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In this paper, based on the parabolic interpolation inequality and inductive argument, we study the space-time decay estimates of higher-order time and spatial derivatives of strong solutions for the 3D incompressible viscous Camassa–Holm equations provided that the initial datum is well localized. [ABSTRACT FROM AUTHOR]

Geosynchronous orbit synthetic aperture radar (GEO SAR) has a long synthetic aperture time and a large-scale imaging scene. Therefore, various non-ideal factors tend to accumulate, introducing phase errors and decreasing the imaging quality. During the long integration time, troposphere is time varying and space variant, which will result in image shifts and defocusing. According to the characteristics of GEO SAR, this study completes the modelling and the quantitative analysis of tropospheric turbulence. Based on the phase-screen theory, the amplitude and phase random fluctuations caused by the turbulence which will result in the defocus of images are analysed. However, in the natural environment, the imaging of GEO SAR system is affected weakly by the turbulence and this conclusion is proved from the spectral analysis. [ABSTRACT FROM AUTHOR]

We show how to generate the AdS spacetime metric in general Lorentz covariant gauges. In particular we propose an iterative method for solving the Lorentz gauge. [ABSTRACT FROM AUTHOR]

Einstein’s theory of gravity, General Relativity, has been precisely tested on Solar System scales, but the long-range nature of gravity is still poorly constrained. The nearby strong gravitational lens ESO 325-G004 provides a laboratory to probe the weak-field regime of gravity and measure the spatial curvature generated per unit mass, g. By reconstructing the observed light profile of the lensed arcs and the observed spatially resolved stellar kinematics with a single self-consistent model, we conclude that g = 0.97 ± 0.09 at 68% confidence. Our result is consistent with the prediction of 1 from General Relativity and provides a strong extragalactic constraint on the weak-field metric of gravity. [ABSTRACT FROM AUTHOR]

The object of the present paper is to study super quasi-Einstein manifolds. Some geometric properties of super quasi-Einstein manifolds have been studied. We also discuss S(QE)4 spacetime with space-matter tensor and some properties related to it. Finally, we construct an example of a super quasi-Einstein spacetime. [ABSTRACT FROM AUTHOR]

The utilising of space-time adaptive processing (STAP) can effectively enhance the globe navigation satellite system (GNSS) receivers' performance in suppressing harsh, sustained interference. However, STAP may introduce significant biases and distortions on the cross-correlation functions, which would deteriorate acquisition and tracking performance. To achieve high-accuracy GNSS applications in challenging environments, these biases and distortions must be mitigated. A novel distortionless space-time adaptive processor based on minimum variance disstortionless response (MVDR) beamformer is proposed. By combining the information of steering vector and constraining the taps number of tapped delay line to be odd, the proposed processor can maintain the linearity of space-time filter response and it introduces no biases into the code and carrier phase measurements. The effectiveness of the proposed processor is demonstrated by theoretical analysis and simulations. [ABSTRACT FROM AUTHOR]

Objective video quality assessment (VQA) plays an important role in controlling video quality. Most of the existing VQA methods measure motion-related temporal distortion based on optical-flow methods, which are not consistently reliable in modeling general visual dynamics. This paper presents a full-reference temporal distortion measure based on spacetime texture , a uniform and distributive descriptor of a broad set of spacetime structures. Our method measures the distortion of spacetime texture in video with a motion-tuning strategy, which effectively captures temporal distortion along the motion trajectories. Then it estimates self-information based visual saliency for spatial pooling by reusing the motion descriptors. We evaluated our method on two public VQA databases with a wide variety of distortion types, in which the videos were viewed on a large screen or mobile devices. The results show that our method correlates highly with the subjective quality and has high computational efficiency. [ABSTRACT FROM AUTHOR]

We show that linear scalar waves are bounded and continuous up to the Cauchy horizon of Reissner-Nordström-de Sitter and Kerr-de Sitter spacetimes and in fact decay exponentially fast to a constant along the Cauchy horizon. We obtain our results by modifying the spacetime beyond the Cauchy horizon in a suitable manner, which puts the wave equation into a framework in which a number of standard as well as more recent microlocal regularity and scattering theory results apply. In particular, the conormal regularity of waves at the Cauchy horizon-which yields the boundedness statement-is a consequence of radial point estimates, which are microlocal manifestations of the blue-shift and red-shift effects. [ABSTRACT FROM AUTHOR]

The conformal structure of the Schwarzschild-de Sitter spacetime is analysed using the extended conformal Einstein field equations. To this end, initial data for an asymptotic initial value problem for the Schwarzschild-de Sitter spacetime are obtained. This initial data allow to understand the singular behaviour of the conformal structure at the asymptotic points where the horizons of the Schwarzschild-de Sitter spacetime meet the conformal boundary. Using the insights gained from the analysis of the Schwarzschild-de Sitter spacetime in a conformal Gaussian gauge, we consider nonlinear perturbations close to the Schwarzschild-de Sitter spacetime in the asymptotic region. We show that small enough perturbations of asymptotic initial data for the Schwarzschild-de Sitter spacetime give rise to a solution to the Einstein field equations which exists to the future and has an asymptotic structure similar to that of the Schwarzschild-de Sitter spacetime. [ABSTRACT FROM AUTHOR]

In this paper, we present a theoretical and numerical analysis of the free expansion of a Bose-Einstein condensate, where we assume that the single particle energy spectrum is deformed due to a possible quantum structure of spacetime. Also, we consider the presence of interparticle interactions in order to study more realistic and specific scenarios. The modified free velocity expansion of the condensate leads in a natural way to a modification of the uncertainty principle, which allows us to investigate some possible features of the Planck scale regime in low-energy earth-based experiments. [ABSTRACT FROM AUTHOR]

Recently, there has been increased interest in the behavior of wildfires. Behavior includes explaining: incidence of wildfires; recurrence times for wildfires; sizes, scars, and directions of wildfires; and recovery of burned regions after a wildfire. We study this last problem. In particular, we use the annual normalized difference vegetation index (NDVI) to provide a picture of vegetative levels. Employed post-wildfire, it provides a picture of vegetative recovery. The contribution here is to model post-fire vegetation recovery from a different perspective. What exists in the literature specifies a parametric monotone form for the recovery function and then fits it to the available data. However, recovery need not be monotone; NDVI levels may increase or decrease annually according to climate variables. Furthermore, when there is recovery, it need not follow a simple parametric form. Instead, we view recovery in a relative way. We model what NDVI would look like over the fire scar in the absence of a wildfire. Then, we can examine NDVI recovery locally, employing the observed NDVI recovery at a location relative to the predictive distribution of NDVI at that location. We work with wildfire data from the Communidad Autonomía of Aragón in Spain. We develop our approach in two stages. First, we validate the predictability of NDVI in the absence of wildfire. Then, we study annual recovery and evolution of recovery for an illustrative wildfire region. We work within a hierarchical Bayes framework, adopting suitable dynamic spatial models, attaching full uncertainty to our inference on recovery. [ABSTRACT FROM AUTHOR]

We introduce a time-integrator to sample with high order of accuracy the invariant distribution for a class of semilinear stochastic PDEs (SPDEs) driven by an additive space-time noise. Combined with a postprocessor, the new method is a modification with negligible overhead of the standard linearized implicit Euler-Maruyama method. We first provide an analysis of the integrator when applied for SDEs (finite dimension), where we prove that the method has order 2 for the approximation of the invariant distribution, instead of 1. We then perform a stability analysis of the integrator in the semilinear SPDE context, and we prove in a linear case that a higher order of convergence is achieved. Numerical experiments, including the semilinear heat equation driven by space-time white noise, confirm the theoretical findings and illustrate the effciency of the approach. [ABSTRACT FROM AUTHOR]

We generalize the reflection theorem of the Lorentz-Minkowski plane to that of the Lorentz-Minkowski spaces of higher dimensions. As a result, we show that an isometry of the Lorentz-Minkowski spacetime is a composition of at most 5 reflections. [ABSTRACT FROM AUTHOR]

In this work we take a formal approach to the problem of decoupling Proca equations in curved space-times. We use Newman-Penrose two-spinor formalism to represent the Proca vector by one complex and two real scalars. We show that a decoupled second order differential equation for one of the real scalars can be derived if and only if the background space-time admits a covariantly constant null vector. Thus, the background space-time must be a pp-wave vacuum. We evaluate the separability of Proca, Maxwell and Dirac equations on the resulting pp-wave background. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamics of Lemaitre-Tolman-Bondi spacetime with respect to tilted observer in f( R) gravity and obtains significant relationships between tilted and non-tilted observers. We discuss inhomogeneity factor and its evolution with the help of kinematical and dynamical quantities. It is found that for tilted observer the evolution of inhomogeneity factor depends upon heat flux, shear tensor and expansion scalar while for non-tilted observer, it depends only upon shear tensor. We also explore the stability criteria of non-tilted congruence in the presence of dark source term and find that expansion is responsible for instability of non-tilted congruence. [ABSTRACT FROM AUTHOR]

The article reports that the Dutch government's proposal for Europe's Einstein Telescope has put him ahead of rival bids. Researchers in Europe and the United States are thinking about bigger gravitational wave detectors that could survey most of the universe. Three overlapping L-shaped detectors will watch for spacetime distortions, and the observatory will be buried in bedrock several hundred meters down to insulate it from the surface noise of wind and traffic.

We present a novel video stabilization method which models camera motion with a bundle of (multiple) camera paths. The proposed model is based on a mesh-based, spatially-variant motion representation and an adaptive, space-time path optimization. Our motion representation allows us to fundamentally handle parallax and rolling shutter effects while it does not require long feature trajectories or sparse 3D reconstruction. We introduce the 'as-similar-as-possible' idea to make motion estimation more robust. Our space-time path smoothing adaptively adjusts smoothness strength by considering discontinuities, cropping size and geometrical distortion in a unified optimization framework. The evaluation on a large variety of consumer videos demonstrates the merits of our method. [ABSTRACT FROM AUTHOR]

The frequently used analogy of a massive ball distorting an elastic sheet, which is used to illustrate why mass causes spacetime curvature and gravitational attraction, is criticized in this article. A different analogy that draws on the students' previous knowledge of spacetime diagrams in special relativity is suggested. [ABSTRACT FROM AUTHOR]

We show that the global monopole spacetime is one of the exact solutions of the Einstein equations by treating the matter field as a non-linear sigma model, without the weak field approximation applied in the original derivation by Barriola and Vilenkin. Furthermore, we find the physical origin of the topological charge in the global monopole spacetime. Finally, we generalize the proposal which generates spacetime from thermodynamical laws to the case of spacetime with global monopole charge. [ABSTRACT FROM AUTHOR]

The article focuses on the possibility of squeezing quantum noise. Topics discussed include the uncertainty of the observable properties of a physical system in quantum mechanics and the propagation of vacuum fluctuations. Also mentioned are the distortion of spacetime by gravitational waves and the improved use of gravitational-wave detector.

The null Penrose inequality, i.e. the Penrose inequality in terms of the Bondi energy, is studied by introducing a functional on surfaces and studying its properties along a null hypersurface Ω extending to past null infinity. We prove a general Penrose-type inequality which involves the limit at infinity of the Hawking energy along a specific class of geodesic foliations called Geodesic Asymptotically Bondi (GAB), which are shown to always exist. Whenever this foliation approaches large spheres, this inequality becomes the null Penrose inequality and we recover the results of Ludvigsen–Vickers (1983 J. Phys. A: Math. Gen.16 3349–53) and Bergqvist (1997 Class. Quantum Grav.14 2577–83). By exploiting further properties of the functional along general geodesic foliations, we introduce an approach to the null Penrose inequality called the Renormalized Area Method and find a set of two conditions which imply the validity of the null Penrose inequality. One of the conditions involves a limit at infinity and the other a restriction on the spacetime curvature along the flow. We investigate their range of applicability in two particular but interesting cases, namely the shear-free and vacuum case, where the null Penrose inequality is known to hold from the results by Sauter (2008 PhD Thesis Zürich ETH), and the case of null shells propagating in the Minkowski spacetime. Finally, a general inequality bounding the area of the quasi-local black hole in terms of an asymptotic quantity intrinsic of Ω is derived. [ABSTRACT FROM AUTHOR]