Universal hidden order in amorphous cellular geometries

Klatt, Michael A.; Lovrić, Jakov; Chen, Duyu; Kapfer, Sebastian C.; Schaller, Fabian M.; Schönhöfer, Philipp W. A.; Gardiner, Bruce S.; Smith, Ana‐Sunčana; Schröder‐Turk, Gerd E.; Torquato, Salvatore

doi:10.1038/s41467-019-08360-5

Cited by 81 publications

(96 citation statements)

References 66 publications

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“…(50), we see that the upper bound σ (2) U for these structures is exactly the same as σ e given by Eq. (63). Thus, we have rigorously demonstrated that anisotropic structures consisting of sets of intersecting parallel channels achieve the two-point anisotropic generalizations of the Hashin-Shtrikman bound (26) on σ e , regardless of whether they are ordered or disordered, hyperuniform or nonhyperuniform.…”

Section: Demonstration Of Optimality For Intersecting Parallel-channementioning

confidence: 78%

Multifunctional hyperuniform cellular networks: optimality, anisotropy and disorder

Torquato

Chen

2018

Multifunct. Mater.

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Disordered hyperuniform heterogeneous materials are new, exotic amorphous states of matter that behave like crystals in the manner in which they suppress volume-fraction fluctuations at large length scales, and yet are statistically isotropic with no Bragg peaks. It has recently been shown that disordered hyperuniform dielectric two-dimensional cellular network solids possess complete photonic band gaps comparable in size to photonic crystals, while at the same time maintaining statistical isotropy, enabling waveguide geometries not possible with photonic crystals. Motivated by these developments, we explore other functionalities of various two-dimensional ordered and disordered hyperuniform cellular networks, including their effective thermal or electrical conductivities and elastic moduli. We establish the multifunctionality of a class of such low-density networks by demonstrating that they maximize or virtually maximize the effective conductivities and elastic moduli. This is accomplished using the machinery of homogenization theory, including optimal bounds and cross-property bounds, and statistical mechanics. We rigorously prove that anisotropic networks consisting of sets of intersecting parallel channels in the lowdensity limit, ordered or disordered, possess optimal effective conductivity tensors. For a variety of different disordered networks, we show that when short-range and long-range order increases, there is an increase in both the effective conductivity and elastic moduli of the network. Moreover, we demonstrate that the effective conductivity and elastic moduli of various disordered networks derived from disordered "stealthy" hyperuniform point patterns possess virtually optimal values. We note that the optimal networks for conductivity are also optimal for the fluid permeability associated with slow viscous flow through the channels as well as the mean survival time associated with diffusion-controlled reactions in the channels. In summary, we have identified ordered and disordered hyperuniform low-weight cellular networks that are multifunctional with respect to transport (e.g., heat dissipation and fluid transport), mechanical and electromagnetic properties, which can be readily fabricated using 3D printing and lithographic technologies.

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Section: Demonstration Of Optimality For Intersecting Parallel-channementioning

confidence: 78%

Multifunctional hyperuniform cellular networks: optimality, anisotropy and disorder

Torquato

Chen

2018

Multifunct. Mater.

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“…Inflationary expansion explains why the primeval 10 90 causally-disconnected quantum “seeds” [ 31 ] led to the experimentally detected homogeneity and isotropy. Still, inflation would have amplified minute quantum fluctuations (pre-inflation) into slight density ripples of over- and under-density (post-inflation).Here the concept of hyperuniformity comes into play, i.e., the anomalous suppression of density fluctuations on large length scales occurring in amorphous cellular structures of ordered and disordered materials [ 55 ].The evolution of a given set of initial points takes place when, through Lloyd iterations, each point is replaced by the center mass of its Voronoi cell. This corresponds to a gradient descent algorithm which allows a progressive, general convergence to a random minimum in the potential energy surface.…”

Section: Discussionmentioning

confidence: 99%

“…This corresponds to a gradient descent algorithm which allows a progressive, general convergence to a random minimum in the potential energy surface. Klatt et al [ 55 ] report that systems equipped with different initial configurations (such as, e.g., either hyper-fluctuating, or anisotropic, or relatively homogeneous point sets), converge towards the same high degree of uniformity after a relatively small number of Lloyd iterations (about 10 5 ).This means that, in the systems’ final states, independent of the initial conditions, the cell volumes become uniform and the dimension less total energy converges towards values comparable to the deep local energy minima of the optimal lattice. Therefore, we are allowed to describe the cosmic evolution suddenly after the Big Bang in terms of Lloyd iterations, where the initial quantum seeds stand for initial point sets, progressively converted to point sets with a centroidal Voronoi diagram.…”

Section: Discussionmentioning

confidence: 99%

Entropy Balance in the Expanding Universe: A Novel Perspective

Tozzi

Peters

2019

Entropy

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We describe cosmic expansion as correlated with the standpoints of local observers’ co-moving horizons. In keeping with relational quantum mechanics, which claims that quantum systems are only meaningful in the context of measurements, we suggest that information gets ergodically “diluted” in our isotropic and homogeneous expanding Universe, so that an observer detects just a limited amount of the total cosmic bits. The reduced bit perception is due the decreased density of information inside the expanding cosmic volume in which the observer resides. Further, we show that the second law of thermodynamics can be correlated with cosmic expansion through a relational mechanism, because the decrease in information detected by a local observer in an expanding Universe is concomitant with an increase in perceived cosmic thermodynamic entropy, via the Bekenstein bound and the Laudauer principle. Reversing the classical scheme from thermodynamic entropy to information, we suggest that the cosmological constant of the quantum vacuum, which is believed to provoke the current cosmic expansion, could be one of the sources of the perceived increases in thermodynamic entropy. We conclude that entropies, including the entangled entropy of the recently developed framework of quantum computational spacetime, might not describe independent properties, but rather relations among systems and observers.

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“…Furthermore, their results verify that close loop power control supports the received SINR of OLPC to meet the target SINR by compensating the fading effect. 1 Following Slivnyak theorem, a typical user at origin leads to simplified statistical properties of an independent homogeneous Poisson point process (IHPPP) [9]. 2 The terms open loop power control and FPC are used interchangeably in this paper.…”

Section: B Related Workmentioning

confidence: 99%

“…In heterogeneous cellular networks (HetNets), coverage probability, spectrum efficiency, and throughput are significantly enhanced by enriching coverage area of macro base station (MBS) with small base station deployment (SBS D ) [1], [2]. In HetNets, MBS-associated users (MBS-AUs) and SBSassociated users (SBS-AUs) share the same frequency band and, hence, lead to high throughput.…”

Section: Introduction a Motivationmentioning

confidence: 99%

Proactive Uplink Interference Management for Nonuniform Heterogeneous Cellular Networks

et al. 2020

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In homogeneous cellular networks, fractional power control (FPC) is employed to partially compensate the path-loss and, hence, improve uplink (U L) signal-to-interference ratio (SIR). However, this scheme is less effective in heterogeneous cellular networks (HetNets) because: (i) except the typical user, all other users with variable U L transmit power (UTP) act as interferers, (ii) FPC leads to high UTP by edge users and, hence, more interference, and (iii) small base stations (SBSs)' densification further increases network interferences. Leveraging FPC in HetNets, we propose nonuniform SBS deployment (NU-SBS D) to reduce interference and, thus, increase network performance. According to our NU-SBS D model, SBS deployment (SBS D) near macro base station (MBS) is avoided, whereas MBS coverage edge area is enriched with ultra-dense SBS D. NU-SBS D model leads to: (i) better SIR reception of MBS coverage edge users, (ii) fewer SBS D requirement, and (iii) better SBS coverage in the MBS coverage edge area. Moreover, to make a model more proactive, we also consider reverse frequency allocation (RFA) to further abate both U L and downlink (D L) interferences. The coverage probability expressions are derived for both uniform SBS deployment (U-SBS D) and NU-SBS D while using RFA and FPC. Through simulation and numerical results, we characterize coverage probability for different values of SIR threshold, path loss compensation factor, SBS density, users density, and the distance between the typical user and the associated base station. The proposed NU-SBS D model along with RFA leads to reduced network interference as compared with U-SBS D and, thus, leverages FPC in HetNets.

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Universal hidden order in amorphous cellular geometries

Cited by 81 publications

References 66 publications

Multifunctional hyperuniform cellular networks: optimality, anisotropy and disorder

Multifunctional hyperuniform cellular networks: optimality, anisotropy and disorder

Entropy Balance in the Expanding Universe: A Novel Perspective

Proactive Uplink Interference Management for Nonuniform Heterogeneous Cellular Networks

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