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1. Can exotic disordered “stealthy” particle configurations tolerate arbitrarily large holes?

   https://doi.org/10.1039/C7SM01028A  

   Zhang, G.; Stillinger, F. H.; Torquato, S. (January 2017, Soft Matter)

   The probability of finding a spherical cavity or “hole” of arbitrarily large size in typical disordered many-particle systems in the infinite-system-size limit ( e.g. , equilibrium liquid states) is non-zero. Such “hole” statistics are intimately linked to the thermodynamic and nonequilibrium physical properties of the system. Disordered “stealthy” many-particle configurations in d -dimensional Euclidean space  d are exotic amorphous states of matter that lie between a liquid and crystal that prohibit single-scattering events for a range of wave vectors and possess no Bragg peaks [Torquato et al. , Phys. Rev. X , 2015, 5 , 021020]. In this paper, we provide strong numerical evidence that disordered stealthy configurations across the first three space dimensions cannot tolerate arbitrarily large holes in the infinite-system-size limit, i.e. , the hole probability has compact support. This structural “rigidity” property apparently endows disordered stealthy systems with novel thermodynamic and physical properties, including desirable band-gap, optical and transport characteristics. We also determine the maximum hole size that any stealthy system can possess across the first three space dimensions. 

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2. Relevance of packing to colloidal self-assembly

   https://doi.org/10.1073/pnas.1720139115  

   Cersonsky, Rose K.; van Anders, Greg; Dodd, Paul M.; Glotzer, Sharon C. (February 2018, Proceedings of the National Academy of Sciences)

   null (Ed.)

   Since the 1920s, packing arguments have been used to rationalize crystal structures in systems ranging from atomic mixtures to colloidal crystals. Packing arguments have recently been applied to complex nanoparticle structures, where they often, but not always, work. We examine when, if ever, packing is a causal mechanism in hard particle approximations of colloidal crystals. We investigate three crystal structures composed of their ideal packing shapes. We show that, contrary to expectations, the ordering mechanism cannot be packing, even when the thermodynamically self-assembled structure is the same as that of the densest packing. We also show that the best particle shapes for hard particle colloidal crystals at any finite pressure are imperfect versions of the ideal packing shape. 

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3. On the universality of local dissipation scales in turbulent channel flow

   https://doi.org/10.1017/jfm.2015.664  

   Bailey, S. C.; Witte, B. M. (January 2016, Journal of Fluid Mechanics)

   Well-resolved measurements of the small-scale dissipation statistics within turbulent channel flow are reported for a range of Reynolds numbers from $$Re_{{\it\tau}}\approx 500$$ to 4000. In this flow, the local large-scale Reynolds number based on the longitudinal integral length scale is found to poorly describe the Reynolds number dependence of the small-scale statistics. When a length scale based on Townsend’s attached-eddy hypothesis is used to define the local large-scale Reynolds number, the Reynolds number scaling behaviour was found to be more consistent with that observed in homogeneous, isotropic turbulence. The Reynolds number scaling of the dissipation moments up to the sixth moment was examined and the results were found to be in good agreement with predicted scaling behaviour (Schumacher et al. , Proc. Natl Acad. Sci. USA , vol. 111, 2014, pp. 10961–10965). The probability density functions of the local dissipation scales (Yakhot, Physica D, vol. 215 (2), 2006, pp. 166–174) were also determined and, when the revised local large-scale Reynolds number is used for normalization, provide support for the existence of a universal distribution which scales differently for inner and outer regions. 

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4. On the Impact of Relativistic Gravity on the Rate of Tidal Disruption Events

   https://doi.org/10.3847/1538-4357/ac85b3  

   Coughlin, Eric R.; Nixon, C. J. (August 2022, The Astrophysical Journal)

   Abstract The tidal disruption of stars by supermassive black holes (SMBHs) probes relativistic gravity. In the coming decade, the number of observed tidal disruption events (TDEs) will grow by several orders of magnitude, allowing statistical inferences of the properties of the SMBH and stellar populations. Here we analyze the probability distribution functions of the pericenter distances of stars that encounter an SMBH in the Schwarzschild geometry, where the results are completely analytic, and the Kerr metric. From this analysis we calculate the number of observable TDEs, defined to be those that come within the tidal radius r t but outside the direct capture radius (which is, in general, larger than the horizon radius). We find that relativistic effects result in a steep decline in the number of stars that have pericenter distances r p ≲ 10 r g , where r g = GM / c 2 , and that for maximally spinning SMBHs the distribution function of r p at such distances scales as f r p ∝ r p 4 / 3 , or in terms of β ≡ r t / r p scales as f β ∝ β −10/3 . We find that spin has little effect on the TDE fraction until the very-high-mass end, where instead of being identically zero the rate is small (≲1% of the expected rate in the absence of relativistic effects). Effectively independent of spin, if the progenitors of TDEs reflect the predominantly low-mass stellar population and thus have masses ≲1 M ⊙ , we expect a substantial reduction in the rate of TDEs above 10 7 M ⊙ . 

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5. 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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