Vector Tensor Research Articles

Linear perturbations and stability analysis in f(T) Braneworld scenario

We conduct a detailed analysis of the full linear perturbations in the braneworld scenario within f(T) gravity. By decomposing the perturbations of the theory into the scalar, transverse vector, antisymmetric pseudotensor, and symmetric transverse-traceless tensor modes, we derive the quadratic action for each mode. The results indicate that there is a total of one scalar, one massless vector, and one tensor propagating degrees of freedom. Consequently, in comparison to general relativity, no additional degrees of freedom appear under the flat braneworld background in the linearized theory. For a thick brane model with f(T)=T+αT2, we find that it exhibits stability against linear perturbations.

An ADCP Attitude Dynamic Errors Correction Method Based on Angular Velocity Tensor and Radius Vector Estimation

An acoustic Doppler current profiler (ADCP) installed on a platform produces rotational tangential velocity as a result of variations in the platform’s attitude, with both the tangential velocity and radial orientation varying between each pulse’s transmission and reception by the transducer. These factors introduce errors into the measurements of vessel velocity and flow velocity. In this study, we address the errors induced by dynamic factors related to variations in attitude and propose an ADCP attitude dynamic error correction method based on angular velocity tensor and radius vector estimation. This method utilizes a low-sampling-rate inclinometer and compass data and estimates the angular velocity tensor based on a physical model of vessel motion combined with nonlinear least-squares estimation. The angular velocity tensor is then used to estimate the transducers’ radius vectors. Finally, the radius vectors are employed to correct the instantaneous tangential velocity within the measured velocities of the vessel and flow. To verify the effectiveness of the proposed method, field tests were conducted in a water pool. The results demonstrate that the proposed method surpasses the attitude static correction approach. In comparison with the ASC method, the average relative error in vessel velocity during free-swaying movement decreased by 20.94%, while the relative standard deviation of the error was reduced by 17.38%.

Theory of interacting vector dark energy and fluid

In this work, we study interaction between dark energy and dark matter, where dark energy is described by a massive vector field, and dark matter is modelled as a fluid. We present a new interaction term, which affects only perturbations and can give interesting phenomenology. Then we present a general Lagrangian for the interacting vector dark energy with dark matter. For the dark energy, we choose Proca theory with G 3 term to study its phenomenological consequence. For this model, we explore both background and perturbation dynamics. We also present the no-ghost condition for tensor modes, vector modes and scalar modes. Subsequently, we also study the evolution of the overdensities of both baryon and cold dark matter in the high-k limit. We show that the effective gravitational coupling is modified for cold dark matter and baryon. We also choose a simple concrete model and numerically show a suppression of the effective gravitational coupling for cold dark matter. However, in this simple model, the suppression of the effective gravitational coupling does not result in a suppression of the matter overdensity compared to that in the ΛCDM model due to the modified background expansion.

Entropy optimization of a FENE-P viscoelastic model: a numerically guided comprehensive analysis

The influence of polymers on entropy generation processes is substantial, particularly in the fields of fluid dynamics and rheology. The FENE-P (Finitely Extensible Nonlinear Elastic-Peterlin) model describes the polymer’s dynamics as a result of the interaction between the stretching caused by the velocity gradient and the elastic force that restores the polymer to its equilibrium position. Models such as FENE-P aid in understanding and predicting polymer flow behaviour allowing for the reduction of entropy generation by optimizing system designs. A continuum approach is employed to express the heat flux vector and polymer confirmation tensor of the model. The study investigates the complex relationship between polymer conformation, flow dynamics, and heat transfer taking into account the thermophoresis (Soret effect) and mass diffusion-thermal diffusion coupling (Dufour effect) phenomena to optimize processes by reducing entropy. This study illuminates polymer’s significance in entropy minimization, improving engineering design methodologies and applications in materials science, chemical engineering, and fluid dynamics. As result, the presence of polymers leads to a substantial decrease in the total entropy of the system. This understanding provides opportunities for enhancing heat transfer systems, thereby facilitating the development of more efficient and sustainable technology.

Thermal fluctuations, deflection angle, and greybody factor of a high-dimensional Schwarzschild black hole in scalar–tensor–vector gravity

In this study, we examined the thermal fluctuations, deflection angle, and greybody factor of a high-dimensional Schwarzschild black hole in scalar–tensor–vector gravity (STVG). We calculated some thermodynamic quantities related to the correction of the black hole entropy caused by thermal fluctuations and discussed the effect of the correction parameters on these quantities. By analyzing the changes in the corrected specific heat, we found that thermal fluctuations made the small black hole more stable. It is worth noting that the STVG parameter did not affect the thermodynamic stability of this black hole. Additionally, by utilizing the Gauss–Bonnet theorem, the deflection angle was obtained in the weak field limit, and the effects of the two parameters on the results were visualized. Finally, we calculated the bounds on the greybody factor of a massless scalar field. We observed that as the STVG parameter around the black hole increased, the weak deflection angle became larger, and more scalar particles can reach infinity. However, the spacetime dimension has the opposite effect on the STVG parameter on the weak deflection angle and greybody factor.

Bundle-specific tractogram distribution estimation using higher-order streamline differential equation

Streamline tractography locally traces peak directions extracted from fiber orientation distribution (FOD) functions, lacking global information about the trend of the whole fiber bundle. Therefore, it is prone to producing erroneous tracks while missing true positive connections. In this work, we propose a new bundle-specific tractography (BST) method based on a bundle-specific tractogram distribution (BTD) function, which directly reconstructs the fiber trajectory from the start region to the termination region by incorporating the global information in the fiber bundle mask. A unified framework for any higher-order streamline differential equation is presented to describe the fiber bundles with disjoint streamlines defined based on the diffusion vectorial field. At the global level, the tractography process is simplified as the estimation of BTD coefficients by minimizing the energy optimization model, and is used to characterize the relations between BTD and diffusion tensor vector under the prior guidance by introducing the tractogram bundle information to provide anatomic priors. Experiments are performed on simulated Hough, Sine, Circle data, ISMRM 2015 Tractography Challenge data, FiberCup data, and in vivo data from the Human Connectome Project (HCP) for qualitative and quantitative evaluation. Results demonstrate that our approach reconstructs complex fiber geometry more accurately. BTD reduces the error deviation and accumulation at the local level and shows better results in reconstructing long-range, twisting, and large fanning tracts.

On Some Issues of Second Strain Tensor and Velocity Vector Gradient Theories of 3D Bodies and Thin Bodies

On Some Issues of Second Strain Tensor and Velocity Vector Gradient Theories of 3D Bodies and Thin Bodies

Symmetries of spatial correlators of light and heavy mesons in high temperature lattice QCD

The spatial z correlators of meson operators in Nf=2+1+1 lattice QCD with optimal domain-wall quarks at the physical point are studied for seven temperatures in the range of 190–1540 MeV. The meson operators include a complete set of Dirac bilinears (scalar, pseudoscalar, vector, axial vector, tensor vector, and axial-tensor vector), and each for six flavor combinations (u¯d, u¯s, s¯s, u¯c, s¯c, and c¯c). In a recent paper [], I focused on the meson correlators of u and d quarks, and discussed their implications for the effective restoration of SU(2)L×SU(2)R and U(1)A chiral symmetries, as well as the emergence of approximate SU(2)CS chiral spin symmetry. In this work, we extend our study to meson correlators of six flavor contents, and first observe the hierarchical restoration of chiral symmetries in QCD, from SU(2)L×SU(2)R×U(1)A to SU(3)L×SU(3)R×U(1)A, and to SU(4)L×SU(4)R×U(1)A, as the temperature is increased from 190 to 1540 MeV. Moreover, we compare the temperature windows for the emergence of the approximate SU(2)CS symmetry in light and heavy vector mesons, and find that the temperature windows are dominated by the (u¯c,s¯c,c¯c) sectors. Published by the American Physical Society 2024

Probing ultralight scalar, vector and tensor dark matter with pulsar timing arrays

Pulsar timing arrays (PTAs) are sensitive to oscillations in the gravitational potential along the line-of-sight due to ultralight particle pressure. We calculate the probing power of PTAs for ultralight bosons across all frequencies, from those larger than the inverse observation time to those smaller than the inverse distance to the pulsar. We show that since the signal amplitude grows comparably to the degradation in PTA sensitivity at frequencies smaller than inverse observation time, the discovery potential can be extended towards lower masses by over three decades, maintaining high precision. We demonstrate that, in the mass range 10−26−10−23 eV, existing 15-year PTA data can robustly detect or rule out an ultralight component down to O(1−10)% of the total dark matter. Non-detection, together with other bounds in different mass ranges, will imply that ultralight scalar/axion can comprise at most 1−10% of dark matter in the 10−30−10−17 eV range. With 30 years of observation, current PTAs can extend the reach down to 0.1−1%, while next-generation PTAs such as SKA can attain the 0.01−0.1% precision. We generalize and derive predictions for ultralight spin-1 vector (i.e. dark photon) and spin-2 tensor dark components.

Effects of thermal fluctuations on the evaporation of AdS Schwarzschild scalar tensor vector gravity black hole

The Hawking evaporation process has important implications for our understanding of the universe, as it suggests that black holes are not eternal and can eventually evaporate away completely. We evaluate the Hawking evaporation process of AdS Schwarzschild scalar-tensor-vector gravity black hole by using Stefan-Boltzmann law and find out that Hawking evaporation rate depends on the AdS radius l and deviation parameter α of the scalar-tensor-vector gravity. We analyze that for small values of AdS radius l and positive deviation parameter α black hole evaporates quickly. While there is exponential increase in lifetime of the black hole for large AdS radius l and negative deviation parameter α. Moreover, we find out thermodynamical quantities like Helmholtz free energy, internal energy, pressure, enthalpy, Gibbs free energy and specific heat and show that how deviation parameter α and the correction parameter ζ of the first order corrected entropy play vital role on the stability and phase transitions of the black holes.

Application of Extended Eddy-viscosity and Elliptic-Relaxation Approaches to Turbulent Convective Flow in a Partially Divided Cavity

The paper reports on the numerical turbulence model in predicting mass, momentum and heat transfer in a partially divided cavity heated from the side using buoyancy-extended eddy-viscosity and elliptic relaxation approach with the algebraic expressions for the Reynold stress tensor and turbulent heat flux vector. The CDS (central differencing scheme) and LUDS (linear upwind differencing scheme) were used as the discretization method and the governing equations were solved using the finite volume method and Navier-Stokes solver. Validation of the model has been carried out by experimental data of convective flow in the cavity as well as by numerical data DNS (direct numerical simulation). The model agrees very well with the experiment and DNS and it is also able to demonstrate the performance which is comparable to that of the previous advanced second-moment closure model (SMC) in the literature. The results show that the model is suitable for use in simulations of the turbulent convective flow in a cavity with partition and it has the potential to be applied to more complex cavities and a wide range of turbulence levels.

Unifying ordinary and null memory

Based on a recently proposed reinterpretation of gravitational wave memory that builds up on the definition of gravitational waves pioneered by Isaacson, we provide a unifying framework to derive both ordinary and null memory from a single well-defined equation at leading order in the asymptotic expansion. This allows us to formulate a memory equation that is valid for any unbound asymptotic energy-flux that preserves local Lorentz invariance. Using Horndeski gravity as a concrete example metric theory with an additional potentially massive scalar degree of freedom in the gravitational sector, the general memory formula is put into practice by presenting the first account of the memory correction sourced by the emission of massive field waves. Throughout the work, physical degrees of freedom are identified by constructing manifestly gauge invariant perturbation variables within an SVT decomposition on top of the asymptotic Minkowski background, which will in particular prove useful in future studies of gravitational wave memory within vector tensor theories.

A geometrically and thermodynamically compatible finite volume scheme for continuum mechanics on unstructured polygonal meshes

We present a novel Finite Volume (FV) scheme on unstructured polygonal meshes that is provably compliant with the Second Law of Thermodynamics and the Geometric Conservation Law (GCL) at the same time. The governing equations are provided by a subset of the class of symmetric and hyperbolic thermodynamically compatible (SHTC) models introduced by Godunov in 1961. Specifically, our numerical method discretizes the equations for the conservation of momentum, total energy, distortion tensor and thermal impulse vector, hence accounting in one single unified mathematical formalism for a wide range of physical phenomena in continuum mechanics, spanning from ideal and viscous fluids to hyperelastic solids. By means of two conservative corrections directly embedded in the definition of the numerical fluxes, the new schemes are proven to satisfy two extra conservation laws, namely an entropy balance law and a geometric equation that links the distortion tensor to the density evolution. As such, the classical mass conservation equation can be discarded. Firstly, the GCL is derived at the continuous level, and subsequently it is satisfied by introducing the new concepts of general potential and generalized Gibbs relation. The new potential is nothing but the determinant of the distortion tensor, and the associated Gibbs relation is derived by introducing a set of dual or thermodynamic variables such that the GCL is retrieved by dot multiplying the original system with the new dual variables. Once compatibility of the GCL is ensured, thermodynamic compatibility is tackled in the same manner, thus achieving the satisfaction of a local cell entropy inequality. The two corrections are orthogonal, meaning that they can coexist simultaneously without interfering with each other. The compatibility of the new FV schemes holds true at the semi-discrete level, and time integration of the governing PDE is carried out relying on Runge-Kutta schemes. A large suite of test cases demonstrates the structure preserving properties of the schemes at the discrete level as well.

Circular orbits and collisions of particles with magnetic dipole moment near magnetized Kerr black holes in modified gravity

Throughout this work, we explored the dynamics of test particles with magnetic dipole moment around magnetized rotating Kerr black holes in scalar–vector–tensor gravity theory (STVG), known as modified gravity theory (MOG). We assume that the black hole is immersed in external asymptotically uniform magnetic fields. We derive effective potential for circular orbits of the magnetized particles, taking into account both the magnetic and STVG interactions. We study profiles of the position of the innermost stable circular orbits (ISCOs) of the magnetized particles. We show that the MOG interaction is essentially, and the magnetic interaction enhances its effects on the ISCO radius and the angular momentum at ISCO. Also, we consider collisional cases of magnetized particles and the maximum and minimum limits of angular momentum that ensure the particle colliding near the horizon. Finally, we analyze the center-of-mass energy of colliding magnetized particles near the black hole horizon.

Gravitational form factors of the proton from near-threshold vector meson photoproduction* *Supported by the National Natural Science Foundation of China (12065014, 12247101) and the Natural Science Foundation of Gansu province (22JR5RA266). We acknowledge the West Light Foundation of the Chinese Academy of Sciences (21JR7RA201)

We systematically analyze the quark and gluon gravitational form factors (GFFs) of the proton by connecting the energy-momentum tensor and near-threshold vector meson photoproduction (NTVMP). Specifically, the quark contributions of GFFs are determined by applying global fitting to the cross section of the lightest vector meson photoproduction. Combined with the gluon GFFs obtained from heavy quarkonium photoproduction data, the complete GFFs are obtained and compared with the experimental results and lattice quantum chromodynamics determinations. In addition, we use the resonance via Padé (RVP) method based on the Schlessinger point method to obtain a model-independent quark D-term distribution through direct analytical continuation of deeply virtual Compton scattering experimental data. If errors are considered, the results obtained with RVP are essentially consistent with those obtained by NTVMP. Moreover, the comprehensive information on GFFs helps to uncover the mass distribution and mechanical properties inside the proton. This study is not only an important basis for delving into the enigmatic properties of the proton, but also has significance for theoretically guiding future JLab and EIC experimental measurements.

Induced Isotensor Interactions in Heavy-Ion Double-Charge-Exchange Reactions and the Role of Initial and Final State Interactions

The role of initial state (ISI) and final state (FSI) ion–ion interactions in heavy-ion double-charge-exchange (DCE) reactions A(Z,N)→A(Z±2,N∓2) are studied for double single-charge-exchange (DSCE) reactions given by sequential actions of the isovector nucleon–nucleon (NN) T-matrix. In momentum representation, the second-order DSCE reaction amplitude is shown to be given in factorized form by projectile and target nuclear matrix elements and a reaction kernel containing ISI and FSI. Expanding the intermediate propagator in a Taylor series with respect to auxiliary energy allows us to perform the summation in the leading-order term over intermediate nuclear states in closure approximation. The nuclear matrix element attains a form given by the products of two-body interactions directly exciting the n2p−2 and p2n−2 DCE transitions in the projectile and the target nucleus, respectively. A surprising result is that the intermediate propagation induces correlations between the transition vertices, showing that DSCE reactions are a two-nucleon process that resembles a system of interacting spin–isospin dipoles. Transformation of the DSCE NN T-matrix interactions from the reaction theoretical t-channel form to the s-channel operator structure required for spectroscopic purposes is elaborated in detail, showing that, in general, a rich spectrum of spin scalar, spin vector and higher-rank spin tensor multipole transitions will contribute to a DSCE reaction. Similarities (and differences) to two-neutrino double-beta decay (DBD) are discussed. ISI/FSI distortion and absorption effects are illustrated in black sphere approximation and in an illustrative application to data.

Study of quasinormal modes, greybody factors, and thermodynamics within a regular MOG black hole surrounded by quintessence

In this article, we consider a regular black hole (BH) surrounded by quintessence in the scalar–vector–tensor (S–V–T) version of modified gravity (MOG). We examine the implications of the presence of a quintessence scalar field on astrophysical observable such as quasinormal modes (QNMs), greybody factors (GFs), and thermodynamics. In the vicinity of the MOG BH with quintessence, we calculate the effective potential generated by scalar and electromagnetic field perturbation, and then use the sixth order WKB method to compute the frequencies of the QNMs under these perturbations. We also study the impact of the MOG parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} and the quintessence parameter c on QNM frequencies. Our investigation reveals that the combined effects of α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} and c parameters lead to significant decrease in oscillation frequencies, while the imaginary part generally rises. We then examine the GFs associated with the BH and found that as the model parameters α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} and c increase, GF also increases, and thus less scattering. Additionally, we investigate the thermodynamic quantities and geometries for asymptotically expanded MOG BH. Through heat capacities, Helmholtz and Gibbs free energies, it is observed that this BH shows the stable behavior for various choices of the state parameter of the quintessence ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document}. It is also interesting to mentioned here that Weinhold geometry exhibits the repulsive nature and Ruppiener geometry provides the attractive nature of MOG on the particles for most of the choices of ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document}.

A convergence‐enhanced Timoshenko beam element for the stochastic nonlinear analysis of reinforced concrete components

AbstractAn effective and precise physical model is generally required for the performance assessment of reinforced concrete (RC) components. In this study, a convergence‐enhanced Timoshenko beam element considering finite deformation is proposed for the stochastic nonlinear analysis of RC components. The unified framework of the rank 2 correction matrix is obtained by approximating the iterative matrix through the linearly independent basis vectors, and two types of Broyden–Fletcher–Goldfarb–Shanno (BFGS) operators are constructed. Then, a consistent solution scheme with superior numerical stability and efficiency is proposed based on the second kind of BFGS operator and improved quasi‐Newton method. Accurate discretization of the displacement fields and description of nonlinear sectional behavior are achieved by the high‐order Lagrangian interpolation functions, concrete damage‐plasticity model and J2 plasticity model. In an updated Lagrangian formulation, these shape functions and constitutive relationships are used to develop a complete secant stiffness with higher‐order terms in the strain tensor and residual force vector. To validate the proposed Timoshenko beam element, numerical applications involving material nonlinearity and geometrical nonlinearity are conducted. The numerical stability and efficiency of the solution scheme, the shear‐locking free technique, and the oscillation of axial force are thoroughly examined and discussed by solution of RC columns, cantilever beam and progressive collapse of planar RC frame. Finally, the parametric study considering the geometric and material randomness indicates that the RC column designed for flexural failure mode suffered considerable degradation of loading capacity and a larger scatter of residual load.

Inversion of generalized Radon transforms acting on 3D vector and symmetric tensor fields

Currently, theory of the ray transforms of vector and tensor fields is well developed, but the generalized Radon transforms of such fields have not been fully studied. We consider the normal, longitudinal and mixed Radon transforms (with integration over planes) acting on three-dimensional vector and symmetric tensor fields. We prove that these operators are continuous. In case when values of all generalized Radon transforms are known, inversion formulas are derived for componentwise reconstruction of vector and symmetric m-tensor fields, . Novel detailed decompositions of 3D vector and symmetric 2-tensor fields as a sum of pairwise orthogonal terms are obtained. For construction of each term in the sum only one function is required. With usage of these decompositions we have described the kernels and images of the generalized Radon transforms. In addition, we have obtained inversion formulas for each of the generalized Radon transforms acting on 3D vector and symmetric 2-tensor fields and have formulated theorems similar to the projection theorem for the Radon transform. For the cases similar statements are formulated as hypotheses. In addition, we consider the weighted longitudinal Radon transforms of 3D vector fields. Formulas are obtained for reconstructing the potential part of a 3D vector field from the known values of the longitudinal Radon transforms and one weighted Radon transform. Finally, we discuss the problem of vector fields reconstruction in , .

Flow and Heat Transfer of Micropolar Ferrofluid at Stagnation Point on a Horizontal Flat Plate in the Presence of Magnetic Field and Thermal Radiation

Ferrofluid demonstrates Newtonian or non-Newtonian fluid behaviour depending on the characteristics of ferrofluid. Generally, ferrofluid consists of a stable colloidal suspension of single-domain magnetic particles in a base fluid that can assume non-Newtonian fluid behaviour involving a spin vector and microinertia tensor in flow motion. These two properties possess the theory of micropolar fluid which exhibits microrotational motions and spin inertia in microscopic behaviour. Therefore, this theoretical study is focused to investigate the boundary layer of micropolar ferrofluid flow and heat transfer at the stagnation point on the horizontal flat plate. Magnetite (Fe3O4) nanoparticles and water (H2O) compose in ferrofluid exposed to the magnetic field and thermal radiation is considered. The influences of ferroparticles volume fraction and micropolar parameter on the ferrofluid flow and heat transfer are evaluated mathematically. The partial differential equations have been formulated based on purposed assumptions using Tiwari and Das model and are simplified into ordinary differential equations, which are then solved numerically by Runge-Kutta Fehlberg (RFK45) method. The numerical results of the velocity profile, temperature profile, angular velocity profile, reduced skin friction and reduced Nusselt number are scrutinised in different values of ferroparticles volume fraction and micropolar parameter to estimate the ferrofluid flow and heat transfer. It is found the velocity profile of micropolar ferrofluid flow increases when elevates the ferroparticles volume fraction but decreases when increasing the micropolar parameter. Meanwhile, enlarging ferroparticles volume fraction of micropolar ferrofluid also enhances the temperature profile, reduced skin friction and reduced Nusselt number in the presence of magnetic field and thermal radiation parameter.