IA Scholar Query: Simple curl-curl-conforming finite elements in two dimensions.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgThu, 17 Nov 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440An EMA-conserving, pressure-robust and Re-semi-robust reconstruction method for incompressible Navier-Stokes simulations
https://scholar.archive.org/work/yfb37w2tzjfofeubqeg4br46iy
Proper EMA-balance (balance of kinetic energy, linear momentum and angular momentum), pressure-robustness and $Re$-semi-robustness ($Re$: Reynolds number) are three important properties of Navier--Stokes simulations with exactly divergence-free elements. This EMA-balance makes a method conserve kinetic energy, linear momentum and angular momentum in an appropriate sense; pressure-robustness means that the velocity errors are independent of the pressure; $Re$-semi-robustness means that the constants appearing in the error bounds of kinetic and dissipation energies do not explicitly depend on inverse powers of the viscosity. In this paper, based on the pressure-robust reconstruction framework and certain suggested reconstruction operators in [A. Linke and C. Merdon, {\it Comput. Methods Appl. Mech. Engrg.} 311 (2016), 304-326], we propose a reconstruction method for a class of non-divergence-free simplicial elements which admits almost all the above properties. The only exception is the energy balance, where kinetic energy should be replaced by a suitably redefined discrete energy. The lowest order case is the Bernardi--Raugel element on general shape-regular meshes. Some numerical comparisons with exactly divergence-free methods, the original pressure-robust reconstruction methods and the EMAC method are provided to confirm our theoretical results.Xu Li, Hongxing Ruiwork_yfb37w2tzjfofeubqeg4br46iyThu, 17 Nov 2022 00:00:00 GMTTF1 Snowmass Report: Quantum gravity, string theory, and black holes
https://scholar.archive.org/work/ngcj2sx4qnbflikras5jifza4q
We give an overview of the field of quantum gravity, string theory and black holes summarizing various white papers in this subject that were submitted as part of the Snowmass process.Daniel Harlow, Shamit Kachru, Juan Maldacena, Ibrahima Bah, Mike Blake, Raphael Bousso, Mirjam Cvetic, Xi Dong, Netta Engelhardt, Tom Faulkner, Raphael Flauger, Dan Freed, Victor Gorbenko, Yingfei Gu, Jim Halverson, Tom Hartman, Sean Hartnoll, Andreas Karch, Hong Liu, Andy Lucas, Emil Martinec, Liam McAllister, Greg Moore, Nikita Nekrasov, Sabrina Pasterski, Monica Pate, Ana-Maria Raclariu, Krisha Rajagopal, Shlomo Razamat, Steve Shenker, Sakura Schafer-Nameki, Gary Shiu, Eva Silverstein, Douglas Stanford, Brian Swingle, Wati Taylor, Nicholas Warner, Beni Yoshidawork_ngcj2sx4qnbflikras5jifza4qThu, 17 Nov 2022 00:00:00 GMTComputational lower bounds of the Maxwell eigenvalues
https://scholar.archive.org/work/gs6pb5xp2zgwxnwks2azmk6k4i
A method to compute guaranteed lower bounds to the eigenvalues of the Maxwell system in two or three space dimensions is proposed as a generalization of the method of Liu and Oishi [SIAM J. Numer. Anal., 51, 2013] for the Laplace operator. The main tool is the computation of an explicit upper bound to the error of the Galerkin projection. The error is split in two parts: one part is controlled by a hypercircle principle and an auxiliary eigenvalue problem. The second part requires a perturbation argument for the right-hand side replaced by a suitable piecewise polynomial. The latter error is controlled through the use of the commuting quasi-interpolation by Falk--Winther and computational bounds on its stability constant. This situation is different from the Laplace operator where such a perturbation is easily controlled through local Poincar\'e inequalities. The practical viability of the approach is demonstrated in test cases for two and three space dimensions.Dietmar Gallistl, Vladislav Olkhovskiywork_gs6pb5xp2zgwxnwks2azmk6k4iThu, 17 Nov 2022 00:00:00 GMTHilbert Series, the Higgs Mechanism, and HEFT
https://scholar.archive.org/work/ryacmjtn7jehjfdbrc2uk2nuoa
We expand Hilbert series technologies in effective field theory for the inclusion of massive particles, enabling, among other things, the enumeration of operator bases for non-linearly realized gauge theories. We find that the Higgs mechanism is manifest at the level of the Hilbert series, as expected for the partition function of an S-matrix that is subject to the Goldstone equivalence theorem. In addition to massive vectors, we detail how other massive, spinning particles can be studied with Hilbert series; in particular, we spell out the ingredients for massive gravity in general spacetime dimensions. Further methodology is introduced to enable Hilbert series to capture the effect of spurion fields acquiring vevs. We apply the techniques to the Higgs Effective Field Theory (HEFT), providing a systematic enumeration of its operator basis. This is achieved both from a direct and a custodial symmetry spurion-based approach; we compare and contrast the two approaches, and our results to those appearing in previous literature.Lukáš Gráf, Brian Henning, Xiaochuan Lu, Tom Melia, Hitoshi Murayamawork_ryacmjtn7jehjfdbrc2uk2nuoaFri, 11 Nov 2022 00:00:00 GMTTwo conjectures on the Stokes complex in three dimensions on Freudenthal meshes
https://scholar.archive.org/work/nrww2orqmncq5h2r7ka2wmqbmy
In recent years a great deal of attention has been paid to discretizations of the incompressible Stokes equations that exactly preserve the incompressibility constraint. These are of substantial interest because these discretizations are pressure-robust, i.e. the error estimates for the velocity do not depend on the error in the pressure. Similar considerations arise in nearly incompressible linear elastic solids. Conforming discretizations with this property are now well understood in two dimensions, but remain poorly understood in three dimensions. In this work we state two conjectures on this subject. The first is that the Scott-Vogelius element pair is inf-sup stable on uniform meshes for velocity degree k ≥ 4; the best result available in the literature is for k ≥ 6. The second is that there exists a stable space decomposition of the kernel of the divergence for k ≥ 5. We present numerical evidence supporting our conjectures.Patrick E. Farrell, Lawrence Mitchell, L. Ridgway Scottwork_nrww2orqmncq5h2r7ka2wmqbmyThu, 10 Nov 2022 00:00:00 GMTAnalysis of curvature approximations via covariant curl and incompatibility for Regge metrics
https://scholar.archive.org/work/mozax3ev5bazxdqmymy7bunyvq
The metric tensor of a Riemannian manifold can be approximated using Regge finite elements and such approximations can be used to compute approximations to the Gauss curvature and the Levi-Civita connection of the manifold. It is shown that certain Regge approximations yield curvature and connection approximations that converge at a higher rate than previously known. The analysis is based on covariant (distributional) curl and incompatibility operators which can be applied to piecewise smooth matrix fields whose tangential-tangential component is continuous across element interfaces. Using the properties of the canonical interpolant of the Regge space, we obtain superconvergence of approximations of these covariant operators. Numerical experiments further illustrate the results from the error analysis.Jay Gopalakrishnan, Michael Neunteufel, Joachim Schöberl, Max Wardetzkywork_mozax3ev5bazxdqmymy7bunyvqThu, 10 Nov 2022 00:00:00 GMTFlows of geometric structures
https://scholar.archive.org/work/nfwy2cvvbrfbpkvnomokvvhwgm
We develop an abstract theory of flows of geometric H-structures, i.e., flows of tensor fields defining H-reductions of the frame bundle, for a closed and connected subgroup H ⊂SO(n), on any connected and oriented n-manifold with sufficient topology to admit such structures. The first part of the article sets up a unifying theoretical framework for deformations of H-structures, by way of the natural infinitesimal action of GL(n,ℝ) on tensors combined with various bundle decompositions induced by H-structures. We compute evolution equations for the intrinsic torsion under general flows of H-structures and, as applications, we obtain general Bianchi-type identities for H-structures, and, for closed manifolds, a general first variation formula for the L^2-Dirichlet energy functional ℰ on the space of H-structures. We then specialise the theory to the negative gradient flow of ℰ over isometric H-structures, i.e., their harmonic flow. The core result is an almost monotonocity formula along the flow for a scale-invariant localised energy, similar to the classical formulae by Chen–Struwe Struwe1988,Struwe1989 for the harmonic map heat flow. This yields an ϵ-regularity theorem and an energy gap result for harmonic structures, as well as long-time existence for the flow under small initial energy, with respect to the L^∞-norm of initial torsion, in the spirit of Chen–Ding . Moreover, below a certain energy level, the absence of a torsion-free isometric H-structure in the initial homotopy class imposes the formation of finite-time singularities. These seemingly contrasting statements are illustrated by examples on flat n-tori, so long as π_n(SO(n)/H)≠{1}; e.g. when n=7 and H= G_2, or n=8 and H=Spin(7).Daniel Fadel, Eric Loubeau, Andrés J. Moreno, Henrique N. Sá Earpwork_nfwy2cvvbrfbpkvnomokvvhwgmWed, 09 Nov 2022 00:00:00 GMTHigh-density Flexible Neurophotonic Implants
https://scholar.archive.org/work/xvsypd734zburnm467llfgcfde
From research to clinical neuroscience, high-resolution and minimally invasive neural interfaces are needed to study and treat brain function and dysfunction. Recently, optical techniques such as optogenetics and functional fluorescent imaging have enabled unprecedented throughput and specificity for interrogating neural circuits. However, the scattering and absorption of light in the brain tissue limits the resolution and depth of penetration of light-based methods. Therefore, implantable devices are used to deliver or collect light deep in the tissue with high spatial resolution. Currently, implantable optics are typically composed of rigid materials including silicon or silicon dioxide. These stiff materials have a significant mechanical mismatch with the soft brain tissue, triggering tissue damage and scar tissue formation over time. To alleviate these issues and enable minimally invasive chronic optical implants, they must be compact and flexible. This thesis introduces two novel microfabricated device architectures to address this outstanding need in the field. The first, Parylene photonics, uses flexible biocompatible materials – Parylene C and polydimethylsiloxane (PDMS) – to form a novel photonic waveguide platform to passively guide light into or out of the tissue. The second, GaN-on-Parylene micro-light-emitting diodes (µLEDs), uses integrated light sources to generate light directly in the tissue. Due to the flexible polymer material composition and micrometer-scale structures implemented using a novel microfabrication process in both architectures, the devices can be made compact and flexible. In addition, recording electrodes for electrophysiology readout are monolithically integrated to allow for full read-write optogenetic stimulation and electrical recording capabilities in a flexible material platform. I will discuss the design, simulation, fabrication, characterization, and biological demonstration of these novel devices. I present a complete course of work from concept to application for [...]Jay Reddywork_xvsypd734zburnm467llfgcfdeTue, 08 Nov 2022 00:00:00 GMTTurbulence as Clebsch Confinement
https://scholar.archive.org/work/qrlmjshh65cfddfvw4x3lbhb44
We argue that in the strong turbulence phase, as opposed to the weak one, the Clebsch variables compactify to the sphere S_2 and are not observable as wave excitations. Various topologically nontrivial configurations of this confined Clebsch field are responsible for vortex sheets. Stability equations (CVS) for closed vortex surfaces (bubbles of Clebsch field) are derived and investigated. The exact non-compact solution for the stable vortex sheet family is presented. Compact solutions are proven not to exist by De Lellis and Brué. Asymptotic conservation of anomalous dissipation on stable vortex surfaces in the turbulent limit is discovered. We derive an exact formula for this anomalous dissipation as a surface integral of the square of velocity gap times the square root of minus local normal strain. Topologically stable time-dependent solutions, which we call Kelvinons, are introduced. They have a conserved velocity circulation around static loop; this makes them responsible for asymptotic PDF tails of velocity circulation, perfectly matching numerical simulations. The loop equation for circulation PDF as functional of the loop shape is derived and studied. This equation is exactly equivalent to the Schrödinger equation in loop space, with viscosity ν playing the role of Planck's constant. This equivalence opens the way for direct numerical simulation of turbulence on quantum computers. Kelvinons are fixed points of the loop equation at turbulent limit ν→ 0. Area law and the asymptotic scaling law for mean circulation at a large area are derived. The representation of the solution of the loop equation in terms of a singular stochastic equation for momentum loop trajectory is presented.Alexander Migdalwork_qrlmjshh65cfddfvw4x3lbhb44Mon, 07 Nov 2022 00:00:00 GMTChanging perspectives: Formulations of identity in contemporary Australian literature
https://scholar.archive.org/work/o6mk3h52xrcubl5gf6kdaibdqi
Questions of identity occupy a central place in the history of the development of Australian literature and its critical construction and reception. The notions of identity appealed to in the various stages of this development have been closely imbricated with prevailing cultural and critical assumptions and practices. The model of identity that was appealed to in earlier periods of Australian literature and its academic criticism was understandably circumscribed by the Anglo-centric prescriptions of the Colonial Convict period, embellished but not significantly changed by the influence of the Bush Pioneers and a growing Nationalist sentiment enhanced by the spirit of the first world war Anzacs. While, as with all identity models, this one suffered its own ambiguities and slippages, it did successfully exercise a hegemony, reinforced by the then dominant academic practices, that largely excluded the identity experiences of Indigenous people, non-white immigrants, women and those whose sexual orientations lay outside of the parameters of heteronormativity. The Identities that have subsequently been articulated by such previously excluded groups and taken up by those within the academy influenced by developments in postcolonial, feminist, poststructural and postmodern (including Queer) theory have effectively functioned to dismantle the hegemony exerted by earlier unitary and reductive notions of Australian identity. Previously neglected areas of Australian writing such as Indigenous, multicultural and youth literature, as representations of minority identities have articulated often oppositional conceptions of identity to those formulated within the former orthodoxy. Such texts, most particularly those more recent ones which engage with radical rearticulations of sexual identity, have increasingly moved towards fluid conceptions of identity which ultimately serve to pose the question of the usefulness of the unqualified notion The Australian Identity as a meaningful category of analysis for the literature now bein [...]Ayesha E Hallwork_o6mk3h52xrcubl5gf6kdaibdqiWed, 02 Nov 2022 00:00:00 GMTLow energy models of string theory
https://scholar.archive.org/work/regqbziojzdg3hczdeaildhn2u
String theory is the prime candidate for the theory of everything. However, it must be defined in ten dimensions to be consistent. To get 4D physics, the 6 other dimensions should be curled up in a small compact manifold, this procedure is called string compactification. In this review, we will review different compactification schemes proving that in absence of flux, the compact manifold must be a Calabi-Yau manifold. Then, we review compactifications with flux using generalized complex geometry. We then discuss some applications in cosmology like the swampland project and the cosmological models derived from it. We then discuss non relativistic string theories and introduce a toroidal compactifications for such theories. Finally, we discuss some open questions in the field.Poula Tadros, Iiro Viljawork_regqbziojzdg3hczdeaildhn2uTue, 01 Nov 2022 00:00:00 GMTBlack holes and solution generating techniques
https://scholar.archive.org/work/keeaxas4fjfg3gujntcg4lgdpy
Multi-black hole solutions play a relevant role both from the theoretical and the phenomenological point of view. In this Thesis, we construct some regular multi-black hole spacetimes in pure Einstein's General Relativity with the aid of solution generating techniques. We begin with a perspective on the history of solution generating techniques, and then we explain in detail the Ernst formalism and the inverse scattering method. These are the techniques that are applied in the rest of the Thesis. Subsequently, we construct multi-black hole solutions embedded in an external gravitational field: it is possible to obtain an equilibrium configuration in many interesting cases, like a collection of collinear static black holes or a chain of accelerating black holes, by choosing appropriately the multipole parameters of the field. Then, we consider the expanding bubbles of nothing as a background for multi-black hole and black ring solutions. The expanding behaviour of the bubbles provides the force necessary to balance the gravitational attraction among the black holes, and hence to reach the equilibrium. Finally, we construct a solution that represents a black hole embedded in a "swirling" universe, which describes a spacetime whirlpool. Moreover, we discuss the possibility of implementing the swirling background in order to enforce the spin-spin configuration, and reach an equilibrium configuration in a double-Kerr spacetime.Adriano Viganòwork_keeaxas4fjfg3gujntcg4lgdpyTue, 01 Nov 2022 00:00:00 GMTHyperbolic 3-manifolds with boundary of polyhedral type
https://scholar.archive.org/work/ofzkokj335bnpogibkyzj6uwom
Let M be a compact orientable 3-manifold with hyperbolizable interior and non-empty boundary such that all boundary components have genii at least 2. We study an Alexandrov-Weyl-type problem for convex hyperbolic cone-metrics on ∂ M. We consider a class of hyperbolic metrics on M with convex boundary, which we call bent metrics, and which naturally generalize hyperbolic metrics on M with convex polyhedral boundary. We show that for each convex hyperbolic cone-metric d on ∂ M, with few simple exceptions, there exists a bent metric on M such that the induced intrinsic metric on ∂ M is d. Next, we prove that if a bent realization is what we call controllably polyhedral, then it is unique up to isotopy. We exhibit a large subclass of hyperbolic cone-metrics on ∂ M, called balanced, which is open and dense among all convex hyperbolic cone-metrics in the sense of Lipschitz topology, and for which we show that their bent realizations are controllably polyhedral. We additionally prove that any convex realization of a convex hyperbolic cone-metric on ∂ M is bent. Finally, we deduce that there exists an open subset of the space of convex cocompact metrics on the interior of M, including all metrics with polyhedral convex cores, such that the metrics in this subset are (1) globally rigid with respect to the induced intrinsic metrics on the boundaries of their convex cores; (2) infinitesimally rigid with respect to their bending laminations. This gives partial progress towards conjectures of W. Thurston.Roman Prosanovwork_ofzkokj335bnpogibkyzj6uwomMon, 31 Oct 2022 00:00:00 GMTHybrid multi-fluid-particle simulations of the cosmic neutrino background
https://scholar.archive.org/work/3h5lvtczcvcjhojrn63zkuygme
Simulation of the cosmic clustering of massive neutrinos is a daunting task, due both to their large velocity dispersion and to their weak clustering power becoming swamped by Poisson shot noise. We present a new approach, the multi-fluid hybrid-neutrino simulation, which partitions the neutrino population into multiple flows, each of which is characterised by its initial momentum and treated as a separate fluid. These fluid flows respond initially linearly to nonlinear perturbations in the cold matter, but slowest flows are later converted to a particle realisation should their clustering power exceed some threshold. After outlining the multi-fluid description of neutrinos, we study the conversion of the individual flows into particles, in order to quantify transient errors, as well as to determine a set of criteria for particle conversion. Assembling our results into a total neutrino power spectrum, we demonstrate that our multi-fluid hybrid-neutrino simulation is convergent to <3% if conversion happens at z=19 and agrees with more expensive simulations in the literature for neutrino fractions as high as Ω_ν h^2 = 0.005. Moreover, our hybrid-neutrino approach retains fine-grained information about the neutrinos' momentum distribution. However, the momentum resolution is currently limited by free-streaming transients excited by missing information in the neutrino particle initialisation procedure, which restricts the particle conversion to z ≳ 19 if percent-level resolution is desired.Joe Zhiyu Chen, Markus R. Mosbech, Amol Upadhye, Yvonne Y. Y. Wongwork_3h5lvtczcvcjhojrn63zkuygmeFri, 28 Oct 2022 00:00:00 GMTMesh Refinement for Anisotropic Diffusion in Magnetized Plasmas
https://scholar.archive.org/work/edgqxkng3fgc5d3nhi3pqyfbmu
Highly accurate simulation of plasma transport is needed for the successful design and operation of magnetically confined fusion reactors. Unfortunately, the extreme anisotropy present in magnetized plasmas results in thin boundary layers that are expensive to resolve. This work investigates how mesh refinement strategies might reduce that expense to allow for more efficient simulation. It is first verified that higher order discretization only realizes the proper rate of convergence once the mesh resolves the thin boundary layer, motivating the focusing of refinement on the boundary layer. Three mesh refinement strategies are investigated: one that focuses the refinement across the layer by using rectangular elements with a ratio equal to the boundary layer width, one that allows for exponential growth in mesh spacing away from the layer, and one adaptive strategy utilizing the established Zienkiewicz and Zhu error estimator. Across 4 two-dimensional test cases with high anisotropy, the adaptive mesh refinement strategy consistently achieves the same accuracy as uniform refinement using orders of magnitude less degrees of freedom. In the test case where the magnetic field is aligned with the mesh, the other refinement strategies also show substantial improvement in efficiency. This work also includes a discussion generalizing the results to larger magnetic anisotropy ratios and to three-dimensional problems. It is shown that isotropic mesh refinement requires degrees of freedom on the order of either the layer width (2D) or the square of the layer width (3D), whereas anisotropic refinement requires a number on the order of the log of layer width for all dimensions. It is also shown that the number of conjugate gradient iterations scales as a power of layer width when preconditioned with algebraic multigrid, whereas the number is independent of layer width when preconditioned with ILU.Christopher J. Vogl and Ilon Joseph and Milan Holecwork_edgqxkng3fgc5d3nhi3pqyfbmuFri, 28 Oct 2022 00:00:00 GMTEnd-to-end GPU acceleration of low-order-refined preconditioning for high-order finite element discretizations
https://scholar.archive.org/work/nqxvjwwznfcidoxarlvy52tyky
In this paper, we present algorithms and implementations for the end-to-end GPU acceleration of matrix-free low-order-refined preconditioning of high-order finite element problems. The methods described here allow for the construction of effective preconditioners for high-order problems with optimal memory usage and computational complexity. The preconditioners are based on the construction of a spectrally equivalent low-order discretization on a refined mesh, which is then amenable to, for example, algebraic multigrid preconditioning. The constants of equivalence are independent of mesh size and polynomial degree. For vector finite element problems in H( curl) and H( div) (e.g. for electromagnetic or radiation diffusion problems) a specially constructed interpolation-histopolation basis is used to ensure fast convergence. Detailed performance studies are carried out to analyze the efficiency of the GPU algorithms. The kernel throughput of each of the main algorithmic components is measured, and the strong and weak parallel scalability of the methods is demonstrated. The different relative weighting and significance of the algorithmic components on GPUs and CPUs is discussed. Results on problems involving adaptively refined nonconforming meshes are shown, and the use of the preconditioners on a large-scale magnetic diffusion problem using all spaces of the finite element de Rham complex is illustrated.Will Pazner and Tzanio Kolev and Jean-Sylvain Camierwork_nqxvjwwznfcidoxarlvy52tykyFri, 21 Oct 2022 00:00:00 GMTThe geometric data on the boundary of convex subsets of hyperbolic manifolds
https://scholar.archive.org/work/a37kfrrkpjcjbh4tz7u3qmvxay
Let N be a geodesically convex subset in a convex co-compact hyperbolic manifold M with incompressible boundary. We assume that each boundary component of N is either a boundary component of ∂_∞ M, or a smooth, locally convex surface in M. We show that N is uniquely determined by the boundary data defined by the conformal structure on the boundary components at infinity, and by either the induced metric or the third fundamental form on the boundary components which are locally convex surfaces. We also describe the possible boundary data. This provides an extension of both the hyperbolic Weyl problem and the Ahlfors-Bers Theorem. Using this statement for quasifuchsian manifolds, we obtain existence results for similar questions for convex domains Ω⊂^3 which meets the boundary at infinity ∂_∞^3 either along a quasicircle or along a quasidisk. The boundary data then includes either the induced metric or the third fundamental form in ^3, but also an additional "gluing" data between different components of the boundary, either in ^3 or in ∂_∞^3.Qiyu Chen, Jean-Marc Schlenkerwork_a37kfrrkpjcjbh4tz7u3qmvxayFri, 21 Oct 2022 00:00:00 GMTAsymptotic models of acoustic resonators and Leidenfrost flows
https://scholar.archive.org/work/nn5lsqn575a3hhpgkssbtv3whu
In this thesis, we develop and analyse mathematical models of acoustic resonators and Leidenfrost flows through the use of scaling arguments and asymptotic methods. Part I is devoted to the study of acoustic resonators, particularly narrow slits and Helmholtz resonators. A novel feature of our modelling is that dissipative effects are included starting from the fundamental equations of thermoviscous acoustics. In the case of Helmholtz resonators, we begin by analysing the neck region, whose geometry is that of a cylindrical orifice in a rigid plate. We use the method of matched asymptotic expansions to derive analytical formulae for the acoustic impedance of the orifice. Building on this, we present an asymptotic model of a Helmholtz resonator embedded in a wall, as well as 'metasurfaces' formed of arrays of such resonators. Following a similar approach, we also investigate the problem of extraordinary wave transmission through narrow slits in an infinite plate, focusing on the effects of dissipative boundary layers. Part II is devoted to the study of Leidenfrost flows. We are mainly motivated by recent experiments showing that Leidenfrost drops levitated above a solid substrate can exhibit symmetry-breaking spontaneous dynamics. Focusing on drops much smaller than the capillary length, we begin by developing a simplified model of a two-dimensional drop. Our model couples the equations of motion of the drop, which flows like a rigid wheel, and the lubricating flow in the vapour film. In addition to predicting that a stationary drop is unstable above a critical radius, the model also rationalises several experimental observations. We then extend our model to three dimensions and compare linear stability predictions with existing experimental data. Last, we asymptotically investigate the morphology of the vapour film beneath a stationary spherical particle levitating above a liquid bath, describing the evolution of that morphology with particle size.Rodolfo Brandao Macena Lira, Ory Schnitzerwork_nn5lsqn575a3hhpgkssbtv3whuFri, 21 Oct 2022 00:00:00 GMTМеждународная конференция по геометрическому анализу, посвящённая памяти академика Ю.Г. Решетняка, 23–29 октября 2022 г. Тезисы докладов
https://scholar.archive.org/work/f6st4orw5fbjdez56f65ce5q2y
Этот выпуск содержит тезисы некоторых докладов, представленных на Международной конференции по геометрическому анализу, посвящённой памяти академика Ю.Г. Решетняка (23–29 октября 2022 года). Темы докладов относятся к современным направлениям в геометрии, теории управления и анализа, а также к приложениям методов метрической геометрии и анализа в смежных областях математики и прикладных задачах. Конференция организована Математическим центром в Академгородке, номер соглашения № 075-15-2022-281 от 05.04.2022.С. Г. Басалаевwork_f6st4orw5fbjdez56f65ce5q2yWed, 19 Oct 2022 00:00:00 GMTNaked Singularities for the Einstein Vacuum Equations: The Exterior Solution
https://scholar.archive.org/work/2fcgn3u4a5dcdfhi7s3eadnori
In this work we initiate the mathematical study of naked singularities for the Einstein vacuum equations in 3+1 dimensions by constructing solutions which correspond to the exterior region of a naked singularity. A key element is our introduction of a new type of self-similarity for the Einstein vacuum equations. Connected to this is a new geometric twisting phenomenon which plays the leading role in singularity formation. Prior to this work, the only known examples of naked singularities were the solutions constructed by Christodoulou for the spherically symmetric Einstein-scalar-field system, as well as other solutions explored numerically for either the spherically symmetric Einstein equations coupled to suitable matter models or for the Einstein equations in higher dimensions.Igor Rodnianski, Yakov Shlapentokh-Rothmanwork_2fcgn3u4a5dcdfhi7s3eadnoriWed, 19 Oct 2022 00:00:00 GMT