diverse many-particle systems with varying degrees of correlated disorder across length scales, spanning a wide spectrum of hyperuniform, typical nonhyperuniform and antihyperuniform ones. This is accomplished by utilizing an efficient inverse algorithm that determines equilibrium states with up to pair interactions at positive temperature that precisely match targeted forms for both $g_2(r)$ and $S(k)$. Among other results, we realize an example with the strongest hyperuniform property among known positive-temperature equilibrium states, critical-point systems (implying unusual 1D systems with phase transitions) that are not in the Ising universality class, systems that attain self-similar pair statistics under Fourier transformation, and an experimentally feasible polymer model. We show that our pair functions enable one to achieve systems with a wide range of translational order and self-diffusion coefficients $\cal D$, which are inversely related to one another. One can design other realizable pair statistics via linear combinations of our functions or by applying our inverse procedure to other desirable functional forms. Our approach facilitates the inverse design of materials with desirable physical and chemical properties by tuning their pair statistics.

cond-mat.soft↗

arXiv2023

Theoretical Prediction of the Effective Dynamic Dielectric Constant of Disordered Hyperuniform Anisotropic Composites Beyond the Long-Wavelength Regime

Torquato and Kim [Phys. Rev. X 11, 296 021002 (2021)] derived exact nonlocal strong-contrast expansions of the effective dynamic dielectric constant tensor that treat general three-dimensional (3D) two-phase composites, which are valid well beyond the long-wavelength regime. Here, we demonstrate that truncating this general rapidly converging series at the two- and three-point levels is a powerful theoretical tool for extracting accurate approximations suited for various microstructural symmetries. We derive such closed-form formulas applicable to transverse polarization in layered media and transverse magnetic polarization in transversely isotropic media, respectively. We use these formulas to estimate effective dielectric constant for models of 3D disordered hyperuniform layered and transversely isotropic media: nonstealthy hyperuniform and stealthy hyperuniform (SHU) media. In particular, we show that SHU media are perfectly transparent (trivially implying no Anderson localization, in principle) within finite wave number intervals through the third-order terms. For these two models, we validate that the second-order formulas, which depend on the spectral density, are already very accurate well beyond the long-wavelength regime by showing very good agreement with the finite-difference time-domain simulations. The high predictive power of the second-order formulas implies that higher-order contributions are negligibly small, and thus, it very accurately approximates multiple scattering effects. Therefore, there can be no Anderson localization in practice within the predicted perfect transparency interval in SHU media because the localization length should be very large compared to any practically large sample size. Our predictive theory provides a foundation for the inverse design of novel effective wave characteristics of disordered and statistically anisotropic structures.

physics.optics↗

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↗

arXiv2023

Effective Electromagnetic Wave Properties of Disordered Stealthy Hyperuniform Layered Media Beyond the Quasistatic Regime

Disordered stealthy hyperuniform dielectric composites exhibit novel electromagnetic wave transport properties in two and three dimensions. Here, we carry out the first study of the electromagnetic properties of one-dimensional (1D) disordered stealthy hyperuniform layered media. From an exact nonlocal theory, we derive an approximation formula for the effective dynamic dielectric constant tensor ${\boldsymbol \varepsilon}_e({\bf k}_q,ω)$ of general 1D media that is valid well beyond the quasistatic regime and apply it to 1D stealthy hyperuniform systems. We consider incident waves of transverse polarization, frequency $ω$, and wavenumber $k_q$. Our formula for ${\boldsymbol \varepsilon}_e({k}_q,ω)$, which is given in terms of the spectral density, leads to a closed-form relation for the transmittance $T$. Our theoretical predictions are in excellent agreement with finite-difference time-domain (FDTD) simulations. Stealthy hyperuniform layered media have perfect transparency intervals up to a finite wavenumber, implying no Anderson localization, but non-stealthy hyperuniform media are not perfectly transparent. Our predictive theory provides a new path for the inverse design of the wave characteristics of disordered layered media, which are readily fabricated, by engineering their spectral densities.

physics.optics↗

arXiv2023

Computational Design of Anisotropic Stealthy Hyperuniform Composites with Engineered Directional Scattering Properties

Disordered hyperuniform materials are an emerging class of exotic amorphous states of matter that endow them with singular physical properties. Here, we generalize the Fourier-space based numerical construction procedure for designing {\it isotropic} disordered hyperuniform two-phase heterogeneous materials (i.e., composites) developed by Chen and Torquato [Acta Mater. {\bf 142}, 152 (2018)] to {\it anisotropic} microstructures by explicitly incorporating the {\it vector-dependent} spectral density function ${\tilde χ}_{_V}({\bf k})$ of {\it arbitrary form} that is realizable. We demonstrate the utility of the procedure by generating a wide spectrum of {\it anisotropic} stealthy hyperuniform (SHU) microstructures with ${\tilde χ}_{_V}({\bf k}) = 0$ for ${\bf k} \in Ω$. We show how different exclusion-region shapes with various discrete symmetries and varying size affect the resulting statistically anisotropic microstructures as a function of the and phase volume fraction. We find that, among other properties, the directional hyperuniform behaviors imposed by the shape asymmetry (or anisotropy) of certain exclusion regions give rise to distinct anisotropic structures and degree of uniformity in the distribution of the phases on intermediate and large length scales along different directions. Moreover, while the anisotropic exclusion regions impose strong constraints on the {\it global} symmetry of the resulting media, they can still possess almost isotropic {\it local} structures. Our construction algorithm enables one to control the statistical anisotropy of composite microstructures which is crucial to engineering directional optical, transport and mechanical properties of two-phase composite media.

cond-mat.mtrl-sci↗

arXiv2023

Generating large disordered stealthy hyperuniform systems with ultra-high accuracy to determine their physical properties

Hyperuniform many-particle systems are characterized by a structure factor $S({\mathbf{k}})$ that is precisely zero as $|\mathbf{k}|\rightarrow0$; and stealthy hyperuniform systems have $S({\mathbf{k}})=0$ for the finite range $0 < |{\mathbf{k}}| \le K$, called the "exclusion region." Through a process of collective-coordinate optimization, energy-minimizing disordered stealthy hyperuniform systems of moderate size have been made to high accuracy, and their novel physical properties have shown great promise. However, minimizing $S(\mathbf{k})$ in the exclusion region is computationally intensive as the system size becomes large. In this Letter, we present an improved methodology to generate such states using double-double precision calculations on GPUs that reduces the deviations from zero within the exclusion region by a factor of approximately $10^{30}$ for systems sizes more than an order of magnitude larger. We further show that this ultra-high accuracy is required to draw conclusions about their corresponding characteristics, such as the nature of the associated energy landscape and the presence or absence of Anderson localization, which might be masked, even when deviations are relatively small.

cond-mat.stat-mech↗

arXiv2023

The Disordered Heterogeneous Universe: Galaxy Distribution and Clustering Across Length Scales

Studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the distribution of particles at `microscales' to predict physical properties at `macroscales', whether for a liquid, composite material, or entire Universe. The former theory provides an array of techniques to characterize a wide class of microstructures; in this work, we apply them to the distributions of galaxies. We focus on the lower-order correlation functions, `void' and `particle' nearest-neighbor functions, pair-connectedness functions, percolation properties, and a scalar order metric. Compared to homogeneous Poisson and typical disordered systems, the cosmological simulations exhibit enhanced large-scale clustering and longer tails in the nearest-neighbor functions, due to the presence of quasi-long-range correlations. On large scales, the system appears `hyperuniform', due to primordial density fluctuations, whilst on the smallest scales, the system becomes almost `antihyperuniform', and, via the order metric, is shown to be a highly correlated disordered system. Via a finite scaling analysis, we show that the percolation threshold of the galaxy catalogs is significantly lower than for Poisson realizations; this is consistent with the observation that the galaxy distribution contains larger voids. However, the two sets of simulations share a fractal dimension, implying that they lie in the same universality class. Finally, we consider the ability of large-scale clustering statistics to constrain cosmological parameters using simulation-based inference. Both the nearest-neighbor distribution and pair-connectedness function considerably tighten bounds on the amplitude of cosmological fluctuations at a level equivalent to observing twenty-five times more galaxies. These are a useful alternative to the three-particle correlation, and are computable in much reduced time. (Abridged)

astro-ph.CO↗

arXiv2022

Equilibrium States Corresponding to Targeted Hyperuniform Nonequilibrium Pair Statistics

The Zhang-Torquato conjecture [Phys. Rev. E 101, 032124 (2020)] states that any realizable pair correlation function $g_2({\bf r})$ or structure factor $S({\bf k})$ of a translationally invariant nonequilibrium system can be attained by an equilibrium ensemble involving only (up to) effective two-body interactions. To test this conjecture, we consider two singular nonequilibrium models of recent interest that also have the exotic hyperuniformity property: a 2D "perfect glass" and a 3D critical absorbing-state model. We find that each nonequilibrium target can be achieved accurately by equilibrium states with effective one- and two-body potentials, lending further support to the conjecture. To characterize the structural degeneracy of such nonequilibrium-equilibrium correspondence, we compute higher-order statistics for both models, as well as those for a hyperuniform 3D uniformly randomized lattice (URL), whose higher-order statistics can be very precisely ascertained. Interestingly, we find that the differences in the higher-order statistics between nonequilibrium and equilibrium systems with matching pair statistics, as measured by the "hole" probability distribution, provides measures of the degree to which a system is out of equilibrium. We show that all three systems studied possess the \textit{bounded-hole} property, and that holes near the maximum hole size in the URL are much rarer than those in the underlying simple cubic lattice. Remarkably, upon quenching, the effective potentials for all three systems possess local energy minima with stronger forms of hyperuniformity compared to their target counterparts. Our work is expected to facilitate the self-assembly of tunable hyperuniform soft-matter systems.

cond-mat.soft↗

arXiv2022

Realizability of Iso-$g_2$ Processes via Effective Pair Interactions

An outstanding problem in statistical mechanics is the determination of whether prescribed functional forms of the pair correlation function $g_2(r)$ [or equivalently, structure factor $S(k)$] at some number density $ρ$ can be achieved by $d$-dimensional many-body systems. The Zhang-Torquato conjecture states that any realizable set of pair statistics, whether from a nonequilibrium or equilibrium system, can be achieved by equilibrium systems involving up to two-body interactions. In light of this conjecture, we study the realizability problem of the nonequilibrium iso-$g_2$ process, i.e., the determination of density-dependent effective potentials that yield equilibrium states in which $g_2$ remains invariant for a positive range of densities. Using a precise inverse methodology that determines effective potentials that match hypothesized functional forms of $g_2(r)$ for all $r$ and $S(k)$ for all $k$, we show that the unit-step function $g_2$, which is the zero-density limit of the hard-sphere potential, is remarkably numerically realizable up to the packing fraction $ϕ=0.49$ for $d=1$. For $d=2$ and 3, it is realizable up to the maximum ``terminal'' packing fraction $ϕ_c=1/2^d$, at which the systems are hyperuniform, implying that the explicitly known necessary conditions for realizability are sufficient up through $ϕ_c$. For $ϕ$ near but below $ϕ_c$, the large-$r$ behaviors of the effective potentials are given exactly by the functional forms $\exp[-κ(ϕ) r]$ for $d=1$, $r^{-1/2}\exp[-κ(ϕ) r]$ for $d=2$, and $r^{-1}\exp[-κ(ϕ) r]$ (Yukawa form) for $d=3$, where $κ^{-1}(ϕ)$ is a screening length, and for $ϕ=ϕ_c$, the potentials at large $r$ are given by the pure Coulomb forms in the respective dimensions, as predicted by Torquato and Stillinger [\textit{Phys. Rev. E}, 68, 041113 1-25 (2003)].

cond-mat.stat-mech↗

arXiv2022

Precise Determination of Pair Interactions from Pair Statistics of Many-Body Systems In and Out of Equilibrium

The determination of the pair potential $v({\bf r})$ that accurately yields an equilibrium state at positive temperature $T$ with a prescribed pair correlation function $g_2({\bf r})$ or corresponding structure factor $S({\bf k})$ in $d$-dimensional Euclidean space $\mathbb{R}^d$ is an outstanding inverse statistical mechanics problem with far-reaching implications. Recently, Zhang and Torquato conjectured that any realizable $g_2({\bf r})$ or $S({\bf k})$ corresponding to a translationally invariant nonequilibrium system can be attained by a classical equilibrium ensemble involving only (up to) effective pair interactions. Testing this conjecture for nonequilibrium systems as well as for nontrivial equilibrium states requires improved inverse methodologies. We have devised a novel optimization algorithm to find effective pair potentials that correspond to pair statistics of general translationally invariant disordered many-body equilibrium or nonequilibrium systems at positive temperatures. This methodology utilizes a parameterized family of pointwise basis functions for the potential function whose initial form is informed by small- and large-distance behaviors dictated by statistical-mechanical theory. Subsequently, a nonlinear optimization technique is utilized to minimize an objective function that incorporates both the target pair correlation function $g_2({\bf r})$ and structure factor $S({\bf k})$ so that the small- and large-distance correlations are very accurately captured. To illustrate the versatility and power of our methodology, we accurately determine the effective pair interactions of the following four diverse target systems. We found that the optimized pair potentials generate corresponding pair statistics that accurately match their corresponding targets with total $L_2$-norm errors that are an order of magnitude smaller than that of previous methods.

cond-mat.soft↗

arXiv2022

Exclusion Volumes of Convex Bodies in High Space Dimensions: Applications to Virial Coefficients and Continuum Percolation

Using the concepts of mixed volumes and quermassintegrals of convex geometry, we derive an exact formula for the exclusion volume for a general convex body that applies in any space dimension, including both the rotationally-averaged exclusion volume and with the same orientation. We show that the sphere minimizes the dimensionless exclusion volume $v_{ex}(K)/v(K)$ among all convex bodies, whether randomly oriented or uniformly oriented, for any $d$, where $v(K)$ is the volume of $K$. When the bodies have the same orientation, the simplex maximizes the dimensionless exclusion volume for any $d$ with a large-$d$ asymptotic scaling behavior of $2^{2d}/d^{3/2}$, which is to be contrasted with the scaling of $2^d$ for the sphere. We present explicit formulas for quermassintegrals for many nonspherical convex bodies as well as as well as lower-dimensional bodies. These results are utilized to determine the rotationally-averaged exclusion volume for these shapes for dimensions 2 through 12. While the sphere is the shape possessing the minimal dimensionless exclusion volume, among the convex bodies considered that are sufficiently compact, the simplex possesses the maximal dimensionless exclusion volume with a scaling behavior of $2^{1.6618\ldots d}$. We also determine the corresponding second virial coefficient $B_2(K)$ of the aforementioned hard hyperparticles and compute estimates of the continuum percolation threshold $η_c$ derived previously by the authors. We conjecture that overlapping spheres possess the maximal value of $η_c$ among all identical nonzero-volume convex overlapping bodies for $d \ge 2$, randomly or uniformly oriented, and that, among all identical, oriented nonzero-volume convex bodies, overlapping simplices have the minimal value of $η_c$ for $d\ge 2$.

cond-mat.stat-mech↗

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↗

arXiv2022

Local Order Metrics for Two-Phase Media Across Length Scales

The capacity to devise order metrics for microstructures of multiphase heterogeneous media is a highly challenging task, given the richness of the possible geometries and topologies of the phases that can arise. This investigation initiates a program to formulate order metrics to characterize the degree of order/disorder of the microstructures of two-phase media in $d$-dimensional Euclidean space $\mathbb{R}^d$ across length scales. In particular, we propose the use of the local volume-fraction variance $σ^2_{_V}(R)$ associated with a spherical window of radius $R$ as an order metric. We determine $σ^2_{_V}(R)$ as a function of $R$ for 22 different models across the first three space dimensions, including both hyperuniform and nonhyperuniform systems with varying degrees of short- and long-range order. We find that the local volume-fraction variance as well as asymptotic coefficients and integral measures derived from it provide reasonably robust and sensitive order metrics to categorize disordered and ordered two-phase media across all length scales.

cond-mat.soft↗

arXiv2022

Extraordinary Disordered Hyperuniform Multifunctional Composites

A variety of performance demands are being placed on material systems, including desirable mechanical, thermal, electrical, optical, acoustic and flow properties. The purpose of the present article is to review the emerging field of disordered hyperuniform composites and their novel multifunctional characteristics. Disordered hyperuniform media are exotic amorphous states of matter that are characterized by an anomalous suppression of large-scale volume-fraction fluctuations compared to those in "garden-variety" disordered materials. Such unusual composites can have advantages over their periodic counterparts, such as unique or nearly optimal, direction-independent physical properties and robustness against defects. It will be shown that disordered hyperuniform composites and porous media can be endowed with a broad spectrum of extraordinary physical properties, including photonic, phononic, transport, chemical and mechanical characteristics that are only beginning to be discov

cond-mat.mtrl-sci↗

arXiv2022

Sub-diffusive wave transport and weak localization transition in three-dimensional stealthy hyperuniform disordered systems

The purpose of this work is to understand the fundamental connection between structural correlations and light localization in three-dimensional (3D) open scattering systems of finite size. We numerically investigate the transport of vector electromagnetic waves scattered by resonant electric dipoles spatially arranged in 3D space by stealthy hyperuniform disordered point patterns. Three-dimensional stealthy hyperuniform disordered systems (3D-SHDS) are engineered with different structural correlation properties determined by their degree of stealthiness $χ$. Such fine control of exotic states of amorphous matter enables the systematic design of optical media that interpolate in a tunable fashion between uncorrelated random structures and crystalline materials. By solving the electromagnetic multiple scattering problem using Green's matrix spectral method, we establish a transport phase diagram that demonstrates a distinctive transition from a diffusive to a weak localization regime beyond a critical scattering density that depends on $χ$. The transition is characterized by studying the Thouless number and the spectral statistics of the scattering resonances. In particular, by tuning the $χ$ parameter, we demonstrate large spectral gaps and suppressed sub-radiant proximity resonances, facilitating light localization. Moreover, consistently with previous studies, our results show a region of the transport phase diagram where the investigated scattering systems become transparent. Our work provides a systematic description of the transport and weak localization properties of light in stealthy hyperuniform structures and motivates the engineering of novel photonic systems with enhanced light-matter interactions for applications to both classical and quantum devices.

physics.optics↗

arXiv2022

Dynamic Measure of Hyperuniformity and Nonhyperuniformity in Heterogeneous Media via the Diffusion Spreadability

The recently developed concept of spreadability, $\mathcal{S}(t)$, provides a direct link between time-dependent diffusive transport and the microstructure of two-phase media across length scales. We explicitly compute $\mathcal{S}(t)$ for well-known two-dimensional and three-dimensional model structures, including nonhyperuniform fully penetrable spheres and equilibrium hard spheres, as well as hyperuniform sphere packings derived from perfect glasses, uniformly randomized lattices (URL), disordered stealthy point processes and Bravais lattices. We further confirm that the small-, intermediate- and long-time behaviors of $\mathcal{S}(t)$ sensitively capture the small-, intermediate- and large-scale characteristics of the models. In instances in which the spectral density $\tildeχ_{_V}(\mathbf{k})$ has a power-law form $B|\mathbf{k}|^α$ in the limit $|\mathbf{k}|\rightarrow 0$, the long-time spreadability provides a simple means to extract the value of the coefficients $α$ and $B$ that is robust against noise in $\tildeχ_{_V}(\mathbf{k})$ at small wavenumbers. Interestingly, the excess spreadability $\mathcal{S}(\infty)-\mathcal{S}(t)$ for URL packings has nearly exponential decay at small to intermediate $t$, but transforms to a power-law decay at large $t$. Our study of the aforementioned models enables us to devise an algorithm that accurately extracts large-scale behaviors from diffusion data alone. Lessons learned from such analyses of our models are used to determine accurately the large-scale structural characteristics of a sample Fontainebleau sandstone, which we show is nonhyperuniform. Our study demonstrates the practical applicability of the diffusion spreadability to extract crucial microstructural information from real data across length scales and provides a basis for the inverse design of materials with desirable time-dependent diffusion properties.

cond-mat.mtrl-sci↗

arXiv2021

Understanding Degeneracy of Two-Point Correlation Functions via Debye Random Media

It is well-known that the degeneracy of two-phase microstructures with the same volume fraction and two-point correlation function $S_2(\mathbf{r})$ is generally infinite. To elucidate the degeneracy problem explicitly, we examine Debye random media, which are entirely defined by a purely exponentially decaying two-point correlation function $S_2(r)$. In this work, we consider three different classes of Debye random media. First, we generate the "most probable" class using the Yeong-Torquato construction algorithm [Yeong and Torquato, Phys. Rev. E, 57, 495 (1998)]. A second class of Debye random media is obtained by demonstrating that the corresponding two-point correlation functions are effectively realized in the first three space dimensions by certain models of overlapping, polydisperse spheres. A third class is obtained by using the Yeong-Torquato algorithm to construct Debye random media that are constrained to have an unusual prescribed pore-size probability density function. We structurally discriminate these three classes of Debye random media from one another by ascertaining their other statistical descriptors, including the pore-size, surface correlation, chord-length probability density, and lineal-path functions. We also compare and contrast the percolation thresholds as well as the diffusion and fluid transport properties of these degenerate Debye random media. We find that these three classes of Debye random media are generally distinguished by the aforementioned descriptors and their microstructures are also visually distinct from one another. Our work further confirms the well-known fact that scattering information is insufficient to determine the effective physical properties of two-phase media. Additionally, our findings demonstrate the importance of the other two-point descriptors considered here in the design of materials with a spectrum of physical properties.

cond-mat.soft↗

arXiv2021

Diffusion Spreadability as a Probe of the Microstructure of Complex Media Across Length Scales

Consider the time-dependent problem of mass transfer of a solute between two phases and assume that the solute is initially distributed in one phase (phase 2) and absent from the other (phase 1). We desire the fraction of total solute present in phase 1 as a function of time, ${\cal S}(t)$, which we call the {\it spreadability}, since it is a measure of the spreadability of diffusion information as a function of time. We derive exact direct-space formulas for ${\cal S}(t)$ in any Euclidean space dimension $d$ in terms of the autocovariance function as well as corresponding Fourier representations of ${\cal S}(t)$ in terms of the spectral density. We derive closed-form general formulas for the short- and long-time behaviors of the spreadability in terms of crucial small- and large-scale microstructural information, respectively. The long-time behavior of ${\cal S}(t)$ enables one to distinguish the entire spectrum of microstructures that span from hyperuniform to nonhyperuniform media. For hyperuniform media, disordered or not, we show that the "excess" spreadability, ${\cal S}(\infty)-{\cal S}(t)$, decays to its long-time behavior exponentially faster than that of any nonhyperuniform two-phase medium, the "slowest" being antihyperuniform media. The stealthy hyperuniform class is characterized by an excess spreadability with the fastest decay rate among all translationally invariant microstructures. Moreover, we establish a remarkable connection between the spreadability and an outstanding problem in discrete geometry, namely, microstructures with "fast" spreadabilities are also those that can be derived from efficient "coverings" of space. We also identify heretofore unnoticed remarkable links between the spreadability ${\cal S}(t)$ and NMR pulsed field gradient spin-echo amplitude as well as diffusion MRI measurements.

cond-mat.soft↗