Topological Defect-Guided Regular Stacking of Focal Conic Domains in Hybrid-Aligned Smectic Liquid Crystal Shells

We study liquid crystal (LC) shells in hybrid configuration (director tangential to the inside but normal to the outside) as they slowly undergo a transition from a nematic (N) to a smectic-A (SmA) phase. Every shell has two antipodal +1 topological defects, at the thinnest and thickest points, respectively. On cooling from N to SmA, the symmetry axis connecting the defects gradually reorients from along gravity to perpendicular to it, reversibly and continuously, if the LC and aqueous phase are density matched at the N-SmA transition. This suggests reduced density near the defects—reflecting a local reduction in order—under the strong confinement with antagonistic boundary conditions. In the SmA phase, a regular array of focal conic domains (FCDs) develops, templated in position and orientation by the +1 defect at the thinnest point. Around this defect, a single complete toroidal FCD always develops, surrounded by incomplete FCDs. In contrast to similar FCD arrangements on flat aqueous interfaces, this is a stable situation, since the two +1 defects are required by the spherical topology. Our results demonstrate how the topological defects of LC shells can be used to template complex self-organized structures. With a suitable adaption of the LC chemistry, shells might serve as a basis for producing solid particles with complex yet highly regular morphologies.

Curvature Potential Unveiled Topological Defect Attractors

We consider the theoretical and positional assembling of topological defects (TDs) in effectively two-dimensional nematic liquid crystal films. We use a phenomenological Helfrich–Landau–de Gennes-type mesoscopic model in which geometric shapes and nematic orientational order are expressed in terms of a curvature tensor field and a nematic tensor order parameter field. Extrinsic, intrinsic, and total curvature potentials are introduced using the parallel transport concept. These potentials reveal curvature seeded TD attractors. To test ground configurations, we used axially symmetric nematic films exhibiting spherical topology.

Deep Learning on the sphere for weather/climate applications

<p>Deep Learning (DL) has the potential to revolutionize numerical weather predictions (NWP) and climate simulations by improving model components and reducing computing time, which could then be used to increase the resolution or the number of simulations. Unfortunately, major progress has been hindered by difficulties in interfacing DL with conventional models because of i) programming language barriers, ii) difficulties in reaching stable online coupling with models, and iii) the inability to exploit the horizontal spatial information as classical convolutional neural networks can’t be used on spherical unstructured grids.</p><p>We present a solution to perform spatial convolutions directly on the unstructured grids of NWP models. Our convolution and pooling operations work on any pixelization of the sphere (e.g., Gauss-Legendre, icosahedral, cubed-sphere) provided a mesh or the pixel’s locations. Moreover, our solution allows mixing data from different grids and scales linearly with the number of pixels, allowing it to ingest millions of inputs from 3D spherical fields.</p><p>We show that a proper treatment of the spherical topology and geometry of the Earth (as opposed to a projection to the plane, cylinder, or cube) i) yields geometric constraints that provide generalization guarantees (i.e., the learned function does not depend on its localization on the Earth), and ii) induces prior biases that facilitate learning. We demonstrate that doing so improves prediction performance at no computational overhead for data-driven weather forecasting. We trained autoregressive ResUNets on five spherical samplings, covering those adopted by the major meteorological centers.</p><p>We believe that the proposed solution can find immediate use for post-processing (e.g., bias correction and downscaling), model error corrections, linear solvers pre-conditioning, model components emulation, sub-grid parameterizations, and many more applications. To that end, we provide open-source and easy-to-use code accompanied by tutorials.</p>

Topological Born–Infeld charged black holes in Einsteinian cubic gravity

In this paper, we study four-dimensional topological black hole solutions of Einsteinian cubic gravity in the presence of nonlinear Born–Infeld electrodynamics and a bare cosmological constant. First, we obtain the field equations which govern our solutions. Employing Abbott–Deser–Tekin and Gauss formulas, we present the expressions of conserved quantities, namely total mass and total charge of our topological black solutions. We disclose the conditions under which the model is unitary and perturbatively free of ghosts with asymptotically (A)dS and flat solutions. We find that, for vanishing bare cosmological constant, the model is unitary just for asymptotically flat solutions, which only allow horizons with spherical topology. We compute the temperature for these solutions and show that it always has a maximum value, which decreases as the values of charge, nonlinear coupling or cubic coupling grows. Next, we calculate the entropy and electric potential. We show that the first law of thermodynamics is satisfied for spherical asymptotically flat solutions. Finally, we peruse the effects of model parameters on thermal stability of these solutions in both canonical and grand canonical ensembles.

Ruppeiner geometry, phase transitions and microstructures of black holes in massive gravity

Using the new normalized thermodynamic scalar curvature, we investigate the microstructures and phase transitions of black holes in massive gravity for horizons of various topologies. We find that the graviton mass enhances the repulsive interactions of small black holes and weakens the attractive interactions of large black holes, with possibility of new repulsive regions for microstructures in phase space. In addition, the repulsive interactions of small black hole are strong for spherical topology, followed by flat and hyperbolic topology; while, the attractive interactions of large black hole are strong for hyperbolic topology, followed by flat and weakest for spherical topology.

Static black holes without spatial isometries: From AdS multipoles to electrovacuum scalarization

We review recent results on the existence of static black holes (BHs) without spatial isometries in four spacetime dimensions and propose a general framework for their study. These configurations are regular on and outside a horizon of spherical topology. Two different mechanisms allowing for their existence are identified. The first one relies on the presence of a solitonic limit of the BHs; when the solitons have no spatial isometries, the BHs, being a nonlinear bound state between the solitons and a horizon, inherit this property. The second one is related to BH scalarization, and the existence of zero modes of the scalar field without isometries around a spherical horizon. When the zero modes have no spatial isometries, the back-reaction of their nonlinear continuation makes the scalarized BHs inherit the absence of spatial continuous symmetries. A number of general features of the solutions are discussed together with possible generalizations.

Formation of dynamically transversely trapping surfaces and the stretched hoop conjecture

A dynamically transversely trapping surface (DTTS) is a new concept for an extension of a photon sphere that appropriately represents a strong gravity region and has close analogy with a trapped surface. We study formation of a marginally DTTS in time-symmetric, conformally flat initial data with two black holes, with a spindle-shaped source, and with a ring-shaped source, and clarify that $\mathcal{C}\lesssim 6\pi GM$ describes the condition for the DTTS formation well, where $\mathcal{C}$ is the circumference and $M$ is the mass of the system. This indicates that an understanding analogous to the hoop conjecture for the horizon formation is possible. Exploring the ring system further, we find configurations where a marginally DTTS with the torus topology forms inside a marginally DTTS with the spherical topology, without being hidden by an apparent horizon. There also exist configurations where a marginally trapped surface with the torus topology forms inside a marginally trapped surface with the spherical topology, showing a further similarity between DTTSs and trapped surfaces.

Systolic Aspects of Black Hole Entropy

We attempt to provide a mesoscopic treatment of the origin of black hole entropy in (3 + 1)-dimensional spacetimes. We ascribe this entropy to the non-trivial topology of the space-like sections Σ of the horizon. This is not forbidden by topological censorship, since all the known energy inequalities needed to prove the spherical topology of Σ are violated in quantum theory. We choose the systoles of Σ to encode its complexity, which gives rise to the black hole entropy. We present hand-waving reasons why the entropy of the black hole can be considered as a function of the volume entropy of Σ . We focus on the limiting case of Σ having a large genus.