Search Results (275)

The present work applies and extends the previously developed Quantitative Geometrical Thermodynamics (QGT) formalism to the derivation of a Hamiltonian for the damped harmonic oscillator (DHO) across all damping regimes. By introducing complex time, with the real part encoding entropy production and the imaginary part governing reversible dynamics, QGT provides a unified geometric framework for irreversible thermodynamics, showing that the DHO Hamiltonian can be obtained directly from the (complex) entropy production in a simple exponential form that is generalized across all damping regimes. The derived Hamiltonian preserves a modified Poisson bracket structure and embeds thermodynamic irreversibility into the system’s evolution. Moreover, the resulting expression coincides in form with the well-known Caldirola–Kanai Hamiltonian, despite arising from fundamentally different principles, reinforcing the validity of the QGT approach. The results are also compared with the GENERIC framework, showing that QGT offers an elegant alternative to existing approaches that maintains consistency with symplectic geometry. Furthermore, the imaginary time component is interpreted as isomorphic to the antisymmetric Poisson matrix through the lens of geometric algebra. The formalism opens promising avenues for extending Hamiltonian mechanics to dissipative systems, with potential applications in nonlinear dynamics, quantum thermodynamics, and spacetime algebra. Full article

This article presents a novel mathematical formalism for advanced manifold–metric pairs, enhancing the frameworks of geometry and topology. We construct various D-dimensional manifolds and their associated metric spaces using functional methods, with a focus on integrating concepts from mathematical physics, field theory, topology, algebra, probability, and statistics. Our methodology employs rigorous mathematical construction proofs and logical foundations to develop generalized manifold–metric pairs, including homogeneous and isotropic expanding manifolds, as well as probabilistic and entropic variants. Key results include the establishment of metrizability for topological manifolds via the Urysohn Metrization Theorem, the formulation of higher-rank tensor metrics, and the exploration of complex and quaternionic codomains with applications to cosmological models like the expanding spacetime. By combining spacetime generalized sets with information-theoretic and probabilistic approaches, we achieve a unified framework that advances the understanding of manifold–metric interactions and their physical implications. Full article

Energy generation from renewable sources has increased exponentially worldwide, particularly wind energy, which is converted into electricity through wind turbines. The growing demand for renewable energy has driven the development of horizontal-axis wind turbines with larger dimensions, as the energy captured is proportional to the area swept by the rotor blades. In this context, the dynamic loads typically observed in wind turbine towers include vibrations caused by rotating blades at the top of the tower, wind pressure, and earthquakes (less common). In offshore wind farms, wind turbine towers are also subjected to dynamic loads from waves and ocean currents. Vortex-induced vibration can be an undesirable phenomenon, as it may lead to significant adverse effects on wind turbine structures. This study presents a two-dimensional transient model for a rigid body anchored by a torsional spring subjected to a constant velocity flow. We applied a coupling of the Fourier pseudospectral method (FPM) and immersed boundary method (IBM), referred to in this study as IMERSPEC, for a two-dimensional, incompressible, and isothermal flow with constant properties—the FPM to solve the Navier–Stokes equations, and IBM to represent the geometries. Computational simulations, solved at an aspect ratio of $\varphi =4.0$, were analyzed, considering Reynolds numbers ranging from $Re=150$ to Re = 1000 when the cylinder is stationary, and $Re=250$ when the cylinder is in motion. In addition to evaluating vortex shedding and Strouhal number, the study focuses on the characterization of space–time symmetry during the galloping response. The results show a spatial symmetry breaking in the flow patterns, while the oscillatory motion of the rigid body preserves temporal symmetry. The numerical accuracy suggested that the IMERSPEC methodology can effectively solve complex problems. Moreover, the proposed IMERSPEC approach demonstrates notable advantages over conventional techniques, particularly in terms of spectral accuracy, low numerical diffusion, and ease of implementation for moving boundaries. These features make the model especially efficient and suitable for capturing intricate fluid–structure interactions, offering a promising tool for analyzing wind turbine dynamics and other similar systems. Full article

This paper presents new fast algorithms for the fourth type discrete Hartley transform (DHT-IV) for input data sequences of lengths from 3 to 8. Fast algorithms for small-sized trigonometric transforms can be used as building blocks for synthesizing algorithms for large-sized transforms. Additionally, they can be utilized to process small data blocks in various digital signal processing applications, thereby reducing overall system latency and computational complexity. The existing polynomial algebraic approach and the approach based on decomposing the transform matrix into cyclic convolution submatrices involve rather complicated housekeeping and a large number of additions. To avoid the noted drawback, this paper uses a structural approach to synthesize new algorithms. The starting point for constructing fast algorithms was to represent DHT-IV as a matrix–vector product. The next step was to bring the block structure of the DHT-IV matrix to one of the matrix patterns following the structural approach. In this case, if the block structure of the DHT-IV matrix did not match one of the existing patterns, its rows and columns were reordered, and, if necessary, the signs of some entries were changed. If this did not help, the DHT-IV matrix was represented as the sum of two or more matrices, and then each matrix was analyzed separately, if necessary, subjecting the matrices obtained by decomposition to the above transformations. As a result, the factorizations of matrix components were obtained, which led to a reduction in the arithmetic complexity of the developed algorithms. To illustrate the space–time structures of computational processes described by the developed algorithms, their data flow graphs are presented, which, if necessary, can be directly mapped onto the VLSI structure. The obtained DHT-IV algorithms can reduce the number of multiplications by an average of 75% compared with the direct calculation of matrix–vector products. However, the number of additions has increased by an average of 4%. Full article

In this paper, we present a new space-time Galerkin-like method, where we treat the discretization of spatial and temporal domains simultaneously. This method utilizes a mixed formulation of the tensor-train (TT) and quantized tensor-train (QTT) (please see Section Tensor-Train Decomposition), designed for the finite element discretization (Q1-FEM) of the time-dependent convection–diffusion–reaction (CDR) equation. We reformulate the assembly process of the finite element discretized CDR to enhance its compatibility with tensor operations and introduce a low-rank tensor structure for the finite element operators. Recognizing the banded structure inherent in the finite element framework’s discrete operators, we further exploit the QTT format of the CDR to achieve greater speed and compression. Additionally, we present a comprehensive approach for integrating variable coefficients of CDR into the global discrete operators within the TT/QTT framework. The effectiveness of the proposed method, in terms of memory efficiency and computational complexity, is demonstrated through a series of numerical experiments, including a semi-linear example. Full article

Cross-line operation and express–local train coordination are both crucial for enhancing the efficiency of multi-level urban rail transit systems. Most studies address suburban railway operations in isolation, overlooking coordination and inducing supply–demand mismatches that weaken system efficiency. This study addresses the joint optimization of cross-line operation and express–local scheduling by proposing a novel train timetable model. The model determines train service plans and departure times to minimize total system cost, including train operating and passenger travel costs. A space–time network represents integrated train–passenger interactions, and an extended adaptive large neighborhood search (E-ALNS) algorithm is developed to solve the model efficiently. Numerical experiments verify the effectiveness of the proposed approach. The E-ALNS achieves near-optimal solutions with less than 4% deviation from Gurobi. Comparative analysis shows that the proposed hybrid operation mode reduces total passenger travel cost by 6% and improves the cost efficiency ratio by 13% compared to independent operations. Sensitivity analyses further confirm the model’s robustness to variations in transfer walking time, passenger penalties, and waiting thresholds. This study provides a practical and scalable framework for optimizing train timetables in complex cross-line transit systems, offering insights for enhancing system coordination and passenger service quality. Full article

From a space-time perspective, this paper constructs a CA-SHIRS model to study the psychosocial resonance diffusion of food safety risk, using complex network and cellular automata theory. The CA-SHIRS model is a framework that combines cellular automata with SHIRS (Susceptible–Hidden–Infected–Recovered–Susceptible) epidemic modeling. This methodological integration can effectively reflect local interactions and spatial distribution among consumers. Furthermore, this paper analyzes the diffusion mechanism and spatial–temporal evolution of the psychosocial resonance of food safety risk, considering the interaction between consumer heterogeneity and media communication strategies. The primary conclusions are outlined as follows: (1) An increase in infection probability, conversion probability, and immune failure probability causes the psychosocial resonance of food safety risk to spread rapidly across different regions and populations. In contrast, an increase in immune probability helps control the psychosocial resonance of food safety risk. (2) The diffusion threshold of the psychosocial resonance of food safety risk is negatively related to the consumer risk perception level, consumer risk attention, media freedom, and media report authenticity. However, it is positively correlated with consumer sentiment, market noise, and media report tendency. (3) The consumer risk perception level, consumer risk attention, media freedom, and media report authenticity can effectively inhibit the spatial–temporal diffusion of the psychosocial resonance of food safety risk. On the other hand, increases in market noise, consumer sentiment, and media report tendency accelerate the spread of the psychosocial resonance of food safety risk across different regions. Full article

We introduce a novel logarithmic approach within the Baumgarte–Shapiro–Shibata–Nakamura (BSSN) formalism for self-consistently solving the equations of general relativistic hydrodynamics (GRHD) in evolving curved spacetimes. This method employs a “3 + 1” decomposition of spacetime, complemented by the “1 + log” slicing condition and Gamma-driver shift conditions, which have been shown to improve numerical stability in spacetime evolution. A key innovation of our work is the logarithmic transformation applied to critical variables such as rest-mass density, energy density, and pressure, thus preserving physical positivity and mitigating numerical issues associated with extreme variations. Our formulation is fully compatible with advanced numerical techniques, including spectral methods and Fourier-based algorithms, and it is particularly suited for simulating highly nonlinear regimes in which gravitational fields play a significant role. This approach aims to provide a solid foundation for future numerical implementations and investigations of relativistic hydrodynamics, offering promising new perspectives for modeling complex astrophysical phenomena in strong gravitational fields, including matter evolution around compact objects like neutron stars and black holes, turbulent flows in the early universe, and the nonlinear evolution of cosmic structures. Full article

Spatial Modulation (SM) is a promising technique for future wireless communication systems, as it reduces hardware cost and complexity while maintaining good bit error rate (BER) performance in MIMO systems. However, in real-world scenarios, systems often face challenges like antenna correlation and partial knowledge of the channel at the receiver (CSIR). This paper examines the performance of a new communication method called Generalized Quadrature Spatial Modulation (GQSM), combined with Quasi-Orthogonal Space-Time Block Codes (QOSTBC), under realistic fading conditions using Nakagami-m channels. To address the impact of imperfect CSIR, the paper introduces three new QR decomposition-based detection techniques. These methods are specifically designed to reduce errors and enhance reliability in conditions where traditional maximum likelihood (ML) detection performs poorly. A detailed theoretical analysis of all three detection schemes is provided to explain their performance and advantages. Among them, Technique III yields the best results in extensive Monte Carlo simulations, demonstrating improved error performance with significantly lower computational complexity than ML detection. Overall, the proposed detection methods not only overcome the limitations of ML detection but also provide a practical and scalable solution for challenging wireless environments by effectively leveraging the numerical stability of QR decomposition. Full article

An approach is presented to address singularities in general relativity using a complex Riemannian spacetime extension. We demonstrate how this method can be applied to both black hole and cosmological singularities, specifically focusing on the Schwarzschild and Kerr black holes and the Friedmann–Lemaître–Robertson–Walker (FLRW) Big Bang cosmology. By extending the relevant coordinates into the complex plane and carefully choosing integration contours, we show that it is possible to regularize these singularities, resulting in physically meaningful, singularity-free solutions when projected back onto real spacetime. The removal of the singularity at the Big Bang allows for a bounce cosmology. The approach offers a potential bridge between classical general relativity and quantum gravity effects, suggesting a way to resolve longstanding issues in gravitational physics without requiring a full theory of quantum gravity. Full article

As a multimodal fusion task, audio-visual segmentation (AVS) aims to locate sounding objects at the pixel level within a given image. This capability holds significant importance and practical value in applications such as intelligent surveillance, multimedia content analysis, and human–robot interaction. However, existing AVS models typically feature complex architectures, require a large number of parameters, and are challenging to deploy on embedded platforms. Furthermore, these models often lack integration with object tracking mechanisms and fail to address the issue of the mis-segmentation of unvoiced objects caused by environmental noise in real-world scenarios. To address these challenges, this research proposes a lightweight audio-visual segmentation framework incorporating an audio-guided space–time memory network (AG-STMNet). First, a mask generator with a scoring mechanism was developed to identify sounding objects from generated masks. This component integrates Fastsam, a lightweight, pre-trained, object-aware segmentation model, with WAV2CLIP, a parameter-efficient audio-visual alignment model. Subsequently, AG-STMNet, an audio-guided video object segmentation network, was introduced to track sounding objects using video object segmentation techniques while mitigating environmental noise. Finally, the mask generator and AG-STMNet were combined to form the complete framework. The experimental results demonstrate that the framework achieves a mean Intersection over Union (mIoU) score of 41.5, indicating its potential as a viable lightweight solution for practical applications. Full article

Sparse recovery space–time adaptive processing (STAP) has an off-grid feature and high computational complexity. To address these shortcomings, this study proposes a self-calibrating STAP algorithm based on sparse Bayesian learning (SBL). The proposed algorithm constructs a dimensionality reduction dictionary by selecting the steering vectors corresponding to atoms with high power values. Then, a small-scale auxiliary dictionary is constructed with a stepwise search approach to calibrate the uniformly discretized dictionary. In this way, the atoms of the auxiliary dictionary can converge to the clutter ridge adaptively when off-grid occurs. The clutter plus noise covariance matrix is estimated via SBL combined with the updated dictionary. The experimental results demonstrate that the proposed algorithm can effectively suppress the clutter ridge expansion caused by the off-grid problem while reducing the computation burden significantly compared with the existing methods. Full article

This paper proposes a new carrier domain approach to suppress spreading first-order sea clutter in shipborne passive radar systems using Digital Radio Mondiale (DRM) signals as illuminators. The DRM signal is a broadcast signal that operates in the high-frequency (HF) band and employs orthogonal frequency-division multiplexing (OFDM) modulation. In shipborne DRM-based passive radar, sea clutter sidelobes elevate the noise level of the clutter-plus-noise covariance matrix, thereby degrading the target signal-to-interference-plus-noise ratio (SINR) in traditional space–time adaptive processing (STAP). Moreover, the limited number of space–time snapshots in traditional STAP algorithms further degrades clutter suppression performance. By exploiting the multi-carrier characteristics of OFDM, this paper proposes a novel algorithm, termed Space Time Adaptive Processing by Carrier (STAP-C), to enhance clutter suppression performance. The proposed method improves the clutter suppression performance from two aspects. The first is removing the transmitted symbol information from the space–time snapshots, which significantly reduces the effect of the sea clutter sidelobes. The other is using the space–time snapshots obtained from all subcarriers, which substantially increases the number of available snapshots and thereby improves the clutter suppression performance. In addition, we combine the proposed algorithm with the dimensionality reduction algorithm to develop the Joint Domain Localized-Space Time Adaptive Processing by Carrier (JDL-STAP-C) algorithm. JDL-STAP-C algorithm transforms space–time data into the angle–Doppler domain for clutter suppression, which reduces the computational complexity. Simulation results show the effectiveness of the proposed algorithm in providing a high improvement factor (IF) and less computational time. Full article

An approach is presented to resolve key paradoxes in black hole physics through the application of complex Riemannian spacetime. We extend the Schwarzschild metric into the complex domain, employing contour integration techniques to remove singularities while preserving the essential features of the original solution. A new regularized radial coordinate is introduced, leading to a singularity-free description of black hole interiors. Crucially, we demonstrate how this complex extension resolves the long-standing paradox of event horizon formation occurring only in the infinite future of distant observers. By analyzing trajectories in complex spacetime, we show that the horizon can form in finite complex time, reconciling the apparent contradiction between proper and coordinate time descriptions. This approach also provides a framework for the analytic continuation of information across event horizons, resolving the Hawking information paradox. We explore the physical interpretation of the complex extension versus its projection onto real spacetime. The gravitational collapse of a dust sphere with negligible dust is explored in the complex spacetime extension. The approach offers a mathematically rigorous framework for exploring quantum gravity effects within the context of classical general relativity. Full article

We present a study of relic gravitational waves based on a foliated gauge field theory defined over a spacetime endowed with a noncommutative algebraic–geometric structure. As an ontological extension of general relativity—concerning manifolds, metrics, and fiber bundles—the conventional space and time coordinates, typically treated as classical numbers, are replaced by complementary quantum dual fields. Within this framework, consistent with the Bekenstein criterion and the Hawking–Hertog multiverse conception, singularities merge into a helix-like cosmic scale factor that encodes the topological transition between the contraction and expansion phases of the universe analytically continued into the complex plane. This scale factor captures the essence of an intricate topological quantum-leap transition between two phases of the branching universe: a contraction phase preceding the now-surpassed conventional concept of a primordial singularity and a subsequent expansion phase, whose transition region is characterized by a Riemannian topological foliated structure. The present linearized formulation, based on a slight gravitational field perturbation, also reveals a high sensitivity of relic gravitational wave amplitudes to the primordial matter and energy content during the universe’s phase transition. It further predicts stochastic homogeneous distributions of gravitational wave intensities arising from the interplay of short- and long-spacetime effects within the non-commutative algebraic framework. These results align with the anticipated future observations of relic gravitational waves, expected to pervade the universe as a stochastic, homogeneous background. Full article