Averaging gaussian functionals

**space**-

**time**Gaussian colored noise. The temporal covariance kernel $\gamma_0$ is assumed to be locally integrable in this paper. If the spatial covariance kernel is nonnegative and integrable on the whole space, then the spatial average admits Gaussian fluctuation; with some extra mild integrability condition on $\gamma_0$, we are able to provide a functional central limit theorem. These results complement recent studies on the spatial average for SPDEs. Our analysis also allows us to consider the case where the spatial covariance kernel is not integrable: For example, in the case of the Riesz kernel, the first chaotic component of the spatial average is dominant so that the Gaussian fluctuation also holds true.

4/10 relevant

arXiv

Spin-Locality of Higher-Spin Theories and Star-Product Functional Classes

**Space**-

**time**interpretation of spin-locality of theories involving infinite towers of fields is proposed as the property that the theory is

**space**-

**time**local in terms of original constituent fields $\Phi$ and their local currents $J(\Phi)$ of all ranks. Spin-locality is argued to be a proper substitute of locality for theories with finite sets of fields for which the two concepts are equivalent.

5/10 relevant

arXiv

Entropy and Gravitation: From Black Hole Computers to Dark Energy and Dark Matter

**space**-

**time**foam) and turbulence. Expand abstract.

**space**-

**time**foam, dark energy, dark matter and the phenomenon of turbulence. We use three different methods to estimate the foaminess of

**space**-time, which, in turn, provides a back-door way to derive the Bekenstein-Hawking formula for black hole entropy and the holographic principle. Generalizing the discussion for a static

**space**-

**time**region to the cosmos, we find a component of dark energy (resembling an effective positive cosmological constant of the correct magnitude) in the current epoch of the universe. The conjunction of entropy and gravitation is shown to give rise to a phenomenological model of dark matter, revealing the natural emergence, in galactic and cluster dynamics, of a critical acceleration parameter related to the cosmological constant; the resulting mass profiles are consistent with observations. Unlike ordinary matter, the quanta of the dark sector are shown to obey infinite statistics. This property of dark matter may lead to some non-particle phenomenology, and may explain why dark matter particles have not been detected in dark matter search experiments. We also show that there are deep similarities between the problem of "quantum gravity" (more specifically, the holographic

**space**-

**time**foam) and turbulence.

7/10 relevant

arXiv

Lower Bound and **Space**-**time** Decay Rates of Higher Order Derivatives of
Solution for the Compressible Navier-Stokes and Hall-MHD Equations

**space**-

**time**decay rates for the compressible Navier-Stokes and Hall-MHD equations under $H^3-$framework in $\mathbb{R}^3$. First of all, the lower bound of decay rate for the density, velocity and magnetic field converging to the equilibrium status in $L^2$ is $(1+t)^{-\frac{3}{4}}$; the lower bound of decay rate for the first order spatial derivative of density and velocity converging to zero in $L^2$ is $(1+t)^{-\frac{5}{4}}$, and the $k(\in [1, 3])-$th order spatial derivative of magnetic field converging to zero in $L^2$ is $(1+t)^{-\frac{3+2k}{4}}$. Secondly, the lower bound of decay rate for

**time**derivatives of density and velocity converging to zero in $L^2$ is $(1+t)^{-\frac{5}{4}}$; however, the lower bound of decay rate for

**time**derivatives of magnetic field converging to zero in $L^2$ is $(1+t)^{-\frac{7}{4}}$. Finally, we address the decay rate of solution in weighted Sobolev

**space**$H^3_{\gamma}$. More precisely, the upper bound of decay rate of the $k(\in [0, 2])$-th order spatial derivatives of density and velocity converging to the $k(\in [0, 2])$-th order derivatives of constant equilibrium in weighted

**space**$L^2_{\gamma}$ is $t^{-\frac{3}{4}+{\gamma}-\frac{k}{2}}$; however, the upper bounds of decay rate of the $k(\in [0, 3])$-th order spatial derivatives of magnetic field converging to zero in weighted

**space**$L^2_{\gamma}$ is $t^{-\frac{3}{4}+\frac{{\gamma}}{2}-\frac{k}{2}}$.

10/10 relevant

arXiv

Experimental observation of non-reciprocal band-gaps in a **space**-time
modulated beam using a shunted piezoelectric array

**time**of the cell properties. Expand abstract.

**time**of the cell properties. A traveling stiffness profile is obtained by opportunely phasing the temporal modulation of each active element, mimicking the propagation of a plane wave along the material, therefore establishing unidirectional wave propagation at bandgap frequencies.

8/10 relevant

arXiv

Analysis of an Asymptotic Preserving Low Mach Number Accurate IMEX-RK Scheme for the Wave Equation System

**times**, and this can be formulated in terms of the invariance of a

**space**of constant densities and divergence-free velocities. Expand abstract.

**space**of constant densities and divergence-free velocities. An IMEX-RK methodology is employed to obtain a

**time**semi-discrete scheme, and a

**space**-

**time**fully-discrete scheme is derived by using standard finite volume techniques. The existence of a unique numerical solution, its uniform stability with respect to the Mach number, the AP property, and the accuracy at low Mach numbers are established for both

**time**semi-discrete, and

**space**-

**time**fully-discrete schemes. Extensive numerical case studies confirm uniform second order convergence of the scheme with respect to the Mach number, and all the above-mentioned properties.

7/10 relevant

arXiv

Space-**time** calibration of wind speed forecasts from regional climate
models

**space**-

**time**models that extend the main statistical postprocessing approaches to calibrate NWP model outputs. Expand abstract.

**time**-varying bias is usually not accommodated by such models. Its calibration performance is also sensitive to the temporal window used for training. This paper proposes

**space**-

**time**models that extend the main statistical postprocessing approaches to calibrate NWP model outputs. Trans-Gaussian random fields are considered to account for meteorological variables with asymmetric behavior. Data augmentation is used to account for censuring in the response variable. The benefits of the proposed extensions are illustrated through the calibration of hourly 10 m wind speed forecasts in Southeastern Brazil coming from the Eta model.

10/10 relevant

arXiv

New Mathematical Models of GPS Intersatellite Communications in the
Gravitational Field of the Near-Earth **Space**

**space**-

**time**interval, but with account also of the "condition for ISC". Expand abstract.

**space**missions such as GRACE, GRAIL, ACES and others rely on intersatellite communications (ISC) between two satellites at a large distance one from another. The main goal of the theory is to formulate all the navigation observables within the General Relativity Theory (GRT). The same approach should be applied also to the intersatellite GPS-communications (in perspective also between the GPS, GLONASS and Galileo satellite constellations). In this paper a theoretical approach has been developed for ISC between two satellites moving on (one-plane) elliptical orbits based on the introduction of two gravity null cones with origins at the emitting-signal and receiving-signal satellites. The two null cones account for the variable distance between the satellites during their uncorrelated motion. This intersection of the two null cones gives the

**space**-

**time**interval in GRT. Applying some theorems from higher algebra, it was proved that this

**space**-

**time**distance can become zero, consequently it can be also negative and positive. But in order to represent the geodesic distance travelled by the signal, the

**space**-

**time**interval has to be "compatible" with the Euclidean distance. So this "compatibility condition", conditionally called "condition for ISC", is the most important consequence of the theory. The other important consequence is that the geodesic distance turns out to be the

**space**-

**time**interval, but with account also of the "condition for ISC". The geodesic distance is proved to be greater than the Euclidean distance - a result, entirely based on the "two null cones approach" and moreover, without any use of the Shapiro delay formulae. Application of the same higher algebra theorems shows that the geodesic distance cannot have any zeroes, in accord with being greater than the Euclidean distance.

7/10 relevant

arXiv

Free-**space** propagation of spatio-temporal optical vortices (STOVs)

**space**-

**time**energy flow within the pulse and conservation of OAM in space-time. Expand abstract.

**space**-time. In prior work [N. Jhajj et al., Phys. Rev X 6, 031037 (2016)], we demonstrated that a STOV is a universal structure emerging from the arrest of self-focusing collapse leading to nonlinear self-guiding in material media. Here, we demonstrate linear generation and propagation in free

**space**of STOV-carrying pulses. Our measurements and simulations demonstrate STOV mediation of

**space**-

**time**energy flow within the pulse and conservation of OAM in

**space**-time. Single-shot amplitude and phase images of STOVs are taken using a new diagnostic, transient grating single-shot supercontinuum spectral interferometry (TG-SSSI).

7/10 relevant

arXiv

Induction of hierarchy and **time** through one-dimensional probability **space** with certain topologies

**time**through one-dimensional probability

**space**with certain topologies. Expand abstract.

**time**dimension, and system hierarchies. The topological nature of the system is carefully examined and for testing purposes, species density data for a wild Dictyostelia community data are used in conjunction with data derived from liquid-chromatography mass spectrometry of proteins. Utilizing a Clifford algebra, a congruent zeta function, and a Weierstra{beta} p-function in conjunction with a type VI Painleve equation, we confirmed the induction of hierarchy and

**time**through one-dimensional probability

**space**with certain topologies. This process also served to provide information concerning interactions in the model. The previously developed "small s" metric can characterize dynamical system hierarchy and interactions, using only abundance data along

**time**development.

4/10 relevant

bioRxiv