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1. A tensor density measure of topological charge in three-dimensional nematic phases

   https://doi.org/10.1098/rspa.2023.0564  

   Schimming, Cody D; Vinals, Jorge (May 2024, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   A path-independent measure in order parameter space is introduced such that, when integrated along any closed contour in a three-dimensional nematic phase, it yields the topological charge of any line defects encircled by the contour. A related measure, when integrated over either closed or open surfaces, reduces to known results for the charge associated with point defects (hedgehogs) or Skyrmions. We further define a tensor density, the disclination density tensor $\mathbf{D}$, from which the location of a disclination line can be determined. This tensor density has a dyadic decomposition near the line into its tangent and its rotation vector, allowing a convenient determination of both. The tensor $\mathbf{D}$may be non-zero in special configurations in which there are no defects (double-splay or double-twist configurations), and its behaviour there is provided. The special cases of Skyrmions and hedgehog defects are also examined, including the computation of their topological charge from $\mathbf{D}$. 

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2. Asymptotics of noncolliding q-exchangeable random walks

   https://doi.org/10.1088/1751-8121/acedda  

   Petrov, Leonid; Tikhonov, Mikhail (August 2023, Journal of Physics A: Mathematical and Theoretical)

   Abstract We consider a process of noncollidingq-exchangeable random walks on $\mathbb{Z}$making steps 0 (‘straight’) and −1 (‘down’). A single random walk is calledq-exchangeable if under an elementary transposition of the neighboring steps $(\text{down},\text{straight})\to (\text{straight},\text{down})$the probability of the trajectory is multiplied by a parameter $q\in (0,1)$. Our process ofmnoncollidingq-exchangeable random walks is obtained from the independentq-exchangeable walks via the Doob’sh-transform for a nonnegative eigenfunctionh(expressed via theq-Vandermonde product) with the eigenvalue less than 1. The system ofmwalks evolves in the presence of an absorbing wall at 0. The repulsion mechanism is theq-analogue of the Coulomb repulsion of random matrix eigenvalues undergoing Dyson Brownian motion. However, in our model, the particles are confined to the positive half-line and do not spread as Brownian motions or simple random walks. We show that the trajectory of the noncollidingq-exchangeable walks started from an arbitrary initial configuration forms a determinantal point process, and express its kernel in a double contour integral form. This kernel is obtained as a limit from the correlation kernel ofq-distributed random lozenge tilings of sawtooth polygons. In the limit as $m\to \mathrm{\infty }$, $q=e^{-\gamma /m}$withγ > 0 fixed, and under a suitable scaling of the initial data, we obtain a limit shape of our noncolliding walks and also show that their local statistics are governed by the incomplete beta kernel. The latter is a distinguished translation invariant ergodic extension of the two-dimensional discrete sine kernel. 

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3. Deciphering the sensitivity of urban canopy air temperature to anthropogenic heat flux with a forcing-feedback framework

   https://doi.org/10.1088/1748-9326/ace7e0  

   Wang, Linying; Sun, Ting; Zhou, Wenyu; Liu, Maofeng; Li, Dan (August 2023, Environmental Research Letters)

   Abstract The sensitivity of urban canopy air temperature ( $T_a$) to anthropogenic heat flux ( $Q_{AH}$) is known to vary with space and time, but the key factors controlling such spatiotemporal variabilities remain elusive. To quantify the contributions of different physical processes to the magnitude and variability of $\mathrm{\Delta }{T}_a/\mathrm{\Delta }{Q}_{AH}$(where $\mathrm{\Delta }$represents a change), we develop a forcing-feedback framework based on the energy budget of air within the urban canopy layer and apply it to diagnosing $\mathrm{\Delta }{T}_a/\mathrm{\Delta }{Q}_{AH}$simulated by the Community Land Model Urban over the contiguous United States (CONUS). In summer, the median $\mathrm{\Delta }{T}_a/\mathrm{\Delta }{Q}_{AH}$is around 0.01 $\text{K\hspace{0.17em}}{\left(\text{W\hspace{0.17em}}{\text{m}}^{-\text{2}}\right)}^{-1}$over the CONUS. Besides the direct effect of $Q_{AH}$on $T_a$, there are important feedbacks through changes in the surface temperature, the atmosphere–canopy air heat conductance ( $c_a$), and the surface–canopy air heat conductance. The positive and negative feedbacks nearly cancel each other out and $\mathrm{\Delta }{T}_a/\mathrm{\Delta }{Q}_{AH}$is mostly controlled by the direct effect in summer. In winter, $\mathrm{\Delta }{T}_a/\mathrm{\Delta }{Q}_{AH}$becomes stronger, with the median value increased by about 20% due to weakened negative feedback associated with $c_a$. The spatial and temporal (both seasonal and diurnal) variability of $\mathrm{\Delta }{T}_a/\mathrm{\Delta }{Q}_{AH}$as well as the nonlinear response of $\mathrm{\Delta }{T}_a$to $\mathrm{\Delta }{Q}_{AH}$are strongly related to the variability of $c_a$, highlighting the importance of correctly parameterizing convective heat transfer in urban canopy models. 

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4. Thermally generated spin current in the topological insulator Bi ₂ Se ₃

   https://doi.org/10.1126/sciadv.adi4540  

   Jain, Rakshit; Stanley, Max; Bose, Arnab; Richardella, Anthony R.; Zhang, Xiyue S.; Pillsbury, Timothy; Muller, David A.; Samarth, Nitin; Ralph, Daniel C. (December 2023, Science Advances)

   We present measurements of thermally generated transverse spin currents in the topological insulator Bi₂Se₃, thereby completing measurements of interconversions among the full triad of thermal gradients, charge currents, and spin currents. We accomplish this by comparing the spin Nernst magneto-thermopower to the spin Hall magnetoresistance for bilayers of Bi₂Se₃/CoFeB. We find that Bi₂Se₃does generate substantial thermally driven spin currents. A lower bound for the ratio of spin current density to thermal gradient is $\frac{J_s}{{\mathbf{\nabla }}_{\mathit{x}}\mathit{T}}$= (4.9 ± 0.9) × 10⁶ $\left(\frac{\hslash }{2e}\right)\frac{\mathbf{A}{\mathbf{m}}^{-2}}{\mathbf{K}\text{μ}{\mathbf{m}}^{-1}}$, and a lower bound for the magnitude of the spin Nernst ratio is −0.61 ± 0.11. The spin Nernst ratio for Bi₂Se₃is the largest among all materials measured to date, two to three times larger compared to previous measurements for the heavy metals Pt and W. Strong thermally generated spin currents in Bi₂Se₃can be understood via Mott relations to be due to an overall large spin Hall conductivity and its dependence on electron energy. 

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5. Universal parameter to describe the reduction of refraction effects in the scattering of absorbing spheres

   https://doi.org/10.1364/JOSAA.394401  

   Maughan, Justin_B; Sorensen, Christopher_M (August 2020, Journal of the Optical Society of America A)

   The scattered intensity from large spheres with a real part of the refractive index of $n=1.33,1.5,2.0$is investigated as the radius $R$and an imaginary part of the refractive index $\mathrm{\kappa <\#comment/>}$are varied. It is shown that the product of $\mathrm{\kappa <\#comment/>}$and the size parameter $kR$, $\mathrm{\kappa <\#comment/>}\text{kR}$, is a universal parameter describing the quenching of the refraction phenomenon of the scattered light: the refraction hump, the generalized rainbows, and the glory. The physical reason for this is that $\mathrm{\kappa <\#comment/>}\text{kR}$is the inverse of the relative skin depth of light penetration into the sphere, which is demonstrated by calculations of the internal fields that darken universally as $\mathrm{\kappa <\#comment/>}\text{kR}$increases. 

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