Search Results (24)

Nanotechnology has become a transformative field in modern science and engineering, offering innovative approaches to enhance conventional thermal and fluid systems. Heat and mass transfer phenomena, particularly fluid motion across various geometries, play a crucial role in industrial and engineering processes. The inclusion of nanoparticles in base fluids significantly improves thermal conductivity and enables advanced phase-change technologies. The current work examines Powell–Eyring nanofluid’s heat transmission properties on a stretched Riga plate, considering the effects of magnetic fields, porosity, Darcy–Forchheimer flow, thermal radiation, and activation energy. Using the proper similarity transformations, the pertinent governing boundary-layer equations are converted into a set of ordinary differential equations (ODEs), which are then solved using the boundary value problem fourth-order collocation (BVP4C) technique in the MATLAB program. Tables and graphs are used to display the outcomes. Due to their significance in the industrial domain, the Nusselt number and skin friction are also evaluated. The velocity of the nanofluid is shown to decline with a boost in the Hartmann number, porosity, and Darcy–Forchheimer parameter values. Moreover, its energy curves are increased by boosting the values of thermal radiation and the Biot number. A stronger Hartmann number M decelerates the flow (thickening the momentum boundary layer), whereas increasing the Riga forcing parameter Q can locally enhance the near-wall velocity due to wall-parallel Lorentz forcing. Visual comparisons and numerical simulations are used to validate the results, confirming the durability and reliability of the suggested approach. By using a systematic design technique that includes training, testing, and validation, the fluid dynamics problem is solved. The model’s performance and generalization across many circumstances are assessed. In this work, an artificial neural network (ANN) architecture comprising two hidden layers is employed. The model is trained with the Levenberg–Marquardt scheme on reliable numerical datasets, enabling enhanced prediction capability and computational efficiency. The ANN demonstrates exceptional accuracy, with regression coefficients $R\approx 1.0$ and the best validation mean squared errors of $8.52\times {10}^{-10}$, $7.91\times {10}^{-9}$, and $1.59\times {10}^{-8}$ for the Powell–Eyring, heat radiation, and thermophoresis models, respectively. The ANN-predicted velocity, temperature, and concentration profiles show good agreement with numerical findings, with only minor differences in insignificant areas, establishing the ANN as a credible surrogate for quick parametric assessment and refinement in magnetohydrodynamic (MHD) nanofluid heat transfer systems. Full article

Wigner’s little groups are the subgroups of the Poincaré group whose transformations leave the four-momentum of a relativistic particle invariant. The little group for a massive particle is SO(3)-like, whereas for a massless particle, it is E(2)-like. Multiple approaches to group contractions are discussed. It is shown that the Lie algebra of the E(2)-like little group for massless particles can be obtained from the SO(3) and from the SO(2, 1) group by boosting to the infinite-momentum limit. It is also shown that it is possible to obtain the generators of the E(2)-like and cylindrical groups from those of SO(3) as well as from those of SO(2, 1) by using the squeeze transformation. The contraction of the Lorentz group SO(3, 2) to the Poincaré group is revisited. As physical examples, two applications are chosen from classical optics. The first shows the contraction of a light ray from a spherical transparent surface to a straight line. The second shows that the focusing of the image in a camera can be formulated by the implementation of the focal condition to the [ABCD] matrix of paraxial optics, which can be regarded as a limiting procedure. Full article

This study presents a comprehensive multi-objective optimization framework specifically designed for micro-electromechanical systems (MEMS). The framework integrates both traditional and adaptive optimization techniques, named Surrogate-Assisted Multi-Objective Optimization (SAMOO) and Adaptive-SAMOO (A-SAMOO), respectively. By addressing key limitations of traditional approaches, such as the consideration of objective constraints and the provision of multiple design options, the proposed framework enhances both flexibility and practical applicability. Results show that adaptive optimization outperforms traditional offline methods by delivering a greater number and higher quality of optimal solutions while requiring fewer finite element method simulations. The adaptive approach showed a significant advantage by attaining high-quality solutions while requiring only 2.8% of the finite element method (FEM) evaluations compared to traditional methods that do not incorporate surrogate models. This performance boost highlights the advantages of online learning in enhancing the accuracy, speed, and diversity of solutions in MEMS optimization. These optimization schemes were tested on multiple MEMS devices with varying physics and complexities, specifically the U-shaped Lorentz force actuator, serpentine Lorentz force actuator, and thermal actuator. The results highlight the robustness and versatility of the proposed methods, particularly in addressing cases involving discrete design variables and strict objective constraints. This comprehensive, step-by-step framework serves as a valuable resource for researchers and practitioners aiming to optimize MEMS designs from the ground up, providing a reliable and effective approach to multi-objective optimization in MEMS applications. Full article

We investigate the relativistic jet of the powerful radio-emitting blazar J1429+5406 at redshift $z=3.015$. Our understanding of jet kinematics in $z\ge 3$ quasars is still rather limited, based on a sample of less than about 50 objects. The blazar J1429+5406 was observed at a high angular resolution using the method of very long baseline interferometry over more than two decades, between 1994 and 2018. These observations were conducted at five radio frequencies, covering a wide range from $1.7$ to 15 GHz. The outer jet components at ∼20–40 milliarcsecond (mas) separations from the core do not show discernible apparent motion. On the other hand, three jet components within the central 10 mas region exhibit significant proper motion in the range of (0.045–0.16) mas year⁻¹, including one that is among the fastest-moving jet components at $z\ge 3$ known to date. Based on the proper motion of the innermost jet component and the measured brightness temperature of the core, we estimated the Doppler factor, the bulk Lorentz factor, and the inclination angle of the jet with respect to the line of sight. The core brightness temperature is at least $3.6\times {10}^{11}$ K, well exceeding the equipartition limit, indicating Doppler-boosted radio emission. The low jet inclination (≲5.4°) firmly places J1429+5406 into the blazar category. Full article

Explicit formulae for the $4\times 4$ Lorentz transformation matrices corresponding to a pure boost and a pure three-dimensional rotation are very well known. Significantly less well known is the explicit formula for a general Lorentz transformation with arbitrary non-zero boost and rotation parameters. We revisit this more general formula by presenting two different derivations. The first derivation (which is somewhat simpler than previous ones appearing in the literature) evaluates the exponential of a $4\times 4$ real matrix A, where A is a product of the diagonal matrix $\mathrm{diag}(+1,-1,-1,-1)$ and an arbitrary $4\times 4$ real antisymmetric matrix. The formula for $\exp A$ depends only on the eigenvalues of A and makes use of the Lagrange interpolating polynomial. The second derivation exploits the observation that the spinor product ${\eta }^{†}{\overline{\sigma }}^{\mu }\chi$ transforms as a Lorentz four-vector, where $\chi$ and $\eta$ are two-component spinors. The advantage of the latter derivation is that the corresponding formula for a general Lorentz transformation $\Lambda$ reduces to the computation of the trace of a product of $2\times 2$ matrices. Both computations are shown to yield equivalent expressions for $\Lambda$. Full article

This paper examines the possibility of controlling the outcome of measured (flat space-time) relativistic effects, such as time dilation or length contractions, using pure rotations and their nontrivial interactions with Lorentz boosts in the isometry group ${\mathrm{SO}}^{+}(3,1)$. In particular, boost contributions may annihilate leaving only a geometric phase (Wigner rotation), which we see in the complex solutions of the generalized Euler decomposition problem in ${\mathbb{R}}^3$. We consider numerical examples involving specific matrix factorizations, along with possible applications in special relativity, electrodynamics and quantum scattering. For clearer interpretation and simplified calculations we use a convenient projective biquaternion parametrization which emphasizes the geometric phases and for a large class of problems allows for closed-form solutions in terms of only rational functions. Full article

The prominent radio quasar PKS 2215+020 (J2217+0220) was once labelled as a new laboratory for core–jet physics at redshift $z=3.572$ because of its exceptionally extended jet structure traceable with very long baseline interferometric (VLBI) observations up to a ∼600 pc projected distance from the compact core and a hint of an arcsec-scale radio and an X-ray jet. While the presence of an X-ray jet could not be confirmed later, this active galactic nucleus is still unique at high redshift with its long VLBI jet. Here, we analyse archival multi-epoch VLBI imaging data at five frequency bands from $1.7$ to $15.4$ GHz covering a period of more than 25 years from 1995 to 2020. We constrain apparent proper motions of jet components in PKS 2215+020 for the first time. Brightness distribution modeling at 8 GHz reveals a nearly $0.02$ mas yr⁻¹ proper motion (moderately superluminal with apparently two times the speed of light), and provides $\delta =11.5$ for the Doppler-boosting factor in the inner relativistic jet that is inclined within $2^{\circ }$ to the line of sight and has a $\mathsf{\Gamma }=6$ bulk Lorentz factor. These values qualify PKS 2215+020 as a blazar, with rather typical jet properties in a small sample of only about 20 objects at $z>3.5$ that have similar measurements to date. According to the 2-GHz VLBI data, the diffuse and extended outer emission feature at ∼60 mas from the core, probably a place where the jet interacts with and decelerated by the ambient galactic medium, is consistent with being stationary, albeit slow motion cannot be excluded based on the presently available data. Full article

Narrow-line Seyfert 1 (NLS1) galaxies are a peculiar subclass of active galactic nuclei (AGN). Among them, TXS 1206+549 belongs to a small group of radio-loud and $\gamma$-ray-emitting NLS1 galaxies. We focus on the radio properties of this galaxy by analysing archival, high-resolution, very long baseline interferometry (VLBI) imaging observations taken at 8 GHz frequency in six epochs between 1994 and 2018. Using the milliarcsecond-scale radio structure, we can resolve a core and a jet component whose angular separation increases by $(0.055\pm 0.006)$ mas yr⁻¹. This corresponds to an apparent superluminal jet component motion of $(3.5\pm 0.4)c$. From the core brightness temperature and the jet component proper motion, we determine the characteristic Doppler-boosting factor, the bulk Lorentz factor, and the jet viewing angle. We find no compelling evidence for a very closely aligned blazar-type jet. The parameters for TXS 1206+549 resemble those of radio-loud quasar jets with a moderate Lorentz factor ($\Gamma \approx 4$) and $\vartheta \approx {24}^{\circ }$ inclination to the line of sight. Full article

We show that relativistic rotation transformations represent transfer maps between the laboratory system and a local observer on an observer manifold, rather than an event manifold, in the spirit of C-equivalence. Rotation is, therefore, not a parameterised motion on a background space or spacetime, but is determined by a particular sequence of tetrads related by specific special Lorentz transformations or boosts. Because such Lorentz boosts do not form a group, these tetrads represent distinct observers that cannot put together their local descriptions into a manifold in the usual sense. The choice of observer manifold depends on the dynamical situation under consideration, and is not solely determined by the kinematics. Three examples are given: Franklin’s rotation transformation for uniform plane rotation, the Thomas precession of a vector attached to an electron, and the motion of a charged particle in an electromagnetic field. In each case, at each point of its trajectory, there is a distinguished tetrad and a special Lorentz transformation that maps Minkowski space to the spacetime of the local observer on the curve. Full article

The study of quantum resources in the relativistic limit has attracted attention over the last couple of decades, mostly due to the observation that the spin-momentum entanglement is not Lorentz covariant. In this work, we take the investigations of relativistic quantum information a step further, bringing the foundational question of realism to the discussion. In particular, we examine whether Lorentz boosts can affect quantum irrealism—an instance related to the violations imposed by quantum mechanics onto a certain notion of realism. To this end, we adopt as a theoretical platform a model of a relativistic particle traveling through a Mach–Zehnder interferometer. We then compare the quantum irrealism assessed from two different inertial frames in relative motion. In consonance with recent findings in the context of quantum reference frames, our results suggest that the notion of physical realism is not absolute. Full article

The present study investigates the steady three-dimensional flow of a Sisko fluid over a bidirectional stretching sheet under the influence of Lorentz force. Heat transfer effects have been carried out for constant heat flux and Newtonian heating systems. The transformed governing equations of the flow model are solved by using the spectral relaxation method (SRM), taking into account similarity transformations. The effects of controlling parameters on flow and derived quantities have been presented in the form of graphs and tables. Numerical benchmarks are used to characterise the effects of skin friction and heat transfer rates. It is noticed that in the case of Newtonian heating, the rate of heat transfer is higher than that in the constant heat flux case. As the stretching parameter increases, the fluid temperature decreases in both Newtonian heating and constant heat flux. It was discovered that successive over (under) relaxation (SOR) approaches will considerably boost the convergence speed and stability of the SRM system. The current findings strongly agree with earlier studies in the case of Newtonian fluid when the magnetic field is absent. Full article

The Harko, Kovács, and Lobo wormhole (HKLWH) metric contains two free parameters: one is the wormhole throat $r_0$, and the other is a dimensionless deviation parameter $\gamma$ with values $0<\gamma <1$, the latter ensuring the needed violation of the null energy condition at the throat. In this paper, we study the energetics of the HKLWH and the influence of $\gamma$ on the tidal forces in the Lorentz-boosted frame. Finally, we apply a new concept, namely, the probabilistic identity of the object observed by different external observers in terms of the Fresnel coefficients derived by Tangherlini. The intriguing result is that observations can differ depending on the location of the observer, i.e., there is a nonzero probability that the HKLWH will be identified as a black hole even when $\gamma \ne 0$. Full article

The causal set program and the Wolfram physics project leave open the problem of how a graph that is a (3+1)-dimensional Minkowski spacetime according to its simple geodesic distances could be generated solely from simple deterministic rules. This paper provides a solution by describing simple rules that characterize discrete Lorentz boosts between 4D lattice graphs, which combine further to form Wigner rotations that produce isotropy and lead to the emergence of the continuous Lorentz group and the (3+1)-dimensional Minkowski spacetime. On such graphs, the speed of light, the proper time interval, as well as the proper length are all shown to be highly accurate. Full article

In this paper, Lorentz boosts and Wigner rotations are considered from a (complexified) quaternionic point of view. It is demonstrated that, for a suitably defined self-adjoint complex quaternionic 4-velocity, pure Lorentz boosts can be phrased in terms of the quaternion square root of the relative 4-velocity connecting the two inertial frames. Straightforward computations then lead to quite explicit and relatively simple algebraic formulae for the composition of 4-velocities and the Wigner angle. The Wigner rotation is subsequently related to the generic non-associativity of the composition of three 4-velocities, and a necessary and sufficient condition is developed for the associativity to hold. Finally, the authors relate the composition of 4-velocities to a specific implementation of the Baker–Campbell–Hausdorff theorem. As compared to ordinary $4\times 4$ Lorentz transformations, the use of self-adjoint complexified quaternions leads, from a computational view, to storage savings and more rapid computations, and from a pedagogical view to to relatively simple and explicit formulae. Full article

Observations of the synchrotron and inverse Compton emissions from ultrarelativistic electrons in astrophysical sources can reveal a great deal about the energy–momentum relations of those electrons. They can thus be used to place bounds on the possibility of Lorentz violation in the electron sector. Recent $\gamma$-ray telescope data allow the Lorentz-violating electron $c^{\nu \mu }$ parameters to be constrained extremely well, so that all bounds are at the level of $7\times {10}^{-16}$ or better. Full article