Search Results (82)

One extension of general relativity, known as $\mathrm{f}\left(\mathrm{R}\right)$ gravity, where $\mathrm{R}$ denotes the Ricci scalar, is regarded as a promising candidate for addressing the anomalies observed in conventional general relativity. In this work, we apply the field equations of $\mathrm{f}\left(\mathrm{R}\right)$ gravity to a spacetime with spherical symmetry with distinct metric potentials, i.e., $g_{tt}\ne g_{rr}$. By solving the resulting nonlinear differential equations, we derive a novel black hole solution without imposing constraints on the Ricci scalar or on the specific form of $\mathrm{f}\left(\mathrm{R}\right)$ gravity. This solution does not reduce to the Schwarzschild solution of Einstein’s general relativity. This solution is notable because it includes a gravitational mass and extra terms that make the singularities in the curvature stronger than those in black holes from Einstein’s general relativity. We analyze these black holes within the framework of thermodynamics and demonstrate their consistency with standard thermodynamic quantities. Furthermore, we investigate the stability by examining odd-type perturbation modes and show that the resulting black hole is stable. Finally, we derive the coefficients of the two scalar fields and demonstrate that the black hole obtained in this study is free from ghosts. Full article

We study the charged black-hole solutions of a 2 + 1 nonlinear electrodynamical theory with a cosmological constant. Considered as a one-parameter group of theories (the exponent of the squared Maxwell tensor), the causal structure of all possible black holes is scrutinized. We analyze the singularity character that each theory delivers, together with their horizons and the plausible limitations in black-hole charges. The investigation demonstrates a rich structure of three different groups of theories according to the qualitative behavior of the singularity, horizons and limitations in the geometric charges. For such groups, we study the effect of a scalar field propagating in the spacetime of fixed black holes. All analyzed geometries are stable to such linear perturbations, evolving as usual quasinormal spectra of the black holes calculated for the different cases. Full article

Recent observations suggest that General Relativity (GR) faces challenges in fully explaining phenomena in regimes of strong gravitational fields. A promising alternative is the $f\left(R\right)$ theory of gravity, where R denotes the Ricci scalar. This modified theory aims to address the limitations observed in standard GR. In this study, we derive a black hole (BH) solution without introducing nonlinear electromagnetic fields or imposing specific constraints on R or the functional form of $f\left(R\right)$ gravity. The BH solution obtained here is different from the classical Schwarzschild solution in GR and, under certain conditions, reduces to the Schwarzschild (A)dS solution. This BH is characterized by the gravitational mass of the system and an additional parameter, which distinguishes it from GR BHs, particularly in the asymptotic regime. We show that the curvature invariants of this solution remain well defined at both small and large values of r. Furthermore, we analyze their thermodynamic properties, demonstrating consistency with established principles such as Hawking radiation, entropy, and quasi-local energy. This analysis supports their viability as alternative models to classical GR BHs. Full article

Neural networks, mimicking the structural and functional aspects of the human brain, have found widespread applications in diverse fields such as pattern recognition, control systems, and information processing. A critical phenomenon in these systems is synchronization, where multiple neurons or neural networks harmonize their dynamic behaviors to a common rhythm, contributing significantly to their efficient operation. However, the inherent complexity and nonlinearity of neural networks pose significant challenges in understanding and controlling this synchronization process. In this paper, we focus on the synchronization of a class of fractional-order, delayed, and non-autonomous neural networks. Fractional-order dynamics, characterized by their ability to capture memory effects and non-local interactions, introduce additional layers of complexity to the synchronization problem. Time delays, which are ubiquitous in real-world systems, further complicate the analysis by introducing temporal asynchrony among the neurons. To address these challenges, we propose a straightforward yet powerful global synchronization framework. Our approach leverages novel state feedback control to derive an analytical formula for the synchronization controller. This controller is designed to adjust the states of the neural networks in such a way that they converge to a common trajectory, achieving synchronization. To establish the asymptotic stability of the error system, which measures the deviation between the states of the neural networks, we construct a Lyapunov function. This function provides a scalar measure of the system’s energy, and by showing that this measure decreases over time, we demonstrate the stability of the synchronized state. Our analysis yields sufficient conditions that guarantee global synchronization in fractional-order neural networks with time delays and Caputo derivatives. These conditions provide a clear roadmap for designing neural networks that exhibit robust and stable synchronization properties. To validate our theoretical findings, we present numerical simulations that demonstrate the effectiveness of our proposed approach. The simulations show that, under the derived conditions, the neural networks successfully synchronize, confirming the practical applicability of our framework. Full article

We extend a result by one of the authors, established for nonvacuum Einstein gravity, to minimally coupled k-essence scalar–tensor theories. First, we prove that in order to source a Kerr–Schild-type spacetime, the k-essence Lagrangian should be at most quadratic in the kinetic term. This is reduced to linear dependence when the Kerr–Schild null congruence is autoparallel. Finally, we show that solutions of the Einstein equations linearized in Kerr–Schild-type perturbations are also required to solve the full nonlinear system of Einstein equations, selecting once again k-essence scalar fields with linear Lagrangians in the kinetic term. The only other k-essence sharing the property of sourcing perturbative Kerr–Schild spacetimes, which are also exact, is the scalar field constant along the integral curves of the Kerr–Schild congruence, with the otherwise unrestricted Lagrangian. Full article

The Bronnikov generalization of the Fisher naked singularity and Dilatonic black hole spacetimes attracts high interest, as it combines two fundamental transitions of the solutions of Einstein equations. These are the black hole/wormhole “black bounce” transition of geometry, and the phantom/canonical transition of the scalar field, called trapped ghost scalar, combined with an electromagnetic field described by a non-linear electrodynamics. In the present paper, we put restrictions on the parameters of the Fisher (wormhole) and Dilatonic (black hole or wormhole) regularized spacetimes by using frequencies of the epicyclic orbital motion in the geodesic model for explanation of the high-frequency oscillations observed in microquasars or active galactic nuclei, where stellar mass or supermassive black holes are usually assumed. Full article

Dynamical processes during the different stages of evolution of tropical cyclones play crucial roles in their development and intensification, making them one of the most powerful natural forces on Earth. Given their classification as extreme atmospheric events resulting from multiple interacting factors, it is significant to study their dynamical behavior and the nonlinear effects generated by emerging structures during scales and intensity transitions, correlating them with the surrounding environment. This study investigates the extraordinary and record-breaking case of Tropical Cyclone Freddy (2023 Indian Ocean tropical season) from a purely dynamical perspective, examining the superposition of energetic structures at different spatio-temporal scales, by mainly considering thermal fluctuations over 12 days of its evolution. The tool used for this investigation is the Proper Orthogonal Decomposition (POD), in which a set of empirical basis functions is built up, retaining the maximum energetic content of the turbulent flow. The method is applied on a satellite imagery dataset acquired from the SEVIRI radiometer onboard the Meteosat Second Generation-8 (MSG-8) geostationary platform, from which the cloud-top temperature scalar field is remote sensed looking at the cloud’s associated system. For this application, considering Freddy’s very long life period and exceptionally wide path of evolution, reanalysis and tracking data archives are taken into account in order to create an appropriately dynamic spatial grid. Freddy’s eye is followed after its first shape formation with very high temporal resolution snapshots of the temperature field. The energy content in three different characteristic scale ranges is analyzed through the associated spatial and temporal component spectra, focusing both on the total period and on the transitions between different categories. The results of the analysis outline several interesting aspects of the dynamics of Freddy related to both its transitions stages and total period. The reconstructions of the temperature field point out that the most consistent vortexes are found in the outermost cyclonic regions and in proximity of the eyewall. Additionally, we find a significant consistency of the results of the investigation of the maximum intensity phase of Freddy’s life cycle, in the spatio-temporal characteristics of its dynamics, and in comparison with one analogous case study of the Faraji tropical cyclone. Full article

Large-eddy simulation (LES) models are sensitive to numerical discretization because of the large fraction of resolved turbulent energy ($>80\%$) and the strong non-linear interactions between resolved-scale fields with the turbulence subgrid scale (SGS) model. The effects of the Smagorinsky–Lilly SGS model discretization are investigated. Three finite difference schemes are compared. Second-, fourth-, and sixth-order centered difference schemes are used to approximate the spatial derivatives of the SGS model. In the LES of homogeneous isotropic turbulence (HIT), including (non-isotropic) turbulent mixing of a passive scalar, no differences are observed with respect to the SGS model discretization. The HIT LES results are validated against a direct numerical simulation, which resolves all flow scales and does not include an SGS model. In the LES of a moderately stable atmospheric boundary layer, the LES results depend on the SGS discretization for coarse grid resolutions. The second-order scheme performs better at coarse resolutions compared to higher-order schemes. Overall, it is found that higher-order discretizations of the Smagorinsky–Lilly model are not beneficial compared to the second-order scheme. Full article

In this paper, we find several teleparallel $F(T,B)$ solutions for a Robertson–Walker (TRW) cosmological spacetime. We first set and solve the $F(T,B)$-type field equations for a linear perfect fluid. Using similar techniques, we then find new $F(T,B)$ solutions for non-linear perfect fluids with a weak quadratic correction term to the linear equation of state (EoS). Finally, we solve for new classes of $F(T,B)$ solutions for a scalar field source by assuming a power-law scalar field and then an exponential scalar field in terms of the time coordinate. For flat cosmological cases ($k=0$ cases), we find new exact and approximate $F(T,B)$ solutions. For non-flat cases ($k=\pm 1$ cases), we only find new teleparallel $F(T,B)$ solutions for some specific and well-defined cosmological expansion subcases. We conclude by briefly discussing the impact of these new teleparallel solutions on cosmological processes such as dark energy (DE) quintessence and phantom energy models. Full article

We compute the evolution of linear perturbations on top of a background solution of a general nonlinear electromagnetic theory. This evolution can be described in terms of two effective metrics, and we analyze under what conditions they are conformally related so that they can be regarded as analog models of non-trivial gravitational fields in the eikonal approximation. This is the case in Born–Infeld theory. For the background created by a static point electric charge in the Born–Infeld theory, the effective metric describes a wormhole geometry for light rays. Depending on the impact parameter, incoming light rays are either scattered to infinity or approach the wormhole slowing down their pace until they hit the charge at vanishing speed. The same effective wormhole geometry is obtained for a magnetic monopole and a dyon and we relate it to the duality invariance of Born–Infeld electromagnetism. Finally, we analyze the scalar Dirac–Born–Infeld theory and show that the effective wormhole geometry is not generated by a particle with scalar charge. Full article

We investigate the interaction of fermion fields with oscillating domain walls, inspired by breather-type solutions of the sine-Gordon equation, a nonlinear system of fundamental importance. Our study focuses on the fermionic bound states and particle production induced by a time-dependent scalar background field. The fermions couple to two domain walls undergoing harmonic motion, and we explore the resulting dynamics of the fermionic wave functions. We demonstrate that while fermions initially form bound states around the domain walls, the energy provided by the oscillatory motion of the scalar field induces an outward flux of fermions and antifermions, leading to particle production and eventual flux propagation toward spatial infinity. Through numerical simulations, we observe that the fermion density exhibits quasiperiodic behavior, with partial recurrences of the bound state configurations after each oscillation period. However, the fermion wave functions do not remain localized, and over time, the density decreases as more particles escape the vicinity of the domain walls. Our results highlight that the sine-Gordon-like breather background, when coupled non-supersymmetrically to fermions, does not preserve integrability or stability, with the oscillations driving a continuous energy transfer into the fermionic modes. This study sheds light on the challenges of maintaining steady-state fermion solutions in time-dependent topological backgrounds and offers insights into particle production mechanisms in nonlinear dynamical systems with oscillating solitons. Full article

We consider some non-linear non-homogeneous partial differential equations (PDEs) and derive their exact Green function solution as a functional Taylor expansion in powers of the source. The kind of PDEs we consider are dispersive ones where the exact solution of the corresponding homogeneous equations can have some known shape. The technique has a formal similarity with the Dyson–Schwinger set of equations to solve quantum field theories. However, there are no physical constraints. Indeed, we show that a complete coincidence with the statistical field model of a quartic scalar theory can be achieved in the Gaussian expansion of the cumulants of the partition function. Full article

Synthetic microwave focusing methods have been widely adopted in qualitative medical imaging to detect and localize anomalies based on their electromagnetic scattering signatures. This paper discusses the principles, challenges, and limitations of synthetic microwave-focusing techniques in medical applications. It is shown that the various focusing techniques, including time reversal, confocal imaging, and delay-and-sum, are all based on the scalar solution of the electromagnetic scattering problem, assuming the imaged object, i.e., the tissue or object, is linear, reciprocal, and time-invariant. They all aim to generate a qualitative image, revealing any strong scatterer within the imaged domain. The differences among these techniques lie only in the assumptions made to derive the solution and create an image of the relevant tissue or object. To get a fast solution using limited computational resources, those methods assume the tissue is homogeneous and non-dispersive, and thus, a simplified far-field Green’s function is used. Some focusing methods compensate for dispersive effects and attenuation in lossy tissues. Other approaches replace the simplified Green’s function with more representative functions. While these focusing techniques offer benefits like speed and low computational requirements, they face significant ongoing challenges in real-life applications due to their oversimplified linear solutions to the complex problem of non-linear medical microwave imaging. This paper discusses these challenges and potential solutions. Full article

We study the space-time geometry generated by coupling a free scalar field with a noncanonical kinetic term to general relativity in $(2+1)$ dimensions. After identifying a family of scalar Lagrangians that yield exact analytical solutions in static and circularly symmetric scenarios, we classify the various types of solutions and focus on a branch that yields asymptotically flat geometries. We show that the solutions within such a branch can be divided in two types, namely naked singularities and nonsingular objects without a center. In the latter, the energy density is localized around a maximum and vanishes only at infinity and at an inner boundary. This boundary has vanishing curvatures and cannot be reached by any time-like or null geodesic in finite affine time. This allows us to consistently interpret such solutions as nonsingular, lump-like, static compact scalar objects whose eventual extension to the $(3+1)$-dimensional context could provide structures of astrophysical interest. Full article

The traditional receiver employs scalar tracking loops, resulting in degraded navigation performance in weak signal and high dynamic scenarios. An innovative design of a vector tracking receiver based on nonlinear Kalman filter (KF) tracking loops is proposed in this paper, which combines the strengths of both vector tracking and KF-based tracking loops. First, a comprehensive description of the vector tracking receiver model is presented, and unscented Kalman filter (UKF) is applied to nonlinear tracking loop. Second, to enhance the stability and robustness of the KF tracking loop, we introduce square root filtering and an adaptive mechanism. The tracking loop based on square root UKF (SRUKF) can dynamically adjust its filtering parameters based on signal noise and feedback Doppler error. Finally, the proposed method is implemented on a software-defined receiver (SDR), and the field vehicle experiment demonstrates the superiority of this method over other tracking methods in complex dynamic environments. Full article