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1. Designer pair statistics of disordered many-particle systems with novel properties

   https://doi.org/10.1063/5.0189769  

   Wang, Haina; Torquato, Salvatore (January 2024, The Journal of Chemical Physics)

   The knowledge of exact analytical functional forms for the pair correlation function g2(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 database 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 temperatures that precisely match targeted forms for both g2(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 many-particle systems with a wide range of translational order and self-diffusion coefficients 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. 

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2. Hard convex lens-shaped particles: metastable, glassy and jammed states

   https://doi.org/10.1039/c8sm01519h  

   Cinacchi, Giorgio; Torquato, Salvatore (October 2018, Soft Matter)

   We generate and study dense positionally and/or orientationally disordered, including jammed, monodisperse packings of hard convex lens-shaped particles (lenses). Relatively dense isotropic fluid configurations of lenses of various aspect ratios are slowly compressed via a Monte Carlo method based procedure. Under this compression protocol, while ‘flat’ lenses form a nematic fluid phase (where particles are positionally disordered but orientationally ordered) and ‘globular’ lenses form a plastic solid phase (where particles are positionally ordered but orientationally disordered), ‘intermediate’, neither ‘flat’ nor ‘globular’, lenses do not form either mesophase. In general, a crystal solid phase (where particles are both positionally and orientationally ordered) does not spontaneously form during lengthy numerical simulation runs. In correspondence to those volume fractions at which a transition to the crystal solid phase would occur in equilibrium, a ‘downturn’ is observed in the inverse compressibility factor versus volume fraction curve beyond which this curve behaves essentially linearly. This allows us to estimate the volume fraction at jamming of the dense non-crystalline packings so generated. These packings are nematic for ‘flat’ lenses and plastic for ‘globular’ lenses, while they are robustly isotropic for ‘intermediate’ lenses, as confirmed by the calculation of the τ order metric, among other quantities. The structure factors S ( k ) of the corresponding jammed states tend to zero as the wavenumber k goes to zero, indicating they are effectively hyperuniform ( i.e. , their infinite-wavelength density fluctuations are anomalously suppressed). Among all possible lens shapes, ‘intermediate’ lenses with aspect ratio around 2/3 are special because they are those that reach the highest volume fractions at jamming while being positionally and orientationally disordered and these volume fractions are as high as those reached by nematic jammed states of ‘flat’ lenses and plastic jammed states of ‘globular’ lenses. All of their attributes, taken together, make such ‘intermediate’ lens packings particularly good glass-forming materials. 

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3. Persistent homology and topological statistics of hyperuniform point clouds

   https://doi.org/10.1103/PhysRevResearch.6.023107  

   Salvalaglio, Marco; Skinner, Dominic J; Dunkel, Jörn; Voigt, Axel (May 2024, Physical Review Research)

   Hyperuniformity, the suppression of density fluctuations at large length scales, is observed across a wide variety of domains, from cosmology to condensed matter and biological systems. Although the standard definition of hyperuniformity only utilizes information at the largest scales, hyperuniform configurations have distinctive local characteristics. However, the influence of global hyperuniformity on local structure has remained largely unexplored; establishing this connection can help uncover long-range interaction mechanisms and detect hyperuniform traits in finite-size systems. Here, we study the topological properties of hyperuniform point clouds by characterizing their persistent homology and the statistics of local graph neighborhoods. We find that varying the structure factor results in configurations with systematically different topological properties. Moreover, these topological properties are conserved for subsets of hyperuniform point clouds, establishing a connection between finite-sized systems and idealized reference arrangements. Comparing distributions of local topological neighborhoods reveals that the hyperuniform arrangements lie along a primarily one-dimensional manifold reflecting an order-to-disorder transition via hyperuniform configurations. The results presented here complement existing characterizations of hyperuniform phases of matter, and they show how local topological features can be used to detect hyperuniformity in size-limited simulations and experiments. Published by the American Physical Society2024 

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4. Local order metrics for many-particle systems across length scales

   https://doi.org/10.1103/PhysRevResearch.6.033262  

   Maher, Charles Emmett; Torquato, Salvatore (September 2024, Physical Review Research)

   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 ${\sigma }_N^2\left(R\right)$associated with a spherical sampling window of radius $R$(which encodes pair correlations) and an integral measure derived from it ${\mathrm{\Sigma }}_N(R_i,R_j)$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 , ] to devise even more sensitive order metrics. Published by the American Physical Society2024 

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5. Contact criterion for suspensions of smooth and rough colloids

   https://doi.org/10.1039/D0SM00072H  

   Pradeep, Shravan; Hsiao, Lilian C. (June 2020, Soft Matter)

   We report a procedure to obtain the search distance used to determine particle contact in dense suspensions of smooth and rough colloids. This method works by summing physically relevant length scales in an uncertainty analysis and does not require detailed quantification of the surface roughness. We suspend sterically stabilized, fluorescent poly(methyl methacrylate) colloids in a refractive index-matched solvent, squalene, in order to ensure hard sphere-like behavior. High speed centrifugation is used to pack smooth and rough colloids to their respective jamming points, ϕ J . The jammed suspensions are subsequently diluted with known volumes of solvent to ϕ < ϕ J . Structural parameters obtained from confocal laser scanning micrographs of the diluted colloidal suspensions are extrapolated to ϕ J to determine the mean contact number at jamming, 〈 z 〉 J . Contact below jamming refers to nearest neighbors at a length scale below which the effects of hydrodynamic or geometric friction come into play. Sensitivity analyses show that a deviation of the search distance by 1% of the particle diameter results in 〈 z 〉 changing by up to 10%, with the error in contact number distribution being magnified in dense suspensions ( ϕ > 0.50) due to an increased number of nearest neighbors in the first coordination shell. 

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