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1. Phase-factor spectra of turbulent phase screens

   https://doi.org/10.1364/JOSAA.429928  

   Muschinski, Andreas ( August 2021 , Journal of the Optical Society of America A)

   The optical phase$\mathrm{\varphi <\#comment/>}$is a key quantity in the physics of light propagating through a turbulent medium. In certain respects, however, the statistics of the phasefactor,$\mathrm{\psi <\#comment/>}=\exp <\#comment/>(i\mathrm{\varphi <\#comment/>})$, are more relevant than the statistics of the phase itself. Here, we present a theoretical analysis of the 2D phase-factor spectrum$F_{\mathrm{\psi <\#comment/>}}(\mathit{\kappa <\#comment/>})$of a random phase screen. We apply the theory to four types of phase screens, each characterized by a power-law phase structure function,$D_{\mathrm{\varphi <\#comment/>}}(r)=(r/r_c{)}^{\mathrm{\gamma <\#comment/>}}$(where$r_c$is the phase coherence length defined by$D_{\mathrm{\varphi <\#comment/>}}(r_c)=1{\mathrm{r}\mathrm{a}\mathrm{d}}^2$), and a probability density function$p_{\mathrm{\alpha <\#comment/>}}(\mathrm{\alpha <\#comment/>})$of the phase increments for a given spatial lag. We analyze phase screens with turbulent ($\mathrm{\gamma <\#comment/>}=5/3$) and quadratic ($\mathrm{\gamma <\#comment/>}=2$) phase structure functions and with normally distributed (i.e., Gaussian) versus Laplacian phase increments. We find that there is a pronounced bump in each of the four phase-factor spectra$F_{\mathrm{\psi <\#comment/>}}(\mathrm{\kappa <\#comment/>})$. The precise location and shape of the bump are different for the four phase-screen types, but in each case it occurs at$\mathrm{\kappa <\#comment/>}\sim <\#comment/>1/r_c$. The bump is unrelated to the well-known “Hill bump” and is not caused by diffraction effects. It is solely a characteristic of the refractive-index statistics represented by the respective phase screen. We show that the second-order$\mathrm{\psi <\#comment/>}$statistics (covariance function, structure function, and spectrum) characterize a random phase screen more completely than the second-order$\mathrm{\varphi <\#comment/>}$counterparts.

    

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2. Dynamics and thermodynamics of air-driven active spinners

   https://doi.org/10.1039/c8sm00403j  

   Farhadi, Somayeh ; Machaca, Sergio ; Aird, Justin ; Torres Maldonado, Bryan O. ; Davis, Stanley ; Arratia, Paulo E. ; Durian, Douglas J. ( January 2018 , Soft Matter)

   We report on the collective behavior of active particles in which energy is continuously supplied to rotational degrees of freedom. The active spinners are 3D-printed disks, 1 cm in diameter, that have an embedded fan-like structure, such that a sub-levitating up-flow of air forces them to spin. Single spinners exhibit Brownian motion with a narrow Gaussian velocity distribution function, P ( v ), for translational motion. We study the evolution of P ( v ) as the packing fraction and the average single particle spin speeds are varied. The interparticle hydrodynamic interaction is negligible, and the dynamics is dominated by hyperelastic collisions and dissipative forces. As expected for nonequilibrium systems, P ( v ) for a collection of many spinners deviates from Gaussian behavior. However, unlike translationally active systems, phase separation is not observed, and the system remains spatially homogeneous. We then search for a near-equilibrium counterpart for our active spinners by measuring the equation of state. Interestingly, it agrees well with a hard-sphere model, despite the dissipative nature of the single particle dynamics. 

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3. Sharpening the Distance Conjecture in diverse dimensions

   https://doi.org/10.1007/JHEP12(2022)114  

   Etheredge, Muldrow ; Heidenreich, Ben ; Kaya, Sami ; Qiu, Yue ; Rudelius, Tom ( December 2022 , Journal of High Energy Physics)

   A bstract The Distance Conjecture holds that any infinite-distance limit in the scalar field moduli space of a consistent theory of quantum gravity must be accompanied by a tower of light particles whose masses scale exponentially with proper field distance ‖ ϕ ‖ as m ~ exp(− λ ‖ ϕ ‖), where λ is order-one in Planck units. While the evidence for this conjecture is formidable, there is at present no consensus on which values of λ are allowed. In this paper, we propose a sharp lower bound for the lightest tower in a given infinite-distance limit in d dimensions: λ ≥ $$ 1/\sqrt{d-2} $$ 1 / d − 2 . In support of this proposal, we show that (1) it is exactly preserved under dimensional reduction, (2) it is saturated in many examples of string/M-theory compactifications, including maximal supergravity in d = 4 – 10 dimensions, and (3) it is saturated in many examples of minimal supergravity in d = 4 – 10 dimensions, assuming appropriate versions of the Weak Gravity Conjecture. We argue that towers with λ < $$ 1/\sqrt{d-2} $$ 1 / d − 2 discussed previously in the literature are always accompanied by even lighter towers with λ ≥ $$ 1/\sqrt{d-2} $$ 1 / d − 2 , thereby satisfying our proposed bound. We discuss connections with and implications for the Emergent String Conjecture, the Scalar Weak Gravity Conjecture, the Repulsive Force Conjecture, large-field inflation, and scalar field potentials in quantum gravity. In particular, we argue that if our proposed bound applies beyond massless moduli spaces to scalar fields with potentials, then accelerated cosmological expansion cannot occur in asymptotic regimes of scalar field space in quantum gravity. 

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4. Approximate Degree, Secret Sharing, and Concentration Phenomena

   https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2019.71  

   Bogdanov, Andrej ; Mande, Nikhil S. ; Thaler, Justin ; Williamson, Christopher ( September 2019 , Leibniz international proceedings in informatics)

   The epsilon-approximate degree, deg_epsilon(f), of a Boolean function f is the least degree of a real-valued polynomial that approximates f pointwise to within epsilon. A sound and complete certificate for approximate degree being at least k is a pair of probability distributions, also known as a dual polynomial, that are perfectly k-wise indistinguishable, but are distinguishable by f with advantage 1 - epsilon. Our contributions are: - We give a simple, explicit new construction of a dual polynomial for the AND function on n bits, certifying that its epsilon-approximate degree is Omega (sqrt{n log 1/epsilon}). This construction is the first to extend to the notion of weighted degree, and yields the first explicit certificate that the 1/3-approximate degree of any (possibly unbalanced) read-once DNF is Omega(sqrt{n}). It draws a novel connection between the approximate degree of AND and anti-concentration of the Binomial distribution. - We show that any pair of symmetric distributions on n-bit strings that are perfectly k-wise indistinguishable are also statistically K-wise indistinguishable with at most K^{3/2} * exp (-Omega (k^2/K)) error for all k < K <= n/64. This bound is essentially tight, and implies that any symmetric function f is a reconstruction function with constant advantage for a ramp secret sharing scheme that is secure against size-K coalitions with statistical error K^{3/2} * exp (-Omega (deg_{1/3}(f)^2/K)) for all values of K up to n/64 simultaneously. Previous secret sharing schemes required that K be determined in advance, and only worked for f=AND. Our analysis draws another new connection between approximate degree and concentration phenomena. As a corollary of this result, we show that for any d <= n/64, any degree d polynomial approximating a symmetric function f to error 1/3 must have coefficients of l_1-norm at least K^{-3/2} * exp ({Omega (deg_{1/3}(f)^2/d)}). We also show this bound is essentially tight for any d > deg_{1/3}(f). These upper and lower bounds were also previously only known in the case f=AND. 

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5. Geometrical variations of two manganese(II) complexes with closely related quinoline-based tripodal ligands

   https://doi.org/10.1107/S2056989021009786  

   Frey, Steven T. ; Ballot, Jasper G. ; Hands, Allison ; Cirka, Haley A. ; Rinaolo, Katheryn C. ; Phalkun, Nich N. ; Kaur, Manpreet ; Jasinski, Jerry P. ( October 2021 , Acta Crystallographica Section E Crystallographic Communications)

   Structural analyses of the compounds di-μ-acetato-κ 4 O : O ′-bis{[2-methoxy- N , N -bis(quinolin-2-ylmethyl)ethanamine-κ 4 N , N ′, N ′′, O ]manganese(II)} bis(tetraphenylborate) dichloromethane 1.45-solvate, [Mn 2 (C 23 O 2 ) 2 (C 23 H 23 N 3 O) 2 ](C 24 H 20 B)·1.45CH 2 Cl 2 or [Mn(DQMEA)(μ-OAc) 2 Mn(DQMEA)](BPh 4 ) 2 ·1.45CH 2 Cl 2 or [1] (BPh 4 ) 2 ·1.45CH 2 Cl 2 , and (acetato-κ O )[2-hydroxy- N , N -bis(quinolin-2-ylmethyl)ethanamine-κ 4 N , N ′, N ′′, O ](methanol-κ O )manganese(II) tetraphenylborate methanol monosolvate, [Mn(CH 3 COO)(C 22 H 21 N 3 O)(CH 3 OH)](C 24 H 20 B)·CH 3 OH or [Mn(DQEA)(OAc)(CH 3 OH)]BPh 4 ·CH 3 OH or [2] BPh 4 ·CH 3 OH, by single-crystal X-ray diffraction reveal distinct differences in the geometry of coordination of the tripodal DQEA and DQMEA ligands to Mn II ions. In the asymmetric unit, compound [1] (BPh 4 ) 2 ·(CH 2 Cl 2 ) 1.45 crystallizes as a dimer in which each manganese(II) center is coordinated by the central amine nitrogen, the nitrogen atom of each quinoline group, and the methoxy-oxygen of the tetradentate DQMEA ligand, and two bridging-acetate oxygen atoms. The symmetric Mn II centers have a distorted, octahedral geometry in which the quinoline nitrogen atoms are trans to each other resulting in co-planarity of the quinoline rings. For each Mn II center, a coordinated acetate oxygen participates in C—H...O hydrogen-bonding interactions with the two quinolyl moieties, further stabilizing the trans structure. Within the crystal, weak π – π stacking interactions and intermolecular cation–anion interactions stabilize the crystal packing. In the asymmetric unit, compound [2] BPh 4 ·CH 3 OH crystallizes as a monomer in which the manganese(II) ion is coordinated to the central nitrogen, the nitrogen atom of each quinoline group, and the alcohol oxygen of the tetradentate DQEA ligand, an oxygen atom of OAc, and the oxygen atom of a methanol ligand. The geometry of the Mn II center in [2] BPh 4 ·CH 3 OH is also a distorted octahedron, but the quinoline nitrogen atoms are cis to each other in this structure. Hydrogen bonding between the acetate oxygen atoms and hydroxyl (O—H...O) and quinolyl (C—H...O and N—H...O) moieties of the DQEA ligand stabilize the complex in this cis configuration. Within the crystal, dimerization of complexes occurs by the formation of a pair of intermolecular O3—H3...O2 hydrogen bonds between the coordinated hydroxyl oxygen of the DQEA ligand of one complex and an acetate oxygen of another. Additional hydrogen-bonding and intermolecular cation–anion interactions contribute to the crystal packing. 

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