Search Results (29)

This paper studies how intense internal waves (IIWs) affect the holographic reconstruction of the sound field generated by a moving source in a shallow-water environment. It is assumed that the IIWs propagate along the acoustic path between the source and the receiver. The presence of IIWs introduces inhomogeneities into the waveguide and causes significant mode coupling, which perturbs the received sound field. This paper proposes the use of holographic signal processing (HSP) to eliminate perturbations in the received signal caused by mode coupling due to IIWs. Within the HSP framework, we examine the interferogram (the received sound intensity distribution in the frequency–time domain) and the hologram (the two-dimensional Fourier transform of the interferogram) of a moving source in the presence of space–time inhomogeneities caused by IIWs. A key finding is that under the influence of IIWs, the hologram is divided into two regions that correspond to the unperturbed and perturbed components of the sound field. This hologram structure enables the extraction and reconstruction of the interferogram corresponding to the unperturbed field as it would appear in a shallow-water waveguide without IIWs. Numerical simulations of HSP application under the realistic conditions of the SWARM’95 experiment were carried out for stationary and moving sources. The results demonstrate the high efficiency of holographic reconstruction of the unperturbed sound field. Unlike matched field processing (MFP), HSP does not require prior knowledge of the propagation environment. These research results advance signal processing methods in underwater acoustics by introducing efficient HSP methods for environments with spatiotemporal inhomogeneities. Full article

Emerging tensor network techniques for solutions of partial differential equations (PDEs), known for their ability to break the curse of dimensionality, deliver new mathematical methods for ultra-fast numerical solutions of high-dimensional problems. Here, we introduce a Tensor Train (TT) Chebyshev spectral collocation method, in both space and time, for the solution of the time-dependent convection-diffusion-reaction (CDR) equation with inhomogeneous boundary conditions, in Cartesian geometry. Previous methods for numerical solution of time-dependent PDEs often used finite difference for time, and a spectral scheme for the spatial dimensions, which led to a slow linear convergence. Spectral collocation space-time methods show exponential convergence; however, for realistic problems they need to solve large four-dimensional systems. We overcome this difficulty by using a TT approach, as its complexity only grows linearly with the number of dimensions. We show that our TT space-time Chebyshev spectral collocation method converges exponentially, when the solution of the CDR is smooth, and demonstrate that it leads to a very high compression of linear operators from terabytes to kilobytes in TT-format, and a speedup of tens of thousands of times when compared to a full-grid space-time spectral method. These advantages allow us to obtain the solutions at much higher resolutions. Full article

Within the geophysical exploration utilising seismic methods, it is well known that if the explored distances are much greater than the wavelength of the seismic waves with which the exploration is carried out, the ray approach of the wave theory can be used. In this way, when the rays travel through an inhomogeneous medium, they follow curved trajectories, which is imperative to determine the geological features that produce reflection and refraction phenomena. In this paper, a simple algorithm for the calculation of the trajectory of a seismic beam through an inhomogeneous stratum is presented. For this, the construction of a pseudo-Riemannian metric is required from the function of P-wave velocities of the geological stratum. Thus, the problem is inverted because instead of finding the curved trajectory of the seismic beam in a background with a Euclidean metric, it is proposed that the beam follows a geodesic of a curved space-time specific to each stratum, becoming a simple and automatic process using the differential geometry apparatus. For the reader to gain insight into this tool, different geological setups from idealised ones up to a salt dome are presented. Full article

We investigate possible astronomical manifestations of space-time anisotropy. The homogeneous vacuum Kasner solution was chosen as a reference anisotropic cosmological model because there are no effects caused by inhomogeneity in this simple model with a constant degree of anisotropy. This anisotropy cannot become weak. The study of its geodesic structure made it possible to clarify the properties of this space-time. It showed that the degree of manifestation of anisotropy varies significantly depending on the travel time of the light from the observed object. For nearby objects, for which it does not exceed half the age of the universe, the manifestations of anisotropy are very small. Distant objects show more pronounced manifestations; for example, in the distribution of objects over the sky and over photometric distances. These effects for each of the individual objects decrease with time but, in general, the manifestations of anisotropy in the Kasner space-time remain constant due to the fact that new sources come from beyond the cosmological horizon. We analyze observable signatures of the Kasner-type anisotropy and compare it to observations. These effects were not found in astronomical observations, including the study of the CMB. We can assume that the Universe has always been isotropic or almost isotropic since the recombination era. This does not exclude the possibility of its significant anisotropy at the moment of the Big Bang followed by rapid isotropization during the inflationary epoch. Full article

In this study, a numerical solution for degenerate space–time fractional advection–dispersion equations is proposed to simulate atmospheric dispersion in vertically inhomogeneous planetary boundary layers. The fractional derivative exists in a Caputo sense. We establish the maximum principle and a priori estimates for the solutions. Then, we construct a positivity-preserving finite-difference scheme, using monotone discretization in space and L1 approximation on the non-uniform mesh for the time derivative. We use appropriate grading techniques for the time–space mesh in order to overcome the boundary degeneration and weak singularity of the solution at the initial time. The computational results are demonstrated on the Gaussian fractional model as well on the boundary layers defined by height-dependent wind flow and diffusitivity, especially for the Monin–Obukhov model. Full article

The main objective of this article is to examine the stability of Einstein static universe using inhomogeneous perturbations in the context of energy–momentum squared gravity. For this purpose, we used FRW spacetime with perfect matter distribution and formulated static as well as perturbed field equations. We took a minimal model of this theory to investigate the stable regions of the Einstein universe for conserved and non-conserved energy–momentum tensors. We found that stable modes of the Einstein universe appeared in both conserved and non-conserved cases for all values of the equation of state and model parameters corresponding to both open and closed cosmic models. We found that stable solutions in this modified theory were obtained for a broader $\omega$-region compared to other modified theories. Full article

In this work, we would like to address the problem of the effect of bulk matter on the brane cosmological evolution in a general way. We assume that the spatial part of the brane metric is not maximally symmetric, and is, therefore, spatially inhomogeneous. However, we retain the conformal flatness property of the standard cosmological model (FRW), i.e., the Weyl tensor of the induced 4D geometry is zero. We refer to it as Spatially Inhomogeneous Irrotational (SII) brane. It is shown that the model can be regarded as the 5D generalization of the SII spacetimes found recently. Full article

We consider the late-time accelerated universe in the Friedmann–Robertson–Walker (FRW) spacetime with a nonzero curvature, and investigate cosmological models when the cosmic fluid is taken to be inhomogeneous and viscous (bulk viscous), coupled to dark matter. We consider the influence from thermal effects caused by Hawking radiation on the formation of singularities of various classified types, within a finite time. It is shown that under the influence of Hawking radiation, the time of formulation of a singularity and the nature of the singularity itself can change. It is also shown that by jointly taking into account radiation, viscosity, and space curvature, one can obtain a singularity-free universe. The symmetry properties of this kind of theory lie in the assumption about spatial isotropy. The spatial isotropy is also reflected in our use of a bulk instead of a shear viscosity. Full article

Detecting a moving target is an attractive topic in many fields, such as remote sensing. Space-time adaptive processing (STAP) plays a key role in detecting moving targets in strong clutter backgrounds for airborne early warning radar systems. However, STAP suffers serious clutter suppression performance loss when the number of training samples is insufficient due to the inhomogeneous clutter environment. In this article, an efficient sparse recovery STAP algorithm is proposed. First, inspired by the relationship between multiple sparse Bayesian learning (M-SBL) and subspace-based hybrid greedy algorithms, a new optimization objective function based on a subspace penalty is established. Second, the closed-form solution of each minimization step is obtained through the alternating minimization algorithm, which can guarantee the convergence of the algorithm. Finally, a restart strategy is used to adaptively update the support, which reduces the computational complexity. Simulation results show that the proposed algorithm has excellent performance in clutter suppression, convergence speed and running time with insufficient training samples. Full article

Space-time adaptive processing (STAP) encounters severe performance degradation with insufficient training samples in inhomogeneous environments. Sparse Bayesian learning (SBL) algorithms have attracted extensive attention because of their robust and self-regularizing nature. In this study, a computationally efficient SBL STAP algorithm with adaptive Laplace prior is developed. Firstly, a hierarchical Bayesian model with adaptive Laplace prior for complex-value space-time snapshots (CALM-SBL) is formulated. Laplace prior enforces the sparsity more heavily than Gaussian, which achieves a better reconstruction of the clutter plus noise covariance matrix (CNCM). However, similar to other SBL-based algorithms, a large degree of freedom will bring a heavy burden to the real-time processing system. To overcome this drawback, an efficient localized reduced-dimension sparse recovery-based space-time adaptive processing (LRDSR-STAP) framework is proposed in this paper. By using a set of deeply weighted Doppler filters and exploiting prior knowledge of the clutter ridge, a novel localized reduced-dimension dictionary is constructed, and the computational load can be considerably reduced. Numerical experiments validate that the proposed method achieves better performance with significantly reduced computational complexity in limited snapshots scenarios. It can be found that the proposed LRDSR-CALM-STAP algorithm has the potential to be implemented in practical real-time processing systems. Full article

Due to clutter inhomogeneity, the clutter suppression ability of space–time adaptive processing (STAP) is usually constrained by the insufficient number of independent and identically distributed (IID) clutter training samples and, as a result, is sacrificed to achieve the demanded sample reduction. Moreover, since clutter heterogeneity is exacerbated in the real environment, the IID training sample size can be heavily reduced, leading to the deterioration in clutter suppression. To solve this problem, a novel robust space–time joint sparse processing method with airborne active array is proposed. This method has several outstanding advantages: (1) only the single snapshot cell under test (CUT) data is used for the superior clutter suppression performance; and (2) the proposed method completely removes the dependence of the system processing ability on IID training samples. In this paper, the signal model of uniform transmitting subarray diversity is first established to obtain the single snapshot echo observed CUT data. Then, with the matched reconstruction, the single snapshot data are equivalently converted into multi-frame echo data. Finally, a fast multi-frame echo data joint sparse Bayesian algorithm is used to achieve heterogeneous clutter suppression. Numerous experiments were performed to verify the advantages of the proposed method. Full article

A simple gravitational model with torsion is studied, and it is suggested that it could explain the dark matter and dark energy in the universe. It can be reinterpreted as a model using the Einstein gravitational equations where spacetime has regions filled with a perfect fluid with negative energy (pressure) and positive mass density, other regions containing an anisotropic substance that in the rest frame (where the momentum is zero) has negative mass density and a uniaxial stress tensor, and possibly other “luminal” regions where there is no rest frame. The torsion vector field is inhomogeneous throughout spacetime, and possibly turbulent. Numerical simulations should reveal whether or not the equations are consistent with cosmological observations of dark matter and dark energy. Full article

Symanzik’s approach to the description of quantum field systems in an inhomogeneous space-time is used to construct a model for the interaction of neutrino fields with matter. In this way, the problem of the influence of strong inhomogeneities of the medium on the processes of oscillations is considered. As a simple example, a model of neutrino scattering on a material plane is investigated. Within this model, in the collisions of particles with planes, a special filtration mechanism can be formed. It has a significant impact on the dynamics of subsequent neutrino oscillations which are analogous to the Mikheev-Smirnov-Wolfenstein effect at propagation of these particles in an adiabatic medium. Taking into account the possibility of the filtration process in a highly inhomogeneous environment can be useful in planning and carrying out experimental studies of neutrino physics. It can also be considered by investigations of the role of neutrino in astrophysical processes by means of numerical simulations methods. Full article

The Weyl curvature constitutes the radiative sector of the Riemann curvature tensor and gives a measure of the anisotropy and inhomogeneities of spacetime. Penrose’s 1979 Weyl curvature hypothesis (WCH) assumes that the universe began at a very low gravitational entropy state, corresponding to zero Weyl curvature, namely, the Friedmann–Lemaître–Robertson–Walker (FLRW) universe. This is a simple assumption with far-reaching implications. In classical general relativity, Belinsky, Khalatnikov and Lifshitz (BKL) showed in the 70s that the most general cosmological solutions of the Einstein equation are that of the inhomogeneous Kasner types, with intermittent alteration of the one direction of contraction (in the cosmological expansion phase), according to the mixmaster dynamics of Misner (M). How could WCH and BKL-M co-exist? An answer was provided in the 80s with the consideration of quantum field processes such as vacuum particle creation, which was copious at the Planck time (${10}^{-43}$ s), and their backreaction effects were shown to be so powerful as to rapidly damp away the irregularities in the geometry. It was proposed that the vaccum viscosity due to particle creation can act as an efficient transducer of gravitational entropy (large for BKL-M) to matter entropy, keeping the universe at that very early time in a state commensurate with the WCH. In this essay I expand the scope of that inquiry to a broader range, asking how the WCH would fare with various cosmological theories, from classical to semiclassical to quantum, focusing on their predictions near the cosmological singularities (past and future) or avoidance thereof, allowing the Universe to encounter different scenarios, such as undergoing a phase transition or a bounce. WCH is of special importance to cyclic cosmologies, because any slight irregularity toward the end of one cycle will generate greater anisotropy and inhomogeneities in the next cycle. We point out that regardless of what other processes may be present near the beginning and the end states of the universe, the backreaction effects of quantum field processes probably serve as the best guarantor of WCH because these vacuum processes are ubiquitous, powerful and efficient in dissipating the irregularities to effectively nudge the Universe to a near-zero Weyl curvature condition. Full article

We construct recently introduced palatial NC twistors by considering the pair of conjugated (Born-dual) twist-deformed $D=4$ quantum inhomogeneous conformal Hopf algebras ${\mathcal{U}}_{\theta }(su(2,2)⋉T^4$) and ${\mathcal{U}}_{\overline{\theta }}(su(2,2)⋉{\overline{T}}^4$), where $T^4$ describes complex twistor coordinates and ${\overline{T}}^4$ the conjugated dual twistor momenta. The palatial twistors are suitably chosen as the quantum-covariant modules (NC representations) of the introduced Born-dual Hopf algebras. Subsequently, we introduce the quantum deformations of $D=4$ Heisenberg-conformal algebra (HCA) $su(2,2)⋉H_{\hslash }^{4,4}$ ($H_{\hslash }^{4,4}={\overline{T}}^4{⋉}_{\hslash }{T}_4$ is the Heisenberg algebra of twistorial oscillators) providing in twistorial framework the basic covariant quantum elementary system. The class of algebras describing deformation of HCA with dimensionfull deformation parameter, linked with Planck length ${\lambda }_p$, is called the twistorial DSR (TDSR) algebra, following the terminology of DSR algebra in space-time framework. We describe the examples of TDSR algebra linked with Palatial twistors which are introduced by the Drinfeld twist and the quantization map in $H_{\hslash }^{4,4}$. We also introduce generalized quantum twistorial phase space by considering the Heisenberg double of Hopf algebra ${\mathcal{U}}_{\theta }(su(2,2)⋉T^4).$ Full article