Tootfinder

Reconstructing a pseudotree from the distance matrix of its boundary
Jos\'e C\'aceres, Ignacio M. Pelayo
https://arxiv.org/abs/2404.04039 https://<…

Reconstructing a pseudotree from the distance matrix of its boundary
A vertex $v$ of a connected graph $G$ is said to be a boundary vertex of $G$ if for some other vertex $u$ of $G$, no neighbor of $v$ is further away from $u$ than $v$. The boundary $\partial(G)$ of $G$ is the set of all of its boundary vertices. The distance matrix $\hat{D}_G$ of the boundary of a graph $G$ is the square matrix of order $κ$, being $κ$ the order of $\partial(G)$, such that for every $i,j\in \partial(G)$, $[\hat{D}_G]_{ij}=d_G(i,j)$. Given a square matrix $\hat{B}$ of order $κ…

This https://arxiv.org/abs/2403.18594 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Boundary scattering in massless $AdS_3$
We study the boundary integrability problem of the massless sector of $AdS_3 \times S^3 \times T^4 $ string theory. Exploiting the difference-form of the massless scattering theory, we find a very simple and exhaustive list of reflection matrices for all the possible boundary coideal subalgebras - singlet and vector representations, right and left boundary - and check basic properties of our solutions, primarily the boundary Yang-Baxter equation, for all possible combinations of scattering part…

Subgroups arising from connected components in the Morse boundary
Annette Karrer, Babak Miraftab, Stefanie Zbinden
https://arxiv.org/abs/2403.03939 https:/…

Subgroups arising from connected components in the Morse boundary
We study connected components of the Morse boundary and their stabilisers. We introduce the notion of point-convergence and show that if the set of non-singleton connected components of the Morse boundary of a finitely generated group $G$ is point-convergent, then every non-singleton connected component is the (relative) Morse boundary of its stabiliser. The above property only depends on the topology of the Morse boundary and hence is invariant under quasi-isometry. This shows that the topolog…

Weakening the effect of boundaries: `diffusion-free' boundary conditions as a `do least harm' alternative to Neumann
Yufeng Lin, Rich Kerswell
https://arxiv.org/abs/2405.02874

Weakening the effect of boundaries: `diffusion-free' boundary conditions as a `do least harm' alternative to Neumann
In this note, we discuss a poorly known alternative boundary condition to the usual Neumann or `stress-free' boundary condition typically used to weaken boundary layers when diffusion is present but very small. These `diffusion-free' boundary conditions were first developed (as far as the authors know) in 1995 (Sureshkumar & Beris, J. Non-Newtonian Fluid Mech., vol 60, 53-80, 1995) in viscoelastic flow modelling but are worthy of general consideration in other research areas. To illustrate thei…

This https://arxiv.org/abs/2206.02105 has been replaced.
link: https://scholar.google.com/scholar?q=a

Estimating the Morse index of free boundary minimal hypersurfaces through covering arguments
Given a compact Riemannian manifold, of dimension between 3 and 7, with boundary, we adapt Song's method in Song (2023) to the free boundary case to show that the Morse index of a free boundary minimal hypersurface grows linearly with the sum of its Betti numbers, where the constant of growth depends on the area of the free boundary minimal hypersurface in question.

Connecting essential triangulations I: via 2-3 and 0-2 moves
Tejas Kalelkar, Saul Schleimer, Henry Segerman
https://arxiv.org/abs/2405.03539 https://

Connecting essential triangulations I: via 2-3 and 0-2 moves
Suppose that $M$ is a compact, connected three-manifold with boundary. We show that if the universal cover has infinitely many boundary components then $M$ has an ideal triangulation which is essential: no edge can be homotoped into the boundary. Under the same hypotheses, we show that the set of essential triangulations of $M$ is connected via 2-3, 3-2, 0-2, and 2-0 moves. The above results are special cases of our general theory. We introduce $L$-essential triangulations: boundary component…

Regularity near the fixed boundary for transmission systems
Alessio Figalli, Somayeh Khademloo, Sunghan Kim, Henrik Shahgholian
https://arxiv.org/abs/2403.04406

Regularity near the fixed boundary for transmission systems
Given $Ω\subset \mathbb{R}^n$ with $n\geq 2$, $D\subset Ω$ open, and $u:Ω\to \mathbb{R}^m$, we study elliptic systems of the type $$ {\rm div} \big( ( A + (B- A)χ_D)\nabla u\big) = 0 \quad \text{in $Ω\cap B_1$,} $$ for some uniformly elliptic tensors $A$ and $B$ with Hölder continuous entries. We show that, given appropriate boundary data, the Lipschitz regularity of $u$ inside $B_1 \cap D$ is transmitted to $B_{1/2}\cap Ω$ up to the boundary of $Ω$. This corresponds to the boundary cou…

This https://arxiv.org/abs/2401.02850 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Quantum cosmology in teleparallel gravity with a boundary term
We quantize a homogeneous and isotropic universe for two models of modified teleparallel gravity, wherein an arbitrary function of the boundary term, namely $B$, is present in the action and in the other model a scalar field that is non-minimally coupled to both the torsion and boundary term. In this regard, we study exact solutions of both the classical and quantum frameworks by utilizing the corresponding Wheeler-DeWitt (WDW) equations of the models. To correspond to the comprehensive classic…

This https://arxiv.org/abs/2310.05521 has been replaced.
link: https://scholar.google.com/scholar?q=a

The strong form of the Ahlfors-Schwarz lemma at the boundary and a rigidity result for Liouville's equation
We prove a boundary version of the strong form of the Ahlfors-Schwarz lemma with optimal error term. This result provides nonlinear extensions of the boundary Schwarz lemma of Burns and Krantz to the class of negatively curved conformal pseudometrics defined on arbitary hyperbolic domains in the complex plane. Based on a new boundary Harnack inequality for solutions of the Gauss curvature equation, we also establish a sharp rigidity result for conformal metrics with isolated singularities. In t…

This https://arxiv.org/abs/1912.12057 has been replaced.
link: https://scholar.google.com/scholar?q=a

Existence of Schrodinger Evolution with Absorbing Boundary Condition
Consider a non-relativistic quantum particle with wave function inside a region $Ω\subset \mathbb{R}^3$, and suppose that detectors are placed along the boundary $\partial Ω$. The question how to compute the probability distribution of the time at which the detector surface registers the particle boils down to finding a reasonable mathematical definition of an ideal detecting surface; a particularly convincing definition, called the absorbing boundary rule, involves a time evolution for the p…

Decision algorithms for reversibility of one-dimensional non-linear cellular automata under null boundary conditions
Ma Junchi, Chen Weilin, Wang Chen, Lin Defu, Wang Chao
https://arxiv.org/abs/2405.03609

Decision algorithms for reversibility of one-dimensional non-linear cellular automata under null boundary conditions
The property of reversibility is quite meaningful for the classic theoretical computer science model, cellular automata. For the reversibility problem for a CA under null boundary conditions, while linear rules have been studied a lot, the non-linear rules remain unexplored at present. The paper investigates the reversibility problem of general one-dimensional CA on a finite field $\mathbb{Z}_p$, and proposes an approach to optimize the Amoroso's infinite CA surjectivity detection algorithm. Th…

Anatomy of Higher-Order Non-Hermitian Skin and Boundary Modes
Fan Yang, Emil J. Bergholtz
https://arxiv.org/abs/2405.03750 https://ar…

Anatomy of Higher-Order Non-Hermitian Skin and Boundary Modes
The anomalous bulk-boundary correspondence in non-Hermitian systems featuring an intricate interplay between skin and boundary modes has attracted enormous theoretical and experimental attention. Still, in dimensions higher than one, this interplay remains much less understood. Here we provide insights from exact analytical solutions of a large class of models in any dimension, $d$, with open boundaries in $d_c \le d$ directions and by tracking their topological origin. Specifically, we show th…

Weakening the effect of boundaries: `diffusion-free' boundary conditions as a `do least harm' alternative to Neumann
Yufeng Lin, Rich Kerswell
https://arxiv.org/abs/2405.02874

Weakening the effect of boundaries: `diffusion-free' boundary conditions as a `do least harm' alternative to Neumann
In this note, we discuss a poorly known alternative boundary condition to the usual Neumann or `stress-free' boundary condition typically used to weaken boundary layers when diffusion is present but very small. These `diffusion-free' boundary conditions were first developed (as far as the authors know) in 1995 (Sureshkumar & Beris, J. Non-Newtonian Fluid Mech., vol 60, 53-80, 1995) in viscoelastic flow modelling but are worthy of general consideration in other research areas. To illustrate thei…

Limits to positional information in boundary-driven systems
Prashant Singh, Karel Proesmans
https://arxiv.org/abs/2405.04381 https://…

Limits to positional information in boundary-driven systems
Chemical gradients can be used by a particle to determine its position. This \textit{positional information} is of crucial importance, for example in developmental biology in the formation of patterns in an embryo. The central goal of this paper is to study the fundamental physical limits on how much positional information can be stored inside a system. To achieve this, we study positional information for general boundary-driven systems, and derive, in the near-equilibrium regime, a universal e…

Free boundary CMC annuli in spherical and hyperbolic balls
Alberto Cerezo, Isabel Fernandez, Pablo Mira
https://arxiv.org/abs/2403.04595 https://

Free boundary CMC annuli in spherical and hyperbolic balls
We construct, for any $H\in \mathbb{R}$, infinitely many free boundary annuli in geodesic balls of $\mathbb{S}^3$ with constant mean curvature $H$ and a discrete, non-rotational, symmetry group. Some of these free boundary CMC annuli are actually embedded if $H\geq 1/\sqrt{3}$. We also construct embedded, non-rotational, free boundary CMC annuli in geodesic balls of $\mathbb{H}^3$, for all values $H>1$ of the mean curvature $H$.

Dimension quotients as boundary limits
Roman Mikhailov
https://arxiv.org/abs/2405.03979 https://arxiv.org/pdf/2405.03979

Dimension quotients as boundary limits
For a functor from the category of free presentations of a group to the category of all groups we define the boundary limit as an image of the natural map from limit to colimit. We show that the fourth dimension quotient of a group can be naturally described as the boundary limit of a simply-defined functor.

This https://arxiv.org/abs/2402.14512 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Running Coupling and Beta-Functions for HQCD with Heavy and Light Quarks: Isotropic case
We consider running coupling constant and beta-function in holographic models supported by Einstein-dilaton-Maxwell action for heavy and light quarks. To obtain the dependence of the running coupling constant $α$ on temperature and chemical potential we impose boundary conditions on the dilaton field that depend on the position of the horizon. We use two types of boundary conditions: a simple boundary condition with the dilaton field vanishing at the horizon, and a boundary condition that ensu…

This https://arxiv.org/abs/2404.18140 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The Unique stationary boundary property
Let $G$ be a locally compact group and $μ$ an admissible probability measure on $G$. Let $(B,ν)$ be the universal topological Poisson $μ$-boundary of $(G,μ)$ and $Π_s(G)$ the universal minimal strongly proximal $G$-flow. In this note we present an alternative proof to a recent result of Hartman and Kalantar. We show that the following conditions are equivalent: (i) the measure $ν$ is the unique $μ$-stationary measure on $B$, (ii) $(B,G) \cong (Π_s(G),G)$.

Almost periodicity and boundary values of Dirichlet series
Ole Fredrik Brevig, Athanasios Kouroupis, Karl-Mikael Perfekt
https://arxiv.org/abs/2405.03522 h…

Almost periodicity and boundary values of Dirichlet series
We employ almost periodicity to establish analogues of the Hardy--Stein identity and the Littlewood--Paley formula for Hardy spaces of Dirichlet series. A construction of Saksman and Seip shows that the limits in this Littlewood--Paley formula cannot be interchanged. We apply this construction to show that the limits in the definition of the mean counting function for Dirichlet series cannot be interchanged. These are essentially statements about the two different kinds of boundary values that …

On unclosed mappings with Poletsky inequality
Victoria Desyatka, Evgeny Sevost'yanov
https://arxiv.org/abs/2404.03859 https://arx…

On unclosed mappings with Poletsky inequality
The manuscript is devoted to the boundary behavior of mappings with bounded and finite distortion. We consider mappings of domains of the Euclidean space that satisfy weighted Poletsky inequality. Assume that, the definition domain is finitely connected on its boundary and, in addition, on the set of all points which are pre-images of the cluster set of this boundary. Then the specified mappings have a continuous boundary extension provided that the majorant in the Poletsky inequality satisfies…

This https://arxiv.org/abs/2405.02824 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCV_…

Adaptive Guidance Learning for Camouflaged Object Detection
Camouflaged object detection (COD) aims to segment objects visually embedded in their surroundings, which is a very challenging task due to the high similarity between the objects and the background. To address it, most methods often incorporate additional information (e.g., boundary, texture, and frequency clues) to guide feature learning for better detecting camouflaged objects from the background. Although progress has been made, these methods are basically individually tailored to specific …

Grand canonically optimized grain boundary phases in hexagonal close-packed titanium
Enze Chen, Tae Wook Heo, Brandon C. Wood, Mark Asta, Timofey Frolov
https://arxiv.org/abs/2404.04230

Grand canonically optimized grain boundary phases in hexagonal close-packed titanium
Grain boundaries (GBs) profoundly influence the properties and performance of materials, emphasizing the importance of understanding the GB structure and phase behavior. As recent computational studies have demonstrated the existence of multiple GB phases associated with varying the atomic density at the interface, we introduce a validated, open-source GRand canonical Interface Predictor (GRIP) tool that automates high-throughput, grand canonical optimization of GB structures. While previous st…

This https://arxiv.org/abs/2308.12255 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Absorbing boundary conditions for the Helmholtz equation using Gauss-Legendre quadrature reduced integrations
We introduce a new class of absorbing boundary conditions (ABCs) for the Helmholtz equation. The proposed ABCs are obtained by using $L$ discrete layers and the $Q_N$ Lagrange finite element in conjunction with the $N$-point Gauss-Legendre quadrature reduced integration rule in a specific formulation of perfectly matched layers. The proposed ABCs are classified by a tuple $(L,N)$, and achieve reflection error of order $O(R^{2LN})$ for some $R<1$. The new ABCs generalise the perfectly matched di…

New degeneration phenomenon for infinite-type Riemann surfaces
Ryo Matsuda
https://arxiv.org/abs/2405.04178 https://arxiv.org/pdf/240…

New degeneration phenomenon for infinite-type Riemann surfaces
Since the Teichmüller space of a surface $R$ is a deformation space of complex structures defined on $R$, its Bers boundary describes the degeneration of complex structures in a certain sense. In this paper, constructing a concrete example, we prove that if S is a Riemann surface of infinite type, there exists a Riemann surface with the marking, which is homeomorphic to the surface $R$ in the Bers boundary. We also show that many such degenerations exist in the Bers boundary.

This https://arxiv.org/abs/2203.10758 has been replaced.
link: https://scholar.google.com/scholar?q=a

Small-time global approximate controllability for incompressible MHD with coupled Navier slip boundary conditions
We study the small-time global approximate controllability for incompressible magnetohydrodynamic (MHD) flows in smoothly bounded two- or three-dimensional domains. The controls act on arbitrary nonempty open portions of each connected boundary component, while linearly coupled Navier slip-with-friction conditions are imposed along the uncontrolled parts of the boundary. Some choices for the friction coefficients give rise to interacting velocity and magnetic field boundary layers. We obtain su…

This https://arxiv.org/abs/2105.11359 has been replaced.
link: https://scholar.google.com/scholar?q=a

Examples of measures with trivial left and non-trivial right random walk tail boundary
In early 80's Vadim Kaimanovich presented a construction of a non-degenerate measure, on the standard lamplighter group, that has a trivial left and non-trivial right random walk tail boundary. We show that examples of such kind are possible precisely for amenable groups that have non-trivial factors with infinite conjugacy classes property.

On the convergence of zeta functions of prehomogeneous vector spaces
Tobias Finis, Erez Lapid
https://arxiv.org/abs/2405.04153 https://

On the convergence of zeta functions of prehomogeneous vector spaces
We prove a general convergence result for zeta functions of prehomogeneous vector spaces extending results of H. Saito, F. Sato and Yukie. Our analysis points to certain subspaces which yield boundary terms. We study it further in the setup arising from nilpotent orbits. In certain cases we determine the residue at the rightmost pole of the zeta function.

Hypersurfaces with capillary boundary evolving by volume preserving power mean curvature flow
Carlo Sinestrari, Liangjun Weng
https://arxiv.org/abs/2405.02722

Hypersurfaces with capillary boundary evolving by volume preserving power mean curvature flow
In this paper, we introduce a volume- or area-preserving curvature flow for hypersurfaces with capillary boundary in the half-space, with speed given by a positive power of the mean curvature with a non-local averaging term. We demonstrate that for any convex initial hypersurface with a capillary boundary, the flow exists for all time and smoothly converges to a spherical cap as $t \to +\infty$

This https://arxiv.org/abs/2309.05955 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

Trust-Region Neural Moving Horizon Estimation for Robots
Accurate disturbance estimation is essential for safe robot operations. The recently proposed neural moving horizon estimation (NeuroMHE), which uses a portable neural network to model the MHE's weightings, has shown promise in further pushing the accuracy and efficiency boundary. Currently, NeuroMHE is trained through gradient descent, with its gradient computed recursively using a Kalman filter. This paper proposes a trust-region policy optimization method for training NeuroMHE. We achieve th…

This https://arxiv.org/abs/2310.07340 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Tame deformations of highly singular function germs
We give analytic and algebraic conditions under which a deformation of real analytic functions with non-isolated singular locus are locally topologically trivial at the boundary.

Boundary Algebras of Positroids
Jonah Berggren, Khrystyna Serhiyenko
https://arxiv.org/abs/2404.02886 https://arxiv.org/pdf/2404.0288…

Boundary Algebras of Positroids
A dimer model is a quiver with faces embedded into a disk. A consistent dimer model gives rise to a strand diagram, and hence to a positroid. The Gorenstein-projective module category over the completed boundary algebra of a dimer model was shown by Pressland to categorify a cluster structure on the corresponding positroid variety. Outside of the Grassmannian case, boundary algebras of dimer models are not well understood. We give an explicit description of the boundary algebra of a consistent …

Zeno physics of the Ising chain with symmetry-breaking boundary dephasing
Umar Javed, Riccardo J. Valencia-Tortora, Jamir Marino, Vadim Oganesyan, Michael Kolodrubetz
https://arxiv.org/abs/2404.04255

Zeno physics of the Ising chain with symmetry-breaking boundary dephasing
In few-qubit systems, the quantum Zeno effect arises when measurement occurs sufficiently frequently that the spins are unable to relax between measurements. This can compete with Hamiltonian terms, resulting in interesting relaxation processes which depend non-monotonically on the ratio of measurement rate to coherent oscillations. While Zeno physics for a single qubit is well-understood, an interesting open question is how the Zeno effect is modified by coupling the measured spin to a non-tri…

This https://arxiv.org/abs/2309.03871 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Horizon phase spaces in general relativity
We derive a prescription for the phase space of general relativity on two intersecting null surfaces. The boundary symmetry group is the semidirect product of the group of arbitrary diffeomorphisms of each null boundary which coincide at the corner, with a group of reparameterizations of the null generators. The phase space can be extended by acting with half-sided boosts that generate Weyl shocks along the initial data surfaces, and it then includes the relative boost angle between the null su…

This https://arxiv.org/abs/2403.16566 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Non-commutative divergence and the Turaev cobracket
The divergence map, an important ingredient in the algebraic description of the Turaev cobracket on a connected oriented compact surface with boundary, is reformulated in the context of non-commutative geometry using a flat connection on the space of 1-forms on a formally smooth associative algebra. We then extend this construction to the case of associative algebras with any finite cohomological dimension, which allows us to give a similar algebraic description of the Turaev cobracket on a clo…

Wildfire season in Northwest Territories, northern Canada. #Arctic #ClimateChange #Wildfire

On Bias and Its Reduction via Standardization in Source Localization Problems
Joonas Lahtinen
https://arxiv.org/abs/2405.04409 https://

On Bias and Its Reduction via Standardization in Source Localization Problems
In source localization problems, the aim is to locate the sources within a domain that causes given measurements on the boundary. In this type of problem, biasing of the solution is one of the main causes of mislocalization. A technique called standardization was developed to reduce biasing. However, the lack of a mathematical background for this method can cause difficulties in its application and confusion regarding the reliability of solutions. Here, we give a rigorous and generalized backgr…

This https://arxiv.org/abs/2401.12213 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Identifying gap-closings in open non-Hermitian systems by Biorthogonal Polarization
We investigate gap-closings in one- and two-dimensional tight-binding models with two bands, containing non-Hermitian hopping terms, and open boundary conditions (OBCs) imposed along one direction. We compare the bulk OBC spectra with the periodic boundary condition (PBC) spectra, pointing out that they do not coincide, which is an intrinsic characteristic of non-Hermitian systems. The non-Hermiticity, thus, results in the failure of the familiar notions of bulk-boundary correspondence found fo…

Relativistic jet ejections from slim disks
Hajime Inoue
https://arxiv.org/abs/2404.03684 https://arxiv.org/pdf/2404.03684

Relativistic jet ejections from slim disks
An ejection mechanism of relativistic jets from slim disks is studied. Since the radiation pressure is dominant in the slim disk, radiative energy flow arises along the pressure gradient in the vertical direction. The divergence of the radiative flux tells us that the radiative energy flow from a bottom layer near the equatorial plane is absorbed by another layer upper than the boundary surface. The absorbed energy accumulates in the upper layer as the matter advances inward and calculations sh…

This https://arxiv.org/abs/2312.14911 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

Zero-bin subtraction and the $q_{\mathrm{T}}$ spectrum beyond leading power
In this paper, we present an algorithm to construct the qT distribution at NLO accuracy to arbitrary power precision, including the assembly of suitable zero-bin subtrahends, in a mathematically well-defined way for a generic choice of rapidity-divergence regularisation prescription. In its derivation, we divide the phase space into two sectors, the interior of the integration domain as well as the integration boundary, which we include here for the first time. To demonstrate the applicability …

A hydrodynamic model of capillary flow in an axially symmetric tube with a non-slowly-varying cross section and a boundary slip
Masao Iwamatsu
https://arxiv.org/abs/2405.02780

A hydrodynamic model of capillary flow in an axially symmetric tube with a non-slowly-varying cross section and a boundary slip
The capillary flow of a Newtonian and incompressible fluid in an axially symmetric horizontal tube with a non-slowly-varying cross section and a boundary slip is considered theoretically under the assumption that the Reynolds number is small enough for the Stokes approximation to be valid. Combining the Stokes equation with the hydrodynamic model assuming the Hagen-Poiseulle flow, a general formula for the capillary flow in a non-slowly-varying tube is derived. Using the newly derived formula, …

Boundary unique continuation in planar domains by conformal mapping
Stefano Vita
https://arxiv.org/abs/2405.04388 https://arxiv.org/p…

Boundary unique continuation in planar domains by conformal mapping
Let $Ω\subset\mathbb R^2$ be a chord arc domain with small constant. We show that a nontrivial harmonic function which vanishes continuously on a relatively open set of the boundary cannot have the norm of the gradient which vanishes on a subset of positive surface measure (arc length). This result was previously known to be true, and conjectured in higher dimensions by Lin, in Lipschitz domains. Let now $Ω\subset\mathbb R^2$ be a $C^1$ domain with Dini mean oscillations. We prove that a nont…

Orthosystoles and orthokissing numbers
Ara Basmajian, Federica Fanoni
https://arxiv.org/abs/2405.01732 https://arxiv.org/pdf/2405.017…

Orthosystoles and orthokissing numbers
For hyperbolic surfaces with geodesic boundary, we study the orthosystole, i.e. the length of a shortest essential arc from the boundary to the boundary. We recover and extend work by Bavard completely characterizing the surfaces maximizing the orthosystole in the case of a single boundary component. For multiple boundary components, we construct surfaces with large orthosystole and show that their orthosystole grows, as the genus goes to infinity, at the same rate as Bavard's upper bound.

Density in the half-line Schwartz space of functions whose Fourier-Laplace transform has natural boundary the real line
Andreas Chatziafratis, Telemachos Hatziafratis
https://arxiv.org/abs/2403.03718

Density in the half-line Schwartz space of functions whose Fourier-Laplace transform has natural boundary the real line
In this note, we prove that the Fourier-Laplace transform of the typical function (i.e., generic in the sense of Baire category theorem) in the Schwartz class of the half-line, being analytic in the lower half of the complex plane, has natural boundary the axis of the real numbers. We also provide variations and generalizations.

This https://arxiv.org/abs/2301.00526 has been replaced.
link: https://scholar.google.com/scholar?q=a

Unusual acceleration and size effects in grain boundary migration with shear coupling
Grain boundary (GB) migration plays a crucial role in the thermal and mechanical responses of polycrystalline materials, particularly in ultrafine-grained and nano-grained materials exhibiting grain size-dependent properties. This study investigates the migration behaviors of a set of GBs in Ni through atomistic simulations, employing synthetic driving forces and shear stress. Surprisingly, the displacements of some shear-coupling GBs do not follow the widely assumed linear or approximately lin…

Capillary Surfaces in Manifolds with Nonnegative Scalar Curvature and Strictly Mean Convex Boundary
Yujie Wu
https://arxiv.org/abs/2405.03993 https://

Capillary Surfaces in Manifolds with Nonnegative Scalar Curvature and Strictly Mean Convex Boundary
In this paper we use stable capillary surfaces (analogous to the $μ$-bubble construction) to study manifolds with strictly mean convex boundary and nonnegative scalar curvature. We give an obstruction to filling 2-manifolds by such 3-manifolds based on the Urysohn width. We also obtain a bandwidth estimate and establish other geometric properties of such manifolds.

This https://arxiv.org/abs/2404.15439 has been replaced.
link: https://scholar.google.com/scholar?q=a

Thermal boundary conductance and thermal conductivity strongly depend on nearby environment
At the nanoscale, the thermal boundary conductance (TBC) and thermal conductivity are not intrinsic properties of interfaces or materials but depend on the nearby environment. However, most studies focused on single interfaces or superlattices, and the thermal transport across heterostructures formed by multiple different materials is still mysterious. In this study, we demonstrate how much the TBC of an interface is affected by the existence of a second interface, as well as how much the therm…

A single shooting method with approximate Fr\'{e}chet derivative for computing geodesics on the Stiefel manifold
Marco Sutti
https://arxiv.org/abs/2404.04089

A single shooting method with approximate Fréchet derivative for computing geodesics on the Stiefel manifold
This paper shows how to use the shooting method, a classical numerical algorithm for solving boundary value problems, to compute the Riemannian distance on the Stiefel manifold $ \mathrm{St}(n,p) $, the set of $ n \times p $ matrices with orthonormal columns. The proposed method is a shooting method in the sense of the classical shooting methods for solving boundary value problems; see, e.g., Stoer and Bulirsch, 1991. The main feature is that we provide an approximate formula for the Fréchet d…

A hydrodynamic model of capillary flow in an axially symmetric tube with a non-slowly-varying cross section and a boundary slip
Masao Iwamatsu
https://arxiv.org/abs/2405.02780

A hydrodynamic model of capillary flow in an axially symmetric tube with a non-slowly-varying cross section and a boundary slip
The capillary flow of a Newtonian and incompressible fluid in an axially symmetric horizontal tube with a non-slowly-varying cross section and a boundary slip is considered theoretically under the assumption that the Reynolds number is small enough for the Stokes approximation to be valid. Combining the Stokes equation with the hydrodynamic model assuming the Hagen-Poiseulle flow, a general formula for the capillary flow in a non-slowly-varying tube is derived. Using the newly derived formula, …

This https://arxiv.org/abs/2309.05955 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

Trust-Region Neural Moving Horizon Estimation for Robots
Accurate disturbance estimation is essential for safe robot operations. The recently proposed neural moving horizon estimation (NeuroMHE), which uses a portable neural network to model the MHE's weightings, has shown promise in further pushing the accuracy and efficiency boundary. Currently, NeuroMHE is trained through gradient descent, with its gradient computed recursively using a Kalman filter. This paper proposes a trust-region policy optimization method for training NeuroMHE. We achieve th…

This https://arxiv.org/abs/2402.04308 has been replaced.
link: https://scholar.google.com/scholar?q=a

New Well-Posed Boundary Conditions for Semi-Classical Euclidean Gravity
We consider four-dimensional Euclidean gravity in a finite cavity. Dirichlet conditions do not yield a well-posed elliptic system, and Anderson has suggested boundary conditions that do. Here we point out that there exists a one-parameter family of boundary conditions, parameterized by a constant $p$, where a suitably Weyl rescaled boundary metric is fixed, and all give a well-posed elliptic system. Anderson and Dirichlet boundary conditions can be seen as the limits $p \to 0$ and $\infty$ of t…

Stress solution of static linear elasticity with mixed boundary conditions via adjoint linear operators
Ivan Gudoshnikov, Michal K\v{r}\'i\v{z}ek
https://arxiv.org/abs/2405.04320

Stress solution of static linear elasticity with mixed boundary conditions via adjoint linear operators
We revisit stress problems in linear elasticity to provide a perspective from the geometrical and functionalanalytic points of view. For the static stress problem of linear elasticity with mixed boundary conditions we write the associated pair of unbounded adjoint operators. The stress solution is found as an intersection of affine translations of the fundamental subspaces of the adjoint operators. In particular, we treat the equilibrium equation in the operator form, involving spaces of traces…

Analytic torsion for fibred boundary metrics and conic degeneration
J{\o}rgen Olsen Lye, Boris Vertman
https://arxiv.org/abs/2403.04402 https://

Analytic torsion for fibred boundary metrics and conic degeneration
We study the renormalized analytic torsion of complete manifolds with fibred boundary metrics, also referred to as $ϕ$-metrics. We establish invariance of the torsion under suitable deformations of the metric, and establish a gluing formula. As an application, we relate the analytic torsions for complete $ϕ$- and incomplete wedge-metrics. As a simple consequence we recover a result by Sher and Guillarmou about analytic torsion under conic degeneration.

This https://arxiv.org/abs/2312.00287 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Explicit formula of boundary crossing probabilities for continuous local martingales to constant boundary
An explicit formula for the probability that a continuous local martingale crosses a one or two-sided random constant boundary in a finite time interval is derived. We obtain that the boundary crossing probability of a continuous local martingale to a constant boundary is equal to the boundary crossing probability of a standard Wiener process to a constant boundary up to a time change of quadratic variation value. This relies on the constancy of the boundary and the Dambis, Dubins-Schwarz theor…

This https://arxiv.org/abs/2405.03238 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Topological Photonic Structures with Broken Reflection Symmetry
In this work, we present a mathematical theory for Dirac points and interface modes in honeycomb topological photonic structures consisting of impenetrable obstacles. Starting from a honeycomb lattice of obstacles attaining $120^\circ$-rotation symmetry and horizontal reflection symmetry, we apply the boundary integral equation method to show the existence of Dirac points for the first two bands at the vertices of the Brillouin zone. We then study interface modes in a joint honeycomb photonic s…

This https://arxiv.org/abs/2304.07146 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Energy cascade for the Klein-Gordon lattice
We study analytically the dynamics of a $d$-dimensional Klein-Gordon lattice with periodic boundary conditions, for $d \leq 3$. We consider initial data supported on one low-frequency Fourier mode. We show that, in the continuous approximation, the resonant normal form of the system is given by a small-dispersion nonlinear Schrödinger (NLS) equation. By exploiting a result about the growth of Sobolev norms for solutions of small-dispersion NLS, we are able to describe an energy cascade phenome…

This https://arxiv.org/abs/2308.01569 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Optimal Distributed Control for a Cahn-Hilliard-Darcy System with Mass Sources, Unmatched Viscosities and Singular Potential
We study a Cahn-Hilliard-Darcy system with mass sources, which can be considered as a basic, though simplified, diffuse interface model for the evolution of tumor growth. This system is equipped with an impermeability condition for the (volume) averaged velocity $\mathbf{u}$ as well as homogeneous Neumann boundary conditions for the phase function $φ$ and the chemical potential $μ$. The source term in the convective Cahn-Hilliard equation contains a control $R$ that can be thought, for instan…

This https://arxiv.org/abs/2310.10857 has been replaced.
initial toot: https://mastoxiv.page/@ar…

The impact of finite span and wing-tip vortices on a turbulent NACA0012 wing
High-fidelity simulations are conducted to investigate the turbulent boundary layers around a finite-span NACA0012 wing with a rounded wing-tip geometry at a chord-based Reynolds number of $Re_c=200\,000$ and at various angles of attack up to $10^\circ$. The study aims to discern the differences between the boundary layers on the finite-span wing and those on infinite-span wings at equivalent angles of attack. The finite-span boundary layers exhibit: (i) an altered streamwise and a non-zero spa…

This https://arxiv.org/abs/2402.04308 has been replaced.
link: https://scholar.google.com/scholar?q=a

New Well-Posed Boundary Conditions for Semi-Classical Euclidean Gravity
We consider four-dimensional Euclidean gravity in a finite cavity. Dirichlet conditions do not yield a well-posed elliptic system, and Anderson has suggested boundary conditions that do. Here we point out that there exists a one-parameter family of boundary conditions, parameterized by a constant $p$, where a suitably Weyl rescaled boundary metric is fixed, and all give a well-posed elliptic system. Anderson and Dirichlet boundary conditions can be seen as the limits $p \to 0$ and $\infty$ of t…

Energy barriers for boundary nucleation in a two-well model without gauge invariance
Antonio Tribuzio, Konstantinos Zemas
https://arxiv.org/abs/2403.04567 …

Energy barriers for boundary nucleation in a two-well model without gauge invariance
We study energy scaling laws for a simplified, singularly perturbed, double-well nucleation problem confined in a half-space, in the absence of gauge invariance and for an inclusion of fixed volume. Motivated by models for boundary nucleation of a single-phase martensite inside a parental phase of austenite, our main focus in this nonlocal isoperimetric problem is how the relationship between the rank-1 direction and the orientation of the half-space influences the energy scaling with respect t…

This https://arxiv.org/abs/2311.02732 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Solving High Dimensional Partial Differential Equations Using Tensor Neural Network and A Posteriori Error Estimators
In this paper, based on the combination of tensor neural network and a posteriori error estimator, a novel type of machine learning method is proposed to solve high-dimensional boundary value problems with homogeneous and non-homogeneous Dirichlet or Neumann type of boundary conditions and eigenvalue problems of the second-order elliptic operator. The most important advantage of the tensor neural network is that the high dimensional integrations of tensor neural networks can be computed with hi…

Spontaneous Conducting Boundary Channels in 1T-TaS$_{2}$
T. R. Devidas, Jonathan T. Reichanadter, Shannon C. Haley, Matan Sterenberg, Joel E. Moore, Jeffrey B. Neaton, James G. Analytis, Beena Kalisky, Eran Maniv
https://arxiv.org/abs/2405.02036

Spontaneous Conducting Boundary Channels in 1T-TaS$_{2}$
Materials that transition between metal and insulator, the two opposing states that distinguish all solids, are fascinating because they underlie many mysteries in the physics of the solid state. In 1T-TaS$_{2}$, the metal-insulator transition is linked to a series of metastable states of a chiral charge density wave whose basic nature is still an open question. In this work, we show that pulses of current through these materials create current-carrying boundary channels that distinguish the me…

This https://arxiv.org/abs/2403.01583 has been replaced.
link: https://scholar.google.com/scholar?q=a

Universal spectral moment theorem and its applications in non-Hermitian systems
The high sensitivity of the spectrum and wavefunctions to boundary conditions, termed the non-Hermitian skin effect, represents a fundamental aspect of non-Hermitian systems. While it endows non-Hermitian systems with unprecedented physical properties, it presents notable obstacles in grasping universal properties that are robust against microscopic details and boundary conditions. In this Letter, we introduce a pivotal theorem: in the thermodynamic limit, for any non-Hermitian systems with fin…

Testing the Boundary-to-Bound Correspondence with Numerical Relativity
Anuj Kankani, Sean T. McWilliams
https://arxiv.org/abs/2404.03607 https://

Testing the Boundary-to-Bound Correspondence with Numerical Relativity
The Boundary-to-Bound (B2B) correspondence, which connects orbital and radiative observables between bound and unbound orbits, has recently been introduced and demonstrated in the perturbative regime. We produce a large number of numerical relativity simulations of bound and unbound encounters between two nonspinning equal mass black holes in order to test this correspondence in the non-perturbative regime. We focus on testing the radiated energy and angular momentum, as well as orbital paramet…

Caloric functions and boundary regularity for the fractional Laplacian in Lipschitz open sets
Gavin Armstrong, Krzysztof Bogdan, Artur Rutkowski
https://arxiv.org/abs/2403.03840 <…

Caloric functions and boundary regularity for the fractional Laplacian in Lipschitz open sets
We give Martin representation of nonnegative functions caloric with respect to the fractional Laplacian in Lipschitz open sets. The caloric functions are defined in terms of the mean value property for the space-time isotropic $α$-stable Lévy process. To derive the representation, we first establish the existence of the parabolic Martin kernel. This involves proving new boundary regularity results for both the fractional heat equation and the fractional Poisson equation with Dirichlet exterio…

Classifying bulk-edge anomalies in the Dirac Hamiltonian
Hansueli Jud, Cl\'ement Tauber
https://arxiv.org/abs/2403.04465 https://…

Classifying bulk-edge anomalies in the Dirac Hamiltonian
We study the Dirac Hamiltonian in dimension two with a mass term and a large momentum regularization, and show that bulk-edge correspondence fails. Despite a well defined bulk topological index --the Chern number--, the number of edge modes depends on the boundary condition. The origin of this anomaly is rooted in the unbounded nature of the spectrum. It is detected with Levinson's theorem from scattering theory and quantified via an anomalous winding number at infinite energy, dubbed ghost cha…

Hydrodynamics of vortex memory system driven by edge-current and boundary magnetization
Rabiu Musah
https://arxiv.org/abs/2405.03036 https://

Hydrodynamics of vortex memory system driven by edge-current and boundary magnetization
In this study, a magnetohydrodynamic model is developed to study the dynamics of vortices driven by edge-current. Two modeled equations for fluid and magnetic field variables are each transformed into diffusion equation for vorticity and poisson equation for stream function. A numerical solution method is designed using a simplified Lattice Boltzmann method (LBM). The LBM-D2Q5 scheme is utilized to obtain the numerical solutions for the fluid and magnetic field variables. Understanding the hydr…

This https://arxiv.org/abs/2405.03214 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Asymptotic behavior toward viscous shock for impermeable wall and inflow problem of barotropic Navier-Stokes equations
We consider the compressible barotropic Navier-Stokes equations in a half-line and study the time-asymptotic behavior toward the outgoing viscous shock wave. Precisely, we consider the two boundary problems: impermeable wall and inflow problems, where the velocity at the boundary is given as a constant state. For both problems, when the asymptotic profile determined by the prescribed constant states at the boundary and far-fields is a viscous shock, we show that the solution asymptotically conv…

Testing the Boundary-to-Bound Correspondence with Numerical Relativity
Anuj Kankani, Sean T. McWilliams
https://arxiv.org/abs/2404.03607 https://

Testing the Boundary-to-Bound Correspondence with Numerical Relativity
The Boundary-to-Bound (B2B) correspondence, which connects orbital and radiative observables between bound and unbound orbits, has recently been introduced and demonstrated in the perturbative regime. We produce a large number of numerical relativity simulations of bound and unbound encounters between two nonspinning equal mass black holes in order to test this correspondence in the non-perturbative regime. We focus on testing the radiated energy and angular momentum, as well as orbital paramet…

Hydrodynamics of vortex memory system driven by edge-current and boundary magnetization
Rabiu Musah
https://arxiv.org/abs/2405.03036 https://

Hydrodynamics of vortex memory system driven by edge-current and boundary magnetization
In this study, a magnetohydrodynamic model is developed to study the dynamics of vortices driven by edge-current. Two modeled equations for fluid and magnetic field variables are each transformed into diffusion equation for vorticity and poisson equation for stream function. A numerical solution method is designed using a simplified Lattice Boltzmann method (LBM). The LBM-D2Q5 scheme is utilized to obtain the numerical solutions for the fluid and magnetic field variables. Understanding the hydr…

This https://arxiv.org/abs/2403.10090 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Convex co-compact hyperbolic manifolds are determined by their pleating lamination
Convex co-compact 3-dimensional hyperbolic manifolds are uniquely determined by the pleating measured lamination on the boundary of their convex core.

Elliptic fourth-order operators with Wentzell boundary conditions on Lipschitz domains
David Plo\ss
https://arxiv.org/abs/2405.02064 https://

Elliptic fourth-order operators with Wentzell boundary conditions on Lipschitz domains
For bounded domains $Ω$ with Lipschitz boundary $Γ$, we investigate boundary value problems for elliptic operators with variable coefficients of fourth order subject to Wentzell (or dynamic) boundary conditions. Using form methods, we begin by showing general results for an even wider class of operators defined via two (intertwined) quadratic forms by defining very abstract concepts of weak traces. Even in this general setting, we prove generation of an analytic semigroup on the product space…

This https://arxiv.org/abs/2311.12429 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Attractive (s)axions: cosmological trackers at the boundary of moduli space
We study the cosmological evolution of a FLRW universe dominated by the energy density of moduli close to asymptotic regions of moduli space. Due to the structure of the $\mathcal{N}=1$ SUGRA kinetic term, a saxion and an axion residing in the same chiral multiplet are (universally) coupled even if the latter is a flat direction of the potential, resulting in non-trivial dynamics. We generalise known results in the literature to the case of multiple moduli, showing the existence of various ``tr…

Classifying bulk-edge anomalies in the Dirac Hamiltonian
Hansueli Jud, Cl\'ement Tauber
https://arxiv.org/abs/2403.04465 https://…

Classifying bulk-edge anomalies in the Dirac Hamiltonian
We study the Dirac Hamiltonian in dimension two with a mass term and a large momentum regularization, and show that bulk-edge correspondence fails. Despite a well defined bulk topological index --the Chern number--, the number of edge modes depends on the boundary condition. The origin of this anomaly is rooted in the unbounded nature of the spectrum. It is detected with Levinson's theorem from scattering theory and quantified via an anomalous winding number at infinite energy, dubbed ghost cha…

This https://arxiv.org/abs/2402.02919 has been replaced.
link: https://scholar.google.com/scholar?q=a

Attractors in $f(Q,B)$-gravity
We investigate the asymptotic behavior of the cosmological field equations in Symmetric Teleparallel General Relativity, where a nonlinear function of the boundary term is introduced instead of the cosmological constant to describe the acceleration phase of the universe. Our analysis reveals constraints on the free parameters necessary for the existence of an attractor that accurately represents acceleration. However, we also identify asymptotic solutions depicting Big Rip and Big Crunch singul…

This https://arxiv.org/abs/2403.07275 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Coarse-graining black holes out of equilibrium with boundary observables on time slice
In black hole thermodynamics, defining coarse-grained entropy for dynamical black holes has long been a challenge, and various proposals, such as generalized entropy, have been explored. Guided by the AdS/CFT, we introduce a new definition of coarse-grained entropy for a dynamical black hole in Lorentzian Einstein gravity. On each time slice, this entropy is defined as the horizon area of an auxiliary Euclidean black hole that shares the same mass, (angular) momenta, and asymptotic normalizable…

Gauging Centrifugal Instabilities in Compressible Free-Shear Layers Via Nonlinear Boundary Region Equations
Omar Es-SAhli, Adrian Sescu, Yuji Hattori
https://arxiv.org/abs/2403.02435

Gauging Centrifugal Instabilities in Compressible Free-Shear Layers Via Nonlinear Boundary Region Equations
Curved free shear layers emerge in many engineering problems involving complex flow geometries, such as the flow over a backward facing step, flows with wall injection in a boundary layer, the flow inside side-dump combustors, or wakes generated by vertical axis wind turbines, among others. Previous studies involving centrifugal instabilities have mainly focused on wall-flows where Taylor instabilities between two rotating concentric cylinders or Görtler vortices in boundary layers, resulting …

Morse properties in convex projective geometry
Mitul Islam, Theodore Weisman
https://arxiv.org/abs/2405.03269 https://arxiv.org/pdf/2…

Morse properties in convex projective geometry
We study properties of "hyperbolic directions" in groups acting cocompactly on properly convex domains in real projective space, from three different perspectives simultaneously: the (coarse) metric geometry of the Hilbert metric, the projective geometry of the boundary of the domain, and the singular value gaps of projective automorphisms. We describe the relationship between different definitions of "Morse" and "regular" quasi-geodesics arising in these three different contexts. This generali…

On finite group global and gauged $q$-form symmetries in TQFT
Manuel Furlan, Pavel Putrov
https://arxiv.org/abs/2403.04677 https://ar…

On finite group global and gauged $q$-form symmetries in TQFT
We describe a method to implement finite group global and gauged $q$-form symmetries into the axiomatic structure of $d$-dimensional Topological Quantum Field Theory (TQFT) in terms of bordisms decorated by cohomology classes. Namely, on a manifold with a boundary, the gauge field is considered as a class in an appropriate relative cohomology group. It is defined in a way that allows self-consistent cutting and gluing of the manifolds and involves a choice of a $(d-q-2)$-skeleton in the boundar…

Reynolds-number dependence of streamwise velocity variance in wall-bounded turbulent flows
Chenning Tong
https://arxiv.org/abs/2405.03569 https://

Reynolds-number dependence of streamwise velocity variance in wall-bounded turbulent flows
We propose a model for the streamwise velocity variance in wall-bounded turbulent flows. It hypothesizes that the wall-parallel motions of the attached eddies induce internal turbulent boundary layers. A logarithmic variance profile is obtained. The peak value of the variance scaled using the friction velocity has a logarithmic dependence on the ratio the wall-normal length of the flow to the thickness of the internal boundary layer induced by the largest attached eddies ($δ_o$), the latter ha…

This https://arxiv.org/abs/2404.05855 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The nonlinear wave equation with nonlinear Wentzell boundary conditions on time-dependent compact Riemannian manifolds
We prove a local well-posedness result for an evolution problem consisting of a semilinear wave equation with subcritical nonlinearities posed on a time-dependent compact Riemannian manifold and supplied with a nonlinear dynamical boundary condition of Wentzell type.

Strong Cosmic Censorship in Kerr-Newman-de Sitter
Alex Davey, Oscar J. C. Dias, David Sola Gil
https://arxiv.org/abs/2404.03724 https://

Strong Cosmic Censorship in Kerr-Newman-de Sitter
Christodoulou's formulation of Strong Cosmic Censorship (SCC) holds true for Kerr-de Sitter black holes. On the other hand, Reissner-Nordström-de Sitter black holes violate SCC. We do a detailed scan of the parameter space of Kerr-Newman-de Sitter black holes between these two limiting families, to identify the boundary that marks the transition between solutions that respect and violate SCC. We focus our attention on linear scalar field perturbations. SCC is violated inside a (roughly) `spher…

This https://arxiv.org/abs/2305.05897 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Extremal metrics for the eigenvalues of the Laplacian on manifolds with boundary
We show there are no extremal metrics for the eigenvalues of the Neumann Laplacian on any compact manifold. Nonetheless, we construct examples of conformally extremal metrics for the eigenvalues of this operator in any annulus and characterise these special metrics in the general case of a compact manifold of dimension $n \geq 2$. As for the Dirichlet Laplacian, we prove non existence of extremal metrics on any compact surface.

Reynolds-number dependence of streamwise velocity variance in wall-bounded turbulent flows
Chenning Tong
https://arxiv.org/abs/2405.03569 https://

Reynolds-number dependence of streamwise velocity variance in wall-bounded turbulent flows
We propose a model for the streamwise velocity variance in wall-bounded turbulent flows. It hypothesizes that the wall-parallel motions of the attached eddies induce internal turbulent boundary layers. A logarithmic variance profile is obtained. The peak value of the variance scaled using the friction velocity has a logarithmic dependence on the ratio the wall-normal length of the flow to the thickness of the internal boundary layer induced by the largest attached eddies ($δ_o$), the latter ha…

On finite group global and gauged $q$-form symmetries in TQFT
Manuel Furlan, Pavel Putrov
https://arxiv.org/abs/2403.04677 https://ar…

On finite group global and gauged $q$-form symmetries in TQFT
We describe a method to implement finite group global and gauged $q$-form symmetries into the axiomatic structure of $d$-dimensional Topological Quantum Field Theory (TQFT) in terms of bordisms decorated by cohomology classes. Namely, on a manifold with a boundary, the gauge field is considered as a class in an appropriate relative cohomology group. It is defined in a way that allows self-consistent cutting and gluing of the manifolds and involves a choice of a $(d-q-2)$-skeleton in the boundar…

Some Comparison Results for First-Order Hamilton-Jacobi Equations and Second-Order Fully Nonlinear Parabolic Equations with Ventcell Boundary Conditions
Guy Barles (IDP), Emmanuel Chasseigne (IDP)
https://arxiv.org/abs/2405.01899

Some Comparison Results for First-Order Hamilton-Jacobi Equations and Second-Order Fully Nonlinear Parabolic Equations with Ventcell Boundary Conditions
In this article, we consider fully nonlinear, possibly degenerate, parabolic equations associated with Ventcell boundary conditions in bounded or unbounded, smooth domains. We first analyze the exact form of such boundary conditions in general domains in order that the notion of viscosity solutions make sense. Then we prove general comparison results under natural assumptions on the nonlinearities, assuming only that the equation is either coercive (first-order case) or strictly elliptic (secon…

This https://arxiv.org/abs/2403.02669 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Coexistence of topological semimetal states in holography
We introduce a holographic model that exhibits a coexistence state of the Weyl semimetal and the topological nodal line state, providing us with a valuable tool to investigate the system's behavior in the strong coupling regime. Nine types of bulk solutions exhibiting different IR behaviors have been identified, corresponding to nine different types of boundary states. These nine states include four distinct phases, namely the Weyl-nodal phase, the gap-nodal phase, the Weyl gap phase and the ga…

Gravitational collapse in effective loop quantum gravity: beyond marginally bound configurations
Lorenzo Cipriani, Francesco Fazzini, Edward Wilson-Ewing
https://arxiv.org/abs/2404.04192

Gravitational collapse in effective loop quantum gravity: beyond marginally bound configurations
We study gravitational collapse in effective loop quantum gravity, focusing on non-marginally bound configurations in Lemaître-Tolman-Bondi spacetimes. In the homogeneous limit we recover the effective dynamics of loop quantum cosmology for Friedman cosmologies with spatial curvature. We study a particular family of configurations with a homogeneous interior and a sharp boundary where the dust energy density rapidly and continuously decreases to zero. For these configurations, the gravitationa…

First homology groups of the Milnor fiber boundary for generic hyperplane arrangements in $\mathbb{C}^{3}$
Sakumi Sugawara
https://arxiv.org/abs/2404.01555

First homology groups of the Milnor fiber boundary for generic hyperplane arrangements in $\mathbb{C}^{3}$
We study the Milnor fiber boundary for hyperplane arrangements in $\mathbb{C}^3$. This is one of the examples of non-isolated surface singularities, which are studied by Némethi--Szilárd. In this paper, we compute the first homology group of the Milnor fiber boundary for a generic arrangement and prove it is combinatorially determined. In particular, this gives the affirmative answer to the conjecture of Suciu.

Numerical study of a viscous breaking water wave and the limit of vanishing viscosity
Alan Riquier, Emmanuel Dormy
https://arxiv.org/abs/2403.03851 https:/…

Numerical study of a viscous breaking water wave and the limit of vanishing viscosity
We introduce a numerical strategy to study the evolution of 2D water waves in the presence of a plunging jet. The free-surface Navier-Stokes solution is obtained with a finite but small viscosity. We observe the formation of a surface boundary layer where the vorticity is localised. We highlight convergence to the inviscid solution. The effects of dissipation on the development of a singularity at the tip of the wave is also investigated by characterising the vorticity boundary layer appearing …

Boundary Behavior of Compact Manifolds With Scalar Curvature Lower Bounds and Static Quasi-Local Mass of Tori
Aghil Alaee, Pei-Ken Hung, Marcus Khuri
https://arxiv.org/abs/2403.02501

Boundary Behavior of Compact Manifolds With Scalar Curvature Lower Bounds and Static Quasi-Local Mass of Tori
A classic result of Shi and Tam states that a 2-sphere of positive Gauss and mean curvature bounding a compact 3-manifold with nonnegative scalar curvature, must have total mean curvature not greater than that of the isometric embedding into Euclidean 3-space, with equality only for domains in this reference manifold. We generalize this result to 2-tori of Guass curvature greater than $-1$, which bound a compact 3-manifold having scalar curvature not less than $-6$ and at least one other bounda…

This https://arxiv.org/abs/2306.15897 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Global solutions and blow-up for the wave equation with variable coefficients and boundary supercritical source
In this paper, we consider the wave equation with variable coefficients and boundary damping and supercritical source terms. The goal of this work is devoted to prove the local and global existence, and classify decay rate of energy depending on the growth near zero on the damping term. Moreover, we prove the blow-up of the weak solution with positive initial energy as well as nonpositive initial energy.

This https://arxiv.org/abs/2309.08364 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On some isoperimetric inequalities for the Newtonian capacity
Upper bounds are obtained for the Newtonian capacity of compact sets in $\R^d,\,d\ge 3$ in terms of the perimeter of the $r$-parallel neighbourhood of $K$. For compact, convex sets in $\R^d,\,d\ge 3$ with a $C^2$ boundary the Newtonian capacity is bounded from above by $(d-2)M(K)$, where $M(K)>0$ is the integral of the mean curvature over the boundary of $K$ with equality if $K$ is a ball. For compact, convex sets in $\R^d,\,d\ge 3$ with non-empty interior the Newtonian capacity is bounded from…

This https://arxiv.org/abs/2312.16780 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A weighted Reilly formula for differential forms and sharp Steklov eigenvalue estimates
First we establish a weighted Reilly formula for differential forms on a smooth compact oriented Riemannian manifold with boundary. Then we give two applications of this formula when the manifold satisfies certain geometric conditions. One is a sharp lower bound for the first positive eigenvalue of the Steklov eigenvalue problem on differential forms investigated by Belishev and Sharafutdinov (2008) and Karpukhin (2019). The other one is a comparison result between the spectrum of this Steklov …

This https://arxiv.org/abs/2111.10158 has been replaced.
link: https://scholar.google.com/scholar?q=a

A priori estimates for the motion of charged liquid drop: A dynamic approach via free boundary Euler equations
We study the motion of charged liquid drop in three dimensions where the equations of motions are given by the Euler equations with free boundary with an electric field. This is a well-known problem in physics going back to the famous work by Rayleigh. Due to experiments and numerical simulations one expects the charged drop to form conical singularities called Taylor cones, which we interpret as singularities of the flow. In this paper, we study the well-posedness, regularity and the formation…

This https://arxiv.org/abs/2311.09686 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Hausdorff measure bound for the nodal sets of Neumann Laplace eigenfunctions
We study the nodal sets of Neumann Laplace eigenfunctions in a bounded domain with $\mathcal{C}^{1,1}$ boundary. We show that for $u_λ$ such that $Δu_λ+ λu_λ= 0 $ with the Neumann boundary condition $\partial_νu_λ= 0$, we have $\mathcal{H}^{n-1}(\{u_λ= 0\}) \leq C \sqrtλ$.

Oscillatory free boundary problems in stochastic materials
Dami\~ao J. Ara\'ujo, Ginaldo S. S\'a, Eduardo V. Teixeira, Jos\'e Miguel Urbano
https://arxiv.org/abs/2404.03060

Oscillatory free boundary problems in stochastic materials
We investigate a class of free boundary problems with oscillatory singularities within stochastic materials. Our main result yields sharp regularity estimates along the free boundary, provided the power of the singularity varies in a Dini-continuous fashion below a certain threshold. We also reveal an interesting repelling estimate preventing the free boundary from touching the region where the singularity power oscillates above the threshold.

An informal account of recent results on initial-boundary value problems for systems of conservation laws
Laura V. Spinolo, Fabio Ancona, Andrea Marson
https://arxiv.org/abs/2405.02096

An informal account of recent results on initial-boundary value problems for systems of conservation laws
This note aims at providing a rather informal and hopefully accessible overview of the fairly long and technical work [4]. In that paper, the authors established new global-in-time existence results for admissible solutions of nonlinear systems of conservation laws defined in domains with boundaries. The main novelty in [4] is that the solution is constructed by taking into account the underlying viscous mechanism, which is relevant because, in the case of initial-boundary value problems, diffe…

This https://arxiv.org/abs/2308.16405 has been replaced.
initial toot: https://mastoxiv.page/@ar…

On the departure from Monin-Obukhov surface similarity and transition to the convective mixed layer
Large-eddy simulations are used to evaluate mean profile similarity in the convective boundary layer (CBL). Particular care is taken regarding the grid sensitivity of the profiles and the mitigation of inertial oscillations in the simulation spin-up. The nondimensional gradients $ϕ$ for wind speed and air temperature generally align with Monin-Obukhov similarity across cases but have a steeper slope than predicted within each profile. The same trend has been noted in several other recent studi…

This https://arxiv.org/abs/2308.16405 has been replaced.
initial toot: https://mastoxiv.page/@ar…

On the departure from Monin-Obukhov surface similarity and transition to the convective mixed layer
Large-eddy simulations are used to evaluate mean profile similarity in the convective boundary layer (CBL). Particular care is taken regarding the grid sensitivity of the profiles and the mitigation of inertial oscillations in the simulation spin-up. The nondimensional gradients $ϕ$ for wind speed and air temperature generally align with Monin-Obukhov similarity across cases but have a steeper slope than predicted within each profile. The same trend has been noted in several other recent studi…

The existence theorem for the steady-state Navier-Stokes equations with nonhomogeneous slip boundary conditions in two-dimensional multiply-connected bounded domains
Giovanni P. Galdi, Tatsuki Yamamoto
https://arxiv.org/abs/2403.00164

The existence theorem for the steady-state Navier-Stokes equations with nonhomogeneous slip boundary conditions in two-dimensional multiply-connected bounded domains
We study the nonhomogeneous boundary value problem for the steady-state Navier-Stokes equations under the slip boundary conditions in two-dimensional multiply-connected bounded domains. Employing the approach of Korobkov-Pileckas-Russo (Ann. Math. 181(2), 769-807, 2015), we prove that this problem has a solution if the friction coefficient is sufficiently large compared with the kinematic viscosity constant and the curvature of the boundary. No additional assumption (other than the necessary re…