Found 2738 results, showing the newest relevant preprints. Sort by relevancy only.Update me on new preprints

Black hole shadow in the view of freely falling observers

For co-moving observers driven by cosmological constant in Schwarzschild-de Sitter

**space**-time, we find that the angular radius of shadow could increase even when the observers move farther from the black hole. Expand abstract. First sketch of black hole from M87 galaxy was obtained by Event Horizon Telescope, recently. As appearance of black hole shadow reflects

**space**-**time**geometry of black holes, observations of black hole shadow may be another way to test general relativity in strong field regime. In this paper, we focus on angular radius of spherical black hole shadow with respect to freely falling observers. In the framework of general relativity, aberration formulation and angular radius-gravitational redshift relation are presented. For the sake of intuitive, we consider parametrized Schwarzschild black hole and Schwarzschild-de Sitter black hole as representative example. We find that the freely falling observers would observe finite size of shadow, when they go through event horizon. For co-moving observers driven by cosmological constant in Schwarzschild-de Sitter**space**-time, we find that the angular radius of shadow could increase even when the observers move farther from the black hole.83 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv

Global well-posedness of cubic fractional Schr\"odinger equations in one dimension

In this paper, we consider the Cauchy's problem of global existence and scattering behavior of small, smooth, and localized solutions of cubic fractional Schr\"odinger equations in one dimension, \begin{equation*} \mathrm{i} \partial_t u- (-\Delta)^{\frac{\alpha}{2}} u=c_* Expand abstract.

In this paper, we consider the Cauchy's problem of global existence and scattering behavior of small, smooth, and localized solutions of cubic fractional Schr\"odinger equations in one dimension, \begin{equation*} \mathrm{i} \partial_t u- (-\Delta)^{\frac{\alpha}{2}} u=c_*|u|^2u, \end{equation*} where $\alpha \in (\frac{1}{3},1), c_* \in \mathbb{R}$. Our work is a generalization of the result due to Ionescu and Pusateri \cite{IP}, where the case $\alpha=\frac{1}{2}$ was considered. The highlight in this paper is to give a modified dispersive estimate in weighted Sobolev

**spaces**for cubic fractional Schr\"odinger equations, which could be used for $ \alpha \in (\frac{1}{3},1)$. Based on this modified dispersive estimate, we prove the global existence and modified scattering behavior of solutions combining**space**-**time**resonance and bootstrap arguments.84 days ago

4/10 relevant

arXiv

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arXiv

Locally interacting diffusions as **space**-**time** Markov random fields

We consider a countable system of interacting (possibly non-Markovian) stochastic differential equations driven by independent Brownian motions and indexed by the vertices of a locally finite graph $G = (V,E)$. Expand abstract.

We consider a countable system of interacting (possibly non-Markovian) stochastic differential equations driven by independent Brownian motions and indexed by the vertices of a locally finite graph $G = (V,E)$. The drift of the process at each vertex is influenced by the states of that vertex and its neighbors, and the diffusion coefficient depends on the state of only that vertex. Such processes arise in a variety of applications including statistical physics, neuroscience, engineering and math finance. Under general conditions on the coefficients, we show that if the initial conditions form a second-order Markov random field on $d$-dimensional Euclidean space, then at any positive time, the collection of histories of the processes at different vertices forms a second-order Markov random field on path

**space**. We also establish a bijection between (second-order) Gibbs measures on $(\mathbb{R}^d)^V$ (with finite second moments) and a set of**space**-**time**(second-order) Gibbs measures on path space, corresponding respectively to the initial law and the law of the solution to the stochastic differential equation. As a corollary, we establish a Gibbs uniqueness property that shows that for infinite graphs the joint distribution of the paths is completely determined by the initial condition and the specifications, namely the family of conditional distributions on finite vertex sets given the configuration on the complement. Along the way, we establish various approximation and projection results for Markov random fields on locally finite graphs that may be of independent interest.84 days ago

10/10 relevant

arXiv

10/10 relevant

arXiv

Recovering coercivity for the G-equation in general random media

The waiting

**time**is explicitly characterized in terms of the**space**-time means of the velocity field and so mixing estimates on the waiting time can easily be derived. Expand abstract. The G-equation is a popular model for premixed turbulent combustion. Mathematically it has attracted a lot of interest in part because it is a simple example of a Hamilton-Jacobi equation which is only coercive `on average'. This paper shows that, after an almost surely finite waiting time, coercivity is recovered for the G-equation in a small mean, incompressible,

**space**-**time**stationary ergodic velocity field. The argument follows ideas from recent work of Burago, Ivanov and Novikov, while significantly weakening the assumption on the velocity field. The waiting**time**is explicitly characterized in terms of the**space**-**time**means of the velocity field and so mixing estimates on the waiting**time**can easily be derived. Examples are provided.86 days ago

5/10 relevant

arXiv

5/10 relevant

arXiv

A stochastic transport problem with L'evy noise: Fully discrete numerical approximation

Furthermore, the L\'evy process admits values in a possibly infinite-dimensional Hilbert space, hence projections into a finite-dimensional sub

**space**for each discrete point in**time**are necessary. Expand abstract. Semilinear hyperbolic stochastic partial differential equations have various applications in the natural and engineering sciences. From a modelling point of view the Gaussian setting can be too restrictive, since phenomena as porous media, pollution models or applications in mathamtical finance indicate an influence of noise of a different nature. In order to capture temporal discontinuities and allow for heavy-tailed distributions, Hilbert

**space**valued-L\'evy processes (or L\'evy fields) as driving noise terms are considered. The numerical discretization of the corresponding SPDE involves several difficulties: Low spatial and temporal regularity of the solution to the problem entails slow convergence rates and instabilities for space/time-discretization schemes. Furthermore, the L\'evy process admits values in a possibly infinite-dimensional Hilbert space, hence projections into a finite-dimensional subspace for each discrete point in**time**are necessary. Finally, unbiased sampling from the resulting L\'evy field may not be possible. We introduce a fully discrete approximation scheme that addresses these issues. A discontinuous Galerkin approach for the spatial approximation is coupled with a suitable**time**stepping scheme to avoid numerical oscillations. Moreover, we approximate the driving noise process by truncated Karhunen-Lo\'eve expansions. The latter essentially yields a sum of scaled and uncorrelated one-dimensional L\'evy processes, which may be simulated with controlled bias by Fourier inversion techniques.88 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv

A note on the electromagnetic irradiation in a holed spatial region -- a
**space**-**time** approach

We study the role of the topological homological property of a

**space**-**time**with holes (a multiple connected manifold) on the formal solutions of the electromagnetic irradiation problem taking place on theses "holed" space-times. Expand abstract. We study the role of the topological homological property of a

**space**-**time**with holes (a multiple connected manifold) on the formal solutions of the electromagnetic irradiation problem taking place on theses "holed"**space**-times. On three appendixes, additional to the bulk section 1, we also present important studies on this irradiation problem, now on others mathematical frameworks .88 days ago

10/10 relevant

arXiv

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arXiv

Space-efficient, Fast and Exact Routing in **Time**-dependent Road Networks

All existing techniques have a large index size, slow query running

**times**, or may compute subop**timal**paths. Expand abstract. We study the problem of computing shortest paths in massive road networks with traffic predictions. Existing techniques follow a two phase approach: In an offline, preprocessing step, a database index is built. The index only depends on the road network and the traffic patterns. The path start and end are the input of the query phase, in which shortest-paths are computed. All existing techniques have a large index size, slow query running times, or may compute suboptimal paths. In this work, we introduce CATCHUp (Customizable Approximated

**Time**-dependent Contraction Hierarchies through Unpacking), the first algorithm that simultaneously achieves all three objectives. We perform an extensive experimental study on a set of real world instances and compare our approach with state-of-the-art techniques. Our approach achieves up to 30**times**smaller indexes than competing approaches. Additionally, our index can be updated within a few minutes if traffic patterns change.91 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv

Unsupervised **Space**-**Time** Clustering using Persistent Homology

This paper presents a new clustering algorithm for

**space**-**time**data based on the concepts of topological data analysis and in particular, persistent homology. Expand abstract. This paper presents a new clustering algorithm for

**space**-**time**data based on the concepts of topological data analysis and in particular, persistent homology. Employing persistent homology - a flexible mathematical tool from algebraic topology used to extract topological information from data - in unsupervised learning is an uncommon and a novel approach. A notable aspect of this methodology consists in analyzing data at multiple resolutions which allows to distinguish true features from noise based on the extent of their persistence. We evaluate the performance of our algorithm on synthetic data and compare it to other well-known clustering algorithms such as K-means, hierarchical clustering and DBSCAN. We illustrate its application in the context of a case study of water quality in the Chesapeake Bay.94 days ago

10/10 relevant

arXiv

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arXiv

From Infinity to Four Dimensions: Higher Residue Pairings and Feynman Integrals

We study a surprising phenomenon in which Feynman integrals in $D=4-2\varepsilon$ space-time dimensions as $\varepsilon \to 0$ can be fully characterized by their behavior in the opposite limit, $\varepsilon \to \infty$. Expand abstract.

We study a surprising phenomenon in which Feynman integrals in $D=4-2\varepsilon$

**space**-**time**dimensions as $\varepsilon \to 0$ can be fully characterized by their behavior in the opposite limit, $\varepsilon \to \infty$. More concretely, we consider vector bundles of Feynman integrals over kinematic spaces, whose connections have a polynomial dependence on $\varepsilon$ and are known to be governed by intersection numbers of twisted forms. They give rise to differential equations that can be obtained exactly as a truncating expansion in either $\varepsilon$ or $1/\varepsilon$. We use the latter for explicit computations, which are performed by expanding intersection numbers in terms of Saito's higher residue pairings (previously used in the context of topological Landau-Ginzburg models and mirror symmetry). These pairings localize on critical points of a certain Morse function, which correspond to regions in the loop-momentum**space**that were previously thought to govern only the large-$D$ physics. The results of this work leverage recent understanding of an analogous situation for moduli**spaces**of curves, where the $\alpha' \to 0$ and $\alpha' \to \infty$ limits of intersection numbers coincide for scattering amplitudes of massless quantum field theories.94 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv

Spinning test particles in the $\gamma$ **space**time

We consider the motion of spinning particles in the field of a well known vacuum static axially-symmetric spacetime, known as $\gamma$ metric, that can be interpreted as a generalization of the Schwarzschild manifold to include prolate or oblate deformations. Expand abstract.

We consider the motion of spinning particles in the field of a well known vacuum static axially-symmetric spacetime, known as $\gamma$ metric, that can be interpreted as a generalization of the Schwarzschild manifold to include prolate or oblate deformations. We derive the equations of motion for spinning test particles by using the Mathisson-Papapetrou-Dixon equations together with the Tulczyjew spin-supplementary condition, and restricting the motion to the equatorial plane. We determine the limit imposed by super-luminal velocity for the spin of the particle located at the innermost stable circular orbits (ISCO). We show that the particles on ISCO of the prolate $\gamma$ spacetime are allowed to have nigher spin than the corresponding ones in the the oblate case. We determine the value of the ISCO radius depending on the signature of the spin-angular momentum, ${\rm s-L}$ relation, and show that the value of the ISCO with respect to the non spinning case is bigger for ${\rm sL}0$. The results may be relevant for determining the properties of accretion disks and constraining the allowed values of quadrupole moments of astrophysical black hole candidates.

94 days ago

10/10 relevant

arXiv

10/10 relevant

arXiv