Abstract Predicting physical properties of materials with spatially complex structures is one the most challenging problems in material science. One key to a better understanding such geometric characterization their spatial structure. Minkowski tensors are tensorial shape indices that allow quantitative anisotropy and particularly well suited for developing structure‐property relationships tensor‐valued or orientation‐dependent properties. They fundamental indices, some sense being simplest...

The formation of the biophotonic gyroid material in butterfly wing scales is an exceptional feat evolutionary engineering functional nanostructures. It hypothesized that this nanostructure forms by chitin polymerization inside a convoluted membrane corresponding shape endoplasmic reticulum. However, dynamic process, including whether folding and expression are simultaneous or sequential processes, cannot yet be elucidated vivo imaging. We report unusual hierarchical ultrastructure

Abstract Partitioning space into cells with certain extreme geometrical properties is a central problem in many fields of science and technology. Here we investigate the Quantizer problem, defined as optimisation moment inertia Voronoi cells, i.e., similarly-sized ‘sphere-like’ polyhedra that tile are preferred. We employ Lloyd’s centroidal diagram algorithm to solve this find it converges disordered states associated deep local minima. These universal sense their structure factors...

Nuclear matter under the conditions of a supernova explosion unfolds into rich variety spatially structured phases, called nuclear pasta. We investigate role periodic networklike structures with negatively curved interfaces in pasta structures, by static and dynamic Hartree-Fock simulations lattices. As most prominent result, we identify for first time single gyroid network structure cubic chiral $I{4}_{1}23$ symmetry, well-known configuration nanostructured soft-matter systems, both as...

Bacterial adhesion to nanostructured surfaces can be quantified by surface morphometry: the area that is accessible in a certain depth for tethering cell wall molecules equals fraction of force as compared smooth surface.

Understanding the nature and formation of band gaps associated with propagation electromagnetic, electronic, or elastic waves in disordered materials as a function system size presents fundamental technological challenges. In particular, basic question is whether systems exist thermodynamic limit. To explore this issue, we use two-stage ensemble approach to study complete photonic (PBGs) for sequence increasingly large spanning broad range two-dimensional network solids varying degrees local...

We present simulations of neutron-rich matter at subnuclear densities, like supernova matter, with the time-dependent Hartree-Fock approximation temperatures several MeV. The initial state consists $\ensuremath{\alpha}$ particles randomly distributed in space that have a Maxwell-Boltzmann distribution momentum space. Adding neutron background initialized Fermi plane waves calculations reflect reasonable astrophysical matter. This evolves into spherical, rod-like, and slab-like shapes...

The authors combine experiment, theory, and simulations to study the relationship between morphology permeability in models consisting of overlapping circular or elliptical grains. They point out how their may also apply different types structures.

Random, uncorrelated displacements of particles on a lattice preserve the hyperuniformity original lattice, that is, normalized density fluctuations vanish in limit infinite wavelengths. In addition to diffuse contribution, scattering intensity from resulting point pattern typically inherits Bragg peaks (long-range order) lattice. Here we demonstrate how these can be hidden effective diffraction independent and identically distributed perturbations. All if only sum all probability densities...

The local number variance associated with a spherical sampling window of radius $R$ enables classification many-particle systems in $d$-dimensional Euclidean space according to the degree which large-scale density fluctuations are suppressed, resulting demarcation between hyperuniform and nonhyperuniform phyla. To better characterize fluctuations, we carry out an extensive study higher-order moments, including skewness $\gamma_1(R)$, excess kurtosis $\gamma_2(R)$ corresponding probability...

We show that dry scalar-order active field theories (AFTs) are universally hyperuniform, i.e., density fluctuations anomalously suppressed in the long-time limit regardless of integrability or functional form contributions up to third order gradient terms. These AFTs include model B, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi mathvariant="normal">B</a:mi><a:mo>+</a:mo></a:mrow></a:math>, and effective Cahn-Hilliard models. Moreover, variances spectral densities...

Minkowski tensors, also known as tensor valuations, provide robust $n$-point information for a wide range of random spatial structures. Local estimators voxelized data, however, are unavoidably biased even in the limit infinitely high resolution. Here, we substantially improve recently proposed, asymptotically unbiased algorithm to estimate tensors data. Our improved is more and efficient. Moreover generalize theoretical foundations an bias-free estimation interfacial case finite unions...

Abstract For smooth surfaces, chemical composition can be readily analyzed using various spectroscopic techniques, a prominent example is X‐ray photoelectron spectroscopy (XPS), where the relative proportions of elements are mainly determined by intensity ratio element‐specific photoelectrons. However, this analysis becomes more complex for nanorough surfaces like black silicon (b‐Si) due to geometry's steep slopes, which mimic local variations in emission angles. In study, effect explicitly...

<title>Abstract</title> Bicontinuous geometries, both ordered and amorphous, are commonly found in many soft matter systems. Ordered bicontinuous phases can be modelled by periodic minimal surfaces, including Schoen's (G)yroid or Schwarz' (P)rimitive (D)iamond surfaces. By contrast, a surface model for amorphous has been lacking. Here, we study models phases, such as sponge phases. Using the Surface Evolver with novel topology-stabilising minimisation scheme numerically construct surfaces...

We characterize the structure of maximally random jammed (MRJ) sphere packings by computing Minkowski functionals (volume, surface area, and integrated mean curvature) their associated Voronoi cells. The probability distribution functions these cells in MRJ are qualitatively similar to those an equilibrium hard-sphere liquid partly even uncorrelated Poisson point process, implying that such local statistics relatively structurally insensitive. This is not surprising because a single cell...

By experiments and simulations on structured surfaces, we show that S. aureus cells have adhesive patches are heterogeneously distributed across the cell envelope.

A stationary Boolean model is the union set of random compact particles which are attached to points a Poisson point process. For with convex grains we consider recently developed collection shape descriptors, so called Minkowski tensors. By combining spatial and probabilistic averaging define tensor densities model. These global characteristics can be estimated from observations. In contrast local like mean single particle cannot observed directly, since overlap. We relate properties by...

Purpose Structure-property relations, which relate the shape of microstructure to physical properties such as transport or mechanical properties, need sensitive measures structure. What are suitable fabric tensors quantify anisotropic heterogeneous materials? The mean intercept length is among most commonly used characteristics anisotropy in porous media, e.g., trabecular bone medical physics. Yet, this series two papers we demonstrate that it has conceptual shortcomings limit validity its...

We show that it is possible to construct foam-based heterostructures with complete photonic band gaps. Three-dimensional foams are promising candidates for the self-organization of large networks combinations physical characteristics may be useful applications. The largest gap found based on 3D Weaire–Phelan foam, a structure was originally introduced as solution Kelvin problem finding tessellation composed equal-volume cells has least surface area. maximal size 16.9% (at volume fraction...

In the first two papers of this series, we characterized structure maximally random jammed (MRJ) sphere packings across length scales by computing a variety different correlation functions, spectral hole probabilities, and local density fluctuations. From remarkable structural features MRJ packings, especially its disordered hyperuniformity, exceptional physical properties can be expected. Here, employ these descriptors to estimate effective transport electromagnetic via rigorous bounds,...

In the first paper of this series, we introduced Voronoi correlation functions to characterize structure maximally random jammed (MRJ) sphere packings across length scales. present paper, determine a variety different that arise in rigorous expressions for effective physical properties MRJ and compare them corresponding statistical descriptors overlapping spheres equilibrium hard-sphere systems. Such structural bounds formulas transport properties, diffusion reactions constants, elastic...

Through an extensive series of high-precision numerical computations the optimal complete photonic band gap (PBG) as a function dielectric contrast $\alpha$ for variety crystal and disordered heterostructures, we reveal striking universal behaviors sensitivity $\mathcal{S}(\alpha)\equiv d\Delta(\alpha)/d\alpha$, first derivative gap-to-midgap ratio $\Delta(\alpha)$. In particular, all our networks, $\mathcal{S}(\alpha)$ takes form that is well approximated by analytic formula one-dimensional...

Abstract As the length scales of smallest technology continue to advance beyond micron scale it becomes increasingly important equip robotic components with means for intelligent and autonomous decision making limited information. With help a tabular Q-learning algorithm, we design model training microswimmer, navigate quickly through an environment given by various different scalar motility fields, while receiving amount local We compare performances defined via time first passage target,...

Aims. H.E.S.S. observes an increasing number of large extended sources. A new technique based on the structure sky map is developed to account for these additional structures by comparing them with common point source analysis. Methods. Minkowski functionals are powerful measures from integral geometry. They can be used quantify counts map, which then compared expected a pure Poisson background. Gamma-ray sources lead significant deviations background structure. The standard likelihood ratio...